Abstract: A photonic integrated circuit including having a semiconductor substrate having integrated a semiconductor light source, the semiconductor light source comprising: an optically active section comprising a gain section and configured to support a first number of wavelengths, an optically passive section comprising a passive waveguide optically coupled to the optically active section and a passive section mirror optically coupled to the passive waveguide, wherein the optically passive section is configured to support a second number of wavelengths that is lower than the first number; and the optically passive section further comprising a signal shifting structure configured to shift a signal of the light supported by the passive waveguide.

Abstract: A photonic integrated circuit including a semiconductor substrate having integrate a semiconductor light source configured to emit coherent light of at least the first wavelength and the second wavelength, the semiconductor light source having a first factor; a waveguide structure optically coupled to the semiconductor light source, the waveguide structure having a second Q factor that is higher than the first Q factor, the waveguide structure configured to form an optical cavity for at least the light of the first wavelength and the second wavelength; an optical output structure configured to optically couple the waveguide structure with a plurality of optical channels to transmit light of the first wavelength and the second wavelength from the waveguide structure to the plurality of optical channels.

Abstract: In a system, known digitizer signals (known analog signals or digital representations of known analog signals) are generated. The known digitizer signals are input into digitizers (analog-to-digital converter (ADCs) or digital-to-analog converter (DACs)) to output generated digitizer signals (generated digital representations or generated analog signals). The generated digitizer signals are analyzed in relation to the known digitizer signals to generate coupling coefficients, which can be either scalar quantities or finite-impulse-response (FIR) filter functions. Subsequent digitizer signals are generated. The subsequent digitizer signals are modified using the coupling coefficients to generate modified digitizer signals according to formulae. The modified digitizer signals are used directly as digital representations, or are input to the DACs to output modified analog signals that substantially match subsequent analog signals.

Abstract: In a system, known digital representations are generated, and test analog signals are generated using the known digital representations. The test analog signals are transmitted using a transmitter of a transmission system. The test analog signals are received using a receiver of the transmission system and used to generate test received digital representations. The test received digital representations are cross-correlated with the known digital representations to generate a mixing matrix. The mixing matrix is inverted to generate a de-mixing matrix, which is applied to subsequent digital data to be encoded onto a signal and transmitted by the transmitter to generate pre-compensated digital data.

Abstract: In a nonlinear signal filtering system, a signal having a series of signal samples is filtered. The signal samples are affected by interactions with adjacent signal samples and nonlinear distortions. The system contains a series of alternating linear system elements and nonlinear system elements that are used for mitigation of distortion resulting from the nonlinear distortions with memory effects. The linear system elements can scale each signal sample in the series of signal samples by scaling parameters and sums a plurality of consecutive scaled signal samples, and the nonlinear system elements can transform the output of the linear system elements according to instantaneous nonlinear functions.

Abstract: Phase noise is corrected in a communication system including a modulated signal having a constellation including multiple constellation points. The system and methods include a coarse phase recovery followed by a fine phase recovery. Coarse phase corrected points can be generated using an Mth power operation. Fine phase corrected points can be generated by rotating each coarse phase corrected point by an angle that is determined by the location of that coarse phase corrected point in the constellation, and applying a phase offset function to each transformed point. A phase noise mitigated constellation can be generated by derotating the fine phase corrected points.

Abstract: In an improved wavelength-division multiplexed system, transmitters modulate carrier signals that are phase or frequency correlated with each other. Receivers retrieve transmission data from the modulated carrier signals by demodulating and equalizing the modulated carrier signals using oscillating signals that are also phase or frequency correlated with each other. Each oscillating signal has a wavelength that matches a wavelength of a corresponding one of the carrier signals. At least one of the receivers generates process information during the demodulating and equalizing. The process information is sent to at least one other receiver, which uses the process information to retrieve at least a portion of the transmission data.

Abstract: In a transmission system, a transmission signal is generated from transmission data. The transmission signal has a series of shaped pulses, such as raised-cosine or root-raised-cosine shaped pulses, formed using a pulse-shaping filter. A reception signal, based on the transmission signal having passed through a transmission channel, is sampled to generate sampled digital data. The sampled digital data is filtered through a receiver filter to regenerate the transmission data, where the pulse shaping filter and the receiver filter are mismatched.

Abstract: In a nonlinear signal filtering system, a signal having a series of signal samples is filtered. The signal samples are affected by interactions with adjacent signal samples and nonlinear distortions. The system contains a series of alternating linear system elements and nonlinear system elements that are used for mitigation of distortion resulting from the nonlinear distortions with memory effects. The linear system elements can scale each signal sample in the series of signal samples by scaling parameters and sums a plurality of consecutive scaled signal samples, and the nonlinear system elements can transform the output of the linear system elements according to instantaneous nonlinear functions.

