Photonics Research, Volume. 11, Issue 11, 1945(2023)

Broadband infinite-Q plasmons enable intense Smith–Purcell radiation

Zi-Wen Zhang1,2, Chao-Hai Du1,2、*, Yu-Lu Lei2, Juan-Feng Zhu3, and Pu-Kun Liu2
Author Affiliations
  • 1Center for Carbon-based Electronics, School of Electronics, Peking University, Beijing 100871, China
  • 2State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Electronics, Peking University, Beijing 100871, China
  • 3Science, Mathematics and Technology (SMT), Singapore University of Technology and Design, Singapore 487372, Singapore
  • show less
    Figures & Tables(11)
    Illustration of intense Smith–Purcell radiation from symmetry-protected BICs. By elaborately customizing the depth-modulated grating, the BICs are constructed from SSPs over a broad frequency range and are then employed to emit intense Smith–Purcell radiation. Compared with the conventional one, the radiation intensity of BIC-enhanced SPR is increased by several orders of magnitude.
    Formation of SSP-based BICs induced by the asymmetry of the depth-modulated grating. When the asymmetry parameter α of the double-period grating gradually increases from zero and then gradually decreases to zero, the evolution of its dispersion relations indicates the formation process of BIC. (a) Structural illustration and dispersion of the conventional SSP when α=0 and p=d. (b) Structural illustration and folded dispersion of SSP when α ≠ 0 and p=L. (c) Structural illustration and folded dispersion including quasi-BIC modes when α ≈ 0 and p=L. (d) Structural illustration and BIC-embedded dispersion when α=0 and p=d.
    Validation of symmetry-protected BIC from SSPs. (a) Dispersions of symmetry-broken grating and plane wave with incident angle φ=30° in the irreducible Brillouin zone, where α ≈ 0 and p=L. (b) Evolution of the probed spectra of |Ez|2 versus asymmetry parameter α. (c) Probed spectra of |Ez|2 of vertical slices in (b). (d) Dependence of the Q factor of SSP resonance on the asymmetry parameter α. (e) Linear dependence between Q factor and 1/α2. (f) Linear dependence between the maximum of the probed intensity of |Ez|2 and 1/α2.
    Broadband presence verification for symmetry-protected BIC. (a), (c) Dispersion relations of symmetry-broken gratings when α=0.2 and α=0, respectively. (b), (d) Evolutions of the probed spectra of |Ez|2 versus incident angle φ when α=0.2 and α=0, individually, where φ is remapped into wavenumber space.
    Validation of intense Smith–Purcell radiation from SSP-based BIC. (a) Dispersions of symmetry-broken grating and 40-keV e-beam, where α ≈ 0 and p=L. (b) Evolution of the radiation intensity IR versus asymmetry parameter α. (c) Radiation spectra of vertical slices in (b). (d) Dependence of the Q factor of radiation intensity on the asymmetry parameter α. (e) Linear dependence between the Q factor of radiation intensity and 1/α2. (f) Linear dependence between the maximum radiation intensity of |Ez|2 and 1/α2. (g) Radiation spectra of regular Smith–Purcell radiation when α=1. (h) Radiation spectra of intensely enhanced Smith–Purcell radiation near the BIC when α=0.001. (i) Field distribution and far-field directivity of the strongest radiation point in (h).
    Broadband enhancement verification for intense Smith–Purcell radiation from SSP-based BICs. (a) Dispersion relations of symmetry-broken gratings and e-beams when α=0.01. (b) Evolutions of the radiation spectra versus voltage U of e-beams, where U is remapped into wavenumber space. (c) Evolutions of radiation spectra versus radiation angles as voltage U alters.
    Demonstration for SSP-based BIC from ultrathin plasmonic metasurface. (a) Schematic drawing of the unit cell of the ultrathin plasmonic metasurface (periodic in z). (b) Dispersions of symmetry-broken ultrathin plasmonic metasurface and plane wave with incident angle φ=0°, where α ≈ 0 and p=L. (c) Evolution of the reflection spectra (zero-order diffraction) versus asymmetry parameter α. (d) Reflection spectra of vertical slices in (c). (e) Dependence of the Q factor of the resonance of ultrathin plasmonic metasurface on the asymmetry parameter α. (f) Linear dependence between the Q factor of the resonance of ultrathin plasmonic metasurface and 1/α2.
    Experimental setups and verification. (a), (b) Plasmonic antennas fabricated in the microwave band with α=0.4 and α=0, respectively. (c), (d) Measured and simulated S parameters of the plasmonic antennas when α=0.4 and α=0, respectively. (e) Experimental setup for testing the plasmonic antennas. (f) Real experimental setup corresponding to (e).
    Illustration and structural description of the plasmonic antenna. (a) Hybrid CPW-SSP plasmonic antenna. (b) Segment of CPW, where the inner conductor is narrow to wide for phase compensation. (c) Matching transition with gradient grooves and flaring ground. (d) Ultrathin plasmonic grating with modulated depths.
    Theoretical and experimental results of plasmonic antenna. (a), (b) Dispersion relations of ultrathin plasmonic metasurface when α=0.4 and α=0, respectively. (c), (d) Simulated evolutions of the reflection spectra versus incident angle φ when α=0.4 and α=0, respectively, where φ is remapped into wavenumber space. (e), (f) Measured evolutions of the S21 spectra versus radiation angle θ when α=0.4 and α=0, respectively, where θ is remapped into wavenumber space.
    Dispersion curves of SSPs under different modulation periods. The dispersion curves and BIC distribution of SSPs with two, three, four, and five propagation periods within one modulation period are shown in (a), (b), (c), and (d), respectively. The solid black lines represent conventional SSPs, while the dashed red lines represent BIC modes resulting from resonant SSPs’ transformation.
    Tools

    Get Citation

    Copy Citation Text

    Zi-Wen Zhang, Chao-Hai Du, Yu-Lu Lei, Juan-Feng Zhu, Pu-Kun Liu, "Broadband infinite-Q plasmons enable intense Smith–Purcell radiation," Photonics Res. 11, 1945 (2023)

    Download Citation

    EndNote(RIS)BibTexPlain Text
    Save article for my favorites
    Paper Information

    Category: Surface Optics and Plasmonics

    Received: Jul. 5, 2023

    Accepted: Sep. 1, 2023

    Published Online: Nov. 3, 2023

    The Author Email: Chao-Hai Du (duchaohai@pku.edu.cn)

    DOI:10.1364/PRJ.499770

    Topics