Abstract

Various integral diffraction methods are systematically unified into a single framework, clearly illustrating the interconnections among the numerous scalar and rigorous formulations. This hierarchical depiction of the integral methods makes clear the specific approximations inherent in each integral method. The scalar methods are compared in detail with a rigorous open-region formulation of the boundary element method (BEM). The rigorous BEM provides a reference method for accurately determining the diffracted fields for both TE and TM incidence. The rigorous BEM and the various scalar methods are then applied to the case of focusing of normally incident plane waves by diffractive cylindrical lenses with f-numbers ranging from f/2 to f/0.5. From the diffracted-field calculations, a number of performance metrics are determined including focal spot size, diffraction efficiency, reflected and transmitted powers, and focal-plane sidelobe power. The quantitative evaluation of the performance of the scalar methods with these metrics allows the establishment, for the first time, of the region of validity of the various scalar methods for this application. As expected, the accuracy of the scalar methods decreases as the f-number of the diffractive lenses is reduced. Additionally, some metrics, particularly the focal-plane sidelobe power, appear to be particularly sensitive to the approximations in the scalar methods, and as a result their accuracy is significantly degraded.

© 1998 Optical Society of America

Full Article  |  PDF Article

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 (7)

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 (5)

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 (49)

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

Metrics

You do not have subscription access to this journal. Article level metrics 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