**Theodore Mirtchev and Jackson Klein**

**A multitude of scenarios makes a standardized approach for Raman amplifiers almost impossible. Flexible optimizing simulation tools allow developers to explore alternatives and improve amplifier design.**

Technology that appears most promising to support Tbit/s bandwidths employs the inherently broadband nonlinear effect of stimulated Raman scattering (SRS) in Raman fiber amplifiers (RFA) or hybrid erbium-doped fiber amplifers (EDFA) and Raman fiber amplifiers (HRA)^{.1, 2} Raman amplification is also a very cost-effective capacity upgrade solution because it takes place in any type of transmission fiber, either new or already installed.

At the same time, this versatility leads to a number of possible implementation schemes and contexts. The behavior and the quantitative figures of the nonlinear Raman amplifier are very sensitive to all details of the pumps, fibers, and inline passive components—couplers, filters, and so on—within the system. So, a standard universal blueprint for designing Raman amplifiers does not seem possible, apart from some general rules of thumb. Powerful, flexible, and easy-to-use software tools with optimization capabilities can shorten the prototype development cycle and overall time-to-market.

SRS is among the best-understood third-order, nonlinear processes; it was observed experimentally for the first time in 1962 in bulk media^{3} and in 1972 in optical fiber.^{4} It is a process of inelastic scattering of photons over optical phonons (molecular vibration modes). It manifests itself as an exponential growth of a signal (Stokes) wave in the field of intensive pumping with shorter-wavelengths. SRS is automatically phase-matched.

**FIGURE 1. Peak gain coefficient depends on the type and concentration of dopants. Zero temperature Raman gain coefficient spectra of pure fused silica, pure fused GeO _{2}, and silica doped with 25 mol.% GeO_{2} are scaled to the peak gain coefficient of silica.**

SRS is a nonresonant effect with respect to the pump wavelength, which may lie anywhere in the transparency windows of the medium. On the other hand, the frequency difference wp-ws between the pump and signal waves should be resonant with one of the vibrational modes wR of the host medium.

The SRS effect, in principle, is highly dependent on polarization—Raman gain is negligible for orthogonal polarizations of the pump and signal. However, in nonpolarization-maintaining fibers, the gain becomes polarization independent because of mode scrambling. Unfortunately, this polarization independence does not come free—in such cases the gain coefficient is reduced by a factor of two. There is no excess loss if the pump power or injection is absent for some reason, which is not the case with EDFAs and semiconductor optical amplifiers. And there are no dynamic effects or transients because the Raman effect in glasses is characterized by femtosecond response time.

Some of the main parameters of SRS in telecom-grade fused silica fibers5 are: the SRS gain coefficient spectrum peaks at 13.2 THz (~100 nm at pump wavelength lp = 1.55 µm), but extends up to >30 THz. The 3 dB width of the gain coefficient spectrum is 6 to 7 THz (~50 nm at lp = 1.55 µm). The peak gain coefficient is gRpeak(1.55 µm) = 6.4 x 10-13 m/W and is inversely proportional to lp.

However, both the shape of the spectrum and the value of gRpeak depend strongly on the type and concentration of the dopants. For instance, the peak gain coefficient of pure GeO2 is eight to nine times larger than that of fused silica, and their spectra are quite different (see Fig.1).

**RAMAN AMPLIFIERS — SIMULATION**

The challenges in modeling and optimizing RFAs are related mainly to the nonlinear, inefficient nature of SRS, which requires high pump powers and long fibers. All participating optical waves interact with each other and all shorter wavelengths transfer power to every longer one (all longer wavelengths deplete every shorter wavelength), resulting in a complex longitudinal distribution of gain coefficients and noise powers.

Other third-order nonlinear processes among the pumps take place as well, including self-phase modulation (SPM) and cross-phase modulation (XPM), four-wave mixing (FWM), and stimulated Brillouin scattering (SBS). Considerable noise powers and crosstalk are generated via multipath Rayleigh scattering.

An additional challenge comes with the need to build a model that is quantitatively accurate, not only qualitatively. The general features of any of the effects given above are well known.^{5} However, it is their complex interplays and the multitude of details that matters, if such a model is to be used as a practical design tool.

As a result, some of the simplifications usually found in the literature should be rejected. The Raman spectrum of pure fused silica should be used with care, especially for discrete RFAs using DSFs, DCFs, or highly nonlinear fibers Also, dispersion must be accounted for in the real part of the Raman-resonant nonlinear susceptibility.

Assumptions cannot be made that the effective areas and signal/pump overlap integrals are constant. In the region 1.4 to 1.65 µm the effective areas of SMF-28 and a typical dispersion-shifted fiber (DSF) vary by 25% and 50% respectively. This variation can easily result in an order-of-magnitude difference in the calculated output powers.

Therefore, any reliable Raman amplifier model should include a number of important features and effects. For example, a unified spectral approach allows for an arbitrarily number of arbitrary arranged channels—pumps, signals, and amplified spontaneous emission bands (ASE bands). Other desirable features include absolute forward / backward symmetry and wavelength dependency of all fiber parameters.

The amplification of any pump and signal from stimulated Raman scattering in the field of all shorter wavelength co- and counter-propagating pumps and signals should be included. Other essential features include spontaneous Raman amplification of any ASE band in the field of all shorter wavelength co- and counter-propagating waves; depletion of any wave by all longer wavelength co- and counter-propagating pumps and signals.

Also important are multiple orders of Rayleigh scattering, ASE amplification by stimulated and spontaneous Brillouin scattering, depletion of pumps by stimulated Brillouin scattering (negligible for the signals and ASE bands), Raman resonant FWM (requires phase-matching), phase evolution due to SPM and XPM, differentiation of ASE sources, multiple fiber-end reflections, and temperature dependence of gain and noise figure.

