Sensitivity analysis of optically preamplified Stokes-vector receivers using analytically derived formulae for bit-error rate.

This study analyzes the bit-error-rate characteristics of Stokes-vector modulation-demodulation systems employing optically preamplified receivers. We derive unified analytical formulae for the bit-error rate of binary, quad, and octal modulation formats, in which Stokes vectors are modulated in a binary manner per dimension. The receiver sensitivities estimated from the derived bit-error-rate formulae are examined by analyzing the probability-density function of noise in the Stokes-vector direct-detection receiver. In addition, the bit-error-rate formulae enable a comprehensive comparison of the sensitivity among various optical receivers, such as coherent, direct-detection, optically differential direct-detection, and Stokes-vector direct-detection receivers.

Multi-dimensional permutation-modulation format for coherent optical communications.

We introduce the multi-dimensional permutation-modulation format in coherent optical communication systems and analyze its performance, focusing on the power efficiency and the spectral efficiency. In the case of four-dimensional (4D) modulation, the polarization-switched quadrature phase-shift keying (PS-QPSK) modulation format and the polarization quadrature-amplitude modulation (POL-QAM) format can be classified into the permutation modulation format. Other than these well-known modulation formats, we find novel modulation formats trading-off between the power efficiency and the spectral efficiency. With the increase in the dimension, the spectral efficiency can more closely approach the channel capacity predicted from the Shannon's theory. We verify these theoretical characteristics through computer simulations of the symbol-error rate (SER) and bit-error rate (BER) performances. For example, the newly-found eight-dimensional (8D) permutation-modulation format can improve the spectral efficiency up to 2.75 bit/s/Hz/pol/channel, while the power penalty against QPSK is about 1 dB at BER=10(-3).

Eight-state trellis-coded optical modulation with signal constellations of four-dimensional M-ary quadrature-amplitude modulation.

We apply the eight-state trellis-coded modulation (TCM) using signal constellations of four-dimensional M-ary quadrature-amplitude modulation (4D-MQAM) to optical communication systems for the first time to our knowledge. In the TCM scheme, the free distance of the trellis diagram is equal to the minimum distance between constellation points in partitioned subsets, which enlarges the coding gain effectively. In fact, its asymptotic power efficiency is 3-dB larger than that of the set-partitioned 4D-MQAM (SP-4D-MQAM) format, while their spectral efficiencies are the same. Such theoretical predictions are confirmed through computer simulations on eight-state TCM with constellations of 4D-4QAM (i.e., 4D quadrature phase-shift keying: 4D-QPSK) and 4D-16QAM. In particular, eight-state TCM with 4D-QPSK constellations is practically important because of its simple encoder structure, relatively low computational cost, and high coding gain against dual-polarization QPSK (DP-QPSK) and SP-4D-QPSK. Through measurements of its bit-error rate (BER) performance, we confirm that the coding gain against DP-QPSK is about 3 dB at BER=10(-3).

Multi-level signaling in the Stokes space and its application to large-capacity optical communications.

The Stokes vector of an optical signal does not depend on its absolute phase; therefore, we can construct the phase-insensitive optical communication system, using the Stokes vector as a modulation parameter. In such a system, multi-level optical signals can effectively be designed in the three-dimensional Stokes space and demodulated either by direct detection or by coherent detection, where low-complexity digital-signal processing (DSP) is employed. Although this system has the disadvantage that adaptive equalizers can hardly be implemented in the digital domain, it is still an attractive solution to large-capacity (≥ 100 Gbit/s) and medium-or short-reach (≤ 100 km) transmission. In this paper, we discuss the receiver configuration for the multi-level signal in the Stokes space and the efficient DSP algorithm for demodulating such a signal. Simulation results demonstrate that 2-, 4-, 8-, 16-, and 32-ary signals in the Stokes space have good bit-error rate (BER) characteristics. Especially, the 16-ary signal at the moderate symbol rate of 25 Gsymbol/s can reach the bit rate of 100 Gbit/s even by using direct detection.

Electronic polarization-division demultiplexing based on digital signal processing in intensity-modulation direct-detection optical communication systems.

We propose a novel configuration of optical receivers for intensity-modulation direct-detection (IM · DD) systems, which can cope with dual-polarization (DP) optical signals electrically. Using a Stokes analyzer and a newly-developed digital signal-processing (DSP) algorithm, we can achieve polarization tracking and demultiplexing in the digital domain after direct detection. Simulation results show that the power penalty stemming from digital polarization manipulations is negligibly small.

Novel configuration of finite-impulse-response filters tolerant to carrier-phase fluctuations in digital coherent optical receivers for higher-order quadrature amplitude modulation signals.

