Time-wavelength multiple access optical communication systems and methods

[0002] This application claims benefit of Provisional Nos. 60/095,992 filed Aug. 10, 1998 and 60/119,464 filed Feb. 10, 1999.

[0003] The invention pertains to methods and apparatus for optical communication.

[0004] The communication bandwidths available with optical fibers are very large, generally many terahertz (THz). Unfortunately, this bandwidth is too large to be effectively used by a single amplitude-modulated data channel in a practical communication system. Many factors limit the practical use of this bandwidth. These factors include limitations on the modulation rates achievable with conventional electronic devices as well as the high cost of high-bandwidth optical components such as modulators and detectors. In some communication systems, fiber dispersion limits the useful fiber bandwidth.

[0005] Methods for using more of the available fiber bandwidth include several multiplexing methods that permit data transmission at rates exceeding the rates possible for a single amplitude modulated channel. These methods include time-division multiplexing (TDM), wavelength-division multiplexing (WDM), and optical code-division multiple access (OCDMA). Each of these approaches has significant limitations. In TDM, data from one or more data streams is assigned to selected time slots so that each data stream uses a portion of the fiber bandwidth. TDM allows aggregation of data streams from many users, but does not increase the data rate available to a single data stream. Some examples of TDM systems include commercial communication systems that conform to the synchronous optical network (SONET) standard or the synchronous digital hierarchy (SDH) standard.

[0006] Wavelength-division multiplexed (WDM) systems and dense WDM (DWDM) systems transmit data using multiple spectrally displaced narrow-band optical carriers (wavelengths), and each wavelength is temporally encoded. The time-coding is typically a relatively simple amplitude modulation scheme and thus the bandwidth of each wavelength channel is set by limits similar to those of non-WDM systems. WDM systems normally require multiple laser sources, one for each wavelength channel. The number of wavelength channels that can be multiplexed in a single fiber is limited by the spectral channel separation required to compensate for variations in laser wavelength as well as other factors such as the gain bandwidth of optical amplifiers. The available maximum bandwidth is limited by the number of wavelength channels and the per-channel data rate. The spectral channel separations and per-channel data rates of many WDM systems leave significant portions of the fiber bandwidth unused, and higher data rates are theoretically possible.

[0007] OCDMA uses coded data bits whose spectrum exceeds the data transmission rate and spans a spectral window. Multiple approaches to the realization of OCDMA have been proposed. Unfortunately, implementation of OCDMA can be difficult and expensive, and improved methods are needed to take advantage of the full bandwidth of optical fibers.

[0008] The present invention provides, inter alia, optical communication methods and apparatus that use time-wavelength (TW) codes.

[0009] According to a first aspect of the invention, time-wavelength coders (encoders and decoders) are provided that receive input optical signals having a first predetermined time-wavelength spectrum and generate an output signal having a second predetermined time-wavelength spectrum. The first and second predetermined time-wavelength spectra include a plurality of spectral components. The coders provide optical paths for corresponding spectral components of the input optical signals and the path lengths of the optical paths are determined by time-wavelength codes.

[0010] In an illustrative embodiment, a coder comprises an optical fiber that includes a plurality of fiber Bragg gratings defined by spatial variations of an optical property of the fiber. The spatial variations provide predetermined time delays and phase differences for the spectral components. Coherent coders are provided in which the phase differences for the spectral components are predetermined to within about one-half of a wavelength of the associated spectral component. The spatial variations in the optical property of the fiber include variations in at least one of amplitude, spatial period, and spatial phase of the optical property. The Bragg grating can be defined by refractive-index variations, and the refractive-index variations can be in the fiber core, the fiber cladding, or in a coating on the fiber cladding.

[0011] In another representative embodiment, a coder comprises a plurality of optical paths corresponding to spectral components of an input, the optical paths having path lengths selected to produce predetermined delays (and phase shifts) for the spectral components. A beam divider directs the spectral components along the respective optical path and a beam combiner recombines the spectral components after propagation along respective optical paths. In some embodiments, the path lengths are predetermined by a time-wavelength code. For a coherent coder, the path lengths and phase shifts are predetermined to significantly less than λ/2, wherein λ is a wavelength of the spectral component received by a respective optical path. In other embodiments, the path lengths are selected to compensate for dispersion in a transmission medium such as an optical fiber or to convert an optical input coded with a first code into an output corresponding to a second code.

[0012] In another representative embodiment, an encoder is provided that receives a Fourier-transform-limited optical input and produces at least two Fourier-transform-limited spectral components. These spectral components have bandwidths less than or equal to the bandwidth of the optical input and durations longer than the duration of the optical input.

[0013] According to another aspect of the invention, transmitters for an optical communication system are provided. A representative embodiment of such a transmitter comprises a light source that is modulated in response to a data stream, the light source comprising a plurality of spectral components. A time-wavelength encoder receives the modulated optical signal and produces an output signal having a predetermined time-wavelength spectrum.

[0014] According to another aspect of the invention, optical receivers are provided for detecting an optical signal having a time-wavelength spectrum determined by a time-wavelength code. A representative embodiment includes a time-wavelength encoder that receives the optical signal and modifies the time-wavelength spectrum of the optical signal. A photodetector receives the optical signal from the encoder and converts the optical signal into an electrical signal.

[0015] According to yet another aspect of the invention, optical communication systems arm provided. A representative embodiment includes a first and a second series of optical pulses corresponding to a first and a second data stream. A first encoder receives the first series of optical pulses and produces a first coded output having a time-wavelength spectrum determined by a first time-wavelength code. A second encoder receives the second series of optical pulses and produces a second coded output having a time-wavelength spectrum determined by a second time-wavelength code. A combiner receives and combines the first and second coded outputs. A divider receives the combined first and second coded outputs and produces a first output and a second output that are delivered to first and second decoders, respectively.

[0016] According to yet another aspect of the invention, methods are provided for multiplexing a first optical data stream and a second optical data stream, the first and second optical data streams having respective time-wavelength spectra. Time-wavelength codes are selected for encoding and decoding the first and second data streams and the time-dependent spectra of the first and second optical data streams are transformed according to the selected time-wavelength codes. The data streams are combined and transmitted in a transmission medium. The combined optical data streams are received and divided into a first portion and a second portion that are decoded with the selected decoding codes. The first and second portions include contributions from both the first data stream and the second data stream and each portion is nonlinearly detected to reject crosstalk. In a representative embodiment, either the encoding codes or the decoding codes, or both, are selected to compensate for dispersion in the transmission medium.

[0017] According to still another aspect of the invention, a code converter is provided that accepts optical signals having a first time-wavelength spectrum and produces output signals having a second time-wavelength spectrum.

[0018] FIG. 1 is a schematic of a time-wavelength multiple access communication system.

