Metasurface-enhanced lasers can generate visible high-purity orbital angular momentum (OAM) states up to ℓ=100\ell=100 and can lase simultaneously on two spin–orbit (SO) states as far apart as Δℓ=90\Delta\ell=90, but the intracavity physics behind these observations was left unexplained by the original demonstration and remains unresolved. Two phenomena in particular lack any established mechanism or direct measurement: the reported mutual coherence of two lasing OAM components that overlap inside the gain medium yet form concentric annuli with no spatial overlap at the output, and the splitting of the intracavity vortex structure inside the laser crystal. The open problem is to elucidate the underlying dynamics and limits of these intracavity phenomena — establishing whether these two components are mutually coherent, explaining its origin against mode competition, accounting for vortex splitting during propagation through the nonlinear gain crystal and the intracavity metasurface, and determining how the achievable OAM separation, superposition purity, and power scale with gain volume and metasurface size.

Background

Light carries angular momentum in two forms: spin angular momentum (circular polarization, left or right) and orbital angular momentum (OAM), which corresponds to a helical transverse phase eiℓϕe^{i\ell\phi} with integer topological charge (helicity) ℓ\ell. A laser mode carrying OAM is close to a Laguerre–Gaussian (LG) mode, an annular beam indexed by the azimuthal number ℓ\ell and a radial number pp; the "purity" of an OAM laser mode is the fraction of output power residing in the intended (ℓ,p)(\ell,p) component, with p=0p=0 being the radial ground state. In ordinary lasers, intracavity OAM generation relies on spin–orbit (SO) coupling: elements that convert circular spin into OAM through the geometric (Pancharatnam–Berry) phase map each circular polarization onto OAM of opposite helicity, so the two intracavity angular-momentum components are conjugate and the output is restricted to symmetric superpositions on the higher-order Poincaré sphere, which generalizes the polarization Poincaré sphere to combined polarization–OAM states. Sroor et al. (2020) broke this restriction by placing a dielectric TiO2_2-nanopost metasurface (a "J-plate": a subwavelength-patterned phase element implementing an arbitrary spin-to-OAM map via a combination of propagation phase and geometric phase) inside the frequency-doubled green cavity of a gain-switched Nd:YAG laser, where a KTP crystal provides intracavity second-harmonic generation converting 1,064 nm to 532 nm so that the metasurface operates at a visible wavelength. The device produced OAM states up to ℓ=100\ell=100 with roughly 90% of the power in the p=0p=0 component, and simultaneous lasing on two independently chosen SO states as much as Δℓ=90\Delta\ell=90 apart (for example the superposition of ∣H,10⟩|H,10\rangle and ∣V,100⟩|V,100\rangle, horizontal and vertical polarization carrying OAM 10 and 100). The authors reported, without explaining, two intriguing intracavity observations: the two lasing OAM components share the same gain region inside the crystal but, after the metasurface, occupy concentric annular rings with no spatial overlap at the output, yet appear to lase coherently; and the vortex structure splits inside the laser medium. Notably, the authors' own account of the cavity operating principle was subsequently contested in a Matters Arising by Wen, Cadusch, Fang and Crozier (2021), and in their reply the authors conceded that the reciprocity argument they used does not hold for propagation-phase metasurfaces and corrected the corresponding statements in the main text and Supplementary Information. The physical explanation of the intracavity dynamics is therefore not only missing but was shown to be partly incorrect, while the coherence evidence in the original work is circumstantial: the pump is pulsed, the detector integrates over many pulses, and no temporal or spectral analysis distinguished genuine coherent superposition from pulse-to-pulse mode hopping, nor was the purity of the superposition states measured in the LG basis. Related context: the same group outlined a general inverse-design framework for structured-light laser cavities that maximizes pump overlap for higher power (Scholes, Sroor, Ait-Ameur, Zhan and Forbes, 2020), and a recent field review (Forbes, Mkhumbuza and Feng, 2024) surveys OAM lasers from bulk solid-state devices to on-chip microlasers while noting that the physics of intracavity coherence in such sources is what ultimately bounds their capabilities.

Problem Statement

Elucidate the underlying dynamics and limits of the intracavity phenomena of the visible metasurface orbital-angular-momentum (OAM) laser demonstrated by Sroor et al. (2020), as left open by that work and not resolved since. Specifically: (1) establish whether the two lasing spin–orbit components with widely separated OAM (up to Δℓ=90\Delta\ell=90) are mutually coherent, separating genuine coherent superposition from pulse-to-pulse mode hopping — and if so, explain the origin and stability of that coherence against mode competition, given that the two modes overlap inside the gain medium but their output annular rings have no spatial overlap after the metasurface; (2) explain the observed vortex splitting inside the laser medium, that is, how the intracavity vortex structure transforms as the field propagates through the nonlinear gain crystal and the intracavity metasurface, including which symmetry breaking, thermal, or nonlinear mechanism produces it; and (3) determine the limits of these phenomena, including the purity of the lasing superposition states in the Laguerre–Gaussian basis, the maximum OAM separation that can lase coherently, and how these quantities scale with gain volume, metasurface aperture, and output power. The architectural goals named in the same source — scaling to bulk high-power implementations while preserving metasurface spatial resolution and damage threshold, monolithic on-chip miniaturization, and fast switching of the lasing spin–orbit state (for example via pump-polarization control with a suitably chosen nonlinear crystal) — are complementary engineering targets that this elucidation informs, but the scientific question to be answered is the intracavity dynamics and its limits. The question comprises these three jointly posed parts. The coherence in part (1) must be established with evidence that discriminates a mutual coherent superposition from pulse-to-pulse mode hopping—when no direct data can be produced, a validated discriminating protocol can settle it without new data; if part (1) concludes that the components are not mutually coherent, part (3) is to be answered by the limits (maximum usable OAM separation, superposition purity, and their scaling) that such a source can still reach.

References

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