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Using computer simulations, we analyze the bit-error rate (BER) characteristics of the optical transmission system repeated by erbium-doped fiber amplifiers (EDFAs) and two-mode phase-sensitive optical parametric amplifiers (PSAs), where phase-conjugated (PC) twin waves are co-propagating through the link. We focus on the 256 quadrature-amplitude-modulation (QAM) format, whose transmission characteristics are seriously affected by fiber nonlinearity because the required power is significantly high. Changing the repeater spacing and group-velocity dispersion (GVD) of fibers for transmission in the two-mode PSA-based system, we calculate the BERs as a function of the launched power. When the repeater spacing and GVD value of fibers are properly designed, the two-mode PSA-based system can mitigate nonlinear impairments more effectively than the EDFA-based PC twin system.

Using computer simulations, we analyze the bit-error rate (BER) characteristics of a high-order QAM optical transmission system repeated by two-mode phase-sensitive optical parametric amplifiers (PSAs). In this system, an idler, which is a phase-conjugated twin of a signal, propagate through the link together with the signal. One advantage of this system is that the noise figure of two-mode PSAs used as repeaters can approach 0 dB. The other advantage is that two-mode PSAs cancel out self-phase modulation of the signal at each repeater through the interaction between the transmitted signal and idler. Owing to these advantages, the BER characteristics of 16, 64, and 256QAM signals are significantly improved compared with the system using erbium-doped fiber amplifiers and phase-conjugation twin waves, provided that dispersion-shifted fibers are employed for transmission.

We analyze the noise characteristics of an optical transmission system repeated by two-mode phase-sensitive optical parametric amplifiers. In such a system, the non-degenerated signal and idler waves co-propagate through the link, interacting with each other in the optical parametric amplifiers. For the first time, we derive a closed-form expression for the accumulated noise using the quantum-mechanical Langevin-equation approach. The derived noise formula allows calculating the noise figure of the optical-amplifier chain under the influence of the internal loss of the amplifiers and the transmission loss of the link, thereby theoretically demonstrating its low-noise characteristics.

This study develops a theory of noise in optical parametric amplifiers (OPAs) based on the quantum-mechanical Langevin equations. We derive theoretical expressions for the spontaneous emission factor of OPAs for the first time. This enables analyzing the effect of internal loss on the noise characteristics. In addition, we analyze the noise figures of the laser amplifier, phase-insensitive OPA, and phase-sensitive OPA.

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.

Of-late research on Stokes vector receivers for the short-reach optical communications has gained significant attention due to its capability to decode information in multidimension using cost-effective direct-detection technique. Here, we consider the use of InP for potentially low-cost direct-detection-based Stokes vector (SV) receiver. It consists of a 1 × 4 multimode interference power splitter with different combination of polarization converters on output arms, so that input SV is projected onto distinct vectors on the Stokes space. By using the fabricated device, we experimentally demonstrate decoding of two-level and four-level SV-modulated signals at 3 Gbaud. With the potential of monolithically integrating high-speed InP photodetector array on the same chip, it paves the way to realize compact and low-cost SV receivers for multilevel SV modulation formats in future short-reach optical communication links.

Polarization-modulated optical signals can be demodulated via direct detection of Stokes vectors. In this article, we develop a quantum theory of noise in the Stokes vector receiver. Examining the conditions that enable simultaneous measurement of three elements of the Stokes vector, we demonstrate that an optical pre-amplifier in front of the Stokes vector receiver can reduce the power penalty associated with simultaneous measurements, down to the quantum limit of 3 dB. Then, the 3-D Gaussian noise model for the shot noise and optical pre-amplifier noise is discussed. Subsequently, based on the noise analyses, we derive bit error rate formulae for the cubic-lattice polarization modulation format and evaluate the sensitivity of the Stokes vector receiver.

The recently developed digital coherent receiver enables us to employ a variety of spectrally efficient modulation formats such as $M$ -ary phase-shift keying and quadrature-amplitude modulation. Moreover, in the digital domain, we can equalize all linear transmission impairments such as group-velocity dispersion and polarization-mode dispersion of transmission fibers, because coherent detection preserves the phase information of the optical signal. This paper reviews the history of research and development related to coherent optical communications and describes the principle of coherent detection, including its quantum-noise characteristics. In addition, it discusses the role of digital signal processing in mitigating linear transmission impairments, estimating the carrier phase, and tracking the state of polarization of the signal in coherent receivers.

