Hybrid numerical calculation method for bend waveguides

Lucas Garnier (1) , C. Saavedra (2) , Rigoberto Castro-Beltran (2) , José Luis Lucio (2) , Bruno Bêche (1)

1 IPR - Institut de Physique de Rennes
2 University of Guanajuato

The knowledge of how the light will behave in a waveguide with a radius of curvature becomes more and more important because of the development of integrated photonics, which include ring micro-resonators, phasars, and other devices with a radius of curvature. This work presents a numerical calculation method to determine the eigenvalues and eigenvectors of curved waveguides. This method is a hybrid method which uses at first conform transformation of the complex plane generating a new and modified index profile that represent the curvature. Then, on this modified index profile, we use a matrix multilayer formalism; we divide the profile in virtual layers of various indices to calculate both the propagation constants (eigenvalues) and the optical field (eigenvectors) into each of such virtual layers.

Mots clés: Conformal transformations; Multilayer matrix formalism; eigen-values and -vectors

Domaines: Variables complexes [math.CV]; Physique [physics]; Physique Numérique [physics.comp-ph]; Optique / photonique

Lucas Garnier, C. Saavedra, Rigoberto Castro-Beltran, José Luis Lucio, Bruno Bêche. Hybrid numerical calculation method for bend waveguides. Journée Projets Master Photonique et Programmation Matlab, Jan 2017, Rennes, France. 2017. ⟨hal-01445934⟩