WO2002048772A2

WO2002048772A2 - Method and apparatus for producing fiber bragg gratings

Info

Publication number: WO2002048772A2
Application number: PCT/IL2001/001149
Authority: WO
Inventors: David Mendlovic; Uriel Levy; Gal Shabtay; Zeev Zalevsky
Original assignee: Civcom Devices & Systems Ltd.
Priority date: 2000-12-12
Filing date: 2001-12-12
Publication date: 2002-06-20
Also published as: WO2002048772A3; AU2002222477A1

Abstract

A method of fabricating a fiber Bragg grating (FBG) (50), the method comprising: generating changes in phase and/or amplitude of light in a light beam (40) that are functions of two coordinates in a plane on which the beam is incident so as to generate a given optical intensity pattern; and illuminating a segment of optic fiber (22) with the optical intensity pattern to imprint the fiber segment with a spatial variation in its index of refraction that has a pattern (52) responsive to the optical intensity pattern.

Description

METHOD AND APPARATUS FOR PRODUCING FIBER BRAGG GRATINGS

FIELD OF THE INVENTION

The invention relates to fiber Bragg gratings (FBG) and methods of producing such gratings. BACKGROUND OF THE INVENTION

A fiber Bragg grating (FBG) is an optical filter comprising a Bragg grating formed in a segment of optical fiber. The Bragg grating comprises a plurality "Bragg" planes generated by a spatial variation, which is generally periodic with distance along the fiber segment, of the index of refraction of the material from which the fiber segment is formed. Distance between the Bragg planes, which is substantially equal to the period of the variation define characteristic "Bragg wavelengths" of the FBG. The Bragg wavelengths are wavelengths that are equal to an integer multiple of the period of the variations in the index of refraction of the FBG times twice the average index of refraction of the FBG.

The Bragg planes in the FBG reflect energy from light waves that are transmitted into the fiber segment. For light that enters the FBG for which the wavelength of light is substantially equal to a Bragg wavelength of the FBG, reflections of energy from the light by the Bragg planes interfere constructively and the light is strongly reflected. For light that enters the FBG, for which the wavelength of the light is substantially different from a Bragg wavelength of the FBG, the reflections do not interfere constructively and most or substantially all the energy of the light is transmitted through the FBG.

Generally, the amplitude of the variations of the refractive index in a FBG is small and each Bragg plane reflects a relatively small portion of the energy of light that is incident on the FBG. However, the number of the Bragg planes (which is equal to the number of periods of the variations) is generally very large, resulting in a filter that provides for reflectivity in excess of 99% for light having a wavelength substantially equal to a Bragg wavelength of the FBG. In addition, if the period of the variations is constant, the finesse of the filter, which is proportional to the number of Bragg planes in the FBG, is large and the band-stop of the FBG consequently narrow. Chirped FBGs having large band-stops are produced by varying the period of the variations in the index of refraction that generate the Bragg planes of the FBGs. Chirped FBGs are often used to compensate for chromatic dispersion.

A desired variation in the index of refraction of a fiber required to produce a Bragg grating in the fiber is usually generated by exposing the fiber to an intensity pattern of light that varies spatially in substantially a same way as the desired variation in the index of refraction. Generally, UN light is used to generate the variation in the index of refraction. Most materials from which the core of an optical fiber is fabricated are sensitive to UN light, or may have their UN photosensitivity enhanced by adding an appropriate dopant to the core material. For example, the cores of optic fibers are often formed from a silica whose UN photosensitivity can be enhanced by doping with Germanium. Upon exposure to UN light, the index of refraction of a region of the photosensitive core changes permanently by an amount proportional to intensity of the UN light to which the region is exposed. As a result, following exposure to UN light having a desired periodic spatial pattern, a fiber is imprinted with a substantially permanent spatial variation in its index of refraction that images the periodic pattern of the UN light to which the fiber is exposed.

A desired periodic spatial intensity pattern of UN light used to imprint a Bragg grating in an optic fiber and fabricate thereby a FBG is often produced using an interferometer, which generates an interference pattern between two UN laser light beams to produce the intensity pattern. In some processes for imprinting a Bragg grating in a fiber, a suitable UN light source illuminates the fiber through a slit that is moved along the fiber. As the slit and light source move along the fiber, intensity of light that is provided by the light source is varied to expose different regions of the fiber to different intensity light and imprint thereby the fiber with a desired variation in index of refraction.

