Patent Publication Number: US-2023135796-A1

Title: Light-Emitting Devices Providing Asymmetrical Propagation of Light

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation application and claims priority to U.S. Application Serial No. 17/321,112, filed May 14, 2021, which is a continuation application and claims priority to U.S. Application Serial No. 16/656,435, filed Oct. 17, 2019 (now U.S. Patent No. 11,009,193), which is a continuation application and claims priority to U.S. Application Serial No. 16/150,229, filed on Oct. 2, 2018 (now U.S. Pat. No. 10,451,250), which is a continuation application and claims priority to U.S. Application Serial No. 15/865,195, filed on Jan. 8, 2018 (now U.S. Pat. No. 10,408,428), which is a continuation of U.S. Application Serial No. 14/360,046, filed on May 22, 2014 (now U.S. Pat. No. 9,863,605), which is a U.S. National Stage of PCT/US2012/066463, filed on Nov. 23, 2012, which claims the benefit of the following provisional applications: Provisional Application No. 61/563,513, filed on Nov. 23, 2011; Provisional Application No. 61/595,663, filed on Feb. 6, 2012; Provisional Application No. 61/639,683, filed on Apr. 27, 2012; and Provisional Application No. 61/700,724, filed on Sep. 13, 2012. The entire contents of each of these priority applications are hereby incorporated by reference. 
    
    
     BACKGROUND 
     The present technology relates generally to light-emitting devices and, in particular, to light-emitting devices that feature a solid state light-emitting element and a scattering element and an extractor element remote from a light-emitting element. 
     Light-emitting elements are ubiquitous in the modern world, being used in applications ranging from general illumination (e.g., light bulbs) to lighting electronic information displays (e.g., backlights and front-lights for LCDs) to medical devices and therapeutics. Solid state light emitting devices, which include light emitting diodes (LEDs), are increasingly being adopted in a variety of fields, promising low power consumption, high luminous efficacy and longevity, particularly in comparison to incandescent and other conventional light sources. 
     One example of a SSL device increasingly being used for in luminaires is a so-called “white LED.” Conventional white LEDs typically include an LED that emits blue or ultraviolet light and a phosphor or other luminescent material. The device generates white light via down-conversion of blue or UV light from the LED (referred to as “pump light”) by the phosphor. Such devices are also referred to as phosphor-based LEDs (PLEDs). Although subject to losses due to light-conversion, various aspects of PLEDs promise reduced complexity, better cost efficiency and durability of PLED-based luminaires in comparison to other types of luminaires. 
     While new types of phosphors are being actively investigated and developed, configuration of PLED-based light-emitting devices, however, provides further challenges due to the properties of available luminescent materials. Challenges include light-energy losses from photon conversion, phosphor self-heating from Stokes loss, dependence of photon conversion properties on operating temperature, degradation due to permanent changes of the chemical and physical composition of phosphors in effect of overheating or other damage, dependence of the conversion properties on intensity of light, propagation of light in undesired directions in effect of the random emission of converted light that is emitted from the phosphor, undesired chemical properties of phosphors, and controlled deposition of phosphors in light-emitting devices, for example. 
     SUMMARY 
     A variety of light-emitting devices for general illumination utilizing solid state light sources (e.g., light emitting diodes) are disclosed. In general, the devices include a scattering element in combination with an extractor element. The scattering element, which may include elastic and/or inelastic scattering centers, is spaced apart from the light source element. Opposite sides of the scattering element have asymmetric optical interfaces, there being a larger refractive index mismatch at the interface facing the light emitting element than the interface between the scattering element and the extractor element. It is believed that such a structure favors forward scattering of light from the scattering element. In other words, the system favors scattering out of the scattering element into the extractor element over backscattering light towards the light source element. Such a configuration is referred to herein as an Asymmetric Scattering Light Valve (“ASLV”). The extractor element, in turn, is sized and shaped to reduce reflection of light exiting the light-emitting device at the devices interface with the ambient environment. Accordingly, the light-emitting devices may deliver light in a highly efficient, highly homogenized manner. 
     It is known that light from a point source propagating radially outward will be normally incident on a spherical surface centered on the point source. Where the transmission and reflection of the light at the surface is governed by Snell’s law, reflection of light at the surface is a function of the refractive indexes of the media at the surface and is generally minimized because of the normal incident angle. Accordingly, one can apply this principle to the design of a light bulb that includes an extractor element having a spherical exit surface by making the light source within the extractor element sufficiently small and/or making the extractor element sufficiently large so that the light source approximates a point source relative to the exit surface. As a practical matter, however, a source element and a scattering element have a finite size. Moreover, increasing the size of an extractor element relative to a scattering element of fixed size can increase the weight, volume, and/or material cost of a light emitting device. Accordingly, for light-emitting devices that feature a scattering element and an extractor element, there exists a tradeoff between optimizing extraction efficiency from the extractor element with the device’s size and/or cost. 
     The inventors have recognized that there exists a range of relative sizes of the extractor element and scattering element for which high extraction efficiency is achieved with a relatively small extractor element relative to the scattering element. For example, the extractor element and scattering element can be sized relatively so that no light from the scattering optic that directly impinges on the exit surface of the extractor element experiences total internal reflection at the exit surface. For example, the exit surface of the extractor element can be shaped as a spherical dome or shell with a radius R 1  in which the scattering element is contained within an area defined by a respective notional sphere that is concentric with the exit surface and has a radius R OW  = R 1 /n, where n is the refractive index of the extractor element. Such a configuration may be referred to as Weierstrass geometry or Weierstrass configuration. In certain embodiments, all or part of the interface between the scattering element and the extractor element can correspond to the notional surface at Rw. It is believed that such configurations may provide the benefits of the Weierstrass geometry while reducing (e.g., minimizing) the volume of the extractor element. However, while the Weierstrass geometry avoids TIR, light incident on the exit surface will still experience Fresnel reflections, reducing transmission at the exit surface from 100%. 
     In certain embodiments, the exit surface is shaped such that an angle of incidence on the exit surface of the scattered light that directly impinges on the exit surface is less than the Brewster angle. The Brewster angle (also known as the polarization angle) is an angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection. It is believed that such extractor elements not only reduce polarization effects that may be associated with some extractor elements, but also avoid certain polarization-dependent losses that may be associated with, for example, a Weierstrass configuration. For a spherical exit surface, the Brewster condition may be satisfied for light from a scattering element that lies within a corresponding notional spherical or cylindrical surface, referred to as the Brewster radius, R OB . It is believed that sizing the extractor element and scattering element so that the scattering element lies entirely within a notional surface of 1.1 R OB  or less (e.g., in a range from 0.5 R OB  to 1.1 R OB ) can provide a reasonable tradeoff between cost/mass and performance. 
     The light-emitting devices include a recovery enclosure for recycling backscattered light from the scattering element. A variety of forms of recovery enclosures are possible. In some embodiments, the recovery enclosure includes a reflective surface, such as a mirror. This surface can be planar or non-planar. Examples of non-planar reflective surfaces include conical reflectors and parabolic reflectors. In certain embodiments, the recovery enclosure corresponds to an enclosure substantially surrounded by a shell-like scattering element. Such embodiments may recycle backscattered light with high efficiency because a large fraction, e.g., most, backscattered photons re-enter the scattering element without reflecting from an intermediate surface, which can cause further losses. 
     Generally, the light emitting devices can include a single light-emitting element (e.g., a single LED) or multiple light-emitting elements. Embodiments that feature multiple light-emitting elements can include elements with the same or different chromaticity. For example, embodiments can feature multiple similar light-emitting elements to provide a more powerful and/or larger light-emitting device. In some embodiments, the light-emitting device can include light-emitting elements having different chromaticity. Emission intensity from the different light-emitting elements can be varied in order to vary the chromaticity of the light-emitting device. For example, the white point of a white light-emitting device can be varied by increasing or decreasing the contribution from one light-emitting element relative to another. 
     The inventors have also recognized that it is possible to tailor the light emission profile of a light-emitted device by appropriate configuration of the scattering element and/or extractor element. Accordingly, embodiments are disclosed that provide for enhanced emission in certain directions and reduced emission in others. Conversely, in certain embodiments, the shape of the scattering element and/or extractor element are chosen to provide substantially isotropic emission into a range of solid angles. 
     In some embodiments, the exit surface and optical interface between the scattering element and extractor element have the same shape. For example, the exit surface and the optical interface can both be spherical (e.g., concentric spheres of different radius). Alternatively, the exit surface and the optical interface can have different shapes. For example, the exit surface is spherical and the optical interface is ellipsoidal and is entirely contained in a notional Brewster sphere. In general, the shapes of these surfaces can be chosen to provide tailored intensity distributions. 
     In some embodiments, the extractor element can be shaped to introduce anisotropy into the emitted light distribution. For example, the extractor element can include more than one exit surface facets, arranged so that the extractor element has a square or rectangular footprint. Such extractors may be advantageous for illumination of square or rectangular spaces as their light emission patterns will more closely match the space than isotropic emission. 
     In some embodiments, the light emitting devices can include a compound extractor element. Such extractor elements can provide multimodal light distribution, directing light into multiple discrete solid angle ranges. Such extractor elements can be used for light emitting devices that have more than one function (e.g., a ceiling light that provides downlight and directs light towards the ceiling, or a wall light that provides light into a room and along with wall-lighting). 
     An issue with certain solid state light-emitting devices is that their properties change over their lifetime. For example, the white point of a white LED can vary as the device ages. Accordingly, in some embodiments, light emitting devices can include intra-device feedback that enables a device to self-compensate for aging effects. For example, in certain embodiments, light emitting devices include a sensor housed within the device that monitors the intensity of light generated by the device. The device can include feedback electronics (e.g., within the base of the device) that modify the potential applied to the light emitting element(s) in response to variations in the detected intensity. 
     In general, the light emitting devices can be provided in a variety of form factors. In some embodiments, light emitting devices can be provided in the form of standard light bulbs, such as the shape of A-type light bulbs or fluorescent tubes. 
     Various aspects of the invention are summarized below. 
     In general, one innovative aspect of the subject matter described in this specification can be embodied in a light-emitting device that includes multiple light-emitting elements including a first light-emitting element configured to provide light that has a first spectral power distribution during operation, and a second light-emitting element configured to provide light that has a second spectral power distribution different from the first spectral power distribution during operation; a first optical element that has a first surface spaced apart from the first and second light-emitting elements and is positioned to receive light from the first and second light-emitting elements, where the first optical element includes elastic scattering centers arranged to substantially isotropically scatter the light from the first and second light-emitting elements and provide mixed light including light from the first and second light-emitting elements that has a mixed spectral power distribution; and a second optical element formed from a transparent material that has an exit surface, where the second optical element is in contact with the first optical element, there being an optical interface between the first and second optical elements at the place of contact, where the optical interface is opposite the first surface of the first optical element, and the second optical element is arranged to receive a portion of the mixed light through the optical interface; where: the device includes a medium adjacent the first surface of the first optical element that has a refractive index n 0 , and the first optical element includes a material that has a first refractive index n 1 , where n 0  &lt; n 1 ; the transparent material has a refractive index n 2 , where n 0  &lt; n 2 ; the exit surface is a transparent surface that is shaped such that an angle of incidence on the exit surface of the mixed light provided by the first optical element that directly impinges on the exit surface is less than the critical angle for total internal reflection; and the light-emitting device outputs mixed light through the exit surface. 
     The foregoing and other embodiments can each optionally include one or more of the following features, alone or in combination. In some implementations, the light-emitting device can further include a third light-emitting element configured to provide light that has a third spectral power distribution different from the first and second chromaticities during operation; and a fourth light-emitting element configured to provide light that has a fourth spectral power distribution different from the first, second, and third chromaticities during operation; where: the elastic scattering centers further isotropically scatter the light from the third and fourth light-emitting elements; and the mixed light further includes the scattered light from the third and fourth light-emitting elements. In some implementations, a first chromaticity defined by the first spectral power distribution can be different from a second chromaticity defined by the second spectral power distribution. 
     In some implementations, the first optical element can be a shell that defines an enclosure into which light from the light-emitting elements can be emitted, where the shell can be shaped such that at least some light from the first surface directly propagates through the enclosure to the first surface. The shell can have a concave shape with respect to the enclosure. The shell can have an ellipsoidal shape. The ellipsoidal shape can be prolate or oblate. The ellipsoidal shape can be triaxial. The shell can have one or more openings configured to receive the light-emitting elements. In some implementations, the light-emitting device can further include one or more reflectors arranged within the one or more openings, where the one or more reflectors can have one or more reflective surfaces facing the enclosure and configured to enclose the enclosure. 
     In some implementations, the light-emitting device can further include a reflector that has a reflective surface, where the reflective surface and the first surface together can define an enclosure into which all light from the light-emitting elements can be emitted. The reflective surface can be planar, or convex with respect to the enclosure. The first surface can be planar, or convex with respect to the enclosure. The reflective surface can include specular reflective portions, or diffuse reflective portions. The reflective surface can be configured to direct light from the light-emitting elements towards the first surface. 
     In some implementations, the exit surface can include multiple portions, where each portion can be joined to another portion at an edge. The exit surface can have four portions. The exit surface can correspond with a circumscribing surface of an intersection of two orthogonal half cylinders. 
     In some implementations, the light-emitting device can further include a third element formed from a transparent material that can be positioned between the light-emitting elements and the first surface to receive light from the light-emitting elements and provide light to the first surface. The third element can be separated from the first surface by a gap. 
     In some implementations, the light-emitting device can further include a sensor arranged to receive a fraction of the portion of the mixed light prior to being output through the exit surface, where the sensor can be configured to provide a sensor signal based on the fraction of the portion of the mixed light; and a control circuit in communication with the sensor that can be configured to control power provided to the first and second light-emitting elements in response to the sensor signal. The sensor signal can be configured to indicate estimates of one or more of intensity and spectral density distribution of the fraction of the portion of the mixed light. The control circuit can control amounts of power provided to each of the light-emitting elements to reduce variations in the light emitted by the light-emitting device as the light-emitting device ages. The control circuit can control amounts of power provided to the light-emitting elements to reduce variations in the light emitted by the light-emitting device as the light-emitting device changes operating temperature. The control circuit can adjust amounts of power provided to the light-emitting elements to control variations in the light emitted by the light-emitting device based on an input signal provided by a user during operation of the light-emitting device. 
     In some implementations, the second optical element can include a first portion and a light guide, where the first portion can have the exit surface and can be arranged to receive a first portion of the mixed light from the optical interface, and the light guide can be arranged to receive a second portion of the mixed light from the optical interface and can have a guiding surface configured to guide the received second portion of the mixed light away from the optical interface by reflecting at least some of the received second portion of the mixed light. 
     In some implementations, the exit surface can include a first exit surface and a second exit surface, where the first and second exit surfaces can be at least partially transparent, and a step arranged between the first and second exit surfaces. 
     In some implementations, the first optical element can have a substantially uniform effective thickness. In some implementations, n 1  ≈ n 2 . In some implementations, n 0  ≈ 1. In some implementations, the exit surface can be shaped such that an angle of incidence on the exit surface of the mixed light that directly impinges on the exit surface is less than the Brewster angle. 
     In some implementations, for a cross-section, each point, p, on the exit surface can have a corresponding radius of curvature, R(p), and the first and second optical elements can be arranged so that each point on the optical interface is at least a corresponding distance, d(p), from the exit surface, where: 
     
       
         
           
             d 
             
               p 
             
             = 
             R 
             
               p 
             
             * 
             
               
                 1 
                   
                 - 
                 
                   k 
                   / 
                   
                     
                       n 
                       2 
                     
                   
                 
               
             
           
         
       
     
     The value k can be a positive real number such that k &lt; n 2 . In some implementations, k/n 2  can be less than 0.8. In some implementations, k can be less than 1. In some implementations, the value k can be: 
     
       
         
           
             k 
             &lt; 
             
               
                 
                   n 
                   2 
                 
               
               
                 
                   
                     
                       
                         1 
                         + 
                         
                           n 
                           2 
                           2 
                         
                       
                     
                   
                 
               
             
           
         
       
     
     In some implementations, each point on the optical interface can be the distance d(p) from the corresponding nearest point on the exit surface. 
     In some implementations, an axis of symmetry of the first optical element and an axis of symmetry of the second optical element can be collinear. The one or more light-emitting elements can be positioned symmetrically about the axis of symmetry of the first optical element. In some implementations, the first and second optical elements can extend along an axis and can have a cross-section that is substantially unchanged along the axis. In some implementations, the exit surface can be a spherical or cylindrical surface. 
     In some implementations, the medium can be a gas. The gas can be air. In some implementations, the light-emitting elements can include a light-emitting diode. In some implementations, the first optical element can include the elastic scattering centers dispersed within the material that have a refractive index n 1 . In some implementations, the transparent material can be a plastic or a glass. 
     In general, another innovative aspect of the subject matter described in this specification can be embodied in a light-emitting device that includes multiple light-emitting elements including a first light-emitting element configured to provide light that has a first spectral power distribution during operation, and a second light-emitting element configured to provide light that has a second spectral power distribution different from the first spectral power distribution during operation; a first optical element that has a first surface spaced apart from the first and second light-emitting elements and positioned to receive light from the first and second light-emitting elements, where the first optical element includes inelastic scattering centers arranged to convert the light from the first light-emitting element into converted light that is substantially isotropically scattered, and elastic scattering centers arranged to substantially isotropically scatter the light from the second light-emitting element, and provide mixed light that includes the scattered light from the second light-emitting element and the converted light, where the mixed light has a mixed spectral power distribution; and a second optical element formed from a transparent material that has an exit surface, where the second optical element is in contact with the first optical element, there being an optical interface between the first and second optical elements at the place of contact, where the optical interface is opposite the first surface of the first optical element, and the second optical element is arranged to receive a portion of the mixed light through the optical interface; where: the device includes a medium adjacent the first surface of the first optical element that has a refractive index n 0 , and the first optical element includes a material that has a first refractive index n 1 , where n 0  &lt; n 1 ; the transparent material has a refractive index, n 2 , where n 0  &lt; n 2 ; the exit surface is a transparent surface that is shaped such that an angle of incidence on the exit surface of the mixed light provided by the first optical element that directly impinges on the exit surface is less than the critical angle for total internal reflection; and the light-emitting device outputs a predetermined portion of the mixed light through the exit surface. 
     The foregoing and other embodiments can each optionally include one or more of the following features, alone or in combination. In some implementations, the first optical element can be a shell that defines an enclosure into which light from the light-emitting elements can be emitted, where the shell can be shaped such that at least some light from the first surface directly propagates through the enclosure to the first surface. The shell can have a concave shape with respect to the enclosure. The shell can have an ellipsoidal shape. The ellipsoidal shape can be prolate or oblate. The ellipsoidal shape can be triaxial. The shell can have one or more openings configured to receive the light-emitting elements. In some implementations, the light-emitting device can further include one or more reflectors arranged within the one or more openings, where the one or more reflectors can have one or more reflective surfaces facing the enclosure and configured to enclose the enclosure. 
     In some implementations, the light-emitting device can further include a reflector that has a reflective surface, where the reflective surface and the first surface together can define an enclosure into which all light from the light-emitting elements can be emitted. The reflective surface can be planar, or convex with respect to the enclosure. The first surface can be planar, or convex with respect to the enclosure. The reflective surface can include specular reflective portions, or diffuse reflective portions. The reflective surface can be configured to direct light from the light-emitting elements towards the first surface. 
     In some implementations, the exit surface can include multiple portions, where each portion can be joined to another portion at an edge. The exit surface can have four portions. The exit surface can correspond with a circumscribing surface of an intersection of two orthogonal half cylinders. 
     In some implementations, the light-emitting device can further include a third element formed from a transparent material positioned between the light-emitting elements and the first surface to receive light from the light-emitting elements and provide light to the first surface. The third element can be separated from the first surface by a gap. 
     In some implementations, the light-emitting device can further include a sensor arranged to receive a fraction of the portion of the mixed light prior to being output through the exit surface, where the sensor can be configured to provide a sensor signal based on the fraction of the portion of the mixed light; and a control circuit in communication with the sensor that can be configured to control power provided to the light-emitting elements in response to the sensor signal. The sensor signal can be configured to indicate estimates of one or more of intensity and spectral density distribution of the fraction of the portion of the mixed light. The control circuit can control amounts of power provided to the light-emitting elements to reduce variations in the light emitted by the light-emitting device as the light-emitting device ages or changes operating temperature, or based on an input signal provided by a user during operation of the light-emitting device. 
     In some implementations, the second optical element can include a first portion and a light guide, where the first portion can have the exit surface and can be arranged to receive a first portion of the mixed light from the optical interface, and the light guide can be arranged to receive a second portion of the mixed light from the optical interface and can have a guiding surface configured to guide the received second portion of the mixed light away from the optical interface by reflecting at least some of the received second portion of the mixed light. 
     In some implementations, the exit surface can include a first exit surface and a second exit surface, where the first and second exit surfaces can be at least partially transparent, and a step arranged between the first and second exit surfaces. 
     In some implementations, the first optical element can have a substantially uniform effective thickness. In some implementations, n 1  ≈ n 2 . In some implementations, n 0  ≈ 1. In some implementations, the exit surface can be shaped such that an angle of incidence on the exit surface of the mixed light that directly impinges on the exit surface is less than the Brewster angle. 
     In some implementations, for a cross-section, each point, p, on the exit surface can have a corresponding radius of curvature, R(p), and the first and second optical elements can be arranged so that each point on the optical interface is at least a corresponding distance, d(p), from the exit surface, where: 
     
       
         
           
             d 
             
               p 
             
             = 
             R 
             
               p 
             
             * 
             
               
                 1 
                   
                 - 
                 
                   k 
                   / 
                   
                     
                       n 
                       2 
                     
                   
                 
               
             
           
         
       
     
     The value k can be a positive real number such that k &lt; n 2 . In some implementations, k/n 2  can be less than 0.8. In some implementations, k can be less than 1. In some implementations, the value k can be: 
     
       
         
           
             k 
             &lt; 
             
               
                 
                   n 
                   2 
                 
               
               
                 
                   
                     
                       
                         1 
                         + 
                         
                           n 
                           2 
                           2 
                         
                       
                     
                   
                 
               
             
           
         
       
     
     In some implementations, each point on the optical interface can be the distance d(p) from the corresponding nearest point on the exit surface. 
     In some implementations, an axis of symmetry of the first optical element and an axis of symmetry of the second optical element can be collinear. The one or more light-emitting elements can be positioned symmetrically about the axis of symmetry of the first optical element. In some implementations, the first and second optical elements can extend along an axis and can have a cross-section that is substantially unchanged along the axis. In some implementations, the exit surface can be a spherical or cylindrical surface. 
     In some implementations, the medium can be a gas. The gas can be air. In some implementations, the light-emitting elements can include a light emitting diode. In some implementations, the light emitted by the first light-emitting element can include blue light or ultraviolet light. In some implementations, the converted light can be yellow light. In some implementations, the inelastic scattering centers can include a light-conversion material. The light-conversion material can include a phosphor. The light-conversion material can include a quantum dot phosphor. In some implementations, the transparent material can be a plastic or a glass. In some implementations, the inelastic scattering centers can be one and the same as the elastic scattering centers. 
     In general, another innovative aspect of the subject matter described in this specification can be embodied in a light-emitting device that includes one or more light-emitting elements configured to emit light during operation; a first optical element that has a first surface spaced apart from the one or more light-emitting elements and positioned to receive light from the one or more light-emitting elements, where the first optical element includes scattering centers arranged to substantially isotropically scatter the light from the one or more light-emitting elements and to provide scattered light; a second optical element formed from a transparent material that has an exit surface, where the second optical element is in contact with the first optical element, there being an optical interface between the first and second optical elements at the place of contact, where the optical interface is opposite the first surface of the first optical element, and the second optical element is arranged to receive a portion of the scattered light through the optical interface; a sensor arranged to receive a fraction of the portion of the scattered light prior to being output through the exit surface, where the sensor is configured to provide a sensor signal based on the fraction of the portion of the scattered light; and a control circuit in communication with the sensor configured to control power applied to the one or more light-emitting elements in response to the sensor signal; where: the device includes a medium adjacent the first surface of the first optical element that has a refractive index n 0 , and the first optical element includes a material that has a first refractive index n 1 , where n 0  &lt; n 1 ; the transparent material has a refractive index n2, where n 0  &lt; n 2 ; the exit surface is a transparent surface that is shaped such that an angle of incidence on the exit surface of the scattered light that directly impinges on the exit surface is less than the critical angle for total internal reflection; and the light-emitting device outputs scattered light through the exit surface. 
     The foregoing and other embodiments can each optionally include one or more of the following features, alone or in combination. In some implementations, the fraction of the portion of the scattered light received by the sensor can correspond with light reflected in the second optical element at the exit surface. The sensor can be arranged such that the light reflected in the second optical element at the exit surface received by the sensor originates from a large portion of the optical interface. 
     In some implementations, the first optical element can be a shell that defines an enclosure into which light from the one or more light-emitting elements can be emitted, where the shell can be shaped such that at least some light from the first surface directly propagates through the enclosure to the first surface. The shell can have a concave shape with respect to the enclosure. The shell can have an ellipsoidal shape. The ellipsoidal shape can be prolate or oblate. The ellipsoidal shape can be triaxial. The shell can have one or more openings configured to receive the one or more light-emitting elements. In some implementations, the light-emitting device can further include one or more reflectors arranged within the one or more openings, where the one or more reflectors can have one or more reflective surfaces facing the enclosure and configured to enclose the enclosure. 
     In some implementations, the light-emitting device can further include a reflector that has a reflective surface, where the reflective surface and the first surface together can define an enclosure into which all light from the one or more light-emitting elements can be emitted. The reflective surface can be planar, or convex with respect to the enclosure. The first surface can be planar, or convex with respect to the enclosure. The reflective surface can include specular reflective portions, or diffuse reflective portions. The reflective surface can be configured to direct light from the one or more light-emitting elements towards the first surface. 
     In some implementations, the exit surface can include multiple portions, where each portion can be joined to another portion at an edge. The exit surface can have four portions. The exit surface can correspond with a circumscribing surface of an intersection of two orthogonal half cylinders. 
     In some implementations, the light-emitting device can further include a third element formed from a transparent material that can be positioned between the one or more light-emitting elements and the first surface to receive light from the one or more light-emitting elements and provide light to the first surface. The third element can be separated from the first surface by a gap. 
     In some implementations, the sensor signal can be configured to indicate estimates of one or more of intensity and spectral density distribution of the fraction of the portion of the scattered light. The control circuit can control power provided to the one or more light-emitting elements to reduce variations in the light emitted by the light-emitting device as the light-emitting device ages or changes operating temperature, or based on an input signal provided by a user during operation of the light-emitting device. 
     In some implementations, the second optical element can include a first portion and a light guide, where the first portion can have the exit surface and can be arranged to receive a first portion of the scattered light from the optical interface, and the light guide can be arranged to receive a second portion of the scattered light from the optical interface and can have a guiding surface configured to guide the received second portion of the scattered light away from the optical interface by reflecting at least some of the received second portion of the scattered light. 
     In some implementations, the exit surface can include a first exit surface and a second exit surface, where the first and second exit surfaces can be at least partially transparent, and a step arranged between the first and second exit surfaces. 
     In some implementations, the first optical element can have a substantially uniform effective thickness. In some implementations, n 1  ≈ n 2 . In some implementations, n 0  ≈ 1. In some implementations, the exit surface can be shaped such that an angle of incidence on the exit surface of the scattered light that directly impinges on the exit surface is less than the Brewster angle. 
     In some implementations, for a cross-section, each point, p, on the exit surface can have a corresponding radius of curvature, R(p), and the first and second optical elements can be arranged so that each point on the optical interface is at least a corresponding distance, d(p), from the exit surface, where: 
     
