<title>Synthesis of photonic devices by inverse scattering techniques</title>

Abstract

The traditional procedure to synthesize optical devices with specified transmission characteristics is to start from device parameters such as refractive index profile with a known transmission characteristics that is close to the specified characteristics of the device and iteratively change the device parameters until the specified transmission characteristics of the device is achieved. This traditional procedure is time consuming and the choice of initial device parameters that has a transmission characteristics close to the specified characteristics is not always easy. However, techniques based on inverse scattering theory can directly provide the device design parameters given the specified transmission characteristics of the device. The inverse scattering techniques contrasts the traditional design procedure by their ability to yield design parameters in a non-iterative manner. The transmission of electromagnetic radiation in an optical waveguide is governed by vector wave equations which can be simplified to scalar wave equations under the assumption of “weakly guiding” approximation for TE and TM modes. The scalar equations obtained for TE and TM modes can be recast into Schrodinger type of equation that is normally encountered in quantum mechanics. One can draw an analogy between the quantum mechanical problem and the optical device problem. The potential well of the quantum mechanics corresponds to refractive index profile of the optical device problem; the time evolution of wave packets in quantum mechanics corresponds to propagation of optical modes along the axis in an optical device and the existence of discrete bound states in quantum mechanics is analogues to the presence of discrete propagating modes which in the geometrical-optics model corresponds to the modes that satisfy total internal reflection. Now, the refractive index profile; an important device parameter can be reconstructed from an assumed scattering coefficient that characterizes the specified transmission characteristics of the device. An analytical technique based on Gelfand-Levitan-Marchenko integral formulation and an numerical technique that extends the capability of the inverse techniques to provide solutions for generalized reflection coefficients that have been developed by us will be discussed. Design of a class of devices such as intra-chip optical interconnects, all-optical logic devices and efficient guiding structures for integrated optical amplifiers based on the inverse techniques will be discussed. The design of efficient guiding structures for optical amplifiers requires a guiding medium that has same propagation constant for both the signal and the pump. This leads to the inverse theory for reconstruction of energy dependent potentials or wavelength dependent refractive indices. We have solved this problem and we will show you a refractive index profile of a guiding structure obtained by inverse scattering technique that has same propagation constant at 1.55mm and 0.98/mm. The extension of the inverse techniques developed for planar structures to cylindrical structures is not straight forward, rather very cumbersome. However, we have succeeded in developing inverse scattering theory for the design of multimode cylindrical optical waveguides with same propagation constant for all modes and the design of single mode fiber that has the same propagation constants for more than one wavelength. Such structures will find application in image transmission and fiber amplifier design respectively. Our talk will include discussion of these cases.