In some FBG production processes an interference pattern generated by UN light that is incident on a phase plate is used to provide a desired UN intensity pattern for imprinting a fiber segment with a Bragg grating. Generally, the phase plate is a one dimensional phase plate that generates a phase change in light incident on the phase plate as a function of position of incidence of the light relative to a single direction, hereinafter referred to as an "axis", in the plane of the phase plate. (For light incident on the phase plate at any point along a same line perpendicular to the axis, the phase change generated by the phase plate in the incident light is the same.) In some phase plates the phase changes are generated by variations in a surface contour of the plate, for which surface contour, contour lines are straight lines perpendicular to the axis. In some phase plates the phase changes are generated by the index of refraction of the plate material which varies in such a way that isolines, i.e. lines that connect regions of the phase plate having a same value of the index of refraction, are perpendicular to the axis. The axis of the phase plate is aligned parallel to the fiber that is being imprinted with a Bragg grating so that the contour lines or isolines are perpendicular to the fiber. US Patent 5,367,588, the disclosure of which is incorporated herein by reference, describes imprinting a fiber with a variation in index of refraction, to fabricate a FBG, by illuminating the fiber with UN light that passes through a one dimensional phase plate. The phase plate is held in close proximity to the fiber section and generates an interference pattern in the UN light, which is reproduced in a corresponding variation in index of refraction in the fiber segment.

US patent 5,940,568, the disclosure of which is incorporated herein by reference, describes imprinting a Bragg grating in a planar optical wave-guide having a photosensitive core sandwiched between buffer layers. One of the buffer layers is formed with a plurality of parallel grooves that are perpendicular to the axis of the wave-guide. Light that illuminates the buffer layer is diffracted by the grooves and generates an interference pattern in the waveguide that transcribes the wave-guide with a desired periodic variation in the index of refraction of the wave-guide that imprints the Bragg grating.

US Patent 6,174,648 describes a method of producing an FBG having a length longer than 100 mm. To produce the FBG, a long segment of optical fiber is held in a spiral groove formed in a suitable planar substrate. A phase mask is secured parallel to the planar substrate above the fiber. The phase mask has a plurality of elongate pits formed therein that are positioned along a spiral curve that mirrors the spiral groove in which fiber is placed. The long dimension of each groove is substantially perpendicular to the spiral curve at the point along the curve at which the groove is located. Each groove is thereby substantially perpendicular to the fiber. Sections of the phase plate along the spiral curve comprising a plurality of elongate grooves are sequentially illuminated with laser light to form a diffraction pattern in the fiber that imprints the fiber with a desired variation in index of refraction.

Prior art methods of generating intensity patterns of light for imprinting a fiber with a Bragg grating often cannot generate a desired pattern with sufficient accuracy. As a result, a FBG fabricated using prior art methods for generating a light intensity pattern that imprints the fiber with a variation in index of refraction may not provide desired performance. Furthermore, in prior art methods of generating a desired optical intensity pattern for imprinting a Bragg grating in a fiber, the optical intensity pattern is generally determined so as to provide a desired intensity pattern in a "central plane" that passes through the axis of the fiber to be imprinted. The diameter of a typical fiber used for a FBG is relatively small. Therefore, for points off-plane from the central plane that lie in a same cross section of the fiber or, for blazed gratings, for off-plane points in a same "blaze plane" in the fiber, the optical intensity is assumed to be substantially the same as for points along the intersection of the central plane and the cross section or blaze plane. Changes in the optical intensity for different points in a same cross section or blaze plane are not considered to be sufficiently large to substantially compromise performance of the FBG. However, for some situations these assumptions regarding changes in optical intensity for off-plane points may not obtain and the changes may compromise FBG performance.

SUMMARY OF THE INVENTION An aspect of some embodiments of the present invention, relates to providing a method for generating an optical intensity pattern for use in imprinting an optic fiber with a Bragg grating that generally provides more control in generating a desired intensity pattern than prior art methods.

In of some embodiments of the present invention the method is used to provide more control in determining intensity of an optical intensity pattern at points off-plane from a central plane through the fiber axis than can generally be obtained using prior art methods. In some embodiments of the present invention the method is used to provide an optical intensity pattern for imprinting a Bragg grating in a fiber, for which at points in a same cross section of the fiber or, for blazed gratings, for points in a same blaze plane in the fiber, the intensity of the pattern is more uniform than in prior art methods.