       
         
           
             d 
             
               p 
             
             = 
             R 
             
               p 
             
             * 
             
               
                 1 
                   
                 - 
                 
                   k 
                   / 
                   
                     
                       n 
                       2 
                     
                   
                 
               
             
           
         
       
     
     The value k can be a positive real number such that k &lt; n 2 . In some implementations, k/n2 can be less than 0.8. In some implementations, k can be less than 1. In some implementations, the value k can be: 
     
       
         
           
             k 
             &lt; 
             
               
                 
                   n 
                   2 
                 
               
               
                 
                   
                     
                       
                         1 
                         + 
                         
                           n 
                           2 
                           2 
                         
                       
                     
                   
                 
               
             
           
         
       
     
     In some implementations, each point on the optical interface can be the distance d(p) from the corresponding nearest point on the exit surface. 
     In some implementations, an axis of symmetry of the first optical element and an axis of symmetry of the second optical element can be collinear. The one or more light-emitting elements can be positioned symmetrically about the axis of symmetry of the first optical element. In some implementations, the first and second optical elements can extend along an axis and can have a cross-section that is substantially unchanged along the axis. In some implementations, the exit surface can be a spherical or cylindrical surface. 
     In some implementations, the medium can be a gas. The gas can be air. In some implementations, the one or more light-emitting elements can include a light emitting diode. In some implementations, the light emitted by the one or more light-emitting elements can include blue light or ultraviolet light. In some implementations, the scattering centers can include inelastic scattering centers configured to convert at least some light received from the one or more light-emitting elements to converted light having a longer wavelength. The converted light can be yellow light. The inelastic scattering centers can include a light-conversion material. The light-conversion material can include a phosphor. The light-conversion material can include a quantum dot phosphor. 
     In some implementations, the transparent material can be a plastic or a glass. In some implementations, the light-emitting device can include multiple light-emitting elements and the multiple light-emitting elements emit light of different colors. In some implementations, the inelastic scattering centers can be one and the same as the elastic scattering centers. 
     In general, another innovative aspect of the subject matter described in this specification can be embodied in a light-emitting device that includes one or more light-emitting elements configured to emit light during operation; a first optical element that has a first surface spaced apart from the one or more light-emitting elements and positioned to receive light from the one or more light-emitting elements, where the first optical element includes scattering centers arranged to substantially isotropically scatter the light from the one or more light-emitting elements and to provide scattered light; and a second optical element formed from a transparent material that has an exit surface, where the second optical element is in contact with the first optical element, there being an optical interface between the first and second optical elements at the place of contact, where the optical interface is opposite the first surface of the first optical element, and the second optical element is arranged to receive a portion of the scattered light through the optical interface; where: the device includes a medium adjacent the first surface of the first optical element that has a refractive index n 0 , and the first optical element includes a material that has a first refractive index n 1 , where n 0  &lt; n 1 ; the transparent material has a refractive index n 2 , where n 0  &lt; n 2 ; the exit surface is a transparent surface that is shaped such that an angle of incidence on the exit surface of the scattered light that directly impinges on the exit surface is less than the critical angle for total internal reflection; and a combination of a shape of the exit surface of the second optical element and a non-spherical, non-planar shape of the optical interface is configured to output scattered light through the exit surface, where the combination is configured to control the intensity distribution of the output light. 
     The foregoing and other embodiments can each optionally include one or more of the following features, alone or in combination. In some implementations, the intensity distribution can be shaped to match an input requirement of a secondary optical system. The combination can be configured to control directions of peak intensities of the intensity distribution. The first optical element can have three different orthogonal dimensions. The first optical element can have two equal orthogonal dimensions. The first optical element can have three equal orthogonal dimensions. 
     In some implementations, the first optical element can be a shell that defines an enclosure into which light from the one or more light-emitting elements can be emitted, where the shell can be shaped such that at least some light from the first surface directly propagates through the enclosure to the first surface. The shell can have a concave shape with respect to the enclosure. The shell can have an ellipsoidal shape. The ellipsoidal shape can be prolate or oblate. The ellipsoidal shape can be triaxial. The shell can have one or more openings configured to receive the one or more light-emitting elements. In some implementations, the light-emitting device can further include one or more reflectors arranged within the one or more openings, where the one or more reflectors can have one or more reflective surfaces facing the enclosure and configured to enclose the enclosure. 
     In some implementations, the light-emitting device can further include a reflector that has a reflective surface, where the reflective surface and the first surface together can define an enclosure into which all light from the one or more light-emitting elements can be emitted. The reflective surface can be planar, or convex with respect to the enclosure. The first surface can be planar, or convex with respect to the enclosure. The reflective surface can include specular reflective portions, or diffuse reflective portions. The reflective surface can be configured to direct light from the one or more light-emitting elements towards the first surface. 
     In some implementations, the exit surface can include multiple portions, where each portion can be joined to another portion at an edge. The exit surface can have four portions. The exit surface can correspond with a circumscribing surface of an intersection of two orthogonal half cylinders. 
     In some implementations, the light-emitting device can further include a third element formed from a transparent material positioned between the one or more light-emitting elements and the first surface to receive light from the one or more light-emitting elements and provide light to the first surface. The third element can be separated from the first surface by a gap. 
     In some implementations, the light-emitting device can further include a sensor arranged to receive a fraction of the portion of the scattered light prior to being output through the exit surface, where the sensor can be configured to provide a sensor signal based on the fraction of the portion of the scattered light; and a control circuit in communication with the sensor that can be configured to control power provided to the one or more light-emitting elements in response to the sensor signal. The sensor signal can be configured to indicate estimates of one or more of intensity and spectral density distribution of the fraction of the portion of the scattered light. The control circuit can control power provided to the one or more light-emitting elements to reduce variations in the light emitted by the light-emitting device as the light-emitting device ages or changes operating temperature, or based on an input signal provided by a user during operation of the light-emitting device. 
     In some implementations, the second optical element can include a first portion and a light guide, where the first portion can have the exit surface and can be arranged to receive a first portion of the scattered light from the optical interface, and the light guide can be arranged to receive a second portion of the scattered light from the optical interface and can have a guiding surface configured to guide the received second portion of the scattered light away from the optical interface by reflecting at least some of the received second portion of the scattered light. 
     In some implementations, the exit surface can include a first exit surface and a second exit surface, where the first and second exit surfaces can be at least partially transparent, and a step arranged between the first and second exit surfaces. 
     In some implementations, the first optical element can have a substantially uniform effective thickness. In some implementations, n 1  ≈ n 2 . In some implementations, n 0  ≈ 1. In some implementations, the exit surface can be shaped such that an angle of incidence on the exit surface of the scattered light that directly impinges on the exit surface is less than the Brewster angle. 
     In some implementations, for a cross-section, each point, p, on the exit surface can have a corresponding radius of curvature, R(p), and the first and second optical elements can be arranged so that each point on the optical interface is at least a corresponding distance, d(p), from the exit surface, where: 
     
       
         
           
             d 
             
               p 
             
             = 
             R 
             
               p 
             
             * 
             
               
                 1 
                   
                 - 
                 
                   k 
                   / 
                   
                     
                       n 
                       2 
                     
                   
                 
               
             
           
         
       
     
     The value k can be a positive real number such that k &lt; n 2 . In some implementations, k/n 2  can be less than 0.8. In some implementations, k can be less than &lt; 1. In some implementations, the value k can be: 
     
       
         
           
             k 
             &lt; 
             
               
                 
                   n 
                   2 
                 
               
               
                 
                   
                     
                       
                         1 
                         + 
                         
                           n 
                           2 
                           2 
                         
                       
                     
                   
                 
               
             
           
         
       
     
     In some implementations, each point on the optical interface can be the distance d(p) from the corresponding nearest point on the exit surface. 
     In some implementations, an axis of symmetry of the first optical element and an axis of symmetry of the second optical element can be collinear. The one or more light-emitting elements can be positioned symmetrically about the axis of symmetry of the first optical element. In some implementations, the first and second optical elements can extend along an axis and can have a cross-section that is substantially unchanged along the axis. In some implementations, the exit surface is a spherical or cylindrical surface. 
     In some implementations, the medium can be a gas. The gas can be air. In some implementations, the one or more light-emitting elements can include a light emitting diode. In some implementations, the light emitted by the one or more light-emitting elements can include blue light or ultraviolet light. In some implementations, the scattering centers can include inelastic scattering centers configured to convert at least some light received from the one or more light-emitting elements to converted light having a longer wavelength. In some implementations, the converted light can be yellow light. In some implementations, the inelastic scattering centers can include a light-conversion material. The light-conversion material can include a phosphor, or a quantum dot phosphor. 
     In some implementations, the transparent material can be a plastic or a glass. In some implementations, the light-emitting device can include multiple light-emitting elements and the multiple light-emitting elements can emit light of different colors. In some implementations, the inelastic scattering centers can be one and the same as the elastic scattering centers. 
     In general, another innovative aspect of the subject matter described in this specification can be embodied in a light-emitting device that includes one or more light-emitting elements configured to emit light during operation; a first optical element that has a first surface spaced apart from the one or more light-emitting elements and positioned to receive light from the one or more light-emitting elements, where the first optical element includes scattering centers arranged to substantially isotropically scatter the light from the one or more light-emitting elements and to provide scattered light; and a second optical element formed from a transparent material that has an exit surface, where the second optical element is in contact with the first optical element, there being an optical interface between the first and second optical elements at the place of contact, where the optical interface is opposite the first surface of the first optical element, and the second optical element is arranged to receive a portion of the scattered light through the optical interface; where: the device includes a medium adjacent the first surface of the first optical element that has a refractive index n 0 , and the first optical element includes a material that has a first refractive index n 1 , where n 0  &lt; n 1 ; the transparent material has a refractive index n 2 , where n 0  &lt; n 2 ; the exit surface is a transparent surface that includes multiple portions, where each portion is joined to another portion at an edge, and the exit surface is shaped such that an angle of incidence at the exit surface of the scattered light that directly impinges on the exit surface is less than the critical angle for total internal reflection; and a combination of a shape of the exit surface of the second optical element and a shape of the optical interface is configured to output scattered light through the exit surface, where the combination is configured to control the intensity distribution of the output light. 
     The foregoing and other embodiments can each optionally include one or more of the following features, alone or in combination. In some implementations, the intensity distribution can be shaped to match an input requirement of a secondary optical system. The combination can be configured to control directions of peak intensities of the intensity distribution. The first optical element can have three different orthogonal dimensions. The first optical element can have two equal orthogonal dimensions. The first optical element can have three equal orthogonal dimensions. 
     In some implementations, the first optical element can be a shell that defines an enclosure into which light from the one or more light-emitting elements can be emitted, where the shell can be shaped such that at least some light from the first surface directly propagates through the enclosure to the first surface. The shell can have a concave shape with respect to the enclosure. The shell can have an ellipsoidal shape. The ellipsoidal shape can be prolate or oblate. The ellipsoidal shape can be triaxial. The shell can have one or more openings configured to receive the one or more light-emitting elements. In some implementations, the light-emitting device can further include one or more reflectors arranged within the one or more openings, where the one or more reflectors can have one or more reflective surfaces facing the enclosure and configured to enclose the enclosure. 
     In some implementations, the light-emitting device can further include a reflector that has a reflective surface, where the reflective surface and the first surface together can define an enclosure into which all light from the one or more light-emitting elements can be emitted. The reflective surface can be planar, or convex with respect to the enclosure. The first surface can be planar, or convex with respect to the enclosure. The reflective surface can include specular reflective portions, or diffuse reflective portions. The reflective surface can be configured to direct light from the one or more light-emitting elements towards the first surface. 
     In some implementations, the light-emitting device can further include a third element formed from a transparent material positioned between the one or more light-emitting elements and the first surface to receive light from the one or more light-emitting elements and provide light to the first surface. The third element can be separated from the first surface by a gap. 
     In some implementations, the light-emitting device can further include a sensor arranged to receive a fraction of the portion of the scattered light prior to being output through the exit surface, where the sensor can be configured to provide a sensor signal based on the fraction of the portion of the scattered light; and a control circuit in communication with the sensor that can be configured to control power provided to the one or more light-emitting elements in response to the sensor signal. The sensor signal can be configured to indicate estimates of one or more of intensity and spectral density distribution of the fraction of the portion of the scattered light. The control circuit can control power provided to the one or more light-emitting elements to reduce variations in the light emitted by the light-emitting device as the light-emitting device ages or changes operating temperature, or based on an input signal provided by a user during operation of the light-emitting device. 
     In some implementations, the second optical element can include a first portion and a light guide, where the first portion can have the exit surface and can be arranged to receive a first portion of the scattered light from the optical interface, and the light guide can be arranged to receive a second portion of the scattered light from the optical interface and can have a guiding surface configured to guide the received second portion of the scattered light away from the optical interface by reflecting at least some of the received second portion of the scattered light. 
     In some implementations, the exit surface can include a first exit surface and a second exit surface, where the first and second exit surfaces can be at least partially transparent, and a step arranged between the first and second exit surfaces. 
     In some implementations, the first optical element can have a substantially uniform effective thickness. In some implementations, n 1  ≈ n 2 . In some implementations, n 0  ≈ 1. In some implementations, the exit surface can be shaped such that an angle of incidence on the exit surface of the scattered light that directly impinges on the exit surface is less than the Brewster angle. 
     In some implementations, for a cross-section, each point, p, on the exit surface can have a corresponding radius of curvature, R(p), and the first and second optical elements can be arranged so that each point on the optical interface is at least a corresponding distance, d(p), from the exit surface, where: 
     
       
         
           
             d 
             
               p 
             
             = 
             R 
             
               p 
             
             * 
             
               
                 1 
                   
                 - 
                 
                   k 
                   / 
                   
                     
                       n 
                       2 
                     
                   
                 
               
             
           
         
       
     
     The value k can be a positive real number such that k &lt; n 2 . In some implementations, k/n 2  can be less than 0.8. In some implementations, k can be less than &lt; 1. In some implementations, the value k can be: 
     
       
         
           
             k 
             &lt; 
             
               
                 
                   n 
                   2 
                 
               
               
                 
                   
                     
                       
                         1 
                         + 
                         
                           n 
                           2 
                           2 
                         
                       
                     
                   
                 
               
             
           
         
       
     
     In some implementations, each point on the optical interface can be the distance d(p) from the corresponding nearest point on the exit surface. 
     In some implementations, an axis of symmetry of the first optical element and an axis of symmetry of the second optical element can be collinear. The one or more light-emitting elements can be positioned symmetrically about the axis of symmetry of the first optical element. In some implementations, the first and second optical elements can extend along an axis and can have a cross-section that is substantially unchanged along the axis. In some implementations, the exit surface is a spherical or cylindrical surface. 
     In some implementations, the medium can be a gas. The gas can be air. In some implementations, the one or more light-emitting elements can include a light emitting diode. In some implementations, the light emitted by the one or more light-emitting elements can include blue light or ultraviolet light. In some implementations, the scattering centers can include inelastic scattering centers configured to convert at least some light received from the one or more light-emitting elements to converted light having a longer wavelength. The converted light can be yellow light. The inelastic scattering centers can include a light-conversion material. The light-conversion material can include a phosphor, or a quantum dot phosphor. 
     In some implementations, the transparent material can be a plastic or a glass. In some implementations, the light-emitting device can include multiple light-emitting elements and the multiple light-emitting elements can emit light of different colors. In some implementations, the inelastic scattering centers can be one and the same as the elastic scattering centers. 
     In general, another innovative aspect of the subject matter described in this specification can be embodied in a light-emitting device that includes one or more light-emitting elements configured to emit light during operation; a first optical element that has a first surface spaced apart from the one or more light-emitting elements and positioned to receive light from the one or more light-emitting elements, where the first optical element includes scattering centers arranged to substantially isotropically scatter the light from the one or more light-emitting elements and to provide scattered light; and a second optical element formed from a transparent material that has an exit surface, where the second optical element is in contact with the first optical element, there being an optical interface between the first and second optical elements at the place of contact, where the optical interface is opposite the first surface of the first optical element, and the second optical element is arranged to receive a portion of the scattered light through the optical interface; where: the device includes a medium adjacent the first surface of the first optical element that has a refractive index n 0 , and the first optical element includes a material that has a first refractive index n 1 , where n 0  &lt; n 1 ; the transparent material has a refractive index n 2 , where n 0  &lt; n 2 ; the exit surface is a transparent surface that is shaped such that an angle of incidence on the exit surface of the scattered light that directly impinges on the exit surface is less than the Brewster angle; and the light-emitting device outputs a fraction of the scattered light through the exit surface. 
     The foregoing and other embodiments can each optionally include one or more of the following features, alone or in combination. In some implementations, the intensity distribution can be shaped to match an input requirement of a secondary optical system. The combination can be configured to control directions of peak intensities of the intensity distribution. The first optical element can have three different orthogonal dimensions. The first optical element can have two equal orthogonal dimensions. The first optical element can have three equal orthogonal dimensions. 
     In some implementations, the first optical element can be a shell that defines an enclosure into which light from the one or more light-emitting elements can be emitted, where the shell can be shaped such that at least some light from the first surface directly propagates through the enclosure to the first surface. The shell can have a concave shape with respect to the enclosure. The shell can have an ellipsoidal shape. The ellipsoidal shape can be prolate or oblate. The ellipsoidal shape can be triaxial. The shell can have one or more openings configured to receive the one or more light-emitting elements. In some implementations, the light-emitting device can further include one or more reflectors arranged within the one or more openings, where the one or more reflectors can have one or more reflective surfaces facing the enclosure and configured to enclose the enclosure. 
     In some implementations, the light-emitting device can further include a reflector that has a reflective surface, where the reflective surface and the first surface together can define an enclosure into which all light from the one or more light-emitting elements can be emitted. The reflective surface can be planar, or convex with respect to the enclosure. The first surface can be planar, or convex with respect to the enclosure. The reflective surface can include specular reflective portions, or diffuse reflective portions. The reflective surface can be configured to direct light from the one or more light-emitting elements towards the first surface. 
     In some implementations, the exit surface can include multiple portions, where each portion can be joined to another portion at an edge. The exit surface can have four portions. The exit surface can correspond with a circumscribing surface of an intersection of two orthogonal half cylinders. 
     In some implementations, the light-emitting device can further include a third element formed from a transparent material positioned between the one or more light-emitting elements and the first surface to receive light from the one or more light-emitting elements and provide light to the first surface. The third element can be separated from the first surface by a gap. 
     In some implementations, the light-emitting device can further include a sensor arranged to receive a fraction of the portion of the scattered light prior to being output through the exit surface, where the sensor can be configured to provide a sensor signal based on the fraction of the portion of the scattered light; and a control circuit in communication with the sensor that can be configured to control power provided to the one or more light-emitting elements in response to the sensor signal. The sensor signal can be configured to indicate estimates of one or more of intensity and spectral density distribution of the fraction of the portion of the scattered light. The control circuit can control power provided to the one or more light-emitting elements to reduce variations in the light emitted by the light-emitting device as the light-emitting device ages or changes operating temperature, or based on an input signal provided by a user during operation of the light-emitting device. 
     In some implementations, the second optical element can include a first portion and a light guide, where the first portion can have the exit surface and can be arranged to receive a first portion of the scattered light from the optical interface, and the light guide can be arranged to receive a second portion of the scattered light from the optical interface and can have a guiding surface configured to guide the received second portion of the scattered light away from the optical interface by reflecting at least some of the received second portion of the scattered light. 
     In some implementations, the exit surface can include a first exit surface and a second exit surface, where the first and second exit surfaces can be at least partially transparent, and a step arranged between the first and second exit surfaces. 
     In some implementations, the first optical element can have a substantially uniform effective thickness. In some implementations, n 1  ≈ n 2 . In some implementations, n 0  ≈ 1. 
     In some implementations, for a cross-section, each point, p, on the exit surface can have a corresponding radius of curvature, R(p), and the first and second optical elements can be arranged so that each point on the optical interface is at least a corresponding distance, d(p), from the exit surface, where: 
     
       
         
           
             d 
             
               p 
             
             = 
             R 
             
               p 
             
             * 
             
               
                 1 
                   
                 - 
                 
                   k 
                   / 
                   
                     
                       n 
                       2 
                     
                   
                 
               
             
           
         
       
     
     The value k can be a positive real number such that k &lt; n 2 . In some implementations, k/n 2  can be less than 0.8. In some implementations, k can be less than &lt; 1. In some implementations, the value k can be: 
     
       
         
           
             k 
             &lt; 
             
               
                 
                   n 
                   2 
                 
               
               
                 
                   
                     
                       
                         1 
                         + 
                         
                           n 
                           2 
                           2 
                         
                       
                     
                   
                 
               
             
           
         
       
     
     In some implementations, an axis of symmetry of the first optical element and an axis of symmetry of the second optical element can be collinear. The one or more light-emitting elements can be positioned symmetrically about the axis of symmetry of the first optical element. In some implementations, the first and second optical elements can extend along an axis and can have a cross-section that is substantially unchanged along the axis. In some implementations, the exit surface is a spherical or cylindrical surface. 
     In some implementations, the medium can be a gas. The gas can be air. In some implementations, the one or more light-emitting elements can include a light emitting diode. In some implementations, the light emitted by the one or more light-emitting elements can include blue light or ultraviolet light. In some implementations, the scattering centers can include inelastic scattering centers configured to convert at least some light received from the one or more light-emitting elements to converted light having a longer wavelength. In some implementations, the converted light can be yellow light. In some implementations, the inelastic scattering centers can include a light-conversion material. The light-conversion material can include a phosphor, or a quantum dot phosphor. 
     In some implementations, the transparent material can be a plastic or a glass. In some implementations, the light-emitting device can include multiple light-emitting elements and the multiple light-emitting elements can emit light of different colors. In some implementations, the inelastic scattering centers can be one and the same as the elastic scattering centers. 
     In general, another innovative aspect of the subject matter described in this specification can be embodied in a light-emitting device that includes one or more light-emitting elements configured to emit light during operation; a first optical element that has a first surface spaced apart from the one or more light-emitting elements and positioned to receive light from the one or more light-emitting elements, where the first optical element includes scattering centers arranged to substantially isotropically scatter the light from the one or more light-emitting elements and to provide scattered light; a second optical element formed from a transparent material and in contact with the first optical element, there being an optical interface between the first and second optical elements at the place of contact, where the optical interface is opposite the first surface of the first optical element, the second optical element includes a first optic and a light guide, the first optic has an exit surface and is arranged to receive a first portion of the scattered light from the optical interface, and the exit surface is a transparent surface that is shaped such that an angle of incidence at the exit surface of the scattered light that directly impinges on the exit surface is less than the critical angle for total internal reflection, and the light guide is arranged to receive a second portion of the scattered light from the optical interface and has a guiding surface configured to guide the received second portion of the scattered light away from the optical interface by reflecting at least some of the received second portion of the scattered light; where: the device includes a medium adjacent the first surface of the first optical element that has a refractive index n0, and the first optical element includes a material that has a first refractive index n1, where n0 &lt; n1; and the transparent material has a refractive index n2, where n0 &lt; n2. 
     The foregoing and other embodiments can each optionally include one or more of the following features, alone or in combination. In some implementations, the light-emitting device can further include a reflective coating disposed on the guiding surface and configured to reflect the at least some of the received second portion of the scattered light. In some implementations, the light guide can be configured to reflect the at least some of the received second light via total internal reflection. In some implementations, the light guide can be configured to emit predetermined amounts of light at predetermined distances from the one or more light-emitting elements through the guiding surface. The guiding surface can have a surface texture configured to extract the predetermined amounts of light. The light guide can include centers configured to scatter light such that the predetermined amounts of light are emitted at the predetermined distances from the one or more light-emitting elements through the guiding surface. In some implementations, the light guide can have a distal surface configured to emit at least a fraction of the at least some of the received second portion of the scattered light. 
     In some implementations, the first optical element can be a shell that defines an enclosure into which light from the one or more light-emitting elements can be emitted, where the shell can be shaped such that at least some light from the first surface directly propagates through the enclosure to the first surface. The shell has a concave shape with respect to the enclosure. The shell can have an ellipsoidal shape. The ellipsoidal shape can be prolate or oblate. The ellipsoidal shape can be triaxial. The shell can have one or more openings configured to receive the one or more light-emitting elements. In some implementations, the light-emitting device can further include one or more reflectors arranged within the one or more openings, where the one or more reflectors can have one or more reflective surfaces facing the enclosure and configured to enclose the enclosure. 
     In some implementations, the light-emitting device can further include a reflector that has a reflective surface, where the reflective surface and the first surface together can define an enclosure into which all light from the one or more light-emitting elements is emitted. The reflective surface can be planar, or convex with respect to the enclosure. The first surface can be planar, or convex with respect to the enclosure. The reflective surface can include specular reflective portions, or diffuse reflective portions. The reflective surface can be configured to direct light from the one or more light-emitting elements towards the first surface. 
     In some implementations, the exit surface can include multiple portions, where each portion can be joined to another portion at an edge. The exit surface can have four portions. The exit surface can correspond with a circumscribing surface of an intersection of two orthogonal half cylinders. 
     In some implementations, the light-emitting device can further include a third element formed from a transparent material positioned between the one or more light-emitting elements and the first surface to receive light from the one or more light-emitting elements and provide light to the first surface. The third element is separated from the first surface by a gap. 
     In some implementations, the light-emitting device can further include a sensor arranged to receive a fraction of the portion of the scattered light prior to being output from the light-emitting device, where the sensor can be configured to provide a sensor signal based on the fraction of the portion of the scattered light; and a control circuit in communication with the sensor that can be configured to control power provided to the one or more light-emitting elements in response to the sensor signal. The sensor signal can be configured to indicate estimates of one or more of intensity and spectral density distribution of the fraction of the portion of the scattered light. The control circuit can control power provided to the one or more light-emitting elements to reduce variations in the light emitted by the light-emitting device as the light-emitting device ages or changes operating temperature, or based on an input signal provided by a user during operation of the light-emitting device. 
     In some implementations, the first optical element can have a substantially uniform effective thickness. In some implementations, n 1  ≈ n 2 . In some implementations, n 0  ≈ 1. In some implementations, the exit surface can be shaped such that an angle of incidence on the exit surface of the scattered light that directly impinges on the exit surface is less than the Brewster angle. 
     In some implementations, for a cross-section, each point, p, on the exit surface can have a corresponding radius of curvature, R(p), and the first and second optical elements can be arranged so that each point on the optical interface is at least a corresponding distance, d(p), from the exit surface, where: 
     
       
         
