CHAPTER 3 IMPACT OF EDFA GAIN SATURATION ON DYNAMIC RWA

Transcription

1 97 CHAPTER 3 IMPACT OF EDFA GAIN SATURATION ON DYNAMIC RWA 3.1 INTRODUCTION In an optical communication system, the optical signals from the transmitter are attenuated by the optical fiber as they propagate through it. Other optical components, such as multiplexers and couplers, also add loss. After some distance, the cumulative loss of signal strength causes the signal to become too wea to be detected. Before this happens, the signal strength has to be restored. Prior to the advent of optical amplifiers, the only option was to regenerate the signal. A regenerator converts the optical signal to an electrical signal, cleans it up, and converts it bac into an optical signal for onward transmission. Optical amplifiers offer several advantages over regenerators. Regenerators are sensitive to the bit rate and modulation format used by the communication systems, whereas, optical amplifiers are transparent to the bit rate or signal formats. Thus a system using optical amplifiers can be more easily upgraded, for example, to a higher bit rate, without replacing the amplifiers. In contrast, in a system using regenerators, such an upgrade would require all the regenerators to be replaced. Furthermore, optical amplifiers have fairly large gain bandwidths, and as a consequence, a single amplifier can simultaneously amplify several WDM signals. In contrast, separate regenerators are required for each wavelength.

2 98 Optical amplifiers have become an essential component in optical transmission systems and networs to compensate for system losses. Amplifiers are used in three different configurations as shown in Figure 3.1. An optical preamplifier is used just in front of a receiver to improve its sensitivity (Olsson 1989). A power amplifier is used after a transmitter to increase the output power. A line amplifier is used typically in the middle of the lin to compensate for lin losses. The design of the amplifier depends on its configuration. A power amplifier is designed to provide the maximum possible output power. A preamplifier is designed to provide high gain and the highest possible sensitivity, that is, the least amount of additional noise. A line amplifier is designed to provide a combination of all of these. Transmitter Receiver Power amplifier Line amplifier Preamplifier Figure 3.1 Different Configurations of Optical Amplifier There are four types of optical amplifiers: Erbium Doped Fiber Amplifiers, fiber Raman amplifiers, fiber Brillouin amplifiers and semiconductor optical amplifiers. The most common optical amplifier available today EDFA. EDFAs are used in almost all amplified WDM systems, whereas Fiber Raman amplifiers are used in addition to EDFAs in many ultra-long haul systems. The EDFA has a gain bandwidth of about 35 nm in the 1.55 µm wavelength region. The great advantage of EDFA is its capability of simultaneously amplifying many WDM channels. EDFAs spawned a new generation of transmission systems, and almost all-optical fiber transmission systems installed over the last few years use EDFAs instead of regenerators.

3 99 The ey physical phenomenon behind signal amplification in an EDFA is stimulated emission of radiation by atoms in the presence of an electromagnetic field. Spontaneous emission process does not contribute to the gain of the amplifier since the emitted photons may have the same energy as the incident optical signal but they are emitted in random directions, polarizations, and phase. This is unlie the stimulated emission process, where the emitted photons not only have the same energy as the incident photons but also the same direction of propagation, phase and polarization. This phenomenon is usually described by saying that the stimulated emission process is coherent, whereas the spontaneous emission process is incoherent. Spontaneous emission has a deleterious effect on the system. The amplifier treats spontaneous emission radiation as another electromagnetic field, and the spontaneous emission also gets amplified, in addition to the incident optical signal. The amplified spontaneous emission appears as noise at the output of the amplifier. In some amplifier designs, the ASE noise can be large enough so as to saturate the amplifier. In this chapter, the impact of gain saturation and the ASE noise generated by the EDFAs are considered during the dynamic lightpath establishment process. Ramamurthy et al (1999) considered the impact of EDFA gain saturation and the ASE noise during the establishment of a lightpath. However, they have used an approximate EDFA gain model. Deng et al (2004) also use a simple gain model. In this wor, EDFA gain is numerically obtained by solving a transcendental equation called the Saleh equation. In order to obtain the gain quicly, a fast and accurate approach is also suggested. 3.2 ERBIUM DOPED FIBER AMPLIFIERS An EDFA is shown in Figure 3.2. It consists of a length of silica fiber, whose core is doped with ionized atoms (ions), Er 3+, of the rare earth

