REFLECTIVE HOLOGRAPHIC PHASE MASKS

A phase transformation device may include a solid photosensitive material having a planar input facet and one or more reflective holographic phase masks (RHPMs) within a volume of the solid photosensitive material, where a particular one of the one or more RHPMs is formed as a periodic refractive index variation of the photosensitive material along a particular grating vector and further with a particular non-planar lateral phase profile, where at least one of a period of the refractive index variation along the grating vector or an orientation of the grating vector for each of the one or more RHPMs are arranged to reflect via Bragg diffraction light incident on the input facet that satisfies a Bragg condition, and where a phase distribution of the reflected light from a particular one of the one or more RHPMs is modified by the associated non-planar lateral phase profile.

TECHNICAL FIELD

The present disclosure relates generally to holographic phase masks and, more particularly, to reflective holographic phase masks.

BACKGROUND

The growing adoption of lasers in both research and commercial settings has necessitated the need for coherent sources capable of producing on-demand optical beams with specialized waveforms. Various beam-shaping techniques have been developed to transform the spatial profile of a coherent optical beam from the original distribution to other, more desirable structures, which can be accomplished via either phase or amplitude modulation, or a combination of both. These methods rely on a wide selection of available tools, such as physical apertures, diffractive optical elements, phase masks, free-form optics (e.g., digital micro-mirror devices, or the like), or spatial light modulators. However, these beam-shaping tools, whether active or passive, do not address the underlying monochromatic nature of their embedded phase profiles and are further hampered by the complex, high-cost manufacturing processes as well as a restrictive laser-induced damage threshold. There is therefore a need to develop systems and methods to cure the above deficiencies.

SUMMARY

A device is disclosed in accordance with one or more illustrative embodiments of the present disclosure. In one illustrative embodiment, the device includes a solid photosensitive material having a planar input facet. In another illustrative embodiment, the device includes one or more reflective holographic phase masks (RHPMs) within a volume of the solid photosensitive material, where a particular one of the one or more RHPMs is formed as a periodic refractive index variation of the solid photosensitive material along a particular grating vector and further with a particular non-planar lateral phase profile in at least one plane perpendicular to the particular grating vector. In another illustrative embodiment, at least one of a period of the refractive index variation along the grating vector or an orientation of the grating vector for each of the one or more RHPMs are arranged to reflect via Bragg diffraction light incident on the input facet that satisfies a Bragg condition. In another illustrative embodiment, a phase distribution of the reflected light from a particular one of the one or more RHPMs is modified by the associated non-planar lateral phase profile.

A system is disclosed in accordance with one or more illustrative embodiments of the present disclosure. In one illustrative embodiment, the system includes a laser source configured to generate a coherent beam of light. In another illustrative embodiment, the system includes an interferometer with a beamsplitter to split the coherent beam into two arms, a phase mask in one of the two arms providing a non-uniform phase distribution in at least one direction perpendicular to a propagation direction of the coherent beam in the associated one of the two arms, and one or more optical elements configured to combine the laser beam from the two arms in a sample to generate interference within the sample, where the interference pattern corresponds to a periodic intensity variation along a grating vector and provides a non-planar lateral phase profile in at least one plane perpendicular to the particular grating vector, and where at least one of a period of the intensity variation along the grating vector or an orientation of the grating vector for each of the one or more RHPMs are arranged to satisfy a Bragg condition associated with the reflection of light incident on the input facet back out of the input facet.

A laser system is disclosed in accordance with one or more illustrative embodiments of the present disclosure. In one illustrative embodiment, the system includes a gain medium to generate optical gain and a cavity surrounding the gain medium configured to generate output laser light based on the optical gain by the gain medium. In another illustrative embodiment, the cavity includes a reflective phase mask including a solid photosensitive material having a planar input facet and one or more reflective holographic phase masks (RHPMs) within a volume of the solid photosensitive material, where a particular one of the one or more RHPMs is formed as a periodic refractive index variation of the solid photosensitive material along a grating vector normal to the input facet and further with a particular non-planar lateral phase profile in at least one plane perpendicular to the grating vector, where a period of the refractive index variation along the grating vector for each of the one or more RHPMs is arranged to retroreflect via Bragg diffraction light of a particular wavelength, where a phase distribution of the reflected light from each of the one or more RHPMs is modified by the associated non-planar lateral phase profile, and where optical modes of the output laser light associated with the wavelengths reflected by the one or more RHPMs are determined by the associated non-planar lateral phase profiles of the associated RHPMs.

