Spatial Information Lasing Enabled by Full-$k$-Space Bound States in the Continuum

Spatial Information Lasing Enabled by Full- $k$ -Space Bound States in the Continuum

Ruoheng Chai, Wenwei Liu, Zhancheng Li, Yuebian Zhang, Haonan Wang, Hua Cheng, Jianguo Tian, and Shuqi Chen

Phys. Rev. Lett. 132, 183801 – Published 30 April 2024

Abstract

Optical amplification and massive information transfer in modern physics depend on stimulated radiation. However, regardless of traditional macroscopic lasers or emerging micro- and nanolasers, the information modulations are generally outside the lasing cavities. On the other hand, bound states in the continuum (BICs) with inherently enormous $Q$ factors are limited to zero-dimensional singularities in momentum space. Here, we propose the concept of spatial information lasing, whose lasing information entropy can be correspondingly controlled by near-field Bragg coupling of guided modes. This concept is verified in gain-loss metamaterials supporting full- $k$ -space BICs with both flexible manipulations and strong confinement of light fields. The counterintuitive high-dimensional BICs exist in a continuous energy band, which provide a versatile platform to precisely control each lasing Fourier component and, thus, can directly convey rich spatial information on the compact size. Single-mode operation achieved in our scheme ensures consistent and stable lasing information. Our findings can be expanded to different wave systems and open new scenarios in informational coherent amplification and high- $Q$ physical frameworks for both classical and quantum applications.

Received 15 September 2023
Accepted 3 April 2024

DOI:https://doi.org/10.1103/PhysRevLett.132.183801

Physics Subject Headings (PhySH)

Metamaterials Nanophotonics Photonic crystals

Photonic crystal lasers

Atomic, Molecular & Optical

Authors & Affiliations

Ruoheng Chai¹, Wenwei Liu^1,*, Zhancheng Li¹, Yuebian Zhang ¹, Haonan Wang¹, Hua Cheng ^1,†, Jianguo Tian¹, and Shuqi Chen ^1,2,3,‡

¹The Key Laboratory of Weak Light Nonlinear Photonics, Ministry of Education, School of Physics and TEDA Institute of Applied Physics, Nankai University, Tianjin 300071, China
²School of Materials Science and Engineering, Smart Sensing Interdisciplinary Science Center, Nankai University, Tianjin 300350, China
³The Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China

^*Corresponding author: wliu@nankai.edu.cn
^†Corresponding author: hcheng@nankai.edu.cn
^‡Corresponding author: schen@nankai.edu.cn

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Issue

Vol. 132, Iss. 18 — 3 May 2024

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Images

Figure 1
(a) Schematic of spatial information lasing by a full- $k$ BIC resonator. Lasing wave fronts and, thus, information can be engineered by modifying the lasing entropy inside the full- $k$ BIC resonator. (b) Comparison between conventional $k$ -sensitive BICs (light red line, conventional BICs; light blue line, merging BICs) and full- $k$ -space BICs (deep red and deep blue lines). (c) Schematic of asymmetric couplings in the PTMMs. The CFCs combined with the momentum of seeding injection $k_{seeding}$ engineer the Bragg couplings $h_{\pm n}$ , which determine the far-field Fourier components $E_{rad}^{0, \dots, m}$ and, thus, the entropy $S$ . The thickness and the period of the PTMMs are $t$ and $a = 2 t$ , respectively. (d) Simulated band diagram and radiation channel chart of uncoupled guided modes. The bands are folded above the light line by an assumed period $a$ of a homogeneous slab with $ε = 4$ . Light yellow (pink) region, 0th-order (0th- and $\pm 1$ st-order) diffraction channels; dark red (dark blue) lines, FGMs (BGMs).
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Figure 2
(a) Theoretical $Q$ factors and (b) Simulated band dispersions of the sinusoidal PTMMs with the 1st-order CFC. The uniform term $ε_{0}$ is fixed at 4.0, and the 1st-order term $ε_{1}$ is 0.4. Inset graphs show identical eigenstates at high-symmetry $k$ points, implying EPs. Colored regions represent different diffraction channels. Light blue, red, blue, and magenta lines, bands 1–4, respectively; red stars, EP-BIC coincidence points. (c) Simulated $Q (k_{x}, k_{y})$ of band 1 versus $\arctan (1 / | V_{0} |)$ , where $V_{0}$ denotes the imaginary to real part ratio of the PT-modulation depth.
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Figure 3
(a) Bands and $Q$ factors of full- $k$ quasi-BICs supported by the D-PTMM (red, band 2; blue, band 3; dots, simulations; lines, theory). (b) Simulated spectrum of the total radiation energy $I$ . The pink-hatched region highlights lasing zones. (c) Simulated mode profiles of band 3 at the X point at off resonance (i) and on resonance (ii) with a limited-spot Gaussian beam injection $E_{seeding}$ (waist radius $w_{0} = 5 λ_{0}$ , where $λ_{0}$ is the incident wavelength). $R_{0, - 1}$ ( $T_{0, - 1}$ ) are 0th- and $- 1$ st-order reflective (transmissive) lasing channels. (d) Calculated lasing information entropy $S$ of band 3. Information entropy of Hermite-Gaussian envelopes ( ${HG}_{0}$ , ${HG}_{1}$ , and ${HG}_{2}$ ) with cavity size $L = 100 a$ is indicated by gray surfaces.
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Figure 4
Bifurcation diagrams calculated by the laser rate equations, depicting the steady-state maximum and minimum of the amplitude $| E (t) |$ versus the normalized pumping power $P$ ( $P = 1$ at the threshold) in the case of (a) band mode competitions and (b) $k$ -mode competitions. $κ_{\to} / κ_{\leftarrow}$ ( $κ_{ext 2} / κ_{ext 1}$ ) is the asymmetric mode (external) coupling factor in the rate equations.
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