## BIT RATE AND DISTANCE LIMITS

**Bit rate and distance limitations of digital** links are determined by loss and dispersion limitations. The following example is used to illustrate the calculation of the maximum distance for a given bit rate. Consider a 2.5-Gbit/s system at a wavelength of 1550 nm. Assume an average transmitter power of 0 dBm coupled into the fiber. Receiver sensitivity is taken to be 3000 photons per bit, which from Eq. (12) corresponds to an average receiver power of -30.2 dBm. Allowing a total of 8 dB for margin and for connector and cabling losses at the two ends gives a loss allowance of 22.2 dB. If the cabled fiber loss, including splices, is 0.25 dB/km, this leads to a loss-limited transmission distance of 89 km.

**Assuming that the fiber** dispersion is D = 15 ps/kmnm and source spectral width is 0.1 nm, this gives a dispersion per unit length of 1.5 ps/km. Taking the maximum allowed dispersion to be half the interpulse period, this gives a maximum dispersion of 200 ps, which then yields a maximum dispersion-limited distance of 133 km. Thus, the loss-limited distance is controlling.

**Consider what happens if the bit** rate is increased to 10 Gbit/s. For the same number of photons per bit at the receiver, the receiver power must be 6 dB greater than that in the preceding example. This reduces the loss allowance by 6 dB, corresponding to a reduction of 24 km in the loss-limited distance. The loss-limited distance is now 65 km (assuming all other parameters are unchanged). However, dispersion-limited distance scales inversely with bit rate, and is now 22 km. The system is now dispersion-limited. Dispersion-shifted fiber would be required to be able to operate at the loss limit.

### Increasing Bit Rate

**There are two general approaches for increasing the bit rate transmitted on a fiber:** time-division multiplexing (TDM), in which the serial transmission rate is increased, and wavelength-division multiplexing (WDM), in which separate wavelengths are used to transmit independent serial bit streams in parallel. TDM has the advantage of minimizing the quantity of active devices but requires higher-speed electronics as the bit rate is increased. Also, as indicated by the preceding example, dispersion limitations will be more severe.

**WDM allows use of existing lower-speed electronics**, but requires multiple lasers and detectors as well as optical filters for combining and separating the wavelengths. Technology advances, including tunable lasers, transmitter and detector arrays, high-resolution optical filters, and optical amplifiers (Sec. 2.5) are making WDM more attractive, particularly for networking applications (Sec. 2.6).

### Longer Repeater Spacing

**In principal,** there are three approaches for achieving longer repeater spacing than that calculated in the preceding text: lower fiber loss, higher transmitter powers, and improved receiver sensitivity (smaller Np). Silica-based fiber is already essentially at the theoretical Rayleigh scattering loss limit. There has been research on new fiber materials that would allow operation at wavelengths longer than 1.6 |im, with consequent lower theoretical loss values.22 There are many reasons, however, why achieving such losses will be difficult, and progress in this area has been slow.

**Higher transmitter powers are possible**, but there are both nonlinearity and reliability issues that limit transmitter power. Since present receivers are more than 30 dB above the quantum limit, improved receiver sensitivity would appear to offer the greatest possibility. To improve the receiver sensitivity, it is necessary to increase the photocurrent at the output of the detector without introducing significant excess loss. There are two main approaches for doing so: optical amplification and optical mixing. Optical preamplifiers result in a theoretical sensitivity of 38 photons per bit23 (6dB above the quantum limit), and experimental systems have been constructed with sensitivities of about 100 photons per bit.24 This will be discussed further in Sec. 2.5. Optical mixing (coherent receivers) will be discussed briefly in the following text.

