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Research · Publication & note

November 9, 2018 September 9, 2026

Hermitian and Non-Hermitian Mode Coupling in a Microdisk Resonator - Notes

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Journal article

S. Biasi, F. Ramiro-Manzano, F. Turri, P.-É. Larré, M. Ghulinyan, I. Carusotto and L. Pavesi

IEEE Photonics Journal Volume 11 Issue 2 6101114 2019

Published abstract

We make use of a phase-sensitive set-up to study the light transmission through a coupled waveguide-microdisk system. We observe a splitting of the transmission resonance leading to an unbalanced doublet of dips. The experimental data are analyzed by using a phasor diagram that correlates the real and the imaginary parts of the complex transmission. In addition, detailed features are evidenced by a complex inverse representation of the data that maps ideal resonances into straight lines and split resonances into complicated curves. Modeling with finite element method simulations suggests that the splitting and the unbalance is caused by an induced chirality in the propagation of the optical fields in the microdisk due to the interplay between the stochastic roughness and the intermodal dissipative coupling, which yield an asymmetric behavior. An analytical model based on the temporal coupled mode theory shows that both a reactive and a dissipative coupling of the counter-propagating modes by the surface roughness of the ring resonator are required to quantitatively reproduce the experimental observations and the numerical simulations.

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Related publications

Connections within F. Ramiro-Manzano's publication record, selected from shared research topics and evidence reviewed in the source papers.

Figure 3: device and experimental setup
Journal article
Photonics Research 8(8), 1333-1341 (2020)
Unidirectional Reflection from an Integrated “Taiji” Microresonator
A. Calabrese, F. Ramiro-Manzano, H. M. Price, S. Biasi, M. Bernard, M. Ghulinyan, I. Carusotto and L. Pavesi

What the related paper adds

This later paper extends the research direction developed in Hermitian and Non-Hermitian Mode Coupling in a Microdisk Resonator. This work engineers the non-Hermitian coupling deliberately in a taiji microresonator. Its internal S-shaped branch couples counter-propagating modes in a direction-dependent way, preserving reciprocal transmission while producing high-contrast reflection in one direction and almost none in the other.

What this paper adds to the related work

This paper provides an earlier basis for the later development reported in Unidirectional Reflection from an Integrated “Taiji” Microresonator. This paper explains asymmetric resonance doublets by combining phase-sensitive transmission, finite-element simulation and coupled-mode theory. It shows that stochastic surface roughness produces both conservative and dissipative coupling between counter-propagating modes, so a purely Hermitian description cannot reproduce the measured imbalance.

Complete three-stage schematic of the free-space interferometer showing preparation, interference and detection stages
Journal article
IEEE Transactions on Instrumentation and Measurement 67(12), 2863-2871 (2018)
A Free-Space Interferometer for Phase-Delay Measurements in Integrated Optical Devices in Degenerate Pump-and-Probe Experiments
F. Turri, S. Biasi, F. Ramiro Manzano and L. Pavesi

What the related paper adds

This earlier paper establishes a scientific basis for Hermitian and Non-Hermitian Mode Coupling in a Microdisk Resonator. This paper builds a flexible free-space interferometer that measures transmission and phase at the same time during degenerate pump-probe experiments. Lock-in detection separates the weak probe from the pump, and the phasor representation turns subtle changes in integrated waveguides and resonators into an interpretable complex optical response.

What this paper adds to the related work

Building on the earlier contribution A Free-Space Interferometer for Phase-Delay Measurements in Integrated Optical Devices in Degenerate Pump-and-Probe Experiments, this paper advances the research line. This paper explains asymmetric resonance doublets by combining phase-sensitive transmission, finite-element simulation and coupled-mode theory. It shows that stochastic surface roughness produces both conservative and dissipative coupling between counter-propagating modes, so a purely Hermitian description cannot reproduce the measured imbalance.