4 100 element Erbium. This fiber is pumped using a signal from a laser, typically, at a wavelength of 980 nm or 1480 nm. In order to combine the output of the pump laser with the input signal, the doped fiber is preceded by a wavelengthselective coupler. Signal in 1550 nm Erbium fiber Isolator Signal out Pump Wavelength-selective coupler Residual pump Figure 3.2 An Erbium doped Fiber Amplifier At the output, another wavelength-selective coupler may be used if needed to separate the amplified signal from any remaining pump signal. Usually, an isolator is used at the input and/or output of any amplifier to prevent reflections into the amplifier. A combination of several factors has made the EDFA the amplifier of choice in today s optical communication systems: the availability of compact and reliable high power semiconductor pump lasers, polarization independence, easy coupling of light into transmission fiber, device simplicity and negligible crosstal when amplifying WDM signals Principle of Operation The energy levels of Erbium ions in silica glass are shown in Figure 3.3 and are labeled E 1, E 2 and E 3 in order of increasing energy. Several other levels in Er 3+ are not shown. Each energy level that appears as a discrete line in an isolated ion of Erbium is split into multiple energy levels when these ions are introduced into silica glass. This process is termed as Star splitting. Moreover, glass is not a crystal and thus does not have a regular

5 101 structure. Thus the Star splitting levels introduced are slightly different for individual Erbium ions, depending on the local surroundings seen by those ions. Macroscopically, when viewed as a collection of ions, this has the effect of spreading each discrete energy level of an Erbium ion into a continuous energy band. This spreading of energy levels is a useful characteristic for optical amplifiers since they increase the frequency or wavelength range of signals that can be amplified. Within each energy band, the Erbium ions are distributed in the various levels in a nonuniform manner by a process nown as thermalization. It is due to this thermalization process that an amplifier is capable of amplifying several wavelengths simultaneously. E 4 (Fluoride glass only) 980 nm E 3 E nm 980 nm 1480 nm E 1 Figure 3.3 Energy levels in the Er 3+ ions of Silica Glass The fourth energy level E 4 is present in fluoride glass but not in silica glass. The difference between the energy levels is labeled in terms of the wavelength in nm of the photon corresponding to it. The upward arrows indicate wavelengths at which the amplifier can be pumped to excite the ion into the higher energy level. The 980 nm transition corresponds to the band gap between the E 1 and E 3 levels. The 1480 nm transition corresponds to the gap between the bottom of the E 1 band to the top of the E 2 band. The

6 102 downward transitions represent the wavelength of photons emitted due to spontaneous and stimulated emission. In the case of Erbium ions in silica glass, the set of frequencies that can be amplified by stimulated emission from the E 2 band to the E 1 band corresponds to the wavelength range nm, a bandwidth of 50 nm, with a pea around 1543 nm. This is one of the low attenuation windows of standard optical fiber used by optical systems. The ionic population in the three levels is denoted by N 1, N 2 and N 3. In thermal equilibrium, N 1 > N 2 > N 3. The population inversion condition for stimulated emission from E 2 to E 1 is N 2 >N 1 and can be achieved by a combination of absorption and stimulated emission as follows. The energy difference between the E 1 and E 3 levels corresponds to a wavelength of 980 nm. So if optical power at 980 nm-called the pump power-is injected into the amplifier, it will cause transition from E 1 to E 3. Since N 1 > N 3, there will be a net absorption of the 980 nm power. This is called pumping. The ions that have been raised to level E 3 by this process will quicly transit to level E 2 by the spontaneous emission process. The lifetime for this process, τ 32, is about 1 µs. Atoms from level E 2 will also transit to level E 1 by the spontaneous emission process, but the lifetime for this process, τ 21, is about 10 ms, which is much larger than τ 32. Moreover, if the pump power is sufficiently large, ions that transit to the E 1 level are rapidly raised again to the E 3 level only to transit to the E 2 level again. The net effect is that most of the ions are found in level E 2, and thus population inversion is achieved between the E 2 and E 1 levels. Therefore, if a signal in the nm bands is injected into the fiber, it will be amplified by stimulated emission from the E 2 to E 1 level.

