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Complete crossing of Fano resonances in an optical microcavity

Photonics Research, 5, 168 (2017)

DOI: 10.1364/PRJ.5.000168

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Complete crossing of Fano resonances in an optical microcavity via nonlinear tuning

M. Bernard, Fernando Ramiro-Manzano,L. Pavesi,Georg Pucker, I. Carusotto and Mher Ghulinyan

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 line shapes 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 exper- imental results, which confirm the validity of the developed theory.

Summary

Microcavities that can confine electromagnetic radiation and enhance light-matter interactions, such as on-chip microresonators, have been proven to be of significant interest for the development of photonics for telecommunications. These devices have the potential for use in signal filtering and nonlinear frequency generation processes, and their compatibility with the silicon platform makes them suitable for scalability. However, spectral tunability of the resonant features is required for practical applications, and this is often achieved via electrical micro-heaters that exploit the thermo-optic effect to modify the refractive index of the environment, thus changing the optical path of the device. This approach, however, has a global action and does not allow for tuning spectral channels separately.

In this study, we propose an all-optical approach to relatively detune the resonances within a microresonator by exploiting the thermo-optical effect at a local level. They demonstrate this effect by applying it to a whispering gallery resonator-waveguide system, which exhibits Fano interference features. The continuous detuning is used to explore complete mode crossings between two resonances, allowing the fine tuning of the system into a critical interaction condition and the suppression of one of the modes.

The resonator-waveguide system is modeled theoretically via a set of nonlinear equations that take into account the local heating. The developed model is validated by numerical simulations, which are in excellent agreement with experimental results. The authors suggest that their theoretical approach can be generalized and extended to other material nonlinearities and photo in order to achieve high-speed modulation of the spectral response in multimode resonator devices.

Overall, this study demonstrates the potential of all-optical approaches for spectral tunability in microresonator devices, with possible applications in telecommunications and other areas of photonics.

Figures

explanation cross resonances by nonlinear effects

Fig 1. Schematic representation of 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, pos- sibly going through a crossing. (b) Continuous tuning of a doublet of resonances may be obtained via nonlinearities, such as a localized thermo-optic effect.

Nonlinear wavelength shift and bistability

Fig 3. 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. When sweeping the spectrum using a high-power laser (solid line), the resonance shifts progressively due to the increasing nonlinear effect, resulting in a spectrum with an apparent discontinuity, where the cavity mode de-locks from the pump laser.

Optical setup scheme for cross resonances due to non linear effects

Fig. 4. 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. The output also is collected with a taper fiber, split, and fed to an OSA and a broadband germanium detector.

Fig 6. 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. The thermo-optic nonlinearity, induced by the pumped doublet, also affects the other resonances (b), allowing for a relative detuning of the peaks as shown by the transmission color map. (c) Selected trans- mission spectra show the transformation of the Fano resonance in the vicinity of the critical phase point, where a complete disappearance of the Rs1 peak feature takes place (panel C). The probe spectrum time-evolution, together with the pump dynamic transmission is represented in Visualization 1.

map of spectra of crossing resonances, shifted by thermo-optic effects

Fig. 7. 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. (d) The selected spectra, under 2 W pump, demonstrate three cases of the relative detuning, which changes from positive (A) to negative (C) passing through the 𝛿𝜔120=0 condition (B). The probe spectrum time evolution, together with the pump dynamic transmission with input power 2.0 W is represented in Visualization 2.

Simulation and experiments of crossing resonances by nonlinear thermal effects

Fig. 8. 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. (15). (b) Experimental transmission map as a function of both pump and probe wavelength is shown. (c) Relative coupling 𝜂1 among the two radial family modes to the waveguide, extracted from results in panel (b). Successively, 𝜂1
is used to compute the Γ and Δ matrices of Eq. (10) to also take into account the changes in the coupling induced by the thermally induced 𝛿𝑛(𝑟)
. Panel (d) shows the transmission map as a function of both pump and probe wavelength using the simulated in (a) pump excitation for Eq. (16).

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