A system is disclosed in accordance with one or more illustrative embodiments of the present disclosure. In one illustrative embodiment, the system includes two or more transmitters configured to generate modulated light beams at two or more wavelengths. In another illustrative embodiment, the system includes a multiplexer configured to receive the modulated light beams and direct the modulated beams along a transmission pathway. In another illustrative embodiment, the system includes two or more detectors. In another illustrative embodiment, the system includes a demultiplexer configured to receive the modulated light beams from the transmission pathway and direct the modulated light beams along separate paths to the two or more detectors. In another illustrative embodiment, the system includes one or more phase transformation devices formed as a solid photosensitive material having a planar input facet and two or more reflective holographic phase masks (RHPMs) within a volume of the solid photosensitive material, where a particular one of the two or more RHPMs is formed as a periodic refractive index variation of the solid photosensitive material along a particular grating vector and further with a particular non-planar lateral phase profile in at least one plane perpendicular to the particular grating vector, where at least one of a period of the periodic refractive index variation along the grating vector or an orientation of the grating vector for each of the two or more RHPMs are arranged to reflect via Bragg diffraction light incident on the input facet that satisfies a Bragg condition, and where a phase distribution of the reflected light from a particular one of the one or more RHPMs is modified by the associated non-planar lateral phase profile. In another illustrative embodiment, at least one of the one or more phase transformation devices is configured to operate as at least one of the multiplexer or the demultiplexer.

DETAILED DESCRIPTION

Embodiments of the present disclosure are directed to reflective holographic phase masks. Some embodiments of the present disclosure are directed to a reflective holographic phase mask (RHPM) formed as a volume Bragg grating (VBG) within the volume of solid photosensitive material, where the period and/or orientation of the VBG are arranged to provide reflection of incident light via Bragg diffraction, and where a lateral phase profile of the VBG in a plane perpendicular to the grating vector is non-uniform. Put another way, an RHPM as disclosed herein includes a non-planar phase profile of the reflecting VBG in a lateral plane orthogonal to the grating vector.

In this configuration, the non-planar lateral phase profile of the RHPM modifies a phase profile of a beam reflected via Bragg diffraction (e.g., a phase profile in a plane perpendicular to a propagation direction). In a general sense, the RHPM may have any non-planar lateral phase profile such that the RHPM may provide apply any desired phase transformation to a reflected beam.

VBGs are generally described in Igor V. Ciapurin, et al., “Modeling of phase volume diffractive gratings, part 1: transmitting sinusoidal uniform gratings,” Optical Engineering 45 (2006) 015802, 1-9; and Igor V. Ciapurin, et al., “Modeling of phase volume diffractive gratings, part 2: reflecting sinusoidal uniform gratings, Bragg mirrors,” Optical Engineering 51 (2012) 058001, 1-10, both of which are incorporated herein by reference in their entireties. Further, transmissive VBGs (e.g., VBGs for which light satisfying a Bragg condition is diffracted as a transmitted beam) configured as transmissive phase masks are described generally in U.S. Patent Publication No. 2016/0116656 published on Apr. 28, 2016, which is incorporated herein by reference in its entirety.

It is contemplated herein that an RHPM as disclosed herein may have substantially different properties than a transmissive phase mask based on a transmissive VBG. In particular, an RHPM may provide a substantially narrower bandwidth for light redirected via Bragg diffraction than corresponding light diffracted a transmissive VBG, which may make RHPMs particularly useful for, but not limited to, multiplexing and demultiplexing applications, laser applications, and the like.

In some embodiments, two or more RHPMs are fabricated in a common volume of a photosensitive material. Such a configuration may be characterized as a multiplexed RHPM or a multiplexed grating structure. In this configuration, each RHPM may be designed with different characteristics to induce reflection via Bragg diffraction under different conditions such as, but not limited to, different wavelengths, different incidence angles, or different reflection angles. In some embodiments, a phase transformation device with two or more RHPMs is configured as a multiplexer (MUX). For example, the two or more RHPMs may be designed to accept light with different characteristics and redirect them along a common path via reflective Bragg diffraction. In some embodiments, a phase device with two or more RHPMs is configured as a demultiplexer (DEMUX). For example, the two or more RHPMs may be designed to split an incident beam into two or more beams. As an illustration, a wavelength demultiplexer may direct one wavelength of light along one path, a second wavelength of light along a second path, and so on. Further, since each RHPM also includes a non-planar lateral phase profile (which may be the same or different than other multiplexed RHPMs), such a device may further provide individualized phase control of each reflected beam.

