Abstract
We employ a combination of asymptotic methods to speed up the computation of fields in the focal region of a diffractive lens (DL). The DL is treated locally as a linear grating with a slowly varying period and groove orientation. We employ rigorous electromagnetic diffraction theory locally to obtain the field just behind the DL. A simple diffracted-ray formula is derived for the field in the focal region of the DL at observation points that are not in the immediate vicinity of the optical axis. A careful study of the range of validity of this formula is made. For observation points that are not in the immediate vicinity of the optical axis the new algorithm is 3 × 105 times faster than the application of numerical integration to the double integrals involved and approximately 1000–1200 times faster than a recently published algorithm based on using asymptotic theory to replace the double integral with a single integral.
© 2000 Optical Society of America
Full Article | PDF ArticleMore Like This
Velauthapillai Dhayalan and Jakob J. Stamnes
Appl. Opt. 39(34) 6332-6340 (2000)
Jakob J. Stamnes
J. Opt. Soc. Am. 73(1) 96-109 (1983)
Sergei V. Kukhlevsky, Francesco Flora, Alessandro Marinai, Katalin Negrea, Libero Palladino, Armando Reale, Giuseppe Tomassetti, Antonio Ritucci, Gergely Nyitray, and Laszlo Kozma
Appl. Opt. 39(6) 1059-1063 (2000)