7 103 Several levels other than E 3 are higher than E 2 and, in principle, can be used for pumping the amplifier. But the pumping process is more efficient because it uses less pump power for a given gain, at 980 nm than these other wavelengths. Another possible choice for the pump wavelength is 1480 nm. Pumping at 1480 nm is not efficient as 980 nm pumping. The degree of population inversion that can be achieved by 1480 nm pumping is also lower. The higher the population inversion, the lower the noise figure of the amplifier. Thus 980 nm is preferred to realize low noise amplifiers. However, higher power pump lasers are available at 1480 nm, compared to 980 nm, and thus 1480 nm pump finds applications in amplifiers designed to yield high output powers. Another advantage of the 1480 nm pump is that the pump power can also propagate with low loss in silica fiber that is used to carry signals. Therefore, the pump laser can be located remotely from the amplifier itself. This feature is used in some systems to avoid placing any active components in the middle of the lin. An EDFA can be operated in three configurations. In co-directional pumping, the pump signal is injected from the same direction as the signal flow. In counter-directional pumping, the signal and pump are injected in opposite directions. In dual pumping, two pumps are used. In practice, most amplifiers deployed in real systems are more complicated. Two stage designs are more commonly used. The two stages are optimized differently. The first stage is designed to provide low noise, and the second stage is designed to produce high output power. Apart from EDFAs operating in the C band ( nm), EDFAs have also been developed to operate in the L band (1565 to 1625 nm). There are significant differences in the design of C- and L-band EDFAs. These amplifiers are usually realized as separate devices, rather than as a single device.

8 Gain Saturation in EDFA An important consideration in designing amplified systems is the saturation of the EDFA (Desurvire et al 1989). Gain saturation is the signal power dependent gain compression that an amplifier suffers when the input signal strength becomes large. Depending on the pump power and the amplifier design itself, the output power of the amplifier is limited. As a result, when the input signal power is increased, the amplifier gain drops. This is called gain saturation. This behavior can be captured approximated by the following equation: P G = 1 + P sat in G ln G max (3.1) Here, G max is the unsaturated gain, and G the saturated gain of the amplifier, P sat is the internal saturation power of the amplifier, and P in is the input signal power. Deng et al (2004) have used equation (3.1) in their wor to model the EDFA. The saturated gain is less than the unsaturated gain. EDFA gain saturation can degrade the received signal quality and increase the receiver BER Gain Dispersion in EDFA Gain dispersion refers to the wavelength dependence of the gain of an EDFA. Since the population density at the various levels within a band is different, the gain of an EDFA becomes a function of the wavelength. When such an EDFA is used in a WDM communication system, different WDM channels undergo different degrees of amplification. The wavelength dependence of gain is referred to as gain dispersion. This is a critical issue in WDM systems with cascaded amplifiers.

9 105 One way to improve the flatness of the amplifier gain is to use fluoride glass fiber instead of silica fiber, doped with Erbium (Rajiv Ramaswami and Sivarajan 1998). Such amplifiers are called Erbium Doped Fluoride Fiber Amplifiers (EDFFAs). However, there are certain drawbacs to using fluoride glass. The noise performance of EDFFA is poorer than EDFA. Fluoride fiber is difficult to handle. It is brittle, difficult to splice with conventional fiber, and susceptible to moisture. Another approach to flatten the EDFA gain is to use a filter inside the amplifier. Long period fiber gratings and dielectric thin film filters are currently the leading candidates for this application (Giles 1997 and Dung et al 1998). Most commercially available amplifiers are able to provide gain flatness of less than 1 db ripple across the nominal band (Deng et al 2004). 3.3 FIBER RAMAN AMPLIFIERS Stimulated Raman scattering (SRS) is one of the nonlinear impairment that affects signals propagating through the optical fibers. The same nonlinearity can be exploited to provide amplification as well. SRS is an interaction between light waves and the vibrational modes of silica molecules. If a photon of energy hν 1 is incident on a molecule having a vibrational frequency ν m, the molecule can absorb some energy from the photon. In this interaction, the photon is scattered, thereby attaining a lower frequency ν 2 and a corresponding lower energy hν 2. The modified photon is called a Stoes photon. Because the optical signal wave that is injected into a fiber is the source of the interacting photons, it is often called the pump wave, since it supplies power for the generated wave. This process generates scattered light at a wavelength longer than that of the incident light. If another signal is present at this longer wavelength, the SRS light will amplify it and the pump wavelength signal will decrease in power. Consequently, SRS can

10 106 severely limit the performance of a multichannel optical communication system by transferring energy from short-wavelength channels to neighboring higher-wavelength channels. This is a broadband effect that can occur in both directions. The Raman gain spectrum is fairly broad and the pea of the gain is centered about 13 THz below the frequency of the pump signal used. Using pumps around nm provides Raman gain in the nm window. A few ey attributes distinguish Fiber Raman amplifiers from EDFAs. Unlie EDFAs, Raman effect can be used to provide gain at any wavelength. Raman amplification relies on simply pumping the same silica fiber used for transmitting the data signals, so it can be used to produce lumped or discrete amplifiers, as well as distributed amplifiers. In the lumped case, the fiber Raman amplifier consists of a sufficiently long spool of fiber along with the appropriate pump lasers in a pacage. In the distributed case, the fiber can simply be the fiber span of interest with the pump attached to one end of the span. Fiber Raman amplifiers are used in addition to EDFAs in many ultra long haul systems. 3.4 FIBER BRILLOUIN AMPLIFIERS The operating principle behind fiber Brillouin amplifiers is essentially the same as for fiber amplifiers except that the optical gain is provided by Stimulated Brillouin Scattering (SBS). SBS arises when light waves scatter from acoustic waves. The resultant scattered wave propagates principally in the bacward direction in single mode fibers. This bacward scattered light experiences gain from the forward propagating signals, which leads to depletion of the signal power. Fiber Brillouin amplifiers are also pumped optically and a part of the pump power is transferred to the signal. SBS differs from SRS in three important aspects which affect the operation of

