Wavelength dispersive device with temperature compensation

The invention relates to fiber-optic wavelength dispersive devices incorporating a wavelength dispersive reflector that provides auto-compensation of variations of output spectral characteristic with temperature and includes a transmissive dispersion that is followed by a beam-folding reflecting surface in a double-pass configuration grating and is coupled to a wedged shaped prism.

TECHNICAL FIELD

The present invention relates to optical dispersive devices incorporating diffraction gratings, and in particular to compensation of temperature-related shifts in such devices.

BACKGROUND OF THE INVENTION

Optical wavelength dispersive devices (WDD) often use diffraction gratings to spatially disperse different wavelength of incoming light and direct them along differing optical paths. Such grating-based WDD typically also includes an input aperture to launch light into the device, and collimating or focusing optical elements having optical power such as lenses and curved mirrors to form spectrally dispersed images on a focal surface.

One common embodiment of a WDD is a spectrograph, wherein a plurality of detector elements are disposed at the focal surface for measuring the intensity of the spectral components of the incoming light beam. Another important embodiment of a WDD is a wavelength selective switch (WSS), wherein an optical fiber is disposed at the input aperture, a plurality of controllable switching elements such as micro-electro-mechanical (MEMS) micro-mirrors are disposed at the focal surface, and the switching elements are effective in redirecting spectral components of the input optical signal back into a selected output optical fiber. Examples of such devices are disclosed in U.S. Pat. No. 6,097,859 issued Aug. 1, 2000 to Solgaard et al; U.S. Pat. No. 6,498,872 issued Dec. 24, 2002 to Bouevitch et al; U.S. Pat. No. 6,707,959 issued Mar. 16, 2004 to Ducellier et al; U.S. Pat. No. 6,810,169 issued Oct. 26, 2004 to Bouevitch, and U.S. Pat. Publication No. 2007/0242953 published Oct. 18, 2007 to Keyworth et al, which are incorporated herein by reference.

Another example of a WDD is a wavelength blocker (WB), or a dynamic gain equalizer (DGE). In these devices, dispersed images corresponding to de-multiplexed wavelength channels may be formed upon an array of liquid crystal cells, which independently rotate the state of polarization of the wavelength channels to either partially attenuate or completely block selected channels from passing back through the polarization diversity unit in the front end. Examples of WB and DGE backend units are disclosed in U.S. Pat. No. 7,014,326 issued Mar. 21, 2006 to Danagher et al; U.S. Pat. No. 6,498,872 issued Dec. 24, 2002 to Bouevitch et al; and U.S. Pat. No. 6,810,169 issued Oct. 26, 2004 to Bouevitch, which are incorporated herein by reference.

Another example of a WDD is a fiber optic multiplexer/demultiplexer, where an optical fiber is disposed at the input aperture, and a plurality of output optical fibers are disposed at the dispersed focal plane to receive the dispersed spectral components.

FIG. 1illustrates a top view of a typical platform100for a WDD in which a spherical reflector120receives a beam of light from a front-end unit122. The spherical reflector120reflects the beam of light to a diffraction grating124, which disperses the beam of light into its constituent wavelength channels. The wavelength channels are again redirected by the spherical mirror120to a backend unit126.

In the case of a WB or a DGE the front end unit122can include a single input/output port with a circulator, which separates incoming from outgoing signals, or one input port with one output port. Typically the front end unit122will include a polarization diversity unit for ensuring the beam (or sub-beams) of light has a single state of polarization. The backend unit126for a WB or a DGE includes an array of liquid crystal cells, which independently rotate the state of polarization of the wavelength channels to either partially attenuate or completely block selected channels from passing back through the polarization diversity unit in the front end122.

In the case of a wavelength selective switch (WSS) the front end unit122is illustrated inFIG. 2and includes an array132of input/output fibers132A to132D, each of which may have a corresponding lens134A to134D, respectively, forming a lens array134. An angle to offset, or switching, lens136converts the lateral offset of the input fibers132A to132D into an angular offset at a point138, which is imaged by the spherical lens120onto the backend unit126. The lens array134can be removed depending on the relative positions of the switching lens136. The backend unit126in a WSS is typically a MEMS array of tilting mirrors which can be used to steer each of the demultiplexed beams to one of several positions corresponding to a desired output port. The angle introduced at the back end unit126is then transformed by the angle to offset lens136to a lateral offset corresponding to the desired input/output fiber132A to132D. Alternatively, a liquid crystal phased array (LC or LCoS, if incorporated on a silicon driver substrate) can be used to redirect the light.

