Observation of an exceptional point in a two-dimensional ultrasonic cavity of concentric circular shells

Observation of a half-illuminated mode in an open Penrose cavity

The illumination problem in mathematics questions the existence of a bounded region in which light rays from a point light source do not illuminate the whole region. Since Penrose disproved the illumination problem with elliptical reflective boundaries, the interest has mostly remained in ray optics mainly because there can be no completely dark region for light waves due to diffraction. Here, in a two-dimensional Penrose cavity with elliptical boundaries, we report experimental observation of a symmetry-broken mode in the long-wavelength regime with the half of the cavity region with reflection symmetry almost unilluminated in the steady state. The half-illuminated mode (HIM) was observed in an acoustic cavity by using the schlieren method. The HIM originated from the coherent superposition of near-degenerate modes, among which two scarred modes with opposite parities played a major role. The illuminated part of the HIM could be even flipped by choosing different coefficients in the coherent superposition of the participating modes. The HIM of the Penrose cavity provides new perspective to the illumination problem in an open system.

Thermalization Dynamics of Nonlinear Non-Hermitian Optical Lattices

We develop a rigorous theoretical framework based on principles from statistical mechanics that allows one to predict the equilibrium response of classical non-Hermitian arrangements in the weakly nonlinear regime. In this respect, we demonstrate that a pseudo-Hermitian configuration can always be driven into thermal equilibrium when a proper nonlinear operator is paired with the linear Hamiltonian of the system. We show that, in this case, the system will thermodynamically settle into an irregular pattern that does not resemble any known statistical distribution. Interestingly, this stable equilibrium response is associated with a Rayleigh-Jeans law when viewed within an appropriately transformed space that displays unitary dynamics. By considering a non-Hermitian Su-Schrieffer-Heeger chain, our results indicate that the thermodynamic equilibrium will always favor the edge modes instead of the ground state, in stark contrast to conventional nonlinear Hermitian configurations. Moreover, non-Hermitian lattices are shown to exhibit unusually high heat capacities, potentially acting as optical heat reservoirs to other Hermitian systems, by employing only a small number of sites and low power levels.

Simultaneous determination of the shape and refractive index of a deformed microjet cavity from its resonances

Measuring the boundary shape of a deformed liquid microjet is of great importance for using it as an optical resonator for various applications. However, there have been technical challenges due to transparency and uncertainty in the refractive index of the liquid. In this study, we have developed a spectroscopic technique that enables simultaneous determination of the boundary shape and the refractive index of a liquid deformed microjet. A detailed procedure of the technique based on imposition of one-to-one correspondence between experimentally observed resonances and numerically calculated ones are presented along with the measurement results including the refractive index of ethanol between a wavelength of 550 nm and 670 nm.

Schlieren-style stroboscopic nonscan imaging of the field-amplitudes of acoustic whispering gallery modes

We report a schlieren-style stroboscopic phase-contrast field-amplitude imaging of two-dimensional acoustic whispering gallery modes in a circular shell cavity immersed in liquid. A schlieren signal is combined with a presplit reference beam to enable nonscan field-amplitude imaging. Excitation mechanisms of standing and traveling eigenmodes, respectively, are analyzed with acoustic ray simulations presented in a Poincaré surface of sections. The time evolutions for both standing and traveling eigenmodes are reconstructed using the stroboscopic capability.

Maximal Shannon entropy in the vicinity of an exceptional point in an open microcavity

The Shannon entropy as a measure of information contents is investigated around an exceptional point (EP) in an open elliptical microcavity as a non-Hermitian system. The Shannon entropy is maximized near the EP in the parameter space for two interacting modes, but the exact maximum position is slightly off the EP toward the weak interaction region while the slopes of the Shannon entropies diverge at the EP. The Shannon entropies also show discontinuity across a specific line in the parameter space, directly related to the exchange of the Shannon entropy as well as the mode patterns with that line as a boundary. This feature results in a nontrivial topological structure of the Shannon entropy surfaces.

Non-PT-symmetric two-layer cylindrical waveguide for exceptional-point-enhanced optical devices

We investigate the exceptional points in a two-layer cylindrical waveguide structure consisting of absorbing and non-absorbing dielectrics. We show that, by tuning the core to total radius ratio and the refractive index of the core layer in such a structure, the complex effective indices of two waveguide modes can coalesce so that an exceptional point is formed. We show that the sensitivity of the effective index of the waveguide mode to variations of the refractive index of the material filling the shell layer is enhanced at the exceptional point. In addition, we show that larger sensitivity enhancement is obtained for smaller perturbations. Our results could potentially contribute to the development of a new generation of chip-scale exceptional-point-enhanced optical waveguide devices for modulation, switching, and sensing.

Curved Nanomembrane-Based Concentric Ring Cavities for Supermode Hybridization

We report the mode interactions and resonant hybridization in nanomembrane-formed concentric dual ring cavities supporting whispering gallery mode resonances. Utilizing a rolled-up nanomembrane with subwavelength thickness as an interlayer, dual concentric microring cavities are formed by coating high-index nanomembranes on the inner and outer surfaces of the rolled-up dielectric nanomembrane. In such a hybrid cavity system, the conventional fundamental mode resonating along a single ring orbit splits into symmetric and antisymmetric modes confined by concentric dual ring orbits. Detuning of the coupled supermodes is realized by spatially resolved measurements along the cavity axial direction. A spectral anticrossing feature is observed as a clear evidence of strong coupling. Upon strong coupling, the resonant orbits of symmetric and antisymmetric modes cross over each other in the form of superwaves oscillating between the concentric rings with opposite phase. Notably, the present system provides high flexibilities in controlling the coupling strength by varying the thickness of the spacer layer and thus enables switching between strong and weak coupling regimes. Our work offers a compact and robust scheme using curved nanomembranes to realize novel cavity mode interactions for both fundamental and applied studies.

Shannon entropy and avoided crossings in closed and open quantum billiards

The relation between Shannon entropy and avoided crossings is investigated in dielectric microcavities. The Shannon entropy of the probability density for eigenfunctions in an open elliptic billiard as well as a closed quadrupole billiard increases as the center of the avoided crossing is approached. These results are opposite to those of atomic physics for electrons. It is found that the collective Lamb shift of the open quantum system and the symmetry breaking in the closed chaotic quantum system have equivalent effects on the Shannon entropy.

Unidirectional reflectionless phenomena in a non-Hermitian quantum system of quantum dots coupled to a plasmonic waveguide

Unidirectional reflectionless phenomena are investigated theoretically in a non-Hermitian quantum system composed of several quantum dots and a plasmonic waveguide. By adjusting the phase shifts between quantum dots, single- and dual-band unidirectional reflectionlessnesses are realized at exceptional points based on two and three quantum dots coupled to a plasmonic waveguide, respectively. In addition, single- and dual-band unidirectional perfect absorptions with high quality factors are obtained at the vicinity of exceptional points.