Some embodiments of the present disclosure are directed to systems and methods for fabricating an RHPM. In some embodiments, an RHPM is fabricated by placing a solid photosensitive material in an interferometer to generate an interference pattern having the desired characteristics of the RHPM, where one arm of the interferometer includes a phase mask. In this configuration, an interference pattern in the photosensitive material may have the same phase profile as the phase mask in the arm of the interferometer. The light associated with the interference pattern may then induce a material change in the photosensitive material that can be exploited to provide a permanent refractive index variation. An RHPM may be fabricated in any photosensitive material of any type such as, but not limited to, a glass or a polymer. For example, when the photosensitive material is a photo-thermal-refractive (PTR) glass, the light associated with the interference pattern may induce a precipitation of crystalline phases in the glass. A subsequent heat treatment of such a PTR glass (e.g., in an oven) may result in a permanent periodic refractive index variation within the bulk of the glass that corresponds to the desired interference pattern.

It is contemplated herein that it may be necessary to illuminate the solid photosensitive material from opposing facets (or at least multiple facets) to provide interference with a desired orientation in the photosensitive material. For example, it may be desirable to fabricate an RHPM having a grating vector that is substantially perpendicular to a facet of the solid material (e.g., an input facet). In some embodiments, such an arrangement is achieved by placing a solid photosensitive material with two parallel polished facets between two prisms designed to generate an interference pattern between the two facets.

Additional embodiments of the present disclosure are directed to systems or devices that include one or more RHPMs.

For example, some embodiments of the present disclosure are directed to a communications system providing wavelength division multiplexing (WDM). Such a system may include one or more RHPMs as multiplexers to combine modulated light at different wavelengths along a common path for propagation along a communication channel and/or one or more RHPMs as demultiplexers to separate the light from the communication channel along separate paths for separate detection of the modulated light at the different wavelengths.

As another example, some embodiments of the present disclosure are directed to a laser including a phase transformation device with one or more RHPMs within a laser cavity to control a phase of generated laser light (e.g., coherent light) and thus an optical mode of the generated laser light. In particular, the phase transformation device may include one or more RHPMs, each designed to retroreflect light of a selected wavelength within a gain profile of a gain medium and each further designed to provide a non-planar lateral phase profile to control an optical mode of light at the corresponding wavelengths. Such a configuration may support simultaneous generation of laser light with multiple wavelengths and/or multiple optical modes. Further, the bandwidth of the laser light may be controlled by a bandwidth of light reflected by an RHPM via Bragg diffraction, which may be typically be narrow (e.g., on the order of picometers in some cases).

Referring now toFIGS.1-12, RHPMs are described in greater detail, in accordance with one or more embodiments of the present disclosure.

A traditional VBG is formed as a grating structure associated within the volume of a solid material (e.g., a solid photosensitive material) with a periodic variation of refractive index along a grating vector

This grating structure is typically extended in directions perpendicular to the grating vector k. The refractive index n of such a traditional VBG may be, but is not required to be, a simple sinusoidal function:

where the grating vector k corresponds to z (e.g., a Z axis in an XYZ coordinate space), d is a period of the VBG along the z direction (e.g., the grating vector k), and ϕ0corresponds to a constant phase term. In this way, the refractive index of a traditional VBG at the XY plane (or a lateral plane orthogonal to the grating vector more generally) may be constant. Such a traditional VBG may have a uniform phase distribution Φ(x, y)=, where the phase associated with any position in any lateral plane is constant across the VBG. Put another way, such a traditional VBG may be characterized by a planar lateral phase profile.

In embodiments, an RHPM is formed as a VBG with a non-planar lateral phase distribution arranged to reflect light via Bragg diffraction. Using a similar non-limiting construct as above, the refractive index of such an RHPM may be characterized as:

where the RHPM may have an arbitrary lateral phase distribution Φ(x, y).

FIGS.1A-1Cdepict a phase transformation device100formed as an RHPM102within a volume104of photosensitive material106, in accordance with one or more embodiments of the present disclosure. In particular,FIGS.1A-1Cdepict a non-limiting configuration of a phase transformation device100with a single RHPM102within a volume104of the phase transformation device100which has a grating vector108oriented along a Z-axis of an XYZ coordinate space. However, it is noted that the grating vector k of a RHPM102may generally be oriented in any direction with respect to the input facet110so long as a condition for Bragg diffraction is satisfied for at least one wavelength of light incident on the input facet110and the associated reflected beam also exits the input facet110.

FIG.1Ais a perspective view of the phase transformation device100, in accordance with one or more embodiments of the present disclosure. In particular,FIG.1Adepicts a phase transformation device100as a solid block of material (e.g., photosensitive material106) with an input facet110oriented in an XY plane. In this orientation, the refractive index of the RHPM102may be described by Equation (2).