           
             d 
             
               p 
             
             = 
             R 
             
               p 
             
             * 
             
               
                 1 
                   
                 - 
                 
                   k 
                   / 
                   
                     
                       n 
                       2 
                     
                   
                 
               
             
           
         
       
     
     The value k can be a positive real number such that k &lt; n 2 . In some implementations, k/n 2  can be less than 0.8. In some implementations, k can be less than 1. In some implementations, the value k can be: 
     
       
         
           
             k 
             &lt; 
             
               
                 
                   n 
                   2 
                 
               
               
                 
                   
                     
                       
                         1 
                         + 
                         
                           n 
                           2 
                           2 
                         
                       
                     
                   
                 
               
             
           
         
       
     
     In some implementations, each point on the optical interface can be the distance d(p) from the corresponding nearest point on the exit surface. 
     In some implementations, an axis of symmetry of the first optical element and an axis of symmetry of the second optical element can be collinear. The one or more light-emitting elements can be positioned symmetrically about the axis of symmetry of the first optical element. In some implementations, the first and second optical elements can extend along an axis and can have a cross-section that is substantially unchanged along the axis. In some implementations, the exit surface can be a spherical or cylindrical surface. 
     In some implementations, the medium is a gas. The gas can be air. In some implementations, the one or more light-emitting elements can include a light emitting diode. In some implementations, the light emitted by the one or more light-emitting elements can include blue light or ultraviolet light. In some implementations, the scattering centers can include inelastic scattering centers configured to convert at least some light received from the one or more light-emitting elements to converted light having a longer wavelength. The converted light can be yellow light. The inelastic scattering centers can include a light-conversion material. The light-conversion material can include a phosphor, or a quantum dot phosphor. 
     In some implementations, the transparent material can be a plastic or a glass. In some implementations, the light-emitting device can include multiple light-emitting elements and the multiple light-emitting elements can emit light of different colors. In some implementations, the inelastic scattering centers can be one and the same as the elastic scattering centers. 
     In general, another innovative aspect of the subject matter described in this specification can be embodied in a light-emitting device that includes one or more light-emitting elements configured to emit light during operation; a first optical element that has a first surface spaced apart from the one or more light-emitting elements and positioned to receive light from the one or more light-emitting elements, where the first optical element includes scattering centers arranged to substantially isotropically scatter the light from the one or more light-emitting elements and to provide scattered light; and a second optical element formed from a transparent material, where the second optical element is in contact with the first optical element, there being an optical interface between the first and second optical elements at the place of contact, where the second optical element is arranged to receive a portion of the scattered light through the optical interface, and the second optical element includes an exit surface including a first exit surface and a second exit surface, where the first and second exit surfaces are at least partially transparent and shaped such that an angle of incidence at the first and second exit surfaces of at least some of the scattered light that directly impinges thereon is less than the critical angle for total internal reflection, and the second optical element further includes a step arranged between the first and second exit surfaces; where: the device includes a medium adjacent the first surface of the first optical element that has a refractive index n0, and the first optical element includes a material that has a first refractive index n1, where n0 &lt; n1; the transparent material has a refractive index n2, where n0 &lt; n2; and the light-emitting device outputs light through the first and second exit surfaces. 
     The foregoing and other embodiments can each optionally include one or more of the following features, alone or in combination. In some implementations, the first exit surface can intersect at least one optical axis of the one or more light-emitting elements and the step can be arranged such that the first exit surface is recessed relative to the second exit surface. In some implementations, the first exit surface can intersect at least one optical axis of the one or more light-emitting elements and the step can be arranged such that the second exit surface is recessed relative to the first exit surface. In some implementations, the step can include a reflective surface. In some implementations, the step can include a transparent surface. In some implementations, at least one of the first and second exit surfaces can be translucent. 
     In some implementations, the first optical element can be a shell that defines an enclosure into which light from the one or more light-emitting elements can be emitted, where the shell can be shaped such that at least some light from the first surface directly propagates through the enclosure to the first surface. The shell can have a concave shape with respect to the enclosure. The shell can have an ellipsoidal shape. The ellipsoidal shape can be prolate or oblate. The ellipsoidal shape can be triaxial. The shell can have one or more openings configured to receive the one or more light-emitting elements. In some implementations, the light-emitting device can further include one or more reflectors arranged within the one or more openings, where the one or more reflectors can have one or more reflective surfaces facing the enclosure and configured to enclose the enclosure. 
     In some implementations, the light-emitting device can further include a reflector that has a reflective surface, where the reflective surface and the first surface together can define an enclosure into which all light from the one or more light-emitting elements can be emitted. The reflective surface can be planar, or convex with respect to the enclosure. The first surface can be planar, or convex with respect to the enclosure. The reflective surface can include specular reflective portions, or diffuse reflective portions. The reflective surface can be configured to direct light from the one or more light-emitting elements towards the first surface. 
     In some implementations, the light-emitting device can further include a third element formed from a transparent material positioned between the one or more light-emitting elements and the first surface to receive light from the one or more light-emitting elements and provide light to the first surface. The third element can be separated from the first surface by a gap. 
     In some implementations, the light-emitting device can further include a sensor arranged to receive a fraction of the portion of the scattered light prior to being output from the light-emitting device, where the sensor can be configured to provide a sensor signal based on the fraction of the portion of the scattered light; and a control circuit in communication with the sensor that can be configured to control power provided to the one or more light-emitting elements in response to the sensor signal. The sensor signal can be configured to indicate estimates of one or more of intensity and spectral density distribution of the fraction of the portion of the scattered light. The control circuit can control power provided to the one or more light-emitting elements to reduce variations in the light emitted by the light-emitting device as the light-emitting device ages or changes operating temperature, or based on an input signal provided by a user during operation of the light-emitting device. 
     In some implementations, the first optical element can have a substantially uniform effective thickness. In some implementations, n 1  ≈ n 2 . In some implementations, n 0  ≈ 1. In some implementations, the exit surface can be shaped such that an angle of incidence on the exit surface of the scattered light that directly impinges on the exit surface is less than the Brewster angle. 
     In some implementations, for a cross-section, each point, p, on the exit surface can have a corresponding radius of curvature, R(p), and the first and second optical elements can be arranged so that each point on the optical interface is at least a corresponding distance, d(p), from the exit surface, where: 
     
       
         
           
             d 
             
               p 
             
             = 
             R 
             
               p 
             
             * 
             
               
                 1 
                   
                 - 
                 
                   k 
                   / 
                   
                     
                       n 
                       2 
                     
                   
                 
               
             
           
         
       
     
     The value k can be a positive real number such that k &lt; n 2 . In some implementations, k/n 2  can be less than 0.8. In some implementations, k can be less than 1. In some implementations, the value k can be: 
     
       
         
           
             k 
             &lt; 
             
               
                 
                   n 
                   2 
                 
               
               
                 
                   
                     
                       
                         1 
                         + 
                         
                           n 
                           2 
                           2 
                         
                       
                     
                   
                 
               
             
           
         
       
     
     In some implementations, each point on the optical interface can be the distance d(p) from the corresponding nearest point on the exit surface. 
     In some implementations, an axis of symmetry of the first optical element and an axis of symmetry of the second optical element can be collinear. The one or more light-emitting elements can be positioned symmetrically about the axis of symmetry of the first optical element. In some implementations, the first and second optical elements can extend along an axis and can have a cross-section that is substantially unchanged along the axis. In some implementations, the exit surface can be a spherical or cylindrical surface. 
     In some implementations, the medium can be a gas. The gas can be air. In some implementations, the one or more light-emitting elements can include a light emitting diode. In some implementations, the light emitted by the one or more light-emitting elements can include blue light or ultraviolet light. In some implementations, the scattering centers can include inelastic scattering centers configured to convert at least some light received from the one or more light-emitting elements to converted light having a longer wavelength. The converted light can be yellow light. The inelastic scattering centers can include a light-conversion material. The light-conversion material can include a phosphor, or a quantum dot phosphor. 
     In some implementations, the transparent material can be a plastic or a glass. In some implementations, the light-emitting device can include multiple light-emitting elements and the multiple light-emitting elements can emit light of different colors. In some implementations, the inelastic scattering centers can be one and the same as the elastic scattering centers. 
     Various references are incorporated herein by reference. In the event of conflict between the present disclosure and any incorporated disclosure, including definitions, the present specification controls. The details of one or more embodiments of the subject matter described in this specification are set forth in the accompanying drawings and the description below. Other features, aspects, and advantages of the subject matter will become apparent from the description, the drawings, and the claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1 A  is a schematic diagram of an example of an ASLV light-emitting device having an extractor element that satisfies Brewster’s condition. 
         FIG.  1 B  shows an example of a spectrum of output light of an ASLV light-emitting device. 
         FIGS.  2 A- 2 D  show aspects of an example of a light-emitting device having a hemispherical scattering element. 
         FIG.  3    shows an example of a light-emitting device having a concave scattering element. 
         FIG.  4    shows an example of a light-emitting device having a flat scattering element. 
         FIG.  5    shows an example of a light-emitting device having a flat scattering element and a recovery enclosure recessed inside an extractor. 
         FIG.  6    shows an example of a light-emitting device having a convex scattering element. 
         FIG.  7    shows an example of a light-emitting device having a spherical scattering element and a recovery enclosure encompassed by an extractor. 
         FIG.  8    shows an example of a light-emitting device having a concave scattering element, and a recovery enclosure with a protruded base. 
         FIG.  9 A  is a schematic diagram of an example of an ASLV light-emitting device having multiple light-emitting devices and a scattering element with elastic and inelastic scattering centers. 
         FIG.  9 B  shows examples of spectra of output light of ASLV light-emitting devices including a scattering element with elastic and inelastic scattering centers. 
         FIG.  10 A  is a schematic diagram of an example of an ASLV light-emitting device having multiple light-emitting devices and a scattering element including elastic scattering centers. 
         FIG.  10 B  shows examples of spectra of output light of ASLV light-emitting devices including a scattering element with elastic scattering centers. 
         FIG.  11    shows an example of a light-emitting device having multiple light-emitting devices, a concave scattering element, and a recovery enclosure with a recessed base. 
         FIG.  12    shows an example of a light-emitting device having multiple light-emitting devices and a concave scattering element. 
         FIG.  13    is a schematic diagram of an example of an ASLV light-emitting device having an intra-system source feedback. 
         FIGS.  14 - 16    show configurations of intra-device feedback for light-emitting devices. 
         FIG.  17    is a schematic diagram of an example of a feedback circuit used to provide intra-device light-source feedback in an ASLV light-emitting device. 
         FIG.  18    is a schematic diagram of an example of an ASLV light-emitting device having a non-spherical, non-planar optical interface that controls intensity distribution of output light. 
         FIGS.  19 A- 19 B  show aspects of an example of a light-emitting device having an ellipsoidal scattering element. 
         FIGS.  20 A- 20 B  show aspects of another example of a light-emitting device having an ellipsoidal scattering element. 
         FIGS.  21 A- 21 E  show aspects of an example of a light-emitting device having an ellipsoidal scattering element with unequal orthogonal axes. 
         FIG.  22    shows an example of an elongated light-emitting device that uses multiple light-emitting devices having an ellipsoidal scattering element with unequal orthogonal axes. 
         FIGS.  23 A- 23 B  show aspects of an example of a light-emitting device having an ellipsoidal scattering element that encloses a recovery enclosure. 
         FIGS.  24 A- 24 B  show aspects of an example of a light-emitting device having an elongated scattering element that encloses a recovery enclosure. 
         FIGS.  25 A- 25 C  show aspects of an example of a light-emitting device having a scattering element shaped as an ellipsoidal segment that encloses a recovery enclosure. 
         FIGS.  26 A- 26 B  show aspects of an example of a light-emitting device having a spherical scattering element that is off-centered relative to an extractor element and encloses a recovery enclosure. 
         FIGS.  27 A- 27 B  show aspects of an example of a light-emitting device having an ellipsoidal scattering element that is off-centered relative to an extractor element and encloses a recovery enclosure. 
         FIG.  28    shows aspects of an example of a light-emitting device having an extractor shaped as an ellipsoidal segment. 
         FIG.  29    is a schematic diagram of an example of an ASLV light-emitting device having an extractor element with three or more portions arranged to control intensity distribution of output light. 
         FIGS.  30 A- 30 D  show aspects of an example of a light-emitting device having a hemispherical scattering element and an extractor shaped as a squared hemisphere. 
         FIGS.  31 A- 31 D  show aspects of an example of a light-emitting device having a hemispherical scattering element and an extractor shaped as crossed elliptic cylinders. 
         FIG.  32    is a schematic diagram of an example of an ASLV light-emitting device having an extractor element with two exit surfaces separate by a step. 
         FIGS.  33 A- 33 B  show aspects of an example of a light-emitting device having a hemispherical scattering element and a step in an exit surface of an extractor element. 
         FIGS.  34 A- 34 B  show aspects of an example of a light-emitting device having an elliptical scattering element and a step in an exit surface of an extractor element. 
         FIGS.  35 A- 35 B  show aspects of an example of a light-emitting device having a rectangular scattering element and a step in an exit surface of an extractor element. 
         FIG.  36    shows an example of a light-emitting device having a rectangular scattering element and an extractor element with an exit surface that has a step and extends beyond a 90° angle from the optical axis. 
         FIG.  37    shows an example of a light-emitting device having light-emitting devices of multiple chromaticities arranged on rectangular mount, and a step in an exit surface of an extractor element. 
         FIG.  38    is a schematic diagram of an example of an ASLV light-emitting device having an extractor element that includes a Weierstrass portion and a light guide. 
         FIG.  39    shows an example of a light-emitting device having a compound extractor element. 
         FIG.  40    shows another example of a light-emitting device having a compound extractor element. 
         FIG.  41    shows aspects of a light-emitting device having compound extractor element. 
         FIG.  42    shows an example of a light-emitting device having multiple rotationally symmetric scattering elements and a common, elongated extractor element. 
         FIG.  43    shows an example of a light-emitting device having an elongated scattering element and an elongated extractor element. 
     
    
    
     Like elements in different figures are identified with the same reference numeral. 
     DETAILED DESCRIPTION 
       FIG.  1 A  shows a schematic diagram of an example of a light-emitting device  100  that includes a light-emitting element  110  (LEE), a scattering element  120  (also referred to as a first optical element), an extractor element  130  (also referred to as a second optical element), and a recovery enclosure  140 . Light-emitting device  100  efficiently provides broadband, homogenized light to an ambient environment across a broad range of angles. 
     The light-emitting element  110  is configured to produce and emit light during operation. A spectral power distribution of light emitted by the light-emitting element  110  (also referred to as pump light) can be blue, for instance. The spectral power distribution for visible light is referred to as chromaticity. In general, the light-emitting element  110  is a device that emits radiation in a region or combination of regions of the electromagnetic spectrum for example, the visible region, infrared and/or ultraviolet region, when activated by applying a potential difference across it or passing a current through it, for example. The light-emitting element  110  can have monochromatic, quasi-monochromatic, polychromatic or broadband spectral emission characteristics. Examples of light-emitting elements that are monochromatic or quasi-monochromatic include semiconductor, organic, polymer/polymeric light-emitting diodes (LEDs). In some implementations, the light-emitting element  110  can be a single specific device that emits the radiation, for example an LED die, or/and can be a combination of multiple instances of the specific device that emit the radiation together. Such light-emitting device  110  can include a housing or package within which the specific device or devices are placed. As another example, the light-emitting element  110  includes one or more lasers and more specifically semiconductor lasers, such as vertical cavity surface emitting lasers (VCSELs) and edge emitting lasers. In embodiment utilizing semiconductor lasers, the scattering element functions to reduce (e.g., eliminate) spatial and temporal coherence of the laser light, which may be advantageous where the light emitting device may be viewed directly by a person. Further examples of a light-emitting element  110  include superluminescent diodes and other superluminescent devices. 
     The scattering element  120  has a first surface (also referred to as a light-entry surface) spaced apart from the light-emitting element  110  and positioned to receive the light from the light-emitting element  110 . The scattering element  120  includes scattering centers arranged to substantially isotropically scatter the light from the light-emitting element  110  and to provide scattered light. The scattered light includes elastically scattered pump light and inelastically scattered pump light. The elastically scattered pump light includes photons that have undergone elastic scattering at the scattering centers, and the inelastically scattered pump light includes photons that have undergone inelastic scattering at the scattering centers. For example, the spectral distribution of photons remains substantially unchanged due to elastic scattering or change in effect of inelastic scattering. Elastic scattering entails refraction of light at a scattering center, for example. As another example, inelastic scattering entails emission of light from a scattering center in effect of light that was previously absorbed by the scattering center. With respect to the technology described in this specification, inelastic scattering typically is associated with one visible or ultraviolet (UV) incoming photon and one visible outgoing photon. Scattering of light by a scattering center can result from effects such as light conversion, refraction, and/or other effect and/or combination thereof. The distribution of a plurality of outgoing photons that result from inelastic scattering at one scattering center is isotropic depending on, for example, the ability of the scattering centers to perform light conversion. The distribution of a plurality of outgoing photons that result from elastic scattering at multiple scattering centers is isotropic depending on, for example, shapes, arrangements and/or compositions of the scattering centers. A scattering center can include one or more portions that each scatter light in one or more ways, for example, by light conversion, refraction or other effect. Scattering centers include discontinuities in the composition or structure of matter. In order to achieve a predetermined degree of randomness in its propagation, light has to undergo multiple elastic scattering events. As such multiple scattering events are required to exceed a predetermined randomness, for example, when the light is scattered by interaction with scattering centers that scatter light merely by refraction. Scattering centers can include light-converting material (LCM) and/or non-light converting material, for example. Light conversion via LCM is a form of inelastic scattering. 
     LCM is a material which absorbs photons according to a first spectral distribution and emits photons according to a second spectral distribution, as described below in connection with  FIG.  1 B . The terms light conversion, wavelength conversion and/or color conversion are used interchangeably. Light-converting material is also referred to as photoluminescent or color-converting material, for example. Light-converting materials can include photoluminescent substances, fluorescent substances, phosphors, quantum dots, semiconductor-based optical converters, or the like. Light-converting materials also can include rare earth elements. 
       FIG.  1 B  shows an emission spectrum  111  for a blue LED. The blue LED can be used as the light-emitting element  110  in the light-emitting device  100 . In addition,  FIG.  1 B  shows an absorption spectrum  112  and an emission spectrum  113  of the scattering centers, along with a spectrum of the scattered light  115  (the latter is represented with a dotted-line.) Spectral power distribution of the elastically scattered light is the same as the spectral power distribution of the pump light (corresponding to the spectrum  111 .) Moreover, the absorption spectrum of the scattering centers  112  overlaps the spectrum of the light emitted by the light-emitting element  111 . Spectral power distribution of the inelastically scattered light is different from the pump light. For instance, inelastically scattered light will have a spectrum  113  that is shifted (e.g., Stokes shifted) to longer wavelengths than the pump light spectrum  111 . For example, where the pump light is blue, e.g., corresponding to the spectrum  111 , inelastically scattered light can be characterized by an overall yellow/amber color, e.g., corresponding to the spectrum  113 . Moreover, the spectrum of the scattered light  115  is a combination of the spectrum  111  of the elastically scattered light and spectrum  113  of the inelastically scattered light. 
     In this manner, the scattering element  120  substantially randomizes the direction of propagation of light received from light-emitting element  110  by scattering substantially all light entering the scattering element  120 , while allowing substantial portions of light to pass through the scattering element  120 . The extractor element  130  is formed from a transparent material, such as a transparent glass or a transparent organic polymer, having an exit surface. The exit surface of the extractor element  130  is generally a curved, transparent surface. In other words, changes in the scattered light passing through the exit surface can generally be described by Snell’s law of refraction, as opposed to, for example, an opaque or diffuse surface where further scattering of transmitted light occurs. The extractor element  130  is in contact with the scattering element  120 , such that there is an optical interface between the scattering and extractor elements at the place of contact, and the optical interface is opposite the first surface of the scattering element. The scattering element  120  has substantially uniform thickness, such that a distance between the optical interface and the first surface of the scattering element  120  is constant for any point of the optical interface. Moreover, the extractor element  130  is arranged so that light scattered through the optical interface enters the extractor element  130 . Light from the scattering element  120  that directly reaches the exit surface of the extractor element  130  is referred to as forward light. 
     Further, the light-emitting device  100  includes a medium, such as a gas (e.g., air), adjacent the first surface of the scattering element having a refractive index n0, and the scattering element  120  includes a material having a first refractive index n1, where n0 &lt; n1. Light from the scattering element  120  that reaches the first surface is referred to as backward light. Because n0 &lt; n1, the first surface allows only a fraction of the backward light to escape into the low-index medium. The transparent material of the extractor element  130  has a refractive index n2, where n0 &lt; n2. As such, the amount of transmitted forward light is greater than the amount of backward light transmitted into the low index medium, and the light emitting device  100  asymmetrically propagates scattered light. In such a case, depending on the degree of asymmetry between n0 and n2, the optical interface between the scattering element  120  and the extractor element  130  permits varying ratios of forward to backward light transmission. The maximum asymmetry in this ratio is reached if n2 is equal or larger than n1. Light emitting devices that feature asymmetric optical interfaces (i.e., different refractive index mismatches) on opposing sides of the scattering element are referred to as asymmetric scattering light valves (ASLV), or ASLV light-emitting devices. Hence, the light-emitting device  100  is an ASLV light-emitting device  100 . 
     The exit surface of the extractor element  130  is a transparent surface on which the scattered light that directly impinges on the exit surface experiences little or no total internal reflection (TIR). In this manner, the exit surface transmits a large portion of light impinging thereon that directly propagates thereto from the scattering element and propagates in at least certain planes and outputs it into the ambient of the extractor element on first pass. The light output through the exit surface can be used for illumination or indication functions provided by the ASLV light-emitting device  100  or for further manipulation by another optical system that works in conjunction with the ASLV light-emitting device  100 . 
     In some embodiments, the exit surface of the extractor element  130  is shaped as a spherical or a cylindrical dome or shell with a radius R1 in which the optical interface is disposed within an area defined by a respective notional sphere or cylinder that is concentric with the exit surface and has a radius R OW  = R1/n, wherein n is the refractive index of the extractor element  130 . Such a configuration is referred to as Weierstrass geometry or Weierstrass configuration. It is noted that a spherical Weierstrass geometry can avoid TIR for rays passing through the area circumscribed by a corresponding notional R1/n sphere irrespective of the plane of propagation. A cylindrical Weierstrass geometry can exhibit TIR for light that propagates in planes that intersect the respective cylinder axis at shallow angles even if the light passes through an area circumscribed by a corresponding notional R OW  = R1/n cylinder. 
     It is noted that other ALSV light-emitting devices described in this specification have exit surfaces with other shapes and/or other geometrical relations with respect to the optical interface. For instance, a non-spherical or non-cylindrical exit surface of the extractor element  130  can be employed to refract light and aid in shaping an output intensity distribution in ways different from those provided by a spherical or cylindrical exit surface. The definition of the Weierstrass geometry can be extended to include exit surfaces with non-circular sections by requiring that the optical interface falls within cones, also referred to as acceptance cones, subtended from points p of the exit surface whose axes correspond to respective surface normals at the points p and which have an apex of 2*Arcsin(k/n), wherein k is a positive number smaller than n. It is noted that the exit surface needs to be configured such that the plurality of all noted cones circumscribe a space with a non-zero volume. It is further noted that k is assumed to refer to a parameter that determines the amount of TIR at an uncoated exit surface that separates an optically dense medium, having n&gt;1, on one side of the exit surface making up the extractor element  130  from a typical gas such as air with n ~ 1.00 at standard temperature and pressure conditions, on the opposite side of the exit surface. Depending on the embodiment, k can be slightly larger than 1 but is preferably less than 1. If k &gt; 1, some TIR may occur at the exit surface inside the extractor element  130 . In some embodiments, this results in the optical interface being at least R(p)*(1-k/n) away from the exit surface in a direction normal to the exit surface at a point p thereof. Here, R(p) is the local radius of curvature of the exit surface at the point p, and n is the refractive index of the extractor element  130 . For a spherical or cylindrical exit surface with k = 1, the boundaries circumscribed by the noted cones correspond with a spherical or cylindrical Weierstrass geometry, respectively. Some embodiments are configured to allow for some TIR by choosing k &gt; 1. In such cases, k/n is limited to k/n &lt; 0.8, for example. 
     In summary, an ASLV light-emitting device  100  is said to satisfy the Weierstrass configuration if a radius R O  of the optical interface is less than or equal to R O  ≤ R OW  = R1/n, where R1 and n respectively are the radius and index of refraction of the extractor element  130 . Equivalently, the extractor element  130  of an ASLV light-emitting device  100  is said to satisfy the Weierstrass configuration if a radius R 1  of an extractor element  130 , which has an index of refraction n, is equal to or larger than R 1  ≥ R 1W  = nR O , where R O  is the radius of the optical interface of the ASLV light-emitting device  100 . 
     In some embodiments, the exit surface is shaped such that an angle of incidence on the exit surface of the scattered light that directly impinges on the exit surface is less than the Brewster angle. In this case, k is not just smaller than 1 to avoid TIR at the exit surface of the extractor element  130  for light propagating in at least one plane, but k is made so small that certain Fresnel reflections are additionally avoided. In such a case, k is chosen to be smaller than n(1 + n 2 ) -½ . For example, with respect to light propagating in planes of symmetry of spherical or cylindrical Weierstrass geometries, rays that propagate through an area circumscribed by a concentric notional sphere or cylinder of radius R0 = R1(1 + n 2 ) -½ , will impinge on the exit surface at or below the Brewster angle. More generally, p-polarized light that impinges at a point p of the exit surface from within directions bound by a cone subtended from the point p with apex 2*Arctan(⅟n) whose axis corresponds with the surface normal at the point p will not be reflected at the exit surface. Such a configuration is referred to as Brewster geometry (or Brewster configuration), or more specifically a Brewster sphere or a Brewster cylinder, for example. In such embodiments the distance between the exit surface and the optical interface is larger than R1 
     
       
         
           
             
               
                 1 
                 − 
                 
                   
                     
                       
                         1 
                         + 
                         
                           n 
                           2 
                         
                       
                     
                   
                   
                     − 
                     
                       1 
                       2 
                     
                   
                 
               
             
             . 
           
