Abstract:
A lens comprises a bottom surface, a reflecting surface, a first refracting surface obliquely angled with respect to a central axis of the lens, and a second refracting surface extending as a smooth curve from the bottom surface to the first refracting surface. Light entering the lens through the bottom surface and directly incident on the reflecting surface is reflected from the reflecting surface to the first refracting surface and refracted by the first refracting surface to exit the lens in a direction substantially perpendicular to the central axis of the lens. Light entering the lens through the bottom surface and directly incident on the second refracting surface is refracted by the second refracting surface to exit the lens in a direction substantially perpendicular to the central axis of the lens. The lens may be advantageously employed with LEDs, for example, to provide side-emitting light-emitting devices. A lens cap attachable to a lens is also provided.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This invention is related to U.S. patent application Ser. No. 09/849,042 filed May 4, 2001, entitled “Side Emitting LED,” and to U.S. patent application Ser. No. 09/849,084 filed May 4, 2001, entitled “LED Lens”. Both of these applications are assigned to the assignee of the present invention and incorporated herein by reference in their entirety. 
    
    
     FIELD OF THE INVENTION 
     This invention relates generally to light emitting devices and more particularly to side emitting light emitting diodes (LEDs). 
     BACKGROUND 
     FIG. 1A illustrates a conventional LED package  10 . LED package  10  has a hemispherical lens  12  of a type well-known in the art. Package  10  may also have a reflector cup (not shown), in which an LED chip (not shown) resides, that reflects light emitted from the bottom and sides of the LED chip toward the observer. In other packages, other types of reflectors reflect the LED chip&#39;s emitted light in a particular direction. 
     Lens  12  creates a field of illumination  14  roughly along a longitudinal package axis  16  of LED package  10 . The vast majority of light emitted from an LED package  10  with a hemispherical lens  12  is emitted upwards away from LED package  10  with only a small portion emitted out from the sides of LED package  10 . 
     FIG. 1B illustrates a known light emitting diode (LED) package  30  with a longitudinal package axis  26 . LED package  30  includes an LED chip  38 , a lens  32  with straight vertical sidewall  35  and a funnel-shaped top surface  37 . There are two main paths in which the light will travel through package  30 . The first light path P 1  is desirable with the light emitted from chip  38  and traveling to surface  37  where total internal reflection (TIR) causes the light to exit through sidewall  35  at approximately 90 degrees to the longitudinal axis. The second light path P 2  is light emitted from chip  38  towards sidewall  35  at an angle causing TIR or a reflection from sidewall  35  causing the light to exit package  30  at an angle not close to perpendicular to the longitudinal axis. This path is not desirable and limits the efficiency of side extracted light. 
     FIG. 2 illustrates the conventional LED package  10  of FIG. 1 coupled along an edge of a portion of a refractive light guide  20 . LED package  10  is positioned on the edge of light guide  20  along the width of light guide  20 . Light rays R 1 , R 2 , R 3  emitted by LED package  10  are propagated along the length of light guide  20 . FIG. 3 illustrates a plurality of conventional LED packages  10  positioned along the width of light guide  20  of FIG.  2 . These conventional LED/light guide combinations are inefficient as they require a large number of LED packages  10  to illuminate the light guide and result in coupling inefficiencies due to relatively small acceptance angles. These conventional LED packages  10  must be arranged along the entire length of one side of light guide  20  to fully illuminate light guide  20 . 
     A need exists for an LED package to couple efficiently to shallow reflectors and thin light guides. A need also exists for an LED package to allow these secondary optical elements to have relatively large illuminated areas. 
     SUMMARY 
     In accordance with one embodiment, a lens comprises a bottom surface, a reflecting surface, a first refracting surface obliquely angled with respect to a central axis of the lens, and a second refracting surface extending as a smooth curve from the bottom surface to the first refracting surface. Light entering the lens through the bottom surface and directly incident on the reflecting surface is reflected from the reflecting surface to the first refracting surface and refracted by the first refracting surface to exit the lens in a direction substantially perpendicular to the central axis of the lens. Light entering the lens through the bottom surface and directly incident on the second refracting surface is refracted by the second refracting surface to exit the lens in a direction substantially perpendicular to the central axis of the lens. 
