Analysis of step- and graded-index optical waveguides by solving Helmholtz eigenproblem through Fourier analysis and iterative Lanczos reduction

Michele A. Forastiere; Giancarlo C. Righini

doi:10.1117/12.298216

12 January 1998 Analysis of step- and graded-index optical waveguides by solving Helmholtz eigenproblem through Fourier analysis and iterative Lanczos reduction

Michele A. Forastiere, Giancarlo C. Righini

Author Affiliations +

Proceedings Volume 3278, Integrated Optic Devices II; (1998) https://doi.org/10.1117/12.298216
Event: Optoelectronics and High-Power Lasers and Applications, 1998, San Jose, CA, United States

Abstract

A method of solution of the scalar Helmholtz eigenproblem for dielectric waveguides is presented. The fundamental idea is the expansion of the electric field on a discrete basis of sine functions which go to zero at the calculation window boundaries, for both transverse directions. A matrix eigen problem is correspondingly built up from the Helmholtz polynomial functions defined over rectangular domains. The solution algorithm takes advantage of the well-known Lanczos reduction technique, allowing for the straightforward evaluation of discrete eigen values within any desired precision order. The Lanczos algorithm, here combined with the Fourier-analysis technique, allows to examine very large-sized cases without the problem of storage space lacing. In this work, a few examples of propagation analysis are shown referring to both step-index and graded-index integrated optical structures, and the calculation results are compared with those obtained by commercial BPM algorithms and the effective index method.

Citation Download Citation

Michele A. Forastiere and Giancarlo C. Righini "Analysis of step- and graded-index optical waveguides by solving Helmholtz eigenproblem through Fourier analysis and iterative Lanczos reduction", Proc. SPIE 3278, Integrated Optic Devices II, (12 January 1998); https://doi.org/10.1117/12.298216

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available