Abstract: In a system, known digitizer signals (known analog signals or digital representations of known analog signals) are generated. The known digitizer signals are input into digitizers (analog-to-digital converter (ADCs) or digital-to-analog converter (DACs)) to output generated digitizer signals (generated digital representations or generated analog signals). The generated digitizer signals are analyzed in relation to the known digitizer signals to generate coupling coefficients, which can be either scalar quantities or finite-impulse-response (FIR) filter functions. Subsequent digitizer signals are generated. The subsequent digitizer signals are modified using the coupling coefficients to generate modified digitizer signals according to formulae. The modified digitizer signals are used directly as digital representations, or are input to the DACs to output modified analog signals that substantially match subsequent analog signals.

Abstract: Timing recovery systems and methods can include receiving a signal with Nyquist shaped pulses, sampling the signal using an analog-to-digital converter at a sampling rate, generating a plurality of delayed sampled signals from the received pulses, resampling each delayed sampled signal to 1 sample per symbol, taking the absolute value of each resampled signal, raising the absolute value of each resampled signal to the fourth power, taking the mean of the fourth power of the absolute value of each resampled signal, feeding all of the mean values into a phase estimator, and using the output from the phase estimator for timing correction. The output from the phase estimator can either be fed back to the analog-to-digital converter, or to an interpolation stage that adjusts sampling instants of the sampled signals output from the analog-to-digital converter, to correct the timing.

Abstract: In a transmission system, a transmission signal is generated from transmission data. The transmission signal has a series of shaped pulses, such as raised-cosine or root-raised-cosine shaped pulses. A reception signal, based on the transmission signal having passed through a transmission channel, is sampled to generate sampled digital data. The sampled digital data is filtered through a super-Gaussian filter to regenerate the transmission data.

Abstract: In a system, known digitizer signals (known analog signals or digital representations of known analog signals) are generated. The known digitizer signals are input into digitizers (analog-to-digital converter (ADCs) or digital-to-analog converter (DACs)) to output generated digitizer signals (generated digital representations or generated analog signals). The generated digitizer signals are analyzed in relation to the known digitizer signals to generate coupling coefficients, which can be either scalar quantities or finite-impulse-response (FIR) filter functions. Subsequent digitizer signals are generated. The subsequent digitizer signals are modified using the coupling coefficients to generate modified digitizer signals according to formulae. The modified digitizer signals are used directly as digital representations, or are input to the DACs to output modified analog signals that substantially match subsequent analog signals.

Abstract: In a nonlinear signal filtering system, a signal having a series of signal samples is filtered. The signal samples are affected by interactions with adjacent signal samples and nonlinear distortions. The system contains a series of alternating linear system elements and nonlinear system elements that are used for mitigation of distortion resulting from the nonlinear distortions with memory effects. The linear system elements can scale each signal sample in the series of signal samples by scaling parameters and sums a plurality of consecutive scaled signal samples, and the nonlinear system elements can transform the output of the linear system elements according to instantaneous nonlinear functions.

Abstract: In a system, known digital representations are generated, and test analog signals are generated using the known digital representations. The test analog signals are transmitted using a transmitter of a transmission system. The test analog signals are received using a receiver of the transmission system and used to generate test received digital representations. The test received digital representations are cross-correlated with the known digital representations to generate a mixing matrix. The mixing matrix is inverted to generate a de-mixing matrix, which is applied to subsequent digital data to be encoded onto a signal and transmitted by the transmitter to generate pre-compensated digital data.

Abstract: In a system, known digitizer signals (known analog signals or digital representations of known analog signals) are generated. The known digitizer signals are input into digitizers (analog-to-digital converter (ADCs) or digital-to-analog converter (DACs)) to output generated digitizer signals (generated digital representations or generated analog signals). The generated digitizer signals are analyzed in relation to the known digitizer signals to generate coupling coefficients, which can be either scalar quantities or finite-impulse-response (FIR) filter functions. Subsequent digitizer signals are generated. The subsequent digitizer signals are modified using the coupling coefficients to generate modified digitizer signals according to formulae. The modified digitizer signals are used directly as digital representations, or are input to the DACs to output modified analog signals that substantially match subsequent analog signals.

Abstract: In a transmission system, a transmission signal is generated from transmission data. The transmission signal has a series of shaped pulses, such as raised-cosine or root-raised-cosine shaped pulses. A reception signal, based on the transmission signal having passed through a transmission channel, is sampled to generate sampled digital data. The sampled digital data is filtered through a super-Gaussian filter to regenerate the transmission data.

Abstract: In an improved wavelength-division multiplexed system, transmitters modulate carrier signals that are phase or frequency correlated with each other. Receivers retrieve transmission data from the modulated carrier signals by demodulating and equalizing the modulated carrier signals using oscillating signals that are also phase or frequency correlated with each other. Each oscillating signal has a wavelength that matches a wavelength of a corresponding one of the carrier signals. At least one of the receivers generates process information during the demodulating and equalizing. The process information is sent to at least one other receiver, which uses the process information to retrieve at least a portion of the transmission data.