         
       
     
     In summary, an ASLV light-emitting device  100  is said to satisfy the Brewster configuration if a radius R 0  of the optical interface is less than or equal to R O  ≤ R OB  = R1(1 + n 2 ) -½ , where R 1  and n are the radius and index of refraction of the extractor element  130 . Note that for a given radius R 1  of the extractor element  130 , an optical interface of the ASLV light-emitting device  100  that satisfies the Brewster condition has a maximum radius R OB  that is smaller than a maximum radius R OW  of an optical interface of the ASLV light-emitting device  100  that satisfies the Weierstrass condition. Equivalently, the extractor element  130  of index of refraction n is said to satisfy the Brewster configuration if a radius R 1  of the extractor element  130  is equal to or larger than R 1  ≥ R 1B  = R O  (1 + n 2 ) +½ , where R O  is the radius of the optical interface of the ASLV light-emitting device  100 . Note that for a given radius R O  of the optical interface of the ASLV light-emitting device  100 , an extractor element  130  that satisfies the Brewster condition has a minimum radius R 1B  that is larger than a minimum radius Riw of an extractor element  130  that satisfies the Weierstrass condition. 
     In some implementations, the extractor element  130  has an elongated or non-elongated shape. As described below in this specification, the extractor element  130  can be shaped to partially or fully circumscribe the scattering element  120 . Such an extractor element  130  provides one or more hollows or cavities and one or more openings or holes. Openings and holes form apertures to receive light from the light-emitting element  110  and direct the light at the first surface of the scattering element  120 . Accordingly, the extractor element  130  is shaped as a shell or other shape with a certain thickness or thickness profile. 
     In some embodiments, the scattering element  120  is partially of fully surrounded by the extractor element  130  and the optical interface includes corresponding portions of the surface of the scattering element. In some embodiments, the extractor element  130  and the scattering element  120  are integrally formed. In an example of such an integral formation, the optical interface is a notional interface drawn between regions of a corresponding integrally formed object, such that the optical interface substantially includes interfaces formed by the scattering centers. This may be the case, when the scattering element  120  includes scattering centers inside a material that is the same as the material used to form the extractor element  130 , for example. In this manner, the scattering element  120  can be shaped as a tile, disc, spherical or aspherical shell or dome, tubular, prismatic or other elongate shell, or other structure to provide a predetermined spatial profile of conversion properties to achieve a predetermined light-output profile including color and/or brightness homogeneity from the scattering element  120 . 
     Furthermore, the recovery enclosure  140  encloses the medium adjacent the first surface of the scattering element. The recovery enclosure  140  is arranged and configured to recover a portion of the scattered light that propagates through the first surface into the medium. This means that the recovery enclosure  140  redirects at least a portion of the scattered light back towards the scattering element  120  so that at least some of this light exits the scattering element  120  into the extractor element  130 . As explained in reference to embodiments below, the design of the recovery enclosure  140  can be selected to reduce the amount of scattered light that returns to the light-emitting element  110  (where it can be absorbed). For instance, the recovery enclosure  140  can be defined by the first surface of the scattering element  120  and/or one or more additional optical components that redirect such back-scattered light and/or via certain configuration of the scattering element as described below in this specification. For example, the recovery enclosure  140  can be formed by the first surface of the scattering element  120  and an optical coupler as described below in connection with  FIG.  4   . As another example, the recovery enclosure  140  can be formed by the first surface of a hollow extractor element  130  as described below in connection with  FIG.  6   . The backscattered light recovered from the recovery enclosure  140  further increases asymmetry in the propagation of light through the ASLV light-emitting device  100 . 
     Additionally, the ASLV light-emitting device  100  outputs scattered light through the exit surface into the ambient environment. The spectrum  115  of the light output by the ASLV light-emitting device  100  is shown in  FIG.  1 B . Generally, the scattering element  120  can provide sufficient mixing of the elastically and inelastically scattered light so that the chromaticity of the light exiting the light-emitting device  100  is substantially uniform, e.g., isotropic, through a large range of angles. For example, light-emitting device  100  can provide white light with a white point that varies by 5% or less (e.g., 4% or less, 3% or less, 2% or less, 1% or less) across a range of solid angles such as, for example, 0.1 sr or more, 0.3 sr or more, 0.5 sr or more, 1 sr or more, 2 sr or more, π sr or more, 4 sr or more, 2π sr or more, 3π sr or more. 
     In general, the shape, size, and composition of the recovery enclosure  140 , scattering element  120 , and extractor element  130  can vary. The characteristics of each component are selected based on the characteristics of the other components and the desired performance of the light-emitting device  100 . This will be apparent from the discussion of specific embodiments of light-emitting devices described below. 
     An ASLV light-emitting device  100  can be used in applications such as general illumination. Additionally, the ASLV light-emitting device  100  can be used for display illumination, e.g., projection displays, backlit LCD’s, signage, etc. 
     Moreover, an ASLV light-emitting device  100  can be fabricated using conventional extrusion and molding techniques and conventional assembly techniques, as described below in this specification for specific embodiments. Components of the ASLV light-emitting device  100  can include one or more organic or inorganic materials, for example acrylic, silicone, polypropylene (PP), polyethylene terephthalate (PET), polycarbonate, polyvinylidene fluoride such as KynarTM, lacquer, acrylic, rubber, polyphenylene sulfide (PPS) such as RytonTM, polysulfone, polyetherimide (PEI), polyetheretherketone (PEEK), polyphenylene oxide (PPO) such as NorylTM, glass, quartz, silicate, adhesive, other polymers organic or inorganic glasses and/or other materials. 
       FIG.  2 A  shows aspects of an example of an ASLV light-emitting device  200  having a hemispherical scattering element  220 . The ASLV light-emitting device  200  includes a light-emitting element  210  (e.g., a blue pump LED), the scattering element  220 , an extractor element  230 , and a flat reflector  245  (e.g., a mirror.) The scattering element  120  has a first surface  215  spaced apart from the light-emitting element  210  and positioned to receive the light from the light-emitting element  210 . The light-emitting element  210  is inserted into an opening (e.g., having a radius Rd) of the flat reflector  245 . In some implementations, the reflector  245  extends to at least the first surface of the scattering element  220 . In other implementations, the reflector  245  extends to at least an exit surface of the extractor element  230 . The scattering element  220  is located on the inside of the extractor element  230  adjacent an air filled semispherical enclosure  240  of radius R O  of the extractor element  230  to form an optical interface  225 . The enclosure  240  encloses the light-emitting element  210  and its surrounding reflector  245 . In some implementations, the extractor element  230  has an exit surface  235  of radius R1 that is concentric with the optical interface  225 , such that the extractor element  230  satisfies the Brewster configuration R 1  ≥ R 1B . The Brewster radius is given by R 1B  = R O  (1 + n1 2 ) +½ , where R O  is the radius of the optical interface  225  of the ASLV light-emitting device  200 , and n1 denotes the index of refraction of the material of the extractor element  230 . As the extractor element  230  satisfies the Brewster configuration, an angle of incidence on the exit surface  235  of the scattered light that directly impinges on the exit surface  235  is less than the Brewster angle, and as such, the scattered light that directly impinges on the exit surface  235  experiences little or no total internal reflection thereon. 
     In this example, light propagation asymmetry arises from the materials on the inside (index n0) and outside (index n1) of the scattering element  220  with index np being unequal. For instance, if np = 1.5 and n0 = 1.0, that is n0 &lt; np, a large fraction (~75%) of the isotropically distributed photons impinging on the first surface  215  will be reflected by TIR back into the scattering element  220  and only a smaller fraction (~25%) will be transmitted backwards into the recovery enclosure  240  from where some may reach the light-emitting element  210 . At the optical interface  225 , the condition np ≤ n1 will guarantee that substantially all photons reaching the optical interface  225  will transition into the extractor element  230 , and the Brewster condition will further guarantee that practically all these photons will transmit into air without TIR through the exit surface  235 . Only a small fraction (down to about ~4% depending on incidence angle) will be returned by Fresnel reflection at the exit surface  235 . 
       FIG.  2 B  illustrates how an amount  270  of Lambertian distributed light emitted from a point on the top of the spherical optical interface  225 , that is reflected at the spherical exit surface  235  of radius R1, depends on a radial distance r = R O /R OB  of such a point from the center “O” of the spherical exit surface  235 .  FIG.  2 B  also illustrates how a volume of the extractor element  280  depends on the radial distance r, further assuming that the optical interface  225  is spherical and hence r is equal to a normalized radius of the optical interface  225 . It is noted that the radial distance r = R O /R OB  is indicated in units of the Brewster Radius R OB  = R1/sqrt(1+(n1)^2) for the optical interface  225 , where R O  is the (non-normalized) radius of the optical interface. The situation illustrated in  FIG.  2 B  refers to an index of refraction ratio of n1=1.5. This represents an example of a plastic or glass to air interface (n0 = 1). The amount of reflected light  270  is indicated in units of the amount of light that is reflected at an exit surface  235  when the radius of the optical interface  225  is the Brewster Radius R O  = R OB , or r = 1. The volume  280  is indicated in units of the volume of an extractor element  230  of radius R1, when the radius of the optical interface  225  is the Brewster Radius R O  = R OB , or r = 1. The upper limit of r represented in  FIG.  2 B  is r = 1.2 and corresponds to the Weierstrass Radius R OW  = R1/n1. As shown in  FIG.  2 B , reducing r of the optical interface  225  from the Weierstrass Radius (R O  = R OW , or r = 1.2) to the Brewster Radius (R O  = R OB , or r = 1) reduces the amount of reflected light  270  to less than 50% while the volume  280  of the extractor element  280  increases by less 20%. For situations when the ASLV light-emitting device  200  satisfies the Brewster condition, r ≤ 1, the maximum angles of incidence of the light impinging on the exit surface  235  are below the Brewster Angle, and thus approach normal incidence. Below the Brewster Limit, where r ≤ 1, Fresnel reflection losses  270  are within about 20% of the value of the reflection coefficient for normal incidence, ((n1/n2-1) /(n1/n2+1))^2. Normal incidence corresponds to a “point-like” optical interface, or r = 0. 
     In this manner, the volume  280  of an extractor element  230  at the Brewster condition, r = 1, is beneficially 20% less than the volume  280  of an extractor element  230  that experiences only Fresnel reflections, r = 0, for a penalty increase in reflection losses of 20%. Meanwhile, the volume  280  of the extractor element  230  at the Brewster condition, r = 1, suffers a 20% penalty increase compared to the volume  280  of an extractor element  230  at the Weierstrass condition, r = 1.2, but benefits from a decrease in reflection losses of more than 50%. Accordingly, an ASLV light-emitting device  200  with an optical interface  225  with a radius R O  about equal to the Brewster Radius, R OB , provides a reasonable performance/cost ratio. In some implementations, the ASLV light-emitting device  200  can be fabricated to have an optical interface  225  with a radius R O  about 0.9*R OB , 0.75*R OB  or 0.5*R OB . In some implementations, the ASLV light-emitting device  200  can be fabricated to have an optical interface  225  with a radius R O  about 1.05*R OB , or 1.1*R OB . 
     The structure of the ASLV light-emitting device  200  shown in  FIG.  2 A  reduces internal photon losses by (1) minimizing backscattering from the scattering element  220  into the recovery enclosure  240  towards the pump, (2) guaranteeing that most backscattered photons are returned to the scattering element  220  with one or less reflection events on the reflector  245 , (3) reducing the average time a photon spends in the loss-prone scattering element  220  by providing a first pass transmission into the extractor  230  for any photon reaching the index matched optical interface  225  between scattering element  220  and extractor element  230 . Compared with a symmetric structure (e.g., having an air gap between phosphor  220  and extractor  230  or very thin extractor shell  230 ), the ASLV light-emitting device  200  reduces photon losses in the photon recovery enclosure  240  between light-emitting element  210  and scattering element  220  or absorption losses within the scattering element  220  by approximately a factor of 3x. 
       FIG.  2 D  shows an intensity distribution  290  output by an ASLV light-emitting device similar to the ASLV light-emitting device  200 . In this example, the reflector  245  extends to the exit surface  235  of the extractor element  230 , because it is desired that the ASLV light-emitting device  200  output some light into backward direction. In this manner, although the intensity distribution  290  has a forward bias, it covers a solid angle of &gt;2π sr, since light originating from the upper part of the scattering element  220  and propagating towards the lower edges of the extractor  230  will be refracted into angles &gt; 90° from the optical z-axis. 
     The example of ASLV light-emitting device  200  illustrated in  FIG.  2 C , has a reflector  245  that extends beyond the edge of the exit surface  235  to turn most of the scattered light into a forward direction (e.g., the positive direction of the z-axis.) An intensity distribution of the light output by the ASLV light-emitting device shown in  FIG.  2 D  also depends on the reflector shape outside of the exit surface  235 . For instance, the reflector  245 , which extends outside the exit surface  235 , can be curved or bent upwards, e.g., in the +z direction, to narrow the output intensity distribution. For effective photon recovery in the recovery enclosure  240 , it is important to fabricate the reflector  245  from a material with high reflectivity to return scattered light to the scattering element  220 . 
     To first order, it is believed that specular and diffuse reflectors  245  having the same percentage reflectance offer comparable performance in the ASLV light-emitting device  200 . At the intersection of the Brewster extractor element  235  with the reflector  245 , some degree of diffusivity helps in suppressing wave-guided modes and converts these modes into “escape” modes (i.e. modes that leak, or escape, from the ASLV light-emitting device 200). The choice of diffusivity can vary. Some reflecting materials slightly decrease their reflectivity with increasing diffusivity. The choice of diffusivity can be determined by efficiency considerations as well as other lamp design parameters such as angular intensity distribution. 
     Specific examples of elongated embodiments of scattering elements are described below in this specification in connection with  FIGS.  19 - 25   . Additional examples of elongated embodiments of extractor elements are described below in this specification in connection with  FIGS.  28  and  30 - 31   . 
     While the foregoing embodiment includes a hemispherical scattering element, other concave shapes of the scattering element are also possible as described below in this specification. For example,  FIG.  3    shows an ASLV light-emitting device  300  having a mostly concave scattering element  320 . The light-emitting device  300  includes a light-emitting element  310  inserted into an opening of a reflector  345 , a scattering element  320  deposited on the inside of an air filled recovery enclosure  340  of an extractor element  330  enclosing the pump  310  and its surrounding reflector  345 . The scattering element  320  has uniform thickness and forms an optical interface  325  with the extractor element  330 , such that the index n1 of the extractor element  330  is higher than or equal to the index np of the scattering element  320 . The extractor element  330  has an exit surface  335  of radius R1 that satisfies the Brewster condition for most of the extent of the optical interface  325 . Specifically in the example illustrated in  FIG.  3   , the optical interface  325  is contained within a nominal sphere of radius R OB  that is concentric with the exit surface  335 . Other examples of light-emitting devices having such concave scattering elements are described below. 
       FIG.  4    shows an example of ASLV light-emitting device  400 , shown in cross-section, having a planar scattering element  420 . In addition to scattering element  420 , ASLV light-emitting device  400  includes an extractor element  410  and a primary optical sub-system  402 . In this example, the ASLV light-emitting device  400  is configured as a light bulb. The primary optical sub-system  402  includes an LEE  460  and an optical coupler  450 . The ASLV light-emitting device  400  is rotationally symmetric about an axis z that passes through the LEE  460 . 
     During operation, light-emitting element  460  emits pump light, at least some of which propagates through optical coupler  450  towards a light-entry surface  415  of scattering element  420 . The optical coupler  450  is configured to collimate light from light-emitting element  460  in order to maintain steep incidence angles of light from the LEEs  460 . It is believed that maintaining steep incidence angles reduces the amount of Fresnel reflections at the light-entry surface  415 , reduces the overall amount of back-reflected source light and therefore improves the overall efficiency of the ASLV light-emitting device  400 . The optical coupler  450  can be configured to provide a specular, diffuse, TIR or otherwise reflective mantle  451 . As such, the optical coupler  450  can be configured as a substantially solid object or an object with a cavity. 
     The optical coupler  450  has a conical cross section and is nominally rotationally symmetric about the z-axis. In general, other forms of optical couples can be used. For example, optical couplers can have a regular or irregular polygonal, or otherwise configured cross section. Depending on the embodiment, the optical coupler  450  is configured to redirect at least a portion of light that escapes from the scattering element  420  through the light-entry surface  415  towards the optical coupler  450  back to the light-entry surface  415 . In this manner, the optical coupler  450  and the light-entry surface  415  of the scattering element  420  form a recovery enclosure for the ASLV light-emitting device  400 . 
     The optical coupler  450  can use TIR and/or a reflective coating to direct light and accordingly configured as a solid or hollow object. The coupler  450  is used in combination with an additional optical element that provides a diffuse, specular or otherwise reflective cone-shaped opening having a white, metallic or other surface that is separated from the reflective mantle  451  by an air gap to further improve recovery of light received from a scattering element  420  including materials having refractive indices larger than one. The reflective surface of such an additional optical element reflects back and optionally diffuses light that escapes from the optical coupler  450  through the reflective mantle  451  and thereby improves chances for reentry of the escaped light into the optical coupler  450  in such directions that it will propagate towards the light-entry surface  415 . The optical coupler can be configured as a compound parabolic concentrator, a conical or other element, for example. 
     In some implementations, the extractor element  410  is a solid spherical dome of radius R1 and the scattering element  420  as a circular disk. In some implementations, the extractor element can include a gel or a liquid. In this example, the scattering element  420  abuts the extractor element  410  to form an optical interface  425 . The scattering element  420  includes active (e.g., inelastic) and passive (e.g., elastic) scattering centers. The optical elements  410  and  420 , and primary optical sub-system  402  are held in place by a suitable support structure, which maintains a gap  440  between scattering element  420  and optical coupler  450 . Gap  440  is used to provide diffused white light from blue pump light provided by the one or more LEEs  460 . 
     The gap  440  can be filled by air, some other gas, or evacuated. While gap  440  is shown to have a substantially homogenous thickness, more generally, gap  440  can have a thickness that varies. In addition, gap  440  can be relatively narrow. For example, gap  440  can have a thickness of about 1 mm or less (e.g., 0.5 mm or less, 0.2 mm or less). 
     As described above, scattering element  420  is a planar element having a light-entry surface  415  facing light emitting element  460 . 
     To mitigate the amount of light from the LEEs  460  that may escape transmission into the scattering element  420  via the outer perimeter of the air gap  440  and therefore may be lost or cause undesired chromaticity effects (e.g., unwanted blue light) a number of measures may be employed. Such measures include reducing the thickness of the air gap  440 , widening of the scattering element  420 , disposition of a non-transmissive ring with optional inside reflective surface around the perimeter of the air gap, and/or other measures, for example. 
     The extractor element  410  includes a transparent material with refractive index n. The scattering element  420  is disposed within a portion of space defined by a notional sphere of Brewster radius, R OB . This means that light that is incident on exit surface  401  emanating from the optical interface  425  satisfies the Brewster condition, and is limited to angles of incidence at the exit surface greater than the Brewster angle. Light from the one or more LEEs  460  is guided by the optical coupler  450  via the air gap  440  to the light-entry surface  415  and into the scattering element  420 . The transmission of the light from the air gap  440   into the scattering element  420  may be subject to some reflection depending on angle of incidence due to Fresnel losses but is not subject to total internal reflection as the scattering element  420  is optically denser. Light propagating within the scattering element  420  that impinges on the light-entry surface  415  at angles larger than the critical angle with respect to the interface normal, however, does undergo TIR. 
     A portion of light that enters the scattering element  420  is inelastically scattered by the scattering element  420  and thereby wavelength converted and randomized in its directions of propagation. The other portion is elastically scattered without wavelength conversion as it passes through the scattering element  420  and is thereby also randomized in its directions of propagation. Light may have to undergo multiple elastic scattering events to achieve a predetermined level of randomization in the directions of its propagation. Light that is backscattered or otherwise directed towards the light-entry surface  415  from within the scattering element  420  may be subject to TIR depending on its angle of incidence with respect to the light-entry surface  415 . Like considerations apply for light impinging on the secondary surface  417 . Consequently such light is preferably redirected back into the scattering element  420  and/or the extractor element  410 . 
       FIG.  5    shows another example of ASLV light-emitting device  500  that includes a planar scattering element  520 . The ASLV light-emitting device  500  includes a light-emitting element  530  (e.g., an LEE die) operatively disposed on a support member  590 . The light-emitting element  530  is provided with electrical interconnections for providing electrical power to the light-emitting element  530 . The light-emitting element  530  has a textured surface  531  configured to provide predetermined optical extraction of light from the light-emitting element  530 . A scattering element  520  is operatively associated with the light-emitting element  530  from which it is separated by a low-index medium  540 . The low-index medium  540  may be air or other material that provides a refractive index lower than the refractive index of the scattering element  520 . 
     The width of the scattering element  520  and the distance thereof from the light-emitting element  530  is determined based on the light-emission pattern of the light-emitting element  530  in such a way that the scattering element  520  can capture a predetermined portion of the light emitted by the light-emitting element  530  under operating conditions. As the light-emission pattern of the light-emitting element  530  has a predetermined divergence, the scattering element  520  is wider than the light-emitting element  530 . The divergence depends on the characteristics of the light-emitting element  530  and the properties of the optical boundary between the light-emitting element  530  and the low-index medium  540 . 
     The scattering element  520  is supported by a peripheral enclosure  525  surrounding the light-emitting element  530 . Depending on the embodiment, the peripheral enclosure  525  and the scattering element  520  may be formed of like or different materials. The peripheral enclosure  525  and the scattering element  520  may be integrally or otherwise formed. The peripheral enclosure  525  surrounds the light-emitting element  530  in order to block escape of pump light from the light-emitting element  530 . As such the peripheral enclosure  525  may be configured to convert pump light into converted light and provide mixed light similar in properties to the light provided by the scattering element  520 . The peripheral enclosure  525  may further be configured to provide good thermal contact between the scattering element  520  and the support member  590 . 
     The extractor element  510  is formed from a transparent material with refractive index n and is configured as a rotationally symmetric dome, e.g., a segment of a sphere of radius R1. The scattering element  520  is configured as a rectangular plate. In the example illustrated in  FIG.  5   , the scattering element  520  and the extractor element  510  are configured in accordance with a Brewster condition. As such, the scattering element  520  is contained within a notional sphere of radius R OB  concentric with an exit surface  515  of the dome sphere  510 . The scattering element  520  includes elastic and inelastic scattering. The example LEE is used to provide diffused white light from blue pump light provided by the light-emitting element  530 . 
     It is noted that a portion of the low-index medium that is proximate the light-emitting element  530  may be replaced with encapsulant (e.g., a silicone or organic encapsulant) that is optically denser than the low-index medium and forms a suitably light-transmissive optical interface with the remaining low-index medium. Such a configuration, albeit more complex and possibly resulting in a larger LEE package, may improve the efficacy of light extraction from the light-emitting element  530  into the low-index medium in comparison to the configuration of the example ASLV light-emitting device  500 . 
     While the foregoing embodiments feature planar scattering elements, in general, the shape of the scattering element is not so limited.  FIG.  6    shows an example of ASLV light-emitting device  600  having a convex scattering element  620 . The ASLV light-emitting device  600  further includes an extractor element  630  coupled to the scattering element  620  to form a convex optical interface  625 . The index of refraction n1 of the extractor element  630  is equal to or larger than index of refraction of the scattering element  620 . The extractor element  630  has an exit surface  635  shaped like a dome of radius R1. 
     The convex scattering element  620  is disposed within a portion of space defined by a notional sphere of Brewster radius, R OB  concentric with the exit surface  635 . This means that light that is incident on exit surface  635  emanating from the optical interface  625  satisfies the Brewster condition, and is limited to angles of incidence at the exit surface greater than the Brewster angle. 
     The ASLV light-emitting device  600  further includes an optical coupler  645  configured as a hollow reflector, for example. The optical coupler  645  is filled with a low-index medium, for example air or inert gas. In this configuration, a combination of the hollow reflector of the optical coupler  645  and a surface of the scattering element  620  facing the light-emitting element  610  forms a recovery enclosure  640  for the ASLV light-emitting device  600 . 
     Although, the ASLV light-emitting device  600  has similar structure with the ASLV light-emitting device  400 , the extractor element  630  of the former has higher power than the extractor element  610  of the latter. In this manner, the ASLV light-emitting device  600  has a stronger forward bias (along the +z axis) than the ASLV light-emitting device  400 . 
     In the foregoing embodiments, ASLV light-emitting devices feature recovery enclosures that feature at least one reflective surface. However, in some embodiments, the recovery enclosure can be devoid of reflective surfaces. For example,  FIG.  7    shows an example of a ASLV light-emitting device  700  that has a concave scattering element  720 , and a recovery enclosure  740  encompassed by an extractor  710 . The ASLV light-emitting device  700  has a rotationally symmetric generally spherical configuration and includes an extractor element  710 , a scattering element  720  and a light-emitting device  760  configured to emit blue light under operating conditions. The scattering element  720  includes active and passive scattering centers and is configured to convert a portion of the blue light provided by the light-emitting device  760  to generate white light. The extractor element  710  and the scattering element  720  can be injection molded in a multi-shot process. The ASLV light-emitting device  700  may further include for example a socket for establishing an electromechanical connection to a source of power, drive electronics, electrical connections and cooling elements. 
     The extractor element  710  and the scattering element  720  include materials having refractive indices of about 1.5 to 1.7 or larger, for example. The extractor element  710  and the scattering element  720  are configured as nesting spherical shells. The scattering element  720  includes a cavity formed as a hollow recovery enclosure  740  that is filled with a low-index medium, for example air or inert gas. The scattering element  720  defines an aperture surrounded by walls  717  and substantially abuts sides of the light-emitting device  760  so that substantially all light from the light-emitting device  760  is emitted into the recovery enclosure  740  during operating conditions. 
     Depending on the size of the light-emitting device  760 , the solid angle occupied by the scattering element  720  as subtended from the scattering element  720  itself and viewed through the recovery enclosure  740  may be close to 2π, or otherwise referred to as 2π minus epsilon. Likewise, the solid angle occupied by the scattering element  720  as subtended from a point within the recovery enclosure  740  may be close to 4π, or otherwise referred to as 4π minus epsilon. Like considerations apply to the total cumulative solid angle in embodiments with more than one light-emitting device  760 . Corresponding light-emitting devices may be referred to accordingly. Consequently, the ratio of amounts of light that originate from the scattering element  720  and impinge on the light-emitting device  760  versus those which impinge on the scattering element  720 , can be controlled, to some degree, via geometrical aspects of the ASLV light-emitting device  700 . 
     An exit surface of the extractor element  710  is spherical and has a radius R1.The scattering element  720  is disposed concentric with the extractor element  710  within a portion of space defined by a notional sphere of Brewster radius, R OB . In the example illustrated in  FIG.  7   , an optical interface formed between the scattering element  720  and the extractor element is substantially the Brewster sphere. This means that light that is incident on the exit surface of the extractor element  710  emanating from the scattering element  720  satisfies the Brewster condition, and is limited to angles of incidence at the exit surface greater than the Brewster angle. 
