A Frequency Domain Design Approach for the Generation of Arbitrary Transfer Function Based on Generalized Optical Transversal Filters

We present a technique to realize arbitrary optical transfer functions based on the use of delay lines and optical waveguide couplers. In particular, this technique is a modification of an optical transversal filter. Following this technique, the transfer function is expressed as a truncated Fourier series with the tap coefficients that are either purely real or purely imaginary. The output ports of an optical waveguide coupler, conveniently and precisely, provide a transmission function that is either purely real or purely imaginary and thus, fit perfectly for the experimental realization of such transfer functions. The use of simple components, such as couplers and delay lines, alleviates the need for bulky electro-optic phase shifters and reduces the complexity of the integration process. To exemplify this approach, an optical field differentiator is implemented. Moreover, the effect of the practical aspects such as frequency dependence of the refractive index and variations of the coupling ratios of optical waveguide couplers, on the resulting transfer function are analytically investigated.