     The inventive lens may be advantageously employed to provide side-emitting light-emitting devices that may be used with light guides and reflectors that have very thin profiles and/or large illuminated areas. 
     In accordance with another embodiment, a light-emitting device comprises a light-emitting semiconductor device and a lens. The lens comprises a bottom surface, a reflecting surface, a first refracting surface obliquely angled with respect to a central axis of the lens, and a second refracting surface extending as a smooth curve from the bottom surface to the first refracting surface. Light emitted by the semiconductor device, entering the lens through the bottom surface, and directly incident on the reflecting surface is reflected from the reflecting surface to the first refracting surface and refracted by the first refracting surface to exit the lens in a direction substantially perpendicular to the central axis of the lens. Light emitted by the semiconductor device, entering the lens through the bottom surface, and directly incident on the second refracting surface is refracted by the second refracting surface to exit the lens in a direction substantially perpendicular to the central axis of the lens. 
     The inventive light-emitting device may be efficiently coupled to shallow reflectors and to thin light guides. Secondary optics employed with the inventive light-emitting device may have relatively large illuminated areas. 
     In accordance with another embodiment, a lens cap comprises a bottom surface attachable to a lens, a reflecting surface, a first refracting surface obliquely angled with respect to a central axis of the lens cap, and a second refracting surface extending as a smooth curve from the bottom surface to the first refracting surface. Light entering the lens cap through the bottom surface and directly incident on the reflecting surface is reflected from the reflecting surface to the first refracting surface and refracted by the first refracting surface to exit the lens cap in a direction substantially perpendicular to the central axis of the lens. Light entering the lens cap through the bottom surface and directly incident on the second refracting surface is refracted by the second refracting surface to exit the lens cap in a direction substantially perpendicular to the central axis of the lens cap. The inventive lens cap may provide advantages similar to or the same as those described above. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1A illustrates a conventional LED package. 
     FIG. 1B illustrates another conventional LED package. 
     FIG. 2 illustrates a cross-sectional view of a conventional edge-illuminated light guide. 
     FIG. 3 illustrates a perspective view of the light guide of FIG.  2 . 
     FIG. 4 illustrates one embodiment of the invention. 
     FIG. 5A illustrates a cross-sectional view of the LED package of FIG.  4 . 
     FIG. 5B illustrates a cross-sectional view of the lens mating to the housing of the LED package base. 
     FIG. 5C illustrates a close-up of the lens/housing mating of FIG.  5 B. 
     FIG. 5D illustrates a cross-sectional view of a lens cap mating to an LED package. 
     FIG. 5E illustrates ray-traces of one embodiment of a lens. 
     FIG. 5F illustrates ray-traces of another embodiment of a lens. 
     FIG. 5G illustrates ray-traces of a further embodiment of a lens. 
     FIG. 6 illustrates side-emission of light from the LED package of FIG.  4 . 
     FIG. 7A illustrates a cross-sectional view of the side-emission of light from the LED package of FIG. 4 into two light guides. 
     FIG. 7B illustrates a cross-sectional view of the LED package of FIG. 4 inserted into a blind hole in a light guide. 
     FIG. 7C illustrates a cross-sectional view of the LED package of FIG. 4 inserted into a through hole in a light guide. 
     FIG. 7D illustrates a cross-sectional of the LED package of FIG. 4 inserted into a through hole in a light guide that is thinner than the height of the LED package. 
     FIG. 8 illustrates a perspective view of a light guide. 
     FIG. 9A illustrates a cross-sectional view of the LED package of FIG. 4 mounted in a blind-hole of a light guide. 
     FIG. 9B illustrates a cross-sectional view of the LED package of FIG. 4 mounted in a blind-hole of a light guide. 
     FIG. 9C illustrates a cross-sectional view of the LED package of FIG. 4 mounted in a blind-hole of a light guide. 