FIG.1Bis a side view of the phase transformation device100along a grating vector108(e.g., Z direction here) associated with a first location in a plane transverse to the grating vector108(e.g., X and Y coordinates), in accordance with one or more embodiments of the present disclosure.FIG.1Cis a side view of the phase transformation device100along the grating vector108with a second location in a plane transverse to the grating vector108, in accordance with one or more embodiments of the present disclosure. As illustrated inFIGS.1B and1C, the phase of the RHPM102along the grating vector108(e.g., along the Z direction here) associated with different locations of a plane orthogonal to the grating vector108(e.g., the XY plane here) may be non-uniform. It is to be understood that althoughFIGS.1B and1Cdepict the phase as constant over a finite length in the Y direction and as a square wave in the Z direction for illustration, the lateral phase distribution Φ(x, y) may generally be any function supported by the photosensitive material106.

FIG.1Afurther depicts an input beam112of light incident on the input facet110and a reflected beam114of light emanating from the input facet110upon reflective Bragg diffraction from a RHPM102within the volume104of the phase transformation device100.

As used herein, the term reflected beam114is used to describe light that is reflected based on Bragg diffraction by a RHPM102. For example, a condition for reflective Bragg diffraction may be:

where d is the period of the RHPM102along the grating vector, n is the average refractive index of the processed solid photosensitive material106including the RHPM102, θBis a Bragg angle (e.g., an incidence angle of the input beam112and a corresponding reflection angle of the reflected beam114as measured from the grating vector108), and λBis the wavelength of diffracted light. It is contemplated herein that the conditions for reflective Bragg diffraction in Equation (3) for a particular RHPM102with fixed properties may be satisfied for different combinations of the wavelength λBand the angle θB, which allows for tunable operation of the RHPM102and the phase transformation device100more generally.

A RHPM102may generally be designed to provide reflection via Bragg diffraction (e.g., according toFIG.3) for at least one wavelength of light incident on the input facet110, where the reflected beam114also exits the same input facet110. In this configuration, the phase transformation device100may operate as a reflective optical element based on the principles of Bragg diffraction.

Referring now toFIGS.2and3, characteristics of transmissive and reflective VBGs are described in greater detail.

It is contemplated herein that a reflective VBG (e.g., a RHPM102as disclosed herein) may have substantially different properties than a transmissive VBG. For example, the Bragg condition associated with a transmissive VBG may be characterized as:

using the same variables as defined for Equation (3). As evident by Equations (3) and (4), a transmissive VBG requires a substantially larger Bragg angle θBfor a given grating period d in a given material, which in turn results in substantially different spectroscopic properties for transmissive and reflective VBGs.

FIGS.2and3represent characteristics of transmissive and reflective VBGs with different associated periods designed to provide Bragg reflection for a common wavelength λBand Bragg angle θBfor comparative purposes.

FIG.2is a series of plots illustrating characteristics of a transmissive VBG, in accordance with one or more embodiments of the present disclosure. In particular, plot202depicts diffraction efficiency as a function of angular deviation for a particular wavelength, and plot204depicts the diffraction efficiency and phase deviation as a function of wavelength.

FIG.3is a series of plots illustrating characteristics of a reflective VBG (e.g., a RHPM102), in accordance with one or more embodiments of the present disclosure. In particular, plot302depicts diffraction efficiency as a function of angular deviation for a particular wavelength, and plot304depicts the diffraction efficiency and phase deviation as a function of wavelength.

ComparingFIGS.2and3, the reflective VBG (e.g., as described byFIG.3) exhibits substantially narrower selectivity for Bragg diffraction than a comparable transmissive VBG. For instance, the bandwidths of diffracted light by a reflective VBG as a function of both wavelength and angle are substantially narrower than corresponding bandwidths of diffracted light by a transmissive VBG. As a result, a reflective VBG (e.g., a RHPM102as disclosed herein) may generally be well-suited, for narrow bandwidth applications such as, but not limited to, wavelength multiplexing/demultiplexing, wavelength/phase control within a laser cavity, or the like.

Referring now toFIGS.4A-5C, various non-limiting examples of RHPMs102with non-planar lateral phase distributions are illustrated, in accordance with one or more embodiments of the present disclosure.

In some embodiments, a RHPM102includes two or more regions, where the lateral phase distribution is uniform within each region, but different regions may have different phases. The lateral phase distribution Φ(x, y) of such a RHPM102may be characterized as a step function along one or more directions.

