I. C. Goyal

A novel design of a dispersion compensating fiber

We propose a novel dispersion compensating fiber design consisting of two highly asymmetric concentric cores. We show that the fundamental mode of the proposed fiber can have very large negative dispersion values [/spl sim/-5100 ps/(nm.km)] with larger mode field diameter (/spl sim/8-9 /spl mu/m) relative to the existing dispersion compensating fibers.

Bent planar waveguides and whispering gallery modes: a new method of analysis

A matrix method for analyzing bent planar optical waveguides is discussed. The method is a modification of an earlier method which yields bend loss directly, inasmuch as a nonuniform refractive index is approximated by a series of linear profiles rather than a series of uniform profiles. The method can be used with absorbing or leaky structures. The effect of whispering gallery modes has also been studied. It appears that a whispering gallery explanation given by H.J. Harris and P.F. Castle (1986) may not be adequate. >

Propagation characteristics of single mode optical fibers with arbitrary index profiles: A simple numerical approach

We present here a rapidly converging numerical procedure for the direct evaluation of the propagation constant and its first and second derivatives in single mode optical fibers with arbitrary refractive index profiles. To illustrate the procedure we have also used it to evaluate the propagation constant and its derivatives in single mode optical fibers with power law profiles in the presence of a Gaussian axial index dip, and hence, studied the effect of a dip on the dispersion characteristics of the fibers.

Mean lifetime calculations of quantum well structures: a rigorous analysis

A matrix method that is applicable to an arbitrary potential variation represented by a set of linear functions such as multiple quantum well structures in the presence of a static electric field is described. An analytical expression for the mean lifetime of the quasi-bound state of a single quantum well in the presence of a static electric field is obtained. >

Beam propagation under frustrated total reflection

Abstract We report a study of the beam propagation problem with reference to the phenomenon of frustrated total reflection, and obtain analytical expressions for the reflected and transmitted fields and their lateral shifts as a function of the frustrating layer thickness. We consider an incident gaussian beam and discuss its propagation through a lossless dielectric layered structure.

Modified Airy function method for the analysis of tunneling problems in optical waveguides and quantum-well structures

A simple method for the analysis of tunneling through an arbitrary one-dimensional potential barrier, based on the modified Airy function approach, is presented. Truncated step-linear, step-exponential, parabolic, and quartic potential barriers are considered. The results are compared with those obtained by the conventional WKBJ, modified WKBJ, and matrix methods. The effect of the truncation level on the tunneling coefficient is investigated. The tunneling coefficient is sensitive to the truncation level. For the step-linear potential, the tunneling coefficient is a monotonically decreasing function of the truncation level, while for the parabolic potential, it oscillates before saturating to a constant value. >

Modal characteristics of bent dual mode planar optical waveguides

Modal characteristics of bent dual-mode planar optical waveguides are obtained. The bending-induced changes in the modal power distribution is found to be quite different for the two modes. Surprisingly, unlike the fundamental mode, bending causes the fractional modal power for the second mode to increase in the inner core-half and to decrease in the outer core-half of the waveguide. Interestingly, this leads to a decrease in effective index of the second mode due to bending at sufficiently high V-values. >

Accurate solutions to Schrodinger's equation using modified Airy functions

A formulation that utilizes the Airy functions is applied to Schrodingers equation for a spherically symmetric potential. It is shown that the computational procedure is very simple and allows a very accurate description of bound-state wave functions and the corresponding eigenvalues. It is also demonstrated that the eigenvalues can be determined from the tabulated zeros of the Airy function with as much ease as the WKB method affords. In composing this modified Airy function solution to the WKB solution for the wave function, the first-order solution in each case is used. >

An Approximate Solution to the Wave Equation - Revisited

We revisit here an old but neglected approximate analytic solution to the electromagnetic wave equation. Our method of derivation is reminiscent of the WKB methodology but the solution, although approximate, is much more accurate than the traditional WKB solution and can be used with almost as much ease. The method is extremely powerful but, to our knowledge, has never been used by the optics community, where its use in analyzing optical fibers and integrated optical waveguides would be beneficial.

Matrix method for determining propagation characteristics of optical waveguides

We have transformed the scalar wave equation into a matrix eigenvalue equation, the diagonalization of which gives the guided modes and a discrete representation of the radiation modes. The method is simple and can be used for arbitrary refractive index profiles.