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Research · Publication & note

April 12, 2017 September 9, 2026

Complete Crossing of Fano Resonances in an Optical Microcavity via Nonlinear Tuning - Notes

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Published abstract

We report on the modeling, simulation, and experimental demonstration of complete mode crossings of Fano resonances within chip-integrated microresonators. The continuous reshaping of resonant lineshapes is achieved via nonlinear thermo-optical tuning when the cavity-coupled optical pump is partially absorbed by the material. The locally generated heat then produces a thermal field, which influences the spatially overlapping optical modes, allowing us to alter the relative spectral separation of resonances. Furthermore, we exploit such tunability to continuously probe the coupling between different families of quasi-degenerate modes that exhibit asymmetric Fano interactions. As a particular case, we demonstrate a complete disappearance of one of the modal features in the transmission spectrum as predicted by Fano [Phys. Rev. 124, 1866 (1961)]. The phenomenon is modeled as a third-order nonlinearity with a spatial distribution that depends on the stored optical field and thermal diffusion within the resonator. The performed nonlinear numerical simulations are in excellent agreement with the experimental results, which confirm the validity of the developed theory.

Figures

Figure 1 from Complete Crossing of Fano Resonances
Figure 1. Summary. Diagram showing the mode-crossing possibilities. (a) Azimuthal modes of two radial families progressively shift at each increment of the azimuthal number due to the difference in FSR, possibly going through a crossing.

© 2017 Chinese Laser Press. Source: M. Bernard et al., Photonics Research 5(3), 168-175 (2017), DOI 10.1364/PRJ.5.000168. Reproduced on the author’s personal website under the rights retained in the journal’s copyright transfer agreement.

Figure 2 from Complete Crossing of Fano Resonances
Figure 2. Summary. Simulated thermal distribution generated by (a) the first and (b) the second optical radial family modes. The contour lines show the modes’ electric field profiles.

© 2017 Chinese Laser Press. Source: M. Bernard et al., Photonics Research 5(3), 168-175 (2017), DOI 10.1364/PRJ.5.000168. Reproduced on the author’s personal website under the rights retained in the journal’s copyright transfer agreement.

Figure 3 from Complete Crossing of Fano Resonances
Figure 3. Summary. Resonant line shape modification under a sweeping pump in the presence of optical nonlinearity. The cold cavity spectrum (dashed line) is obtained with a weak probe.

© 2017 Chinese Laser Press. Source: M. Bernard et al., Photonics Research 5(3), 168-175 (2017), DOI 10.1364/PRJ.5.000168. Reproduced on the author’s personal website under the rights retained in the journal’s copyright transfer agreement.

Figure 4 from Complete Crossing of Fano Resonances
Figure 4. Summary. Experimental setup. A tunable laser amplified with an EDFA is mixed with the broadband signal of a BOA and shone into the sample with a taper fiber.

© 2017 Chinese Laser Press. Source: M. Bernard et al., Photonics Research 5(3), 168-175 (2017), DOI 10.1364/PRJ.5.000168. Reproduced on the author’s personal website under the rights retained in the journal’s copyright transfer agreement.

Figure 5 from Complete Crossing of Fano Resonances
Figure 5. Summary. Experimental cold cavity spectrum of the resonator. Three azimuthal modes are present for the families R₁, R₂, and R₃.

© 2017 Chinese Laser Press. Source: M. Bernard et al., Photonics Research 5(3), 168-175 (2017), DOI 10.1364/PRJ.5.000168. Reproduced on the author’s personal website under the rights retained in the journal’s copyright transfer agreement.

Figure 6 from Complete Crossing of Fano Resonances
Figure 6. Summary. Results of the pump and probe experiment. Panel (a) shows the cold (dashed) and hot (solid) cavity transmission spectra of the device around the strongly pumped resonance doublet.

© 2017 Chinese Laser Press. Source: M. Bernard et al., Photonics Research 5(3), 168-175 (2017), DOI 10.1364/PRJ.5.000168. Reproduced on the author’s personal website under the rights retained in the journal’s copyright transfer agreement.

Figure 7 from Complete Crossing of Fano Resonances
Figure 7. Summary. Pump and probe experiments demonstrating a complete crossing of the modes. Panels (a), (b), and (c) represent the same experiment under different input power conditions of 0.5, 1, and 2 W, respectively.

