Theoretical Comparative Analysis of BER in Multi-Channel Systems With Strip and Photonic Crystal Silicon Waveguides

We present a comparative analysis of the performance of multi-channel photonic systems containing strip or photonic crystal (PhC) silicon (Si) waveguides in the presence of white Gaussian noise. Specifically, we consider a multi-wavelength optical signal propagating either in a strip single-mode Si photonic waveguide (Si-PhW) or in a Si PhC waveguide (Si-PhCW), each channel consisting of a CW nonreturn-to-zero ON–OFF keying modulated signal. The output signal is demultiplexed and the signal in each channel is analyzed using direct-detection optical receivers. We describe the propagation of the optical signal in the Si-PhW and Si-PhCW using a linearized model and validate our main results by employing a rigorous theoretical model that incorporates all relevant linear and nonlinear optical effects and the mutual interaction between free-carriers and the optical field. The bit error rate (BER) of the transmitted signal is calculated by using both a time- and frequency-domain Karhunen–Loeve expansion method. Our analysis suggests that due to enhanced nonlinear effects, for comparable optical power, a similar BER is achieved in a PhC waveguide about $100\times$ shorter than a strip one, with a particularly strong signal degradation being observed in the slow-light regime of the Si-PhCW.