FIG.4Ais a perspective view of a phase transformation device100with a single RHPM102having a lateral phase distribution Φ(x, y) characterized as a 1D step function, in accordance with one or more embodiments of the present disclosure. Inset402depicts a top view of the phase transformation device100. In particular,FIG.4Aillustrates a non-limiting configuration of a phase transformation device100with a single RHPM102having a binary lateral phase distribution. For example, the RHPM102inFIG.4Aincludes a first region404-1and a second region404-2with phases that differ by π. For instance, the phase of the first region404-1may be characterized as Φ=0 and the phase of the second region404-2may be characterized as Φ=π.

FIG.4Bis a side view of a phase transformation device100with a single RHPM102having a lateral phase distribution Φ(x, y) characterized as a 2D step function, in accordance with one or more embodiments of the present disclosure. In particular,FIG.4Bdepicts a RHPM102with lateral phase distribution Φ(x, y) providing four regions (e.g., quadrants), where one set of opposing quadrants (e.g.,406-1and406-3) have a relative phase of 0 (Φ=0) and a second set of opposing quadrants (e.g.,406-2and406-4) have a relative phase of π (Φ=π).FIG.4Cis an experimental far-field spatial distribution of a reflected beam114after interaction with the RHPM102depicted inFIG.4B, in accordance with one or more embodiments of the present disclosure. In particular,FIG.4Cdepicts mode conversion of a Gaussian input beam112to a beam with a transverse electromagnetic mode (TEM)11profile in the far field.

It is noted that althoughFIGS.4A-4Cdepict square regions, a RHPM102may generally have any number of regions of constant phase, where the various regions have any shapes and distributions, and where each of the various regions may have an arbitrary phase value.

In some embodiments, a RHPM102includes a non-uniform lateral phase profile characterized by a continuous function along one or more directions.

FIG.5depicts three non-limiting examples502,504,506of continuous non-planar lateral phase distributions suitable for a RHPM102within a phase transformation device100, in accordance with one or more embodiments of the present disclosure.

Referring now toFIG.6, a phase transformation device100may generally include any number of RHPMs102within a common volume104of photosensitive material106. Further, each RHPM102may have any selected orientation of a grating vector108as well as any selected lateral phase distribution (e.g., phase distribution Φ in a lateral plane orthogonal to the associated grating vector). In this way, the refractive index distribution in the volume104of the phase transformation device100may be a complex function with periodicity in multiple directions associated with multiple grating vectors. A phase transformation device100with multiple RHPMs102with multiple grating vectors108may be well suited for, but not limited to, applications involving multiplexing and/or demultiplexing of light.

FIG.6is a simplified top view of a phase transformation device100having three RHPMs102with different grating vectors (labeled as108-1,108-2, and108-3), in accordance with one or more embodiments of the present disclosure. For clarity of illustration, the RHPMs102are depicted inFIG.6by the associated grating vectors108-1,108-2, and108-3rather than varying refractive index profiles.

Referring generally toFIGS.1A-6, it is recognized herein that an RHPM102may provide highly-selective operation to selectively reflect light that satisfied a Bragg condition regardless of the spectrum of the associated input beam112. For example, in the case that a spectrum of the input beam112is broader than an operational bandwidth of a particular RHPM102, the RHPM102may selectively reflect only the narrow bandwidth satisfying the Bragg condition and transmit the remaining wavelengths.

Referring now toFIG.7, fabrication of an RHPM102is described in greater detail.FIG.7is a simplified schematic of an interferometer702for fabricating an RHPM102, in accordance with one or more embodiments of the present disclosure.

In some embodiments, an RHPM102is formed by placing a photosensitive material106in an interferometer702such that an interference pattern associated with a desired reflective VBG is formed in the photosensitive material106. In this way, one or more properties of the photosensitive material106may change in response to the incident illumination such that the interference pattern is exposed in the photosensitive material106. As necessary, additional steps such as, but not limited to, heating the photosensitive material106may be performed to render the exposed interference pattern more permanent.

The photosensitive material106may include any photosensitive material known in the art suitable for supporting a phase transformation device100. For example, the photosensitive material106may include a photosensitive glass, a photosensitive polymer, or the like.

In some embodiments, the photosensitive material106includes PTR glass. For example, PTR glass may include one or more photosensitive dopants and/or one or more halogen ions. As an illustration PTR glass may include, but is not limited to, sodium aluminosilicate glass containing sodium fluoride (NaF) and potassium bromide (KBr) along with silver, cerium, tin, and/or antimony oxides. Such a material may produce various photoionized states upon exposure with ultraviolet (UV) light (typically including silver) that may further crystallize into nucleation centers (e.g., nanoclusters, crystalline phases, or the like) upon thermal treatment (e.g., heating and/or cooling). Any suitable device may be used to provide the heat treatment including, but not limited to, an oven. Further, species such as NaF, NaBr, or the like may be formed during the thermal treatment. The resulting exposed interference pattern may be patterned into the volume of the photosensitive material106. However, it is recognized herein that various compositions of PTR glass may be developed and that the present disclosure is not limited to any particular composition or any particular thermal treatment profile.

