Slow thermo-optomechanical pulsations in suspended one-dimensional photonic crystal nanocavities

Piergiacomo Z. G. Fonseca, Irene Alda, Francesco Marino, Alexander Cuadrado, Vincenzo D'Ambrosio, Jan Gieseler, and Romain Quidant

Phys. Rev. A 102, 053518 – Published 30 November 2020

Abstract

We investigate the nonlinear optical response of suspended one-dimensional (1D) photonic crystal nanocavities fabricated on a silicon nitride chip. Strong thermo-optical nonlinearities are demonstrated for input powers as low as $2 μ W$ and a self-sustained pulsing regime is shown to emerge with periodicity of several seconds. As the input power and laser wavelength are varied the temporal patterns change in period, duty cycle, and shape. This dynamics is attributed to the multiple timescale competition between thermo-optical and thermo-optomechanical effects and closely resembles the relaxation oscillations states found in mathematical models of neuronal activity. We introduce a simplified model that reproduces all the experimental observations and allows us to explain them in terms of the properties of a 1D critical manifold which governs the slow evolution of the system.

Received 7 September 2020
Accepted 10 November 2020

DOI:https://doi.org/10.1103/PhysRevA.102.053518

Physics Subject Headings (PhySH)

Neuronal dynamics Nonlinear optics Photonic crystals

Nonlinear DynamicsAtomic, Molecular & Optical

Authors & Affiliations

Piergiacomo Z. G. Fonseca ^1,*, Irene Alda¹, Francesco Marino², Alexander Cuadrado³, Vincenzo D'Ambrosio^1,4, Jan Gieseler¹, and Romain Quidant ^1,5,6,†

¹ICFO – Institut de Ciències Fotòniques, Mediterranean Technology Park, 08860 Castelldefels, Barcelona, Spain
²Istituto Nazionale di Ottica, Via Sansone 1, I-50019 Sesto Fiorentino, Florence, Italy
³Escuela de Ciencias Experimentales y Tecnología, University Rey Juan Carlos, Móstoles, 28933, Madrid, Spain
⁴Dipartimento di Fisica, Università di Napoli Federico II, Complesso Universitario di Monte S. Angelo, Via Cintia, 80126 Napoli, Italy
⁵ICREA – Institució Catalana de Recerca i Estudis Avançats, 08010 Barcelona, Spain
⁶Nanophotonic Systems Laboratory, Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland

^*piergiacomo.fonseca@gmail.com
^†rquidant@ethz.ch

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Vol. 102, Iss. 5 — November 2020

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Images

Figure 1
(a) Schematic processing steps and corresponding optical microscope images of the sample. (1) The ${Si}_{3} N_{4}$ membrane before any fabrication step. (2) The sample after spin coating of a $\sim 300$ -nm-thick film of resist (CSAR 62) and 1 min baking to stabilize the resist. (3) After exposure to an electron beam at 30 kV and $166 μ A$ of emission current for 1 h. The sample is then introduced into a developer (AR600-546) and a stopper (IPA), to remove the exposed regions and provide a mask for the following etching procedure. (4) The sample after 10 min RIE of the ${Si}_{3} N_{4}$ performed with $O_{2}$ and ${CHF}_{3}$ gases. (5) After 1 min $O_{2}$ cleaning process for resist lift-off. (b) SEM image of the PhC nanocavity with the Bragg grating couplers. (c) COMSOL simulation of the electric field profile at resonance.
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Figure 2
Schematic of the experimental setup. Light is coupled in and out of the nanocavity via a high numerical aperture microscope objective. The input light is linearly polarized to minimize waveguide propagation losses. A $4 f$ system is used to image the nanocavity onto an IR camera, and a D-shaped mirror allows us to only detect the output light from the cavity.
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Figure 3
Cavity transmission spectra at different input powers at (a) atmospheric pressure and (b) $p ≃ 0.5 mbar$ , taken by scanning the laser wavelength across resonance. (c) Time trace of the transmission intensity for input power $P_{in} = 2.25 μ W$ and detuning $δ = λ_{res} - λ_{L} = - 0.13 nm$ . (d) Transmission spectra as obtained by numerical integration of Eqs. (1, 2, 3), by tuning the detuning parameter $δ_{0}$ in the interval [2, $- 2$ ] (from shorter to longer wavelengths) with a scan rate $ɛ = 10^{- 3}$ .
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Figure 4
Experimental time traces of cavity transmission signal in the SSP regime: (a) Fixed input power $P_{in} = 2.5 μ W$ and detunings $δ_{1} = - 0.14 nm$ , $δ_{2} = - 0.12 nm$ , $δ_{3} = - 0.11 nm$ , $δ_{4} = - 0.10 nm$ , $δ_{5} = - 0.09 nm$ , $δ_{6} = - 0.08 nm$ . (b) Fixed detuning $δ = - 0.13 nm$ and input powers $P_{1} = 2.25 μ W$ , $P_{2} = 2.35 μ W$ , $P_{3} = 2.4 μ W$ , $P_{4} = 2.5 μ W$ , $P_{5} = 2.6 μ W$ , $P_{6} = 2.8 μ W$ .
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Figure 5
Comparison between experimental (black) and numerical [red (light)] time traces of the optical intensity. Simulations are obtained using the normalized detuning $δ_{0}$ given by experimental parameters $δ / γ \sim - 1.08$ , and an input power $P_{in}$ given by (a) $P_{2} = 2.25 μ W$ , (b) $P_{3} = 2.35 μ W$ , (c) $P_{4} = 2.5 μ W$ , and (d) $P_{5} = 2.8 μ W$ .
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Figure 6
Numerical phase-space trajectories (red (light) curves) together with the critical manifold (black curve) Eq. (8) in the ( $I_{c}, θ$ ) plane for $δ_{0} = 1.08$ . (a) $P_{in} = 2.25 μ W$ , (b) $P_{in} = 2.5 μ W$ , (c) $P_{in} = 2.8 μ W$ . Solid (dashed) curves indicate the stable (unstable) branches $Σ_{H, L}$ ( $Σ_{R}$ ) of the manifold coalescing at the fold points $F_{1, 2}$ (see text).
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