We propose a novel configuration of the finite-impulse-response (FIR) filter adapted by the phase-dependent decision-directed least-mean-square (DD-LMS) algorithm in digital coherent optical receivers. Since fast carrier-phase fluctuations are removed from the error signal which updates tap coefficients of the FIR filter, we can achieve stable adaptation of filter-tap coefficients for higher-order quadrature-amplitude modulation (QAM) signals. Computer simulations show that our proposed scheme is much more tolerant to the phase noise and the frequency offset than the conventional DD-LMS scheme. Such theoretical predictions are also validated experimentally by using a 10-Gsymbol/s dual-polarization 16-QAM signal.

Characterization of semiconductor-laser phase noise and estimation of bit-error rate performance with low-speed offline digital coherent receivers.

We develop a systematic method for characterizing semiconductor-laser phase noise, using a low-speed offline digital coherent receiver. The field spectrum, the FM-noise spectrum, and the phase-error variance measured with such a receiver can completely describe phase-noise characteristics of lasers under test. The sampling rate of the digital coherent receiver should be much higher than the phase-fluctuation speed. However, 1 GS/s is large enough for most of the single-mode semiconductor lasers. In addition to such phase-noise characterization, interpolating the taken data at 1.25 GS/s to form a data stream at 10 GS/s, we can predict the bit-error rate (BER) performance of multi-level modulated optical signals at 10 Gsymbol/s. The BER degradation due to the phase noise is well explained by the result of the phase-noise measurements.

Analyses of wavelength- and polarization-division multiplexed transmission characteristics of optical quadrature-amplitude-modulation signals.

We theoretically study optical transmission characteristics of wavelength-division multiplexed (WDM) and polarization-multiplexed (POLMUX) signals using high-order optical quadrature-amplitude-modulation (QAM) formats up to 256. First, we conduct intensive computer simulations on bit-error rates (BERs) in WDM POLMUX QAM transmission systems and find maximum transmission distances under the influence of nonlinear impairments. Next, to elucidate the physics behind such nonlinear transmission characteristics, we calculate the distribution of constellation points for QAM signals as functions of the the launched power, the transmission distance, and the symbol rate. These results lead to a closed-form formula for BER of any QAM formats. From such formula, we derive simple laws that determine the maximum transmission distance and the optimum power as functions of the QAM order and the symbol rate. These laws can well explain the simulation results.

Adaptive frequency-domain equalization in digital coherent optical receivers.

We propose a novel frequency-domain adaptive equalizer in digital coherent optical receivers, which can reduce computational complexity of the conventional time-domain adaptive equalizer based on finite-impulse-response (FIR) filters. The proposed equalizer can operate on the input sequence sampled by free-running analog-to-digital converters (ADCs) at the rate of two samples per symbol; therefore, the arbitrary initial sampling phase of ADCs can be adjusted so that the best symbol-spaced sequence is produced. The equalizer can also be configured in the butterfly structure, which enables demultiplexing of polarization tributaries apart from equalization of linear transmission impairments. The performance of the proposed equalization scheme is verified by 40-Gbits/s dual-polarization quadrature phase-shift keying (QPSK) transmission experiments.

Performance analyses of polarization demultiplexing based on constant-modulus algorithm in digital coherent optical receivers.

In the digital coherent optical receiver, we can achieve polarization demultiplexing in the digital domain, using a two-by-two matrix controlled by the constant-modulus algorithm (CMA). In this paper, after elucidating the physics behind CMA for polarization demultiplexing, we discuss the performance limit of CMA-based polarization demultiplexing through computer simulations. The method of improving its performance is also demonstrated.

Clock recovering characteristics of adaptive finite-impulse-response filters in digital coherent optical receivers.

We analyze the clock-recovery process based on adaptive finite-impulse-response (FIR) filtering in digital coherent optical receivers. When the clock frequency is synchronized between the transmitter and the receiver, only five taps in half-symbol-spaced FIR filters can adjust the sampling phase of analog-to-digital conversion optimally, enabling bit-error rate performance independent of the initial sampling phase. Even if the clock frequency is not synchronized between them, the clock-frequency misalignment can be adjusted within an appropriate block interval; thus, we can achieve an asynchronous clock mode of operation of digital coherent receivers with block processing of the symbol sequence.

Highly-sensitive coherent optical detection of M-ary frequency-shift keying signal.

We demonstrate M-ary frequency-shift keying (FSK) optical modulation and digital coherent detection, aiming at applications to space communications, where high receiver sensitivity is the most crucial consideration. The proposed FSK transmitter and receiver are based on the coherent orthogonal frequency-division multiplexing (OFDM) technique and feature simple configuration and low computational complexity. By offline bit-error rate measurements using a 256-FSK signal without the forward error-correction code, we obtain the receiver sensitivity as high as 3.5 photons per bit at the bit-error rate of 10(-3). The experimental result is in good agreement with simulations.

Equalization of nonlinear transmission impairments by maximum-likelihood-sequence estimation in digital coherent receivers.