This chapter illustrates the construction of the optical repeater based on O/E and E/O conversion. Through the binary decision process, one can regenerate the signal, removing the waveform distortion and restoring the power level. Such signal regeneration is performed by optical repeaters, which are periodically placed in the fiber link. Since the repeater includes the 3R functions, namely “reshaping,” “retiming,” and “regeneration". The chapter deals with the principle of operation of the repeater, and discusses the future direction of research and development. The quality of the digital information is maintained over a long distance owing to the 3R functions, because one can eliminate noise and signal distortion at every repeater. However, bit error inevitably occurs through the decision process. The chapter discusses how the bit error occurs through the binary decision process. Since erbium-doped fiber amplifiers (EDFA) have become practical devices, the repeater that employs an EDFA has also been introduced into optical transmission systems.

Direct-detection-based Stokes-vector receivers can demodulate multi-level SOP-modulated signals. A theoretical analysis of their performances in terms of receiver sensitivity and spectral efficiency is presented.

Demodulation of polarization-modulated signals can be done via Stokes-vector direct detection. We analyze the receiver sensitivity for the multi-level polarization-modulation format having the cubic-lattice constellation in the three-dimensional Stokes space.

We propose a novel method of in-band estimation of optical signal-to-noise ratio (OSNR) using a digital coherent receiver, where OSNR is determined from second- and fourth-order statistical moments of equalized signals in any modulation format. Our proposed method is especially important in recently-developed Nyquist wavelength-division multiplexed (WDM) systems and/or reconfigurable optical-add/drop-multiplexed (ROADM) networks, because in these systems and networks, we cannot apply the conventional OSNR estimation method based on optical-spectrum measurements of the in-band signal and the out-of-band noise. Effectiveness of the proposed method is validated with computer simulations of Nyquist-WDM systems and ROADM networks using 25-Gbaud quadrature phase-shift keying (QPSK) and 16 quadrature-amplitude modulation (16-QAM) formats.

The realization of an entanglement distribution optical fiber network connecting multiple parties would permit implementation of many information security applications such as entanglement-based quantum key distribution and quantum secret sharing. However, due to material absorption and scattering in optical fiber, photons that are the carriers of quantum entanglement experience loss during propagation and the overall photon arrival rate can be very low in such a network. One way to increase photon arrival rate is to make full use of the available transmission bandwidth of optical fiber and this is achievable via wavelength-multiplexing. We review our recent work on wavelength-multiplexed entanglement distribution and discuss system design considerations from a telecommunication engineering perspective.

The digital coherent receiver, which is a combination of a phase-diversity optical homodyne receiver and digital signal processing (DSP), can demodulate any multilevel coded optical signals without relying upon an optical phase-locked loop. However, the maximum symbol rate processed by such a receiver is limited by the speed of electric analog-to-digital converters and digital signal processors. Although real-time operation at 10 Gsymbol/s using an application-specific integrated circuit has recently been demonstrated, it is still difficult to increase the symbol rate beyond 40 Gsymbol/s. In order to cope with this difficulty, we propose a novel scheme, which employs a local oscillator (LO) pulsed at the subharmonic frequency of the symbol rate, enabling time-division demultiplexing of the signal at the digital coherent receiver. We demonstrate that the new type of digital coherent receiver operating at 10 Gsymbol/s can demodulate the aggregate symbol rate of 160 Gsymbol/s. From these results, we can expect ultrafast coherent optical fiber communication in the future.

In this paper, we investigate the sensitivity of the digital coherent receiver both theoretically and experimentally. The receiver sensitivity close to the shot-noise limit is demonstrated in the 10-Gbit/s binary phase-shift keying system with the help of a low-noise optical preamplifier. We also introduce polarization diversity into our receiver. Maximal-ratio polarization combining in the digital domain makes the receiver sensitivity independent of the state of polarization of the incoming signal without power penalty.

