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

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
Log in to access OSA Member Subscription

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
Log in to access OSA Member Subscription

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
Log in to access OSA Member Subscription

Related Journal Articles

• Electromagnetic analysis of diffraction gratings by the finite-difference time-domain method (JOSAA)
• Use of grating theories in integrated optics (JOSAA)
• Grazing-Incidence Iridescence from a Butterfly Wing (AO)
• Diffractive elements with novel antireflection film stacks (OE)
• Area-coded effective medium structures, a new type of grating design (OL)

Related Conference Papers

• Research on multi-layer diffractive optical elements and their application to camera lenses
• Approximate diffraction theories: Efficient modeling of diffractive optical elements
• Large-aperture diffractive optical elements for high power laser and space applications
• Dispersion-compensated Lau-like processor
• Accurate modelling of line-defect photonic crystal waveguides with the RCWA