[0019] FIG. 2 is a graph of power as a function of time and wavelength for an input pulse to the communication system of FIG. 1.

[0020] FIG. 3 is a schematic of the encoder of the communication system of FIG. 1.

[0021] FIG. 4 is a schematic of a decoder of the communication system of FIG. 1.

[0022] FIG. 5 is a schematic of an alternative encoder.

[0023] FIG. 6 is a schematic of an alternative encoder.

[0024] FIG. 7 is a schematic of an alternative encoder using wavelength-dependent couplers.

[0025] FIG. 8 is a schematic of an alternative encoder that includes grating segments formed in an optical fiber.

[0026] FIG. 9 is a schematic of a two-channel time-wavelength multiple access communication system.

[0027] FIG. 10A is a graph of a time-wavelength spectrum of an input pulse.

[0028] FIG. 10B is a graph of power as a function of time for the input pulse of FIG. 10A.

[0029] FIG. 10C is a graph of energy as a function of wavelength for the input pulse of FIG. 10A.

[0030] FIG. 10D is a graph of a time-wavelength spectrum of a coded output produced by encoding the input pulse of FIG. 10A.

[0031] FIG. 10E is a graph of power as a function of time for the coded output of FIG. 10D.

[0032] FIG. 10F is a graph of a time-wavelength spectrum of a decoded output produced by decoding the coded output of FIG. 10D with an unmatched decoder.

[0033] FIG. 10G is a graph of power as a function of time for the decoded output of FIG. 10F.

[0034] FIGS. 11A-11B are schematics of fiber Bragg grating encoders or decoders.

[0035] FIG. 12A is a graph of a time-wavelength spectrum of an input pulse.

[0036] FIG. 12B is a graph of energy as a function of wavelength for the input pulse of FIG. 12A.

[0037] FIG. 12C is a graph of power as a function of time for the input pulse of FIG. 12A.

[0038] FIG. 12D is a graph of a time-wavelength spectrum of a coded output produced by encoding the input pulse of FIG. 12A.

[0039] FIG. 12E is a graph of energy per unit wavelength as a function of wavelength for the coded output of FIG. 12D.

[0040] FIG. 12F is a graph of power as a function of time for the coded output of FIG. 12D.

[0041] FIG. 12G is a graph of a time-wavelength spectrum of a decoded output produced by decoding the coded output of FIG. 12D with a coherently matched decoder.

[0042] FIG. 12H is a graph of power as a function of time for the decoded output of FIG. 12G.

[0043] FIG. 12I is a graph of a time-wavelength spectrum of a decoded output produced by decoding the coded output of FIG. 12D with a coherently unmatched decoder.

[0044] FIG. 12J is a graph of power as a function of time for the decoded output of FIG. 12I.

[0045] FIG. 13A-13C are graphs of optical power as a function of time for an input pulse, a decoded output obtained by decoding with controlled phase shifts, and a decoded output obtained with uncontrolled phase shifts.

[0046] FIG. 14 is a schematic of a communication system that includes fiber Bragg grating encoders and decoders.

[0047] FIG. 15A shows the time-wavelength spectrum of a chirped pulse.

[0048] FIG. 15B is a graph of energy as a function of wavelength for the chirped pulse of FIG. 15A.

[0049] FIG. 15C is a graph of power as a function of time for the chirped pulse of FIG. 15A.

[0050] FIG. 15D shows the time-wavelength spectrum of the chirped pulse of FIG. 15A after encoding with a time-wavelength code.

[0051] Methods and apparatus are disclosed for optical time-wavelength multiple access (TWMA) communication. In optical TWMA communication, communication channels are distinguished by encoding an input optical signal according to a predetermined code to produce a coded output. The coded output has a time-wavelength spectrum (TWS) determined by the code and the TWS of the input optical signal, wherein a time-wavelength spectrum (TWS) is defined as the power per unit wavelength of an optical signal as a function of both time and wavelength (or frequency). If the input optical signal is a pulse, the coded output is typically a series of pulses, each pulse corresponding to a spectral component of the input optical signal. The coded output can be decoded according to a matched code to transform the decoded output into an output having a TWS similar to that of the input optical signal, a TWS selected for dispersion compensation or code conversion as discussed below, or other predetermined TWS.

[0052] Some embodiments of TWMA communication systems include sets of time-wavelength (TW) codes for encoding and decoding each of a plurality of data streams. The codes for encoding and decoding a selected data stream are referred to as “matched” and produce a predetermined (“matched”) output. In one example, coding and decoding with matched codes produce a decoded output that is substantially similar to a non-encoded input. Codes for encoding and decoding different data streams are unmatched, and generally produce an output having a relatively long duration in comparison with the non-encoded input. The unmatched portion of a decoded output is referred to as “crosstalk.” Matched decoding of a selected data stream is accompanied by unmatched decoding of another data stream, producing a matched output and crosstalk. Time-wavelength codes are conveniently chosen with a computer search of randomly selected codes (or all codes) to identify codes having characteristics falling within chosen bounds such as codes having low crosstalk. In some cases, codes are selected to compensate dispersion in a transmission medium or to transform a coded output produced with a first code into a coded output corresponding to a second code.

[0053] An encoder and decoder are generally referred to as “matched” if the relative delays imparted to the spectral components are equal and opposite, or if the total delays are substantially the same for all spectral components after decoding. In addition, an encoder and decoder are referred to as matched if the relative delays are matched, inclusive of transports medium delays. If an encoder produces relative delays φ₁, φ₂, . . . , φ_nin spectral components λ₁, λ₂, . . . , λ_n, respectively, as defined by a first code, then the matched decoder produces relative delays −φ₁, −φ₂, . . . , −φ_n. Alternatively, if a code is represented as a transfer function Ψ=exp[−jφ_i(λ_i)], where j=(−1)^½, then the transfer function of the matched code is the complex conjugate, i.e., Ψ*=exp[jφ_i(λ_i)]. As noted previously, in some cases an encoder and decoder are matched to compensate for dispersion or other propagation effects in order to produce a short pulse or other selected output. For example, if a transmission medium such as a fiber imposes relative delays θ₁, . . . , θ_non spectral components λ₁, λ₂, . . . , λ_nthat are represented as X=exp[−jθ_i(λ_i)], then the transfer functions of the encoder code can be modified to ΨX* or that of the decoder code can be modified to Ψ*X*. Alternatively, both the encoder and decoder codes can be modified to include portions of the necessary correction,.

