Abstract: In this paper, the application of the Mode Matching
(MM) method in the case of photonic crystal waveguide
discontinuities is presented. The structure under consideration is
divided into a number of cells, which supports a number of guided
and evanescent modes. These modes can be calculated numerically
by an alternative formulation of the plane wave expansion method
for each frequency. A matrix equation is then formed relating the
modal amplitudes at the beginning and at the end of the structure.
The theory is highly efficient and accurate and can be applied to
study the transmission sensitivity of photonic crystal devices due to
fabrication tolerances. The accuracy of the MM method is compared
to the Finite Difference Frequency Domain (FDFD) and the Adjoint
Variable Method (AVM) and good agreement is observed.
Abstract: In high powered dense wavelength division
multiplexed (WDM) systems with low chromatic dispersion,
four-wave mixing (FWM) can prove to be a major source of noise.
The MultiCanonical Monte Carlo Method (MCMC) and the Split
Step Fourier Method (SSFM) are combined to accurately evaluate the
probability density function of the decision variable of a receiver,
limited by FWM. The combination of the two methods leads to more
accurate results, and offers the possibility of adding other optical
noises such as the Amplified Spontaneous Emission (ASE) noise.