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APL Photonics

Optical multi-stability in a nonlinear high-order microring resonator filter

Jin Li, Luigi Di Lauro, Alessia Pasquazi, Marco Peccianti, David Moss, Roberto Morandotti, Brent E. Little, Sai Tak Chu

Published May 1, 2020• 58 citations
Publisher

Abstract

We theoretically analyze and experimentally demonstrate optical bi-stability and multi-stability in an integrated nonlinear high-order microring resonator filter based on high-index contrast doped silica glass. We use a nonlinear model accounting for both the Kerr and thermal effects to analyze the instability behavior of the coupled-resonator based filter. The model also accurately predicts the multi-stable behavior of the filter when the input frequency is slightly detuned. To understand the role of the intracavity power distribution, we investigate the detuning of the individual rings of the filter from the optical response with a pump–probe experiment. Such a measurement is performed scanning the filter with a low-power probe beam tuned a few free spectral ranges away from the resonance where the pump is coupled. A comprehensive understanding of the relationship between the nonlinear behavior and the intracavity power distribution for the high-order microring resonator filter will help the design and implementation of future all-optical switching systems using this type of filter.

DOI
10.1063/5.0002941

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We theoretically analyze and experimentally demonstrate optical bi-stability and multi-stability in an integrated nonlinear high-order microring resonator filter based on high-index contrast doped silica glass. We use a nonlinear model accounting for both the Kerr and thermal effects to analyze the instability behavior of the coupled-resonator based filter. The model also accurately predicts the multi-stable behavior of the filter when the input frequency is slightly detuned. To understand the role of the intracavity power distribution, we investigate the detuning of the individual rings of the filter from the optical response with a pump–probe experiment. Such a measurement is performed scanning the filter with a low-power probe beam tuned a few free spectral ranges away from the resonance where the pump is coupled. A comprehensive understanding of the relationship between the nonlinear behavior and the intracavity power distribution for the high-order microring resonator filter will help the design and implementation of future all-optical switching systems using this type of filter.
Optical bistability (BI) and self-pulsation (SP) in high-QQQ silicon microring resonators (MRRs) induced by thermo-optical (TO) effect and other nonlinear effects are theoretically studied with coupled mode theory and linear stability analysis method. It is found that the boundaries for both BI and SP are mainly restricted by two counteracting effects: free carrier dispersion effect and TO effect. If the refractive index changes of a MRR caused by these two effects are on the same order of magnitude, the output power will exhibit much more complicated dependence on the input power and wavelength, namely, input-power-dependent multi-BI and multi-SP regions will exist at certain input wavelength range. The controllability of multi-BI and multi-SP phenomena by the input power and input wavelength could be very useful in all-optical nonlinear devices.
In this work, we experimentally study the optical bistability (BI) behavior in active silicon microring resonators (MRR). A stable hysteresis loop response at the output port is demonstrated at a power level higher than the BI threshold, taking into account the different detuning and free carrier life-times. That hysteresis is observed at low and high BI thresholds, which can be used for all-optical switching and optical routers. The MRR is placed inside a reverse-biased PIN junction and fabricated by CMOS technology. It records a loaded Q-factor, linewidth (3 dB width of the spectrum), and extinction ratio (ER) around105,15.310^{5},15.3105,15.3pm, and 20 dB, respectively.
Over the past few decades, optical ring resonators have attracted a considerable amount of attention as versatile elements for a wide range of applications ranging from telecommunication and sensing to basic scientific research [1,2]. The silicon-on-insulator (SOI) material system is a mature fabrication technique and provides the ability to implement microring resonators. In addition, the high confinement of light and the large third-order nonlinearity of silicon at wavelengths in the near infrared, typically around 1.4-1.6 µm, can be utilized for a number of applications by microring resonator devices [3,4]. The optical bistability observed in silicon-based microring resonators have been theoretically investigated and numerically simulated through various sophisticated techniques [5-9]. However, only recently unifying analytical theories regarding nonlinear effects of optical bistability in microring resonators in terms of a slowly varying envelope approach have been reported [10,11]. Previously, we analytically described the nonlinear response of microring resonators consisting of an add-drop filter with feedback and showed that Fano lineshapes can be adjusted by the resonator parameters [12]. In this chapter, we extend our work to examine the optical bistabililty in such microring resonators and test the analytical results with those predicted by the OptiFDTD software package.
We describe the optical bistability phenomenon in a silicon-on-insulator microring resonators device by using an analytical theory, which includes both linear and nonlinear effects such as two-photon absorption, Kerr effect, free carrier and thermo-optic effect (TOE). We show that the bistable switching threshold and the hysteresis loop width can be tuned by geometrical parameters of the device and by the nonlinear parameters. The accuracy of the analytical approach is verified by comparing the spectrum responds with the predicting data from a commercial finite-difference time-domain software tool, and a very close agreement is found between the two when TOE is incorporated in analytical theory. In addition, our analysis reveals that a new type of hysteresis loop occurs at low input intensity. The mode suppression of the designed device by Vernier effect for tunable filter applications is also briefly discussed.
Resonance shift and bistability in a silicon microring resonator operating at higher optical power levels pose serious difficulties, especially in nonlinear four wave mixing process. A solution of parking a laser wavelength around any of the resonances of a microring resonator and operating at any power levels is explored by integrating a microheater. We have shown with the existing theoretical model that the previous history of phase detuning in a silicon microring resonator determines the effective gain in stimulated four wave mixing process. The experimental results have been shown to be closely matching with the simulation results. For a microring resonator of radius 50 μm, an improved stimulated four wave mixing gain of ~ 11.6 dB has been observed while thermo-optically blue-shifting resonances in comparison to that of red-shifting resonances, for a launched pump power of 8.4 mW operating at a slightly off-resonant wavelength λp. The proposed technique can be used in designing actively controlled efficient photon sources in a large-scale integrated quantum photonic circuit operating at λ ~ 1550 nm.
The microring resonators have potential applications for the photonic integrated circuits. The dynamical phenomena of the two coupled microrings require a simple and efficient numerical formalism for solution of the system. We employ an analytical formula to calculate the optical tristability inside the two coupled microrings that takes into account Kerr nonlinearity and the effect of loss. We also compare the analytical results with the results from 3D finite-difference time-domain simulation. In addition, we show it is possible to obtain configurations which can tune the tristable region. This could be useful for designing optical logic applications.