11 107 the fiber Brillouin amplifiers considerably: amplification occurs only when the signal beam propagates in a direction opposite to that of the pump beam, the stoes shift for SBS is smaller (~10 GHz) by three orders of magnitude compared with that of SRS and depends on the pump frequency and Brillouin gain spectrum is extremely narrow. Fiber Brillouin amplifiers can be used as a preamplifier to improve the receiver sensitivity. The narrow bandwidth of fiber Brillouin amplifiers can be used to advantage in coherent and mutichannel light wave systems. 3.5 SEMICONDUCTOR OPTICAL AMPLIFIERS Semiconductor Optical Amplifiers (SOAs) actually preceded EDFAs, although they are not as good as EDFAs for use as amplifiers. However, they are finding other applications in switches and wavelength converter devices. The two major types of SOAs are the resonant, Fabry- Perot amplifier (FPA) and the nonresonant, traveling-wave amplifier (TWA). TWAs are more widely used than FPAs because they have a larger optical bandwidth, high saturation power, and low polarization sensitivity. Population inversion in an SOA is achieved by forward biasing a pn junction. In practice, a simple pn junction is not used, but a thin layer of a different semiconductor material is sandwiched between the p-type and n-type regions. Such a device is called a heterostructure. The SOAs have a more rapid gain response, which is on the order of 1 ps to 0.1 ns. This results in both advantages and limitations. The advantage is that SOAs can be used for implementation of both switching and signal processing functions in optical networs. The limitation is that the rapid carrier response causes the gain at a particular wavelength to fluctuate with the signal rates up to several Gb/s.

12 108 Since this affects the overall gain, the signal gain at other wavelengths also fluctuates. This gives rise to crosstal effects when a broad spectrum of wavelengths must be amplified. In this wor, only EDFAs are considered. Amplifiers are not perfect devices. They introduce noise, and this noise accumulates as the signal passes through multiple amplifiers along its path due to the analog nature of the amplifier. The gain of the amplifier depends on the total input power. For high input powers, the EDFA tend to saturate and the gain drops. Further, the gain of the EDFA is not flat over the entire passband, thus some channels see more gain than others. Ideally, a sufficiently high output power is required to meet the needs of the networ applications. The gain should be flat over the operating wavelength range, and the gain should also be insensitive to variations in the input power of the signal. In chapter 2, it is assumed that the EDFAs always deliver the desired small signal gain irrespective of the input signal power or wavelength. However, the ASE noise generated in the EDFAs has been taen into account. In this chapter, ASE noise, EDFA gain saturation and gain dispersion have been considered during lightpath establishment for a connection request. This requires the online computation of the gain of the EDFAs used in the networ. This chapter also presents a fast and accurate approach to obtain the signal gain of EDFAs. EDFA gain dynamics originating from adding and dropping optical signals at EDFAs (Sun et al 1996 and Sun et al 1997) is not considered. Ramamurthy et al (1999), Deng et al (2004) and Yang and Ramamurthy et al (2005) have also not considered EDFA gain dynamics in their wor. However, Tian and Kinoshita (2003) have demonstrated that with the combination of electrical feedforward and feedbac automatic gain control (AGC), the power excursion caused by fast channel adding/dropping processes can be minimized.

