KR20010033934A - Composite diffraction gratings for signal processing and optical control applications - Google Patents

Abstract

The present invention provides a complex grating structure that performs a spectral filtering function having a complex value programmed in an input optical signal. The grating produced according to the invention is a composite grating consisting of a plurality of sub gratings. Individual sub-grids control the diffraction of a particular optical subband width of the light, which distributes controllable amplitude and phase changes to a specific subband width of light from the operating input direction to the operating output direction, where the diffraction of the light is in the full operating band. Controlled in width. The sub-grid set comprising the composite grating collectively controls the diffraction of the operating bandwidth of the light from the operating input direction to the operating output direction. Individual composite grids according to the present invention are programmed through their configuration or their dynamic modification to provide the desired spectrum filtering function. The complex structures according to the invention can be used for general spectrum filtering applications, but they occupy an attractive position, particularly in the area of optical waveform processing, generation and detection.

Description

COMPOSITE DIFFRACTION GRATINGS FOR SIGNAL PROCESSING AND OPTICAL CONTROL APPLICATIONS

The present invention relates to spectrum filtering, optical communication, optical multiplexing, optical code-division multiple access, and optical code generation and detection.

Summary of the Invention

The present invention provides a structure (i.e., a diffraction grating of a single design) that performs a spectrum filtering function having a programmed complex-valued input signal. Gratings manufactured according to the invention are called composite gratings in the sense that they consist of a plurality of sublattices. The sub lattice is a meaning of Fourier decomposition of the complex spatial shape but may be physically distinct or present. Individual sub-grids control the diffraction of a particular optical subband width of light from the actuation input direction to the actuation output direction. The set of sub-grids comprising the composite grating collectively controls the diffraction of the operating bandwidth of the light from the operating input direction to the operating output direction. The individual subgrids distribute the controllable amplitude and phase change to a particular subbandwidth of the diffractive light, which diffraction controls within the full operating bandwidth range. Complex gratings according to the present invention are programmed through their structure or their dynamic modification to provide the desired spectrum filtering function. In the programming process, the physical coefficients of the subgrid, such as spatial phase, amplitude, spatial period, etc., are formed and set such that the individual subgrids provide the desired amplitude and phase change to the diffraction band width. Although the composite grating according to the present invention can be used for general spectrum filtering applications, the composite grating occupies an attractive position, particularly in the field of optical waveform processing, generation, and detection. Optical waveforms can be encoded to represent information and thus the invention is naturally applicable to optical data processing, generation, and detection.

The composite grating according to the present invention has a number of specific embodiments and settings. The composite grating according to the present invention can be embodied in volume, surface, or waveguide grating and can also be constructed using frequency-selective active materials such as europium-doped nitrile oxide. The composite grating can be implemented in the same form using an active material that does not have natural frequency selectivity, such as glass or lithium niobate. The basic design element of the present composite grating invention is to use a Fourier or physical definition grating to control the diffraction of the subbandwidth of light from the actuation input to the actuation output direction. Control here means that the structural characteristics of the subgrid determine the phase and amplitude factors associated with the output and input light fields within the subband allocated to the subgrid. Sub-grids, which typically include composite gratings, do not require the absence of overlapping sub-bandwidths but control sub-bands that do not actually overlap. Subbands, optionally controlled by the subgrid, need to span the entire operating bandwidth of the composite grid.

The composite grating according to the present invention is fundamentally different from grating devices known in the art. Known gratings accept multieolored light incident along a certain input direction and also disperse the light so that individual colors emerge along a path separated at an angle from the path of the other incident color. The composite grating according to the present invention accommodates multi-layered light incident along a certain input direction while simultaneously changing the relative amplitude and phase of the various component colors and diffracts the individual color parts in the operating output direction.

The composite grating device according to the invention can be used, for example, for optical code-division multiple access (OCDMA) data links. In this application, a composite grating device is used to code optical signals within a range of multiple communication channels with channel-specific time codes and then to detect channels separately based on their applied time code. The ability to apply channel specific time-code and then separately detect based on the time-code allows multiplexing of multiple time-codes that are distinct from optical communication channels in a single transmission means. The composite surface grating of the present invention can be used in any application where the ability to achieve spectrum filtering is used, such as instant pattern recognition, spectrum equalization, optical encryption and decryption, and dispersion compensation.