This paper describes optical signal processing based on optical phase modulation and subsequent optical filtering, which is applicable to 160-Gb/s optical time-division multiplexed (OTDM) subsystems. Ultrafast phase modulation of an optical signal is done by self-phase modulation (SPM) and cross-phase modulation (XPM) when an optical pulse passes through a nonlinear optical fiber. Such phase modulation induces the spectral shift of the optical signal. Various types of optical signal processing are realized simply by filtering out the spectral-shifted component. Using SPM-based pulse reshaping in a 500-m-long silica-based highly nonlinear fiber (HNLF), we demonstrate highly stable generation of a 10-GHz 2-ps optical pulse train tunable over the entire C band. A phase-locked loop (PLL) can suppress the slow phase drift of the output pulse train induced by fluctuations of the nonlinear fiber length, enabling the application of the pulse generator to a 160-Gb/s OTDM transmitter. Based on XPM in a 2-m-long photonic crystal fiber, optical time-division demultiplexing of 160-Gb/s optical signals is demonstrated. The long-term stability is drastically improved as compared with the device composed of a conventional silica-based HNLF, because the short fiber length reduces the phase fluctuation between the signal and control pulses. Instead of nonlinear fibers, an electrooptic modulator such as a (LN) modulator also performs the phase modulation in a more practical manner. We propose and demonstrate an optoelectronic time-division demultiplexing scheme for a 160-Gb/s OTDM signal, which consists of an LN phase modulator driven by a 40-GHz electrical clock and an optical bandpass filter (BPF). We also demonstrate base-clock recovery from a 160-Gb/s optical signal with an optoelectronic PLL. The phase comparator is simply composed of an LN phase modulator and an optical BPF, ensuring the stable and reliable operation in the 160-Gb/s receiver.

An alternative application of distributed Raman amplification (DRA) for ultralong-haul optical fiber transmission is proposed. In our study, the DRA is employed in a transmission system using midway optical phase conjugation (OPC) for amplifying an optical signal and, at the same time, for constructing signal power evolution, which is symmetrical with respect to the midpoint of the system where the OPC is performed. Then, the nonlinear signal waveform distortions that are caused by the Kerr effect, as well as fiber dispersion, are almost completely compensated by the OPC, whereas the fiber loss is compensated by the DRA. Three possible symmetrical signal power maps - a power map that has a reverse sign of the power map that is caused by lump amplification, a flat signal power map, and an arbitrary symmetrical signal power map - are numerically designed by using appropriate Raman pump powers. We show that the flat power map exhibits smaller difference from the target and a higher optical signal-to-noise ratio and requires lower pump power than the other two power maps. Numerical simulation results demonstrate that, by employing the flat power maps with a span of 40 km, a single-wavelength signal whose data rate is 160 Gb/s can be successfully transmitted over 5000 km, and the Kerr effect is sufficiently suppressed near limitation due to the nonlinear accumulation of noise. Finally, we study the feasibility of expanding our method to wavelength-division-multiplexed signal transmission by designing a DRA gain with multiple-wavelength pumping to simultaneously obtain a flat power map and a wide-and-flat gain bandwidth. By using four-wavelength Raman pumps while carefully choosing pump wavelengths and their powers, we achieve the DRA gain that simultaneously gives a fluctuation of the signal power of only 3.5%, a gain ripple of only 5.3%, and, at the same time, a gain bandwidth of as wide as 46 nm.

We demonstrate group velocity dispersion (GVD) and dispersion slope (DS) compensation devices based on enhanced thermal chirping of glued fiber Bragg gratings (FBGs). By gluing a uniform FBG onto a uniform Zn channel for the GVD compensator and a linearly tapered Zn channel for the DS compensator, the thermal sensitivity of the FBG is enhanced. The thermal chirping of the FBG is given by the thermal expansion of a Zn channel, the thermooptic effect, and the thermal expansion of the optical fiber. Controlling the temperature distributions of the uniform FBG performs the tuning of GVD and/or DS, as well as their center wavelengths. These compensation devices can tune their GVD or DS while maintaining a constant center wavelength and change their center wavelengths while preserving constant GVD or DS values. The GVD can be tuned from -123.39 to -57.29 ps/nm with the center wavelength at 1552.9 nm, while the center wavelength can be shifted 2.2 nm with a GVD value of about -105 ps/nm. On the other hand, the DS can be tuned from -8.88 to -24.44 ps/nm2 with the center wavelength at 1554.5 nm, while the center wavelength can be shifted 0.6 nm with a DS value of about -10.4 ps/nm2.