13 GAIN MODEL OF EDFA The gain models proposed by Desurvire (1989) and Morel and Laming (1989) are based on numerical integration and also involve measurement of amplifier parameters which is time consuming and also inaccurate. Saleh et al (1990) proposed a gain model for EDFAs which is based on a single transcendental equation. In this wor, the model proposed by Saleh et al (1990) is used to obtain the gain of the Erbium doped fiber amplifiers. Saleh et al (1990) describe an analytic method for fully characterizing the gain of an EDFA that is based on easily measured monochromatic absorption data. The analytic expressions, which involve the solution of one transcendental equation, can predict the signal gains and pump absorption in an amplifier containing an arbitrary number of pumps and signals from arbitrary directions. The derivation of the Saleh equation is presented below. Saleh et al (1990) considered a two level system with an arbitrary number of input beams. A two level EDFA uses the 4 I 15/ 2 and the 4 I 13/ 2 levels of the Erbium atom. When embedded in glass fiber, these fine structure levels are Star broadened. This allows pumping at a wavelength near 1480 nm to provide gain in the nm range. They have considered an amplifier of length L with a density of active atoms ρ within an active volume of cross-sectional area A. An arbitrary number N of light beams of wavelength λ and power P (z, t) travel through the amplifier in a direction indicated by u. Signal and pump beams are treated identically, i.e., a given beam can be either a pump or a signal. For beams entering at z = 0, have u = 1, while beams entering at z = L have u = -1. In this derivation, power is expressed in units of photons per unit time i.e., the actual power normalized by the photon energy. The rate equation for the fractional population of ions in the upper state N 2 (z, t) is

14 110 N P (z,t) 2(z, t) N 2(z, t) 1 = z τ ρa z N u j j (3.2) j= 1 where τ is the spontaneous lifetime of ions at the upper energy level. The fractional population of the lower state N 1 (z, t) is obtained from N 1 (z, t) + N 2 (z, t) = 1. The light in the fiber is subject to absorption or stimulated emission at rates that depend on wavelength. The cross section for stimulated emission and absorption at wavelength λ are change of power in the th beam is described by e σ and a σ, respectively. The P (z, t) = ρu Γ z e a a [( σ +σ ) N (z, t) σ ] P (z, t) where Γ is the confinement factor at wavelength λ. 2 (3.3) Under steady state conditions, the population densities and optical power are independent of time. Then remembering that N 2 (z, t) by setting ( z, t) rewritten as 2 u = 1 and obtaining N 2 = 0 in equation (3.2), equation (3.3) can be t u dp (z) 1 dp P (z) P dz N j = α + u IS j (3.4) K j= 1 where α and IS P are the absorption constant and intrinsic saturation power of the th beam respectively and are given by α =ργ σ a IS A P = (3.5) e a Γ ( σ +σ )τ

15 111 Finally equation (3.4) is integrated to obtain out in α L P in P out P = P e exp (3.6) IS P where in P and out P are the input and output powers of the th beam and where N P in in = P j= 1 N in j out out P (3.7) P out = j j= 1 are the total input and output powers, respectively. For u = 1, in P and out P are the powers at z = 0 and z = L, respectively, whereas for u = -1, the locations of the input and output beams are reversed. Equation (3.6) can be reduced to a single transcendental equation by summing it over : N P out = A e = 1 BPout A = P in e 1 B = IS P αl e Pin IS P, (3.8) Equation (3.8) is referred to as the Saleh equation. If α, IS P and the input powers are nown, this equation can be solved for P out. Once solved, the result can be inserted into equation (3.6) to compute directly the output power at each wavelength. The gain at wavelength λ can then be calculated since in P and out P are nown. out P

16 112 The above results are applicable even when the amplifier is pumped in the 980 nm region. In this case, e σ = 0 in equation (3.5). 3.7 FAST AND ACCURATE SIGNAL GAIN ESTIMATION Deng et al (2004) use the approximate EDFA gain model given by equation (3.1). Ramamurthy et al (1999) also use an approximate EDFA gain model. In this wor, EDFA gain is obtained using the Saleh model. The gain of an EDFA can be obtained by solving the transcendental equation (3.8) mentioned above. It can be solved using standard numerical techniques lie the bisection method and the Newton-Raphson method. The above mentioned numerical techniques require an initial guess for the root. Newton-Raphson method is the method of choice as it converges quadratically near the root when provided with a proper guess for the root. Equation (3.8) involves exponential quantities, and hence arithmetic overflow can occur at high input power if the initial guess for the root is far away from the actual root (Roudas et al 1999). Therefore a proper initial guess for the root is essential. It is observed, while solving the transcendental equation (3.8), that an initial guess of P in /x ini (where x ini 1) for the root enables the numerical method to converge to the solution without any arithmetic overflow error. For the EDFA reported by Bononi and Rusch (1998), Newton-Raphson method converges to the desired root quicly when x ini taes a value of It is further observed that for the above EDFA, the actual root can be expressed as P in /x fin, where x fin varies from 1.01 to The above methods hold good for multisignal propagation also. This approach is used in this wor to obtain the EDFA gain when pumped at 1480 nm or 980 nm for single and multiwavelength propagation. This guess converges to the actual root without any overflow errors.