     Light that propagates from the recovery enclosure  740  into the scattering element  720  is subject to some reflection depending on angle of incidence due to Fresnel losses but is not subject to total internal reflection as the scattering element  720  is optically denser than the low-index medium inside the recovery enclosure  740 . Light from inside the scattering element  720  that is directed back at the recovery enclosure  740  and does not undergo TIR, will escape from the scattering element  720  into the recovery enclosure  740 . Short of being absorbed, both types of light will propagate through the recovery enclosure  740  and impinge somewhere else on the scattering element  720  and may be recycled back into the light output by the ASLV light-emitting device  700 , or impinge on the light-emitting device  760  and be likely converted into heat. Depending on the size of the light-emitting device  760  relative to the diameter of the scattering element  720 , the likelihood that back-scattered light may be lost to heat can be relatively small and the optical efficiency of the ASLV light-emitting device  700  can be relatively high. 
     Light that scatters from the scattering element  720  into the extractor element  710  will not undergo TIR at the exit surface as the ASLV light-emitting device  700  satisfies the Brewster condition. Due to Fresnel reflections, only a portion of such light, however, will transmit into an ambient region of the ASLV light-emitting device  700 . The portion that is reflected back will interact with the scattering element  720  and propagate accordingly. 
       FIG.  8    shows an ASLV light-emitting device  800  having a concave scattering element  820  and a recovery enclosure  840  with a protruded base  850 . The ASLV light-emitting device  800  further includes a light-emitting element  860 , an scattering element  820 , and a recovery enclosure  840 . The light-emitting element  860  is configured to emit blue light under operating conditions. The scattering element  820  is at least partially encompassed by the extractor  810 . Additionally, the scattering element  820  includes active and passive scattering centers and is configured to convert a portion of the blue light provided by the light-emitting device  860  to generate white light. The extractor element  810  and the scattering element  820  include materials having refractive indices of about 1.5 to 1.7 or larger, for example. The recovery enclosure  840  is filled with a low-index medium, for example air or inert gas. The ASLV light-emitting device  800  is coupled via the base  850  to a socket for establishing an electromechanical connection to a source of power, drive electronics, electrical connections and cooling elements. 
     The ASLV light-emitting device  800  has a rotationally symmetric (around the z-axis) configuration of a spherical segment. The extractor element  810  and the scattering element  820  are configured as nesting shells shaped as spherical segments. Further, the extractor element  810  and the scattering element  820  can be injection molded in a multi-shot process. The extractor element  810  includes a flat surface  817  of annular shape. In some implementations, the annular surface  817  includes a reflector to reflect scattered light from the scattering element  820  to the exit surface of the extractor element  810 . In other implementations, the annular surface  817  is uncoated and scattered light from the scattering element  820  can internally reflect at the annular surface  817  toward the exit surface of the extractor element  810 , or transmit through the exit surface of the extractor element  810  to the ambient. The light output by the ASLV light-emitting device  800  through the annular surface  817  would be output as a backward portion of an intensity distribution. 
     The light-emitting element  860  is mounted on a top surface of the base  850 . The scattering element  820  defines an aperture aligned with the inner diameter of the annular surface  817  to accommodate the base  850  so that substantially all light from the light-emitting element  860  is emitted into the recovery enclosure  840  during operating conditions. The base  850  protrudes inside the recovery enclosure  840  and is shaped as a truncated cone or pyramid. Side surface of the base  850  is arranged to face the recovery enclosure  840  and has a reflecting coating configured to reflect yellow and blue light back-scattered from the scattering element  820 . In this manner, the recovery enclosure  840  is formed by a combination of a light-entry surface of the scattering element  820  and the reflecting side surface of the protruded base  850 . 
     Light that propagates from the recovery enclosure  840  into the scattering element  820  is subject to some reflection depending on angle of incidence due to Fresnel losses but is not subject to total internal reflection as the scattering element  820  is optically denser than the low-index medium inside the recovery enclosure  840 . Light from inside the scattering element  820  that is directed back at the recovery enclosure  840  and does not undergo TIR, will escape from the scattering element  820  into the recovery enclosure  840 . Short of being absorbed, both types of light will propagate through the recovery enclosure  840  and either (i) impinge somewhere else on the scattering element  820  and may be recycled back into the light output by the ASLV light-emitting device  800 , or (ii) undergo a single reflection on the side surface of the base  850  before re-entering the scattering element  820 , or (iii) impinge on the light-emitting device  860  and be likely converted into heat. Depending on the size of the light-emitting device  860  relative to the diameter of the scattering element  820 , the likelihood that back-scattered light may be lost to heat can be relatively small and the optical efficiency of the ASLV light-emitting device  800  can be relatively high. 
     An exit surface of the extractor element  810  is spherical and has a radius R1.The scattering element  820  is disposed concentric with the extractor element  810  within a portion of space defined by a notional sphere of Brewster radius, R OB . In the example illustrated in  FIG.  8   , an optical interface formed between the scattering element  820  and the extractor element  810  is substantially the Brewster sphere. This means that light that is incident on the exit surface of the extractor element  810  emanating from the scattering element  820  satisfies the Brewster condition, and is limited to angles of incidence at the exit surface greater than the Brewster angle. Light that scatters from the scattering element  820  into the extractor element  810  will not undergo TIR at the exit surface as the ASLV light-emitting device  800  satisfies the Brewster condition. Due to Fresnel reflections, only a portion of such light, however, will transmit into an ambient region of the ASLV light-emitting device  800 . The portion that is reflected back will interact with the scattering element  820  and propagate accordingly. 
     While the foregoing embodiments of ASLV light-emitting devices each include a single light-emitting element, embodiments can, in general, include more than one light-emitting element. Referring to  FIG.  9 A , an ASLV light-emitting device  900  includes first and second light-emitting elements  910 . ASLV light-emitting device  900  further includes a scattering element  920  (also referred to as a first optical element), an extractor element  930  (also referred to as a second optical element), and a recovery enclosure  940 . 
     The first light-emitting element is configured to provide light having a first spectral power distribution during operation, and the second light-emitting element is configured to provide light having a second spectral power distribution different from the first spectral power distribution during operation. Spectral power distribution of light emitted by the first light-emitting element (also referred to as pump light) can be blue, and spectral power distribution of light emitted by the second light-emitting element can be red, for instance. The scattering element  920  has a first surface (also referred to as a light-entry surface) spaced apart from the first and second light-emitting elements  910  and is positioned to receive the light from the first and second light-emitting elements  910 . The scattering element  920  includes inelastic scattering centers arranged to convert the blue light from the first light-emitting element into converted light, e.g., yellow light, that is substantially isotropically scattered, and elastic scattering centers arranged to substantially isotropically scatter the light from the second light-emitting element. In this manner, the scattering element  920  provides mixed light including the red scattered light from the second light-emitting element and the yellow converted light, such that the mixed light has a mixed spectral power distribution (that includes yellow and red). In some implementations, the elastic scattering centers of the scattering element  920  further substantially isotropically scatter a portion of the light from the first light-emitting element. In such case, the scattering element  920  provides mixed light including the red scattered light from the second light-emitting element, blue scattered light from the first light-emitting element, and the yellow converted light, such that the mixed light has a mixed spectral power distribution (that includes blue, yellow and red). 
       FIG.  9 B  shows an emission spectrum  911  for a blue LED and another emission spectrum  914  for a red LED. The blue and red LEDs can be used as the first and second light-emitting elements, respectively, in the ASLV light-emitting device  900 . Further,  FIG.  9 B  shows an absorption spectrum  912  and an emission spectrum  913  of the inelastic scattering centers. The emission spectrum  913  of the inelastic scattering centers corresponds to the spectrum of the converted light. Spectral power distribution of the scattered red light or blue light is the same as the spectral power distribution of the second light-emitting element or the first light-emitting element, respectively (corresponding to the spectra  914  or  911 , respectively.) Moreover, the absorption spectrum of the scattering centers  912  overlaps the spectrum of the light emitted by the first light-emitting element  910 . Spectral power distribution of the converted light is different from the pump light. For instance, the converted light will have a spectrum  913  that is shifted (e.g., Stokes shifted) to longer wavelengths than the pump light spectrum  911 . For example, where the pump light is blue, e.g., corresponding to the spectrum  911 , the converted light can be characterized by an overall yellow/amber color, e.g., corresponding to the spectrum  913 . Furthermore,  FIG.  9 B  shows a spectrum of the mixed light  915  (represented with a dashed-line) corresponding to a case when the blue pump light is fully converted to yellow light. In this case, the spectrum of the mixed light  915  is a combination of the spectrum  914  of the elastically scattered red light and the spectrum  913  of the converted yellow light. Additionally,  FIG.  9 B  shows another spectrum of the mixed light  917  (represented with a dotted-line.) The spectrum of the mixed light  917  is a combination of the spectra  911  and  914  of the elastically scattered blue and red light and the spectrum  913  of the converted yellow light. 
     Referring again to  FIG.  9 A , the extractor element  930  is formed from a transparent material having an exit surface. The exit surface is generally a curved, transparent surface. In other words, changes in the mixed light passing through the exit surface can generally be described by Snell’s law of refraction, as opposed to, for example, an opaque or diffuse surface where scattering of transmitted light occurs. The extractor element  930  is in contact with the scattering element  920 , such that there is an optical interface between the scattering and extractor elements at the place of contact, and the optical interface is opposite the first surface of the scattering element  920 . Moreover, the extractor element  930  is arranged so that a portion of the mixed light enters the extractor element  930  through the optical interface. 
     Further, the ASLV light-emitting device  900  includes a medium adjacent the first surface of the scattering element  920  having a refractive index n0, and the scattering element  920  includes a material having a first refractive index n1, where n0 &lt; n1. The transparent material has a refractive index, n2, where n0 &lt; n2. Furthermore, the recovery enclosure  940  encloses the medium adjacent the first surface of the scattering element  920 . The recovery enclosure  940  is arranged and configured to recover a portion of the mixed light that propagates through the first surface into the medium. In some implementations, the exit surface of the extractor element  930  is a transparent surface that is shaped such that an angle of incidence on the exit surface of the mixed light provided by the scattering element  920  that directly impinges on the exit surface is less than the critical angle for total internal reflection. In this case, the extractor element  930  is said to satisfy the Weierstrass condition, as described above in connection with  FIG.  1 A . In some implementations, the exit surface of the extractor element  930  is shaped such that an angle of incidence on the exit surface of the mixed light provided by the scattering element  920  that directly impinges on the exit surface is less than the Brewster angle. In this case, the extractor element  930  is said to satisfy the Brewster condition, as described above in connection with  FIG.  1 A . Additionally, the ASLV light-emitting device  900  outputs a predetermined portion of the mixed light through the exit surface into the ambient environment. As described above, examples of spectra  915  and  917  of the light output by the ASLV light-emitting device  900  are shown in  FIG.  9 B . 
     While the foregoing embodiments of ASLV light-emitting devices include multiple light-emitting elements in combination with a scattering element that contains elastic and inelastic scattering centers, embodiments can, in general, include multiple light-emitting elements in combination with a scattering element that contains only elastic scattering centers.  FIG.  10 A  shows a diagram of an example of yet another ASLV light-emitting device  1000  that includes first and second light-emitting elements  1010 , a scattering element  1020  (also referred to as a first optical element), an extractor element  1030  (also referred to as a second optical element), and a recovery enclosure  1040 . 
     The first light-emitting element is configured to provide light having a first spectral power distribution during operation, and the second light-emitting element is configured to provide light having a second spectral power distribution different from the first spectral power distribution during operation. Spectral power distribution of light emitted by the first light-emitting element can be blue, and spectral power distribution of light emitted by the second light-emitting element can be red, for instance. The scattering element  1020  has a first surface (also referred to as a light-entry surface) spaced apart from the first and second light-emitting elements  1010  and positioned to receive the light from the first and second light-emitting elements  1010 . The scattering element  1020  includes elastic scattering centers arranged to substantially isotropically scatter the light from the first and second light-emitting elements  1010  and provide mixed light including blue light from the first light-emitting element and red light from the second light-emitting element, such that the mixed light has a mixed spectral power distribution (that includes blue and red.) In some implementations, the ASLV light-emitting device  1000  includes a third and fourth light-emitting elements configured to provide light respectively having third and fourth spectral power distributions during operation. For example, the third spectral power distribution is green, and the fourth spectral power distribution is yellow. In this case, the elastic scattering centers of the scattering element further substantially isotropically scatter the light from the third and fourth light-emitting elements. In such case, the scattering element  1020  provides mixed light including the red scattered light from the second light-emitting element, blue scattered light from the first light-emitting element, green scattered light from the third light-emitting element, and yellow scattered light from the fourth light-emitting element, such that the mixed light has another mixed spectral power distribution (that includes blue, green, yellow and red). 
       FIG.  10 B  shows an emission spectrum  1011  for a blue LED and another emission spectrum  1014  for a red LED. The blue and red LEDs can be used as the first and second light-emitting elements, respectively, in the ASLV light-emitting device  1000 . Further,  FIG.  9 B  shows a spectrum of the mixed light  1015  (represented with a dashed-line) corresponding to a case when the ASLV light-emitting device includes blue and red LEDs. In this case, the spectrum of the mixed light  1015  is a combination of the spectra  1011  and  1014  of the elastically scattered blue and red light. Additionally,  FIG.  10 B  shows an emission spectrum  1012  for a green LED and another emission spectrum  1013  for a yellow LED. The green and yellow LEDs can be used as the third and fourth light-emitting elements, respectively, along with the blue and red LEDs in the ASLV light-emitting device  1000 . Furthermore,  FIG.  10 B  shows another spectrum of the mixed light  1017  (represented with a dotted-line) corresponding to the case when the light-emitting device includes blue, green, yellow and red LEDs. In this case, the spectrum of the mixed light  1017  is a combination of the spectra  1011 ,  1012 ,  1013  and  1014  of the elastically scattered blue, green, yellow and red light. 
     Returning to  FIG.  10 A , the extractor element  1030  is formed from a transparent material having an exit surface. The exit surface is generally a curved, transparent surface. In other words, changes in the mixed light passing through the exit surface can generally be described by Snell’s law of refraction, as opposed to, for example, an opaque or diffuse surface where scattering of transmitted light occurs. The extractor element  1030  is in contact with the scattering element  1020 , such that there is an optical interface between the scattering and extractor elements at the place of contact, and the optical interface is opposite the first surface of the scattering element. Moreover, the extractor element  1030  is arranged so that a portion of the mixed light enters the extractor element  1030  through the optical interface. 
     Further, the ASLV light-emitting device  1000  includes a medium adjacent the first surface of the scattering element  1020  having a refractive index n0, and the scattering element includes a material having a first refractive index n1, where n0 &lt; n1. The transparent material has a refractive index n2, where n0 &lt; n2. Furthermore, the recovery enclosure  1040  encloses the medium adjacent the first surface of the scattering element  1020 . The recovery enclosure  1040  is arranged and configured to recover a portion of the mixed light that propagates through the first surface into the medium. In some implementations, the exit surface is a transparent surface that is shaped such that an angle of incidence on the exit surface of the mixed light provided by the scattering element  1020  that directly impinges on the exit surface of the extractor element  1030  is less than the critical angle for total internal reflection. In this case, the extractor element  1030  is said to satisfy the Weierstrass condition, as described above in connection with  FIG.  1 A . In some implementations, the exit surface is shaped such that an angle of incidence on the exit surface of the mixed light provided by the scattering element  1020  that directly impinges on the exit surface of the extractor element  1030  is less than the Brewster angle. In this case, the extractor element  1030  is said to satisfy the Brewster condition, as described above in connection with  FIG.  1 A . Additionally, the ASLV light-emitting device  1000  outputs mixed light through the exit surface into the ambient environment. As described above, examples of spectra  1015  and  1017  of the light output by the ASLV light-emitting device  1000  are shown in  FIG.  10 B . 
       FIG.  11    shows such an ASLV light-emitting device  1100  having multiple light-emitting devices  1160 . In addition, the ASLV light-emitting device  1100  includes a concave scattering element  1120 , and a recovery enclosure  1140  with a recessed base. The ASLV light-emitting device  1100  has a generally spherical configuration. The light-emitting devices  1160  include pump (e.g., blue) LED packages and red LED packages operatively disposed on a substrate with a recess. The surface  1150  adjacent the LED packages is formed as a recessed dish and is specular reflective to effectively direct light impinging thereon back into the recovery enclosure  1140 . This surface  1150  may also be diffuse or mixed diffuse-specular reflective. The LED packages are disposed in the recess of the substrate. The shape of the substrate can be varied to affect beam shaping. 
     The scattering element  1120  includes active and passive scattering centers. The active scattering centers are configured to convert (inelastically scatter) the light provided by the light-emitting device  1160  to yellow/amber light, and the passive scattering centers are configured to elastically scatter the pump light and the red light. In this manner, the scattering element  1120  mixes the converted yellow/amber light with the scattered blue and red light to generate white light. The extractor element  1110  and the scattering element  1120  may be formed in a multi-shot molding process. The ASLV light-emitting device  1100  further includes diffuse reflective layers  1117  and a passive cooler. The ASLV light-emitting device  1100  may further include for example one or more sockets for establishing an electromechanical connection to a source of power, drive electronics, electrical connections and one or more heat sinks. The ASLV light-emitting device  1100  may be configured as a replacement for light bulbs of various sizes and configurations. 
     In this example, the extractor element  1110  and the scattering element  1120  are configured as nesting spherical shells. The scattering element  1120  forms a hollow, recovery enclosure  1140  that is filled with a low-index medium, for example air or inert gas. The extractor element  1110  defines an aperture bordered by the diffuse reflective layers  1117 . The scattering element  1120  substantially abuts the sides of the light-emitting device  1160  so that substantially all light from the light-emitting device is emitted into the recovery enclosure  1140  during operating conditions. The section of the spherical shells, that is the particular angular portion of an otherwise full spherical shell, can be varied to affect beam shaping and mixing of light provided by the ASLV light-emitting device  1100 . The inclination of the surfaces of the extractor element  1110  that are coupled with the reflective layers  1117  and/or the recess in the substrate of the light-emitting device  1160  may be different than illustrated. Such surfaces may also be non-planar to reflect light in a predetermined manner different from planar surfaces to affect efficiency and beam shaping. 
     In this example, the scattering element  1120  is disposed concentric with the extractor element  1110  within a portion of space defined by a notional sphere of radius R/n wherein R is the radius of the exit surface of the extractor element  1110 . In this example, the scattering element  1120  has the shape of a spherical shell with an outer radius R/n. It is noted that the scattering element  1120  may have an outer radius that is smaller or larger than R/n. It is also noted that all or portions of the scattering element  1120  may be disposed outside the notional concentric sphere of R/n. Generally, the more the scattering element  1120  extends into the space outside of the notional concentric sphere of radius R/n, the more TIR may occur at the exit surface of the extractor element  1110 . It is further noted, that the scattering element  1120  may have a non-spherical shape, for example a body with regular or irregular polygonal facets. It is also noted that the extractor element of other examples may have a generally curved but non-spherical and non-cylindrical exit surface, as described below in this specification. 
       FIG.  12    shows another example of an ASLV light-emitting device  1200  having multiple light-emitting devices  1260  and a concave scattering element  1220 . In this example, the ASLV light-emitting device  1200  has an elongate, e.g., along the y-axis perpendicular to the page, generally cylindrical configuration and includes an extractor element  1210  in addition to the scattering element  1220  and the multiple light-emitting devices  1260 . The light-emitting devices  1260  include blue and red LED packages operatively disposed on a generally planar substrate. The surface of the substrate  1245  between the LED packages can have a specular reflective, a diffuse reflective, a mixed specular and diffuse reflective, or other reflective coating to effectively direct light impinging thereon back into the recovery enclosure  1240 . The scattering element  1220  includes active and passive scattering centers and is configured to convert the light provided by the light-emitting device  1260  to generate white light as described above in connection with  FIGS.  9 - 11   . The extractor element  1210  and the scattering element  1220  may be formed by extrusion. The ASLV light-emitting device  1200  further includes reflective layers  1217  and a passive cooler  1250 . The ASLV light-emitting device  1200  may further include for example one or more sockets for establishing an electromechanical connection to a source of power, drive electronics and electrical connections. The ASLV light-emitting device  1200  may be configured as a replacement for a fluorescent tube or a combination of a fluorescent tube and troffer. 
     The extractor element  1210  and the scattering element  1220  are configured as nesting cylindrical shells. The scattering element  1220  forms a hollow, recovery enclosure  1240  that is filled with a low-index medium, for example air or inert gas. The extractor element  1210  defines an aperture bordered by reflective layers  1217 . The scattering element  1220  substantially abuts the sides of the light-emitting devices  1260  so that substantially all light from the light-emitting devices is emitted into the recovery enclosure  1240  during operating conditions. The section of the cylindrical shells, that is the particular angular portion of an otherwise full cylindrical tube, can be varied to affect beam shaping and mixing of light provided by the ASLV light-emitting device  1200 . The inclination of the surfaces of the extractor element  1210  that are coupled with the reflective layers  1217  may be different than illustrated. Such surfaces may also be non-planar to reflect light in a predetermined manner different from planar surfaces. As such the reflective layers  1217  may affect efficiency and further affect beam shaping. 
     The scattering element  1220  is disposed concentric with the extractor element  1210  within a portion of space defined by a notional cylinder of radius R/n wherein R is the radius of the exit surface of the extractor element  1210 . In this example, the scattering element  1220  has the shape of a cylindrical shell with an outer radius R/n. It is noted that the scattering element may have an outer radius that is smaller or larger than R/n. It is also noted that all or portions of the scattering element may be disposed outside the notional concentric cylinder of R/n. Generally, the more the scattering element extends into the space outside of the notional concentric cylinder of radius R/n, the more TIR may occur at the exit surface of the extractor element  1210 . It is further noted, that the scattering element  1220  may have a non-cylindrical cross section, for example a regular or irregular polygonal section. 
     In general, embodiments of ASLV light-emitting devices can include components in addition to the light-emitting element(s), scattering element, extractor element and base structure. For example,  FIG.  13    shows a schematic diagram of an example of an ASLV light-emitting device  1300  that includes an intra-system source feedback unit  1350 , a light-emitting element  1310 , a scattering element  1320  (also referred to as a first optical element), an extractor element  1330  (also referred to as a second optical element), and a recovery enclosure  1340 . 
     The light-emitting element  1310  is configured to produce and emit light during operation. In a first case, the light-emitting element  1330  includes one or more blue LEDs. In a second case, the light-emitting element  1310  includes two or more different ones of red, green, blue or yellow LEDs. The scattering element  1320  has a first surface (also referred to as a light-entry surface) spaced apart from the light-emitting element  1310  and positioned to receive the light from the light-emitting element  1310 . The scattering element  1320  includes scattering centers arranged to substantially isotropically scatter the light from the light-emitting element  1310  and to provide scattered light. The scattered light includes elastically scattered blue, green or red light and inelastically scattered blue light in the form of converted yellow light. Spectral power distribution of the elastically scattered light is the same as the spectral power distribution of the blue, green or red light, and spectral power distribution of the inelastically scattered light can be yellow, for instance. Spectra  111 ,  911 ,  1011 ,  1012 ,  1013 ,  1014  of the elastically scattered blue, green, yellow and red light and spectra  113 ,  913  of the inelastically scattered pump blue in the form of yellow light are shown in  FIGS.  1 B,  9 B and  10 B  along with corresponding spectra the scattered light. 
     Referring again to  FIG.  13   , the extractor element  1330  is formed from a transparent material having an exit surface. The exit surface is generally a curved, transparent surface. In other words, changes in the scattered light passing through the exit surface can generally be described by Snell’s law of refraction, as opposed to, for example, an opaque or diffuse surface where further scattering of transmitted light occurs. The extractor element  1330  is in contact with the scattering element  1320 , such that there is an optical interface between the scattering and extractor elements at the place of contact, and the optical interface is opposite the first surface of the scattering element. Moreover, the extractor element  1330  is arranged so that light scattered through the optical interface enters the extractor element  1330 . 
     Further, the ASLV light-emitting device  1300  includes a medium adjacent the first surface of the scattering element having a refractive index n0, and the scattering element  1320  includes a material having a first refractive index n1, where n0 &lt; n1. The transparent material has a refractive index n2, where n0 &lt; n2. In some implementations, the exit surface is a transparent surface that is shaped such that an angle of incidence on the exit surface of the scattered light that directly impinges on the exit surface is less than the critical angle for total internal reflection. In this case, the extractor element  1330  is said to satisfy the Weierstrass condition, as described above in connection with  FIG.  1 A . In some implementations, the exit surface is a transparent surface that is shaped such that an angle of incidence on the exit surface of the scattered light that directly impinges on the exit surface is less than the Brewster angle. In this case, the extractor element  1330  is said to satisfy the Brewster condition, as described above in connection with  FIG.  1 A . Furthermore, the recovery enclosure  1340  encloses the medium adjacent the first surface of the scattering element. The recovery enclosure  1340  is arranged and configured to recover a portion of the scattered light that propagates through the first surface into the medium. Additionally, the ASLV light-emitting device  1300  outputs scattered light through the exit surface into the ambient environment. As described above, the light output by the ASLV light-emitting device  1300  has a spectral power distribution corresponding to the spectrum  115  shown in  FIG.  1 B . 
     The intra-system source feedback unit  1350  includes a sensor arranged to receive a fraction of the portion of the scattered light prior to being output through the exit surface. The sensor is configured to provide a sensor signal based on the fraction of the portion of the scattered light. Moreover the sensor includes a color detector, an intensity detector, or a combination of both. For the first case when the light-emitting element  1310  includes one or more blue LEDs, the sensor is an intensity sensor and the sensor signal indicates intensity values corresponding to the scattered blue light and converted yellow light. For the second case when the light-emitting element  1310  includes two or more different ones of blue, green, yellow or red LEDs, the sensor is a color sensor and the sensor signal indicates color values corresponding to the mixed light. In the latter case, the color sensor may also be configured to provide an intensity signal to indicate intensity values of the mixed light. 
