In this paper we have analyzed the modal dispersion characteristics of two unconventional Bragg waveguides namely hypocycloidal and elliptical Bragg waveguide by the use of very simple matrix method. We are using matrix equation which replaces the boundary condition. We obtained the characteristic equation analytically. In both cases all the outputs are showing in the form of dispersion curves and we are also trying to compare their dispersion characteristics. It is seen that in case of hypocycloidal Bragg waveguide [1] the cut off frequency increases with the decrease of cladding layers .But in case of elliptical Bragg waveguide [2], when the cladding layer decreases from six layered to four layered the cutoff frequency increases and from four layer to two layer the cutoff frequency become decreases.

The paper presents an all-optical 3 bit up counter with complete Boolean functionality as a representative circuit for modeling and optimization of monolithically integrated components. Here, the proposed logic unit design is based on nonlinear effects in semiconductor optical amplifiers (SOA).These equations are first solved to generate the pump, probe and conjugate pulses in a SOA. The pulse behavior are analyzed and applied to realize behavior of all-optical NAND gate. Next, the logic is used to implement All-Optical D Flip-Flop logic, and its function is verified with the help of truth table. Finally with the help of three D Flip-Flops, a 3-bit up counter is proposed.

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