17 113 The above approach has been used to obtain the gain of the EDFA reported by Bononi and Rusch (1998). The amplifier is pumped at 980 nm. The pump power is 18.4 dbm. The signal wavelengths are nm and nm. The absorption constants are [0.257, 0.145, 0.125] m -1 and the intrinsic saturation power are [0.44, 0.197, 0.214] mw at [980, , ] nm, respectively. The fluorescence life time is 10.5 ms. The length of the EDFA can be adjusted to obtain the desired gain to suit the specific requirements. Figure 3.4 shows the EDFA gain for the two different signals mentioned above assuming that only one signal propagates through the amplifier at a time. The length of the EDFA is 18 m. It can be seen that different wavelengths are amplified differently. This is referred to as gain dispersion. To obtain the signal gain for each input signal power, the initial guess for the root is selected as P in /x ini, where P in is the sum of the signal and pump power. The value of x ini is chosen as Table 3.1 presents various power of the input signal at nm and the corresponding gain obtained. It also indicates the values of x fin that resulted when the numerical method converges to the actual root.

18 114 Gain (db) nm nm Input signal power (dbm) Figure 3.4 Signal Gain versus input Signal Power at Wavelengths of nm and nm Table 3.1 Number of iterations required by Newton-Raphson method to converge to the desired root for different input Signal power. Pump power is 18.4 dbm, Signal wavelength is nm and guess for the root (i.e., P out ) is P in /x ini with x ini = 1.01 Input signal power (dbm) Signal gain (db) x fin Number of iterations required

19 115 Table 3.2 presents the various input power and the corresponding gain obtained for the input signal at nm. It also indicates the value of x fin that resulted when the numerical method has converges to the actual root. Table 3.2 Number of iterations required by Newton-Raphson Method to converge to the desired root for different input signal power. Pump power is 18.4 dbm, Signal wavelength is nm and guess for the root (i.e., P out ) is P in /x ini with x ini = 1.01 Input signal power (dbm) Signal gain (db) x fin Number of iterations required It can be observed that x fin varies from 1.01 to As the amplifier approaches saturation, x fin also approaches the lower bound of Figure 3.5 shows the signal gain for the two signals when they propagate through the amplifier together.

20 116 Signal gain (db) nm nm Input signal power (dbm) Figure 3.5 Signal Gain versus Signal Power when Signals at nm and nm co-propagate through the Amplifier Table 3.3 shows the input powers of the two signals and the corresponding signal gains obtained when the two signals are traveling through the amplifier together. The pump power is 18.4 dbm. The initial guess for the root is P in /x ini, where x ini =1.01. It can be observed that even in the case of two signals traveling through the amplifier, the value of x fin ranges from 1.01 to This is valid even if the length of the EDFA is altered. However, if the pump power is changed, the above range for x fin does not hold good. Table 3.4 shows the number of iteration required for different initial guesses for the root. Two values of input power are considered. The length of the EDFA is 18 m. Signal wavelength is nm and the pump power is 18.4 dbm.

21 117 Table 3.3 Number of iterations required by Newton-Raphson method when the signals at nm and nm propagate together in the amplifier. Pump power is 18.4 dbm and guess for the root (i.e., P out ) is P in /x ini, with x ini = 1.01 Input power of the signal at nm (dbm) Input power of the signal at nm (dbm) Gain for the signal at nm (db) Gain for the signal at nm (db) x fin Number of iterations required Table 3.4 Number of iterations required for different guesses of the root Input signal power (dbm) Number of iterations required Guess for the root P in /1.01 P in / P in P in /2-40 dbm dbm

22 118 It can be seen that an initial guess of P in /x ini with x ini =1.01 requires the minimum number of iterations compared with the other initial guesses. Hence this approach is called fast and accurate. The guess of P in /x ini is found to hold true even for 1480 nm pumping. Saleh et al (1990) consider an EDFA pumped at 1480 nm to amplify a 1550 nm signal. The length of the EDFA is 387 cm. The absorption constants are [0.792, 0.876] m -1 and the intrinsic saturation power being [0.549, 0.272] mw at [1480, 1550] nm, respectively. The general guess of P in /x ini, with x ini =1.01 has been used in the Newton-Raphson method and the results obtained for different signal/pump power matches well with the results of Saleh et al (1990) and are shown in Figure 3.6. When the signal power is 0 dbm, x fin varies from to for the pump powers shown in Figure 3.6. For the signal power of 26.7 dbm, x fin varies from to Signal power = 0dBm Signal power = -26.7dBm 5 Gain (db) Pump power (dbm) Figure 3.6 Signal Gain versus input Signal Power using 1480 nm pumping

