Enhanced Polarization Locking in VCSELs

Abstract: While optical injection locking (OIL) of vertical-cavity surface-emitting lasers (VCSELs) has been widely studied in the past, the polarization dynamics of OIL have received far less attention. Recent studies suggest that polarization locking via OIL could enable novel computational applications such as polarization-encoded Ising computers. However, the inherent polarization preference and limited polarization switchability of VCSELs hinder their use for such purposes. To address these challenges, we fabricate VCSELs with tailored oxide aperture designs and combine these with bias current tuning to study the overall impact on polarization locking. Experimental results demonstrate that this approach reduces the required injection power (to as low as 3.6 μW) and expands the locking range. To investigate the impact of the approach, the spin-flip model (SFM) is used to analyze the effects of amplitude anisotropy and bias current on polarization locking, demonstrating strong coherence with experimental results.

• The paper shows that tailored oxide aperture designs combined with bias current optimization significantly reduce the injection power needed for robust polarization locking.
• The study finds that minimizing intrinsic amplitude anisotropy enables effective polarization switching, lowering the threshold from 248µW to as little as 3.6µW over a ±10 GHz range.
• The spin-flip model analysis corroborates experimental results, offering practical insights for energy-efficient, scalable VCSEL-based photonic computation.

Enhanced Polarization Locking in VCSELs: Aperture Engineering and Bias Optimization

Introduction

Optical injection locking (OIL) in vertical-cavity surface-emitting lasers (VCSELs) is a central technique in high-frequency photonics, allowing synchronization of a slave laser (SL) to a master laser (ML) for frequency, phase, and polarization control. While OIL's role in frequency and phase stabilization is well-known, polarization dynamics—particularly polarization locking via OIL—have recently garnered significant attention due to their application potentials in photonic Ising machines and optical neural networks, where robust and energy-efficient polarization encoding is required. A major obstacle in practical realization is the inherent amplitude anisotropy of VCSELs, which leads to dominant and resistant polarization states, impeding effective polarization locking and requiring high injection powers.

Experimental Approach: Aperture Design and Bias Control

This study systematically addresses the intrinsic polarization locking limitations of VCSELs by engineering the oxide aperture geometry and optimizing the bias current. Seven distinct aperture structures were fabricated using a GaAs-based wafer with DBR mirrors and selective oxidation, including square and several cruciform geometries with varying aspect ratios and angular orientations. These aperture designs allow targeted control of amplitude anisotropy between the orthogonal polarization directions. The experimental setup features tunable ML/SL combinations, polarization-resolved light injection, and comprehensive polarization state/spectral measurements.

The role of bias current is also interrogated, with tests performed at three regimes: just above threshold (LC), at the current-induced polarization switching point (SP), and at high-current (HC, 10 mA). Polarization locking behavior was evaluated versus injection power and frequency detuning in each bias regime.

Figure 2: OIL performance of VCSELs with distinct tailored apertures, with SEM images, polarization-resolved LI curves, and locking diagrams as a function of injection power and detuning.

Results: Polarization Locking Enhancement by Aperture and Bias Tuning

Aperture-Induced Anisotropy Control

VCSELs with high amplitude anisotropy (e.g., square or cruciform apertures aligned with the gain anisotropy direction) exhibit stable, unswitchable polarization states, requiring high injection power (>300~µW) for polarization locking. In contrast, engineered apertures that minimize intrinsic anisotropy (e.g., cruciform rotated by 90° so the long arm is vertical) demonstrate unstable, switchable polarization states with dramatically lower locking thresholds. For these devices, polarization can be switched with increasing bias, and OIL achieves robust locking at reduced injection power and over a wider detuning range.

As the bias is decreased from the HC regime to the LC regime, a significant reduction in minimum injection power for locking is observed—from 248~µW at HC to as low as 3.6~µW at LC. Furthermore, the locking range is substantially broadened in switchable devices, illustrating the efficacy of aperture engineering combined with bias optimization.

Comparative OIL Performance

Relative to the state-of-the-art, the method achieves competitive injection power thresholds while maintaining a broad locking range, a regime mostly unattainable by edge-emitting and alternative VCSEL OIL approaches. Notably, the approach delivers a minimum injection power of 3.6~µW for robust polarization locking across a detuning range of ±10 GHz, optimizing both energy efficiency and operational tolerance.

Spin-Flip Model Analysis

The polarization dynamics are analyzed using the spin-flip model (SFM), incorporating spin populations ($n^+$, $n^-$), amplitude anisotropy ($\gamma_a$), and injection parameters. Simulations corroborate that systems with minimized $\gamma_a$ demonstrate polarization switching under increasing pumping current, while those with strong $\gamma_a$ are polarization-fixed. Under OIL with orthogonally polarized injection, only VCSELs with low anisotropy realize locking; strong-anisotropy devices are resilient to polarization capture by the injected field.

Increasing the pump current in the low-anisotropy case (fixed $\gamma_a = 0$) narrows the locking range and increases the required injection power, matching trends in the experimental data. At high bias, strong ML injection (high $E_{\text{inj}}$) eventually induces polarization locking, though with reduced stability, as evidenced by polarization oscillations.

(Figure 3)

Figure 1: SFM-based polarization dynamics under varying amplitude anisotropy; locking occurs only for low-anisotropy and is suppressed when the intrinsic gain anisotropy dominates.

(Figure 4)

Figure 3: Locking maps and polarization angle statistics from SFM, demonstrating reduced locking range and increased injection threshold as bias (pumping $\eta$) increases, even when $\gamma_a = 0$.

Implications and Future Directions

This work directly targets practical challenges in implementing polarization-encoded photonic computation, including Ising solvers and optical neural networks. By providing a path to lasing elements that require lower injection energies for polarization switching, large-scale arrays—where shared or distributed ML power is required—become feasible. This is particularly impactful in integrated systems, where overall energy budget and robustness across fabrication tolerances are critical.

Theoretically, the results delineate the boundary conditions for OIL-based polarization control, linking physical aperture geometry to the interplay of amplitude anisotropy, bias current, and locking efficacy. This allows precise design tradeoffs for VCSEL-based computational and communication systems.

Future research will likely extend aperture engineering to non-conventional or active tuning geometries (e.g., MEMS-controlled anisotropy), explore further reduction of locking thresholds via hybrid photonic structures such as metasurfaces, and integrate polarization control with on-chip photonic interconnects. Expansion into coherent optical computing architectures and advanced imaging modalities can be anticipated, leveraging the improved stability and efficiency of polarization locking demonstrated.

Conclusion

Tailored oxide aperture designs in VCSELs, in conjunction with bias current optimization, provide a direct, effective method to enhance polarization locking in OIL by suppressing amplitude anisotropy and fostering polarization switchability. Experiment and spin-flip model analysis confirm that minimizing intrinsic anisotropy and reducing bias current lowers the minimum injection power required for robust polarization locking and expands the frequency detuning tolerance. These advances have immediate impact for polarization-based photonic computation and pave the way for more scalable and energy-efficient VCSEL array systems.