**Coherent Systems**. A photodetector provides an output current proportional to the magnitude square of the electric field that is incident on the detector. If a strong optical signal (local oscillator) coherent in phase with the incoming optical signal is added prior to the photode-tector, then the photocurrent will contain a component at the difference frequency between the incoming and local oscillator signals. The magnitude of this photocurrent, relative to the direct detection case, is increased by the ratio of the local oscillator to the incoming field strengths. Such a coherent receiver offers considerable improvement in receiver sensitivity. With on-off keying, a heterodyne receiver (signal and local oscillator frequencies different) has a theoretical sensitivity of 36 photons per bit, and a homodyne receiver (signal and local oscillator frequencies the same) has a sensitivity of 18 photons per bit. Phase-shift keying (possible with coherent systems) provides a further 3-dB improvement. Coherent systems, however, require very stable signal and local oscillator sources (spectral linewidths need to be small compared to the modulation bandwidth) and matching of the polarization of the signal and local oscillator fields.25

**An advantage of coherent systems,** more so than improved receiver sensitivity, is that because the output of the photodetector is linear in the signal field, filtering for WDM demultiplexing may be done at the difference frequency (typically in the microwave range). This allows considerably greater selectivity than is obtainable with optical filtering techniques. The advent of optical amplifiers has slowed the interest in coherent systems.

## OPTICAL AMPLIFIERS

**There are two types of optical amplifiers:** laser amplifiers based on stimulated emission and parametric amplifiers based on nonlinear effects (Chap. 8 in Ref. 18). The former are currently of most interest in fiber-optic communications. A laser without reflecting end faces is an amplifier, but it is more difficult to obtain sufficient gain for amplification than it is (with feedback) to obtain oscillation. Thus, laser oscillators were available much earlier than laser amplifiers.

**Laser amplifiers are now available with** gains in excess of 30 dB over a spectral range of more than 30 nm. Output saturation powers in excess of 10 dBm are achievable. The amplified spontaneous emission (ASE) noise power at the output of the amplifier, in each of two orthogonal polarizations, is given by

where G is the amplifier gain, Bo is the bandwidth, and the spontaneous emission factor nsp is equal to 1 for ideal amplifiers with complete population inversion.

### Comparison of Semiconductor and Fiber Amplifiers

**There are two principal types of laser amplifiers:** semiconductor laser amplifiers (SLAs) and doped-fiber amplifiers. The erbium-doped-fiber amplifier (EDFA), which operates at a wavelength of 1.55 |im, is of most current interest.

**The advantages of the SLA,** similar to laser oscillators, are that it is pumped by a DC current, it may be designed for any wavelength of interest, and it can be integrated with elec-trooptic semiconductor components.

**The advantages of the EDFA** are that there is no coupling loss to the transmission fiber, it is polarization-insensitive, it has lower noise than SLAs, it can be operated at saturation with no intermodulation owing to the long time constant of the gain dynamics, and it can be integrated with fiber devices. However, it does require optical pumping, with the principal pump wavelengths being either 980 or 1480 nm.

### Communications Application of Optical Amplifiers

There are four principal applications of optical amplifiers in communication systems:26,27

**1.** Transmitter power amplifiers

**2.** Compensation for splitting loss in distribution networks

**3.** Receiver preamplifiers

**4.** Linear repeaters in long-distance systems

**The last application is of particular importance for long**-distance networks (particularly undersea systems), where a bit-rate-independent linear repeater allows subsequent upgrading of system capacity (either TDM or WDM) with changes only at the system terminals. Although amplifier noise accumulates in such long-distance linear systems, transoceanic lengths are achievable with amplifier spacings of about 60 km corresponding to about 15-dB fiber attenuation between amplifiers.

**However,** in addition to the accumulation of ASE, there are other factors limiting the distance of linearly amplified systems, namely dispersion and the interaction of dispersion and nonlinearity.28 There are two alternatives for achieving very long-distance, very high-bit-rate systems with linear repeaters: solitons, which are pulses that maintain their shape in a dispersive medium,29 and dispersion compensation.30

## FIBER-OPTIC NETWORKS

**Networks are communication systems used** to interconnect a number of terminals within a defined geographic area—for example, local area networks (LANs), metropolitan area networks (MANs), and wide area networks (WANs). In addition to the transmission function discussed throughout the earlier portions of this topic, networks also deal with the routing and switching aspects of communications.

