Analysis of arbitrary index profile planar optical waveguides and multilayer nonlinear structures: a simple finite difference algorithm

Abstract

we present here a simple numerical method to obtain the mode effective indices as well as field distributions of modes of any arbitrary profile planar optical waveguide. The method is based on the solutions of scalar and semivectorial Helmoltz's equation by finite difference algorithm and devised with a field convergence technique. This approach is quite general and can be applied straightforwardly to calculate the guided as well as quasior leaky modes of any arbitrary planar structure without the need to solve any eigenvalue equation or any complex matrix formalism. Besides providing the ease of application, the algorithm is particularly useful for waveguides with any graded index profile or with irregular multilayered structure and multilayered waveguides with a localised arbitrary nonlinear film. The performance of our method is verified against typical problems with analytical solutions or having results known otherwise, and is shown to yield results with good accuracy.

Analysis of Novel Chirped Types of Refractive Index Profile Metamaterial Planar Slab Optical Waveguide by Finite-Element Method for Sensor Application

“…When propagation constant β is obtained, we can calculate the power confinement characteristics for a waveguide having an arbitrary refractive index profile. Power flow in the waveguide for the TE mode is given by [12][13][14][15],…”

“…Usually they used the transfer matrix of transmitted and reflected beam amplitudes in multilayer to get the S. Raghuvanshi propagation properties of an optical planar waveguides with multilayer index profiles. Instead of the transfer matrix method or any other analytical method, the finite element method (FEM) is more an efficient whenever the waveguide would have a continuous in-homogenous refractive index or negative refractive index while having an arbitrary geometry [10][11][12][13][14][15]. In this paper, a FEM waveguide analysis for slab waveguides is described.…”

Supercontinuum generation in visible to mid-infrared region in square-lattice photonic crystal fiber made from highly nonlinear glasses

“…Firstly, to calculate the modal properties, e.g., mode effective index (n eff ), effective mode area, group velocity dispersion (GVD) of square-lattice PCFs, we have implemented the field convergence algorithm, based on finite difference discretization of Helmholtz's equation in the scalar or semi-vectorial form [23,24].The formulation is simple to implement and yields the key data, the effective mode-index and the field profiles very precisely and efficiently. The mode-index and field obtained from the mode analysis are used to describe most of the guided mode properties, e.g., dispersion, nonlinearity, mode-field area etc.…”

Modeling of single mode optical fiber having a complicated refractive index profile by using modified scalar finite element method

“…Since in our FEM formulation we are dealing with a single mode fiber with degenerate mode (HE 11 mode having same polarization state in principal), hence the error generated by scalar FEM while compared to vectorial FEM is negligible [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31].…”