In operation as a WSS, a multiplexed beam of light is launched into the front-end unit122and optionally passes through the polarization diversity unit formed of a polarization beam splitter and a waveplate to provide two beams of light having the same state of polarization. The two beams of light are transmitted to the spherical reflector120and are reflected therefrom towards the diffraction grating124. The diffraction grating124separates each of the two beams into a plurality of channel sub-beams of light having different central wavelengths. The plurality of channel sub-beams are transmitted to the spherical reflector120, which redirects them to the MEMS or LC phased array126, where they are incident thereon as spatially separated spots corresponding to individual spectral channels.

Each channel sub-beam can be reflected backwards along the same path or a different path, which extends into or out of the page inFIG. 1to the array of fibers132, which would extend into the page. Alternatively, each channel sub-beam can be reflected backwards along the same path or a different path, which extends in the plane of the page ofFIG. 1. The sub-beams of light are transmitted, from the MEMS or LC phased array126, back to the spherical reflector120and are redirected to the diffraction grating124, where they are recombined and transmitted back to the spherical reflector120to be transmitted to a predetermined input/output port shown inFIG. 2.

In all such devices it is often desirable to have the positions of the spectrally dispersed images on the focal surface remain fixed as the temperature of the device is varied. However, as the temperature of the optical system of the WDD changes, the optical beam path through the WDD may vary, resulting in shifts of the dispersed images at the focal surface. In principle, it should be possible to choose optical materials and design mechanical support structures to make the positions of the spectrally dispersed images on the focal surface invariant over temperature. In practice however, this is often difficult or impossible, as materials with required thermal characteristics may not exist, or may have other properties or costs which make them impractical. Furthermore, modifying the design of the imaging optics to achieve temperature invariance may compromise the imaging properties of the optical system.

It is therefore an object of the present invention to provide means that would compensate for the temperature dependence of the optical system of a WDD without significantly complicating its optical design or significantly increasing its cost.

It is another object of the present invention to provide a WDD having a dispersive subsystem which produces a pre-determined non-zero shift in diffracted angle over temperature for passive compensation of temperature-induced variations in the device performance.

SUMMARY OF THE INVENTION

In accordance with the invention, there is provided a fiber optic wavelength dispersive device comprising: a front-end unit comprising a first port for launching an input optical signal; a wavelength dispersive reflector for receiving the input optical signal, for dispersing the input optical signal into a plurality of sub-beams of light with different central wavelengths, and for directing said sub-beams back at first angles along first optical paths in a dispersion plane; a spherical reflector for redirecting the input optical signal launched from the first port to the wavelength dispersive reflector, and for redirecting the sub-beams from the wavelength dispersive reflector back along second spatially separated optical paths; and, an array of beam receiving elements for receiving each of the sub-beams at a different location along the array according to the central wavelength thereof.

According to one aspect of the invention, the wavelength dispersive reflector comprises a transmissive dispersion grating (TDG) for receiving the input optical signal and for transmitting each of the plurality of sub-beams of light therethrough at a different angle of diffraction, a reflective surface spaced from the TDG for reflecting the plurality of sub-beams of light back through the transmissive dispersion grating for diffracting thereon, and a first wedged prism of an optically transparent material for refracting each of the sub-beams of light in the dispersion plane at an angle of refraction dependent on the temperature of the device, the first wedged prism having an apex angle, wherein a shift in the angles of refraction of the sub-beams provided by the first wedged prism due to a change in the temperature of the device at least partially compensates for a shift in the angles of diffraction caused by the change in the temperature of the device.

According to one aspect of the invention, the apex angle of the first wedged prism is such that the first wedged prism is effective to cause the first angles to vary with the temperature of the housing at a rate of at least 1 μrad/C so as to counteract temperature-induced variations of the second optical paths that occur outside of the wavelength dispersive reflector.

According to one aspect of the invention, the first wedged prism has a first surface facing the diffraction grating and a second surface defining the apex angle with the first surface, and wherein the first wedged prism is oriented with an apex side thereof away from the TDG.

DETAILED DESCRIPTION

Embodiments of the invention are illustrated inFIGS. 3,9, and13, with selected constituent elements and sub-systems shown inFIGS. 4-7, and11in various embodiments thereof. In all these figures, like reference labels are used to identify like elements. In some figures, axes of a same Cartesian coordinate system (x,y,z) may be shown to illustrate spatial relationships between views represented in different figures.

FIG. 3illustrates an improved wavelength dispersive device (WDD)200incorporating elements of the present invention, which in its different embodiments may operate as a WSS, a DGE, a WB, or a spectrometer. The WDD200is generally based on a WDD platform100that is illustrated inFIG. 1and described in U.S. Pat. No. 6,707,959 to Ducellier et al, which is assigned to the assignee of the instant application and is incorporated herein by reference.