[0054] In a TWMA communication system, optical signals are encoded by redistributing optical power in time, or wavelength, or both time and wavelength. The redistribution is specified with time-wavelength (TW) codes. For convenience in describing TW coding, an optical pulse or other optical signal is divided into “time chips” and “wavelength chips” (spectral components) that are defined as portions of the optical signal within a specified time interval or wavelength interval, respectively. A time-wavelength (TW) chip is an interval in time and wavelength that is a product of the time and wavelength intervals of corresponding time and wavelength chips. In a graph of a TWS of an optical signal, a time-wavelength chip is represented by an area bounded by corresponding time and wavelength chips. In some cases, the area of a time-wavelength chip is selected to be about λ²/c, where λ is the chip wavelength, and c is the vacuum speed of light. A time-wavelength chip of such area represents a “Fourier-transform-limited optical pulse.” Time-wavelength chips of larger area are also useful and, if necessary, can be described as aggregations of time-wavelength chips having the transform-limited area λ²/c.

[0055] An optical signal is characterized by a time-bandwidth product that is defined as a product of a spectral width Δλ and a temporal duration Δt of the optical signal. The spectral width and temporal duration are defined by, for example, a spectral wavelength and temporal full-width at half maximum of the TWS of the optical signal. The TWS of an optical signal having a large time-bandwidth product, i.e., ΔλΔt>>λ²/c, can be more complex than that of optical signals for which the time-bandwidth product is small, i.e., ΔλΔt≈λ²/c. If the time-bandwidth product ΔtΔλ is approximately λ²/c, then the optical signal is referred to as “transform limited,” and selecting an optical power as a function of time (or wavelength) permits estimation of the dependence of the power of the optical signal on wavelength (time).

[0056] In some embodiments, a coded optical signal is decoded such that the spectral components of the optical signal are recombined with interferometric accuracy, i.e., so that the relative delays (phase shifts) of the spectral components after encoding and decoding are predetermined to significantly less than λ/2, wherein λ is an average wavelength of the optical signal. Encoders, decoders, and communication systems that maintain such interferometric accuracy are referred to as “coherent,” while those that do not are referred to as “incoherent.” For convenience, encoders and decoders are both referred to as “coders.”

[0057] FIG. 1 illustrates an example TWMA communication system according to the invention. An input optical pulse 11 is directed to an encoder 13, producing a coded output 15. An optical fiber 17 or other optical transmission medium transmits the coded output 15 to a decoder 19. The decoder 19 transforms the coded output 15 into an output pulse 21 that is directed to a detector 23.

[0058] FIG. 2 illustrates power of the input optical pulse 11 as a function of wavelength and time. As shown in FIG. 2, the input optical pulse 11 has a constant spectral power density P_λ(t) during a time interval Δt₁₁and a constant spectral width Δλ₁₁during the time interval Δt₁₁. The total power of the input optical pulse 11 is P=P_λΔλ₁₁. The input pulse 11 is selected for purpose of illustration and is a non-Fourier-transform-limited pulse. In some examples discussed below, Fourier-transform-limited pulses are used.

[0059] The encoder 13 divides the input optical pulse 11 into three spectral components, λ₁, λ₂, λ₃, each having a spectral width Δλ₁₁/3 and a temporal duration Δt₁₁. Other divisions of the input optical pulse 11 into spectral components are possible, including divisions into spectral components of unequal spectral width or total energy. Referring to FIG. 3, the encoder 13 includes reflectors 39, 41, 43 and dichroic reflectors 31, 33, 35, 37. The dichroic reflectors 31, 35, and reflectors 39, 41 define an optical path 45 for the spectral component λ₃. The dichroic reflectors 31, 33, 37 and the reflector 43 define an optical path 47 for the spectral component λ₂. The dichroic reflectors 31, 37, 35 transmit the spectral component λ₁along an axis 49 defining an optical path 51.

[0060] The dichroic reflector 31 receives the input optical pulse 11 and reflects the spectral components λ₂, λ₃to the dichroic reflector 33 that reflects the spectral component λ₂and transmits the spectral component λ₃to the reflector 39. The reflectors 39, 41 reflect the spectral component λ₃to the dichroic reflector 35 that reflects the spectral component λ₃so that the spectral component λ₃propagates along the optical path 51. After reflection by the dichroic reflector 33, the spectral component λ₂reflected by the reflector 43 and the dichroic reflector 37 propagate along the optical path 51. Table 1 summarizes the properties of the dichroic reflector 31, 33, 35, 37.

[0061] In Table 1, “R” denotes high reflectivity and “T” denotes high transmittance. Values denoted by “−” need not be specified for the operation of the encoder 13.

[0062] The optical paths 45, 47, 51 impart delays to the spectral components λ₃, λ₂, λ₁, respectively, producing the coded output 15 from the input optical pulse 11. The spectral components λ₁, λ₂, λ₃enter the encoder 13 together but exit at different times. The spectral component λ₁exits the encoder 13 first, followed by the spectral components λ₂, λ₃. The relative delays of the spectral components λ₁, λ₂, λ₃are set by the lengths of the optical paths 51, 47, 45.

[0063] The decoder 19 receives the coded output 15 (the delayed spectral components λ₁, λ₂, λ₃) after transmission through the optical fiber 17. FIG. 4 illustrates the decoder 19. The decoder 19 includes dichroic reflectors 61, 63, 65, 67 and reflectors 69, 71, 73 that define optical paths 75, 77, 81 for the spectral components λ₁, λ₂, λ₃, respectively. The lengths of the optical paths 75, 77, 81 are selected to reassemble the spectral components λ₁, λ₂, λ₃into the output pulse 21 that propagates along an axis 79. The sum of the path lengths in the encoder 13 and in the decoder 19 for the spectral components λ₁, λ₂, λ₃are selected so that the total optical path lengths are substantially equal for the three spectral components λ₁, λ₂, λ₃. The total path lengths can also be selected to compensate for relative delays among the spectral components λ₁, λ₂, λ₃produced in the optical fiber 17 by dispersion.

[0064] FIGS. 5-6 illustrate additional encoder/decoder configurations. Referring to FIG. 5, an encoder 101 includes dichroic reflectors 103, 105, 107, 109 and reflectors 111, 113. The dichroic reflectors 103, 105, 107, 109 define an optical path 117 for the spectral component λ₂, the dichroic reflectors 103, 105, 107, 109, and the reflectors 111, 113 define an optical path 115 for the spectral component λ₃. The spectral component λ₃, propagates through the dichroic reflectors 103, 109 along an optical path 119. The optical paths 115, 117, 119 delay the spectral components to produce the coded output 15. The configuration of the encoder 101 can be modified to produce a decoder by selecting optical paths to reassemble a coded output.

[0065] FIG. 6 illustrates an encoder 141 that includes dichroic reflectors 143, 145, 147, 149 and reflectors 151, 153, 155, 157. The dichroic reflectors 143, 145 and the reflectors 151, 153 define an optical path 159; the dichroic reflectors 147, 149 and the reflectors 155, 157 define an optical path 161, and a through optical path 163 is defined by transmission through the dichroic reflectors 143, 145, 147, 149. The dichroic reflectors 143, 145, 147, 149 can be configured to produce the coded output 15 of FIG. 4 or configured to produce other coded outputs.

