Numerical analysis of the three co-directional guided modes in optical period dielectric waveguides using inverse Gaussian apodization

We describe and analyze the inverse Gaussian apodization among the three co-directional guided modes using the supermodes theory and the transfer matrix method. The propagation condition is related to the two phase matching distribution induced by two long period co-spatial gratings. It is seen that one input mode can be converted into another two modes with each mode having two peaks at its transmission spectrum. Through adopting the inverse Gaussian apodization, the input mode A turns to having two peaks while the converted mode B has six peaks and mode C has three peaks around the central frequency in the transmission spectrum. Of particular interest is when adjusting the maximum coupling apodization strength from 100 to 1500, the frequency space in mode A changes nearly linearly from 340 GHz to 5100 GHz which is twice of the mode B at each coupling strength, while the mode C can be turned nearly linearly from 350 GHz to 5200 GHz. Additionally, the power at the central frequency of input mode A will almost totally move to the converted mode C. This kind of design can form the basis for a new generation of multi-wavelength-tunable bandpass optical filtering mode converting, add/drop multiplexing and optical switching.