Figure 6: pump and probe experiment
Journal article
Photonics Research 5(3), 168-175 (2017)
Complete Crossing of Fano Resonances in an Optical Microcavity via Nonlinear Tuning
M. Bernard, F. Ramiro-Manzano, L. Pavesi, G. Pucker, I. Carusotto and M. Ghulinyan

What the related paper adds

This earlier paper establishes a scientific basis for Hermitian and Non-Hermitian Mode Coupling in a Microdisk Resonator. This study uses local thermo-optical tuning to drive two interacting Fano resonances through a complete crossing. The experiment continuously changes their spectral separation and asymmetry and reaches the critical condition where one modal feature disappears, offering a controlled probe of intermode coupling inside one integrated cavity.

What this paper adds to the related work

Building on the earlier contribution Complete Crossing of Fano Resonances in an Optical Microcavity via Nonlinear Tuning, this paper advances the research line. This paper explains asymmetric resonance doublets by combining phase-sensitive transmission, finite-element simulation and coupled-mode theory. It shows that stochastic surface roughness produces both conservative and dissipative coupling between counter-propagating modes, so a purely Hermitian description cannot reproduce the measured imbalance.

Featured image for Intermode reactive coupling induced by waveguide-resonator interaction
Journal article
Phys. Rev. A 90, 053811 (2014)
Intermode reactive coupling induced by waveguide-resonator interaction
M. Ghulinyan, F. Ramiro-Manzano, N. Prtljaga, M. Bernard, L. Pavesi, G. Pucker and I. Carusotto

What the related paper adds

This earlier paper establishes a scientific basis for Hermitian and Non-Hermitian Mode Coupling in a Microdisk Resonator. This work identifies a waveguide-induced reactive coupling between different radial mode families of a microdisk, analogous to an off-diagonal Lamb shift. The resulting Fano line shapes connect open-system theory, full-vector simulations and measured transmission, showing that the access waveguide actively reshapes the cavity spectrum.

What this paper adds to the related work

Building on the earlier contribution Intermode reactive coupling induced by waveguide-resonator interaction, this paper advances the research line. This paper explains asymmetric resonance doublets by combining phase-sensitive transmission, finite-element simulation and coupled-mode theory. It shows that stochastic surface roughness produces both conservative and dissipative coupling between counter-propagating modes, so a purely Hermitian description cannot reproduce the measured imbalance.

Research fields

Top-down

A lithographically defined bus waveguide is vertically coupled to a wedge microdisk resonator. The integrated geometry gives controlled access to several radial mode families whose interaction is altered by unavoidable sidewall and surface disorder.

Simulations & fits

Three-dimensional field calculations and disorder-dependent coupling models reproduce balanced, unbalanced and hidden resonance doublets. Complex-plane and inverse-transmission representations make the Hermitian frequency splitting and non-Hermitian linewidth coupling separately visible.

Characterization

A phase-sensitive interferometric setup measures the complex waveguide transmission rather than intensity alone. Phasor trajectories reveal induced chirality and asymmetry that would be difficult to identify from the two transmission dips by themselves.

RESEARCH TOPICS

CouplingThat control rules out the bus-disk junction as the main source. The remaining coupling between clockwise and counter-clockwise resonator modes is attributed to stochastic surface roughness and its coupling to external radiation channels.InterferenceIntensity alone can hide the mode interaction. A free-space Mach-Zehnder interferometer measures both transmitted power and phase while the laser is swept, revealing split resonances with unequal lobes and cases where phase splitting remains visible even when the transmission dip appears unsplit.MultimodeThe disk supports clockwise and counter-clockwise waves and more than one radial family; Figures 2(b,c) show the first and second radial field profiles. Those reactive and dissipative contributions explain why splitting, linewidth and lobe amplitude vary between azimuthal resonances even within the same fabricated disk.ResonatorsWith Q around 105, small surface perturbations become spectrally resolvable and the wedge microdisk provides a sensitive test of non-Hermitian mode theory. The resonator is therefore used as an experimental platform for distinguishing internal mode coupling from loading and radiative loss.
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