[0066] The encoders 101, 141 of FIGS. 5-6, respectively, are selected as illustrative examples. The delays between the spectral components λ₁, λ₂, λ₃in these encoders are multiples of a common delay, but unequal delays can be accommodated. In addition, encoders and decoders can use two or more spectral components and the spectral components need not be contiguous. The dichroic reflectors can be multilayer mirrors, diffraction gratings, or other wavelength-dependent reflectors or devices.

[0067] FIG. 7 illustrates an encoder 181 that comprises three wavelength-dependent couplers 183, 185, 187. The three couplers 183, 185, 187 are similar and only the coupler 183 is described. The coupler 183 comprises waveguides 189, 191 (such as optical fibers or waveguide channels in a substrate) placed in proximity to each other so that optical radiation propagating in the waveguide 191 transfers to the waveguide 189. This transfer is generally a function of wavelength so that for a selected coupling length only certain wavelengths transfer to the waveguide 189. A selected spectral component, e.g., the spectral component λ₁, is coupled from the waveguide 191 to the waveguide 189 and transmitted through a delay line 193. The coupler 185 directs the spectral component λ₁to a waveguide 197 and directs the spectral component λ₂to a waveguide 195. The spectral component λ₂is transmitted by a delay line 199 and then recombined with the spectral components λ₁, λ₂by the coupler 187.

[0068] FIG. 8 illustrates an encoder 201 that includes grating segments 203, 205, 207 separated by waveguide sections 215, 217 and formed in a core 209 of an optical fibers 211. An input pulse 212 is directed into an input surface 213 of the encoder 201 along an input direction and the grating segments 203, 205, 207 reflect selected spectral components λ₁, λ₂, λ₃, respectively, back to the input surface 213 along an output direction 244. The grating segments 203, 205, 207 are selected to reflect the respective selected wavelength components and the lengths of the waveguide sections. 215, 217 can be selected to achieve predetermined delays among the spectral components λ₁, λ₂, λ₃. As illustrated in FIG. 8, the spectral components λ₁, λ₂, λ₃are reflected by grating segments 203, 205, 207, respectively, so that a coded output 220 is produced in which spectral component λ₁exits the input surface 213 first, followed by spectral components λ₂, λ₃.

[0069] The encoder 201 also can serve to decode the coded output 220 if the coded output 220 is directed to an input surface 223 at the opposite end of the encoder 201. The spectral component λ₁enters first but travels through the grating segments 205, 207 before reflecting from the grating segment 203. Therefore, the spectral component λ₁receives a relative delay equal to the relative delay imparted to the spectral component λ₃during encoding. The spectral component λ₂receives a delay equal to the relative delay imparted to the spectral component λ₂during encoding. The spectral component λ₃receives a delay equal to the relative delay imparted to the spectral component λ₁during encoding. As a result, a decoded output is produced that is similar to the input pulse 212.

[0070] Complex time-wavelength coding can be accomplished with a fiber grating coder having continuously varying spatial phase, period, and amplitude. By using multiperiod gratings, time-wavelength codes having multiple simultaneous spectral components can be produced. In addition to an optical delay between the wavelength components created by propagation along the length of a grating segment, grating segments can be separated by spaces having no diffracting elements, thereby adding additional delays between the spectral components.

[0071] Grating segments can be positioned to compensate (or pre-compensate) for the dispersion introduced by propagation of the time-wavelength coded output through an optical fiber. Thus, the fiber grating can function both as an encoder (decoder) and a dispersion precompensator (post-compensator). The relative delay associated with a particular frequency chip can be pre- or post-compensated by introducing a compensating shift in the position of the corresponding grating segment of the coder. The grating segments can overlap spatially even for high diffraction efficiencies for dispersion compensation.

[0072] Fiber grating coders can operate in a transmission direction. One such coder includes a broadband reflective grating segment at an output end of the coder, effectively redirecting an input bit back through the coder and producing a time-wavelength code in the forward (transmission) direction.

[0073] Many other types of TWMA encoders and decoders are possible. Generally, an encoder/decoder imparts specific temporal delays, phase shifts, and amplitudes to a predetermined set of wavelength chips, determined by a set of TW codes. For convenience, encoder/decoder temporal delays and phase shifts can be specified separately, but the specification of a temporal delay with interferometric precision is sufficient. Similarly, specification of a phase shift includes specification of a temporal delay. Generally temporal delays are much longer than the period of an optical signal while phase shifts are less than a few periods. In one embodiment, a coder separates spectral components spatially using a first diffractive device comprising uniformly spaced surface or bulk diffractive elements. Once the spectral components are spatially separated, the temporal delays, phases, and amplitude of the individual spectral components can be modified before recombining. The amplitude, phase, or temporal delay of the spectral channels can be changed with a programmable coder. Recombination is effected using a second grating device. Alternatives to surface or bulk gratings include photonic integrated circuit devices such as arrayed waveguide gratings (AWGs).

[0074] Optical signals coded and decoded according to TW codes support transmission of multiple data channels over a single fiber or other transmission medium. The optical data stream for each channel is encoded with a selected TW code bit. Multiple channels, each with different TW codings, are multiplexed (combined) into a single fiber. The data channels are demultiplexed with decoders. Threshold detection can be used at the output of each decoder to select only those of a selected channel.

[0075] FIG. 9 illustrates a two-channel optical communication system 300 that receives input pulses 303A, 303B from different data streams. The input pulses have power spectra as shown in FIG. 2. The communication system 300 includes encoders 305A, 305B that receive and encode the respective input pulses 303A, 303B, producing coded outputs 307A, 307B that are directed through a transmission medium 309, such as an optical fiber. After transmission through the transmission medium 309, decoders 311A, 311B receive the coded outputs 307A, 307B and produce decoded outputs 313A, 313B, respectively, and direct the decoded outputs 313A, 313B to respective detectors 319A, 319B. The detectors 319A, 319B include respective threshold circuits 320A, 320B that set respective detection thresholds P₁, P₂.

