Deterministic Control of Extreme Events in a semiconductor VCSEL via Polarization-Engineered Optical Feedback

TL;DR

Deterministic control of optical extreme events in a VCSEL is demonstrated by exploiting polarization dynamics under polarization-selective external feedback. The method uses a $\lambda/2$-waveplate to tune the nonlinear interaction between TE and TM modes, producing heavy-tailed TM fluctuations that arise from deterministic energy exchange with TE. The results show strong bipolar TE–TM correlations and long-range memory in event timing, with event rate and intensity tunable non-monotonically by the waveplate angle $\theta$. This platform enables systematic studies of extreme events in dissipative nonlinear photonics and points to practical uses in optical sensing, random-number generation, and secure communications.

Abstract

Extreme events, or rogue waves, are high-amplitude, rare occurrences that emerge across diverse physical systems and often defy conventional statistical predictions. While optical systems provide a controlled setting for studying these phenomena, achieving deterministic control over their generation remains challenging. Here, we demonstrate a novel approach to induce and precisely modulate extreme events in a semiconductor VCSEL using polarization-controlled optical feedback. By integrating a $λ$/2-waveplate into a polarization-selective external cavity, we regulate the nonlinear interaction between TE and TM modes. This setup triggers high-intensity, heavy-tailed fluctuations in the TM mode, exhibiting clear signatures of extreme events. We show that these events arise from deterministic energy exchange between modes, as evidenced by strong bipolar correlations and long-range temporal memory. The waveplate angle serves as an effective external parameter, enabling non-monotonic tuning of the event rate, intensity, and temporal clustering. Our study establish a platform for exploring extreme events in dissipative systems, with implications for nonlinear photonics and optical technologies.

Figures (6)

• Figure 1: Experimental setup and fundamental characterizations: (a) Experimental setup. Coll., Collimator; BS, non-polarizing beamsplitter; PBS$_1$ and PBS$_2$, polarizing beamsplitters; M$_1$, M$_2$ and M$_3$, high-reflectivity mirrors; $\lambda$/2, half-wave plate; ISO$_1$ and ISO$_2$, optical isolators; PD$_1$ and PD$_2$, fast photodetectors; PM, power meter. (b) Temporal dynamics within 10 ns of the TE and TM modes of the VCSEL under the condition of free running and J = 3.00 mA. (c) the corresponding RF spectra of the TE and TM modes. (d) Intensity distribution histograms of the TE and TM modes.
• Figure 2: Dynamical signatures of polarization mode competition under optical feedback. (a) Measured optical feedback power as a function of the $\theta$/2-waveplate rotation angle ($\theta$). The orange circle marks the operating point ($\theta = 30^\circ$, $P_{fb} \approx 82 \mu W$) for the subsequent analysis. (b) RF spectra of the TE (blue) and TM (red) modes under orthogonal polarization feedback. (c) Autocorrelation functions of the TE (blue) and TM (red) modes. (d) Cross-correlation function between the TE and TM modes.
• Figure 3: Spatiotemporal dynamics reveal distinct behaviors of TE and TM modes under optical feedback. The horizontal axis represents time over one period ($0-10.2$ ns), and the vertical axis is the roundtrip number. (a) TE mode; (b) TM mode.
• Figure 4: Characterization of extreme events: (a) Time series of the TE (blue) and TM (red) modes, showing high-amplitude chaotic pulses in the TM mode correlated with in-phase or anti-phase counterparts in the TE mode. (b) Log-linear intensity histograms for both modes. The dash line indicates the threshold of the extreme events accordingly to the definition given in the text. Green columns indicate the extreme events. (c) Distribution of time intervals between extreme events, showing broad timing variability. (d) Pie chart quantifying the phase relationship between TE and TM modes during extreme events.
• Figure 5: Controlling extreme event statistics via feedback polarization tuning. (a)-(c), Optimal regime at $\theta = 30^\circ$: (a), Intensity probability distribution of the TM mode showing a pronounced heavy tail. Extreme events, defined as intensities exceeding $\langle I\rangle+8\sigma_{I}$, are highlighted in green. (b), Distribution of time intervals between consecutive extreme events, displaying concentrated timing. (c), Phase correlation analysis revealing balanced in-phase and anti-phase relationships with the TE mode. (d)-(f), Detuned regime at $\theta = 40^\circ$: (d), Intensity distribution showing reduced heavy-tail statistics. (e), Broader distribution of inter-event intervals indicating more sporadic timing. (f), Shifted phase correlation suggesting perturbed energy exchange symmetry. (g)-(i), Detuned regime at $\theta = 50^\circ$.