Spectral phase singularity and topological behavior in perfect absorption

Letter

Spectral phase singularity and topological behavior in perfect absorption

Mengqi Liu, Weijin Chen, Guangwei Hu, Shanhui Fan, Demetrios N. Christodoulides, Changying Zhao, and Cheng-Wei Qiu

Phys. Rev. B 107, L241403 – Published 8 June 2023

Abstract

Perfect absorbers, which can achieve total absorption of all incoming energy, have been extensively studied in the last decades for various important technologies in general wave systems. Here, we show that perfect absorption (PA) is generically associated with topological spectral phase singularity (SPS), carrying conserved and tunable quantized topological invariants in spectral space. The order of topological invariant $\tilde{v}$ depends on the number of degenerate outgoing channels. Two commonly studied absorbers, mirror-backed and all-dielectric structures, are reexamined from a topological perspective to reveal the generation, evolution, and annihilation of SPSs with $\tilde{v} = \pm 1$ or even high orders (i.e., $\tilde{v} = \pm 2, \pm 4$ ). A strategy based on charge conservation of SPSs to design dual-band perfect absorbers has been established. Our findings establish the topological origin of the robust existence of PA. More broadly, in this letter, we highlight topology as the fundamental property of conventional scattering behaviors. This insight could lead to opportunities in applications such as biosensing, topological metasurfaces, and micro/nano thermal radiation.

Received 13 September 2022
Revised 25 April 2023
Accepted 26 April 2023

DOI:https://doi.org/10.1103/PhysRevB.107.L241403

Physics Subject Headings (PhySH)

Light-matter interaction Nanophotonics Optical & microwave phenomena Topological effects in photonic systems

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Mengqi Liu ^1,2, Weijin Chen², Guangwei Hu ³, Shanhui Fan ³, Demetrios N. Christodoulides⁴, Changying Zhao ^1,*, and Cheng-Wei Qiu ^2,†

¹Institute of Engineering Thermophysics, MOE Key Laboratory for Power Machinery and Engineering, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
²Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117583, Singapore
³Department of Electrical Engineering, Ginzton Laboratory, Stanford University, Stanford, California 94305, USA
⁴Center for Research and Education in Optics and Lasers (CREOL), The College of Optics and Photonics, University of Central Florida, Orlando, Florida 32816, USA

^*changying.zhao@sjtu.edu.cn
^†chengwei.qiu@nus.edu.sg

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Issue

Vol. 107, Iss. 24 — 15 June 2023

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Images

Figure 1
Topological nature of perfect absorption (PA) points associated with spectral phase singularities (SPSs). (a) Schematic of the multiport multimode system. The subscripts U and D denote the upper and downside channels. (b) The mirror-backed one-port system, along with (c) its typical reflection phase in parameter space. (d)–(g) Possible relations between radiative loss $Γ_{e}$ and material loss $Γ_{α}$ at $ω = ω_{0}$ : linear type for all $Γ_{α}$ ; linear type for $Γ_{e}$ in (d) and hyperbolic type for $Γ_{e}$ in (e)–(g). The $s p$ could represent the system parameter, like thickness, period, or incident angle.
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Figure 2
High-order perfect absorption (PA)-related spectral phase singularities (SPSs). (a) Schematic of the two-port system. (b) Evolution trajectory of reflection-type SPSs ( $r = 0$ , dashed line) and transmission-type SPSs ( $t = 0$ , full line). The red pentagram denotes the position of PA point. The topological charges are marked in different projection planes: $ω - Γ_{e}^{a} / Γ_{α}^{a}$ space (blue) and $ω - Γ_{e}^{s} / Γ_{α}^{s}$ space (red), along with (c) the corresponding reflection or transmission phase. (d) Generation rules of high-order SPSs viewing the phase of $φ_{r \times t} = arg (r \times t)$ in $ω - Γ_{e}^{a} / Γ_{α}^{a}$ space (left) and $φ_{r / t} = arg (r / t)$ in $ω - Γ_{e}^{s} / Γ_{α}^{s}$ space (right).
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Figure 3
Topological behaviors of spectral phase singularities (SPSs) in metal-insulator-metal (MIM) perfect absorbers. (a) Schematic of the MIM absorber, composed of a bottom Au mirror, $Si O_{2}$ interlayer, and Au gratings. The $p$ polarization ( $E_{x}, H_{y}, k_{z}$ ) is considered. (b) Reflection phase ( $φ_{r_{0}}$ ) viewing in $λ - H$ space. The +1 SPS is denoted with a red star, along with (c) the corresponding perfect absorption (PA) spectrum ( $H = 18$ nm). (d) A design principle for dual-band perfect absorbers based on the charge evolution of topological phase singularity: (left) no PA with annihilated SPSs and (right) dual-peak PA points with two revival SPSs. (e) Typical cases for presenting the evolution of SPSs in $λ - p$ space, at $H = 25$ nm and different $h$ . (f) Absorption spectra with dual PA peaks for cases with different $H$ were obtained based on the method in (d). The circles in white or gray represent PA points associated with −1 or +1 SPSs in $λ - p$ space.
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Figure 4
Topological behaviors of high-order spectral phase singularities (SPSs) in all-dielectric perfect absorbers. (a) Schematic of the all-dielectric absorber, composed of periodic a-Si nanodisks sitting on a glass substrate. (b) Absorption (black), reflection (blue), and transmission (red) spectra, together with the phase $φ_{r} (v = - 1)$ and $φ_{t} (v = + 1)$ in $λ - L$ space. The $λ_{0}$ denotes the wavelength of PA point. (c) Generation of high-order SPSs in the phase of $arg [(r_{p} / t_{p}) \times (r_{s} / t_{s})]$ changing with different $p_{x}$ at a fixed $d = 160$ nm. (d) Three typical phases of $arg (r_{p} / t_{p})$ : (top) $p_{x} = 290$ nm, $d = 170$ nm; (middle) $p_{x} = 270$ nm, $d = 160$ nm; and (bottom) $p_{x} = 250$ nm, $d = 150$ nm. (e) Topological robustness of high-order SPSs: absorption spectra with PA peaks as the diameter $d$ changes.
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