In some embodiments of the present invention the method is used to fabricate a FBG for which a desired spatial variation in the index of refraction of the FBG generally reproduces a desired variation more accurately than a variation in index of refraction in a prior art FBG reproduces a desired variation.

In accordance with an embodiment of the present invention, an optical intensity pattern for imprinting a Bragg grating in a fiber is generated by a computer generated hologram (CGH). A CGH generally provides substantially more control and flexibility in generating a desired optical intensity pattern than conventional one-dimensional phase plates or gratings. CGHs are often used, for example, to shape light beams, generate displays such as heads up displays, and generate 3D optical wave fronts used for measuring a shape of an optical element. A CGH is usually formed either as a transmission or a reflection mask that is partitioned into a plurality of small pixels, each of which is configured so as to impart a desired phase and/or amplitude to light that is respectively transmitted through or reflected from the pixel. Numerous methods for "encoding" pixels in a CGH with desired phases and/or amplitudes are known. Some of these methods are described in US Patent 6,166,833 the disclosure of which is incorporated herein by reference. By encoding pixels in a CGH with appropriate phases and/or amplitudes, an optical intensity pattern for use in fabricating a FBG can be generated when the CGH is properly illuminated that reproduces a desired intensity pattern with accuracy generally greater than can be obtained using a one-dimensional phase plate.

In accordance with an embodiment of the present invention, the desired optical intensity pattern to be generated using a CGH is an optical intensity pattern defined as a function of position in a given desired "active" volume. The CGH can be positioned relative to an optic fiber to be imprinted with a Bragg grating responsive to the optical intensity pattern generated by the CGH so that the active volume overlaps at least a portion of the volume of the fiber.

In accordance with an embodiment of the present invention, pixels in the CGH are encoded responsive to desired intensity values in the active volume so that in the active volume an optical intensity pattern generated by the CGH is substantially the same as the desired intensity pattern. In some embodiments of the present invention phases and/or amplitudes of pixels in the CGH are determined as convergence values provided by an iteration algorithm. Optionally, the iteration algorithm is an algorithm described in US Patent Application 09/277,322, the disclosure of which is incorporated herein by reference. There is therefore provided, in accordance with an embodiment of the present invention a method of fabricating a fiber Bragg grating (FBG), the method comprising: generating changes in phase and/or amplitude of light in a light beam that are functions of two coordinates in a plane on which the beam is incident so as to generate a given optical intensity pattern; and illuminating a segment of optic fiber with the optical intensity pattern to imprint the fiber segment with a spatial variation in its index of refraction that has a pattern responsive to the optical intensity pattern.

Optionally, the pattern of the variation in index of refraction is substantially the same as the optical intensity pattern.

In some embodiments of the present invention generating the changes in phase and/or amplitude comprises: configuring a reflection or transmission mask to impart a given phase and/or amplitude to light incident on the mask that is a function of two coordinates of the point of incidence of the light on a plane of the mask and directing the light beam to be incident on the mask. Optionally configuring a mask comprises providing a mask partitioned into a plurality of pixels and coding each pixel in the mask to impart the given phase and/or amplitude to light that is incident on the pixel.

Optionally coding of the pixels is determined responsive to the given intensity pattern using an iteration algorithm.

In some embodiments of the present invention the given optical pattern is defined by intensity values for points located on a same plane.

In some embodiments of the present invention the given optical pattern is defined by intensity values at points having a three dimensional spatial distribution. In some embodiments of the present invention for any two points on a same cross section of the fiber, the intensity of the optical intensity pattern is substantially the same.

In some embodiments of the present invention for which the Bragg grating comprises blazed Bragg planes for any two points in the fiber on any same plane through the fiber parallel to the blazed Bragg planes, the intensity of the optical intensity pattern is substantially the same.

There is further provided a fiber Bragg grating formed in an optic fiber in accordance with an embodiment of the present invention wherein for all points on a same cross section of the fiber the index of refraction of the fiber is substantially the same.

There is further provided a fiber Bragg grating comprising blazed Bragg planes formed in an optic fiber in accordance with an embodiment of the present invention wherein for all points on a same plane in the fiber parallel to the blazed Bragg planes the index of refraction of the fiber is substantially the same.