The authors propose third-generation small and high-speed saturable absorbers to replace semiconductor-based saturable absorbers and optical-fiber-based nonlinear devices. The device is based on the carbon nanotube (CNT). This paper discusses the characteristics of CNT-based saturable absorbers. The present status of research on passively mode-locked fiber lasers using CNT-based saturable absorbers is reported. © 2007 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 90(2): 17– 24, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.20272

We propose digital-signal-processing algorithms that achieve fast decoding and LLR-computation for high-order set-partitioned 4D-QAM formats based on their parity-check functions. Computer-simulation results show that computational complexity of the decoder can significantly be reduced with negligible power penalty using such algorithms.

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).

The digital coherent optical receiver has enabled practical 100-Gbit/s optical transmission systems. After summarizing the history of coherent optical communications, this talk discusses the impact of the combination of analog optics and digital electronics.

We analyze the performance of digital coherent receivers with symbol-rate ADC, aiming at short/medium-reach applications (

The circular-birefringence fiber (CBF) or the so-called twisted fiber provides novel attractive potential for all-optical signal-processing applications. Unlike a standard nonpolarization-maintaining (non-PM) fiber, where the polarization dependence of chi(3) nonlinearity is averaged out by the residual birefringence, the CBF behaves as a perfectly isotropic fiber in terms of nonlinear wave propagation. The CBF, therefore, allows the utilization of the intrinsic absolute polarization dependence of chi (3) nonlinearity in realizing novel functions that can never be obtained with a non-PM fiber. Several types of CBF are successfully fabricated by twisting commercial non-PM fibers at 15 turns/m, and their unique potential is experimentally demonstrated. First, a novel type of all-optical intensity discriminator is realized using the effect of ellipse rotation in CBF, which is absent in a non-PM fiber. The demonstrated device is directly applicable to all-optical data reshaping, pulse compression, pedestral suppression, and enhanced mode-locking of fiber lasers. Next, a 160-Gb/s polarization-insensitive wavelength conversion is demonstrated by using cross-phase modulation in CBF with a circularly polarized probe wave. In addition to its simplicity and robustness, the scheme is readily upgradable to polarization-insensitive all-optical data regeneration

We experimentally demonstrate a practical benefit of our proposed continuous-wave (CW) supercontinuum (SC) generating ring laser scheme in terms of low-cost device implementation and then investigate its output intensity noise property, as a further study to our previous paper of Ref. [J.H. Lee, Y. Takushima, K. Kikuchi, Opt. Lett. 30 (2005) 2599]. First, we implement a practical and low-cost CW SC laser using a double clad Er/Yb codoped fiber and a highly nonlinear dispersion-shifted fiber (HNL-DSF). Unlike the scheme in Ref. [J.H. Lee, Y. Takushima, K. Kikuchi, Opt. Lett. 30 (2005) 2599] the gain medium of an Er/Yb fiber is clad-pumped by low quality multimode pump LDs to underline the fact that our proposed scheme does not require any high power single-mode laser pump. A SC of a bandwidth larger than 470 nm is readily achieved. Next, we measure relative-intensity-noise (RIN) of the generated SC and compare it with that of a pumped Er/Yb fiber ASE. The SC laser is found to have a much higher RIN than the ASE due to the nonlinear amplification of quantum fluctuations both in the seed light oscillation and in the Raman scattering process.

This paper describes a phase-diversity homodyne receiver that which can cope with multilevel modulation formats. The carrier phase drift is estimated with digital signal processing (DSP) on the homodyne-detected signal, entirely restoring the complex amplitude of the incoming signal. Our DSP-based phase-estimation scheme consists of a simple and demultiplexable architecture that allows the system to reach significantly higher performance than conventional optical delay detection. Since the whole optical signal information is preserved with our receiver, various kinds of postprocessing of the received signal become possible. For example, we can demultiplex wavelength-division/optical time-division multiplexed channels and compensate for group velocity dispersion of fibers as well as the nonlinear phase noise in the electrical domain. We also experimentally evaluate the performance of our receiver. Our offline bit-error rate experiments show the feasibility of transmitting polarization-multiplexed 40-Gb/s quadrature phase-shift keying signals over 200 km with channel spacing of 16 GHz, leading to spectral efficiency of 2.5 b/s/Hz