Revealing non-Hermitian band structure of photonic Floquet media.

Periodically driven systems are ubiquitously found in both classical and quantum regimes. In the field of photonics, these Floquet systems have begun to provide insight into how time periodicity can extend the concept of spatially periodic photonic crystals and metamaterials to the time domain. However, despite the necessity arising from the presence of nonreciprocal coupling between states in a photonic Floquet medium, a unified non-Hermitian band structure description remains elusive. We experimentally reveal the unique Bloch-Floquet and non-Bloch band structures of a photonic Floquet medium emulated in the microwave regime with a one-dimensional array of time-periodically driven resonators. These non-Hermitian band structures are shown to be two measurable distinct subsets of complex eigenfrequency surfaces of the photonic Floquet medium defined in complex momentum space.

Salient role of the non-Hermitian coupling for optimizing conditions in multiple maximizations of inter-cavity light transfer.

We reveal that non-Hermitian lossy couplings in an inter-cavity light transfer process are crucial for an optimum light transfer, unlike the prevailed belief. Our results turn out the fact that the light transfer can have multiple maxima following the increased inter-cavity distance. To validate this finding both in the weak and strong coupling regimes, we demonstrate our claim in the vicinity of the so-called exceptional point. We believe our results can contribute to realizing coupled-optical-cavity-based devices which is functional with an ultra-efficient light transfer, especially when the device scale is as small as the operation wavelength.

Transformation cavities with a narrow refractive index profile.

Recently, gradient index cavities, or so-called transformation cavities, designed by conformal transformation optics, have been studied to support resonant modes with both high Q-factors and emission directionality. We propose a new, to the best of our knowledge, design method for transformation cavities to realize a narrower width of the refractive index profile, a great advantage in experimental implementations, without losing the benefits of conformal mapping. We study resonant modes with both high Q-factors and directional emission in newly designed transformation cavities, where the refractive index profile is 50% narrower than in previously proposed transformation cavities. By varying a system parameter with a fixed maximal value of the refractive index profile inside the cavity, the width of the refractive index profile narrows, the Q-factors become higher, and the near and far field patterns maintain their properties, namely, conformal whispering gallery modes and bidirectional emission, respectively.

Boundary integral equation method for resonances in gradient index cavities designed by conformal transformation optics.

In the case of two-dimensional gradient index cavities designed by the conformal transformation optics, we propose a boundary integral equation method for the calculation of resonant mode functions by employing a fictitious space which is reciprocally equivalent to the physical space. Using the Green's function of the interior region of the uniform index cavity in the fictitious space, resonant mode functions and their far-field distributions in the physical space can be obtained. As a verification, resonant modes in limaçon-shaped transformation cavities were calculated and mode patterns and far-field intensity distributions were compared with those of the same modes obtained from the finite element method.

Oscillation death in coupled counter-rotating identical nonlinear oscillators.

We study oscillatory and oscillation suppressed phases in coupled counter-rotating nonlinear oscillators. We demonstrate the existence of limit cycle, amplitude death, and oscillation death, and also clarify the Hopf, pitchfork, and infinite period bifurcations between them. Especially, the oscillation death is a new type of oscillation suppressions of which the inhomogeneous steady states are neutrally stable. We discuss the robust neutral stability of the oscillation death in non-conservative systems via the anti-parity-time-symmetric phase transitions at exceptional points in terms of non-Hermitian systems.

Optimization of conformal whispering gallery modes in limaçon-shaped transformation cavities.

Directional light emission from high-Q resonant modes without significant Q-spoiling has been a long standing issue in deformed dielectric cavities. In limaçon-shaped gradient index dielectric cavities recently proposed by exploiting conformal transformation optics, the variation of Q-factors and emission directionality of resonant modes was traced in their system parameter space. For these cavities, their boundary shapes and refractive index profiles are determined in each case by a chosen conformal mapping which is taken as a coordinate transformation. Through the numerical exploration, we found that bidirectionality factors of generic high-Q resonant modes are not directly proportional to their Q-factors. The optimal system parameters for the coexistence of strong bidirectionality and a high Q-factor was obtained for anisotropic whispering gallery modes supported by total internal reflection.

Statistical properties of chaotic microcavities in small and large opening cases.

We study the crossover behavior of statistical properties of eigenvalues in a chaotic microcavity with different refractive indices. The level spacing distributions change from Wigner to Poisson distributions, as the refractive index of a microcavity decreases. We propose a non-Hermitian matrix model with random elements describing the spectral properties of the chaotic microcavity, which exhibits the crossover behaviors as the opening strength increases.

Flat-band localization and self-collimation of light in photonic crystals.

We investigate the optical properties of a photonic crystal (PC) composed of a quasi-one-dimensional flat-band lattice array through finite-difference time-domain simulations. The photonic bands contain flat bands (FBs) at specific frequencies, which correspond to compact localized states as a consequence of destructive interference. The FBs are shown to be nondispersive along the Г → X line, prohibiting optical transmission with incident light in x direction. On the other hand, the photonic band for the FB frequency is found to be dispersive along the Г → Y line, resulting in nonzero optical transmission. Such anisotropic optical response of the PC due to the FB localization of light in a single direction only results in a self-collimation of light propagation throughout the PC at the FB frequency.