Brief description of the drawings

1 is a diagrammatic view of the interaction of a dichroic incident radiation system with a complex surface grating consisting of two sublattices leading to the generation of diffracted output beams.

2A and 2B show the operation of the complex diffraction grating according to the present invention applied to instantaneous waveform recognition. The composite grating shown is transmitted along the operational output direction, and recognizes the instantaneous waveform in response to an optical signal incident on the grating along the operational input direction, and also through configuration to generate an optical signal having a specific address instantaneous waveform or Dynamically programmed The address waveform and the recognition waveform are different and the recognition waveform is generated only in response to the input optical signal which generates the address instantaneous waveform. In FIG. 2A, an optical signal whose instantaneous waveform is substantially similar to the addressing instantaneous waveform of the composite grating is transmitted along the operational output direction and impinges on the grating along the operational input direction which results in the generation of the optical signal carrying the recognition instantaneous waveform. In FIG. 2B, an optical signal whose actual waveform is actually different from the address instantaneous waveform programmed into the composite grating is hit by a grating causing the generation of an output signal whose instant waveform is actually different from the recognition waveform.

As an introduction, consider a transmission grating of width l schematically shown in FIG. The grating does not change analytically along the y axis, but also aligns with its surface perpendicular to the z axis, and also by a plane wave light beam consisting of two wavelength components, λ _i = c / ν _i (i = 1,2) Suppose along the direction k _i ⊥y. We further assume that the grating has a surface shape that characterizes the absorptive or phase response consisting of a linear sum of two sinusoidal subgrids of wavelength Λ _j (j = 1,2). The interaction of two subgrids and dichroic input beams generally forms four output beams for the initial order of the grid. Just for the sake of limitation, let us assume that the first order diffraction is shown. The output direction is denoted by k _ij corresponding to the interaction between the j th subgrid and the i th light component. If λ ₁ / Λ ₁ = λ ₂ / Λ ₂ , two beams of the output beams may overlap as shown in FIG. 1 and also include a working output beam. The direction along the superimposed output beam is referred to as the operating output direction. Light transmitted according to the operating output direction can be separated from light diffracted in the other direction by appropriate spatial filtering. The light beams and gratings described herein are provided with various properties for the purpose of explanation. The assignment of these attributes is not meant to be limited in any way to the present invention. Attributes assigned for explanatory purposes include planar wave optical beam properties, transmission grating shapes, analytical invariance along the y axis, planar grating shapes, surface grating positions, sinusoidal sub-grating properties, and operations at first diffraction orders.

Generalizing the scenario of FIG. 1 for N input frequencies and N sub gratings, one can obtain operational output beams that assist from all input wavelengths when tidal control from individual input wavelengths is controlled by a particular sub-grid. According to the present invention, by controlling the amplitude and relative phase of the sub-grid, the amplitude and phase of the light spectrum components in the actuating output beam are controlled. In other words, the complex grating device constitutes a complex spectrum filter with a specific transfer function for the selected operational input direction and for a particular operational output direction.

To express this idea more quantitatively, we can express a general input beam as a sum over N _ν discontinuous spectral components as

[One]

Where E _i0 is a complex number and gives the phase and amplitude of the field component at frequency ν _i , r ₀ is a fixed reference position taken to be the center of the grating, and k _in represents the direction of propagation of the input beam. The optical signal carrying any momentary waveform can be developed as in equation [1]. In general, the spacing between frequency components must be less than or equal to the inverse waveform duration and the evolution must include sufficient spectrum components to span the spectrum region occupied by the optical signal. We assume that the grating is determined by several N _g sinusoidal transfer sub-grids, with the added amplitude transfer function given by [2].

[2]

Where a _j is a real number, K _j (= x / Λ _j ) is a parameter of the _jth subgrid, x is a unit vector along the x-coordinate direction, and Λ _j is the space period of the jth subgrid , ξ _j is the spatial phase of the j th subgrid from r ₀ . The spatial phase ξ _j of the sub-grating is of great importance in the present invention for providing control over the optical phase of the diffracted spectrum component. The assumption that a _j is a real number, that is, the sub-grid is an amplitude-only sub-grid, is for simplicity of explanation and is not meant to limit the invention. A very general characteristic amplitude or phase subgrid with a space independent of a _j (a _j = a _j (r)) can be replaced without departing from the spirit of the invention.

Recalling the Fraunhofer and thin grating constraints, the diffracted output field resulting from the interaction of the j th subgrid and the i th input spectrum component can be written as

[3]

here

[4]

And m = ± 1 depend on whether the subgrid is operated at a positive or negative first diffraction order. In Fig. 1, only the positive first order is shown, k _ij is the output direction and η (r ₀ ) ≡ (ν _i k _in / c-mK _j ) · r ₀ selects r ₀ = 0 For convenience, this is a phase factor that depends on the zero point of the erase. The diffraction integration derived from equation [3] is the input and output directions k _in and k _ij , i.e.

[5]

Provides a common constraint _{in which} θ _in is the selected operating input angle, φ _ij is the output angle, and the i th wavelength component is diffracted by the j th subgrid as shown in FIG. 1. The assumptions of thin gratings and first order Fraunhofer diffraction have been made here for the sake of brevity and are not meant to be limited to any form of the invention.

Now consider the special case where N _g = N _ν = N and λ _i / Λ _j have the same constant value for all i = j. This second assumption ensures that all diffracted beams with i = j exit along a common output direction, i.e., φ _ij = Φ _out (i = j = 1, ..., N). Angle Φ _out is the operating output angle. The transfer vector corresponding to the operational output direction is represented by k _out . The signal transmitted from the operating output direction can be written as

[6]

It should be noted that no sub-grid can contain the entire spectrum of the input beam if it does not cancel the amplitude. The assumption of the components of the individual spectra provided a sub-grid configured to diffract a portion of the spectrum in the direction of the operating output. The individual spectral components in the working output beam are multiplied by a factor H _ij whose phase and amplitude are determined by the spatial phase and amplitude of the ith subgrid. therefore Denotes a version of the input beam that has been filtered spectrally. The filtering function is determined dynamically during programming or during the operation of the composite grating during its manufacture. Any filtering function H (v) can be applied in discrete form if the discontinuity is good enough. Equation [6] indicates that the discontinuous form of the transfer function can be applied when H _ij is set equal to H (ν _i ). Equation [4] thus represents the amplitude and spatial phase required for a subgrid grating the subband width of light in the vicinity of v _i from the actuation input direction to the actuation output direction.

In a first preferred embodiment, a set of sub-grids is written on the surface of the substrate to form a composite grid. The sub-grid acts to diffract radiation incident in the selected operating output direction from the selected operating input direction. In the process of mapping the optical signal striking the composite grating from the operational input direction along the operational output direction, the composite grating distributes the programmed spectrum filtering function. In this embodiment, the programmed spectrum filtering function acts to convert an input pulse with a particular address instantaneous waveform into an output pulse with a particular recognized instantaneous waveform. At this moment the composite grating effectively acts as an instantaneous waveform converter. The function can be used to equal instantaneous waveform detection. The detection of the output signal by electronic means or other means, which is primarily sensitive to an optical signal having a waveform substantially identical to the recognition waveform, allows the user to conclude that the input signal has delivered an address waveform. If the recognition instantaneous waveform is selected to be an instantaneously short and strong pulse, its differential detection is particularly convenient by the apparatus known in the art.

2A and 2B illustrate the operation of a composite surface grating used as a momentary waveform transducer / detector in accordance with the present invention. 2A and 2B, an optical signal composed of spectrum components within the operating band width of the optical waveform 100 transmitted with the composite surface grating 102 impinges on the composite surface grating 102 along the input path 101, Trigger the generation of the optical signaling optical waveform 103 along the output path 104. The input path 101 is actually similar to the designated operational input path of the compound surface grating 102 and the output path 104 is actually similar to the designated operational output path of the compound grating 102. In FIG. 2A, the incident light waveform 100A is actually similar to the address instantaneous waveform of the programmed composite grating 102, and the output light waveform 103A along the operational output path 104 is the programmed composite grating 102. Is actually similar to the instantaneous waveform. In Fig. 2B, the incident light waveform 100B is actually different from the address instantaneous waveform of the programmed complex grating 103, and the output light waveform 103B along the operational output direction 104 is the programmed complex grating 102 ) Is actually different from the instantaneous waveform. It should be noted that any input signal transmitted along path 101 within the operating bandwidth range of the composite grating and also comprising a spectrum component may generate an output signal along the operating output direction. However, the output signal will only have a specific programmed recognition waveform if the input signal has a programmed address waveform.

Now consider the design of a composite surface grating according to this embodiment of the invention. First specified are the address instantaneous waveform and the recognition instantaneous waveform, and their center frequency. The total bandwidth of the latter is contained within the bandwidth of the former. An important amount that can be derived from a specified waveform is the minimum spectrum structure width of the optical signal carrying the address or recognition instantaneous waveform. The minimum spectrum structure width is the minimum frequency distance at which the Fourier spectrum of the optical signal loaded by the address or recognition waveform represents the structure. In general, the minimum spectral structure width may be set equal to the inverse of the larger address or recognition instantaneous waveform duration. The reason why the minimum spectral structure width is important is that the structure width sets the maximum frequency band width that can be controlled by the individual subgrids having the composite grating. This means, in turn, that the subgrid must have as precise or finer spectrum resolution as the minimum spectrum structure width. The bandwidth of the optical signal carrying the recognition waveform δν _out or address waveform δν _in can be derived from the specified individual waveforms. The minimum spectral structure width also represents the minimum spectral resolution needed to encode or program the spectral transfer function of interest into a complex grid.

With regard to the composite grating, its operational input and output direction must be specified. The operating input and output angles, and the sub lattice periodicity, are selected according to bias [5], depending on substrate and manufacturing constraints that limit the range of sub lattice periods that can be conveniently implemented. The choice of operating angle also depends on the need to perform the spectral resolution of the subgrid more sophisticated than the minimum spectral structure width. The lattice spectrum resolution is given by the following equation [7].

[7]

Where c is the speed of light in the environment of the composite grating and l is the subgrid width. For a fixed grating width, the choice of operating angle providing the maximum angle change from input to output provides maximum spectral resolution. Providing the actuation output direction to be essentially anti-parallel to the actuation input direction maximizes the grating spectrum resolution for a fixed grating width.

The amount (1 / δν _g ), i.e., lattice processing time, is important because it provides an upper limit on the instantaneous length of the waveform that can be distinguished from complete unity. If a signal with a duration longer than 1 / δν _g is incident on the composite grating, the instantaneous output signal may be derived from the auxiliary duration of the input signal of approximately length (1 / δν _g ).

The minimum number N _{g, min} of the desired subgrid is equal to the bandwidth of the desired recognition instantaneous waveform divided by the minimum spectral structure width.

In order to construct a composite grating, it is necessary to determine its detailed surface structure. Decomposition of the structure by the sum of the subgrids is a means used to determine the lattice structure. The sub lattice exists as a discontinuous physical seal, for example in a structure in which the composite structure consists of several layers. Alternatively, the sub lattice may be present in the sense of an element of one complex shaped Fourier decomposition. In the latter case, the physical reality of the sub-grid can be emphasized by the manufacturing method of making the complex grid structure through the addition of several elements that each distribute the function of the sub-grid. For example, in holographic grating fabrication, a composite grating can be made through several exposures, with each exposure forming a sub grating having a particular period, amplitude, and spatial phase. With appropriate control of the exposure parameters, the sub-grid parameters can be programmed to map a particular sub-bandwidth of light from the actuation input direction to the actuation output direction.

Now, suppose we need one composite grating that detects the address instantaneous waveform E _A (t) with the Fourier spectrum E _A (v). It is required that the composite grating be short and operate to generate a strong output waveform (recognition waveform) when the input optical signal carries an address instantaneous waveform. One spectrum filtering function that can provide this behavior is H (ν) = αE ^* _A (ν), where α is a constant and E ^* _A (ν) is a conjugate complex number of E _A (ν). The spectral filtering function H (ν) is defined by E _out (ν) = H (ν) E _in (ν), where E _in (ν) and E _out (ν) are incident along the operating input direction. It is also a spectrum of the optical signal emitted according to the direction of the operating output.