[0076] The encoders 305A, 305B code the input pulses 303A, 303B so that the spectral components λ₁, λ₂, λ₃exit the encoders 305A, 305B in the order [λ₁, λ₂, λ₃], [λ₁, λ₃, λ₂], respectively. The encoders 305A, 305B impart relative delays to the spectral components λ₁, λ₂, λ₃of [1,2,3], [1,3,2], respectively. For convenience, the relative delays of the spectral components λ₁, λ₂, λ₃are written as [J, K, L], where J, K, and L are the relative delays in arbitrary units. The decoders 311A, 311B receive portions of both of the coded outputs 307A, 307B. The decoder 311A is matched to the coded output 307A, and provides relative delays of [3, 2, 1] to the spectral components λ₁, λ₂, λ₃. Combining the relative delays for the encoder 305A and the decoder 311A, the spectral components λ₁, λ₂, λ₃of the input pulse 303A receive total relative delays of [4, 4, 4], i.e., the three spectral components receive no relative delays as a result of the encoding/decoding process. The decoder 311B is similarly matched to the coded output 307B, and provides relative delays of [3, 1, 2] to the spectral components λ₁, λ₂, λ₃. Combining the relative delays for the encoder 305B and the decoder 311B, the spectral components λ₁, λ₂, λ₃of the input pulse 303B receive delays of [4, 4, 4], i.e., the three spectral components receive no relative delays as a result of the encoding/decoding process.

[0077] The decoders 311A, 311B also receive portions of the coded outputs 307B, 307A, respectively, that are not matched. For example, the decoder 311A provides relative delays of [3,2,1]. Acting upon the coded output 307B having relative delays of [1,3,2], the spectral components λ₁, λ₂, λ₃exit the decoder 311A with relative delays of [4,5,3]. The decoded output 313A includes a decoded portion 315A that comprises the spectral components of the coded output 307A having no relative delays and a crosstalk portion 317A that comprises the spectral components of the coded output 307B having relative delays [4,5,3]. The decoded output 313B similarly includes a decoded portion 315B corresponding to the spectral components of the input pulse 303B with no relative delays and a crosstalk portion 317B that comprises the spectral components of the coded output 307A. The relative delays of the spectral components of the crosstalk portion 317B are [4,3,5]. The detectors 319A, 319B recover the input data from the input pulses 303A, 303B by setting the detection thresholds P₁, P₂such that the crosstalk portions 317A, 317B are below the thresholds P₁, P₂and are discarded. In the preceding discussion, it is assumed that the coded outputs 307A, 307B temporally overlap. However, the coded outputs 307A, 307B need not temporally overlap and temporal non-overlap of the coded outputs 307A, 307B can reduce the importance of crosstalk.

[0078] Threshold detection as described in, for example, co-pending patent application 09/132,006, incorporated herein by reference, can be used to distinguish a selected signal obtained by matched decoding and crosstalk resulting from mismatched decoding. Other types of linear, nonlinear, optical, or electronic thresholding can also be used to differentiate between matched and unmatched decoding events.

[0079] In the communication systems of FIGS. 1 and 9, input pulses are divided into three spectral components. Communication systems in which the input pulses are divided into two, three, or more spectral components are also possible. FIGS. 10A-10G illustrate encoding and decoding with five spectral components. FIG. 10A is a graph of a TWS of an input pulse. The magnitude of the optical power P_λ(t) is indicated by the density of contour lines, with areas in which contour lines are more closely spaced corresponding to higher powers. FIG. 10B is a graph of input pulse power as a function of time and FIG. 10C is a graph of input energy per unit wavelength as a function of wavelength. FIGS. 10B-10C illustrate input pulse power and spectrum, but do not show the dependence of input pulse wavelength on time that is displayed in FIG. 10A.

[0080] The input pulse is encoded by applying relative delays [3, 5, 4, 1, 2] to spectral components λ₁, λ₂, λ₃, λ₄, λ₅. The coded output is shown in FIGS. 10D-10E. In FIG. 10D, the power of the coded output is shown as a function of both time and wavelength, with areas in which contour lines are more closely spaced corresponding to higher powers. FIG. 10E shows the power of the coded output as a function of time. By imposing the relative delays [3, 5, 4, 1, 2] on the input pulse, a substantially constant output power is produced.

[0081] The coded output of FIG. 10D is decoded by imposing relative delays between the five spectral components so that the five spectral components are reassembled. A matched decoder imposes relative delays [3, 1, 2, 5, 4] and reassembles the input pulse. In a communication system using this coded output, a portion of the coded output is directed to and decoded by unmatched decoders, producing crosstalk. For example, if relative delays [4, 5, 2, 1, 3] are provided by a decoder, the crosstalk has relative delays [7, 10, 6, 2, 5]. FIGS. 10F-10G show this crosstalk as a function of time and wavelength.

[0082] FIG. 11A is a schematic of an encoder 401 (or a decoder) for a communication system in which an input pulse is divided into as many as eight spectral components. The encoder 401 includes N=8 fiber Bragg grating segments 405_iarranged in a core 421 and along an axis 409 of an optical fiber 407 or other waveguide. Variations in refractive index, reflectivity, absorbance, or other optical property define the grating segments 405_i; these variations are indicated as alternating light and dark bands in FIG. 11A. For convenience, the optical property variations in each of the grating segments 405_ihave a fixed period. In other embodiments, the optical property variations defining the grating segments 405_iare more complex, including variations for apodization or other spectral or temporal profile shaping, as described in A. Othonos, “Fiber Bragg Gratings,” Rev. Sci. Instrum., vol. 68, pp. 4309-4341 (December 1997) which is incorporated herein by reference. For example, one or more of the grating segments 405_ican be chirped for dispersion compensation or can be apodized to reduce spectral component overlap. In addition, the grating segments 405_ineed not be uniformly spaced nor have the same length. The grating segments 405_ican spatially overlap. Such overlaps are included in encoders that use more complex codes in which several frequency components are partially encoded by a single grating segment. More complex gratings, such as blazed gratings, gratings with non-sinusoidal refractive index or other variations, or gratings that operate in higher orders can be used. The encoder 401 defines time chips of uniform duration, but time chips of unequal duration can also be used.

[0083] In the example encoder 401, the grating segments 405_iextend from an x-coordinate x_aito an x-coordinate x_bialong an x-axis 409 and have refractive-index variations of magnitude Δn_i. The total length L of the encoder 401 is L=x_b8−x_a1. The refractive-index variations h_i(x) of each of the grating segments 405_iare:

[0084] h_i(x)=Δn_i𝑓_i(2π(x−x_i)/Λ_i) for x_ai≦x≦x_bi, and  (1)

[0085] h_i(x)=0 elsewhere,

[0086] wherein 𝑓_iis a periodic function of period 2π,|𝑓_i|≦½, x_iis an x-coordinate that specifies the spatial phase of the grating segment 405_i, and Λ_iis the spatial period of the grating segment 405_i.

[0087] A complete mathematical analysis of the encoder 401 can be performed using methods described in, for example, A. Othonos, “Fiber Bragg Gratings,” Rev. Sci. Instrum., vol. 68, pp. 4309-4341 (December 1997). A simple analysis is presented herein, based on the assumptions that the refractive-index variations in the grating segments 405_iare sinusoidal and that the grating segments 405_ioperate in first order. (The first-order grating operation satisfies Equation 2 below.) As mentioned above, more complex variations are possible and the simple analysis is presented for purposes of illustration.

