Fourier Transform of Two Component Quasi-Periodic Optical Superlatticen

Coupling wave equations that describe some complicated nonlinear optical processes, including three or more wave vector mismatches, can not be correctly solved by using real number type Fourier coefficients. These coefficients are connected with the reciprocal vectors for quasi-phase matching those nonlinear processes in an optical super lattice. Complex number type Fourier coefficients including phase factor have to be applied in these difficult situations. An analytical expression is derived by using the projection method for generating a quasi-periodic optical super lattice.