The accuracy of finite-difference computations is limited by the errors inherent in the classical three-point formula for ∂_x² (of order h²) and in the discretization of discontinuities in the refractive index (of order from h⁰ to h²). Various improvements are reviewed and analyzed, both for normal-mode derivations and for the beam propagation method (BPM). For the BPM it seems that sophisticated discretizations for discontinuities have a limited interest, whereas using a h⁴-accurate three-point formula for ∂_x² often allows the use of fewer grid points and hence faster computations; also it makes the operation of transparent boundaries with Bérenger layers considerably more efficient. Finally, the permittivity should always be averaged mesh by mesh.

© 1997 Optical Society of America

[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