[0088] The center wavelength λ_iof the grating segment 405_iis given by the Bragg condition for a grating of spatial period Λ_i:

[0089] λ_i=2n_oΛ_i,  (2)

[0090] wherein n_ois the average refractive index in the fiber core 421. The reflected light receives a relative phase delay φ_ithat depends on the spatial shift x_iof the grating segment 405_i, wherein

[0091] φ_i=−2πx_i/Λ_i.  (3)

[0092] The reflectivity R_i(the intensity-reflection coefficient or diffraction efficiency) of each of the grating segments 405_iat the Bragg center wavelength λ_iis approximately:

[0093] R_i=[tan h(πΔn_i(x_bi−x_ai)/λ_i)]².  (4)

[0094] For very small reflectivity (R_i<<1), Equation (4) simplifies to:

[0095] R_i=(πΔn_i(x_bi−x_ai)/λ_i)²  (5)

[0096] The relative delays Δτ_iof the optical signals received from the grating segments 405_iare

[0097] Δτ_i=2x_ain_o/c,  (6)

[0098] where c is the vacuum speed of light. The duration of the reflected signal from a grating segment sets the duration of the corresponding time chip.

[0099] If the encoder 401 receives an input pulse of duration τ_phaving spectral components that are reflected by the grating segments 405_i, then a coded output is produced. If the input pulse duration τ_pis shorter than propagation times n_o(x_bi−x_ai+1)/2c between the grating segments 405_i, then the coded output comprises a series of as many as N pulses, the i^thpulse having a relative delay of Δτ_i, a relative intensity proportional to the reflectivity R_i, relative phase delay of φ_i, and center wavelength λ_i. After reflection by the encoder 401, the input pulse is transformed into a coded output having an approximate duration τ_p+τ_p, where τ_p=n_oL/c and L=x_b8−x_a1. The time interval τ_pis referred to herein as the processing time of the encoder 401. The input pulse generally includes substantial energy in spectral components at one or more of the center wavelengths λ_iof the encoder 401.

[0100] If an input pulse thus encoded is incident upon an unmatched fiber grating decoder of length L, then the duration of the decoder output can be as long as approximately 2τ_p+τ_p. If the encoder and decoder gratings are “matched”, and are comprised of segments of approximate length d=x_bi−x_ai, then the decoded output typically contains a short, high-power pulse having a duration of less than about Δτ_p=n_od/c. (If the input pulse is encoded/decoded coherently, the short, high-power pulse can be as short as about τ_p, even if τ_p<Δτ_pas is discussed below, for transform-limited or non-transform-limited pulses.)

[0101] A parameter set {N,Λ_i,Δn_i,x_i,x_ai,x_bi} for i=1,N defines the encoder 401 and a corresponding matched decoder is defined by the parameter set {N,Λ_N−i,Δn_N−i,−x_N−i,x_b(N−i),x_a(N−i)}. The parameters Λ_i, Δn_i, x_i, x_ai, x_biare defined above. Examination of the parameter sets for the encoder and decoder reveals that a matched decoder is the same as the encoder but for encoding and decoding the optical signals are directed into opposite ends of the fiber.

[0102] FIG. 11B is a schematic of an encoder 451 that includes N=8 grating segments 455_ithat are defined by variations in an optical property of a coating 461 and a cladding 463 of an optical fiber 465. In alternative encoders, grating segments are defined in either a coating or a cladding of an optical fiber or other optical waveguide. In order to increase the interaction of the optical signal propagating in a core 467 of the optical fiber 465 with the coating 461, the cladding 463 can be partially or totally removed by etching, polishing, or other process.

[0103] In a TWMA communication system using codes generated by fiber grating encoders having the same bandwidth and physical length, aggregate data transfer rates (f_a) of less than about

[0104] f_a=1/(2t_p+τ_p)  (9)

[0105] produce minimal crosstalk between time-wavelength channels. Higher aggregate data bandwidths lead to increasing overlap between mismatched time-wavelength codes (i.e., crosstalk) at the output of an unmatched decoder. A maximum useful bandwidth, substantially in excess of f_a, is determined by selecting acceptable levels of crosstalk and bit-error rates. In a practical TWMA communication system, the maximum number of simultaneous channels depends on many factors, including noise in the optical signal and noise added in detection (conversion from an optical signal to an electrical signal), total bandwidth and per-channel bandwidth, acceptable bit-error rate, optical losses, time-wavelength codes selected, and whether coherent or incoherent encoders/decoders are used.

[0106] FIGS. 12A-12G illustrate coherent encoding and decoding with five spectral components. FIG. 12A is a graph of a TW spectrum P_λ(t) of an input pulse. The magnitude of P_λ(t) is indicated by contour lines, with areas having more closely spaced lines corresponding to higher powers. FIG. 12B is a graph of input pulse energy per unit wavelength as a function of wavelength, and FIG. 12C is a graph of input pulse power as a function of time. FIGS. 12B-12C illustrate input-pulse spectrum and power, but do not show the dependence of input-pulse wavelength on time that is displayed in FIG. 12A.

[0107] The input pulse is encoded by applying relative delays [3, 5, 4, 1, 2] to spectral components λ₁, λ₂, λ₃, λ₄, λ₅. The coded output is shown in FIGS. 12D-12F. In FIG. 12D, the power per unit wavelength of the coded output is shown as a function of both time and wavelength, with denser contour lines corresponding to higher values. FIG. 12F shows the power of the coded output as a function of time and FIG. 12E shows the energy per unit wavelength of the coded output as a function of wavelength. By imposing the relative delays [3, 5, 4, 1, 2] on the input pulse, a substantially constant output power is produced. Referring to FIG. 12D, each of the spectral components has a temporal duration longer than the duration of the input pulse. This is a consequence of dividing a Fourier-transform-limited input pulse into spectral components. Because the spectral bandwidths of the spectral components are less than that of the input pulse, the temporal durations must be longer.

[0108] The coded output of FIG. 12D is decoded by imposing relative delays between the five spectral components so that the five spectral components are reassembled. A matched decoder imposes relative delays [3, 1, 2, 5, 4] and reassembles the input pulse, as shown in FIGS. 12G-12H. In a communication system using different coders and decoders for different channels, a portion of the coded output of FIG. 12D is decoded by an unmatched decoder, producing crosstalk in a communication channel. For example, if relative delays [4, 5, 2, 1, 3] are provided by a decoder, the crosstalk has relative delays [7, 10, 6, 2, 5]. FIGS. 12I-12J show this crosstalk as a function of time.