To determine the sub lattice parameters that provide a complex lattice transfer function equal to αE ^* _A (ν), we spectrally decompose the input and address instantaneous waveforms in the discrete Fourier sum as in equation [1]. The expansion coefficients for the input and address waveforms are E _i0 and E ^A _i0, respectively. The individual complex expansion coefficients E ^A _i0 can be written as the product of the real amplitude and the complex phase factor, ie E ^A _i0 = a ^A _i exp (iξ _i ). The field transfer in the direction k _out depending on the filtering function H (ν) = αE ^* _A (ν) is given by the following equation [8].

[8]

This expression is given by equation [6] if a _j = a ^A _i and ξ _j = -ξ _i (for all i = j = 1, ..., N _n ) [9] Is the same as

Expression [9] is the following expression,

[10]

Note that this is a special case of the given subgrid having the form of.

H (ν) = αE ^* _A (ν) in Equation [10], H _ii means a specific subgrid as seen with respect to Equation [4], and i denotes the i ^th frequency subband. When the subgrid is configured to satisfy the condition of equation [9] or [10], the signal coming from the composite grating along the operating output direction k _out will experience the filtering function H (ν) = αE ^* _A (ν). will be. In the time domain, the output signal has an instantaneous waveform representing the cross correlation between the address waveform and the input waveform. As is known in the art, cross-correlation is an effective means of recognizing similarity between waveforms. In the case where the input waveform and the address waveform span the same carrier frequency and are essentially the same, the cross-correlation is mainly made up of short, strong pulses.

The direct relationship between the amplitude and phase of the subgrid with the composite grating and the Fourier component's amplitude and phase in the address waveform shown in equation [9] shows that the spatial shape of the composite grating programmed to recognize the address waveform is associated with the address waveform itself. The explanation is very simple. The composite grating can be observed as a spatial carrier with an envelope function. The above equation indicates that the spatial waveform of the composite grating is provided by a Fourier transform of the desired spectral filtering function, which is scaled appropriately.

Consider a composite grating designed as described above to form a short recognition waveform transmitted in accordance with the operational output direction in response to a particular address instantaneous waveform incident along the operational input direction. When a short pulse is directed to a composite grating anti-parallel to the actuation output direction, the optical signal carrying the time-regressed address instantaneous waveform is emitted anti-parallel to the actuation input direction. The short pulse bandwidth quoted in this discussion is estimated to span the bandwidth of the optical signal carrying the address waveform, which is designed to detect the complex lattice.

Multiple composite gratings can be superimposed on the same substrate to produce a device that can operate on multiple input waveforms. Multiple composite gratings can have an operational output direction that is different from the common operational input direction, where the individual composite gratings and the individual operational output directions provide different spectrum filtering functions. Conversely, a composite grating can have a common, operational, output direction, and a different, operational, input direction, with each input direction generating an output signal that is experiencing a different spectrum filtering function. In addition, the overlapping composite gratings can each have a single operational input and output direction.

In a second preferred embodiment, the composite grating can be configured such that its operational input and output directions lie anti-parallel along a line comprising the sub grating spatial wave vector. In a second refinement of the second preferred embodiment, the composite grating is configured to explicitly receive and process an input optical signal that delivers a short instantaneous waveform. In a third refinement of the second preferred embodiment, the composite grating is specifically programmed to generate an output optical signal delivering an instantaneous short recognition instantaneous waveform in response to an input pulse delivering a particular address instantaneous waveform. In a fourth refinement of the second preferred embodiment, the composite grating is embedded in the volume of the substrate of the active material. In a fifth improvement of the second embodiment, the substrate consists of an optical waveguide, which may be an optical fiber. In a sixth refinement of the preferred embodiment, the subgrid has a position dependent amplitude and phase which leads to a position dependent reflectance.