The WDD200includes a light redirecting element having optical power in the form of a concave, for example spherical, reflector205, which receives a beam of light from a front-end unit122followed by an optional beam-shaping lens135, and reflects it to a wavelength dispersive reflector (WDR) subsystem206, which will be referred to hereinafter as the WDR206. The WDR206disperses the beam of light incident thereupon into its constituent wavelength channels in a dispersion plane it defines, and reflects or directs them in the form of channel sub-beams back towards the spherical mirror205, with each channel sub-beam having a different central wavelength. The channel sub-beams are reflected from the WDR206at first angles215along first optical paths233, of which only one is shown inFIG. 3for clarity, and which lie in the dispersion plane that is generally parallel to the plane ofFIG. 3. The first angles215, which depend on the sub-beam central wavelength, are also referred to herein as the output (sub-beam) angles of the WDR. The channel sub-beams are then redirected by the spherical mirror205to a back-end unit208, which includes an array of beam receiving elements235, also referred to herein generally as the array235, wherein each of the sub-beams is received at a different location along the array235according to the central wavelength of the respective sub-beam.

InFIG. 3, the optical path of the input optical signal from the front-end unit122to the spherical reflector205is indicated by a reference label201, the optical path of the input optical signal from the spherical reflector205to the WDR206is indicated by a reference label232, the first optical paths of the channel sub-beams from the WDR206to the spherical reflector205are indicated by a reference label233, and the second optical paths of the channel sub-beams from the spherical reflector205to the array of beam receiving elements235are indicated by a reference label230; the same label that is used to indicate an optical path may also be used herein to indicate light beams or sub-beams propagating along the respective optical path, so that for example channel sub-beams that impinge on the array of beam receiving elements235are generally referred to herein as the sub-beams230.

FIG. 4Aillustrates by way of example the array of beam receiving elements235, upon which three sub-beams230A,230B and230C having different center wavelengths λA, λBand λC, impinge. By design the array235receives the three sub-beams230A,230B and230C at elements2351,2352and2354, respectively, at different locations281,282and283along the array as defined by the respective central wavelengths. Preferably, the array235is disposed in a focal surface of the spherical reflector205, which, in cooperation with elements204and206, forms spectrally dispersed images of an input device aperture, such as the aperture of an optical fiber port of the WDD200, upon the array235.

In one embodiment wherein the WDD200operates as a WSS, the front end unit122may be as illustrated inFIG. 2, and may include an array of input/output optical ports132A to132D, each of which may have a corresponding lens of a lens array134coupled thereto for shaping the respective input/output beams; although four ports are shown, the WDD200in this embodiment may have any number of ports greater that two as suitable for a particular application. By way of example, the port132D functions as an input port through which an input optical signal is launched, and is referred to hereinafter also as the first port. An angle to offset lens136, also referred to herein as the switching lens136, converts the lateral offset of the input/output ports132A to132D relative to an optical axis111into an angular beam offset at a point138, which is imaged by the spherical mirror205onto the array of beam receiving elements235. The lens array134is optional and can be absent in some embodiments. The optical ports132A-D may be coupled to a ID fiber array128, and may be in the form of ends of single mode optical fibers laid out in a row in parallel v-groves in a fiber array unit (FAU)132.

In the WSS embodiment, the array of the beam receiving elements235may be an actuation array comprising a plurality of beam deflectors, which may be in the form of a micro-electro-mechanical (MEMS) array of tilting mirrors which can be used for selectively redirecting one or more of the channel sub-beams back to the spherical reflector205for reflecting said one or more of the sub-beams therefrom back to the WDR206for recombination into an output beam, whereupon the output beam, propagating generally along the optical path232in the opposite to the input optical signal direction, is redirected by the spherical reflector205and the switching lens136of the front-end unit122to a selected one of the fiber-optic ports132.

Referring toFIG. 5, one such embodiment of the back-end unit208, which is shown in a side view in a plane normal to the plane ofFIG. 3, includes a vertical fold mirror231reflecting channel sub-beams230coming from the spherical mirror205downwardly into the plane ofFIG. 3, each towards a different tilting MEMS mirror235, only one of which is shown inFIG. 5. The tilting mirrors235direct the channel sub-beams back via the fold mirror231and the spherical mirror205towards WDR206, where they are recombined into one or more output beams and directed back to couple into the front-end unit122. The beam tilt angle241introduced at the back end unit208is transformed by the switching lens136to a lateral offset corresponding to the desired input/output fiber port132A to132D. Alternatively, the actuation array235may include a liquid crystal phased array (LC or LCoS, if incorporated on a silicon driver substrate) that is operable to redirect the light as shown inFIG. 5, as described for example in U.S. Pat. No. 6,707,959 that is incorporated herein by reference.