     FIG. 10 illustrates a cross-sectional view of the LED package of FIG. 4 mounted in a through-hole of a light guide. 
     FIG. 11 illustrates a conventional LED package coupled to a reflector. 
     FIG. 12 illustrates the LED package of FIG. 4 in combination with a shallow reflector. 
     FIG. 13 illustrates a cross-sectional view of a light-emitting device in accordance with another embodiment. 
     FIG. 14 illustrates ray traces through the lens illustrated in FIG.  13 . 
     FIG. 15 illustrates a cross-sectional view of the lens illustrated in FIG. 13 superimposed over a cross-sectional view of a lens in accordance with another embodiment. 
     FIG. 16 illustrates a cross-sectional view of a lens cap mating to an LED package in accordance with another embodiment. 
    
    
     Use of the same reference symbols in different figures indicates similar or identical items. It should be noted that the dimensions in the figures are not necessarily to scale. 
     DETAILED DESCRIPTION 
     FIG. 4 illustrates an example of a side emitting LED package  40  in accordance with one embodiment of the invention. LED package  40  includes a longitudinal package axis  43 , an LED package base  42  and a lens  44 . Lens  44  is coupled to LED package base  42 . Longitudinal package axis  43  passes through the center of LED package base  43  and lens  44 . As seen in FIG. 5A, a surface of LED package base  42  supports an LED chip  52  (a semiconductor chip having a light emitting pn junction) for generating light. LED chip  52  may be one of any number of shapes, including but not limited to a truncated inverted pyramid (TIP) (shown), cube, rectangular solid, or hemisphere. LED chip  52  includes a bottom surface that may be in contact with, or coated with, a reflective material. Although LED chip  52  may emit light from all of its sides, base  42  is generally configured to reflect emitted light upwards towards lens  44  along the longitudinal axis of the package. Such bases are conventional and may include a parabolic reflector in which LED chip  52  resides on a surface of package base  42 . One such package is shown in U.S. Pat. No. 4,920,404, assigned to the present assignee and incorporated herein by reference. 
     Lens  44  may be manufactured as a separate component using a number of well-known techniques such as diamond turning (i.e., the lens is shaped by a lathe with a diamond-bit), injection molding, and casting. Lens  44  is made of a transparent material, including but not limited to cyclic olefin copolymer (COC), polymethylmethacrolate (PMMA), polycarbonate (PC), PC/PMMA, silicones, fluorocarbon polymers, and polyetherimide (PEI). Lens  44  includes an index of refraction (n) ranging from between about 1.35 to about 1.7, preferably about 1.53, but could have an index of refraction higher or lower based on the material used. In the alternative, lens  44  may be formed onto LED package base  42  and LED chip  52  by various techniques including but not limited to injection molding (e.g., insert molding), and casting. 
     There is a volume  54  between lens  44  and LED chip  52 . Volume  54  may be filled and sealed to prevent contamination of LED  52  using silicone. Volume  54  may also be in a vacuum state, contain air or some other gas, or be filled with an optically transparent material, including but not limited to resin, silicone, epoxy, water or any material with an index of refraction in the range of, for example, about 1.35 to about 1.7 that may be injected to fill volume  54 . The material inside volume  54  may be colored to act as a filter in order to allow transmission of all or only a portion of the visible light spectrum. If silicone is used, the silicone may be hard or soft. Lens  44  may also be colored to act as a filter. 
     Lens  44  includes a refractive portion  56  (which may, but does not necessarily, include one or more sawteeth as shown) and a total internal reflection (TIR) funnel portion  58 . The sawtooth portion  56  is designed to refract and bend light so that the light exits from lens  44  as close to 90 degrees to the longitudinal package axis  43  as possible. The sawteeth or refractive surfaces  59  of the sawtooth portion  56  are all light transmissive. Any number of sawteeth  59  may be used within a sawtooth portion of a given length. Lens  44  may be formed as a single piece or, in the alternative, as separate components coupled together. 