© 2017 Chinese Laser Press. Source: M. Bernard et al., Photonics Research 5(3), 168-175 (2017), DOI 10.1364/PRJ.5.000168. Reproduced on the author’s personal website under the rights retained in the journal’s copyright transfer agreement.

Figure 8 from Complete Crossing of Fano Resonances
Figure 8. Summary. Experimental and simulated data of the pump and probe experiment. (a) Experimental pump transmission spectrum of the loaded cavity (black line) is simulated (dashed red) by inserting the cold cavity fit parameters into Eq.

© 2017 Chinese Laser Press. Source: M. Bernard et al., Photonics Research 5(3), 168-175 (2017), DOI 10.1364/PRJ.5.000168. Reproduced on the author’s personal website under the rights retained in the journal’s copyright transfer agreement.

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Article access and reuse

The Version of Record is openly available from the journal. The Photonics Research copyright transfer agreement permits authors to reuse all or part of the work, including the publisher-formatted version, on their personal web homepage when the Chinese Laser Press copyright notice is retained. The figures below are the complete original compositions extracted from the article PDF and are reproduced with that notice.

Related publications

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

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What the related paper adds

This later paper extends the research direction developed in Complete Crossing of Fano Resonances in an Optical Microcavity via Nonlinear Tuning. 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 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.

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Hermitian and Non-Hermitian Mode Coupling in a Microdisk Resonator
S. Biasi, F. Ramiro-Manzano, F. Turri, P.-É. Larré, M. Ghulinyan, I. Carusotto and L. Pavesi

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This later paper extends the research direction developed in Complete Crossing of Fano Resonances in an Optical Microcavity via Nonlinear Tuning. 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.

What this paper adds to the related work

This paper provides an earlier basis for the later development reported in 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.

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 later paper extends the research direction developed in Complete Crossing of Fano Resonances in an Optical Microcavity via Nonlinear Tuning. 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

This paper provides an earlier basis for the later development reported in A Free-Space Interferometer for Phase-Delay Measurements in Integrated Optical Devices in Degenerate Pump-and-Probe Experiments. 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.

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 Complete Crossing of Fano Resonances in an Optical Microcavity via Nonlinear Tuning. 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 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.

Research fields

Top-down

An integrated microcavity supporting overlapping radial mode families is used as a controllable Fano system. Its patterned resonator-waveguide geometry allows selected cavity resonances to be addressed without globally retuning the entire photonic circuit.

Simulations & fits

Coupled-mode equations include absorption-induced heating and the different spatial overlap of each optical mode with the thermal field. The model and thermal simulations explain how nonlinear tuning carries two Fano resonances through a complete crossing.

Characterization

Pump-power-dependent transmission spectra track the continuous reshaping, suppression and reappearance of the resonances. Simultaneous broadband and tunable-laser measurements distinguish genuine mode interaction from an apparent crossing caused only by line-shape asymmetry.

RESEARCH TOPICS

CouplingThe relative weights depend on where the waveguide lies under the radial field lobes; moving it inward can even make the second family couple more strongly than the fundamental. The coupled-mode model uses these independently determined weights, radiative rates and detuning to explain why a narrow resonance can be suppressed or enhanced by a broader neighbour rather than assigning every line-shape change to heating.InterferenceWhen resonances from two radial families approach, their excitation pathways interfere. The transmission spectrum therefore records coherent interference between families, not simply the sum of two Lorentzian dips.MultimodeBecause the two combs are slightly mismatched, selected members repeatedly approach and cross across the measured wavelength range. FEM field profiles and thermal simulations show that the two radial orders deposit heat in different regions, which changes how efficiently a pumped mode shifts its neighbour.NonlinearA strong pump changes the refractive index primarily through absorption-induced heating and shifts a selected cavity resonance. The nonlinear effect is used as a tuning mechanism for coherent multimode interference rather than reported only as bistability of a single resonance.ResonatorsTheir different linewidths and thermal overlaps provide the asymmetry needed for pronounced Fano features. The study shows that a single high-Q cavity can be treated as an interacting set of modal families, enabling spectral reconfiguration without fabricating two separate resonators.
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