In another embodiment wherein the WDD200operates as a DGE or a WB, the beam receiving elements125may be LC-based reflectors including LC cells for controllably rotating the polarization of the sub-beams to selectively attenuate or block the sub-beams, as described for example in U.S. Pat. No. 6,498,872 and No 6,810,169, which are incorporated herein by reference. In this embodiment, the front-end unit may include a single input/output fiber optic port followed by a circulator or one input port and one output port.

In yet another embodiment the beam receiving elements125may be photodetectors forming a photodetector array, and the WDD200operates as a spectrograph, wherein electrical signal generated by each of the photodetectors is associated with a different wavelength.

In any of the aforedescribed embodiments, an aberration correction element204may be optionally installed between the spherical reflector205and the back-end unit208in the optical paths230of the channel sub-beams and, in some embodiments, in the optical paths201of the input beam. The purpose of this correction element is to modify the paths of the optical signals focused by the spherical mirror205, so as to effectively rotate a best fit planar surface approximation focal plane associated with the spherical reflector205into coplanar coincidence with the optical signal-receiving surface of the array235. Examples of suitable field-flattening aberration correction elements that may be used for this purpose include a portion or segment of a cylindrical lens and an optically transparent wedged prism. The aberration correction element204will be referred to hereinafter as the aberration correction prism204.

Again with reference toFIG. 3, the WDR206according to one aspect of the invention includes a transmission diffraction grating (TDG)211, which may be embodied as a relief grating formed on a transmissive substrate210, and a wedge-shaped prism207having a reflective back surface223forming with a front surface222an apex angle225γ. The wedge-shaped prism will also be referred to herein as a first wedged prism207, a first prism207or simply as a prism207. As illustrated inFIG. 6in somewhat greater detail, the TDG211disperses the beam of light incident along the optical path232into its constituent wavelength channels by means of diffraction, and transmits these channels in the form of channel sub-beams along divergent optical paths242towards the first prism207, which according to one aspect of the invention operates as a beam-fold mirror redirecting the channel sub-beams back through the TDG211, where they experience a second diffraction, whereby advantageously doubling the wavelength dispersion power of the TDG211.

According to another aspect of the invention, the first prism207compensates for temperature-induced variations in performance-affecting properties of different optical and opto-mechanical elements of the device, as will be described hereinbelow. The first prism207may be made with different optical materials that are substantially transparent in the operating wavelength range of the WDD200, including, but not limited to: optical glasses, optical plastics, optical crystals, and may also include gases, liquids or vacuum. The optical material of the prism207may be selected to have positive or negative dn/dT or a combination thereof in order to obtain a desired variation in refraction over temperature. By way of example, the substrate210of the TDG211and the first prism207are made from fused silica. The front and back surfaces222,223of the prism207will also be referred to herein as the first and second surface or face of said prism, respectively.

Referring again toFIG. 4A, it is desirable that the locations281-283in the array235, at which the channel sub-beams230A-230C impinge, depend only upon the central wavelengths of the sub-beams and do not change during the device operation or over lifetime of the device for any give central wavelength within an operating wavelength range of the device. However, variations of the device temperature may affect these locations by causing the sub-beams201A-201C to shift along the array, for example as illustrated by an arrow228inFIG. 4A.FIG. 4Bshows by way of example new positions of the sub-beams230A-230C along the array235that are shifted from the original ‘design’ locations281-283due to a change in the device temperature. In the context of this invention, the term “device temperature” is used to mean the ambient temperature within the respective WDD, which is typically defined by the temperature of the device housing and varies in time in a substantially same way as the temperature of each optical element of the device. For example, inFIG. 4Bthe sub-beam201A is shown to impinge at a new location281′ that is shifted from the design location281by Δy, with the other sub-beams experiencing a similar temperature-induced shift. This temperature induced shift may detrimentally affect output spectral characteristics of the WDD200. For example in the WSS embodiment where the array elements235are tiltable micro-mirrors, the spectral content and the central wavelength of sub-beams reflected by each of the micro-mirrors235may change due to the thermal shift of the incident sub-beams, leading to a spectral shift of the output beam.

