A rigorous analysis of the propagation of transverse-electric modes in two-dimensionally periodic media is presented, based on an exact solution of the wave equation. The modulation functions studied lead to Mathieu and Hill equations. It is shown that the complete inhibition of the propagation of transverse-electric modes in a modulated plane is possible. Several modulation functions of the permittivity are studied in order to find the one for which the modulation depth necessaryfor the observation of a frequency band gap is minimized. In particular, thin grids and closely packed arrays of square rods are considered. The allowed angles of propagation of waves whose frequency is not contained within a forbidden band are also presented.

© 1991 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