BRIEF DESCRIPTION OF FIGURES Non-limiting examples of embodiments of the present invention are described below with reference to figures attached hereto and listed below. In the figures, identical structures, elements or parts that appear in more than one figure are generally labeled with a same numeral in all the figures in which they appear. Dimensions of components and features shown in the figures are chosen for convenience and clarity of presentation and are not necessarily shown to scale. Fig. 1 schematically shows imprinting an optic fiber with a Bragg grating using an optical intensity pattern generated by a one dimensional phase plate, in accordance with prior art; Fig. 2 schematically shows imprinting an optic fiber with a Bragg grating using an optical intensity pattern generated by a CGH, in accordance with an embodiment of the present invention;

Fig. 3 schematically shows the fiber and CGH shown in Fig. 2 and a volume in which a desired optical intensity pattern to be generated by the CGH is defined, in accordance with an embodiment of the present invention; and

Fig. 4 shows a graph in which optical transmission of a conventional FBG is compared to optical transmission of a simulated FBG, in accordance with an embodiment of the present invention. DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

Fig. 1 schematically shows using a one-dimensional phase plate 20 to imprint an optic fiber 22 with a Bragg grating 24 having Bragg planes represented by edge shaded disks 26 to form a FBG 28, in accordance with prior art. In Fig. 1 phase plate 20 is by way of example a

"surface contour phase" plate formed with a plurality of parallel grooves 30 using any of various micromachining methods known in the art.

Phase plate 20 is positioned above fiber 22 with the plane of the phase plate parallel to an optic axis 32 of the fiber and grooves 30 perpendicular to the axis. Phase plate 20 is illuminated with, optionally, UN light 40, which after passing through the phase plate forms an interference pattern (not shown) that illuminates fiber 22 with a spatial intensity pattern of UN light. The intensity pattern produces a permanent change in the index of refraction of fiber 22, which change in the index of refraction has a spatial pattern substantially the same as the intensity pattern of UN light 40 that illuminates the fiber. The change in the index of refraction generates Bragg planes 26.

The depth and width of grooves 30 and their spacing are determined using methods known in the art so that the intensity pattern generated by phase plate 20 reproduces a desired intensity pattern that varies periodically with distance along fiber 22 in a central plane 42 through axis 32 of the fiber. The period of the variation is chosen to define desired Bragg wavelengths for FBG 24. The number of periods is chosen to provide FBG 24 with a required finesse. Generally, a FBG comprises many thousands of Bragg planes 26 and a phase plate 20 used to imprint the Bragg planes has many thousands of grooves 30. For convenience of presentation only a few grooves 30 in phase plate 20 and only a small number of Bragg planes 26 are shown in Fig. 1. It is noted that often a number of Bragg planes that can be imprinted in a fiber at one time by a single phase plate is not sufficient to form a FBG in the fiber having a required finesse. In such a case the phase plate is often moved along the fiber to sequentially imprint a sufficient number of sections of the fiber with Bragg planes so that a total number of Bragg planes imprinted in the fiber provides a FBG with the required finesse.

The diameter of the cross section of fiber 22 is usually on the order of 10 microns and the intensity pattern of UN light 40, which is formed by phase plate 20 and illuminates fiber 22, is assumed to be substantially the same for all points in a same cross section of the fiber. However, in some situations, the assumption of "cross-sectional" uniformity for the intensity pattern may not rigorously apply and the optical intensity for points in a same cross section of fiber 22 may vary sufficiently so as to degrade performance of FBG 24. To schematically indicate this possible variability in intensity, disks 26 representing Bragg planes imprinted in fiber 22 are shown having non-uniform thickness and as being tapered in directions perpendicular to central plane 42.

Whereas Bragg planes 26 are schematically shown as spatially sharply defined disks, in general a spatial light pattern generated by a phase plate in a fiber, and as a result the imprinted variation in the fiber's index of refraction, varies smoothly with distance along the fiber. Usually, a desired optical intensity pattern variation to be generated by a phase plate in a fiber so as to imprint the fiber with a Bragg grating is an harmonic variation, which is often modulated by a suitable "apodizing function". The apodizing function, which may for example be a raised cosine function, provides a smooth transition between a region of the fiber imprinted by the phase plate with a Bragg grating and a non-imprinted region of the fiber.