     Funnel portion  58  is designed to have a TIR surface. The TIR surface reflects light such that light exits from lens  44  as close to 90 degrees to a longitudinal package axis  43  of LED package  40  as possible. In one implementation, approximately 33% of the light emitted from LED chip  52  is reflected off the TIR surface of funnel-shaped portion  58  of lens  44 . A metallization layer (e.g., aluminum) may be placed on top of funnel portion  58  to prevent light transmission through the TIR surface. A coating or film (e.g., a U.V. inhibitor) may be placed on top of the funnel portion  58  to prevent degradation of the lens as PC degrades in the presence of U.V. light. 
     The interface between lens  44  and LED package base  42  may also be sealed using any well-known sealant, such as Room Temperature Vulcanizing (RTV) or the like. 
     FIG. 5B illustrates a cross-sectional view of alternative mating of lens  44  to housing  46  of LED package base  42 . For clarity, LED chip  52  and other features of base  42  are not shown. Lens  44  may also be attached to LED package base  42  by various attachment methods, including but not limited to snap-fitting, friction-fitting, heat staking, adhesive bonding, and ultra-sonic welding. The features of lens  44 , as shown in FIG. 5B, are applicable to lenses that are either formed as a separate component or encapsulated onto LED package base  42 . FIG. 5C illustrates a close-up of the lens/housing mating of FIG.  5 B. Surface S may snap fit into surface R. Surface S may friction fit tight with surface R. Surface T may be welded to surface U using various methods including, without limitation, plastic welding, sonic welding, and linear welding. Sealing or bonding involves several possible combinations, such as surface S and/or T of lens  44  being sealed/bonded to surface R and/or U of housing  46 . 
     FIG. 5D illustrates a cross-sectional view of a lens cap  55  mating to a conventional LED package  10  with a hemispherical lens  12 . Lens cap  55  may be affixed to lens  12  of LED package  10  by an optical adhesive, for example. Lens cap  55  includes a refractive portion  56  (which may, but does not necessarily, include one or more sawteeth as shown) and reflective funnel portion  58  that may contain the same and/or similar features that operate in the same and/or similar manner, as described above and below, as refractive and TIR portions  56 ,  58  of lens  44 . 
     FIGS. 5E,  5 F and  5 G illustrates ray-traces of light through lenses of various curvatures on the top surface of the lens. The features shown in FIGS. 5E-5G are applicable to lenses that are injection molded, cast or otherwise formed. In one implementation, approximately 33% of the light emitted from LED chip  52  (not shown; light is shown emitted from die focal point F) is reflected off the TIR surface I. FIG. 5E illustrates a curved funnel-shaped portion  58  where Surface I is defined from a curve that maintains an angle greater than the critical angle for TIR but directs the light out of the lens roughly at 90 degrees to longitudinal package axis  53 . FIG. 5F illustrates a bent-line funnel-shaped portion  58  where Surface I is defined from a line bent into two linear portions, each portion at an angle greater than the critical angle for TIR but directs the light out of the package roughly at 90 degrees to the package axis. FIG. 5G illustrates a linear funnel-shaped portion  58  where Surface I is defined by a straight line at an angle greater than the critical angle for TIR but directs the light out of the package roughly at 90 degrees to the package axis. 
     In FIGS. 5E-5G, Surface H works with surface I to emit light perpendicular to longitudinal package axis  53 . The angle defined by surface I relative to the die is roughly 80 degrees. Surfaces A, B, C, D &amp; E have surface normals such that the incident light ray is refracted out of the lens at approximately 90 degrees to the longitudinal package axis  53 . Surfaces F, G &amp; H are approximately parallel to direct incident light rays in order to minimize the amount of direct light transmitted through these surfaces. Surfaces below line N refract light out of the package. Surfaces above line M will direct light out of the lens through a combination of TIR and refraction. Lines&#39;s M &amp; N need to be in close proximity of each other to optimize side emission and minimize emission in the longitudinal direction. FIGS. 5E-5G show two zones: zone refraction at approximately 45 degrees or more from longitudinal package axis  53  and zone TIR/refraction at up to approximately 45 degrees from longitudinal package axis  53 . For example, in FIGS. 5E-5G, an approximately 40 degree TIR/refraction zone is shown. The interface between the two zones is approximately 45 degrees from the longitudinal package axis  53 . A distance X between Line M and Line N is kept at a minimum in order to optimize the side extraction of light from the lens. Line M may equal Line N (i.e., X=0). 
