Quasinormal Mode Analysis in Electromagnetic Resonators

Quasinormal modes (QNMs) provide a rigorous framework for describing the resonant behaviour of open electromagnetic systems, where leakage and absorption render the underlying operators non-Hermitian. Each QNM is characterised by a complex eigenfrequency whose real part corresponds to the resonant frequency and whose imaginary part quantifies radiative and dissipative loss. By expanding the electromagnetic Green’s function in the QNM basis, one obtains compact expressions for key observables such as the local density of states, Purcell enhancement and spectral line-shapes. This modal decomposition elucidates the interplay between high-Q and low-Q resonances, clarifies interference phenomena including Fano resonances, and underpins efficient semi-analytical and perturbative methods. Recent advances have resolved long-standing issues of mode normalisation, completeness and mode coupling, enabling accurate modelling of photonic crystals, plasmonic nanostructures and hybrid metal–dielectric cavities. The QNM approach unifies classical and quantum descriptions of light–matter interaction, offering both physical insight and computational economy in the design of sensors, switches and nanoscale light sources.

Research from Nature Portfolio

Recent studies have demonstrated that classical interference of QNMs can reproduce the Purcell effect and Lamb shift traditionally viewed as quantum phenomena. By analysing a waveguide-cavity geometry in a planar photonic crystal, it was shown that the spectral shift and lifetime modification of an emitter arise from the same Fano-type interference between resonant and continuum modes. This work establishes a direct link between non-Hermitian modal theory and observable spectral features, revealing that radiative decay rates can be engineered by tuning the relative phase and loss parameters of coupled QNMs. The findings underscore the power of QNM analysis in capturing complex emitter–resonator interactions without invoking zero-point quantum fluctuations.

Quasinormal Mode Analysis in Electromagnetic Resonators publication trend

The graph below shows the total number of articles in quasinormal mode analysis in electromagnetic resonators across all publications each year (not limited to Nature Index journals).

Technical terms

Quasinormal mode (QNM): An eigenmode of an open, non-Hermitian system characterised by a complex frequency, representing both oscillation and decay.

Non-Hermitian operator: An operator whose eigenvalues are complex, reflecting energy leakage or absorption in open systems.

Fano resonance: An asymmetric spectral line-shape arising from interference between a discrete resonance and a continuum of modes.

Purcell effect: Enhancement (or suppression) of a quantum emitter’s spontaneous emission rate due to its electromagnetic environment.

Complex mode volume: A generalisation of the electromagnetic mode volume to dissipative systems, combining amplitude and phase information of QNMs.

Local density of states (LDOS): A frequency-resolved measure of the electromagnetic modes available to an emitter at a given position.

References

1. First-order perturbation theory of eigenmodes for systems with interfaces. Physical Review Research (2023).
2. Tailoring Fano Lineshape in Photonic Local Density of States by Losses Engineering. Advanced Quantum Technologies (2023).
3. Normalization, orthogonality, and completeness of quasinormal modes of open systems: the case of electromagnetism [Invited].. Optics Express (2022).
4. Purcell effect and Lamb shift as interference phenomena. Scientific Reports (2016).
5. Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics. New Journal of Physics (2014).