Fig. 2 schematically shows imprinting a Bragg grating 50 comprising Bragg planes represented by edge shaded disks 52 in a fiber 22 to form a FBG 54 using an optical intensity pattern generated by a CGH 56, in accordance with an embodiment of the present invention. CGH 56 comprises a suitable substrate 58 formed with a plurality of optionally square pixels 60, two of which are indicated for clarity of visualization by shaded squares 64 immediately above the pixels that they indicate. By way of example, CGH 56 is a phase only CGH in which each pixel 60 is divided into two equal regions 61 and 62 each of which is encoded with a desired phase. A desired phase is encoded in a region 61 or 62 of a pixel 60 by etching the region to a depth in substrate 58 that decreases an optical path length through the substrate by the desired phase for light having a wavelength for which the CGH is to be used. Various depths for regions 61 and 62 of pixels 60 are shown in Fig. 2. It is noted that there are numerous different ways for encoding a CGH known in the art and CGHs encoded in ways different from the way in which CGH 56 is encoded may be used in the practice of the present invention. For example, a pixel of a CGH similar to CGH 56 may be divided into more than two phase-coded regions or phase-coded regions having different sizes. A pixel of a CGH may also be both phase and amplitude coded, using for example a method similar to that described in an article by A.W. Lohmann and D.P. Paris in Appl. Opt. 6; p 739; 1967, the disclosure of which is incorporated herein by reference.

CGH 56 is located above optic fiber 22 with the plane of the CGH parallel to optic axis 32 of the fiber. Optionally, UN light 40 is directed so that the light is incident on CGH 56 in a direction optionally normal to the plane of the CGH. Pixels 60 are phase encoded so that after passing through CGH 56 UN light 40 forms an interference pattern that illuminates fiber 22 with a an intensity pattern of UN light that imprints a desired Bragg grating in the fiber.

CGH 56 generally provides substantially more flexibility in generating a desired optical intensity pattern than a prior art one dimensional phase plate such as shown in Fig. 1 and can generally be used to reproduce a desired optical intensity pattern with greater accuracy than a one-dimensional phase plate. As a result, FBG 54 produced using CGH 56, in accordance with an embodiment of the present invention, may provide enhanced performance relative to a FBG produced using prior art one dimensional phase plates.

In particular, in accordance with some embodiments of the present invention, CGH 56 is designed to generate an optical intensity pattern in fiber 22, that is determined responsive to intensities of a desired intensity pattern defined at a plurality of points having a three- dimensional distribution in a volume region of the fiber. For example, in some embodiments of the present invention CGH 56 is designed so that for all points in a volume region of fiber 22 located on any same cross section of the fiber, the optical intensity that it produces when illuminated by UN light 40 is substantially uniform. CGH 56 will thereby produce an intensity pattern that may be substantially more uniform across any given cross section of fiber 22 than an intensity pattern produced by prior art one-dimensional phase plates. The enhanced "cross- sectional" uniformity is schematically indicated by disks 52 having a constant thickness.

In some embodiments of the present invention, CGH 56 is designed responsive to a desired optical intensity pattern defined in a volume using an iterative algorithm, such as an iterative algorithm described in US Patent Application 09/277,322 referenced above. An iterative algorithm used to design CGH 56, in accordance with an embodiment of the present invention, and in particular an iterative algorithm similar to that discussed in application 09/277,322 is discussed below with reference to Fig. 3.

Fig. 3 schematically shows CGH 56 and optic fiber 22 shown in Fig. 2 and a coordinate system 70 used to define positions of the CGH and optic fiber and features thereof. Let a surface 57 of CGH 56, which surface 57 faces fiber 22, lie in the xy-plane of coordinate system 70 and let optic axis 32 of optic fiber 22 be parallel to the x-axis and lie in the xz- plane. Assume that optic axis 32 of fiber 22 is displaced along the z-axis from the plane of CGH 56 by a distance z₀. Let an optical intensity pattern that CGH 56 is desired to provide be represented by I])(x,y,z) and have an amplitude Al )(x,y,z) - Ϊ£^ '^(x,γ,z). Let I )(x,y,z) be defined, optionally, in a rectangular volume of space 72, i.e. an "active volume", that is centered on optic axis 32 and bounded by planes 74 and 76 parallel to the xy-plane at z = (z₀- Δz) and z = (z₀+Δz) respectively.

