Surface non-linear wave convolution on thin-film photonic crystal waveguides

摘要

In signal and system analysis, the concept of convolution is very important. It can be implemented optically using non-linear-optic effects by interacting, or Mixing, two contra-directed surface waves in the non-linear thin-film photonic crystal waveguide. Complex electric field aaplitudes are derived using Maxwell's equations that take the polarization into account and general solutions are then found by using the Variation of ParaieterE method. In reality, it is the non-linear part of the polarization that allows the lixing of two surface waves to generate a third wave, In order for this optical nixing process to take place effectively, both frequency- and phase-iatching conditions Bust be satisfied. Both collinear and non-collinear interactions are being considered. All derived electric field amplitudes are intensities that nay be regarded as signals, Convolution may then be impleaented using the above non-linear-optic effects. Because predicted signals are often discussed in tens of their Fourier transfoms, the convolution concept is being studied in both frequency- and tiie-doiains. Convolution kernels are being looked into graphically and the convoluted wave is being analyzed according to the Convolution theoren and the Input-Output Description of a systea. Finally, the optical implemntation of the Fourier transform using a lens is briefly looked into.