23 IMPACT OF EDFA GAIN SATURATION ON THE BLOCKING PERFORMANCE OF 15-NODE NETWORK OF INTERCONNECTED RINGS In this section, the impact of EDFA gain saturation on the blocing probability of 15-node networ of interconnected rings is studied. The networ topology is shown in Figure 3.7. Table 3.5 presents the system parameters used in this study. The absorption and emission cross sections at the signal wavelength (λ) are determined using the curve fitting technique (Desurvire 1994). First the normalized experimental absorption and emission line shapes are obtained by a linear superposition of eight Gaussian line shapes. Ramamurthy et al (1999) have used only a single line shape in their gain model. The normalized absorption cross section line shapes at various signal wavelengths are obtained using (Desurvire 1994) 8 2 ( λ λ ) ai Ia ( λ) = a exp 4log2 ai 2 (3.9) i= 1 λai where a ai, λ ai and λ ai refer to pea intensity, center wavelength and line width of the i th Gaussian line shape respectively and are presented in Table 3.6. Similarly, the normalized emission cross section line shape at various signal wavelengths have been obtained using 8 2 ( λ λ ) ei Ie ( λ) = a exp 4log2 ei 2 (3.10) i= 1 λei The values of a ei, λ ei and λ ei are presented in Table 3.7. The parameters listed in Table 3.6 and 3.7 have been obtained from Desurvire (1994). The results obtained using equation (3.9) is normalized to unity and hence it is multiplied

24 120 by ( pea absorption cross section value of the Erbium doped fiber) to obtain the actual absorption cross section at the signal wavelengths. The results obtained using equation (3.10) is multiplied by (pea emission cross section value of the Erbium doped fiber) to obtain the actual emission cross section at the signal wavelengths (Desurvire 1994). Absorption constants and the intrinsic saturation power at various wavelengths are obtained with the help of the EDFA parameters listed in Table 3.5 and using equation (3.5). Table 3.8 lists the absorption constants and the intrinsic saturation power for the various wavelengths used in this wor Figure node Networ of interconnected Rings

25 121 Table 3.5 System Parameters and their Values used to Study the Impact of EDFA Gain Saturation Parameters Multiplexer loss (L mx ) Demultiplexer loss (L dm ) Switch characteristic loss (L s ) Waveguide/fiber coupling loss (L w ) Switch loss (L sw ) (for a P P switch) Tap loss (L tap ) Fiber loss (L f ) Desired input EDFA gain (G in ) 4 db 4 db 1 db 1 db Values (2log 2 P)L s + 4 L w 1 db 0.2 db/m 22 db Desired output EDFA gain (G out ) 18 db at nodes 1, 6, 7 & 13 Pump wavelength (λ p ) Pump input power ( P p in ) 16 db, elsewhere 980 nm 18.4 dbm Core radius of EDFA ( r) µm Core area of EDFA (A) m 2 Overlap factor of EDFA (Γ) 0.5 Florescence time of EDFA (τ) 10.5 ms Ion density of EDFA (ρ) ions/m 3 Number of wavelengths 8 Wavelength Spacing Bit rate per channel Optical Bandwidth ( B 0 ) Electrical bandwidth ( B e ) ASE factor (n sp ) 1.5 RMS thermal current Bandwidth, 100 GHz 2.5 Gb/s 36 GHz 2 GHz A η th Hz

26 122 Table 3.6 Parameters used to find Normalized Absorption Line Shape i a ai λ ai (nm) λ ai (nm) Table 3.7 Parameters used to find Normalized Emission Line Shape i a ei λ ei (nm) λ ei (nm)

27 123 Table 3.8 Absorption Constant and Intrinsic Saturation Power at various Wavelengths Wavelength ( nm) Intrinsic saturation power ( mw) Absorption constant (m -1 ) Figure 3.8 shows the gain characteristics of the input EDFA used in this wor at two different wavelengths. It can be seen that gain dispersion is negligible. Gain dispersion is crucial in WDM systems with cascaded amplifiers.

