Modeling of surface roughness in deeply etched photonic MEMS mirrors and filters

We study the impact of the surface roughness on the response of deeply etched silicon Bragg mirrors and resonators. The transfer matrix method is extended to account for the roughness in multilayered systems. The model is first verified numerically using the finite difference time domain (FDTD) method for surface roughness values up to 80 nm at a wavelength of 1550 nm. The response of the mirrors and filters having an RMS roughness of 30 nm is calculated by the developed model and compared with the numerical results of the FDTD results, and it shows a good agreement. Then the model results are compared with the experimental data of a Bragg mirror and filter, fabricated by the deep reactive ion etching Bosch process of silicon on an insulator wafer; they show a very good agreement in the insertion loss and 3-dB bandwidth due to the roughness model. Finally, the transmission, 3-dB bandwidth and quality factor of the optical filters based on single, double, and triple silicon layer mirrors are examined using the model and accounting for Gaussian beam excitation. The presented model can be used to guide the requirements on the fabrication quality of optical surfaces and the choice of the optimum number of layers.