Self-sustained gigahertz electronic oscillations in ultrahigh-$Q$ photonic microresonators

Self-sustained gigahertz electronic oscillations in ultrahigh- $Q$ photonic microresonators

Mohammad Soltani, Siva Yegnanarayanan, Qing Li, Ali A. Eftekhar, and Ali Adibi

Phys. Rev. A 85, 053819 – Published 17 May 2012

Abstract

We report on theoretical and experimental observations of self-sustained fast [gigahertz (GHz)] electronic oscillations resulting from coupled electron-photon dynamics in ultrahigh- $Q$ Si microdisk resonators with cw pumping. Our theoretical analysis identifies conditions for generating steady-state GHz oscillations while suppressing thermal oscillations [megahertz (MHz)] with submilliwatt input laser power. Such fast oscillations are tunable via changing the free-carrier (FC) lifetime of the resonator. Integrating a $p$ - $i$ - $n$ diode with these high- $Q$ resonators for controlling the FC lifetime promises the realization of an integrated voltage-controlled oscillator (VCO) in a silicon photonics chip.

Received 15 July 2011

DOI:https://doi.org/10.1103/PhysRevA.85.053819

Authors & Affiliations

Mohammad Soltani^*, Siva Yegnanarayanan^†, Qing Li, Ali A. Eftekhar, and Ali Adibi^‡

School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA

^*Present address: Laboratory of Atomic and Solid State Physics, Physics Department, Cornell University, Ithaca, New York 14850, USA.
^†Present address: MIT Lincoln Laboratory, 244 Wood St., Lexington, Massacusetts 02420, USA.
^‡Corresponding author: adibi@ece.gatech.edu

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Issue

Vol. 85, Iss. 5 — May 2012

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Images

Figure 1
(a) Schematic of a waveguide-TWR coupling. (b) Theoretical results for the variation of the transmission coefficient ( $P_{out}$ / $P_{in}$ ) versus laser wavelength detuned from the cold resonance of the TWR at different FC lifetimes. The symmetric Lorentzian in this figure is the linear low input power spectrum of the device. The resonator parameters are shown in the box.Reuse & Permissions
Figure 2
Theoretical demonstration of simultaneous slow and fast oscillations in the response of the waveguide-TWR structure in Fig. 1a: (a) Output power of the waveguide, (b) resonance wavelength change, (c) temperature, and (d) FC density as functions of time. For this analysis, $P_{in} = 0.5$ mW, $δ ω = 3 ω_{0} / Q_{0}, τ_{FC} = 0.4$ ns, and the rest of the parameters are given in the box in Fig. 1.Reuse & Permissions
Figure 3
(a) Experimental setup used for monitoring the time-domain and spectral-domain response of the resonator. The scanning electron microscopy (SEM) image of the measured microdisk is shown in the setup. (b) Measured resonance transmission ( $T$ $=$ $P_{out} /$ $P_{in}$ ) spectrum at low powers (the solid green curve) and at high powers ( $P_{in} \approx 200$ μW) when the input laser wavelength is swept from left to right (the dotted blue curve) and from right to left (the dotted red curves). $δ λ_{L}$ is the laser wavelength detuning from the cavity resonance. The resonance wavelength is near 1532 nm.Reuse & Permissions
Figure 4
Experimental results for temporal oscillations of the microdisk resonator shown in Fig. 3a. (a) Observation of simultaneous steady-state slow (MHz) and fast (GHz) oscillations. A zoomed view of the fast oscillation is shown on the right. (b) Spectrum of the oscillations. The left inset shows the spectral components of the slow oscillations, and the right inset shows the spectrum of the fast oscillations.Reuse & Permissions
Figure 5
Generation of pure fast oscillations. (a) Onset of fast oscillations of the waveguide-TWR at two input power levels of 0.5 mw (red) and 1 mW (blue), and; (b) the contour plots of resonator normalized energy versus resonance wavelength change ( $Δ λ_{0}$ ) with respect to laser detuning ( $δ λ_{L}$ ); In (a) and (b), $δ ω = 3 ω_{0} / Q_{0}$ and $τ_{FC}$ $=$ 1 ns. (c) Spectrum of the output power for different FC lifetimes as indicated; In (c), $P_{in} = 1$ mW and $δ ω = 3 ω_{0} / Q_{0}$ . (d) Spectrum of the first harmonic of the oscillations at different laser detuning levels. In (d), $P_{in} = 4$ mW and $τ_{FC}$ $=$ 1.5 ns. The box in Fig. 1 contains the rest of the resonator parameters for the above simulations.Reuse & Permissions

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