**Passive optical networks utilize couplers to distribute signals to users.** In an N x N ideal star coupler, the signal on each input port is uniformly distributed among all output ports. If an average power PT is transmitted at a transmitting port, the power received at a receiving port (neglecting transmission losses) is

where 8N is the excess loss of the coupler. If N is a power of 2, an N x N star may be implemented by log2 N stages of 2 x 2 couplers. Thus, it may be conservatively assumed that

The maximum bit rate per user is given by the average received power divided by the product of the photon energy and the required number of photons per bit (Np). The throughput Y is the product of the number of users and the bit rate per user, and from Eqs. (24) and (25) is therefore given by

Thus, the throughput (based on power considerations) is independent of N for ideal couplers (82 = 0) and decreases slowly with N (~N-017) for 10 log (1 – 82) = 0.5 dB. It follows from Eq. (26) that for a power of 1 mW at X = 1.55 |im and with Np = 3000, the maximum throughput is 2.6 Tbit/s.

**This may be contrasted with a tapped bus**, where it may be shown that optimum tap weight to maximize throughput is given by 1/N,leading to a throughput given by31

**Thus, even for ideal (8 = 0) couplers,** the throughput decreases inversely with the number of users. If there is excess coupler loss, the throughput decreases exponentially with the number of users and is considerably less than that given by Eq. (26). Consequently, for a power-limited transmission medium, the star architecture is much more suitable than the tapped bus. The same conclusion does not apply to metallic media, where bandwidth rather than power limits the maximum throughput.

**Although the preceding text indicates the large throughput** that may be achieved in principle with a passive star network, it doesn’t indicate how this can be realized. Most interest is in WDM networks.32 The simplest protocols are those for which fixed-wavelength receivers and tunable transmitters are used. However, the technology is simpler when fixed-wavelength transmitters and tunable receivers are used, since a tunable receiver may be implemented with a tunable optical filter preceding a wideband photodetector. Fixed-wavelength transmitters and receivers involving multiple passes through the network are also possible, but this requires utilization of terminals as relay points. Protocol, technology, and application considerations for gigabit networks (networks having access at gigabit rates and throughputs at terabit rates) is an extensive area of current research.32,33

## ANALOG TRANSMISSION ON FIBER

**Most interest in fiber-optic communications is centered around digital transmission,** since fiber is generally a power-limited rather than a bandwidth-limited medium. There are applications, however, where it is desirable to transmit analog signals directly on fiber without converting them to digital signals. Examples are cable television (CATV) distribution and microwave links such as entrance links to antennas and interconnection of base stations in mobile radio systems.

### Carrier-to-Noise Ratio (CNR)

**Optical intensity modulation is generally the** only practical modulation technique for incoherent-detection fiber-optic systems. Let f(t) be the carrier signal that intensity modulates the optical source. For convenience, assume that the average value of f(t) is equal to 0, and that the magnitude of f(t) is normalized to be less than or equal to 1. The received optical power may then be expressed as

where m is the optical modulation index

The carrier-to-noise ratio is then given by

CNR is plotted in Fig. 3 as a function of received optical power for a bandwidth of B = 4 MHz (single video channel), optical modulation index m = 0.05, ^ = 0.8 A/W, RIN = -155 dB/Hz, and VN> = 7 pA/vN. At low received powers (typical of digital systems) the CNR is limited by thermal noise. However, to obtain the higher CNR generally needed by analog systems, shot noise and then ultimately laser RIN become limiting.

### Analog Video Transmission on Fiber34

**It is helpful to distinguish between single-channel** and multiple-channel applications. For the single-channel case, the video signal may directly modulate the laser intensity [amplitude-modulated (AM) system], or the video signal may be used to frequency-modulate an electrical subcarrier, with this subcarrier then intensity-modulating the optical source [frequency-modulated (FM) system]. Equation (30) gives the CNR of the recovered subcarrier. Subsequent demodulation of the FM signal gives an additional increase in signal-to-noise ratio. In addition to this FM improvement factor, larger optical modulation indexes may be used than in AM systems. Thus FM systems allow higher signal-to-noise ratios and longer transmission spans than AM systems.

