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We describe a method to estimate the capacity limit of fiber-optic communication systems (or ?fiber channels?) based on information theory. This paper is divided into two parts. Part 1 reviews fundamental concepts of digital communications and information theory. We treat digitization and modulation followed by information theory for channels both without and with memory. We provide explicit relationships between the commonly used signal-to-noise ratio and the optical signal-to-noise ratio. We further evaluate the performance of modulation constellations such as quadrature-amplitude modulation, combinations of amplitude-shift keying and phase-shift keying, exotic constellations, and concentric rings for an additive white Gaussian noise channel using coherent detection. Part 2 is devoted specifically to the "fiber channel.'' We review the physical phenomena present in transmission over optical fiber networks, including sources of noise, the need for optical filtering in optically-routed networks, and, most critically, the presence of fiber Kerr nonlinearity. We describe various transmission scenarios and impairment mitigation techniques, and define a fiber channel deemed to be the most relevant for communication over optically-routed networks. We proceed to evaluate a capacity limit estimate for this fiber channel using ring constellations. Several scenarios are considered, including uniform and optimized ring constellations, different fiber dispersion maps, and varying transmission distances. We further present evidences that point to the physical origin of the fiber capacity limitations and provide a comparison of recent record experiments with our capacity limit estimation.

Capacity Limits of Optical Fiber Networks

We examine the current performance and future demands of interconnects to and on silicon chips. We compare electrical and optical interconnects and project the requirements for optoelectronic and optical devices if optics is to solve the major problems of interconnects for future high-performance silicon chips. Optics has potential benefits in interconnect density, energy, and timing. The necessity of low interconnect energy imposes low limits especially on the energy of the optical output devices, with a ~ 10 fJ/bit device energy target emerging. Some optical modulators and radical laser approaches may meet this requirement. Low (e.g., a few femtofarads or less) photodetector capacitance is important. Very compact wavelength splitters are essential for connecting the information to fibers. Dense waveguides are necessary on-chip or on boards for guided wave optical approaches, especially if very high clock rates or dense wavelength-division multiplexing (WDM) is to be avoided. Free-space optics potentially can handle the necessary bandwidths even without fast clocks or WDM. With such technology, however, optics may enable the continued scaling of interconnect capacity required by future chips.

Device Requirements for Optical Interconnects to Silicon Chips

Squeezed states of the electromagnetic field have been generated by nondegenerate four-wave mixing due to Na atoms in an optical cavity. The optical noise in the cavity, comprised of primarily vacuum fluctuations and a small component of spontaneous emission from the pumped Na atoms, is amplified in one quadrature of the optical field and deamplified in the other quadrature. These quadrature components are measured with a balanced homodyne detector. The total noise level in the deamplified quadrature drops below the vacuum noise level.

Observation of squeezed states generated by four-wave mixing in an optical cavity

The drive for higher performance in optical fiber systems has renewed interest in coherent detection. We review detection methods, including noncoherent, differentially coherent, and coherent detection, as well as a hybrid method. We compare modulation methods encoding information in various degrees of freedom (DOF). Polarization-multiplexed quadrature-amplitude modulation maximizes spectral efficiency and power efficiency, by utilizing all four available DOF, the two field quadratures in the two polarizations. Dual-polarization homodyne or heterodyne downconversion are linear processes that can fully recover the received signal field in these four DOF. When downconverted signals are sampled at the Nyquist rate, compensation of transmission impairments can be performed using digital signal processing (DSP). Linear impairments, including chromatic dispersion and polarization-mode dispersion, can be compensated quasi-exactly using finite impulse response filters. Some nonlinear impairments, such as intra-channel four-wave mixing and nonlinear phase noise, can be compensated partially. Carrier phase recovery can be performed using feedforward methods, even when phase-locked loops may fail due to delay constraints. DSP-based compensation enables a receiver to adapt to time-varying impairments, and facilitates use of advanced forward-error-correction codes. We discuss both single- and multi-carrier system implementations. For a given modulation format, using coherent detection, they offer fundamentally the same spectral efficiency and power efficiency, but may differ in practice, because of different impairments and implementation details. With anticipated advances in analog-to-digital converters and integrated circuit technology, DSP-based coherent receivers at bit rates up to 100 Gbit/s should become practical within the next few years.

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Coherent detection in optical fiber systems

The trend toward higher bit rates in lightwave communications has increased interest in dispersion-shifted fiber to minimize dispersion penalties. At the same time optical amplifiers have increased interest in wavelength multiplexing. These two methods of increasing system capacity, if used together, can result in severe degradation due to fiber nonlinearity. This paper discusses the impact of the principal nonlinearity, four-photon mixing, and describes strategies that allow simultaneous use of high bit rates and WDM. >

Four-photon mixing and high-speed WDM systems

System fading caused by polarization-mode dispersion is investigated at 1.7 Gb/s using highly-birefringent, dispersion-shifted fiber at 1.55 mu m. The observed fading, which is manifested by random fluctuations of the bit error rate for a fixed receiver power, is observed to depend on the environmental conditions of the fiber, with the time constant for fading varying from minutes to hours depending on the rate of change of the ambient temperature. The mean dispersion penalty inferred from the observed fluctuations in the bit error rate is consistent with a square-law dependence on the polarization-mode dispersion for small penalties. >

Fading in lightwave systems due to polarization-mode dispersion

The authors introduce simple techniques to solve gain equalization problems in amplified wavelength-multiplexed lightwave transmission systems. By adjusting the channel powers at the terminals in a prescribed way, either the output powers or the output signal-to-noise ratios of all the channels can be equalized. All adjustments can be made using information provided by system telemetry. No new equipment, upgrades, or adjustments are required at intermediate amplifier sites. >

Equalization in amplified WDM lightwave transmission systems

Crosstalk due to four-wave mixing (FWM) is the dominant nonlinear effect in long-haul multichannel optical communication systems employing dispersion-shifted fiber. A method is discussed to find non-uniform channel separations for which no four-wave mixing product is superimposed on any of the transmitted channels, therefore suppressing FWM crosstalk. The residual crosstalk, due to channel power depletion only, is analytically evaluated for intensity-modulated repeaterless wavelength-division-multiplexed (WDM) systems and compared to experimental results. The theory includes the effect of the channel depletion on the amplitude of each phase-matched FWM wave. The probability of error is evaluated including the statistics of the pattern dependent channel depletion. The BER curve computed for an 8-channel WDM system is found to be in good agreement with experimental results. In the experiment, repeaterless transmission of eight 10 Gb/s WDM channels over 137 km (11 Tb/s-km) of dispersion-shifted fiber was demonstrated and error-free operation was achieved over a wide range of input powers using unequally spaced channels. The same system with equally spaced channels could not achieve a probability of error lower than 10/sup -6/. The use of unequal channel spacing allowed fiber input power to be increased by as much as 7 dB, which could be translated into a fivefold increase of the bit rate per channel (and therefore of the system capacity), or to an increase in the system length of about 30 km. >

WDM systems with unequally spaced channels

Spontaneous backward Brillouin scattering is demonstrated to be a sensitive probe of fibre characteristics using a heterodyne detection technique. Relative differences in GeO2 concentration from fibre to fibre as small as 0.01% can be detected.

R.W. Tkach

Papers

Four-photon mixing and high-speed WDM systems

Fading in lightwave systems due to polarization-mode dispersion

Equalization in amplified WDM lightwave transmission systems

WDM systems with unequally spaced channels

Spontaneous Brillouin scattering for single-mode optical-fibre characterisation