     FIG. 6 illustrates a cross-section of the emission of light from LED package  40  of FIG.  4 . Lens  44  of LED package  40  creates a radiation pattern  62  roughly perpendicular to longitudinal package axis  66  of LED package  40 . In FIG. 6, this radiation pattern  62  is approximately perpendicular to LED package axis  66  and illustrates relative light intensity and distribution. This field of illumination  62  surrounds LED package  40  and is roughly disk-or toroidal-shaped. Light is emitted from lens  44  approximately parallel to an optical plane  64 . 
     The side-emission of light allows even a single LED package  40  to illuminate multiple light guides  72 , as seen in FIG. 7A, for example. FIG.  7 A. illustrates two planar light guides placed nearly end-to-end with space for at least one LED package  40  between light guides  72 . The side-emission of light from the LED package  40  allows light to enter each light guide  72 . The LED package  40  may also be inserted into the body of light guide  72 . Light guides of various shapes may be used. The sides along the length of the light guides may be planar or taper. For example, a single side emitting LED package  40  may be placed at the center of a disk-shaped light guide (not shown). As light is emitted from the side of LED package  40  over 360 degrees (i.e., in all directions from the center of LED package  40 ), the light enters the light guide and is refracted and reflected throughout the entire light guide (not shown). 
     The light guide can be made from optically transmissive materials, including but not limited to PC or PMMA. The light guide may be of constant thickness or tapered. Side emission of light allows efficient illumination of thin light guides with a thickness in the optimum range of 2 to 8 mm. FIG. 7B illustrates an example of a light guide  73  with a thickness of 5.0 mm which is greater than the height of lens  44 . As the thickness of light guide  73  is greater than the height of the lens  44 , a blind-hole  94  may be used in light guide  73  to allow coupling of the LED package  40 . The dimensions of lenses  44  of FIGS. 7B,  7 C &amp;  7 D are measured from the focal point F of lens  44 . FIG. 7C illustrates an example of a light guide  75  with a thickness of 4.5 mm and equal to the height of lens  44 . As the thickness of light guide  75  is equal to the height of lens  44 , a through-hole  96  may be used in light guide  75  to allow coupling of LED package  40 . FIG. 7D illustrates side-emission of light from the LED of FIG. 4 into a light guide  77  thinner than the height of lens  44 . As the thickness of light guide  77  is less than the height of lens  44 , a through-hole  96  must be used in the light guide  77  to allow coupling of LED package  40 . Even though light guide  77  is thinner than the height of lens  44 , a large portion of the light emitted from LED chip  52  will still be directed into light guide  77  as the bulk of the light emitted from LED chip  52  is emitted from the sides of lens  44 . The large portion of the light emitted from lens  44  is targeted toward a light guide  77  that is positioned midway up the height of the lens. For example, the light emitted out the side of lens  44  near the top will be directed slightly downward and the light emitted out the side of lens  44  near the bottom will be directed slightly upward. The portion of light directed into light guide.  77  decreases as the thickness of light guide  77  relative to lens  44  decreases. Light guide  77  may be any shape including, without limitation, straight, tapered, rectangular, round or square. 
     It should be understood that the dimensions shown in FIGS. 7B-7D are meant to be illustrative but not limiting. In other implementations lenses and light guides may have dimensions either larger or smaller than those of the illustrated implementations. 
     FIG. 8 illustrates a perspective view of an end-portion of a planar light guide  82 . The side emitting LED package  40  allows LED package  40  to be placed inside light guide  82 . One or more holes  86  are made in the body of light guide  82  with a corresponding number of LED assemblies  40  placed within holes  86 . Holes  86  may be made to any desired depth in light guide  82 , including but not limited to the entire thickness of light guide  82 . Lens  44  of LED package  40  may not touch light guide  82 . A reflective coating or film  84  may be placed on at least one of the ends of light guide  82  to increase the internal illumination of light guide  82 . 
