All-optical reconfiguration of far-field singularities in a photonic-crystal laser

TL;DR

This work introduces an all-optical scheme to reconfigure far-field singularities in a photonic-crystal laser by shaping a pump-induced mesoscopic envelope that localizes a Bloch band into trapped states. The momentum-space singularity of the underlying monopolar bound state in the continuum at the Gamma point remains fixed, while the real-space polarization textures are programmable via the pump geometry, enabling tunable singular-beam emission without altering subwavelength unit-cell geometry. The authors validate the approach with a honeycomb photonic crystal, showing single-spot, two-spot, and multi-spot pumping can generate controlled real-space singularities that scale with the envelope nodal structure, all in quantitative agreement with an envelope-function theory. The method promises ultrafast, reconfigurable structured light in active photonic lattices and could enable applications in quantum simulation, neuromorphic photonics, and programmable laser networks.

Abstract

Singular optics has emerged as an important research area with diverse applications, yet controlling optical singularities in nanophotonic emitters is typically limited by fixed subwavelength geometries and diffraction-limited control. Here, we circumvent this limitation and demonstrate an all-optical mechanism for reconfiguring far-field singularities in a photonic crystal laser. The underlying principle involves optical pumping, which creates a mesoscopic potential landscape whose spatial variations are slow compared to the lattice period. Such a potential localizes a Bloch band into trapped states whose envelope functions, and thus far-field singularity textures, are defined by the pump geometry. Using a honeycomb photonic crystal that supports a symmetry-protected bound state in the continuum, we achieve room-temperature telecom-band lasing with real-space polarisation singularities that are reconfigurable in both number and position, while the intrinsic momentum-space singularity at the $Γ$-point is preserved. The experimental observations align quantitatively with an analytical framework that combines the Bloch mode of the structure and envelope function theory, establishing envelope engineering as a versatile route to programmable singular-light emission in active photonic lattices.

Figures (8)

• Figure 1: Concept: (a) In the absence of pumping, a Bloch resonance of a PhC slab is delocalized over the lattice and radiates into the continuum with a fixed momentum-space far-field pattern $\mathbf{E}_{\mathrm{far}}(\mathbf{k}_\parallel)$. (b) A shaped optical pump injects carriers and creates a smooth in-plane potential that localizes the Bloch band into a trapped state with envelope $F(\mathbf{r}_\parallel)$. In momentum space, the trapped-state emission inherits the Bloch-mode topology but is modulated by the envelope spectrum, $\mathbf{E}^{\mathrm{trap}}_{\mathrm{far}}(\mathbf{k}_\parallel)\propto F(\mathbf{k}_\parallel)\mathbf{E}_{\mathrm{far}}(\mathbf{k}_\parallel)$. (c) Schematic of the all-optical control of the photonic crystal laser with singularities. The far-field singularities in the real-space can be controlled by the optical pump.
• Figure 2: The fabricated photonic crystal device and its dispersion:(a) Schematic of the fabricated honeycomb PhC slab. The lattice has a period $\Lambda = a\sqrt{3}$ with lattice constant $a = 445~\mathrm{nm}$, hole diameter $d = 335~\mathrm{nm}$, and total membrane thickness $t = 240~\mathrm{nm}$. (b) Atomic-force-microscopy (AFM) image of the fabricated surface. (c) Numerically computed band structure using Legume, showing the lowest-energy band that hosts a monopolar symmetry-protected BIC at the $\Gamma$-point. The band is nearly isotropic and displays a negative effective mass. (d) Experimental angle-resolved photoluminescence along the $\Gamma\!-\!\text{K}$ and $\Gamma\!-\!\text{M}$ directions, exhibiting the vanishing radiative loss at $\Gamma$ which is characteristic of the BIC. The dashed line represents a parabolic fit to the measured dispersion.
• Figure 3: Lasing characterization and farfield measurements for single pump spot:(a) Schematic of single spot pumping on the PhC with spot size $\sigma$. The pump creates a potential $V(\mathbf{r}_\parallel)$, which induces a trapped-state envelope function $F(\mathbf{r}_\parallel)$. (b) Experimental energy-momentum dispersion along $k_x$ below ($p<p_{th}$), around ($p \sim p_{th}$) and above threshold ($p>p_{th}$) pump power density ($p$) for spot waist $\sigma_1= 3.2$µm . The fundamental mode is fitted with a parabola with $\alpha = -13.4$ meV·µm$^2$, and the confinement energy ($\Delta$E) is the difference between the trapped mode energy and energy at $\Gamma$-point (E$_{\Gamma})$. (c) Total integrated trapped-state intensity vs pump power density $p$ for three pump waists $\sigma_1=3.2$µm, $\sigma_2= 7.1$µm, $\sigma_3= 11.1$ µm. (d) Confinement energy $\Delta$E vs pump power for the three spot waist. (e–h) Far-field characterization of the trapped state above threshold for $\sigma=$3.2µm . Panels show (left) experimental momentum-space and real-space intensity and polarization textures and (right) corresponding analytical predictions from the envelope-function model. The yellow stars mark the polarization singularities. The theoretical results were calculated with the parameter $V_0=$ 4.8 meV. [Refer Extended Fig.\ref{['fig:Extended_Figure_1']} for the polarization resolved farfield lasing images.]
• Figure 4: Nearfield maps for single pump:(a) Large-area SNOM (left panel), analytical model (middle), and FDTD numerical (right) of near-field map of the trapped state under a single Gaussian pump. The white dashed line box represents the measurement region. (b) Zoomed-in near-field amplitude showing the fast spatial oscillations of the Bloch resonance on the scale of the photonic crystal lattice. (c) Polarization-resolved mapping of the in-plane electric field.
• Figure 5: Two-spot pumping and the demonstration of reconfigurable singularities in the farfield:(a) Schematic of two trapped states induced by a double pump spot with varying separation distance L with fixed spot waist $\sigma$= 3.25µm. (b) Energy-momentum dispersion along $k_x$ for various $L$ (14.9, 11.9, 10.4, 7.2µm), decreasing from top panel (14.9µm) to the bottom panel (7.2µm). Far-field patterns (for $L$=7.2µm) in momentum and real space for both Bonding (d) and Anti-bonding (e) modes, and the experimental results (left) are supported by the analytical/theory results (right). Singularities are denoted by yellow stars. The theoretical results are calculated with parameter $V_0=$4.6 meV. [Refer fig.\ref{['fig:Extended_Figure_2']} for the corresponding polarization resolved farfield lasing images.]