Abstract
It is a scientific fact that all-optical signal processing technology is an effect approach to overcome the inherent speed limitations of conventional electronics; this is because of the rapid development of high-speed optical communication networks. This manuscript is dedicated to investigate the fractional modeling of microring resonators subject to the inputs and outputs of the two all-optical ring resonators. The mathematical modeling is based on ring resonators within the limitations of time-dependent relations and coupled mode theory. The mathematical analysis is prescribed for amplitude subject to the initial and boundary conditions’ validations along with two categories of source terms, namely, periodic and exponential sources. The fractional mathematical model of microring resonators is solved by means of Laplace transform method by employing the concept of infinite series and gamma functions.The graphical illustration is discussed via fractional techniques of Atangana-Baleanu and Caputo-Fabrizio fractional operator on the basis of embedded parameters namely optical frequency and quality factor lifetime of photon. At last, a comparative analysis of amplitude is also presented for knowing the hidden aspects of microring resonators through classical verses non classical approaches.
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