Improved analysis of the propagating beam method in longitudinally perturbed optical waveguides

Propagating Beam Analysis of Bent Optical Waveguides

“…The curves marked 'pbm' and 'pbm, Fres.' While some of the residual errors can be explained by the finite steplength (Δζ = 9.42 μπι) [2], we believe that the errors observed on our Fresnel calculations are related to the large angles described by the wavefronts in the equivalent straight waveguide with respect to the waveguide axis. The curves marked 'n efr ' and 'n,.…”

“…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.…”

“…Our initial excitation is the n = 0 mode of the unperturbed waveguide normalized to unit power. The constant " in (1) has been set to 2 be independent of the method chosen. have been calculated by propagating the electric field in the profile of (5) and (6) using the formalisms of (1) and (2), respectiveley.…”

“…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).…”