Application of a variational principle to systems with radiation loss
- 1 January 1983
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Journal of Quantum Electronics
- Vol. 19 (1), 106-117
- https://doi.org/10.1109/jqe.1983.1071730
Abstract
A variational principle for the frequency of electromagnetic systems with radiation is derived from Maxwell's equations. Expressions for the quality factorQare obtained in three illustrative examples: a leaky transmission line resonator, a grating coupler, and a curved slab waveguide. Extensive numerical results for theQof the grating coupler are presented in normalized form. By optimization of the variational expressions with respect to the amplitudes of the forward and backward waves, coupled-mode equations are derived for a grating structure. The variational formulas agree with results obtained from a perturbational analysis.Keywords
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