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Quasinormal Mode Theories and Applications in Classical and Quantum Nanophotonics

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Advances in Near-Field Optics

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Abstract

This chapter presents theories and applications of optical quasinormal modes (QNMs), which can be used to solve a wide range of cavity problems in classical and quantum nanophotonics. Special emphasis is placed on obtaining intuitive, few-mode analytical expressions for the electromagnetic Green functions which connect to important figures of merit in cavity optics such as Purcell’s formula. We give the basic background theory, starting from Maxwell’s equations and classical mode expansion techniques, as well as normal modes, QNMs, and regularized QNMs, followed by a description of quantized QNMs, which form the foundation for developing rigorous quantum optical descriptions in nanophotonics and non-Hermitian resonant systems. We then show various instructive examples ranging from simple 1D cavities, which have analytical solutions, to plasmonic dimer modes, to complicated hybrid modes formed by coupled metal-dielectric systems, and QNM coupled-mode theory for coupled resonators.

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Notes

  1. 1.

    An exception to this assumption will be made later when introducing a specific form for the mode normalization.

  2. 2.

    We define cavity or resonator as basically the same thing in this chapter, namely, a structure that allows resonant modes to form.

  3. 3.

    PML boundaries implement an absorbing/outgoing boundary condition numerically.

  4. 4.

    Some works also compute approximate modes from a plane wave solution, i.e., not source-free, but this is manifestly not a mode [37].

  5. 5.

    Note this is different to the wave vector solution for continuous modes, usually written with a subscript, e.g., \(\beta _k\) or \(\tilde \beta _\mu \) as discussed earlier.

  6. 6.

    Of course, we could also start with cavity 2 and add in cavity 1.

  7. 7.

    Though in practice, for high-Q resonators, the normalization is likely quite accurate for most problems [42].

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Acknowledgements

We acknowledge Queen’s University and the Natural Sciences and Engineering Research Council of Canada for the financial support and CMC Microsystems for the provision of COMSOL Multiphysics to facilitate this research. We also acknowledge support from the Alexander von Humboldt Foundation through a Humboldt Research Award. We thank Reuven Gordon, Philip Kristensen, Chris Gustin, Chelsea Carlson, Marten Richter, and Andreas Knorr for their useful comments and collaborations related to some of the work presented in this chapter.

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Authors and Affiliations

  1. Department of Physics, Engineering Physics and Astronomy, Queen’s University, Kingston, ON, Canada

    Juanjuan Ren & Stephen Hughes

  2. Department of Physics, Engineering Physics and Astronomy, Queen’s University, Kingston, ON, Canada

    Sebastian Franke

  3. Technische Universität Berlin, Institut für Theoretische Physik, Nichtlineare Optik und Quantenelektronik, Berlin, Germany

    Sebastian Franke

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    Reuven Gordon

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Ren, J., Franke, S., Hughes, S. (2023). Quasinormal Mode Theories and Applications in Classical and Quantum Nanophotonics. In: Gordon, R. (eds) Advances in Near-Field Optics. Springer Series in Optical Sciences, vol 244. Springer, Cham. https://doi.org/10.1007/978-3-031-34742-9_3

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