Nonlinear dynamics of spatial soliton in a Kerr micro-ring

TL;DR

The paper tackles phase-enabled spatial soliton dynamics in a Kerr micro-ring and the associated OAM control. It introduces a generalized intra-cavity LLE with phase via $\hat{\mathcal{R}}_\zeta$, and analyzes MI and soliton formation under TE/TM cross-phase modulation in an AlN micro-ring. MI analyses, detuning scans, and split-step simulations reveal pathways from CW to modulational instability, to multi-soliton states, and finally to a single soliton; with $\zeta=1$ tooth-OAM mapping yields tooth-resolved intensity and phase, enabling controlled topological charges across comb teeth. The results connect OAM readout to temporal soliton dynamics, enabling phase-engineered, high-dimensional photonic resources for integrated spectroscopy and coherent communications.

Abstract

The input pump light field can be split into two transverse modes, after entering a AIN microring, which can generate rich nonlinear effects. The cross-phase modulation (XPM) effect in magnetic(TM) polarization mode can cause a refractive index alteration of the micro-ring, the electric(TE) polarization mode and TM polarization mode will display different values and generate a phase change. By adjusting the magnitude of the input TE polarization mode and TM polarization mode, we can achieve a series of phase distributions. By controlling the phase of the electromagnetic field, we can control orbital angular momentum (OAM). The traditional LLE does not take phase into account, in this paper, we obtain a generalized LLE includes phase case. Our research suitable for precision spectroscopy, optical communication links, and coherent information processing.

Figures (7)

• Figure 1: A high-$Q$ AlN micro-ring generation a Kerr micro-comb pirmoradi2025integrated
• Figure 2: (a) AlN micro-ring near $1550nm$ with parameters are as follows: radius: $\simeq 40\mu m$, thickness: $\sim 1.1\mu m$, $SiO_2$ over-cladding: $\sim 1.5\mu m$, cross section area: $1.3\mu\ m \times 1.0\mu m$. Modulation-instability (MI) gain spectrum $g$ versus mode number $\mu$ at the operating point $\Delta=3.5 m^{-1}$ with the CW background intensity $Y_0=5.6665 mW^2$ (anomalous-dispersion). The shaded regions indicate mode bands with positive gain that seed initial comb sidebands. (b) Continuous-wave (CW) bistability curve $Y$ as a function of detuning $\Delta$ at fixed normalized pump power $X=32.2624 mW^2$, showing the multi-valued steady-state branches used to identify the detuning-scan path toward soliton formation.
• Figure 3: Evolution of the intra-cavity field at slow-time steps (round-trips). Left column: temporal intensity profiles $|F(\tau)|^{2}$ in the fast-time domain; right column: corresponding optical spectra in dB versus mode number. (a,b) Roundtrip $=200$: CW background with small fluctuations and a nearly single-line spectrum. (c,d) Roundtrip $=1600$: emergence of a periodic modulation (MI/Turing pattern) accompanied by initial sidebands. (e,f) Roundtrip $=2300$: multi-soliton state with multiple pulses in the time domain and a broadened comb spectrum. (g,h) Roundtrip $=4000$: a stable single-soliton state featuring a clean isolated pulse and a smooth, broadband comb envelope.
• Figure 4: Temporal evolution of Kerr-comb dynamics during a pump-cavity detuning scan. (a) Normalized intra-cavity power versus slow-time step (roundtrip), showing the transition from a CW background to an unstable regime and subsequent step-like soliton formation. (b) The programmed detuning $\Delta$ as a function of slow time (linear sweep followed by a hold). (c) Spatiotemporal map of the intra-cavity intensity $|F(\tau,t)|^{2}$ over the fast time $\tau$ and the slow time $t$. The dynamical stages including: (i) CW buildup, (ii) modulational-instability-driven patterns/chaos, (iii) soliton switching with stepwise changes in the average intra-cavity power, and (iv) a final stationary soliton state.
• Figure 5: Overview of chaotic teeth-OAM conversion. Top: selected comb lines (a chaotic-state snapshot). Middle: intensity distributions. Bottom: phase profiles with topological charges $\ell=\{-3,-2,-1,1,1,2,3\}$ and comb-tooth modes $\mu=\{-15,-10,-5,0,5,10,15\}$.