According to equation [7], the maximum processing time of the composite grating can be achieved for θ _in = π / 2 and φ _out = -π / 2, ie the input direction is parallel to the sub lattice wave vector and the output direction is It is passed in the opposite direction. In this limitation, the lattice bandwidth is δν _g = c / 2ℓ. Maximizing the grating processing time, or maximizing the grating spectrum resolution, is important because it is possible to minimize the physical length of the grating required for the spectral transfer function with a given minimum spectrum structure width. The processing time of a composite grating with anti-parallel actuation input and output directions (or any other geometry) can be increased if the grating is buried in the substrate of refractive index n. In this case, the lattice resolution bandwidth is δν _g = c / 2L, where c is the speed of light in vacuum. For example, the use of a glass substrate with a refractive index of 1.5 results in a 5 percent increase in grating processing time for a fixed size or a 5 percent reduction in grating size for a fixed processing time. Note that in this geometry (θ _in = π / 2), a given subgrid can diffract only light whose wavelength is less than or equal to the design wavelength for that subgrid.

Now consider the design of a composite grating when the operational input and output directions lie anti-parallel along a line defined by a sub-grid wave vector. We start by specifying the spectral filtering function to be performed. Since the input and output angles are chosen to be π / 2 and -π / 2, respectively, the spatial wavelengths of the individual subgrids are equal to one-half wavelength of the subband width, which is designed to diffract special subgrids according to diffraction conditions. same. When light is transferred into the material and interacts with the grating, there is a wavelength of light in the material described above. Since the angle is fixed, the physical length l of the grating is chosen to ensure that the spectral resolution of the composite grating is sufficient to solve the minimum spectral structure width characteristic of the desired spectral transfer function. Note that when the sub lattice is buried at the refractive index n of the medium, the sub lattice is the optical path length n 1, which determines the lattice resolution rather than the physical length 1.

Composite gratings whose operational input and output directions lie in anti-parallel along a line comprising the sub-grid spatial wave vectors can be constructed in optical waveguides and optical fibers. In this case, the subgrid typically includes a periodic modulation of the refractive index for the induced wave region, cladding region or all of these regions. The subgrid must be composed of the spatial phase and amplitude required to achieve the desired spectrum transfer function. In waveguide implementations of composite gratings designed to provide high efficiency diffraction, the amplitude of the sub-grating can be tapered to be relatively smaller at the input end of the composite grating and relatively larger at the opposite end. The taper serves to equalize backscattered light because the input light is weakened.

We have repeatedly mentioned the electromagnetic radiation that enters the composite grating with light and is diffracted from the composite grating, but the composite grating has a range of electromagnetic spectra from radio to microwave, infrared, visible, ultraviolet and more. Naturally, it can be operatively configured to receive electromagnetic radiation within any portion.

While the present invention has been described in connection with the preferred embodiments, it will be appreciated by those skilled in the art that various changes may be made without departing from the spirit and scope of the invention.

Claims (25)