     In addition, the intra-system source feedback unit  1350  includes a control circuit in communication with the sensor and configured to adjust power applied to the light-emitting element  1310  in response to the sensor signal. In some implementations, the fraction of the portion of the scattered light received by the sensor corresponds to light reflected in the extractor element  1330  at the exit surface. For instance, the sensor can be arranged such that the light reflected in the extractor element  1330  at the exit surface received by the sensor originates from a large portion of the optical interface. 
     Turning now to specific embodiments of devices with intra-system feedback,  FIG.  14    shows an ASLV light-emitting device  1400  including an example configuration of intra-device feedback. The ASLV light-emitting device  1400  includes an extractor element  1410 , a scattering element  1420 , an optical coupler  1450  and one or more detectors  1490 . The ASLV light-emitting device  1400  further includes two or more of red, green, blue or yellow LEEs  1460 . The scattering element  1420  includes passive scattering centers only. 
     The optical coupler  1450  is configured to redirect light from the LEEs  1460  to a predetermined angular range around the z-axis in order to provide suitable incidence thereof at the scattering element  1420 . The optical coupler  1450  is further configured as a recovery enclosure of the ASLV light-emitting device  1400  to redirect predetermined amounts of light received from the scattering element  1420  back to the scattering element  1420 . The optical coupler  1450  has a hollow configuration with a specular reflective inside  1440 . The optical coupler has one or more diffuse reflective shoulders  1453 . 
     The ASLV light-emitting device  1400  further includes one or more reflectors  1480 . Each reflector  1480  is configured to redirect a portion of light that is emitted sideways from the scattering element  1420  towards corresponding ones of the one or more detectors  1490 . The optical coupler  1450  has an opening or transparent section  1451  associated with each of the one or more reflectors  1480  to allow some light from the extractor element  1410  and/or the scattering element  1420  to pass to the detectors  1490 . 
     The one or more detectors  1490  may be configured as RGB detectors. The extractor element  1410  may be configured as a Weierstrass sphere, cylinder or torus, for example. The LEEs  1460  are grouped by color and operatively interconnected with a suitable drive system (e.g., like the one described below in connection with  FIG.  17   .) The operative interconnection is configured to allow independent control of the LEEs  1460  by color. Each group of LEEs can include one or more LEEs  1460  of like color. The LEEs per groups may be interconnected in serial, parallel and/or both serial and parallel manners. The ASLV light-emitting device  1400  may have a rotationally symmetrical, elongate, toroidal or other configuration, for example. 
     As described herein, a suitably configured example ASLV light-emitting device can provide intra-lamp color mixing that is suitable to enable feedback control of independently addressable multi-color LEEs based on intra-lamp feedback. Each LEE provides a radiation pattern. Different color LEEs can have substantially different radiation patterns. Furthermore, different LEEs of like color also can have substantially different radiation patterns. Other complications can result from misalignments between the optical axes of different LEEs, which may be caused by the assembly process, inherent properties of the LEEs or other aspects, for example. Without the scattering element  1420 , the resulting far-field variations would be difficult to specify and possibly result in undesired color variations as the root cause of this goes back to the difficulty of guaranteeing an identical angular distribution of every spectral component of white light. On the other hand, a properly configured ASLV light-emitting device  1400  can provide a color-independent angular intensity distribution on the downstream side of the scattering element  1420 . 
     In this example, the detectors  1490  are disposed to sample scattered light downstream of the optical path after the scattering element  1420 . The illustrated detector  1490  is positioned so it can detect portions of light that is emitted sideways from the edge of the scattering element  1420 . Other detectors, if any, may be configured otherwise. 
     Such intra-lamp color sampling represents a valid color mix of the color distribution in the far field. A suitably configured scattering element  1420  can provide very efficient color mixing without the losses associated with scattering further downstream in the optical path. Intra-lamp sampling and feedback loops (e.g., like the ones described in connection with  FIG.  17   ) avoid the wiring or wireless communications cost associated with far-field sampling. This may remove a significant impediment of realizing cost effective digital color tuning in broad segments of the general lighting market, for example. 
       FIG.  15    shows an ASLV light-emitting device  1500  including another example configuration of intra-device feedback. The ASLV light-emitting device  1500  includes an optical element  1510 , a scattering element  1520 , an optical coupler  1550  and a detector  1590 . The ASLV light-emitting device  1500  further includes one or more blue pumps and one or more red LEDs that form a light emitting element  1560 . The scattering element  1520  is configured to scatter and to convert blue pump light into white light and to scatter red light without conversion. The scattering element  1520  includes active and passive scattering centers. The optical coupler  1550  is configured to collimate light from the LEE  1560  to a predetermined degree in order to provide suitable incidence thereof at the scattering element  1520 . 
     The optical coupler  1550  optionally may be configured to provide good redirection of light from the scattering element  1520  back to the scattering element  1520 . The optical coupler  1550  has a hollow configuration with a specular reflective inside  1540  and, hence, the optical coupler  1550  forms, in combination with the scattering element  1520 , a recovery enclosure for the ASLV light-emitting device  1500 . The ASLV light-emitting device  1500  further includes a reflector  1580  configured to reflect light from the extractor element  1510  and the scattering element  1520  (back) into the extractor element  1510 . The reflector  1580  has an opening or transparent section  1581  associated with an opening or transparent section  1551  in the optical coupler  1550 . The openings or transparent sections  1551  and  1581  allow some light from the optical element  1510  to pass to the detectors  1590 . 
     In this example, one detector  1590  is provided and is configured as a CCT (correlated color temperature) detector to provide an indication of the CCT of the light in the extractor element  1510 . The extractor element  1510  is configured as a Weierstrass sphere. The LEEs  1560  are grouped by color and operatively interconnected with a suitable drive system. The operative interconnection is configured to allow independent control of the LEEs  1560  by color. Each group of LEEs can include one or more LEEs  1560  of like color. The LEEs per groups may be interconnected in serial, parallel and/or both serial and parallel manners. The ASLV light-emitting device  1500  may have a rotationally symmetrical configuration. The drive system may be configured to allow feedback control of the CCT and flux output of the ASLV light-emitting device  1500 . 
     The detector  1590  is disposed to sample scattered light downstream of the optical path after the scattering element  1520 . The detector  1590  is positioned so it can detect portions of light that is reflected back into the optical element  1510  by Fresnel reflection at the outer surface of the optical element  1510 . 
     According to another example the blue pump LEEs may be replaced with white LED packages. In such an example, the scattering element may be configured to merely scatter light. 
       FIG.  16    shows an ASLV light-emitting device  1600  including yet another configuration of intra-device feedback. The ASLV light-emitting device  1600  has a generally toroidal configuration and includes an extractor element  1610 , a scattering element  1620  and a light-emitting device  1660 . The light-emitting device  1660  includes two or more of red, green, blue and yellow LED packages operatively disposed on a substrate. The surface of the substrate between the LED packages has a specular reflective coating to effectively direct light impinging thereon back into a recovery enclosure  1640 . The scattering element  1620   includes passive scattering centers and is configured to mix the light provided by the light-emitting device  1660  to generate white light. The extractor element  1610  and the scattering element  1620  may be formed by extrusion. The ASLV light-emitting device  1600  further includes a detector  1690  and reflective layers  1617 . The ASLV light-emitting device  1600  may further include for example one or more sockets for establishing an electromechanical connection to a source of power, drive electronics, electrical connections and cooling elements. 
     The extractor element  1610  and the scattering element  1620  are configured as nesting cylindrical shells. The scattering element  1620  forms a hollow, recovery enclosure  1640  that is filled with a low-index medium, for example air or inert gas. The extractor element  1610  defines an aperture bordered by reflective layers  1617 . The scattering element  1620  substantially abuts the sides of the light-emitting device  1660  so that substantially all light from the light-emitting device  1660  is emitted into the recovery enclosure  1640  during operating conditions. The section of the cylindrical shells, that is the particular angular portion of an otherwise full cylindrical tube, can be varied to affect beam shaping and mixing of light provided by the ASLV light-emitting device  1600 . The inclination of the surfaces of the extractor element  1610  that are coupled with the reflective layers  1617  may be different than illustrated. Such surfaces may also be non-planar to reflect light in a predetermined manner different from planar surfaces. 
     The scattering element  1620  is disposed concentric with the extractor element  1610  within a portion of space defined by a notional cylinder of radius R/n wherein R is the radius of the exit surface of the extractor element  1610 . This configuration may be referred to as a cylindrical Weierstrass geometry and avoids TIR at the exit surface for all light that directly propagates in a plane perpendicular to the cylinder axis thereto from the optical junction the scattering element  1620 . This geometry also avoids TIR for light that propagates in planes that are oblique to the plane perpendicular to the cylinder axis so long the critical angle for TIR is not exceeded. 
     The detector  1690  is configured as a CCT detector to provide an indication of the CCT of the light in the extractor element  1610 . The detector  1690  is disposed to sample scattered light downstream of the optical path after the scattering element  1620 . The LED packages of the light-emitting device  1660  are grouped by color and operatively interconnected with a suitable drive system. The operative interconnection is configured to allow independent control of the LED packages of the light-emitting device  1660  by color. A group of LED packages can include one or more LED packages of like color. The LED packages in a group may be interconnected in serial, parallel and/or both serial and parallel manners. The drive system may be configured to allow feedback control of the CCT and flux output of the ASLV light-emitting device  1600 . 
       FIG.  17    shows a schematic diagram of a feedback circuit  1700  used to provide intra-system source feedback in an ASLV light-emitting device. In this example, the feedback circuit  1700  includes a photonic sensing unit  1720  and a controller  1730 . 
     The photonic sensing unit  1720  is placed downstream from a scattering element of the ASLV light-emitting device to sense scattered light propagating within an extractor element of the ASLV light-emitting device. In some implementations, the photonic sensing unit  1720  can include a color detector, an intensity detector, or a combination of both. In some implementations, one or more of the detectors can be arranged such that mostly scattered light that is Fresnel-reflected at an exit interface of the extractor element is being sensed. Moreover, the one or more detectors can be arranged such that the scattered light reflected by the exit surface of the extractor element and received by the sensor originates from a large portion of an optical interface between the scattering element and the extractor element. 
     The controller unit  1730  can be implemented as hardware, software or a combination of both. For example, the controller unit  1730  can be implemented as a software driver executed by a specialized or general purpose chip. The controller unit  1730  parses sensing signals received from the photonic sensing unit  1720 . Parsed signal values are compared by the controller unit  1730  to reference color values or reference intensity values, referred to as reference values. The controller unit  1730  accesses such reference values in one or more lookup tables, for instance. For example, the controller unit  1730  selectively transmits adjustment signals to a power driver to adjust relative power values for a combination of different color light-emitting elements  1710 , in response to sensing that chromaticity of the scattered light propagating in the extractor element has changed. As another example, the controller unit  1730  selectively transmits adjustment signals to the power driver to adjust power values for one or more light-emitting elements  1710 , in response to sensing that the intensity of the scattered light propagating in the extractor element has changed. 
     Optionally, the feedback circuit  1700  can include a non-photonic propert(y/ies) sensing unit  1740 . Examples of non-photonic properties sensed by this unit are temperature, voltage drop, etc. In such implementations, the controller unit  1730  parses the non-photonic sensing signals received from the non-photonic propert(y/ies) sensing unit  1740  in combination with the photonic sensing signals received from the photonic sensing unit  1720 . Values of the parsed combination of photonic and non-photonic sensing signals are used by the controller unit  1730  to transmit adjustment signals to the driver that drives the LEEs  1710 . 
     As described above in this specification, the shape of the scattering element can vary and examples of scattering elements having non-planar and non-spherical or cylindrical shapes are described above. In general, the shape of the scattering element can be selected to provide specific optical characteristics of the ASLV light-emitting device. For example,  FIG.  18    shows a schematic diagram of an example of an ASLV light-emitting device  1800  that includes a light-emitting element  1810 , a scattering element  1820  (also referred to as a first optical element), an extractor element  1830  (also referred to as a second optical element), and a recovery enclosure  1840 . 
     The light-emitting element  1810  is configured to produce and emit light during operation. A spectral power distribution of light emitted by the light-emitting element  1810  (also referred to as pump light) can be blue, for instance. The spectral power distribution for visible light is referred to as chromaticity. The scattering element  1820  has a first surface (also referred to as a light-entry surface) spaced apart from the light-emitting element and positioned to receive the light from the light-emitting element  1810 . The scattering element  1820  includes scattering centers arranged to substantially isotropically scatter the light from the light-emitting element and to provide scattered light. The scattered light includes elastically scattered pump light and inelastically scattered pump light. Spectral power distribution of the elastically scattered light is the same as the spectral power distribution of the pump light, and spectral power distribution of the inelastically scattered light can be yellow, for instance. A spectrum  111  of the elastically scattered pump light and a spectrum  113  of the inelastically scattered pump light are shown in  FIG.  1 B  along with a spectrum  115  of the scattered light. 
     Referring again to  FIG.  18   , the extractor element  1830  is formed from a transparent material having an exit surface. The exit surface is generally a curved, transparent surface. In other words, changes in the scattered light passing through the exit surface can generally be described by Snell’s law of refraction, as opposed to, for example, an opaque or diffuse surface where further scattering of transmitted light occurs. The extractor element  1830  is in contact with the scattering element  1820 , such that there is an optical interface between the scattering and extractor elements at the place of contact, and the optical interface is opposite the first surface of the scattering element. Moreover, the extractor element  1830  is arranged so that light scattered through the optical interface enters the extractor element  1830 . 
     Further, the ASLV light-emitting device  1800  includes a medium adjacent the first surface of the scattering element having a refractive index n0, and the scattering element  1820  includes a material having a first refractive index n1, where n0 &lt; n1. The transparent material has a refractive index n2, where n0 &lt; n2. In some implementations, the exit surface is a transparent surface that is shaped such that an angle of incidence on the exit surface of the scattered light that directly impinges on the exit surface is less than the critical angle for total internal reflection. In this case, the extractor element  1830  is said to satisfy the Weierstrass condition, as described above in connection with  FIG.  1 A . In some implementations, the exit surface is a transparent surface that is shaped such that an angle of incidence on the exit surface of the scattered light that directly impinges on the exit surface is less than the Brewster angle. In this case, the extractor element  1830  is said to satisfy the Brewster condition, as described above in connection with  FIG.  1 A . Furthermore, the recovery enclosure  1840  encloses the medium adjacent the first surface of the scattering element. The recovery enclosure  1840  is arranged and configured to recover a portion of the scattered light that propagates through the first surface into the medium. 
     Additionally, a combination of a shape of the exit surface of the second element and a non-spherical, non-planar shape of the optical interface is configured to (i) output scattered light through the exit surface, and (ii) control the intensity distribution of the output light. For example, the combination is configured to control directions of peak intensities of the output intensity distribution. In this manner, the output intensity distribution can be shaped to match an input requirement of a secondary optical system, for instance. Moreover, the light output by the ASLV light-emitting device  1800  has a spectral power distribution corresponding to the spectrum  115  shown in  FIG.  1 B . 
     Depending on the embodiment, the scattering element  1820  can be configured as one or more sheets having a thickness of down to 200 microns or less, it can be configured as one or more bodies with several millimeter long sides or diameters and a fraction of a millimeter thickness, or it can be configured as one or more dome-shaped or box-shaped objects of up to several centimeter size and a thickness of the order of down to a millimeter or thinner. 
     In some embodiments, the scattering element is ellipsoidal in shape.  FIG.  19 A  shows an ASLV light-emitting device  1900  having an ellipsoidal scattering element  1920 . The extractor element  1930  has an exit surface  1935  of radius R1. In this example, the scattering element  1920  is shaped as an ellipsoidal segment with its long axis along the optical z-axis within a notional R O  semi-sphere. In some implementations, the R O  semi-sphere represents the Weierstrass sphere, while in other implementations the R O  semi-sphere represents the Brewster sphere. A recovery cavity  1940  is formed from a light-entry surface of the scattering element  1920  and a planar reflector  1945 . The recovery cavity  1940  is filled with a gas, e.g., air, or is evacuated. An index of refraction np of the scattering element  1920  is smaller than or equal to an index of refraction n1 of the extractor element  1930 . A light-emitting element  1910  is located in an aperture of the planar reflector  1945  and emits light in the recovery cavity  1940 . In some implementations, the planar reflector  1945  extends laterally to the outer edge of the scattering element  1920 . In other implementations, the planar reflector  1945  extends laterally to the exit surface of the extractor element  1935 . In other implementations, the planar reflector  1945  extends laterally farther out than the exit surface of the extractor element  1935 , for example to a radius of 1.2x, 1.5x or 2.0xR1. 
       FIG.  19 B  shows an intensity distribution  1990  of light output by an ASLV light-emitting device similar to the ASLV light-emitting device  1900 . The intensity distribution  1990  indicates that such an ASLV light-emitting device favors transverse (in the ± directions of the x-axis, simply referred to as lateral or side) emission at the expense of on-axis intensity (along the z-axis.) In general, the intensity distribution of light output by an ASLV light-emitting device is biased along a direction perpendicular to the largest cross-section of the extractor element  1920 . 
       FIG.  20 A  shows another ASLV light-emitting device  2000  having an ellipsoidal scattering element  2020 . In this example, the scattering element  2020  is shaped as an ellipsoidal segment with its short axis along the optical z-axis. The extractor element  2030  has an exit surface  2035  of radius R1. In this example, the scattering element  2020  is shaped as an ellipsoidal segment with its long axis perpendicular to the optical z-axis within a notional R O  semi-sphere. In some implementations, the R O  semi-sphere represents the Weierstrass sphere, while in other implementations the R O  semi-sphere represents the Brewster sphere. A recovery cavity  2040  is formed from a light-entry surface of the scattering element  2020  and a planar reflector  2045 . The recovery cavity  2040  is filled with a gas, e.g., air, or is evacuated. An index of refraction np of the scattering element  2020  is larger than or equal to an index of refraction n1 of the extractor element  2030 .A light-emitting element  2010  is located in an aperture of the planar reflector  2045  and emits light in the recovery cavity  2040 . In some implementations, the planar reflector  2045  extends laterally to the outer edge of the scattering element  2020 . In other implementations, the planar reflector  2045  extends laterally to the exit surface of the extractor element  2035 . In other implementations, the planar reflector  2045  extends laterally farther out than the exit surface of the extractor element  2035 , for example to a radius of 1.2x, 1.5x or 2.0xR1. 
       FIG.  20 B  shows an intensity distribution  2090  of light output by an ASLV light-emitting device similar to the ASLV light-emitting device  2000 . The intensity distribution  2090  indicates that such an ASLV light-emitting device favors on-axis (along the z-axis or simply referred to as forward) intensity at the expense of lateral emission (in the ± directions of the x-axis.) In this case, the intensity distribution is biased along the z-direction because the largest cross-section (x-y) of the scattering element  2020  is the x-y cross-section. In addition, note that as long as the entire scattering element  2020  is within the R O  semi-sphere, there is almost no TIR at the outer extractor/air interface  2035 . 
       FIGS.  21 A- 21 B  show side-view cross-sections of another ASLV light-emitting device  2100 .  FIG.  21 C  shows a bottom view cross-section of the same device. The ASLV light-emitting device  2100  has an ellipsoidal scattering element  2120  with unequal orthogonal axes along the x-, y-, and z-axes. In this example, the scattering element  2120  is shaped as a semi-ellipsoid with axes that satisfy a ratio 2:1:4 in the x:y:z directions. The ASLV light-emitting device  2100  further includes a light-emitting element  2110 , a planar reflector  2145 , and an extractor element  2130 . 
     The extractor element  2130  is hemispherical and has an exit surface  2135  of radius R1 that is concentric with the semi-ellipsoidal scattering element  2120 . The long axis of the scattering element  2120  is oriented along the optical z-axis of the ASLV light-emitting device  2100  within a notional R O  semi-sphere. In some implementations, the R O  semi-sphere represents the Weierstrass sphere, while in other implementations the RO semi-sphere represents the Brewster sphere. A recovery cavity  2140  is formed from a light-entry surface of the scattering element  2120  and the planar reflector  2145 . The recovery cavity  2140  is filled with a gas, e.g., air, or is evacuated. An index of refraction np of the scattering element  2120  is smaller than or equal to an index of refraction n1 of the extractor element  2130 . The light-emitting element  2110  is located in an aperture of the planar reflector  2145  and emits light in the recovery cavity  2140 . In some implementations, the planar reflector  2145  extends laterally to the outer edge of the scattering element  2120 . In other implementations, the planar reflector  2145  extends laterally to the exit surface of the extractor element  2135 . 
       FIG.  21 D  shows an x-z intensity distribution  2190  of light output by an ASLV light-emitting device similar to the ASLV light-emitting device  2100 . In this example, the reflector  2145  extends to the exit surface  2135  of the extractor element  2130 . In this manner, although the intensity distribution  2190  has a forward bias, it covers a solid angle of &gt;2π sr, since light originating from the upper part of the scattering element  2120  and propagating towards the lower edges of the extractor  2130  will be refracted into angles &gt; 90° from the optical z-axis.  FIG.  21 E  shows an intensity distribution  2192  of light output by the same embodiment of ASLV light-emitting device  2100  that has the reflector  2145  extending to the exit surface  2135  of the extractor element  2130 . The intensity distribution  2192  indicates that such an ASLV light-emitting device favors transverse (in the ± directions of the y-axis, simply referred to as lateral or side) emission at the expense of on-axis intensity (along the z-axis) and the longitudinal intensity (along the x-axis). 
     In general, the intensity distribution of light output by an ASLV light-emitting device is biased along a direction perpendicular to the largest cross-section of the scattering element  2120 . Because the x-z cross-section is larger than either of the y-z or x-y cross-sections, the ASLV light-emitting device  2100  issues most of the output light in the y-direction (laterally), while less of the output light is issued in the x-direction (along the longitudinal direction of the ASLV light-emitting device  2100 ) or in the z-direction (forward.) 
     In another implementation, the scattering element  2120  of the ASLV light-emitting device  2100  can be shaped as a semi-ellipsoid with axes that satisfy a ratio 4:2:4 in the x:y:z directions. In this other case, because the x-y and x-z cross-sections are larger than the y-z cross-section, an ASLV light-emitting device  2100  would issue most of the output light in the z-direction (forward) and in the y-direction (laterally), while only a fraction of the output light is issued in the x-direction (along the longitudinal direction of the ASLV light-emitting device  2100 .) 
       FIG.  22    shows a lighting fixture  2200  including multiple ASLV light-emitting devices  2210  disposed in a longitudinal x-direction of a base substrate  2205 . For example, each of the ASLV light-emitting devices  2210  can correspond to the ASLV light-emitting device  2100  that has a scattering element shaped as a semi-ellipsoid with axes that satisfy a ratio 4:2:4 in the x:y:z directions. In such case, the lighting fixture  2200  outputs most of the light in the z-direction (forward) and y-direction (laterally), while only a small fraction of the output light is output light along the longitudinal x-direction of the base substrate  2205 . 
       FIG.  23 A  shows an ASLV light-emitting device  2300  having an ellipsoidal scattering element  2320  that encloses a recovery enclosure  2340 . The ASLV light-emitting device  2300  has a rotationally symmetric mixed spherical and ellipsoidal configuration about the z-axis and includes an extractor element  2310 , a scattering element  2320  and a light-emitting device  2360  configured to emit blue light under operating conditions. The scattering element  2320  includes active and passive scattering centers and is configured to convert a portion of the blue light provided by the light-emitting device  2360  to generate white light. The extractor element  2310  and the scattering element  2320  can be injection molded in a multi-shot process. In this example, the ellipsoidal scattering element  2320  is disposed concentric with the exit surface of the extractor element  2310  and is contained within a notional R O  semi-sphere. In some implementations, the R O  semi-sphere represents the Weierstrass sphere, while in other implementations the R O  semi-sphere represents the Brewster sphere. 
     The ASLV light-emitting device  2300  may further include for example a socket for establishing an electromechanical connection to a source of power, drive electronics, electrical connections and cooling elements. 
     The extractor element  2310  is configured as a shell with a spherical exit surface on the outside and an ellipsoidal surface on the inside. The scattering element  2320  is configured as an ellipsoidal shell abutting the inside of the extractor element  2310 . The scattering element  2320  forms a hollow recovery enclosure  2340  that is filled with a low-index medium, for example air or inert gas. Varying the shape of the scattering element  2320  provides for a degree of beam shaping. The scattering element  2320  defines an aperture surrounded by walls  2317  and substantially abuts sides of a pillar supporting the light-emitting device  2360  so that substantially all light from the light-emitting device is emitted into the recovery enclosure  2340  during operating conditions. Varying the distance between the light-emitting device  2360  and the scattering element  2320 , that is the height of the light-emitting device  2360  above the bottom of the scattering element  2320 , provides for another degree of beam shaping. 
       FIG.  23 B  shows an intensity distribution  2390  of light output by the ASLV light-emitting device  2300 . The intensity distribution  2390  indicates that the ASLV light-emitting device  2300  favors transverse (lateral or side) emission (in the ± directions of the x-axis), at the expense of on-axis intensity (along the z-axis) because the lateral cross-section of the scattering element  2320  is larger than the on-axis cross-section of the same. 
       FIG.  24 A  shows an ASLV light-emitting device  2400  having an elongated scattering element  2420  that encloses a recovery enclosure  2440 . The ASLV light-emitting device  2400  has a rotationally symmetric mixed spherical and cylindrical configuration and includes a spherical extractor element  2410 , a scattering element  2420  and a light-emitting device  2460  configured to emit blue light under operating conditions. The scattering element  2420  includes active and passive scattering centers and is configured to convert a portion of the blue light provided by the light-emitting device  2460  to generate white light. The extractor element  2410  and the scattering element  2420  can be injection molded in a multi-shot process. The ASLV light-emitting device  2400  may further include for example a socket for establishing an electromechanical connection to a source of power, drive electronics, electrical connections and cooling elements. 
     The extractor element  2410  has a spherical exit surface on the outside and a surface on the inside that is adequately shaped to match the scattering element  2420 . The scattering element  2420  is clad to the inside of the extractor element  2410  and located within a region bound by particular notional sphere determined by the spherical exit surface of the extractor element  2410 . In some implementations, the particular notional sphere is the Weierstrass sphere. In some implementations, the particular notional sphere is the Brewster sphere. The scattering element  2420  forms a hollow recovery enclosure  2440  that is filled with a low-index medium, for example air or inert gas. Varying the shape and/or dimensions of the scattering element  2420  provides for a degree of beam shaping. 
       FIG.  24 B  shows an intensity distribution  2490  of light output by the ASLV light-emitting device  2400 . The intensity distribution  2490  indicates that the ASLV light-emitting device  2400  outputs two narrow lobes (of width approximately 10°), such that each of the two narrow lobes has a transverse (lateral or side) component (in the + or - direction of the x-axis) about equal to an on-axis component (along the z-axis). In addition, the ASLV light-emitting device  2400  outputs a forward lobe (along the z-axis) with a magnitude that is about half a magnitude of the two narrow lobes. 
     In this example, the scattering element  2420  has a tubular center portion  2425  with dome-shaped caps  2421  and  2423  disposed at each end of the center portion  2425 . The tubular center portion  2425  may be a cylinder, a prism or other object with a parallel or tapered wall. The dome-shaped caps  2421  and  2423  may have different or equal shapes. The dome-shaped caps  2421  and  2423  may have a hemi-spherical, parabolic, hyperbolic, elliptical or other shape. It is noted that such a scattering element may be configured for positioning light-emitting devices elsewhere other than illustrated in  FIG.  24 A , for example, proximate the circumference in the center of the center portion  2425 . 