As the temperature of the optical system of the WDD200changes, a number of effects may cause the optical beam paths through the system to vary with temperature, resulting in the shifts of the locations281-283at which the sub-beams are received by the array325. These effects include thermal expansion or contraction of different elements in proportion to their respective coefficients of thermal expansion (CTE), thermally-induced changes of refraction index n of optical elements in proportion to rates dn/dT of the refractive index change with temperature of the particular optical materials, which cause angles of refraction in the system to vary according to Snell's Law, and relative displacement of different optical elements due to thermal expansion gradients of a supporting mechanical structure.

Choosing optical materials and designing mechanical support structures to make the positions of the spectrally dispersed images on the focal surface invariant over temperature may not be practical or possible, as materials with the required values of dn/dT and CTE may not exist, or may have other properties or costs which make them impractical. Furthermore, modifying the design of the imaging optics to achieve temperature invariance may compromise imaging properties of the optical system.

By way of example, in one embodiment elements136,204,205,210and207are made of low expansion fused silica material. Elements122,136,204,205,210,207, and208are held together with a low expansion Invar metal frame schematically show at250, also referred to herein as a housing. The array235is in the form of a MEMS chip held on a Pyrex substrate, which is mounted on an alumina ceramic carrier (not shown). The invar frame250is attached to the ceramic carrier with a post located near the MEMS chip235. Despite using low expansion materials, computer aided analysis showed an unacceptably large thermal shift of the sub-beam receiving locations281-283at the MEMS array235, before benefits of the present invention are realized as described hereinbelow.

Some of the effects that may cause this temperature-induced shift in the WDD200include: variations in refracted angles at the surfaces of the switching lens136, the optional beam-shaping lens135, and the aberration correction prism204due to the dependence of the index of refraction n of a transmissive optical element on its temperature T, which is typically characterized by the dn/dT parameter of the respective optical material; thermal expansion of the TDG211, which causes diffraction angles experiencing by the sub-beams to vary with T; variation of the focal length of the spherical mirror205due to its thermal expansion; thermal expansion of the array235; translation of the array235relative to the invar frame due to the differential thermal expansion of the invar frame and ceramic carrier; tilts and translation of elements122,135,204,205,206,208relative to one another due to CTE of the invar frame, and distortion of the invar frame due to differential expansion of the invar frame and the ceramic carrier.

Aspects of the present invention related to compensation of thermally-induced shifts in the WDD200will now be described with reference toFIG. 7, which illustrates the internal structure and operation of the WDR206in greater detail.

According to one aspect of the invention, the WDR206produces a pre-determined non-zero shift in a diffraction angle over temperature, which counteracts and at least partially compensates temperature-induced variations of optical paths201,232of the input optical beam, and temperature-induced variations of the optical paths230of the channel sub-beams from the spherical mirror205to the array235, which occur outside of the wavelength dispersive reflector.

Functioning of the embodiment of the WDR206ofFIGS. 3 and 7according to this aspect of the invention can be explain by considering the propagation of a single channel sub-beam therein.

Referring toFIG. 7, the input optical signal232impinges upon the transmission diffraction grating211at an angle of incidence θ1, and is dispersed into a plurality of transmitted sub-beams, of which a single channel sub-beam242is shown. The transmitted channel sub-beam represented by a ray242is diffracted by the TDR211at an angle θ2according to the grating equation (1):

where m is the diffraction order, λ is the central wavelength of the sub-beam in vacuum, d is the grating period of the TDG211, and nais the refractive index of the surrounding medium, for example air.

Ray242is incident on the first surface222of the prism207at an angle of incidence θ3given by equation (2):
θ3=β−θ2(2)

where β is the angle between the TDG211and the first surface222of the prism207, and is also referred to herein as the prism orientation angle. The wedged-shaped prism207has an index of refraction ng, and an apex angle γ. Ray242is refracted at the first surface222following Snell's law, then reflected at the reflective second, or back surface223of the prism207, then is refracted again at the first surface222, and exits prism207as a ray243at an angle of refraction θ4, which is related to θ3according to the following equation (3):

Ray243is coupled back to the TDG211at an angle of incidence θ5that is given by equation (4):
θ5=β−θ4(4)

Upon transmitting through the TDG211, the ray243is diffracted a second time thereupon, and exists the TDG211with the channel sub-beam233at an angle θ6thereto. The angle θ6, which defines the first angle215and the direction of the first optical path233of the corresponding channel sub-beam relative to the TDG211, satisfies the diffraction equation (5):

The WDR206is thus effective in producing a wavelength dependent angle θd=θ6−θ1between the input beam232and the channel sub-beam233, which has been twice diffracted by the TDG211.

