Numerical investigation of mode coupling in sinusoidally modulated GRIN planar waveguides

Abstract

We study mode coupling in planar 2-D graded-index optical waveguides with the beam propagation method. In particular we examine the effect of periodic radial deformations along the axis of a parabolic refractiveindex waveguide and compare our results to the results of perturbation theory.

Propagating Beam Analysis of Bent Optical Waveguides

“…In two previous papers, we studied the application of the propagating beam method to periodically perturbed waveguides with zero radius of curvature [1,2]. Here we will extend our results to bent optical waveguides.…”

“…Finally, we wish to call the reader's attention to the fact that the final calculations in our previous paper [1], which concern waveguides centred at a fixed position but with sinusoidal in-phase displacements of the positive and negative waveguide radii, along the waveguide axis do not reflect the properties of sinusoidally bent optical waveguide. In fact, since the refractive index near the waveguide center remains almost unchanged along the waveguide studied in the previous paper, the mode coupling coefficients of the lowest order modes for these waveguides are orders of magnitude smaller than the mode coupling coefficients of bent waveguides with analogous displacement of the waveguide boundaries.…”

“…β is a constant with dimension (lenght)" 1 independent of the mode number with a value between the cladding wavenumber and the maximum wavenumber of the waveguide [5]. If we base our analysis on the Fresnel equation we find iAz 3 2 E(x, z + Az) = exp( -ikn 0 Az) exp I -4n 0 k function) and subsequently evaluate the inner product of the electric field at equally spaced points along the waveguide with appropriate eigenfunctions [1,2]. However, as the length of the bent waveguide is increased the propagating beam becomes decreasingly paraxial compromising the accuracy of (1) and (2).…”

Non-Hermitian Mode Cleaning in Periodically Modulated Multimode Fibers

“…Generally, the reduction of turbulence in optical fibers cannot be achieved by conventional means. For instance, the modulation of the fiber parameters along the propagation direction (modulation of refraction index, dispersion, nonlinearity) can indeed lead to mode coupling effects in the linear case [8,9], or to the parametric (Faraday) modulational instabilities in nonlinear case [10][11][12], which generally broaden the angular spectra, but not to a reduction of the turbulence, neither to mode-cleaning of the spatial structure of the beam.…”