Enhanced Polarization Locking in VCSELs

Zifeng Yuan; Dewen Zhang; Lei Shi; Yutong Liu; Aaron Danner

physics.opticsApr 2, 2026

Enhanced Polarization Locking in VCSELs

Authors: Zifeng Yuan, Dewen Zhang, Lei Shi, Yutong Liu, Aaron Danner

Organizations: National University of Singapore, Department of Electrical and Computer Engineering, Singapore

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.

Figures & tables

Figure 1: (a) Experimental schematic illustrating the free-space OIL setup. ML: master laser, SL: slave laser, LP: linear polarizer, HWP: half-wave plate, BS: beam splitter, OSA: optical spectrum analyzer. (b) Poincaré sphere showing the polarization states of the ML, the SL unlocked and locked. (c) Spectral of the ML under varying operating conditions. (d) Spectral of the SL in the unlocked and locked states. The peak intensity has been shifted to 0 dB.

Figure 2: OIL performance for VCSELs with tailored aperture designs. (a)–(g) correspond to: (a) square aperture; (b)–(e) cruciform aperture (1:0.7 aspect ratio, rotated by 0°, 30°, 60°, and 90°); (f)–(g) cruciform aperture (1:0.6 aspect ratio, without and with 90° rotation). The first column shows scanning electron microscope images, the second column presents LI curves for horizontal and vertical polarizations, and the remaining columns display locking diagrams at low current (LC), switching point (SP, omitted for non-switchable VCSELs), and high current (HC). The locking diagrams illustrate the absolute polarization difference, $\Delta\theta=|\theta_{\text{SL}}-\theta_{\text{ML}}|$ , where $\theta_{\text{SL}}$ and $\theta_{\text{ML}}$ are the absolute azimuths of SL and ML measured by the polarimeter. A dashed line indicates the boundary between unlocked and locked states. The minimum injection power required for successful polarization locking is highlighted.

Year	Minimum injection power	Locking range	Wavelength (nm)	SL Laser type	Ref.
$\cdots$	$3.6\,\mu\text{W}$	$\Delta f=(-10,+10)\,\text{GHz}$	838.25	VCSEL	This work
2024	$2.5\,\mu\text{W}$	$\Delta f=-12.46\,\text{GHz}$ ∗	850	VCSEL	[ 26 ]
2023	$94\,\mu\text{W}$	$\Delta f=-23.58\,\text{GHz}$ ∗	976.77	VCSEL	[ 59 ]
2023	$-19\,\text{dB}$	$\Delta f=(0,+30)\,\text{GHz}$	1547	VCSEL	[ 60 ]
2017	$25.1\,\mu\text{W}^{*}$	$\Delta f=+0.5\,\text{GHz}^{*}$	1540	VCSEL	[ 12 ]
2017	$11\,\mu\text{W}^{*}$	$\cdots$	850	VCSEL	[ 61 ]

Table 1: Summary of OIL performance from some recent papers (2000 to present).

Symbol	Value
$\gamma_{a}$	$0$ / $-30$	GHz
$\gamma_{s}$	$50$	GHz
$\gamma_{p}$	$2$	GHz
$\gamma$	$1$	GHz
$\eta$	$[1.1,3.4]$
$\kappa$	$300$	GHz

Table 2: SFM parameters.

Figure 3: VCSEL polarization dynamics under different amplitude anisotropy conditions: (a)–(c) for $\gamma_{a}=0$ and (d)–(f) for $\gamma_{a}=-30~\mathrm{GHz}$ . (a), (d) Evolution of polarization states of a solitary VCSEL with increasing electrical pumping term ( $\eta$ ). For $\gamma_{a}=0$ , the polarization switches from $x$ -dominant (black curve) to $y$ -dominant (red curve) as $\eta$ increases, while for $\gamma_{a}=-30~\mathrm{GHz}$ , the polarization remains $x$ -dominant. (b), (e) Both VCSELs are biased at $\eta=1.1$ , and the ML emits linearly polarized light at 45° injected into the SL at $t=40~\mathrm{ns}$ . (c), (f) Locking maps showing $\Delta\theta=|\theta_{\text{SL}}-\theta_{\text{ML}}|$ for varying $E_{\text{inj}}$ and frequency detuning ( $\Delta\omega$ ) at $\eta=1.1$ .

Figure 4: VCSEL OIL performance under different bias current conditions for $\gamma_{a}=0$ , with locking maps shown at $\eta=1.2$ (a) and $\eta=3.4$ (b). Below the locking maps, the linear polarization angles of the SLs under OIL are shown for certain $E_{\text{inj}}$ values, corresponding to the black-boxed regions in the locking maps. At $\eta=3.4$ , the polarization dynamic of the VCSEL under OIL with $E_{\text{inj}}=0.3$ and $\Delta\omega=0$ is illustrated in the top-right inset of (b).

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Photonic Computing

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We introduce a cavity-enhanced optical architecture for collective quantum processing in which logical qubits are encoded in the polarization subspace of recirculating intracavity modes. The physical carrier and computational degree of freedom are explicitly separated: harmonic cavity bundles provide a stable resonant substrate, while programmable polarization transformations implement single-qubit operations. A polarization-selective nonlinear interaction in the entanglement region generates tunable controlled-phase gates, enabling a universal gate set. A parameter-scaling analysis shows that order-unity conditional phases are attainable in centimeter-scale cavities using experimentally accessible solid-state nonlinear media, without requiring extreme nonlinear coefficients, millisecond photon lifetimes, or sub-hertz laser stabilization. The results indicate that resonant recirculation provides a physically plausible platform for cavity based collective quantum architectures.

Abstract

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