When the ambient temperature T inside the WDD200changes, a thermal expansion or contraction of the substrate material of the TDG211changes the grating period d, resulting in changes in the diffraction angles θ6and θ2. If the grating period at a reference temperature T0is equal to d0, and the linear coefficient of thermal expansion (CTE) of the substrate material is α, the period d at a different temperature T can be found from the following equation (6):
d(T)=d0[1+α(T−T0)]  (6)

The refractive indices naand ngmay also be functions of temperature, as described by the following equations (7) and (8):

The rate of change of the WDR diffraction angle θ6with temperature can be determined using equations (1) through (8), which take into account the temperature dependencies of the angles of diffraction on the TDG211, and the angles of refraction on the front surface222of the prism207.

By way of example,FIG. 8shows a dependence of the rate of change R of the first angle215at the output of the WDR206with temperature due to a combined effect of the temperature-induced changes in the TDR211and in the first prism207. The results shown inFIG. 8have been computed using equations (1)-(8) for the following exemplary embodiment of the WDD200: line spacing of the TDG211966.2 lines/mm, the first incident angle θ1is 44 degrees, both the grating substrate and prism are made of fused silica glass, having a coefficient of thermal expansion of 0.5 ppm/° C., and a dn/dT of 8.4×10−6per ° C. at λ=1550 nm.

In this example, the TDG211alone, in the absence of the prism207with only the reflective surface233, is responsible for an angular shift of the first optical path233with temperature at a rate of approximately R=−2.6 μrad/C, where μrad stands for microradians. At an apex angle γ=γ0˜7.5 degrees and β about 60 degrees, the temperature-induced variations in the sub-beam refraction at the prism207exactly compensate the temperature-induced variations of the sub-beam diffraction at the TDG211, resulting in R=0. Note that negative values of the apex angle correspond to a slope of the first face222which is opposite to that shown inFIG. 7, i.e. when the first prism207is oriented with an apex side217thereof towards the TDG211. In this embodiment, in order for the first prism207to counteract the effects of temperature variations of the TDG211, the first prism207should be oriented with the apex side thereof217away from the TDG211, as shown inFIGS. 3 and 7.

It may be preferable to select the prism207so that it over-compensates or under-compensates the beam-tilting effect of a temperature expansion of the TDG211, so that the WDR206could compensate for temperature-induced variations in the second optical path201that occur outside of the WDR206.

It will be appreciated that equations (1)-(8), and the results shown inFIG. 8, although generally correctly illustrating certain features of the present invention, are approximate, and a more rigorous design of the optical subs-system of the WDD200, including effects of the device temperature variations, may require using commercial computer aided design software as known to those skilled in the arts. In particular, finite element analysis software available for example from ANSYS, Inc. can be used to calculate mechanical displacements and distortions of the packaging, frames, and optical elements. Optical ray tracing software such as ZEMAX® or CODE V® can then be used to calculate the optical effects of temperature, taking into account the aforementioned mechanical distortions and displacements, along with changes in the refractive index of optical materials and media, and diffractive properties of the diffractive elements.

In the optical design of the WDD200with a particular grating period do, angles θ1and θ6may be chosen to give a desired combination of grating dispersion, diffraction efficiency, and optical imaging properties. In such embodiments wherein θ1and θ6are fixed by the system design, the channel sub-beam shift Δy at the array235over temperature for a particular center wavelength may be computed using various commercially available software for optical ray-tracing and opto-mechanical FEA (finite element analysis) known to those skilled in the art.

As we found, by suitably selecting the apex angle γ of the prism207and the orientation thereof relative to the WDG211as defined by the angle β between the front surface222of the prism207and the TDG211, temperature-induced variations of the second optical paths201can be substantially eliminated or at least significantly reduced, resulting in a significant reduction or elimination of the channel sub-beam shift Δy at the array235, and making the locations at the array235at which channel sub-beams of given central wavelengths are received substantially temperature independent in an operating temperature range of the device.

In particular, the angles γ and β can be selected for providing a desired value of the first angle215at a reference temperature, while causing the first angle215to vary with the temperature of the device at a non-zero rate R so as to counteract and substantially cancel temperature-induced variations of the optical paths232and230that occur outside of the WDR206. According to one aspect of the invention, the apex angle and orientation of the first prism207is preferably chosen so that the temperature rate R of the angular tilt of the sub-beams233at the output of the WDR206is at least 1 μrad/C.