In some embodiments, an RHPM102is formed in a photosensitive material106directly as a result of exposure with light without the need for thermal treatment.

In some embodiments, the interferometer702includes a beamsplitter704(e.g., a non-polarizing beamsplitter) to split incident light706suitable for exposing the desired interference pattern in the photosensitive material106into two paths associated with arms of the interferometer702(e.g., signal and reference arms). The light706may have any spectral properties and intensity suitable for exposing the interference pattern in the photosensitive material106. For example, in the case of PTR glass, the light706may include UV illumination (e.g., 325 nm, or the like).

In some embodiments, the interferometer702further includes various optical elements (e.g., mirrors708, or the like) to direct the light706in the two arms of the interferometer702to the photosensitive material106at angles necessary to produce a desired interference pattern associated with an RHPM102as disclosed herein. For example, as depicted inFIG.7, a photosensitive material106having parallel polished faces may be placed between a pair of prisms710or other suitable elements (e.g., mirrors, or the like) to direct light through the parallel facets and generate an interference pattern with a grating vector that is substantially perpendicular to the polished facets. In this configuration, one of the polished facets of the photosensitive material106may operate as the input facet110as illustrated inFIG.1A. Further, the orientation of the grating vector k and/or the grating period d may be tuned or otherwise controlled based on the geometry of the prisms710(or other mirrors, or the like) and/or the angles at which the light706is directed into each of the facets. As an illustration, illumination of a photosensitive material106using the interferometer702depicted inFIG.7with light706having a wavelength of 325 nm at a recording angle of θrecmay result in Bragg diffraction of such light at an angle of −θRec. In some embodiments, one or more components of the interferometer702(e.g., the prisms710, mirrors708, or the like) are adjustable to allow adjustments of the grating vector k and/or the grating period d associated with the interference pattern. For example, one or more components of the interferometer702may be mounted on translation stages (e.g., rotational stages, linear stages, or the like) suitable for adjusting the associated angles and/or positions.

In some embodiments, the interferometer702further includes a phase plate712located in one arm of the interferometer702(e.g., the signal arm as illustrated inFIG.7). In this configuration, a phase plate712may modify the phase distribution of the RHPM102such that the RHPM102has a non-planar lateral phase profile Φ. Inset714further depicts a perspective view of the phase plate712with a non-limiting configuration of a binary transmissive phase profile.

It is contemplated herein that a reflected beam114associated with Bragg diffraction from an RHPM102fabricated with an interferometer702as depicted inFIG.7may have a phase profile that matches or is controlled by (e.g., depends on) the phase profile of the phase plate712. Further, this is true for any wavelength of light reflected via Bragg diffraction by the RHPM102(e.g., any wavelength for which the Bragg diffraction condition in Equation (3) is satisfied and for which the arrangement of the RHPM102and the input beam112allow for the reflected beam114to exit the input facet110as described above).

In this way, the phase profile induced on a reflected beam114from the RHPM102may be controlled by selection of the phase profile of the phase plate712used during fabrication of the RHPM102.

In some embodiments, multiple RHPMs102are fabricated in a single piece of photosensitive material106through successive exposures to interference patterns by the interferometer702. For instance, various components of the interferometer702(e.g., the prisms710, mirrors708, or the like) may be modified for each exposure to provide a selected grating vector108and/or period for each RHPM102. In the case of a photosensitive material106including PTR glass or other material benefiting from a thermal treatment to generate a permanent refractive index change in the pattern of the exposed interference pattern, such a thermal treatment may be performed after all exposures or between exposures as desired for the selected composition.

Referring now toFIGS.8-12, various non-limiting systems and devices incorporating at least one RHPM102are described in greater detail, in accordance with one or more embodiments of the present disclosure.

In some embodiments, two or more RHPMs102are formed in a photosensitive material106(e.g., within a common volume104of the photosensitive material106) as a phase transformation device100, where each RHPM102is designed to provide Bragg diffraction of a selected wavelength of light with a specified reflection angle relative to the input facet110, and where each RHPM102has a different non-planar lateral phase profile Φ. For example, properties of each RHPM102such as, but not limited to, the period d, the orientation of the grating vector108relative to the input facet110, and/or the non-planar lateral phase profile Φ may be independently selected. In this configuration, the phase transformation device100may simultaneously operate as a reflective phase mask with defined reflection angles for multiple beams of light.

