Perfectly Absorbing Exceptional Points and Chiral Absorbers

William R. Sweeney, Chia Wei Hsu, Stefan Rotter, and A. Douglas Stone

Phys. Rev. Lett. 122, 093901 – Published 5 March 2019

Abstract

We identify a new kind of physically realizable exceptional point (EP) corresponding to degenerate coherent perfect absorption, in which two purely incoming solutions of the wave operator for electromagnetic or acoustic waves coalesce to a single state. Such non-Hermitian degeneracies can occur at a real-valued frequency without any associated noise or nonlinearity, in contrast to EPs in lasers. The absorption line shape for the eigenchannel near the EP is quartic in frequency around its maximum in any dimension. In general, for the parameters at which an operator EP occurs, the associated scattering matrix does not have an EP. However, in one dimension, when the $S$ matrix does have a perfectly absorbing EP, it takes on a universal one-parameter form with degenerate values for all scattering coefficients. For absorbing disk resonators, these EPs give rise to chiral absorption: perfect absorption for only one sense of rotation of the input wave.

Received 23 July 2018

DOI:https://doi.org/10.1103/PhysRevLett.122.093901

Physics Subject Headings (PhySH)

Angular momentum of light Classical optics Geometrical & wave optics Light-matter interaction Photonics

Bragg structures Complex media Optical microcavities Waveguides

Atomic, Molecular & Optical

Authors & Affiliations

William R. Sweeney^1,*, Chia Wei Hsu², Stefan Rotter³, and A. Douglas Stone^2,4

¹Department of Physics, Yale University, New Haven, Connecticut 06520, USA
²Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
³Institute for Theoretical Physics, Vienna University of Technology (TU Wien), A-1040 Vienna, Austria
⁴Yale Quantum Institute, Yale University, New Haven, Connecticut 06520, USA

^*william.sweeney@yale.edu

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Issue

Vol. 122, Iss. 9 — 8 March 2019

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Images

Figure 1
Scattering from coupled cavity structures at CPA EP for asymmetric (a)–(f) and symmetric (g)–(i) end mirrors. (a),(d),(g) Absorption line shapes of eigenchannels (solid): CPA channel (blue) reaches 100% absorption at the EP frequency $ω_{0}$ . In (a),(d) CPA line shape is quartic [see (c)], while in (d) non-CPA channel (red) is quadratic. In (g) we have an EP of $S$ and the line shape is not quartic. Scattering coefflcients $| r_{L} |^{2}$ , $| r_{R} |^{2}$ , $| t |^{2}$ are shown as green, blue, and red dashed lines; in (g) they become degenerate at $ω_{0}$ , as predicted for an EP of $S$ matrix at zero. (b),(e),(h) Schematics of structures: cavities (red) with lengths $L_{1}$ , $L_{2}$ , and unequal absorption, emitting to free space through end mirrors. Right mirror is perfect in (b), permeable but unequal to left in (e) and equal to left in (h); parameter values are given in Supplemental Material S1 [38]. (f),(i) CPA EP modes: generic case of unequal coupling (f) yields asymmetric asymptotic values for $| ψ |^{2}$ , implying $S$ not at EP. The CPA mode for nongeneric case of equal coupling (i) has equal asymptotic values, implying that $S$ is at an EP.
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Figure 2
Chiral CPA EP of WGMs of absorbing microdisk perturbed by point scatterers. (a) CCW incident CPA EP mode. Intensity plotted as color scale, curves of constant phase (white), disk boundary and scatterers (blue). Curvature of phase fronts shows sense of rotation, denoted by arrow. Uniform intensity along rim indicates running wave in disk. (b) Input fluxes carried in each angular momentum channel for CPA EP (CCW) input. Dominant channel (denoted by star) carries 80% of flux; CPA input is $> 99.9 %$ absorbed. (c) Total field (incident and scattered) for reverse chirality input. Internal intensity shows standing wave oscillations due to presence of backscattering. (d) As in (b), input fluxes (red), output (blue), for CW input. Here we find $\sim 1 %$ scattering across many channels, giving a total of 17% scattered flux (83% absorption).
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Figure 3
Chiral absorption from CPA EP waveguide-microdisk system. (a) Reflection $| r_{L} |^{2}$ (gray), $| r_{R} |^{2}$ (red solid), and transmission $| t |^{2}$ (blue) for disk with complex index azimuthal grating, tuned to CPA EP. TCMT prediction [Eq. (4)] for $r_{R}$ in dashed red. Inset: one-sided absorption spectrum for left illumination (green) and right (red). (b) Intensity of total field (incident & scattered) for left illumination, corresponding to CPA EP. (c) Same as (b) but for right illumination. Note standing wave of (c) vs running wave of (b) indicates strong coupling between CW and CCW modes only for right incidence, causing chiral absorption.
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