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Application of a variational principle to systems with radiation loss

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2 Author(s)
Haus, H. ; Massachusetts Institute of Technology, Cambridge, MA, USA ; Islam, Mohammed N.

A variational principle for the frequency of electromagnetic systems with radiation is derived from Maxwell's equations. Expressions for the quality factor Q are obtained in three illustrative examples: a leaky transmission line resonator, a grating coupler, and a curved slab waveguide. Extensive numerical results for the Q 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.

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Quantum Electronics, IEEE Journal of  (Volume:19 ,  Issue: 1 )