Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets

Physical Review A (Impact Factor: 2.81). 06/1990; 41(9):5187-5198. DOI: 10.1103/PhysRevA.41.5187
Source: PubMed


Laser cavities are open systems, in that energy can leak to the outside via output coupling. The ‘‘normal modes’’ are therefore quasinormal modes, with eigenvalues that are complex and eigenfunctions that extend outside the cavity, such that any normalization integral is dominated by the region outside; in short, such systems are non-Hermitian. This paper addresses the question: How is the complex eigenvalue (i.e., the mode frequency) changed when the cavity is perturbed by a small change of dielectric constant? The usual time-independent perturbation theory fails because of non-Hermiticity. By generalizing the work of Zeldovich [Sov. Phys.—JETP 12, 542 (1961)] for scalar fields in one dimension, we express the change of frequency in terms of matrix elements involving the unperturbed eigenfunctions, so that the problem is reduced to quadrature. We then apply the formalism to shape perturbations of a dielectric microdroplet, and give analytic formulas for the frequency shifts of the morphology-dependent resonances. These results are, surprisingly, independent of the radial wave function, so that all integrals can be performed and explicit algebraic expressions are given for axially symmetric perturbations.

    • "It can, however, easily be generalized to the case of a side-coupled cavity, including the effect of an additional scattering center in the waveguide [36]. We notice, that the proper calculation of the various coupling factors is complicated by the open nature of the cavity, which implies that even the definition of the proper cavity volume is nontrivial [13] and needs to be carried out within the framework of non-Hermitian differential equations [34] [37]. As a model for the carrier density, we assume that it is determined by linear and nonlinear absorption effects, "
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    ABSTRACT: This chapter focuses on the properties of nanocavities that are relevant to their application in all-optical switching, lasers and light emitting diodes (LEDs), as well as cavity quantum electrodynamics (QED). It discusses different structures that have been used to realize optical cavities with sizes on the order of a wavelength, in particular focusing on micropillar and photonic crystal cavities. The chapter also discusses how these cavities often, but not always, can be represented by effective Fabry–Perot cavities in which case one can benefit from the well-established understanding of the properties and possibilities of such cavities. It is devoted to cavity-based switches. The chapter describes the properties of emitters embedded in cavities. It also describes the properties of LEDs and lasers exploiting the Purcell effect to enhance the light emission. This analysis pertains to the semi-classical regime where numerous emitters (material transitions) are in resonance with the cavity.
    No preview · Chapter · Jan 2015
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    • "Resonant modes are central in nanophotonics and quantum optics and pave the way for enhanced lightmatter interactions with potential applications in energy efficient photovoltaics, integrated photonic circuits and quantum information technology. Examples of resonant modes include the well-known Mie resonances of spherical objects [1] [2] and localized surface plasmons of plasmonic nanoparticles, with applications in photovoltaics [3], surface-enhanced Raman scattering [4] or as " plasmon rulers " [5]. Likewise, the optical modes of microcavities in micropillars or photonic crystals (PhCs) have been used for enhancement of the Purcell effect of quantum emitters [6] and for realizing cavity quantum electrodynamics experiments [7] and single-photon emission [8] [9] as well as for demonstrating nanolasers [10] and optical switching [11]. "
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    ABSTRACT: We present a numerical method for calculating quasi-normal modes of open nanophotonic structures. The method is based on scattering matrices and a unity eigenvalue of the roundtrip matrix of an internal cavity, and we develop it in detail with electromagnetic fields expanded on Bloch modes of periodic structures. This procedure is simpler to implement numerically and more intuitive than previous scattering matrix methods, and any routine based on scattering matrices can benefit from the method. We demonstrate the calculation of quasi-normal modes for two dimensional photonic crystals where cavities are side-coupled and in-line-coupled to an infinite waveguide.
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    • "Several theoretical analyses of the phenomenon have also been carried out in recent years [13] [14] [15]. "
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