As shown in U.S. Patent 6,166,833 referenced above, the effect of encoding the two phases in each pixel 60 of CGH 56 is mathematically equivalent to encoding the pixel with a phase and amplitude, which are functions of the phases. Let the amplitude and phase encoded in a pixel 60 responsive to the two phases encoded in the pixel be represented by A(x',y') and φ(x',y') respectively, where x' and y' are x and y coordinates respectively of the pixel in the z=0 plane. Assuming that UN light 40 is incident on CGH 56 normal to the plane of the CGH, i.e. parallel to the z-axis, after passing through CGH 56, the UN light has a wave front, in the plane at z=0, that has a complex amplitude proportional to A(x',y')exptφ(x',y').

The coordinates x' and y' of an "nm-th" pixel 60 are nΔx' and mΔy¹, where Δx¹ and Δy' are the x and y dimensions of pixels 60 (Δx' and Δy' may or may not be equal) and n and m are discrete indices. The complex amplitude A(x',y')exptφ(x',y') and functions derived therefrom are therefore discrete functions properly described as functions of the discrete indices n and m. However, for economy and convenience of presentation it is assumed in the discussion that A(x',y')exptφ(x',y') and functions derived therefrom are continuous functions of continuous position coordinates. Mathematical manipulations, which in consistency with the discrete nature of the coordinates x' and y' of pixels 60 would involve summations over indices n and m are, represented by integrations. For a given complex wave front of UN light 40 at the z = 0 plane, the complex wave front at a plane parallel to the xy plane at z = z^ in active volume 72 that results from propagation of light from the z = 0 plane may be determined using an appropriate transfer function, such as a Fresnel transfer function or a Fourier transfer function. Let a transfer function that "propagates" a wave front from a point x', y' in the z = 0 plane to a point at coordinates x, y in the z^ plane be represented by T(x,y,z] _:,x',y'). If a complex amplitude at coordinate (x,y) in the z^ plane, which is determined from A(x',y')exptφ(x',y') is represented by

= T(x,y,z]_c,x',y')A(x',y')exptφ(x',y^l), where repeated coordinates indicate integration over appropriate ranges of the repeated coordinates. The expression T(x,y,z] _:,x',y^,)A(x',y')exptφ(x',y') therefore represents a double integration of the form JJA(x',y^,)exp(tφ(χ' ,y')T(x',y',x,y,z, )dx'dy', where integration is over the area of CGH 56.

Similarly, let

represent the inverse of T(x,y,zj_c,x',y').

propagates a wave from a point at coordinates x,y in the zj plane "back" to a point x'y' in the z=0 plane.

To determine values for phases to be encoded in each pixel 60 of CGH 56 so that the CGH provides an intensity pattern in the active volume that approximates AIj)(x,y,z), in accordance with an embodiment of the present invention, each pixel 60 is encoded with two arbitrary initial phases. Let the initial phase assigned to a pixel 60 result in an initial amplitude and phase coding for the pixels represented by A₀(x',y')exptφ₀(x',y')).

For each of a plurality of N planes parallel to the xy plane in active volume 72 and having z coordinates z^ with 1< k < N the complex amplitude of the UN wave front in the plane responsive to A₀(x',y')exptφ₀(x',y') *^s determined. By way of example, in Fig. 3 volume 72 is shown with Ν = 7 "z^ planes" labeled z\ through zη, of which planes z\ and zη optionally coincide with planes 74 and 76. Let the complex amplitude in the zj- plane at coordinate (x,y) that is determined from A₀(x',y')exptφ₀(x',y') be represented by B₀(x,y,z]_c)exptθ₀(x,y,z]_c). B_o(x,y,z]₁)expi0_o(x,y,z]_: ) may be written B₀(x,y,zk)expiθ_o(x,y,z_]s) = T(x,y,zk,x',y')A₀(x',y')exptφ₀(x',y'). An adjusted optical wave front in plane z^ is then determined by replacing each B₀(x,y,zk) by its corresponding desired value AIi)(x,y,zk), multiplied by a suitable normalization factor that assures conservation of energy. The phase φ₀(x',y') is not adjusted. The adjusted optical wave front for each plane z is then propagated back to the z=0 plane using the transfer function

to determine an interim wave front A'zk(x',y')exptφ'(x',y') at the z=0 plane. An average of the interim wave fronts

planes, optionally weighted by a suitable weighting function, is then used to define a new amplitude and phase coding for pixels 60 represented by Aι(x',y')exptφι(x',y')). The new coding is then processed similarly to the manner in which coding

A₀(x',y')expz^'φ₀(x',y')) is processed to determine a next coding, A2(x',y')expz^'φ2(x'-y') for pixels 60. The process is repeated until it converges to coding values for pixels 60 for which

CGH 56 provides a suitably accurate approximation to the desired intensity pattern Ij)(x,y,z) in active volume 72.