[0109] FIGS. 13A-13C illustrate a feature of coherent TWMA coding. FIG. 13A shows power as a function of time for an approximately transform-limited input pulse. FIG. 13B shows power for the encoded/decoded output pulse obtained by dividing the input pulse into three spectral components and recombining the components coherently. FIG. 13C shows power for the encoded/decoded output pulse obtained by recombining the three spectral components used to obtain the output of FIG. 13B. However, in FIG. 13C, the spectral components are recombining with phase errors of approximately λ/4. The output of FIG. 13C is very much longer than the input shown in FIG. 13A, even for such a small phase error. For coherent TWMA systems that use bandwidth-limited optical pulses, spectral components are recombined with appropriate phase relationships in order to obtain short output pulses. Similarly, for coherent TWMA systems that use non-bandwidth-limited optical pulses, the matched, coherent coding and decoding produces an output pulse of the same character as the input pulse. Since incoherent TWMA systems produce output pulses that, on average, are non-transform limited, a non-transform-limited input pulse may be used without significantly broadening the output pulse duration.

[0110] FIG. 14 is a schematic diagram of a TWMA communication system 501 that comprises a laser 510 (or other light source) that emits a series of pulses at a wavelength of λ=1.54 μm (frequency 194.805 THz) in a beam 512. A beamsplitter 513 divides the beam 512 into beams 515, 516, 517, 518. Modulators 515a, 516a, 517a, 518areceive respective beams 515, 516, 517, 518 and modulate the respective beams in correspondence to data streams supplied by data sources (not shown in FIG. 14). The series of pulses of modulated beams 515b, 516b, 517b, 518bare temporally and spectrally suited to respective encoders 519, 520, 521, 522, either due to the TWS of the pulses directly from the laser 510 or as modified by the respective modulators 515a, 516a, 517a, 518a. The spectral bandwidths of the beams 515b, 516b, 517b, 518bpreferably include spectral components that are encoded by the encoders 519, 520, 521, 522, respectively.

[0111] The modulated beams 515b, 516b, 517b, 518bare directed through respective optical circulators 515c, 516c, 517c, 518cand through respective fibers 515d, 516d, 517d, 518dor other transmission media to the respective encoders 519, 520, 521, 522. The encoders 519, 520, 521, 522 encode respective modulated beams 515b, 516b, 517b, 518band direct the coded outputs back through the fibers 515d, 516d, 517d, 518d. The coded outputs are directed by the respective optical circulators 515c, 516c, 517c, 518cinto respective fibers 515e, 516e, 517e, 518eor other transmission media. In the communication system 501, the optical circulators 515c, 516c, 517c, 518cdirect input optical signals to respective encoders and the coded outputs to respective fibers, but other devices (such as beamsplitters) can be used to separate the inputs and coded outputs. A beam combiner 523 receives the coded outputs and directs the coded outputs into an optical fiber 511 or other transmission medium, A beamsplitter or fused coupler can serve as the beam combiner 523.

[0112] After transmission through the fiber 511, an optical power splitter 513a(e.g., a beamsplitter or fused coupler) receives the combined coded outputs from the fiber 511 and forms beams 515f, 516f, 517f, 518f. Optical circulators 515g, 516g, 517g, 518gdirect the respective beams 515f, 516f, 517f, 518falong respective fibers 515h, 516h, 517h, 518hto decoders 519a, 520a, 521a, 522a, respectively. The decoders 519a, 520a, 521a, 522agenerate respective decoded outputs that propagate back through the respective fibers 515h, 516h, 517h, 518hto the respective optical circulators 515g, 516g, 517g, 518gand then through respective fibers 515i, 516i, 517i, 518ito respective detectors 515j, 516j, 517j, 518ithat transform the decoded outputs (optical signals) into electrical signals. The detectors 515j, 516j, 517j, 518jhave sufficient bandwidth to distinguish time chips. The decoded outputs include modulation corresponding to the modulation of the matched input plus crosstalk from the other data streams.

[0113] The encoders 519, 520, 521, 522 accept uncoded data streams and produce respective coded outputs. The decoders 519a, 520a, 521a, 522aaccept coded data and produce respective output signals having characteristic structure whenever matching input time-wavelength codes are accepted. The decoders 519a, 520a, 521a, and 522a(preferably fiber gratings) impart respective wavelength specific time delays, phase shifts, and attenuations. The TWMA communication system 501 can be either a coherent or an incoherent system, depending on the control of the phase shifts or relative phase shifts of the encoders 519, 520, 521, 522 and the decoders 519a, 520a, 521a, 522a.

[0114] For the communication system 501, the decoders 519a, 520a, 521a, 522aare desirably segmented gratings such as shown in FIG. 11A. The grating segments have sinusoidal refractive index variations, a common index grating amplitude of Δn_i=Δn=1.5×10⁻⁴, and a background index of refraction n_o=1.5 for each segment. These values provide an approximate reflectivity of R_i=R=80% in an operational bandwidth of the grating segment. The encoders 519a, 520a, 521a, 522ahave eight contiguous grating segments (i.e., x_ai=x_b1), each grating segment has a length (d) of d=4 mm, and the combined length of all the grating segments is L=3.2 cm. The time interval t_pof the encoders 519a, 520a, 521a, 522ais 320 ps with a time chip of Δt=40 ps. The filtering bandwidth of these encoders is Δν{tilde over (=)}200 GHz=1.59 nm and the filtering bandwidth of individual grating segments is δν=25 GHz=0.20 nm. There are eight adjacent wavelength chips (spectral components) with center-to-center wavelength separations of 0.20 nm. These encoders are designed for a laser wavelength of λ=1.54 μm. The time-wavelength codes of this embodiment are so-called “full spectrum codes”, i.e., they divide an optical input into equal spectral components.

[0115] The encoders 519, 520, 521, 522 are designed to accept temporally transform-limited input pulses of approximate duration τ_p=2-4 ps and generate coded outputs having a duration of about 320 ps. Longer, non-Fourier-transform-limited input pulses can be used if coded outputs of longer duration are acceptable. If the encoders 519-522 encode an input pulse having a spectral width approximately equal to the spectral width of the encoders 519-522 and a constant optical power as a function of wavelength across the spectral width, then full-spectrum coded outputs are produced, i.e., coded outputs having wavelength chips of approximately equal energies. The encoders 519-522 can be used with more complex input pulses or coded optical signals as well.

[0116] The structures of the grating segments for the encoders 519-522 and decoders 519a-522adetermine the wavelength chip sequence produced. The encoders 519-522 and decoders 519a-52ahave 0.20-nm wide wavelength chips and 40-ps duration time chips. Table 2 lists the parameters of the encoders 519-522. The phase shifts of the spectral components reflected by the grating segments are given relative to a reference reflected optical field at the appropriate chip wavelength, but reflected from a grating segment with x_i=0.