     The scattering element  2420  defines an aperture surrounded by walls  2417  and substantially abuts sides of a pillar supporting the light-emitting device  2460  so that substantially all light from the light-emitting device is emitted into the recovery enclosure  2440  during operating conditions. 
       FIG.  25 A  shows an ASLV light-emitting device  2500  having a recovery enclosure  2540  enclosed by a combination of (i) a scattering element  2520  shaped as an ellipsoidal segment and (ii) a planar reflector  2545 . In this example, the planar reflector  2545  is normal to the x-z plane and slanted by a slant angle with respect to the y-axis. The extractor element  2530  has an exit surface  2535  of radius R1. In this example, the scattering element  2520  is contained within a notional R O  semi-sphere. In some implementations, the R O  semi-sphere represents the Weierstrass sphere, while in other implementations the R O  semi-sphere represents the Brewster sphere. The recovery enclosure  2540  can include gas, e.g. air, or can be evacuated. In some implementations, the planar reflector  2545  is formed at the planar interface between air, inside the recovery enclosure  2540  and the material of the extractor element  2530 . In this case, scattered light (whether pump light or converted light) internally reflects at the planar reflector  2545 . In other implementations, the planar reflector  2545  can be coated with a reflective material. 
     The scattering element  2520  defines an aperture surrounded by walls  2517  and substantially abuts sides of a pillar supporting a light-emitting device  2510  so that substantially all light from the light-emitting device is emitted into the recovery enclosure  2540  during operating conditions. Varying the distance between the light-emitting device  2510  and the scattering element  2520 , that is the height of the light-emitting device  2510  above the bottom of the scattering element  2520 , provides for another degree of beam shaping. 
       FIG.  25 B  shows an x-z intensity distribution  2590  of light output by an ASLV light-emitting device similar to the ASLV light-emitting device  2500  in a plane x-z perpendicular to the flat reflector  2545 . The x-z intensity distribution  2590  indicates that the ASLV light-emitting device  2500  outputs a narrow lobe (of width approximately 5°) and oriented at an angle with respect to the z-axis. The angle of the narrow lobe corresponds to the slant angle of the flat reflector  2545 .  FIG.  25 C  shows a y-z intensity distribution  2592  of light output by an ASLV light-emitting device similar to the ASLV light-emitting device  2500  in a plane y-z that has a normal rotated by the given angle with respect to the normal of the flat reflector  2545 . The y-z intensity distribution  2592  indicates that the ASLV light-emitting device  2500  outputs two side lobes respectively oriented mostly in the + and - directions of the y-axis. 
       FIG.  26 A  shows an ASLV light-emitting device  2600  having a spherical scattering element  2620  that is off-centered relative to a spherical extractor element  2630  and encloses a recovery enclosure  2640 . The spherical scattering element  2620  is contained within a Weierstrass sphere corresponding to an exit surface  2635  of the spherical extractor element  2630 . Moreover, the center of the spherical scattering element  2620  is offset with respect to the center of the spherical extractor element  2630  by a distance Δz. The extractor element  2630  has an exit surface  2635  of radius R1. In this example, the scattering element  2620  is contained within a notional R O  semi-sphere. In some implementations, the R O  semi-sphere represents the Weierstrass sphere, while in other implementations the R O  semi-sphere represents the Brewster sphere. The recovery enclosure  2640  can include gas, e.g. air, or can be evacuated. 
     The scattering element  2620  defines an aperture surrounded by walls  2617  and substantially abuts sides of a pillar supporting a light-emitting device  2610  so that substantially all light from the light-emitting device is emitted into the recovery enclosure  2640  during operating conditions. Varying the distance between the light-emitting device  2610  and the scattering element  2620 , that is the height of the light-emitting device  2610  above the bottom of the scattering element  2620 , provides for another degree of beam shaping. 
       FIG.  26 B  shows an intensity distribution  2690  of light output by an ASLV light-emitting device similar to the ASLV light-emitting device  2600 . The intensity distribution  2690  indicates that the ASLV light-emitting device  2400  favors on-axis (along the z-axis or simply referred to as forward) emission at the expense of lateral emission (in the ± directions of the x-axis.) The reason for the on-axis bias of the intensity distribution  2690  is that, for this device, an optical power of the exit surface of the extractor element  2635  is larger on-axis than laterally. 
       FIG.  27 A  shows an ASLV light-emitting device  2700  having an ellipsoidal scattering element  2720  that is off-centered relative to a spherical extractor element  2710  and encloses a recovery enclosure  2740 . The ellipsoidal scattering element  2720  has its long axis along the x-axis and is contained within a Weierstrass sphere corresponding to an exit surface  2735  of the spherical extractor element  2730 . Moreover, the ellipsoidal scattering element  2720  is offset with respect to the center of the spherical extractor element  2730  by a distance Δz. The extractor element  2730  has an exit surface  2735  of radius R1. In this example, the scattering element  2720  is contained within a notional R O  semi-sphere. In some implementations, the R O  semi-sphere represents the Weierstrass sphere, while in other implementations the R O  semi-sphere represents the Brewster sphere. The recovery enclosure  2740  can include gas, e.g. air, or can be evacuated. 
     The scattering element  2720  defines an aperture surrounded by walls  2717  and substantially abuts sides of a pillar supporting a light-emitting device  2710  so that substantially all light from the light-emitting device is emitted into the recovery enclosure  2740  during operating conditions. Varying the distance between the light-emitting device  2710  and the scattering element  2620 , that is the height of the light-emitting device  2710   above the bottom of the scattering element  2720 , provides for another degree of beam shaping. 
       FIG.  27 B  shows an x-z intensity distribution  2790  of light output by an ASLV light-emitting device similar to the ASLV light-emitting device  2700 . The x-z intensity distribution  2790  indicates that, in the x-z plane, the ASLV light-emitting device  2700  favors on-axis (along the z-axis or simply referred to as forward) emission at the expense of lateral emission (in the ± directions of the x-axis.) The reason for the on-axis bias of the intensity distribution  2790  is that, for this device, an optical power of the exit surface of the extractor element  2735  is larger on-axis than laterally. Moreover, note that the intensity distribution  2790  has a stronger on-axis bias than the intensity distribution  2590  because devices similar to the ASLV light-emitting device  2700  have a stronger on-axis optical power than devices similar to the ASLV light-emitting device  2500 . 
     The distribution of light emitted from the ASLV light-emitting device also depends on the shape of the exit surface. Accordingly, varying the shape of the exit surface from spherical (rotationally symmetric embodiments) and cylindrical (elongate embodiments) can also provide different intensity distributions relative to spherical and/or cylindrical embodiments. 
       FIG.  28    shows an ASLV light-emitting device  2800  having an extractor element  2830 / 2830 ′ shaped as an ellipsoidal segment. The ASLV light-emitting device  2800  further includes a light-emitting element  210 , a scattering element  220  and a planar reflector  245 . A recovery enclosure  240  is formed from a light-entry surface of the scattering element  220  and planar reflector  245 . The recovery enclosure is filled with a gas, e.g., air, or is evacuated. An index of refraction np of the scattering element  220  is larger than or equal to an index of refraction n1 of the extractor element  230 . 
     A configuration of the ASLV light-emitting device  2800  for which the ellipsoidal segment is a hemisphere  230  corresponds to the ASLV light-emitting device  200  described above in connection with  FIG.  2 A . In this case, an exit surface  235  of the hemispherical extractor  230  satisfies the Brewster condition, and hence, the Weierstrass condition. However, an apex of the extractor element  2830  (or  2830 ′) is further away from the scattering element  220  compared to the apex of the extractor element  230 . Hence, a configuration of an exit surface of the extractor  2835  (or  2835 ′) increases the forward bias or on-axis intensity of light output by the ASLV light-emitting device  2800  along the z-axis relative to the corresponding on-axis intensity of light output by the ASLV light-emitting device  200 . However, in the case of the ASLV light-emitting device  2800 , linearly truncated side walls of its exit surface  2835  (or  2835 ′) may result in some TIR losses. 
     As described above in this specification, an ASLV light-emitting device uses (i) an extractor element having a radius R to efficiently extract light from a scattering element immersed in a Weierstrass R/(n1/n0) sphere concentric to an exit surface of the extractor element, and (ii) a recovery enclosure at least partially bounded by the scattering element to return most of the light that escapes from the scattering element into the recovery enclosure. More refined analysis shows that the R/(n1/0) limit can still allow for quite significant reflection losses at the exit surface of the extractor, due to an increasing reflection coefficient at incidence angles less than the Critical Angle, arcsin(n1/n0)), but greater than the Brewster Angle, arctan(n1/n0), where n0 is an index of refraction of the ambient, e.g., n0 = 1 for air, and n1 is an index of refraction of the extractor element. 
     Further as described above in this specification, a scattering element smaller than the critical or Brewster limit radius, can have a variety of shapes, such as flat, part spherical, either more or less than hemi-spherical, or ellipsoids, of both prolate and oblate form, so long as they are entirely contained within preferably the Brewster radius limit. These shapes of the scattering element can create either narrower or wider flux distribution patterns with respect to the optical z-axis of the ASLV light-emitting devices as desired for end applications. However, the intensity distributions typically have a symmetry corresponding to the symmetry of the ASLV light-emitting device. Thus, a rotationally symmetric ASLV light-emitting device will typically provide an intensity distribution pattern being similarly rotationally symmetric. Using such ASLV light-emitting devices in a rectilinear environment, such as a room with a square or rectangular footprint, diagonal, corner-to-corner luminance will fall off between such sources spaced on a grid. 
     Accordingly, ASLV light-emitting devices may be formed having shapes more suited to providing illumination to rectilinear spaces. For example, the ASLV light-emitting devices described below have a square form exit surface of the extractor element, and are referred to as asymmetric square light valve (ASQLV). Such ASQLV light-emitting devices may be more efficient in corner illumination than rotationally symmetric ASLV light-emitting devices. An example of an ASQLV extractor profile has a plan view (e.g., footprint of a top view) that is square, rather than circular. The ASQLV extractor has a cross section sideways on that is generally a simple conic section. Examples of such sideways cross sections of the ASQLV extractor include circular as well as prolate, and oblate ellipse forms. In other examples, the sideways cross sections of the ASQLV extractor include parabolic and hyperbolic sections. Other geometries can also be used, but these simple conic forms are illustrative of the general concept of this technology. 
       FIG.  29    shows a schematic diagram of an example of an ASLV light-emitting device  2900  that includes a light-emitting element  2910 , a scattering element  2920  (also referred to as a first optical element), an extractor element  2930  (also referred to as a second optical element), and a recovery enclosure  2940 . 
     The light-emitting element  2910  is configured to produce and emit light during operation. A spectral power distribution of light emitted by the light-emitting element  2910  (also referred to as pump light) can be blue, for instance. The spectral power distribution for visible light is referred to as chromaticity. The scattering element  2920  has a first surface (also referred to as a light-entry surface) spaced apart from the light-emitting element  2910  and positioned to receive the light from the light-emitting element  2910 . The scattering element  2920  includes scattering centers arranged to substantially isotropically scatter the light from the light-emitting element  2910  and to provide scattered light. The scattered light includes elastically scattered pump light and inelastically scattered pump light. Spectral power distribution of the elastically scattered light is the same as the spectral power distribution of the pump light, and spectral power distribution of the inelastically scattered light can be yellow, for instance. A spectrum  111  of the elastically scattered pump light and a spectrum  113  of the inelastically scattered pump light are shown in  FIG.  1 B  along with a spectrum  115  of the scattered light. 
     Referring again to  FIG.  29   , the extractor element  2930  is formed from a transparent material having an exit surface. The exit surface is generally a curved, transparent surface. In other words, changes in the scattered light passing through the exit surface can generally be described by Snell’s law of refraction, as opposed to, for example, an opaque or diffuse surface where further scattering of transmitted light occurs. The extractor element  2930  is in contact with the scattering element  2920 , such that there is an optical interface between the scattering and extractor elements at the place of contact, and the optical interface is opposite the first surface of the scattering element. Moreover, the extractor element  2930  is arranged so that light scattered through the optical interface enters the extractor element  2930 . 
     Further, the ASLV light-emitting device  2900  includes a medium adjacent the first surface of the scattering element having a refractive index n0, and the scattering element  2920  includes a material having a first refractive index n1, where n0 &lt; n1. The transparent material has a refractive index n2, where n0 &lt; n2. The exit surface is a transparent surface that includes multiple portions, such that each portion of the exit surface is joined to another portion at an edge. In some implementations, each portion of the exit surface is shaped such that an angle of incidence at each portion of the exit surface of the scattered light that directly impinges on the portion of the exit surface is less than the critical angle for total internal reflection. In this case, the extractor element  2930  is said to satisfy the Weierstrass condition, as described above in connection with  FIG.  1 A , for each portion of the exit surface. In some implementations, each portion of the exit surface is shaped such that an angle of incidence at each portion of the exit surface of the scattered light that directly impinges on the portion of the exit surface is less than the Brewster angle. In this case, the extractor element  2930  is said to satisfy the Brewster condition, as described above in connection with  FIG.  1 A , for each portion of the exit surface. 
     Furthermore, the recovery enclosure  2940  encloses the medium adjacent the first surface of the scattering element. The recovery enclosure  2940  is arranged and configured to recover a portion of the scattered light that propagates through the first surface into the medium. Additionally, a combination of a shape of the multiple portions of the exit surface of the second element and a shape of the optical interface is configured to (i) output scattered light through the exit surface, and (ii) control the intensity distribution of the output light. Moreover, the light output by the ASLV light-emitting device  2900  has a spectral power distribution corresponding to the spectrum  115  shown in  FIG.  1 B . 
       FIGS.  30 A- 30 B  show aspects of an example of an ASLV light-emitting device  3000  having a hemispherical scattering element  3020  and an extractor element  3030  that is circular in an x-z cross-section or a y-z cross-section, and has a square footprint in an x-y cross-section. The extractor element  3030  of the ASLV light-emitting device  3000  includes a volume common to two crossed semi-circular cylinders, hence, the extractor element  3030  is a cushion shaped object, whose section parallel to the sides of the square (in planes x-z or y-z), through the center, is a semi-circle. Planes through this center at other angles to the sides have oblate ellipsoidal sections, reaching a maximum eccentricity along the diagonals of the square form. The shortest cross section of the extractor element  3030  of the ASLV light-emitting device  3000  is a semicircle, and the longest is an oblate ellipse. 
     Many other choices are possible as desired, for example the longest section seen above could be made a semi-circle, in which case, all other sections would be prolate ellipses, instead of oblate. Any cross-section between the shortest parallel to the sides (in planes x-z or y-z), and the longest diagonal section, can be made circular, in which case an exit surface of the extractor element would be narrower prolate ellipse, and wider oblate ellipse, as desired for an end application. For each of these forms of an exit surface of the extractor element  3035 , the scattering element  3020  is contained within a volume of the extractor element which satisfies, for all possible ray directions, at least the critical angle (corresponding to the Weierstrass) condition, and preferably the Brewster angle incidence condition. The scattering element  3020  can itself have a variety of shapes within the limits of the Critical or Brewster condition volumes, to further control the flux distribution patterns obtainable from the scattering element. 
       FIG.  30 C  shows x-y far field illuminance (intensity distribution)  3080  in an x-y plane perpendicular to an optical z-axis, and  FIG.  30 D  shows x-z far field illuminance (intensity distribution)  3090  in an x-z plane that contains the optical z-axis corresponding the ASLV light-emitting device  3000 . The extractor element  3030  of the ASLV light-emitting device  3000  is shaped like crossed semi-circular cylinders with a conic constant K of zero (K = 0). The diagonal is an oblate ellipse. The results illustrated in  FIGS.  30 C- 30 D  show that the ASLV light-emitting device  3000  has better far field illuminance in the diagonal corner directions, and thus, gives better area illuminance patterns, compared to the rotationally symmetric ASLV light-emitting device  200 , described above in connection with  FIGS.  2 A- 2 D . This example of extractor shape enables the ASLV light-emitting device  3000  to provide more intensity in the diagonal directions of the square room, leading to better illuminance in the corners, compared to a rotationally uniform pattern. 
     A wide range of possible illuminance or intensity patterns are available with different forms for the cushion shaped extraction surface  3035 , and different forms of the internal effective light emitting volume of the scattering element  3020 . 
       FIGS.  31 A- 31 B  show aspects of an example of an ASLV light-emitting device  3100  having a hemispherical scattering element  3120  and an extractor element  3130  shaped like crossed elliptic cylinders, with a diagonal section that is circular and a square footprint in the x-y plane. In this example, the ellipse has K = -0.5.  FIG.  31 C  shows x-y far field illuminance (intensity distribution)  3180  in an x-y plane perpendicular to an optical z-axis, and  FIG.  31 D  shows x-z far field illuminance (intensity distribution)  3190  in an x-z plane that contains the optical z-axis corresponding the ASLV light-emitting device  3100 . 
     While the foregoing embodiments feature extractor elements that include a single exit surface or facet exit surfaces, other embodiments are also possible. For example,  FIG.  32    shows a schematic diagram of an example of an ASLV light-emitting device  3200  that includes an extractor element  3230  that has first and second exit surfaces separated by a step. The light-emitting device  3200  also includes a light-emitting element  3210 , a scattering element  3220  (also referred to as a first optical element), and a recovery enclosure  3240 . 
     The light-emitting element  3210  is configured to produce and emit light during operation. A spectral power distribution of light emitted by the light-emitting element  3210  (also referred to as pump light) can be blue, for instance. The spectral power distribution for visible light is referred to as chromaticity. The scattering element  3220  has a first surface (also referred to as a light-entry surface) spaced apart from the light-emitting element  3210  and positioned to receive the light from the light-emitting element  3210 . The scattering element  3220  includes scattering centers arranged to substantially isotropically scatter the light from the light-emitting element and to provide scattered light. The scattered light includes elastically scattered pump light and inelastically scattered pump light. Spectral power distribution of the elastically scattered light is the same as the spectral power distribution of the pump light, and spectral power distribution of the inelastically scattered light can be yellow, for instance. A spectrum  111  of the elastically scattered pump light and a spectrum  113  of the inelastically scattered pump light are shown in  FIG.  1 B  along with a spectrum  115  of the scattered light. 
     Referring again to  FIG.  32   , the extractor element  3230  is formed from a transparent material and is in contact with the scattering element  3220 , such that there is an optical interface between the scattering and extractor elements at the place of contact, and the optical interface is opposite the first surface of the scattering element. Moreover, the extractor element  3230  is arranged so that light scattered through the optical interface enters the extractor element  3230 . 
     Further, the ASLV light-emitting device  3200  includes a medium adjacent the first surface of the scattering element having a refractive index n0, and the scattering element includes a material having a first refractive index n1, where n0 &lt; n1. The transparent material has a refractive index n2, where n0 &lt; n2. The first and second exit surfaces are generally curved, transparent surfaces. In other words, changes in the scattered light passing through the first and second exit surfaces can generally be described by Snell’s law of refraction, as opposed to, for example, an opaque or diffuse surface where further scattering of transmitted light occurs. In some implementations, the first and second exit surfaces are at least partially transparent and shaped such that an angle of incidence at the first and second exit surfaces of at least some of the scattered light that directly impinges thereon is less than the critical angle for total internal reflection. In this case, the extractor element  3230  is said to satisfy the Weierstrass condition, as described above in connection with  FIG.  1 A , for each of the exit surfaces. In some implementations, the first and second exit surfaces are shaped such that an angle of incidence at the first and second exit surfaces of at least some of the scattered light that directly impinges thereon is less than the Brewster angle. In this case, the extractor element  3230  is said to satisfy the Brewster condition, as described above in connection with  FIG.  1 A , for each of the exit surfaces. Furthermore, the recovery enclosure  3240  encloses the medium adjacent the first surface of the scattering element. The recovery enclosure  3240  is arranged and configured to recover a portion of the scattered light that propagates through the first surface into the medium. Additionally, the ASLV light-emitting device  3200  outputs scattered light through the first and second exit surfaces into the ambient environment. As described above, the light output by the ASLV light-emitting device  3200  has a spectral power distribution corresponding to the spectrum  115  shown in  FIG.  1 B . 
     For example, the first surface can be arranged to intersect an optical axis of the light-emitting element  3200 . In some implementations, the first exit surface is recessed relative to the second exit surface. In other implementations, the second exit surface is recessed relative to the first exit surface. Moreover, the step can include one of a reflective surface or a transparent surface. In some implementations, at least one of the first and second exit surfaces is translucent. 
     An ASLV light-emitting device  3200  having multiple exit surfaces separated by a step can provide different magnifications for light emanating from the scattering element  3200  in directions corresponding to the exit surfaces. In this manner, the relative magnification of the exit surfaces can be adjusted to bias an intensity distribution of the ASLV light-emitting device  3200  in a direction of one of the exit surfaces. Example implementations of the ASLV light-emitting device  3200  are described below in connection with  FIGS.  33 - 37   . 
       FIG.  33 A  shows an ASLV light-emitting device  3300  having a hemispherical scattering element  3320  and a step  3333  arranged between a first exit surface  3335 - 1  and a second exit surface  3335 - 2  of an extractor element  3330 . The first surface  3335 - 1  is arranged to intersect an optical z-axis of the ASLV light-emitting device  3300 . The ASLV light-emitting device  3300  further includes a light-emitting element  3310  and a planar reflector  3345 . A recovery cavity  3340  is formed from a light-entry surface of the scattering element  3320  and the planar reflector  3345 . The recovery cavity  3340  is filled with a gas, e.g., air, or is evacuated. An index of refraction np of the scattering element  3320  is larger than or equal to an index of refraction n1 of the extractor element  3330 . The light-emitting element  3310  is located in an aperture of the planar reflector  3345  and emits light in the recovery cavity  3340 . 
     The scattering element  3320  is contained within a notional R O  semi-sphere. In some implementations, the R O  semi-sphere represents the Weierstrass sphere corresponding to the shorter of radius R11 of the first exit surface  3335 - 1  and radius R12 of the second exit surface  3335 - 2 . For the example illustrated in  FIG.  33 A , the first exit surface  3335 - 1  is recessed relative to the second exit surface  3335 - 2  hence a radius R12 of the second exit surface  3335 - 2  is shorter than a radius R11 of the first exit surface  3335 - 1 . In this manner, the Weierstrass condition is satisfied for the second exit surface of the extractor  3335 - 2 . In some implementations, the R O  semi-sphere represents the Brewster sphere corresponding to the shorter of radius R11 of the first exit surface  3335 - 1  and radius R12 of the second exit surface  3335 - 2 . When R12 &lt; R11, the Brewster condition is satisfied for the second exit surface of the extractor  3335 - 2 . 
     To reduce potential TIR light losses at the step  3333  between the first  3335 - 1  and second  3335 - 2  exit surfaces of the extractor element  3330 , the step  3333  is formed as a two-sided mirror. As radius R12 of the second  3335 - 2  exit surface of the extractor  3330  satisfies the Weierstrass condition, most rays hitting the mirror of the step  3333  on the central side transmit through the first exit surface  3335 - 1  without TIR. All rays transmitted from the outer edge of the scattering element  3320  towards the upper edge of the second exit surface  3335 - 2  of the extractor  3330  hit the outside of the mirror of the step  3333  and are redirected in a backwards direction at &gt; 90° to the optical z-axis. An optional extension of the mirror  3345  of the recovery enclosure  3340  can turn most of these rays back into a forward direction (along the +z axis.) 
     The planar reflector  3345  extends laterally to the outer edge of the extractor element  3320 . In some implementations, the planar reflector  3345  extends laterally to an outer edge of the second exit surface  3335 - 2 , to a distance equal to a radius R12. In other implementations, the planar reflector  3345  extends laterally farther out than the second exit surface  3335 - 2 , for example to a distance between R12 and R11, or to a distance of 1.2x, 1.5x or 2.0xR11. 
       FIG.  33 B  shows an intensity distribution  3390  output by an ASLV light-emitting device similar to the ASLV light-emitting device  3300 . Although the scattering elements of the ASLV light-emitting device  3300  and of the ASLV light-emitting device  200  are both hemispherical, the intensity distribution  3390  has a stronger forward bias that the intensity distribution  290 . The reason for the noted increase in forward bias is that the center exit surface of the extractor element  3335 - 1  of the ASLV light-emitting device  3300  has optical power that is larger than the optical power of the corresponding portion of the exit surface of the extractor element  235  of the ASLV light-emitting device  200 . Moreover, the intensity distribution  3390  covers a solid angle of &gt;2π sr since light originating from the upper part of the scattering element  3320  and propagating towards the lower edges of the extractor  3330  will be refracted into angles &gt; 90° from the optical z-axis. 
       FIG.  34 A  shows an ASLV light-emitting device  3400  having an elliptical scattering element  3420  and a step  3433  arranged between a first exit surface  3435 - 1  and a second exit surface  3335 - 2  of an extractor element  3430 . The first surface  3435 - 1  is arranged to intersect an optical z-axis of the ASLV light-emitting device  3400 . The ASLV light-emitting device  3400  further includes a light-emitting element  3410  and a planar reflector  3445 . A recovery cavity  3440  is formed from a light-entry surface of the scattering element  3420  and the planar reflector  3445 . The recovery cavity  3440  is filled with a gas, e.g., air, or is evacuated. An index of refraction np of the scattering element  3420  is larger than or equal to an index of refraction n1 of the extractor element  3430 . The light-emitting element  3410  is located in an aperture of the planar reflector  3445  and emits light in the recovery cavity  3440 . 
     The semi-ellipsoidal scattering element  3420  is contained within a notional R O  semi-sphere. In some implementations, the R O  semi-sphere represents the Weierstrass sphere corresponding to the shorter of radius R11 of the first exit surface  3435 - 1  and radius R12 of the second exit surface  3435 - 2 . For the example illustrated in  FIG.  34 A , the first exit surface  3435 - 1  is recessed relative to the second exit surface  3435 - 2  hence a radius R12 of the second exit surface  3435 - 2  is shorter than a radius R11 of the first exit surface  3435 - 1 . In this manner, the Weierstrass condition is satisfied for the second exit surface of the extractor  3435 - 2 . In some implementations, the R O  semi-sphere represents the Brewster sphere corresponding to the shorter of radius R11 of the first exit surface  3435 - 1  and radius R12 of the second exit surface  3435 - 2 . When R12 &lt; R11, the Brewster condition is satisfied for the second exit surface of the extractor  3435 - 2 . 
     To reduce potential TIR light losses at the step  3433  between the first  3435 - 1  and second  3435 - 2  exit surfaces of the extractor element  3430 , the step  3433  is formed as a two-sided mirror. As radius R12 of the second  3435 - 2  exit surface of the extractor  3430  satisfies the Weierstrass condition, most rays hitting the mirror of the step  3433  on the central side transmit through the first exit surface  3435 - 1  without TIR. All rays transmitted from the outer edge of the scattering element  3420  towards the upper edge of the second exit surface  3435 - 2  of the extractor  3430  hit the outside of the mirror of the step  3433  and are redirected in a backwards direction at &gt; 90° to the optical z-axis. An optional extension of the mirror  3445  of the recovery enclosure  3440  can turn most of these rays back into a forward direction (along the +z axis.) 
     The planar reflector  3445  extends laterally to the outer edge of the extractor element  3320 . In some implementations, the planar reflector  3445  extends laterally to an outer edge of the second exit surface  3435 - 2 , to a distance equal to a radius R12. In other implementations, the planar reflector  3445  extends laterally farther out than the second exit surface  3435 - 2 , for example to a distance between R12 and R11, or to a distance of 1.2x, 1.5x or 2.0xR11. 
