A modified formulation of Maxwell's equations is presented that includes a complex and nonlinear coordinate transform along one or two Cartesian coordinates. The added degrees of freedom in the modified Maxwell's equations allow one to map an infinite space to a finite space and to specify graded perfectly matched absorbing boundaries that allow the outgoing wave condition to be satisfied. The approach is validated by numerical results obtained by using Fourier-modal methods and shows enhanced convergence rate and accuracy.
The quest for enhanced light-matter interactions has enabled a tremendous increase in the performance of photonic-crystal nanoresonators in the past decade. State-ofthe-art nanocavities now offer mode lifetime in the nanosecond range with confinement volumes of a few hundredths of a cubic micrometer. These results are certainly a consequence of the rapid development of fabrication techniques and modeling tools at micro-and nanometric scales. For future applications and developments, it is necessary to deeply understand the intrinsic physical quantities that govern the photon confinement in these cavities. We present a review of the different physical mechanisms at work in the photon confinement of almost all modern PhC cavity constructs. The approach relies on a Fabry-Perot picture and emphasizes three intrinsic quantities, the mirror reflectance, the mirror penetration depth and the defect-mode group velocity, which are often hidden by global analysis relying on an a posteriori analysis of the calculated cavity mode. The discussion also includes nanoresonator constructs, such as the important micropillar cavity, for which some subtle scattering mechanisms significantly alter the Fabry-Perot picture.
nmPhoton lifetime in photonic crystal nanocavities is mainly limited by Bloch-mode profile mismatches, and by engineering the mirror termination, one may lower the mismatch and increase the lifetime.
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