     FIG. 9A illustrates a side-emitting LED package  40  mounted in a blind-hole  94  of a planar light guide  82 . Top surface  91  of blind-hole  94  is approximately parallel with top surface  95  of planar light guide  82 . Top surface  91  of blind-hole  94  may be coated with a reflective coating or film to reflect light in order to allow for a thinner light guide package with a similar coupling efficiency. 
     FIG. 9B illustrates a side-emitting LED package  40  mounted in a funnel-shaped blind-hole  98  of a planar light guide  82 . The top surface  93  of funnel-shaped blind-hole  98  is approximately parallel with funnel-shaped portion  58  of lens  44  of LED package  40 . Top surface  93  of blind-hole  98  may be coated to reflect light in order to allow for a thinner light guide package with a similar coupling efficiency. The blind hole can have a flat, funnel or curved surface to assist with redirecting light emitted from the LED into the light guide. 
     FIG. 9C illustrates a side-emitting LED package  40  mounted in a v-shaped blind-hole  97  of a planar light guide  82 . The v-shaped top surface  99  of the blind-hole  97  is approximately parallel with funnel-shaped portion  58  of lens  44  of LED package  40 . The blind hole can have a flat, funnel or curved surface to assist with redirecting light emitted from the LED into the light guide. The top surface  99  of blind-hole  97  may be coated to reflect light in order to allow for a thinner light guide package with a similar coupling efficiency. 
     FIG. 10 illustrates a side-emitting LED package  40  mounted in a through-hole  96  of a planar light guide  82 . Through-hole  96  allows LED package  40  to be mounted approximately perpendicular with light guide  82 . 
     FIG. 11 illustrates a conventional LED/reflector arrangement. It is known to use an LED package  10  with a hemispherical lens  12  in combination with a deep reflector  92 . The deep shape of the cavity of reflector  92  collimates light emitted from the hemispherical lens  12  of LED package  10 . This deep reflector cavity is required to control the light. 
     As seen in FIG. 12, a shallow, large-area reflector  102  can be used in combination with a side-emitting LED package  40  to emit light over a broader area than a conventional LED package  10 . The longitudinal package axis  116  of the lens is approximately parallel to a radial axis  122  of reflector  102 . The side-emission of light allows the walls of reflector  102  to be less deep than conventional reflectors  92  (FIG.  11 ). Light is emitted from lens  144  roughly perpendicular to longitudinal package axis  116  of LED package  40 . Side-emitting LED package  40  allows for very high collection efficiencies with shallow large area reflectors compared to conventional LEDs. Shallow reflectors  102  collimate emitted light over a broader area than narrow, deep reflectors  92  used in combination with conventional LED assemblies  10 . Shallow, large-area reflector  102  may be made of BMC bulk molding compound, PC, PMMA, PC/PMMA, and PEI. A reflective film  120  covering the inside of reflector  102  could be metallized, sputtered, or the like with highly reflective materials including, for example, aluminum (Al) and nickel chrome (NiCr). Side-emitting LEDs can achieve higher collection efficiencies with deep or shallow reflectors than the conventional LED/deep reflector combination. 
     Although the LED packages and light-emitting devices disclosed above include a lens  44  having several sawteeth, other embodiments may include a lens having only one sawtooth or no sawteeth. Referring to FIG. 13, for example, in accordance with one embodiment, a light-emitting device  150  includes a lens  152  similar to but differing from lens  44  disclosed above. In particular, lens  152  includes a funnel shaped portion  58  having a reflecting (e.g., totally internally reflecting) surface I and a refracting surface H, but does not include a refractive sawtooth portion such as sawtooth portion  56  of lens  44  (FIG.  5 A). Instead, lower portion  154  of lens  152  has a refracting surface  156  extending as a smooth curve from refracting surface H to a bottom surface  158  of lens  152 . If volume  54  is under vacuum or contains a gas, then bottom surface  158  of lens  152  may be considered to include the interface between volume  54  and the other portions of lens  152 . Alternatively if volume  54  includes a non-gaseous material such as a solid, liquid, or gel, then bottom surface  158  may be considered to include the interface of such material with LED package base  42  and with LED  52 . 
