Interplay of Polarization and Time-Reversal Symmetry Breaking in Synchronously Pumped Ring Resonators

Optically induced breaking of symmetries plays an important role in nonlinear photonics, with applications ranging from optical switching in integrated photonic circuits to soliton generation in ring lasers. In this work we study for the first time the interplay of two types of spontaneous symmetry breaking that can occur simultaneously in optical ring resonators. Specifically we investigate a ring resonator that is synchronously pumped with short pulses of light. In this system we numerically study the interplay and transition between regimes of temporal symmetry breaking (in which pulses in the resonator either run ahead or behind the seed pulses) and polarization symmetry breaking (in which the resonator spontaneously generates elliptically polarized light out of linearly polarized seed pulses). We find ranges of pump parameters for which each symmetry breaking can be independently observed, but also a regime in which a dynamical interplay takes place. Besides the fundamentally interesting physics of the interplay of different types of symmetry breaking, our work contributes to a better understanding of the nonlinear dynamics of optical ring cavities which are of interest for future applications including all-optical logic gates, synchronously pumped optical frequency comb generation, and resonator-based sensor technologies.

Figure 1

Schematic of the different types of symmetry breaking in a dielectric ring resonator. By convention, the pump field is linearly polarized along the $y$ axis. PSB: polarization symmetry breaking, TSB: temporal symmetry breaking.

Figure 2

Numerically simulated evolution of the intracavity field when polarization (a),(b) or temporal (c),(d) symmetry breaking occurs while scanning the pump frequency across a resonance. (a),(c) Intracavity power polarized in the $y$ (blue curve) and $x$ (red curve) directions. (Evolution of the power of the circularly polarized components are also given in (a) as dashed gray lines). The red background denotes the detuning range for which symmetries are broken. (b),(d) Input pulse profiles (gray) and intracavity pulse profiles (blue, red, and green) at particular times in the scanning pointed out by colored arrows. (a),(b) ${\tau }_0=3$, $S_0=\sqrt{3.3}$. (c),(d) ${\tau }_0=1.25$, $S_0=2$. See Supplemental Material [31] for an animated version of the figure.

Figure 3

Chart illustrating the different domains of symmetry breaking in the parameter space of normalized input peak power $|S_0{|}^2$ and pulse duration ${\tau }_0$ with input fields of the form $S_{\pm }(\tau )=S_0\exp [-(\tau /{\tau }_0{)}^2]$. The square, circle, and triangle markers indicate the sets of parameters used in Figs. 2, 2, Figs. 2, 2, and Fig. 4, respectively.

Figure 4

Dynamics of the interplay between polarization and temporal symmetry breaking for two different detuning scanning rates. (a),(e) Evolution of the powers of both polarization components in the linear basis at $\tau =0$. The red background denotes the detuning range for which one or both symmetries are broken. (b)–(c),(f)–(g) 2D color plots of the evolution of the intracavity pulse profile of each polarization component. (d),(h) Evolution of the average power of the $x$ component over the broken symmetry region for a certain level of power noise (black curves) and for another 2 orders of magnitude greater (gray). Detuning scanning rate is $5.6\times {10}^{-4}\mathrm{rad}/\text{round}\text{−}\text{trip}$ for the left column and $2.8\times {10}^{-3}\mathrm{rad}/\text{round}\text{−}\text{trip}$ for the right one. In both cases, ${\tau }_0=2.25$, $S_0=2$. See Supplemental Material [31] for an animated version of the figure.