Referring toFIG.8,FIG.8is a simplified schematic of a phase transformation device100with multiple RHPMs102formed as a multi-beam Bragg retroreflector, in accordance with one or more embodiments of the present disclosure. For example, two or more RHPMs102may be formed with grating vectors108oriented normal to the input facet110and periods d selected to provide reflection via Bragg diffraction of a selected wavelength of light. Further, each of these RHPMs102may have a selected non-planar lateral phase profile Φ.

For example, as depicted inFIG.8, such a phase transformation device100may be configured as a multi-wavelength retroreflector. In this configuration, each RHPM102may be designed to reflect a different wavelength of light via Bragg diffraction.FIG.8depicts a non-limiting example of simultaneous retroreflection of three beams with different center wavelengths and/or bandwidths, represented as λ1±δλ1, λ2±δλ2, and λ3±δλ3. As illustrated inFIG.3, an RHPM102may generally provide highly selective narrowband reflection around a center wavelength for a given incidence angle. In particular, an RHPM102may provide more highly selective reflection of a smaller bandwidth around a center wavelength than a corresponding transmissive VBG.

Further, such a multi-wavelength retroreflector may provide selective control of the phase of each reflected beam114(retroreflected light at each center wavelength). In some embodiments, all of the RHPMs102have the same non-planar lateral phase profile Φ. In some embodiments, at least some RHPMs102have different non-planar lateral phase profiles to impart different phase transformations on different reflected beams114at different wavelengths. As non-limiting illustrations, any of the RHPMs102may have any of the non-planar lateral phase profiles illustrated inFIG.5.

In some embodiments, a phase transformation device100includes two or more RHPMs102arranged to provide multiplexing of two or more beams. For example, multiple input beams112with different angles of incidence (e.g., incidence angles) on the input facet110may be reflected via Bragg diffraction to a common reflection angle relative to the input facet110. In this configuration, each RHPM102may have a grating vector108and/or period selected to provide reflection via Bragg diffraction of a selected wavelength of light to the common reflection angle. Further, each RHPM102may have any selected non-planar lateral phase profile to impart any selected phase distribution on the associated reflected beam114.

FIG.9Ais a simplified schematic of a phase transformation device100with multiple RHPMs102formed as an angle-sensitive multiplexer, in accordance with one or more embodiments of the present disclosure. In this configuration, the grating vector108and/or period of each RHPM102is selected to reflect a common wavelength with different Bragg angles in a way that all associated reflected beams114overlap with a common reflection angle relative to the input facet110. This is represented inFIG.9Aby overlapping reflected beams114with spectral profiles of λ1*±δλ1, λ1**±δλ1, and λ1***±δλ1. The associated RHPMs102in this configuration may have the same or different non-planar lateral phase profiles to provide independent control of the phase of each reflected beam114.

FIG.9Bis a simplified schematic of a phase transformation device100with multiple RHPMs102formed as a wavelength-sensitive multiplexer, in accordance with one or more embodiments of the present disclosure. In this configuration, the grating vector108and/or period of each RHPM102is selected to reflect different wavelengths with different Bragg angles in a way that all associated reflected beams114overlap with a common reflection angle relative to the input facet110. Further, the RHPMs102may have the same or different non-planar lateral phase profiles to provide independent control of the phase of each reflected beam114. This is represented inFIG.9Bby overlapping reflected beams114with spectral profiles of λ1±δλ1, λ2±δλ2, and λ3±δλ3. The associated RHPMs102in this configuration may have the same or different non-planar lateral phase profiles to provide independent control of the phase of each reflected beam114.

In some embodiments, a phase transformation device100includes two or more RHPMs102arranged to provide demultiplexing of two or more beams. For example, multiple input beams112with common incidence angles on the input facet110may be reflected via Bragg diffraction to different reflection angles relative to the input facet110. In this configuration, each RHPM102may have a grating vector108and/or period selected to provide reflection via Bragg diffraction of a selected wavelength of light at the common incidence angle to selected reflection angles. Further, each RHPM102may have any selected non-planar lateral phase profile to impart any selected phase distribution on the associated reflected beam114.

FIG.10Ais a simplified schematic of a phase transformation device100with multiple RHPMs102formed as an angle-sensitive demultiplexer, in accordance with one or more embodiments of the present disclosure. In this configuration, the grating vector108and/or period of each RHPM102is selected to reflect a common wavelength with different Bragg angles in a way that the associated reflected beams114have different reflection angles relative to the input facet110. This is represented inFIG.10Aby non-overlapping reflected beams114with spectral profiles of λ1*±δλ1, λ1**±δλ1, and λ1***±δλ1. The associated RHPMs102in this configuration may have the same or different non-planar lateral phase profiles to provide independent control of the phase of each reflected beam114.