     Similarly to lens  44  disclosed above, lens  152  may be symmetrical (e.g., cylindrically symmetrical) about a central axis  43 . Reflecting surface I of lens  152  may have shapes such as, for example, those described above and depicted in FIGS. 5E-5G for surface I of lens  44 . Lens  152  may be formed from any of the materials and fabricated by any of the methods described above as suitable for fabrication of lens  44 . 
     Referring now to the ray traces illustrated in FIG. 14 as well as to FIG. 13, light emitted by a light-emitting semiconductor device such as LED  52  located approximately at the focal point F of lens  152  may enter lens  152  through bottom surface  158  of the lens. Light emitted from near focal point F that is directly incident on reflecting surface I is reflected from surface I to refracting surface H and refracted by surface H to exit lens  152  in a direction substantially perpendicular to the central axis  43  of the lens. Light emitted from near focal point F that is directly incident on refracting surface  156  is refracted by surface  156  to also exit lens  152  in a direction substantially perpendicular to axis  43 . 
     For convenience of illustration, the light rays illustrated in FIG.  13  and in the other figures are not shown as refracted at the interface of volume  54  with the other portions of lens  152 . Generally, refraction of such light rays at this interface will occur due to a (typically small) difference in the refractive index between the material in volume  54  and the material of the other portions of the lens. The shapes of surfaces I, H, and  156  are typically chosen to take such refraction into account. 
     FIG. 15 illustrates a cross-sectional view of lens  152  superimposed over a cross-sectional view of a lens  160  (dashed line) that includes a single refractive sawtooth. Aside from having only a single refractive sawtooth, lens  160  is substantially similar in structure and function to lens  44  disclosed above. The implementations of lens  152  and  160  shown in FIG. 15 are optimized for use with substantially similar LEDs in substantially similar packages. Hence, the lowermost portions of lens  152  and lens  160  are substantially identical in size and shape. 
     As FIG. 15 shows, the diameter D 1  of the funnel shaped portion  58  of lens  152  is substantially less than the diameter D 2  of its lower portion  154 . In contrast, the diameter of the funnel shaped portion of lens  160  is approximately equal to the diameter of its lowermost portion. In some implementations, the relatively smaller diameter of the funnel shaped portion  58  of lens  152  makes lens  152  easier and less expensive than lens  160  (or other lenses including refractive sawteeth) to manufacture, to insert into and to attach to an LED package, and to fill with, for example, silicone or resin. 
     Light-emitting device  150  may be employed with, for example, light guides and shallow, large-area reflectors similarly as disclosed above for other LED packages and light-emitting devices. 
     In another embodiment (FIG.  16 ), a lens cap  162  mates to a conventional LED. package  10  having a hemispherical lens  12 . Lens cap  162  may be attached to lens  12  by an optical adhesive, for example. Lens cap  162  includes a funnel shaped portion  58  having a reflecting (e.g., totally internally reflecting) surface I and a refracting surface H, as well as a lower portion  154  having a refracting surface  156  extending as a smooth curve from refracting surface H to a bottom surface  158 . Lens cap  162  may have the shapes and symmetries disclosed above for lens  152 , and may be formed from any of the materials and by any of the methods described above as suitable for fabrication of lenses  44  and  152 . As described above with respect to lens  152 , light emitted by LED package  10  is directed by surfaces I, H, and  156  of lens cap  162  in a direction substantially perpendicular to a central axis  43  of the lens cap. 
     The above-described embodiments of the present invention are meant to be illustrative and not limiting. It will thus be obvious to those skilled in the art that various changes and modifications may be made without departing from this invention in its broader aspects. Therefore, the appended claims encompass all such changes and modifications as falling within the true spirit and scope of this invention.