Hybrid numerical calculation method for bend waveguides
Garnier , Lucas
Saavedra , C.
Castro-Beltran , Rigoberto
Lucio , José Luis
Bêche , Bruno
- Publisher: HAL CCSD
Conformal transformations | [ MATH.MATH-CV ] Mathematics [math]/Complex Variables [math.CV] | [ PHYS.PHYS.PHYS-COMP-PH ] Physics [physics]/Physics [physics]/Computational Physics [physics.comp-ph] | Multilayer matrix formalism | [ SPI.OPTI ] Engineering Sciences [physics]/Optics / Photonic | [ PHYS ] Physics [physics] | eigen-values and -vectors
National audience; 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.