FIG.10Bis a simplified schematic of a phase transformation device100with multiple RHPMs102formed as a wavelength-sensitive demultiplexer, in accordance with one or more embodiments of the present disclosure. In this configuration, the grating vector108and/or period of each RHPM102is selected to reflect different wavelengths with different Bragg angles in a way that the associated reflected beams114have different reflection angles relative to the input facet110. This is represented inFIG.10Bby non-overlapping reflected beams114with spectral profiles of λ1±δλ1, λ2±δλ2, and λ3±δλ3. The associated RHPMs102in this configuration may have the same or different non-planar lateral phase profiles to provide independent control of the phase of each reflected beam114.

Referring now toFIG.11,FIG.11is a simplified schematic of a system1100providing multiplexed communication, in accordance with one or more embodiments of the present disclosure. In some embodiments, a system1100includes two or more transmitters1102configured to generate modulated beams1104having different wavelengths (e.g., center wavelengths) and one or more wavelength-selective multiplexers1106to combine the modulated beams1104to a common optical path for transmission over a transmission line1108(e.g., a free-space transmission line, a fiber-optic cable, or a network thereof). In some embodiments, the system1100further includes one or more wavelength-selective demultiplexers1110to receive the light from the transmission line1108(e.g., along a common optical path) and split the modulated beams1104into different optical paths for separate detection by different receivers1112(e.g., photodiodes, avalanche photodiodes, single photon detectors, or the like).

It is contemplated herein that a phase transformation device100with two or more RHPMs102may operate as any of the multiplexers1106and/or the demultiplexers1110. For example, any of the multiplexers1106may be implemented as illustrated inFIG.9B. As another example, any of the demultiplexers1110may be implemented as illustrated inFIG.10B. Further, in this configuration, any such phase transformation device100may selectively control the phase of each associated modulated beam1104as disclosed herein. In this way, the phase profiles of the modulated beams1104may be tailored as desired for efficient operation of the system1100.

Referring now toFIG.12, in some embodiments, a laser system1200includes an intracavity phase transformation device100with one or more RHPMs102to provide highly selective wavelength and mode control laser output, in accordance with one or more embodiments of the present disclosure.

As a non-limiting illustration,FIG.12depicts a laser system1200formed as a gain medium1202within an optical cavity1204arranged to generate a coherent output laser beam1206, in accordance with one or more embodiments of the present disclosure. The gain medium1202may be pumped by any suitable pump source1208. For example, the pump source1208may include an optical pump source to provide pump light within an absorption band of the gain medium1202. As another example, the pump source1208may be an electrical pump source configured to provide electrical pumping of the gain medium1202.

In some embodiments, the laser system1200includes a phase transformation device100with one or more RHPMs102within the optical cavity1204. For example, as illustrated inFIG.12, the phase transformation device100may operate as a mirror within the optical cavity1204.

The phase transformation device100may have any design suitable for operation in the laser system1200. For example, any RHPMs102of the phase transformation device100may be oriented with a grating vector108normal to an input facet110to provide retroreflecting operation.

It is contemplated herein that an RHPM102within an optical cavity1204of a laser system1200may selectively allow lasing of a narrow bandwidth of light that satisfies the Bragg condition and may further control an optical mode of the light within the optical cavity1204based on the non-planar lateral phase profile Φ. As a result, an RHPM102may beneficially facilitate the generation of a highly narrowband output laser beam1206with a highly-controlled optical mode.

It is further contemplated herein that two or more RHPMs102within an optical cavity1204designed for operation with different wavelengths within a gain profile of the gain medium1202may provide an output laser beam1206having multiple narrowband spectral peaks. For example, as illustrated inFIG.8, a single phase transformation device100may include two or more RHPMs102within a common volume104to simultaneously retroreflect multiple wavelengths of light via Bragg diffraction. As another example, though not explicitly shown, a laser system1200may include multiple phase transformation devices100, each including one or more RHPMs102.

Further, each RHPM102within the optical cavity1204may separately control the mode profile of light within the cavity at an associated reflected wavelength based on the associated non-planar lateral phase profile. In some embodiments, multiple RHPMs102reflecting different wavelengths may provide a common optical mode profile for the different wavelengths (e.g., a Gaussian profile). In some embodiments, multiple RHPMs102reflecting different wavelengths may provide different optical mode profiles for the different wavelengths.