Physics Chat
Modelling optical bistability in 1D array of coupled ring resonators
Speaker: Ghada Alharbi (SSOh)
Date: Friday 12 March 2021
Time: 15:00
Venue: Zoom
Since Haldane and Raghu's proposal of the photonic quantum Hall effect [1], photonic topological insulators have been studied very actively creating a new field called topological photonics. In the quantum Hall effect materials the existence of chiral edge modes is a key signature of this type of photonic materials with broken time-reversal symmetry and the chiral modes are topologically protected due to the different Chern numbers between photonic bands. In contrast, photonic structures with time-reversal symmetry, called quantum spin-Hall structure and quantum valley-Hall structures, can have edge modes that are protected by topology. Since no magnetic field is required to break time reversal symmetry, the time-symmetric systems find more applications, for example, photonic topological insulator lasers such as in a 1D Su-Schrieffer-Heeger (SSH) array and in 2D photonic quantum spin-Hall or quantum valley-Hall photonic crystals [2,3]. On the other hand, optical bistability is one of the important nonlinear phenomena, which can be demonstrated in Kerr nonlinear materials. Almost four decades ago, Kaplan et al. theoretically explained the appearance of optical bistability in a single ring resonator and the symmetry between the intensities of clockwise and counter-clockwise modes is broken spontaneously as the pump intensity increases [4]. Very recently, the spontaneous symmetry breaking and the optical bistability have been shown experimentally in a micro-ring resonator [5]. In this presentation, I will present a theoretical model based on the coupled mode theory that describes a nonlinear system of coupled ring resonators in one dimension. We consider the Kerr effect, which gives the self-phase modulations and cross phase modulations, together with alternating coupling coefficients between ring resonators from v to w. With this, we investigate the optical bistability of the coupled modes in the SSH array and explore the effect of Kerr coefficient on zero energy modes, i.e. modes with zero detuning. In our model, we solve the time-domain coupled mode equations using the fourth-order Runge-Kutta method and we will analyse the results by comparing with the solutions of frequency-domain coupled mode equations.
References [1] S. Raghu and F. D.M. Haldane, Phys. Rev. B, vol. 78, 033834, 2008. [2] M. Saba, S. Wong, M. Elman, S. S. Oh, and O. Hess, Phys. Rev. B, vol. 101, 054307, 2020. [3] Y. Gong, S. Wong, A. J. Bennett, D.L. Huffaker, and S. S. Oh, ACS Photon, vol. 7, 2089, 2020. [4] A. E. Kaplan and P. Meystre, Opt. Commun, vol. 40, 229, 1982. [5] L. Del Bino, J. M. Silver, S. L. Stebbings, and P. Del'Haye, Sci. Rep. vol. 7, 43142, 2017
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