We describe a successful introduction of maximum-likelihood-sequence estimation (MLSE) into digital coherent receivers together with finite-impulse response (FIR) filters in order to equalize both linear and nonlinear fiber impairments. The MLSE equalizer based on the Viterbi algorithm is implemented in the offline digital signal processing (DSP) core. We transmit 20-Gbit/s quadrature phase-shift keying (QPSK) signals through a 200-km-long standard single-mode fiber. The bit-error rate performance shows that the MLSE equalizer outperforms the conventional adaptive FIR filter, especially when nonlinear impairments are predominant.

Multi-impairment monitoring from adaptive finite-impulse-response filters in a digital coherent receiver.

We propose a novel and unified algorithm that estimates linear impairments in optical transmission systems from tap coefficients of an adaptive finite-impulse response (FIR) filter in a coherent optical receiver. Measurable impairments include chromatic dispersion (CD), differential group delay (DGD) between two principal states of polarization, second-order polarization-mode dispersion (second-order PMD), and polarization-dependent loss (PDL). We validate our multi-impairment monitoring algorithm by dual-polarization quadrature phase-shift keying (QPSK) transmission experiments.

Unrepeated 200-km transmission of 40-Gbit/s 16-QAM signals using digital coherent receiver.

We demonstrate unrepeated 200-km transmission of 40-Gbit/s 16-QAM signals using a digital coherent receiver, where the decision-directed carrier-phase estimation is employed. The phase fluctuation is effectively eliminated in the 16-QAM system with such a phase-estimation method, when the linewidth of semiconductor lasers for the transmitter and the local oscillator is 150 kHz. Finite-impulse-response (FIR) filters at the receiver compensate for 4,000-ps/nm group-velocity dispersion (GVD) of the 200-km-long single-mode fiber and a part of self-phase modulation (SPM) in the digital domain. In spite of the launched power limitation due to SPM, the acceptable bit-error rate performance is obtained owing to high sensitivity of the digital coherent receiver.

Wavelength-multiplexed distribution of highly entangled photon-pairs over optical fiber.

We report the first experimental demonstration of wavelength-multiplexed entanglement distribution over optical fiber. Forty-four channels of polarization-entangled photon-pairs were produced from a single pulse-pumped, short periodically-poled lithium niobate waveguide and distributed over 10 km of dispersion-shifted optical fiber. Entanglement fidelities of the distributed photon-pairs exceeded 0.86 for all selected channels.

Broadband source of telecom-band polarization-entangled photon-pairs for wavelength-multiplexed entanglement distribution.

Studies on telecom-band entangled photon-pair sources for entanglement distribution have so far focused on their narrowband operations. Fiber-based sources are seriously limited by spontaneous Raman scattering while sources based on quasi-phase-matched crystals or waveguides are usually narrowband because of long device lengths and/or operations far from degeneracy. An entanglement distributor would have to multiplex many such narrowband sources before entanglement distribution to fully utilize the available fiber transmission bandwidth. In this work, we demonstrate a broadband source of polarization-entangled photon-pairs suitable for wavelength-multiplexed entanglement distribution over optical fiber. We show that our source is potentially capable of simultaneously supporting up to forty-four independent wavelength channels.

Distribution of polarization-entangled photonpairs produced via spontaneous parametric down-conversion within a local-area fiber network: theoretical model and experiment.

We present a theoretical model for the distribution of polarization-entangled photon-pairs produced via spontaneous parametric down-conversion within a local-area fiber network. This model allows an entanglement distributor who plays the role of a service provider to determine the photon-pair generation rate giving highest two-photon interference fringe visibility for any pair of users, when given user-specific parameters. Usefulness of this model is illustrated in an example and confirmed in an experiment, where polarization-entangled photon-pairs are distributed over 82 km and 132 km of dispersion-managed optical fiber. Experimentally observed visibilities and entanglement fidelities are in good agreement with theoretically predicted values.

Stable source of high quality telecom-band polarization-entangled photon-pairs based on a single, pulse-pumped, short PPLN waveguide.

We demonstrate a stable source of high quality telecom-band polarization-entangled photon-pairs based on a single, pulse-pumped, short periodically-poled lithium niobate (PPLN) waveguide. Full quantum state tomographic measurement performed on the photon-pairs has revealed a very high state purity of 0.94, and an entanglement fidelity exceeding 0.96 at the low-rate-regime. At higher rates, entanglement quality degrades due to emission of multiple-pairs. Using a new model, we have confirmed that the observed degradation is largely due to double- and triple-pair emissions.

Electronic post-compensation for nonlinear phase fluctuations in a 1000-km 20-Gbit/s optical quadrature phase-shift keying transmission system using the digital coherent receiver.

We demonstrate electronic post-compensation for nonlinear phase fluctuation in a 1000-km 20-Gbit/s optical quadrature phase-shift keying (QPSK) transmission system, where group-velocity dispersion is well managed. The inter-symbol interference (ISI) at the transmitter induces the nonlinear phase fluctuation through self-phase modulation (SPM) of the signal transmitted through a fiber. However, when the optimized phase shift proportional to the intensity fluctuation is given to the complex amplitude of the signal electric field by using a digital coherent receiver, the nonlinear phase fluctuation can be reduced effectively.