By way of example, we computed the sub-beam movement along the array235for an embodiment of the WDD200ofFIG. 3using commercial optical ray-tracing software, for an optical frequency of 193.9 THz, and the following device parameters: the line spacing of the TDG211is 966.2 lines/mm, the first incident angle θ1is 44 degrees, the grating substrate of the TDG211and prisms204and207made of fused silica glass having a coefficient of thermal expansion of 0.5 ppm/° C., and a dn/dT of 8.4×10−6per ° C. at λ=1550 nm. The spherical mirror205has a focal length of f=42.5 mm, with changes Δφ in the WDR output angle215φ being mapped to sub-beam shifts Δy along the array235according to the following equation (9):
Δy=f×Δφ.  (9)

Further in this example, the sub-beam shift Δy along the array235was computed for a temperature change ΔT=50° C. The calculations showed a sub-beam shift Δy of +5.4 μm due to the thermal expansion of the TDG211alone, a shift of +5.7 μm due to refractive index change with temperature of the second aberration correction prism204alone, and a shift of −0.4 μm due to thermal effects on other optical parts, not including the first thermal compensation prism207, combined. Accordingly, the net thermal beam shift that needs to be corrected in this system in the absence of the first prism207is the sum of these 3 values, i.e. +10.7 μm, and in this embodiment is defined primarily by the TDG211and the aberration-correcting prism204. By way of example, a sub-beam shift of 1 μm along the array235may result in about 1 GHz central wavelength error for an optical channel centered at 193.9 THz, so that a net sub-beam shift at the array235of 10.7 μm, if not compensated, may result in about 10.7 GHz error in the central wavelength, which would be detrimental in many applications.

Accordingly, the apex angle γ and the orientation angle α of the first prism207are chosen so its refractive index change over ΔT causes a sub-beam shift Δy=−10.7 μm in order to substantially fully compensate the thermal shifts due to the grating211expansion, refractive index change of the aberration correction prism204, and thermal effects in other optical elements, providing a substantially zero, or less than about 0.3 μm, sub-beam shift Δy at the array235when the device temperature changes by 50 degrees. In this example, the angle β between the grating211and the prism first face222is 71.1°, and the apex angle γ of the first prism207is 15 degrees, corresponding to a rate R of angular tilt with temperature of the sub-beams233at the output of the WDR206of about 2.7 μrad/C. Note that the first prism207is substantially overcompensating the thermal shifts due to the thermal expansion of the TDG211alone, in order to provide a substantially reduced thermal shift of the center wavelength for the entire optical system.

FIGS. 3 and 7illustrate one embodiment of the WDR of the present invention that can be designed to provide angular shifting of the diffracted sub-beams at the output of the WDR with temperature at a pre-defined positive or negative rate, for example with an absolute value greater than 1 μrad/C, thereby enabling passive auto-compensation of thermally-induced changes in the spectral characteristics of a WDD.

FIGS. 9 and 13schematically illustrate two other embodiments of the WDR of the present invention, which are identified with reference labels206′ and206″, which are shown by way of illustration in the context of the same general WDD platform as that ofFIG. 3, and have similar functionality to that of WDR206.

Turning first toFIG. 9, a WDD300is shown that is otherwise identical to WDD200, but with a WDR206′ replacing the WDR206ofFIGS. 3 and 7. The WDD300operates generally as described hereinabove with reference toFIG. 3, with like element having like reference labels.

The WDR206′ ofFIG. 9differs from the WDR206ofFIGS. 3 and 7in that in the WDR206′ the first prism307is positioned in front of the TDG211in the optical paths of the channel sub-beams between the spherical mirror205and the TDG211. A mirror323is disposed optically after the TDG211and provides a reflective surface for reflecting the channel sub-beams transmitted through the TDG211to couple back into the TDG211, so that the TDG211operates in a double-pass configuration for effectively doubling its dispersion power. By suitably selecting the apex angle and orientation of the first prism307with respect to the TDG211, the first prism307may be effective in counteracting the effects of temperature variations on the TDG211and other elements of the device, thus enabling the temperature compensation.

By way of example,FIG. 10illustrates the dependence of the rate of change R of the first angle215at the output of the WDR206′ with temperature for an embodiment wherein the input optical signal is incident upon the first prism307at about zero incidence angle.

Similarly to the WDR206ofFIGS. 3 and 7, the WDR206′ can be configured to provide angular shifting of the diffracted sub-beams with temperature at a pre-defined positive or negative rate, thereby enabling passive auto-compensation of thermally-induced changes in the spectral characteristics of the WDD300, and is thus effective in providing passive auto-compensation of temperature-induced variations in the spectral characteristics of a WDD.