28 Gain (db) Signal wavelength = 1551 nm Signal wavelength = nm Signal power (dbm) Figure 3.8 Gain versus input Signal Power for the input EDFA at Signal Wavelengths of nm and 1551 nm Figure 3.9 shows the gain characteristics of the output EDFA at nm. EDFA of 20 m length is used at the nodes 1, 6, 7 and 13. EDFA of 18 m length is used at the remaining nodes Gain (db) 10 5 L= 20 m L= 18 m Signal power( dbm) Figure 3.9 Gain versus input Power for the output EDFA at a Signal Wavelength of nm

29 125 Figure 3.10 shows the gain characteristics of the output EDFA at nm for length L =20 m and L =18 m. Gain (db) L = 18m L = 20m Signal power (dbm) Figure 3.10 Gain versus input Power for the output EDFA at a Signal Wavelength of nm Calls arrive at the networ following a Poisson process. The traffic over the entire networ is uniformly distributed. The call durations are exponentially distributed with a mean of 1. The number of wavelengths on each lin is 8 and they are: [ , , , , , , and ] nm. The signal power per channel is assumed to be 1 mw at the transmitter. The overall gain of the wavelength routing node compensates for the transmission losses incurred between and within each wavelength routing node, so no in-line EDFAs are used. External intensity modulation is assumed at the transmitters. The discrete event simulation used in this chapter is similar to that discussed in chapter 2. For every dynamically arriving connection request, a route and a free wavelength is determined. The BER at the receiver for this lightpath is estimated. The estimation of BER considers the various transmission impairments. The gain

30 126 of the EDFAs present in the signal route is determined using the fast and accurate approach explained in section 3.7. In addition to the impairments considered in chapter 2, the impact of EDFA gain saturation is also taen into account to estimate the BER. Fixed routing of calls and first-fit wavelength assignment is adopted. A worst case situation of mar state is assumed in all the propagating channels. This ensures that the EDFA gain saturation effect is severe. Further, worst case assumption of mar in all the channels will increase the in band crosstal in the networ. Figure 3.11 shows the impact of a realistic EDFA on the blocing probability performance of the networ. An EDFA which suffers gain saturation is referred to as a realistic EDFA. It can be seen from the figure that a realistic EDFA blocs more calls when compared with an ideal EDFA due to gain saturation even in the absence of in-band crosstal. Gain saturation leads to a reduction of the small signal gain which an EDFA is supposed to provide. Inadequate gain leads to reduced signal power and results in increased BER. The impact of gain saturation and demux/mux in-band crosstal on blocing probability performance is also shown in Figure Switch crosstal ratio is set to 0 and filter crosstal ratio is set to -25 db. It is observed that the presence of gain saturation and in-band crosstal results in more number of calls being bloced compared to the case of an ideal EDFA with no in-band crosstal.

31 127 Blocing probability Realisitic EDFA & No crosstal Ideal EDFA & no crosstal Realisitic EDFA and demux/mux inband crosstal Networ load (Erlangs) Figure 3.11 Impact of Realistic EDFA on 15-node Networ of interconnected Rings It can be concluded from the above discussions that the gain saturation in EDFAs can have severe impact on the received signal quality. It can lead to unsatisfactory BER at the receiver of the destination node and hence leads to increased blocing probability. 3.9 CONCLUSIONS Erbium doped fiber amplifiers are not ideal. Gain saturation, gain dispersion and ASE noise are some of the imperfections of the EDFA which can affect the signal quality over a lightpath. Evaluation of the on-line BER of a lightpath requires the determination of the gain of an EDFA. The gain of the EDFA is governed by a transcendental equation which can be solved using numerical techniques lie Newton-Raphson method. This technique requires an initial guess for the root. If the guess is far from the actual root, overflow errors can occur at high input powers. In this chapter, a guideline to choose

32 128 the initial guess for the root is suggested. This is validated for the EDFA appearing in the literatures. This guess helps to obtain the EDFA gain with minimum iterations. It is also observed that EDFA gain saturation can have a severe impact on the BER of a lightpath. The use of a realistic EDFA accounting for gain saturation effects can lead to an increase in the blocing probability of the networ by even in the absence of crosstal. In other words, the number of calls bloced increases by 2.5% at a traffic load of 50 Erlangs when a realistic EDFA is used. When the crosstal effect is included it is seen that there is a drastic change in the performance. The number of calls bloced increases by almost 30% at a traffic load of 50 Erlangs. It can be concluded that the gain saturation effects has a large impact on the signal quality and BER and a fast and accurate model for online calculation is essential in the process of dynamic RWA. In chapters 2 and 3, crosstal introduced by the switches and demux/mux are considered. Fiber nonlinearities are not considered. Among the nonlinearities, stimulated Raman scattering is regarded as the ultimate power limiting phenomenon in multiplexed optical communications systems. If two or more signals at different wavelengths are injected into a fiber, SRS causes power to be transferred from the lower wavelength channels to higher wavelength channels as long as the wavelength difference is within the bandwidth of the Raman gain. This effect is called as SRS-induced crosstal. In chapter 4, the impact of SRS-induced crosstal is considered while establishing lightpaths. The combined effect of all the above mentioned crosstal effects is also studied.