Mathematical modeling for diffractive optics

David C. Dobson; J. Allen Cox

doi:10.1117/12.170192

28 December 1993 Mathematical modeling for diffractive optics

David C. Dobson, J. Allen Cox

Proceedings Volume 10271, Diffractive and Miniaturized Optics: A Critical Review; 1027104 (1993) https://doi.org/10.1117/12.170192
Event: SPIE's 1993 International Symposium on Optics, Imaging, and Instrumentation, 1993, San Diego, CA, United States

Abstract

Mathematical models for diffractive optics have been developed, and implemented as numerical codes, both for the “direct” problem and for the “inverse” problem. In problems of the “direct” class, the diffractive optic is specified, and the full set of Maxwell’s equations is cast in a variational form and solved numerically by a finite element approach. This approach is well-posed in the sense that existence and uniqueness of the solution can be proved and specific convergence conditions can be derived. As an example, we consider a low order metallic grating, where other approaches are known to have convergence problems, and show the variational method yields exceptionally good convergence. In problems of the “inverse” class, some information about the diffracted field (e.g., the far-field intensity) is given, and the problem is to find the periodic structure in some optimal sense. A new approach is described that applies relaxed optimal design methods to give entirely new grating structures; wave propagation is based on the Helmholtz equation. An example of an angle-optimized antireflective structure and of an ideal array generator are presented.

Citation Download Citation

David C. Dobson and J. Allen Cox "Mathematical modeling for diffractive optics", Proc. SPIE 10271, Diffractive and Miniaturized Optics: A Critical Review, 1027104 (28 December 1993); https://doi.org/10.1117/12.170192

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