       FIG.  34 B  shows an intensity distribution  3490  output by an ASLV light-emitting device similar to the ASLV light-emitting device  3400 . Although the scattering elements of the ASLV light-emitting device  3400  and of the ASLV light-emitting device  1900  are both semi-ellipsoidal, the intensity distribution  3490  has a stronger forward bias that the intensity distribution  1990 . The reason for the noted increase in forward bias is that the center exit surface of the extractor element  3435 - 1  of the ASLV light-emitting device  3400  has optical power that is larger than the optical power of the corresponding portion of the exit surface of the extractor element  1935  of the ASLV light-emitting device  1900 . Moreover, the intensity distribution  3490  covers a solid angle of &gt;2π sr since light originating from the upper part of the scattering element  3420  and propagating towards the lower edges of the extractor  3430  will be refracted into angles &gt; 90° from the optical z-axis. 
       FIG.  35 A  shows an ASLV light-emitting device  3500  having a rectangular scattering element  3520  and a step  3533  arranged between a first exit surface  3535 - 1  and a second exit surface  3535 - 2  of an extractor element  3530 . The rectangular phosphor shape illustrated in  FIG.  35    represents a diagonal cut of the rectangular scattering element  3520  of the ASLV light-emitting device  3500 . The first surface  3535 - 1  is arranged to intersect an optical z-axis of the ASLV light-emitting device  3500 . The ASLV light-emitting device  3500  further includes a light-emitting element  3510  and a planar reflector  3545 . A recovery cavity  3540  is formed from a light-entry surface of the scattering element  3520  and the planar reflector  3545 . The recovery cavity  3540  is filled with a gas, e.g., air, or is evacuated. An index of refraction np of the scattering element  3520  is larger than or equal to an index of refraction n1 of the extractor element  3530 . The light-emitting element  3510  is located in an aperture of the planar reflector  3545  and emits light in the recovery cavity  3540 . 
     The rectangular scattering element  3520  is contained within a notional R O  semi-sphere. In some implementations, the R O  semi-sphere represents the Weierstrass sphere corresponding to the shorter of radius R11 of the first exit surface  3535 - 1  and radius R12 of the second exit surface  3535 - 2 . For the example illustrated in  FIG.  35 A , the first exit surface  3535 - 1  is recessed relative to the second exit surface  3535 - 2  hence a radius R12 of the second exit surface  3535 - 2  is shorter than a radius R11 of the first exit surface  3535 - 1 . In this manner, the Weierstrass condition is satisfied for the second exit surface of the extractor  3535 - 2 . In some implementations, the R O  semi-sphere represents the Brewster sphere corresponding to the shorter of radius R11 of the first exit surface  3535 - 1  and radius R12 of the second exit surface  3535 - 2 . When R12 &lt; R11, the Brewster condition is satisfied for the second exit surface of the extractor  3535 - 2 . 
     To reduce potential TIR light losses at the step  3533  between the first  3535 - 1  and second  3535 - 2  exit surfaces of the extractor element  3530 , the step  3533  is formed as a two-sided mirror. As radius R12 of the second  3535 - 2  exit surface of the extractor  3530  satisfies the Weierstrass condition, most rays hitting the mirror of the step  3533  on the central side transmit through the first exit surface  3535 - 1  without TIR. All rays transmitted from the outer edge of the scattering element  3520  towards the upper edge of the second exit surface  3535 - 2  of the extractor  3530  hit the outside of the mirror of the step  3533  and are redirected in a backwards direction at &gt; 90° to the optical z-axis. An optional extension of the mirror  3545  of the recovery enclosure  3540  can turn most of these rays back into a forward direction (along the +z axis.) 
     The planar reflector  3545  extends laterally to the outer edge of the scattering element  3520 . In some implementations, the planar reflector  3545  extends laterally to an outer edge of the second exit surface  3535 - 2 , to a distance equal to a radius R12. In other implementations, the planar reflector  3545  extends laterally farther out than the second exit surface  3535 - 2 , for example to a distance between R12 and R11, or to a distance of 1.2x, 1.5x or 2.0xR11. 
       FIG.  35 B  shows an intensity distribution  3590  output by an ASLV light-emitting device similar to the ASLV light-emitting device  3500 . Although the intensity distribution  3590  is forward biased, it indicates that the ASLV light-emitting device  3500  favors transverse (in the ± directions of the x- or y-axis, simply referred to as lateral or side) emission at the expense of on-axis emission (along the z-axis.) Moreover, the intensity distribution  3590  covers a solid angle of &gt;2π sr since light originating from the upper part of the scattering element  3520  and propagating towards the lower edges of the extractor element  3530  will be refracted into angles &gt; 90° from the optical z-axis. 
       FIG.  36    shows an ASLV light-emitting device  3600  having a rectangular scattering element  3620  and an extractor element  3630  with a first exit surface  3635 - 1  and a second exit surface  3635 - 2  separated by a step  3633 . In addition, the second exit interface  3635 - 2  extends beyond a 90° angle from the optical z-axis. The first surface  3635 - 1  is arranged to intersect an optical z-axis of the ASLV light-emitting device  3600 . The ASLV light-emitting device  3600  further includes a light-emitting element  3610  and a planar reflector  3645 . A recovery cavity  3640  is formed from a light-entry surface of the scattering element  3620  and the planar reflector  3645 . The recovery cavity  3640  is filled with a gas, e.g., air, or is evacuated. An index of refraction np of the scattering element  3620  is larger than or equal to an index of refraction n1 of the extractor element  3630 . The light-emitting element  3610  is located in an aperture of the planar reflector  3645  and emits light in the recovery cavity  3640 . 
     The rectangular scattering element  3620  is contained within a notional R O  semi-sphere. In some implementations, the R O  semi-sphere represents the Weierstrass sphere corresponding to the shorter of radius R11 of the first exit surface  3635 - 1  and radius R12 of the second exit surface  3635 - 2 . For the example illustrated in  FIG.  36   , the first exit surface  3635 - 1  is recessed relative to the second exit surface  3635 - 2  hence a radius R12 of the second exit surface  3635 - 2  is shorter than a radius R11 of the first exit surface  3635 - 1 . In this manner, the Weierstrass condition is satisfied for the second exit surface of the extractor  3635 - 2 . In some implementations, the R O  semi-sphere represents the Brewster sphere corresponding to the shorter of radius R11 of the first exit surface  3635 - 1  and radius R12 of the second exit surface  3635 - 2 . When R12 &lt; R11, the Brewster condition is satisfied for the second exit surface of the extractor  3635 - 2 . 
     To reduce potential TIR light losses at the step  3633  between the first  3635 - 1  and second  3635 - 2  exit surfaces of the extractor element  3630 , the step  3633  is formed as a two-sided mirror. As radius R12 of the second  3635 - 2  exit surface of the extractor  3330  satisfies the Weierstrass condition, most rays hitting the mirror of the step  3633  on the central side transmit through the first exit surface  3635 - 1  without TIR. All rays transmitted from the outer edge of the scattering element  3620  towards the upper edge of the second exit surface  3635 - 2  of the extractor  3630  hit the outside of the mirror of the step  3633  and are redirected in a backwards direction at &gt; 90° to the optical z-axis. An optional mirror  3650  that extends the recovery enclosure  3640  can turn most of these rays back into a forward direction (along the +z axis) as described below. 
     The mirror  3650  is arranged to extend the planar reflector  3645  that forms the recovery enclosure  3640 . Moreover, the mirror  3650  is shaped to couple at one end with the edge of the scattering element  3620  and at the other end with the edge of the second exit surface of the extractor element  3636 - 2 . As noted above, in the example illustrated in  FIG.  36   , the edge of the second exit surface of the extractor element  3636 - 2  extends below the plane formed by the planar reflector  3645 , and such that the edge of the second exit surface of the extractor element  3636 - 2  has angular coordinate that is larger than 90° with respect to the optical z-axis. In this case, the mirror  3650  includes two planar portions forming an angle with each. In other implementations, the mirror  3650  can be formed as a single, planar or curved (concave or convex) portion. In some cases, the mirror  3650  extends laterally farther out than the second exit surface  3635 - 2 , for example to a distance between R12 and R11, or to a distance of 1.2x, 1.5x or 2.0xR11. 
     In some implementations, the mirror at the step  3633  between the first  3635 - 1  and second  3635 - 2  exit surfaces of the extractor element  3630  can be extended and arranged to reflect light in the backwards direction (in the negative direction of the z-axis). The latter variations are of interest in a pendant design with a designated “down light” distribution in the forward direction (in the positive direction of the z-axis) and a defined “backward lobe” to illuminate the ceiling (in the negative direction of the z-axis.) 
       FIG.  37    shows an ASLV light-emitting device  3700  having a light-emitting element  3710  that includes multiple light-emitting devices of two or more chromaticities arranged on rectangular mount  3710 . The ASLV light-emitting device  3700  also has a step  3733  arranged between a first exit surface  3735 - 1  and a second exit surface  3735 - 2  of an extractor element  3730 . The size of the scattering element  3720  satisfies the Weierstrass condition. The multiple light-emitting devices of the light-emitting element  3710  can potentially be beneficial. For example, the light-emitting element  3710  can have multiple blue pumps to increase light output of the ASLV light-emitting device  3700 . As another example, the light-emitting element  3710  can have multiple blue pumps and red LEDs to improve the efficacy of a warm white luminaire. In the latter example, multiple blue pumps and red LEDs can be independently addressed. For instance, the top LEDs dominating the phosphor illumination at the center can be independently addressed from the side LEDs dominating the side lobes in order to tune color and intensity output by the ASLV light-emitting device  3700  independently for the forward and side lobes. Since all sources are within the scattering element  3720 , the far field intensity distribution can be color invariant. 
     Certain luminaire designs provide a bimodal distribution of light: a central down-cone of light in conjunction with a sheet of light directed sidewise and slightly backwards. The purpose of such a design is typically the dual function of down-light and ceiling illumination. As described below, ASLV devices that have a compound extractor can achieve such intensity distributions while keeping all the efficiency advantages presented by an ASLV light-emitting device. 
     As described above in this specification, certain ASLV designs maximize the forward light direction by using a Weierstrass geometry either as a truncated Weierstrass sphere (see, e.g., examples illustrated in  FIGS.  4 - 6   ) or as a Weierstrass shell (see, e.g., examples illustrated in  FIGS.  2  and  7   ). For maximum extraction of light from a light-emitting element that includes a blue pump and a phosphor element, rotational symmetry and Weierstrass geometry may represent the simplest design that exploits the contribution and value of the ASLV design. 
     Consider a semi-spherical scattering element illuminated by the Lambertian distribution of a light-emitting element described above in connection with  FIG.  2 A . It is believed that the central (top) region of the scattering element  220  will receive a higher level of radiation density than the outer perimeter. However, the light that is back-scattered from the scattering element  220  will be scattered again by the diffuse reflector  245  back into the scattering element  220 . In this manner, the above-noted center-to-edge difference in illumination of the scattering element  220  will be reduced. While specific designs can be configured using optical design software, for example, one should end up with an intensity distribution radiating from the scattering element  220  that is (1) radially symmetric, (2) its brightness is decreasing from center to edge and (3) its angular distribution should be reproducible from device to device. 
       FIG.  38    shows a schematic diagram of another example of an ASLV light-emitting device  3800  configured to meet the above requirements. The ASLV light-emitting device  3800  includes a light-emitting element  3810 , a scattering element  3820  (also referred to as a first optical element), an extractor element  3830  (also referred to as a second optical element), and a recovery enclosure  3840 . 
     The light-emitting element  3810  is configured to produce and emit light during operation. A spectral power distribution of light emitted by the light-emitting element  3810  (also referred to as pump light) can be blue, for instance. The spectral power distribution for visible light is referred to as chromaticity. The scattering element  3820  has a first surface (also referred to as a light-entry surface) spaced apart from the light-emitting element  3810  and positioned to receive the light from the light-emitting element  3810 . The scattering element  3820  includes scattering centers arranged to substantially isotropically scatter the light from the light-emitting element  3810  and to provide scattered light. The scattered light includes elastically scattered pump light and inelastically scattered pump light. Spectral power distribution of the elastically scattered light is the same as the spectral power distribution of the pump light, and spectral power distribution of the inelastically scattered light can be yellow, for instance. A spectrum  111  of the elastically scattered pump light and a spectrum  113  of the inelastically scattered pump light are shown in  FIG.  1 B  along with a spectrum  115  of the scattered light. 
     Referring again to  FIG.  38   , the extractor element  3830  is formed from a transparent and is in contact with the scattering element  3820 , such that there is an optical interface between the scattering and extractor elements at the place of contact, and the optical interface is opposite the first surface of the scattering element. Moreover, the extractor element  3830  is arranged so that light scattered through the optical interface enters the extractor element  3830 . In addition, the extractor element  3830  includes a first portion and a light guide. The first portion has an exit surface and is arranged to receive a first portion of the scattered light from the optical interface. In some implementations, the exit surface of the first portion is a transparent surface that is shaped such that an angle of incidence at the exit surface of the first portion of the scattered light that directly impinges on the exit surface of the first portion is less than the critical angle for total internal reflection. In this case, the first portion of the extractor element  3830  is said to satisfy the Weierstrass condition, as described above in connection with  FIG.  1 A . In some implementations, the exit surface of the first portion is shaped such that an angle of incidence at the exit surface of the first portion of the scattered light that directly impinges on the exit surface of the first portion is less than the Brewster angle. In this case, the first portion of the extractor element  3830  is said to satisfy the Brewster condition, as described above in connection with  FIG.  1 A . 
     The exit surface is generally a curved, transparent surface. In other words, changes in the scattered light passing through the exit surface can generally be described by Snell’s law of refraction, as opposed to, for example, an opaque or diffuse surface where scattering of transmitted light occurs. The light guide is arranged to receive a second portion of the scattered light from the optical interface. Moreover the light guide has a guiding surface configured to guide the received second portion of the scattered light away from the optical interface by reflecting at least some of the received second portion of the scattered light. 
     Further, the ASLV light-emitting device  3800  includes a medium adjacent the first surface of the scattering element having a refractive index n0, and the scattering element  3820  includes a material having a first refractive index n1, where n0 &lt; n1. The transparent material has a refractive index n2, where n0 &lt; n2. Furthermore, the recovery enclosure  3840  encloses the medium adjacent the first surface of the scattering element. The recovery enclosure  3840  is arranged and configured to recover a portion of the scattered light that propagates through the first surface into the medium. The ASLV light-emitting device  3800  outputs scattered light through the exit surface into the ambient environment. As described above, the light output by the ASLV light-emitting device  3800  has a spectral power distribution corresponding to the spectrum  115  shown in  FIG.  1 B . 
     In some implementations, the first portion intersects an optical axis of the light-emitting element  3800 . In some implementations, a reflective coating is disposed on the guiding surface. The reflective coating is configured to reflect the at least some of the received second portion of the scattered light. In some implementations, the light guide is configured to reflect the at least some of the received second light via total internal reflection. In some implementations, the light guide is configured to output predetermined amounts of light at predetermined distances from the light-emitting element  3810  through the guiding surface. For example, the guiding surface has a surface texture configured to extract the predetermined amounts of light. As another example, the light guide includes centers configured to scatter light such that the predetermined amounts of light are emitted at the predetermined distances from the light-emitting element  3810  through the guiding surface. In some implementations, the light guide has a distal surface configured to output at least a fraction of the at least some of the received second portion of the scattered light. 
       FIG.  39    shows an ASLV light-emitting device  3900  having a compound extractor element. An intensity distribution output by the ASLV light-emitting device  3900  can be partitioned in two parts. Part 1 includes a central part of the intensity distribution that is extracted through a first portion of the compound extractor  3930 - 1  in the form of a truncated Weierstrass shell. In this example, the central part of the intensity distribution is shaped as a 90° cone. Part 2, the balance of the intensity distribution that is not in the central cone, is wave-guided sideways through a light guide of the compound extractor  3930 - 2  to an exit surface of the light guide  3935 - 2 / 3935 - 2 ′. In this example, a reflector  3945 , which along with the scattering element  3920  forms a recovery enclosure  3940  of the ASLV light-emitting device  3900 , extends to the exit surface of the light guide  3935 - 2 / 3935 - 2 ′. In this manner, the light scattered by the scattering element  3920  into the light guide  3930 - 2  is guided to the exit surface  3935 - 2 / 3935 - 2 ′ via (i) TIR at a guiding surface  3937  and (ii) reflection at the extension of the reflector  3945 . 
     A shape of the exit surface of the light guide  3935 - 2 / 3935 - 2 ′ determines the Part 2 of the intensity distribution output by the ASLV light-emitting device  3900 . In this manner, the exit surface of the compound extractor includes a central portion of the exit surface  3935 - 1  corresponding to the Weierstrass portion of the compound extractor  3930 - 1 , and a side portion of the exit surface  3935 - 2 ,  3935 - 2 ′ corresponding to the output surface of the light guide  3930 - 2 . These two portions of the exit surface of the compound extractor  3935 - 1 ,  3935 - 2 / 3935 - 2 ′ can yield a bi-modal intensity distribution of the light output by the ASLV light-emitting device  3900 . For example, a particular configuration of the exit surface of the light guide  3935 - 2 ′ can yield a slightly backwards directed cone of light exiting at  95 - 110  degrees relative to the optical axis in order to illuminate a large part of the ceiling. 
     In some embodiments, the light emitted from the scattering element  3920  is split into more than two parts with radial symmetry or into parts that result in an elliptical or other asymmetric intensity distribution in directions (x or y) perpendicular to the optical z-axis. 
     There are several degrees of freedom in shaping the light pattern output by the ASLV light-emitting device  3900 . For example, as described above, the angle of the central portion of the compound extractor  3930 - 1  determines a ratio of central cone to side intensity distribution. Outer radius and thickness of the Weierstrass portion of the compound extractor  3930 - 1  can be varied to optimize axial collimation (along the z-axis.) Deviations from rotational symmetry of the light guide of the extractor element  3930 - 2  guiding the side-light may be used to provide a variety of distribution patterns of the side-light. The shape or surface structure of the exit surfaces  3935 - 2 / 3935 - 2 ′ for the side light can be used to tailor the intensity distribution of the guided side-light. In the example illustrated in  FIG.  39   , a first portion of the exit surface of the light guide  3935 - 2  is arranged at a predetermined angle with respect to the optical z-axis of the ASLV light-emitting device  3900 , and a second portion of the output surface of the light guide  3935 - 2 ′ is arranged at a different angle from the predetermined angle and is configured with non-zero optical power. 
       FIG.  40    shows another ASLV light-emitting device  4000  having a compound extractor element that includes a central portion  4030 - 1  and a light guide  4030 - 2 . In this example, the central portion of the compound extractor  4030 - 1  of the ASLV light-emitting device  4000  spans a cone angle of about 60°. Moreover, an exit surface of the central portion  4035 - 1  satisfies the Weierstrass condition. In this example, a reflector  4045 , which along with the scattering element  4020  forms a recovery enclosure  4040  of the ASLV light-emitting device  4000 , extends to the exit surface of the light guide  4035 - 2 / 4035 - 2 ′. In addition, a guiding surface of the light guide  4037  is coated with a reflective layer. In this manner, the light scattered by the scattering element  4020  into the light guide  4030 - 2  is guided to the exit surface  4035 - 2 / 4035 - 2 ′ via reflections at the guiding surface  4037  and at the extension of the reflector  4045 . 
     A first portion of the exit surface of the light guide  4035 - 2  includes a lens array, e.g., a fly-eye lens, and a second portion of the exit surface of the light guide  4035 - 2 ′ is configured to diffuse the output light. For example, the second portion of the exit surface  4035 - 2 ′ is configured to include indentations, scratches, pits, and the like. 
       FIG.  41    shows an example of a fabrication approach for the central section of the compound extractor  4130 - 1  of an ASLV light-emitting device  4100 . The first step involves molding the side extractor  4130 - 2  and the center extractor  4130 - 1 . The side extractor  4130 - 2   contains a semi-spherical enclosure  4140  where the scattering element  4120  will be deposited. Further, the side extractor  4130 - 2  contains an alignment indentation  4125  where the center extractor  4130 - 1  will mate with the side extractor  4130 - 2 . Next, one can evaporate or glue a top reflector  4137  on the side extractor  4130 - 2 . Next, one can deposit the scattering element  4120  in the enclosure  4140 . Next, one can glue the bottom reflector  4145  with proper reference points to assure that a hole  4105  in the reflector is aligned with the optical z-axis. The final step of the assembly involves a void-free gluing of the center extractor  4130 - a  to the side extractor  4130 - 2  at the indentation  4125 . The exit surfaces of the side extractor  4130 - 2  can either be molded or, if their structure is consistent with flexible tape, the exit surfaces can be glued onto the side walls using void-free index matching glue. 
     ASLV light-emitting devices using a compound extractor (as described above in connection with  FIGS.  39 - 40   ) may be more efficient than light-emitting devices using conventional designs. ASLV designs may avoid scattering 50% or more of the light (e.g., blue and the other colors) back into the LED chips with its losses related to extraction efficiency. In the Weierstrass shell geometry of an ASLV light-emitting device (as described above in connection with  FIG.  2 A , for instance) practically all of the backscattered light is reflected back into the scattering element with one and only one reflection. Only a small fraction of around 10% (depending on geometry) of the back-scattered light hits the chip or other package related surfaces with a chance of getting absorbed. 
     Further, ASLV light-emitting devices using a compound extractor (as described above in connection with  FIGS.  39 - 40   ) may be smaller than light-emitting devices using conventional designs. The radius of the ASLV recovery enclosure may be as small as 5 mm for a Rebel type lamp containing a 1×1 mm 2  chip or as small as 8 mm for a 3×3 mm 2  chip array. Depending on the design of the center extractor alignment mechanism, the thickness of the lateral light guide or side extractor could be as small as cavity radius plus 2 mm. 
     Furthermore, ASLV light-emitting devices using a compound extractor (as described above in connection with  FIGS.  39 - 40   ) may be more modular than light-emitting devices using conventional designs. While a one chip 1×1 mm 2  can be used in 100-500 1 m applications, depending on life expectancy, a 3×3 mm 2  array can serve 2-3 klm applications. In addition multiple ASLV devices can be used in one- or two-dimensional arrays to meet the design demands for a large variety of applications. 
     In addition, ASLV light-emitting devices using a compound extractor (as described above in connection with  FIGS.  39 - 40   ) may have more design flexibility than light-emitting devices using conventional designs. With a cross sectional source area of 25-64 mm 2  and a well-behaved and predictable radiation pattern in the range of 3-6°sr, one has a lot of flexibility in designing an intensity distribution pattern for a variety of applications. 
     Moreover, ASLV light-emitting devices using a compound extractor (as described above in connection with  FIGS.  39 - 40   ) may have lower cost than light-emitting devices using conventional designs. The cost of a lighting system (w/o installation) is determined, generally, by (a) source cost, (b) voltage converter or ballast, (c) precision required for components and their assembly and (d) by the size and weight of the final enclosure. The combination of LED sources with the ASLV-based spectrally independent intensity distribution, gives one a low cost solution for (a) and (c). The low power consumption of LEDs are expected to eventually result in the lowest cost for (b). The final enclosure (d) may still have to be as big as for conventional lighting for reasons of glare control, but the superior internal control of intensity distribution may make enclosure specifications less critical and, therefore, significantly cheaper and result in a better intensity distribution control. 
     Currently, linear fluorescent tubes are widely used for general illumination of indoor spaces. Any efficient SSL source that can imitate or improve the intensity distribution of these tubes is of great interest to the lighting industry. 
     While many of the foregoing embodiments are rotationally symmetric about an axis, e.g., the z-axis, other configurations are also possible. For example, ASLV light-emitting devices incorporating features of above-described embodiments may be ASLV light-emitting devices that are elongated along the y-axis. Hence, rather than an x-z cross-section of a device being rotationally-invariant, the x-z cross-section of an extended device can be translationally invariant in the direction of the extension, e.g., the direction of the y-axis. 
     As discussed previously, elongated embodiments of ASLV light-emitting devices are also contemplated. For example, ASLV light-emitting devices incorporating features of above-described embodiments having the form factor of a conventional fluorescent tube are possible.  FIG.  42    shows an example of an elongated ASLV light-emitting device  4200  having multiple scattering elements  4220  with rotational symmetry around the z-axis and a common, elongated extractor element  4230 . In this example, the extractor element  4230  is composed of a semi-cylindrical rod with indentations  4240  for each single or cluster of LEDs  4210 . The semi-spherical indentations  4240  with the scattering element  4220  on the inside and air gap  4240  between phosphor and LED, represents a hybrid ASLV device. In the radial plane x-z, the hybrid ASLV device works just like the ASLV device described above in connection with  FIG.  2 A . In this manner, most light propagating through the hybrid ASLV device is transmitted on first pass in the x-z plane. 
     In the longitudinal direction (along the y-axis) a large fraction of the scattered light from the scattering element  4220  can be trapped in the extractor element  4230  as wave-guided modes. To convert these wave-guide modes into escape modes, a reflector  4245  on the backside of the semi-cylindrical rod is configured to have a significant degree of diffusivity, i.e. 10-50%. For example, commercially available reflectors can maintain a 97% reflectivity from 12-82% diffusivity. With the proper choice of diffusivity, one can find a design with not more than 3-5 reflections on the backside reflector  4205  of the semi-cylindrical extractor  4230 . Such an ASLV light-emitting device  4200  with a forward biased angular distribution (in the z-direction) can be superior to the luminaire losses based on omnidirectional fluorescent tubes. 
       FIG.  43    shows an ASLV light-emitting device  4300  having an elongated scattering element  4320  and an elongated extractor element  4330 . In this example, the extractor element  4330  is composed of a semi-cylindrical shell with phosphor coverage (that forms the elongated scattering element  4320 ) on the inside over the entire length of the ASLV light-emitting device  4300 . The same mode conversion issue in the longitudinal direction (along the y-axis) that is encountered in the ASLV light-emitting device  4200  also is present in the ASLV light-emitting device  4300 . However, with a reflectivity of 97-98% and an available range of diffusivity from 5-82%, it is believed that superior performance to the omnidirectional linear tubes is achievable. 
     In order to avoid bending of the semi-cylindrical rod/shell both during extrusion/molding and over the temperature range seen during operation, the ASLV light-emitting device  4300  can be fabricated four 1 ft pieces, for instance, that are mounted onto a stiff extruded 4 ft heat sink (e.g., fabricated from Al) covering the entire length of the light-emitting device  4300 . 
     The phosphor consumption of for the ASLV light-emitting device  4200  relative to the ASLV light-emitting device  4300  is lower by the ratio of s/2R, where s denotes the distance between LEDs or LED clusters, and R denotes the inside radius of indentation/grove (4240/4340). 
     Linear light uniformity of a  3600  1 m tube can be achieved with 4-6 elements per linear foot, such that the LED spacing is between 3 and 4 inches. In this manner, 150-225 1 m per LEDs or LED cluster is needed. At today’s performance, the above spec can be achieved with 2 W commercially available LED pumps. 
     In some embodiments, it may be beneficial to reduce (e.g., minimize) the re-entry of photons from the extractor  4330  back into the scattering element  4320 . In the ASLV light-emitting device  4300 , for example, a photon propagating in the longitudinal direction (along the y-axis) within the extractor element  4330  has a very high probability to be TIR back into the scattering element  4320  if this scattering element  4320  covers a cylindrical surface along the entire length of the tube  4330 . In the ASLV light-emitting device  4200 , the scattering element 4220′ at the next LED position is relatively far away relative to a scattering element  4220  of a given LED position, and hence, a longitudinal photon originating at the scattering element  4220  of the given LED has a good chance to be kicked out of the tube  4230  before reaching the next LED position. Therefore, the ASLV light-emitting device  4200  may have lower phosphor related losses than the ASLV light-emitting device  4300 . 
     If light originated at the scattering element  4320  in the ASLV light-emitting device  4300  undergoes several TIR reflections back into the phosphor element  4330 , then it will be depleted of blue photons and the spectral composition of the light will change towards a lower CCT with distance from the blue pump in the longitudinal direction (along the y-axis). This CCT change may not amount to much when the LED spacing is short, i.e. 1-2 times the outer diameter of the cylindrical extractor element  4330 . But it could become an issue when a small number of power-LEDs are used with 6 or more inch separation. Accordingly, in embodiments that feature LED separation of about 6 inches or more, it may be beneficial to compensate for spectral variation along the length of the ASLV light-emitting device  4300  (e.g., by varying the composition of the extractor element  4330  along its length and/or by introducing additional sources of diffusion into the ASLV light-emitting device  4300 ). 
     Other embodiments are in the following claims.