Kerr-Nonlinearity-Induced Mode-Splitting in Optical Microresonators

George N. Ghalanos, Jonathan M. Silver, Leonardo Del Bino, Niall Moroney, Shuangyou Zhang, Michael T. M. Woodley, Andreas Ø. Svela, and Pascal Del’Haye

Phys. Rev. Lett. 124, 223901 – Published 4 June 2020

Abstract

The Kerr effect in optical microresonators plays an important role for integrated photonic devices and enables third harmonic generation, four-wave mixing, and the generation of microresonator-based frequency combs. Here we experimentally demonstrate that the Kerr nonlinearity can split ultra-high- $Q$ microresonator resonances for two continuous-wave lasers. The resonance splitting is induced by self- and cross-phase modulation and counterintuitively enables two lasers at different wavelengths to be simultaneously resonant in the same microresonator mode. We develop a pump-probe spectroscopy scheme that allows us to measure power dependent resonance splittings of up to 35 cavity linewidths (corresponding to 52 MHz) at 10 mW of pump power. The required power to split the resonance by one cavity linewidth is only $286 μ W$ . In addition, we demonstrate threefold resonance splitting when taking into account four-wave mixing and two counterpropagating probe lasers. These Kerr splittings are of interest for applications that require two resonances at optically controlled offsets, e.g., for optomechanical coupling to phonon modes, optical memories, and precisely adjustable spectral filters.

Received 7 November 2019
Revised 25 February 2020
Accepted 7 March 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.223901

Physics Subject Headings (PhySH)

Kerr effect Nonlinear optics Third order nonlinear optical processes

Four-wave mixing Whispering gallery mode resonators

Atomic, Molecular & OpticalNonlinear Dynamics

Authors & Affiliations

George N. Ghalanos ^1,2,3, Jonathan M. Silver ^2,4, Leonardo Del Bino ^2,5, Niall Moroney^1,2,3, Shuangyou Zhang^1,2, Michael T. M. Woodley ^2,5, Andreas Ø. Svela ^2,3, and Pascal Del’Haye ^1,6,2

¹Max Planck Institute for the Science of Light, Staudtstraße 2, 91058 Erlangen, Germany
²National Physical Laboratory, Hampton Road, Teddington TW11 0LW, United Kingdom
³Blackett Laboratory, Imperial College London SW7 2AZ, United Kingdom
⁴City, University of London, EC1V 0HB, United Kingdom
⁵Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
⁶Department of Physics, Friedrich Alexander University Erlangen-Nuremberg, 91058 Erlangen, Germany

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Vol. 124, Iss. 22 — 5 June 2020

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Images

Figure 1
(a) Silica rod WGM resonator with a diameter of 2.7 mm. The region in which light travels around the rod is indicated by the arrows. (b) On-chip silica microtoroid WGM resonator with a diameter of $95 μ m$ . (c) Experimental setup. Light from a single ECDL is split into three branches. The pump branch is up-shifted in frequency by a fixed amount via an AOM. A PI controller allows the pump to be locked at a fixed detuning from resonance. The probe branch is up-shifted by a variable amount via a second AOM, used for spectroscopy. The reference branch is far out of resonance and does not couple into the resonator, and is used for heterodyne detection. (d) The relative frequencies of the three beams, illustrating how the pump is locked at a fixed detuning $δ$ from the SPM-shifted resonance, while the probe beam is scanned around the pump frequency to measure the XPM-shifted resonance. All resonances shown in solid blue originate from the same cold cavity resonance (dashed). Note that $Ω$ and $Δ$ are shown here as frequencies for illustrative purposes but are normalized by the cavity half-linewidth $γ$ in the rest of this Letter.
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Figure 2
(a),(b) Probe spectra measuring the XPM shifts for different pump powers for CW-CCW pump-probe directions. With the pump locked at a fixed detuning from the SPM-shifted resonance, shown as a dashed line, the probe is scanned in frequency to measure the XPM-shifted resonance. Increasing the pump power results in a larger difference between SPM-XPM shifts. (c) XPM-related pump-power-dependent frequency shifts. Each trace corresponds to a different detuning of the pump from the SPM resonance, in terms of half-linewidths ( $γ$ ). Each data point corresponds to the frequency difference between the pump and the center of the XPM-shifted resonance. (d) A $95 μ m$ -wide microtoroid resonator of $5 \times 10^{7} Q$ factor and $5 μ m^{2}$ effective mode area $A_{eff}$ was pumped with 10 mW, resulting in a difference of $70 γ$ between SPM-XPM shifts.
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Figure 3
Measurement of XPM resonance shifts with two counterpropagating probes (red CW, black CCW), for both low and high pump powers, compared to the SPM-shifted pump resonance (dashed) to which the pump laser is locked (blue, CW). Interplay between XPM and FWM leads to a threefold splitting of the microresonator mode at high pump power.
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Figure 4
(a) Transmitted probe power (black) and signal power (red) in the copropagating pump-probe direction, with a simultaneous fit of $| α_{out, 1} |^{2}$ and $| α_{out, - 1} |^{2}$ , respectively. (b) Measured frequency difference between the pump and the center of the copropagating probe resonance vs in-coupled pump power, for different values of $δ / γ$ . These data were taken simultaneously with the counterpropagating data shown in Fig. 2. The solid lines are theoretical curves based on the fitted parameters from Fig. 2. The dashed lines are the fitted shifts of the CCW resonance exactly as in Fig. 2.
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