DocumentCode
1094987
Title
Application of a variational principle to systems with radiation loss
Author
Haus, Hermann A. ; Islam, Mohammed N.
Author_Institution
Massachusetts Institute of Technology, Cambridge, MA, USA
Volume
19
Issue
1
fYear
1983
fDate
1/1/1983 12:00:00 AM
Firstpage
106
Lastpage
117
Abstract
A variational principle for the frequency of electromagnetic systems with radiation is derived from Maxwell\´s equations. Expressions for the quality factor 
are obtained in three illustrative examples: a leaky transmission line resonator, a grating coupler, and a curved slab waveguide. Extensive numerical results for the of 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.
are obtained in three illustrative examples: a leaky transmission line resonator, a grating coupler, and a curved slab waveguide. Extensive numerical results for the of 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
Corrugated waveguides; Dielectric waveguides; Optical couplers; Optical planar waveguides; Optical waveguides; Planar optical waveguide; Transmission-line resonators; Variational methods; Waveguide bends; Couplings; Dielectrics; Electromagnetic radiation; Electromagnetic waveguides; Frequency; Gratings; Maxwell equations; Optical resonators; Optical waveguides; Surface waves;
fLanguage
English
Journal_Title
Quantum Electronics, IEEE Journal of
Publisher
ieee
ISSN
0018-9197
Type
jour
DOI
10.1109/JQE.1983.1071730
Filename
1071730
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