An ordered assembly of the active material and two or more periodic subgrids supported by the active material, each subgrid controlling the diffraction of the specified subbandwidth of the specified radiation from the designated input direction to the specified output direction; The input direction and the output direction are shared by all subgrids, and the ratio of the wavelength of the subbandwidth of the radiation to the wavelength of a given subgrid is controlled by the subgrid constant for all subgrids, and also the diffraction The amplitude and phase of the sub-bandwidth of the generated radiation is controlled by the amplitude and phase of the sub-grid so that whenever the incident radiation is actually similar to the input instantaneous waveform specified according to the specified input direction, the superimposition of the output wave is specified at the specified output instant. Resulting in the generation of an emission wave in the specified output direction together with the waveform Composite diffraction grating. An ordered assembly of two or more sets of active material and two or more periodic subgrids per set supported by the active material, each subgrid having a subband width of radiation from a specified input direction to a specified output direction. Controlling diffraction, wherein the input direction and the output direction are shared by all subgrids within a given set, and the ratio of the wavelength of the subbandwidth of radiation to the wavelength of a given subgrid is for all subgrids within a given set A subband of radiation controlled by the subgrid constant, wherein the ratio of the wavelength of the subbandwidth of radiation controlled by the subgrid in the first set to the wavelength of a given subgrid is controlled by the subgrid in the second set Not equal to the ratio of the wavelength of the width to the wavelength of a given sub-grid, and also of the sub-bandwidth of the diffracted radiation The width and phase are controlled by the amplitude and phase of the subgrid so that the overlap of the exiting wave is produced whenever the incident radiation is actually similar to the input instantaneous waveform specified for the given set along the input direction specified for the given set. Combined with the output instantaneous waveform specified for the given set resulting in the generation of an emission wave in the specified output direction for the given set. The method of claim 1, The input instantaneous waveform comprises a substantially short pulse having an instantaneous duration on the order of the inverse bandwidth of the input instantaneous waveform and the output instantaneous waveform has an instantaneous duration substantially greater than the inverse bandwidth of the output instantaneous waveform. And a temporarily structured waveform having a complex diffraction grating. The method of claim 1, The input instantaneous waveform comprises a temporarily structured waveform having an instantaneous duration substantially greater than the inverse bandwidth of the input instantaneous waveform and the output instantaneous waveform has an instantaneous duration of about the inverse bandwidth of the output instantaneous waveform. A composite diffraction grating comprising substantially short pulses. The method of claim 1, And the input direction is parallel to the wave vector of the sub-grid. The method of claim 5, And the output direction is transmitted in an opposite direction to the input direction. The method of claim 5, And said active material comprises an optical waveguide. The method of claim 7, wherein And the active material comprises optical fibers. The method of claim 1, Wherein the amplitude of the given sub-grating depends on the spatial location in the active material. The method of claim 9, And said active material is an optical waveguide. The method of claim 10, And the optical waveguide comprises an optical fiber. The method of claim 1, The actuating sub-grid grating reflects the sub-bandwidth of radiation controlled by the grating in a specified output direction. The method of claim 1, And said actuating sub-grating transmits the sub-bandwidth of radiation controlled by said sub-grating in a specified output direction. The method of claim 1, And said actuating sub-grid is sinusoidal spatial shape. The method of claim 1, And the actuating sub-grid is of a non-sinusoidal spatial shape. The method of claim 1, And said actuating subgrid is characterized by a spatial shape having a periodic change in the transmission or reflection amplitude, i.e. in the amplitude subgrid. The method of claim 1, And said actuating sub-grating is characterized by a spatial shape having a periodic change in the transmissive or reflected phase, ie the phase sub-grating. The method of claim 1, And said actuating sub-grating is characterized by spatial shape with transmission or reflection amplitude and phase, i.e. a periodic change in the complex sub-grating. The method of claim 2, Wherein said individual sub-grid set is distinguished by the direction of said sub-grid wave vector. The method of claim 1, And said actuating sub-grating is present in the sense of a Fourier decomposition element in the form of a single complex grating. The method of claim 20, And said actuating sub-grating is present as meaning of Fourier decomposition of a single spatial carrier transformed by a specified spatial modulation function. An optical system for generating an output optical waveform from an input optical waveform having a carrier frequency by directing an input optical waveform through a passive periodic structure, And said periodic structure of the passive is characterized by being a complex set of subgrids each having a specific wavelength, direction, amplitude and phase. In the periodic structure of the passive that performs the spectral filtering function in the input light field, The structure is characterized by one or more sets of subgrids that respectively control the diffraction of the incident radiation in accordance with the input instantaneous waveform and the input direction of the incident radiation, whereby the input instantaneous waveform and the input direction are specified. And the sub-grid set can trigger the formation of a specified output instantaneous waveform in accordance with a specified output direction when matched with a specified input direction of the set. In the periodic structure of the passive, which performs a spectral filtering function on the input light field to generate an output copy, The structure is characterized by one or more sets of subgrids, wherein the amplitude and phase of the radiation exiting at a specified frequency are controlled by the amplitude and phase of the subgrids. An optical system having an input light beam of N input wavelengths is characterized by a periodic structure of passiveness, which includes N sub-grids that generate a common output beam that assists from all input wavelengths, Optical assistance, characterized in that the assistance from the individual input wavelength is controlled by a particular subgrid.