Compared to the embodiment ofFIG. 3, one drawback of the embodiment ofFIG. 9, wherein the first prism is separate from the TDG211, is that the channel sub-beams have to pass at least twice each of the faces of the first prism307, thereby experiencing additional optical loss due to undesired reflections at the prism-air interfaces. Moreover, in the WSS embodiment of the WDD300, wherein the array235reflects the sub-beams back for recombining at the TDG211into one or more output beams, the channel sub-beams pass the air-prism interfaces of the prism307as many as eight times in total. Although the faces of the prism307can be anti-reflection coated, the additional optical loss associated therewith nevertheless can be disadvantageous for some applications of the WDD300. Another potential drawback of the WDR206′ ofFIG. 9is the necessity to align three optical elements instead of two when assembling the WDR206′.

Therefore, in another embodiment the first prism307may be made integral with the TDG211, thereby avoiding the aforedescribed potential drawbacks of the WDR design ofFIG. 9. This embodiment of the WDR206′ is schematically shown inFIG. 11, which also shows for illustration optical paths of three channel sub-beams produced by the TDG211from the input optical signal232.

FIG. 12illustrates by way of example the dependence of the rate R of change of the first angle215at the output of the WDR206′ with temperature for the WDR embodiment ofFIG. 11. Clearly, by suitably adjusting the apex angle of the prism307, this embodiment of the WDR206′ can also be configured to compensate both positive and negative shifts of the sub-beam locations on the array235due to temperature changes in opto-mechanical properties of the WDD300outside of the WDR206′.

One potential drawback of this configuration as compared with the embodiment ofFIG. 3is that it may require that the input optical signal and the output channel sub-bands impinge upon the prism-air interface of the first prism307at rather large angles of incidence. For example, when the prism apex angle of the first prism307in the configuration ofFIG. 11is about 5° to compensate for the CTE of the TDG211, the sub-beams233may have to exit the first prism307at an exit angle216of less than 30° to the prism-air interface, which makes providing an effective AR coating thereof more difficult. The difficulties of providing an effective AR coating of the prism307are even greater if the WDR ofFIG. 11has to provide a net angular shift with temperature of the order of 10 μrad/C, as in the example described hereinabove with reference to temperature compensation of the WDD200, which may require the exit angle216to be less than 15°.

Referring now toFIG. 13, a WDD400is illustrated which utilizes another embodiment of the WDR206of the present invention, which is indicated with a reference label206″. The WDD400operates generally as described hereinabove with reference toFIG. 3, with like element having like reference labels.

Similarly to the WDR206ofFIGS. 3 and 7, the WDD206″ includes the TDG211followed with the first prism207′ having the reflective back surface223and the refractive from surface222oriented at an angle to the TDG211. Additionally, the WDR206″ includes a second wedged prism407disposed in front of the TDG211integral therewith facing the spherical reflector205, for refracting the sub-beams at angles of refraction that depend on temperature so as to further counteract temperature-induced variations of the second optical paths that occur outside of the WDR206″. The WDR206″ functions similarly to the WDR206and206′ described hereinabove, and may provide additional advantages by enabling a more flexible optical design of the WDR, at a cost of having an additional optical component.

In another aspect of the invention, the desired variation in the WDR output angle215may be achieved with active temperature control of the first prism207. In one embodiment illustrated inFIG. 14, a heater or thermo-electrical cooler (TEC)401and a temperature sensor402are thermally coupled to the first prism207, and the temperature thereof is controlled in a feedback loop including a temperature controller404, which may also be connected to a second temperature sensor403for measuring the ambient temperature within the device, which may be thermally coupled to the device housing or disposed therewithin at a distance from the first prism. The feedback loop may be controlled by a controller404and have a setpoint which may be varied as a function of the ambient temperature within the device, or of some other input parameter, thereby enabling adjusting the temperature shift of the output sub-beam angle of the WDR206. This arrangement may be advantageous when the exact value of a required temperature shift of the first angle is not known in advance, for example when part tolerances or manufacturing process variations cause the required temperature drift R to vary from device to device. The first prism and TDG in this aspect of the invention may be chosen so as to passively provide a pre-determined value of the temperature shift, and temperature control of the first prism may be added to provide a fine tuning of the amount of temperature shift of the first angle.

It will be appreciated that the shown embodiments may be modified in many different ways within the scope of the present invention while still providing the benefits of the passive auto-compensation of temperature variations in a WDD. For example, although in the embodiments described hereinabove the first prism is configured so as to over-compensate the effect of temperature-induced variations of the TDG on the sub-beam output angle of the WDR, other embodiments are contemplated wherein temperature-induced shifts originated from optical and/or opto-mechanical components of the WDD outside of the WDR has a combined effect that is opposite to that of temperature-induced changes of the TDG, and the first prism is configured so as to under-compensate the effect of temperature-induced variations of the TDG on the sub-beam output angle of the WDR.

Of course numerous other embodiments may be envisioned without departing from the spirit and scope of the invention.