**Two approaches have** been used to transmit multichannel video signals on fiber. In the first (AM systems), the video signals undergo electrical frequency-division multiplexing (FDM), and this combined FDM signal intensity modulates the optical source. This is conceptually the simplest system, since existing CATV multiplexing formats may be used.

**FIGURE 3 CNR as a function of input power. Straight lines indicate thermal noise (-.-.-), shot noise (-), and RIN (…..) limits.**

**In FM systems,** the individual video channels frequency-modulate separate microwave carriers (as in satellite systems). These carriers are linearly combined and the combined signal intensity modulates a laser. Although FM systems are more tolerant than AM systems to intermodulation distortion and noise, the added electronics costs have made such systems less attractive than AM systems for CATV application.

**Multichannel AM** systems are of interest not only for CATV application but also for mobile radio applications to connect signals from a microcellular base station to a central processing station. Relative to CATV applications, the mobile radio application has the additional complication of being required to accommodate signals over a wide dynamic power range.

### Nonlinear Distortion

**In addition to CNR requirements**, multichannel analog communication systems are subject to intermodulation distortion. If the input to the system consists of a number of tones at frequencies mi, then nonlinearities result in intermodulation products at frequencies given by all sums and differences of the input frequencies. Second-order intermodulation gives intermod-ulation products at frequencies mi ± Oj, whereas third-order intermodulation gives frequencies rai ± O ± ra^. If the signal frequency band is such that the maximum frequency is less than twice the minimum frequency, then all second-order intermodulation products fall outside the signal band, and third-order intermodulation is the dominant nonlinearity. This condition is satisfied for the transport of microwave signals (e.g., mobile radio signals) on fiber, but is not satisfied for wideband CATV systems, where there are requirements on composite second-order (CSO) and composite triple-beat (CTB) distortion.

**The principal causes of intermodulation** in multichannel fiber-optic systems are laser threshold nonlinearity,35 inherent laser gain nonlinearity, and the interaction of chirp and dispersion.

## TECHNOLOGY AND APPLICATIONS DIRECTIONS

**Fiber-optic communication application in the** United States began with metropolitan and short-distance intercity trunking at a bit rate of 45 Mbit/s, corresponding to the DS-3 rate of the North American digital hierarchy. Technological advances, primarily higher-capacity transmission and longer repeater spacings, extended the application to long-distance intercity transmission, both terrestrial and undersea. Also, transmission formats are now based on the synchronous digital hierarchy (SDH), termed synchronous optical network (SONET) in the U.S. OC-48 systems* operating at 2.5 Gbit/s are widely deployed, with OC-192 10-Gbit/s systems also available as of 1999. All of the signal processing in these systems (multiplexing, switching, performance monitoring) is done electrically, with optics serving solely to provide point-to-point links.

**For long-distance applications,** dense wavelength-division multiplexing (DWDM), with channel spacings of 100 GHz and with upward of 80 wavelength channels, has extended the bit rate capability of fiber to greater than 400 Gbit/s in commercial systems and up to 3 Tbit/s in laboratory trials.36 For local access, there is extensive interest in hybrid combinations of optical and electronic technologies and transmission media.37,38 Owing to the criticality of communications, network survivability has achieved growing importance, with SONET rings being implemented so that no single cable cut will result in system failure.39

**The huge bandwidth capability of fiber optics** (measured in tens of terahertz) is not likely to be utilized by time-division techniques alone, and DWDM technology and systems are receiving considerable emphasis, although work is also under way on optical time-division multiplexing (OTDM) and optical code-division multiplexing (OCDM).

**Nonlinear phenomena,** when uncontrolled, generally lead to system impairments. However, controlled nonlinearities are the basis of devices such as parametric amplifiers and switching and logic elements. Nonlinear optics will consequently continue to receive increased emphasis.