Fig. 4 shows a graph 80 comparing transmission of a commercially available FBG and a simulated FBG, in accordance with an embodiment of the present invention, similar to FBG 54. The simulated FBG is imprinted with a variation pattern in its index of refraction for which the index of refraction in a given cross section of the FBG is substantially uniform. Curve 82 graphs transmission of the commercially available FBG and curve 84 graphs transmission of the simulated FBG. Both the commercially available FBG and the simulated FBG comprise a same number of Bragg planes. From the graph it is seen that simulated FBG in accordance with an embodiment of the present invention is substantially more efficient in reflecting light in the band-stop of the FBG than the prior art FBG. For many wavelengths in the substantially same band-stop of the two FBGs, the simulated FBG in accordance with an embodiment of the present transmits approximately 15 dB less light than the prior art FBG.

FBGs fabricated in accordance with embodiments of the present invention may advantageously be used in any of many devices that comprise FBGs for control and processing of light and may improve operation of the devices. For example FBGs, produced in accordance with embodiments of the present invention may be used to provide interleavers for use in optical communication systems.

In the description and claims of the present application, each of the verbs, "comprise" "include" and "have", and conjugates thereof, are used to indicate that the object or objects of the verb are not necessarily a complete listing of members, components, elements or parts of the subject or subjects of the verb.

The present invention has been described using detailed descriptions of embodiments thereof that are provided by way of example and are not intended to limit the scope of the invention. The described embodiments comprise different features, not all of which are required in all embodiments of the invention. Some embodiments of the present invention utilize only some of the features or possible combinations of the features. Nariations of embodiments of the present invention that are described and embodiments of the present invention comprising different combinations of features noted in the described embodiments will occur to persons of the art. The scope of the invention is limited only by the following claims.

Claims

1. A method of fabricating a fiber Bragg grating (FBG), the method comprising: generating changes in phase and/or amplitude of light in a light beam that are functions of two coordinates in a plane on which the beam is incident so as to generate a given optical intensity pattern; and illuminating a segment of optic fiber with the optical intensity pattern to imprint the fiber segment with a spatial variation in its index of refraction that has a pattern responsive to the optical intensity pattern.

2. A method according to claim 1 wherein the pattern of the variation in index of refraction is substantially the same as the optical intensity pattern.

3. A method according to claim 1 or claim 2 wherein generating the changes in phase and/or amplitude comprises: configuring a reflection or transmission mask to impart a given phase and/or amplitude to light incident on the mask that is a function of two coordinates of the point of incidence of the light on a plane of the mask and directing the light beam to be incident on the mask.

4. A method according to claim 3 wherein configuring a mask comprises providing a mask partitioned into a plurality of pixels and coding each pixel in the mask to impart the given phase and/or amplitude to light that is incident on the pixel.

5. A method according to claim 4 wherein the coding of the pixels is determined responsive to the given intensity pattern using an iteration algorithm.

6. A method according to any of claims 1-5 wherein the given optical pattern is defined by intensity values for points located on a same plane.

7. A method according to any of claims 1-6 wherein the given optical pattern is defined by intensity values at points having a three dimensional spatial distribution.

8. A method according to claim 7 wherein for any two points on a same cross section of the fiber, the intensity of the optical intensity pattern is substantially the same.

9. A method according to any of claims 7 wherein the Bragg grating comprises blazed Bragg planes and wherein for any two points in the fiber on any same plane through the fiber parallel to the blazed Bragg planes, the intensity of the optical intensity pattern is substantially the same.

10. A fiber Bragg grating formed in an optic fiber in accordance with any of the preceding claims wherein for all points on a same cross section of the fiber the index of refraction of the fiber is substantially the same.

11. A fiber Bragg grating comprising blazed Bragg planes formed in an optic fiber in accordance with any of the preceding claims wherein for all points on a same plane in the fiber parallel to the blazed Bragg planes the index of refraction of the fiber is substantially the same.