[0117] The decoders 519a-522aare similar to the encoders 519-522, respectively, but with the spatial sequence of the grating segments reversed. In the analysis of an encoder using a fiber Bragg grating segment, this reversal is equivalent to changing the refractive-index variation h_i(x) in Eq. (1) to h_i(−x). For example, the decoder 519ais the same as the encoder 519, but the input of the encoder 519 is used as the output of the decoder 519a. For more complex codings, such as those required for dispersion compensation or code conversion, coders and decoders are not so simply related. Representative parameters of the decoders 519a-522aare listed in Table 3.

[0118] For matched decoding, the decoded outputs from decoders 519a, 520a, 521a, 522aapproximately duplicate the original input pulses. Fourier-transform-limited pulses will have durations between approximately 2 ps to 4 ps. Such pulse durations produce low crosstalk. Detectors with longer temporal responses can be used if more crosstalk can be tolerated, or if a longer, non-Fourier-transform-limited input pulse is used, producing a longer output pulse for matched decoding. In addition, nonlinear detection can be used to increase the contrast between the desired decoded signal and crosstalk, especially for slower detectors.

[0119] Referring further to FIG. 14, the communication system 501 also serves as an incoherent communication system as defined previously. Such an incoherent communication system is similar to the coherent system discussed previously except for the encoders 519-522, the decoders 519a-522a, and the detectors 515j, 516j, 517j, 518j. By way of example, the encoders 519-522 and decoders 519a-522ahave sinusoidal refractive-index variations with amplitude Δn_i=Δn=6.0×10⁻⁴, and n_o=1.5. With these parameters, the reflectance of each grating segment is nearly 100% for the corresponding wavelength chip (spectral component). The fiber gratings have eight contiguous (x_ai=x_b(N−1)) grating segments, each grating having a length d=12.5 mm, so that the total grating length L=10.0 cm. The processing time of these encoders/decoders is t_p=ins with a temporal chip time of 125 ps. The overall bandwidth of the encoders/decoders is 9.1 nm and each grating segment has a bandwidth of 0.63 nm. There are eight adjacent 1.2-nm wavelength chips with wavelength spacing equal to 1.2 nm. The encoders/decoders are designed for optical data streams having a central frequency of 194.805 THz (wavelength λ=1.54 pm).

[0120] The encoders 519, 520, 521, 522 are designed to accept input optical pulses having pulse durations in the range of 1 ps to 125 ps, more preferably in the range 50 ps to 100 ps. A matched incoherent decoder does not produce substantially shorter output pulses for input pulses having shorter durations. The encoders 519-522 and decoders 519a-522aare preferably used with an input data rate (f_rep) that is less than about f_rep=500 Mbit/sec so that temporally adjacent bits are well separated after coding to reduce crosstalk. Input data rates be higher, in the range from 500 Mbit/sec to about 10 Gbit/sec, if higher levels of stalk are acceptable.

[0121] Representative parameters of the encoders 519, 520, 521,522 in the incoherent embodiment are listed in Table 4.

[0122] The coded outputs are decoded by decoders 519a-522athat are similar to the encoders 519-522 but reversed as discussed above. The grating segment spatial shifts x_i, and hence φ_i, are not controlled. Representative parameters of the incoherent decoders 519a-522aare listed in Table 5.

[0123] By way of example, each of the decoders 519a-522aproduces an output pulse of approximately 125 ps duration from a matched input. The temporal response of each of the detectors 515j-518jis preferably less than or comparable to τ_p=125 ps. Detectors having still longer response times can be used but tend to decrease channel contrast. Nonlinear detection can be used to increase the contrast between the signal and crosstalk.

[0124] The TW codes used in the embodiments described above have little or no temporal overlap and each time chip contains a single spectral component. More generally, however, a time chip can include several spectral components. An example of such a code is denoted by a wavelength sequence such as [(λ₁:λ₂), λ₄, λ₂, (λ₃:λ₄), λ₅], indicating spectral components for the time chips. The second, third, and fifth time chips contain only a single spectral component (λ₄, λ₂, λ₅, respectively) while each of the first and fourth time chips contains two wavelengths, (λ₁:λ₂) and (λ₃:λ₄), respectively.

[0125] The peak power of an incoherently decoded bit depends in detail on the phase errors introduced into each spectral component by the incoherent encoding/decoding process. In a limiting condition characterized by large numbers of equal amplitude time chips, random phase errors, and transform-limited input bits, incoherent decoding provides peak output powers reduced by N in comparison with coherent coding, where N is the number of time-wavelength chips. Although coherent coding provides superior contrast than incoherent coding in the case of near Fourier-transform-limited input pulses, for some applications, coherent coders generally are unsuitable because of the substantially higher manufacturing cost incurred to provide interferometric phase accuracy. Furthermore, incoherent coding allows for the use of longer non-Fourier-transform-limited input pulses without significant performance degradation. Peak power contrast for matched versus unmatched decoding generally can be improved using time-wavelength codes having large numbers of time chips.

[0126] FIGS. 15A-15C illustrate the time-wavelength spectra of a chirped input pulse. Such an input pulse can be TWMA-encoded resulting in TWS shown in FIG. 15D. Other input pulses can be coded and decoded, such as those containing two or more non-adjacent spectral components, such as spectral components corresponding to longitudinal modes of a laser diode.

[0127] The example encoders and decoders described above encode or decode, respectively, a predetermined code that is defined by the structure of the encoders and decoders. Encoders and decoders also can be dynamically reprogrammable to encode and decode, respectively, various codes. The encoding and decoding produced by a fiber Bragg encoder (such as shown in FIG. 11) is determined by the parameters Δn_i, x_i, x_ai, x_bi, Λ_iof the grating segments. Dynamic control of any of these parameters enables dynamic reprogramming of such an encoder or decoder. For example, x_iand Λ_iare adjustable by adjusting fiber index of refraction or fiber length. The index of refraction can be controlled with, for example, an electric field, pressure, current, temperature, or optical irradiation. A fiber grating may also be created within a system that has spatially localized stretching or compression of the fiber length, thereby changing a combination of x_ai, x_bi, x_i, and Λ_iin a way that is determined by the geometry of the system.

[0128] Although embodiments of the invention are described above with reference to digital communication, it should be understood that TWMA methods and apparatus according to the invention are also suitable for analog communication as well. In addition, TWMA methods and apparatus can be used in conjunction with conventional WDM and TDM systems. For example, coding and encoding can be used with the wavelength channels of a WDM system.

[0129] In addition, various network algorithms can specify encoding and decoding. For example, when a data stream is delivered to a network node, the network node can request a TWMA channel assignment. A network control node then assigns codes to the data stream. When the data stream is removed from that network node, the codes then become available for assignment to other nodes in a manner similar to that of radio-frequency CDMA networks.

[0130] While the invention has been described with reference to example embodiments, it will be understood by those skilled in the art that various changes in format and detail may be made without departing from the spirit and scope of the invention.