Mathematically, the equations of the model form a two-point, multiboundary value problem. The "shooting" method in this case has advantages over the "relaxation" methods since a fairly good initial guess is usually possible. The iterative refinement of results requires a globally convergent Newton-Raphson multidimensional root solver.

The software implementation of the models should offer optimization algorithms, 3-D data display capabilities (such as spectra vs. wavelength vs. length of powers, gain, signal-to-noise ratio (SNR), double Rayleigh scattered power), and control over the combination of phenomena to be included in the calculations. The latter feature allows for separating and studying of trends induced by each individual effect, thus facilitating amplifier optimization. Optiwave has been developing comprehensive new models for the simulation of RFA/HRA as part of its OptiSys_Design and OptiAmp_Design packages.

**DESIGN SIMULATIONS**

As a design example we will study the addition of Raman amplification to a dispersion compensated system. The link consists of SMF-28 transmission fiber and a dispersion-compensating fiber (DCF) doped with 25 mol% GeO2 (see Table 1).

Negligible fiber-end reflections, input coupling losses of 1 dB, and temperature of 300 K are assumed for both fibers. The Raman spectrum of the doped glass shown in Figure 1 (blue curve) was used for the DCF. The average power of input signals is 1 mW. The system is pumped in a backward direction by four diodes each emitting Pi = 200 mW (i = 1,...4) and having equidistant wavelengths in the range of 1470 to1500 nm. In this way it becomes a combination of distributed (SMF-28) and discrete (DCF) Raman amplifiers. We will look at the three possible configurations: DCF-SMF, SMF-DCF-SMF, and SMF-DCF from the points of view of efficiency and noise performance (see Table 2).

Interestingly, the gain performances of the first and second configurations are similar, and the system is almost transparent. When the DCF is at the end, the parameters are quite different. The signal experiences maximum gain >15 dB (equivalent to on-off gain >33 dB) and the peak of the spectrum is shifted toward the longer wavelengths.

The explanation of these facts is straightforward. In the SMF-DCF case the highly nonlinear DCF fiber is pumped first by the undepleted pump power, which results in a very high value of the gain increment SgR (Dwi) Pi / Aieff. The shift of peak gain is a result of the stronger interaction between the pumps. At the output of the DCF there is an 8-dB difference between the pumps at 1570 and 1600 nm. This effective power transfer, from shorter- to longer-wavelength pumps, shifts the aggregate gain spectrum as well.

Note that the symmetric case maintains the best optical signal-to-noise ratio (OSNR). Hence, an evaluation of the performance of the three configurations in terms of bit-error rate (BER) requires full waveform simulation and accounting for dispersion and nonlinearities.

Typical simulation results include the spectra exiting both ends of the DCF (see Fig. 2 left, right) The inband ASE increases by double Rayleigh scattering of the signals and can be clearly seen in Figure 2, left.

**FIGURE 2. The SMF-DCF case spectra can be measured exiting at both ends of the DCF. The total forward output spectrum including pump power reflections is shown at left; measurement of the total backward output spectrum after the DCF, including remaining pump power and reflected signal power, is shown at right. Amplified spontaneous emission increases by double Rayleigh scattering in the bandwidths of the signals.**

Prior to the calculations, the automatic optimization capabilities of the software were used to adjust the wavelengths of the pumps so that the peak of the gain is approximately at 1600 nm. The pump powers were optimized as well, so the DCF lengths needed for dispersion compensation and SRS amplification are approximately the same.

As a second example, we will model the performance of a discrete broadband gain-flattened amplifier using short DCF fiber. The parameters of the fiber are the same as given above, except for the length. The flattening is achieved using the well-known multipump technique used for longer standard fibers.^{6} However, the specifics of the fiber used here considerably alter the achievable parameters. The amplifier is pumped in a backward direction by six laser diodes with equidistant wavelengths in the range 1400 to 1500 nm. Optimizing calculations show that the device performs best with short fibers if the pump powers are 256 (1400 nm), 160, 120, 80, 41 mW (1500 nm), respectively (see Fig. 3).

Gain of approximately 10 ÷ 12 dB (on/off 11.5 ÷ 13.5) can be achieved in 3 km DCF with moderate pump powers (see Fig. 3). The flatness of the gain is approximately 2.2 dB over 90 nm. This value is slightly worse than in long distributed amplifiers and the reason is the narrower Raman gain of the doped fiber. Better flatness can be attained with more pump sources.

The gain coefficient distribution in the amplifier can be viewed in a 3-D representation (see Fig. 4). Such graphic capabilities, along with others showing the gain, signal-to-noise ratio, and other factors, enable the identification of length/wavelength regions where given effects dominate and provide immediate length optimization information.

**REFERENCES**

- T. Nielsen et al., IEEE Photon. Technol. Lett. 10, 1492, (1998).
- H. Masuda et al., IEEE Photon. Technol. Lett. 11, 647, (1999).
- E. Woodbury et al., Proc. IRE, 50, 2347, (1962).
- R. Stolen et al., Appl. Phys. Lett 20, 62, (1972).
- G. Agrawal, Nonlinear Fiber Optics, 2nd Ed., Academic Press Inc., San Diego, CA, (1995).
- Y. Emori et al., Electron. Lett. 35, 1355, (1999).

**Theodore Mirtchev** is a senior research scientist, and Jackson Klein is a product manager, at Optiwave, 16 Concourse Gate 100, Ottawa, K2E 7S8, ON, Canada. They can be reached at 613-224-4700 or mirtchev@optiwave.com or jackson@optiwave.com.