A general approach

The material gain treatment

As explained in Section 7.3, it is neither feasible nor necessary to compute the material's optical properties through the physics based gain model in an “online” manner. It is not feasible because of the huge number of times that the gain model has to be invoked. It is not necessary because on many of the times that the model is called up it provides exactly the same results.

For this reason, we take an “offline” approach by calling up the physics based gain model at a coarse mesh grid constructed by multiple variables (i.e., the electron and hole densities, the temperature and the frequency) which covers the entire device operation range, and by establishing a set of analytical formulas which reproduce the required material optical property (i.e., the stimulated and spontaneous emission gains and the refractive index change) in the device operation range. By assuming a universal polynomial, exponential and rational dependence on the carrier density, temperature and frequency, respectively, such formulas are therefore parameterized with the unknown parameters obtained from searching for the best fit between the results from the formulas and from the rigorous calculation on the mesh grid points. Interpolations might be necessary to refine the mesh grid before such a fitting.

Once the analytical formulas are extracted, they will be used as the material model to replace the rigorous model for calculation of gains and refractive index change in an “online” manner.

Figure 9.1 (a) and (b) show comparisons of the stimulated emission gain and refractive index change calculated by the rigorous gain model and analytical formulas.

For a given active region structure with adjacent layers, the rigorous gain is obtained through the following procedure.