Abstract

The modeling of the scattering of a plane wave at a rough aperiodic surface—as well as its diffraction by a microstructured surface—is possible only by limiting the infinite surface to a window of finite width D. We show that the scattering spectrum at infinity in the Fraunhofer zone can be obtained from the diffraction modeling of a grating of period D whose surface profile coincides with the aperiodic surface in this window. This is justified by adopting the corpuscular representation of light and resorting to Heisenberg’s uncertainty relation applied to the photon’s canonically conjugate variables momentum and position. This approach gives a deep and comprehensive representation of scattering phenomena, and also the limit of what can be meaningfully calculated and measured. Numerical examples of grating profiles demonstrate that results obtained under the widely used Beckmann–Kirchoff approximation are matched. The described approach can solve scattering problems that usual methods cannot, or face difficulties, such as when there is significant roughness with respect to the wavelength.

© 2019 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Analytical modeling and three-dimensional finite element simulation of line edge roughness in scatterometry

Akiko Kato, Sven Burger, and Frank Scholze
Appl. Opt. 51(27) 6457-6464 (2012)

Quasi-geometrical method for Fraunhofer diffraction calculations for three-dimensional bodies

Yu. V. Chugui, V. P. Koronkevitch, B. E. Krivenkov, and S. V. Mikhlyaev
J. Opt. Soc. Am. 71(4) 483-489 (1981)

Mathematical studies in rigorous grating theory

Gang Bao, David C. Dobson, and J. Allen Cox
J. Opt. Soc. Am. A 12(5) 1029-1042 (1995)

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Figures (16)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Tables (1)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Equations (52)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription