Silicon Photonics: Fundamentals and Devices

9.5 Raman Gain Coefficient

In this section, a numerical analysis made by Krause et al. 6 of Raman lasing characteristics in silicon-on-insulator (SOI) waveguides will be presented. The analysis shows that in spite of the presence of detrimental-effect two-photon absorption and free-carrier absorption (FCA), continuous-wave (CW) Raman lasing is possible.

9.5.1 Mathematical Model

The analysis assumes the presence of a SOI waveguide of length L, as shown in Figure 9.3. A pump laser light of wavelength λ_p and power P₀ is coupled to the left-hand side of the waveguide with coupling efficiency T_p. The Stokes wave generated inside the waveguide due to Raman scattering has a wavelength λ_s. The end surfaces of the waveguide are coated with reflective materials. The reflectivities are denoted by R, and the suffixes l, r, p, and s refer, respectively. to the left mirror, right mirror, pump, and Stokes wave. For example, R_p,r denotes the reflectivity of the pump at the left-hand mirror.

Figure 9.3 Structure of the Raman laser used for analysis.

A simple incoherent model that describes the laser in terms of longitudinally varying optical powers of forward- and backward-propagating waves, but neglects phase-related effects, will be used. The model is similar to that using fiber Raman lasers but includes TPA and FCA.

Considering the depletion of pump due to SRS, and including backward propagation, ...