Husimi functions at gradient index cavities designed by conformal transformation optics.

Dielectric cavity systems, which have been studied extensively so far, have uniform refractive indices of their cavities, and Husimi functions, the most widely used phase space representation of optical modes formed in the cavities, accordingly were derived only for these homogeneous index cavities. For the case of the recently proposed gradient index dielectric cavities (called as transformation cavities) designed by optical conformal mapping, we show that the phase space structure of resonant modes can be revealed through the conventional Husimi functions by constructing a reciprocal virtual space. As examples, the Husimi plots were obtained for an anisotropic whispering gallery mode (WGM) and a short-lived mode supported in a limaçon-shaped transformation cavity. The phase space description of the corresponding modes in the reciprocal virtual space is compatible with the far-field directionality of the resonant modes in the physical space.

Amplitude death in a ring of nonidentical nonlinear oscillators with unidirectional coupling.

We study the collective behaviors in a ring of coupled nonidentical nonlinear oscillators with unidirectional coupling, of which natural frequencies are distributed in a random way. We find the amplitude death phenomena in the case of unidirectional couplings and discuss the differences between the cases of bidirectional and unidirectional couplings. There are three main differences; there exists neither partial amplitude death nor local clustering behavior but an oblique line structure which represents directional signal flow on the spatio-temporal patterns in the unidirectional coupling case. The unidirectional coupling has the advantage of easily obtaining global amplitude death in a ring of coupled oscillators with randomly distributed natural frequency. Finally, we explain the results using the eigenvalue analysis of the Jacobian matrix at the origin and also discuss the transition of dynamical behavior coming from connection structure as the coupling strength increases.

Reconfiguration of quantum states in [Formula: see text]-symmetric quasi-one-dimensional lattices.

We demonstrate mesoscopic transport through quantum states in quasi-1D lattices maintaining the combination of parity and time-reversal symmetries by controlling energy gain and loss. We investigate the phase diagram of the non-Hermitian system where transitions take place between unbroken and broken [Formula: see text]-symmetric phases via exceptional points. Quantum transport in the lattice is measured only in the unbroken phases in the energy band-but not in the broken phases. The broken phase allows for spontaneous symmetry-broken states where the cross-stitch lattice is separated into two identical single lattices corresponding to conditionally degenerate eigenstates. These degeneracies show a lift-up in the complex energy plane, caused by the non-Hermiticity with [Formula: see text]-symmetry.

Localization in chaotic systems with a single-channel opening.

We introduce a single-channel opening in a random Hamiltonian and a quantized chaotic map: localization on the opening occurs as a sensible deviation of the wave-function statistics from the predictions of random matrix theory, even in the semiclassical limit. Increasing the coupling to the open channel in the quantum model, we observe a similar picture to resonance trapping, made of a few fast-decaying states, whose left (right) eigenfunctions are entirely localized on the (preimage of the) opening, and plentiful long-lived states, whose probability density is instead suppressed at the opening. For the latter, we derive and test a linear relation between the wave-function intensities and the decay rates, similar to the Breit-Wigner law. We then analyze the statistics of the eigenfunctions of the corresponding (discretized) classical propagator, finding a similar behavior to the quantum system only in the weak-coupling regime.

Rotationally reconfigurable metamaterials based on moiré phenomenon.

Exploiting moiré interference, we make a new type of reconfigurable metamaterials and study their transmission tunability for incident electromagnetic waves. The moiré pattern is formed by overlapping two transparent layers, each of which has a periodic metallic pattern, and the cluster size of the resulting moiré pattern can be varied by changing the relative superposition angle of the two layers. In our reconfigurable metamaterials, both the size and structural shape of the unit cell can be varied simultaneously through moiré interference. We show that the transmission of electromagnetic waves can be controlled from 90% to 10% at 11 GHz by experiments and numerical simulation. The reconfigurable metamaterial proposed here can be applied in bandpass filters and tunable modulation devices.

Exceptional points in coupled dissipative dynamical systems.

We study the transient behavior in coupled dissipative dynamical systems based on the linear analysis around the steady state. We find that the transient time is minimized at a specific set of system parameters and show that at this parameter set, two eigenvalues and two eigenvectors of the Jacobian matrix coalesce at the same time; this degenerate point is called the exceptional point. For the case of coupled limit-cycle oscillators, we investigate the transient behavior into the amplitude death state, and clarify that the exceptional point is associated with a critical point of frequency locking, as well as the transition of the envelope oscillation.

Abnormal high-Q modes of coupled stadium-shaped microcavities.

It is well known that the strongly deformed microcavity with fully chaotic ray dynamics cannot support high-Q modes due to its fast chaotic diffusion to the critical line of refractive emission. Here, we investigate how the Q factor is modified when two chaotic cavities are coupled, and show that some modes, whose Q factor is about 10 times higher than that of the corresponding single cavity, can exist. These abnormal high-Q modes are the result of an optimal combination of coupling and cavity geometry. As an example, in the coupled stadium-shaped microcavities, the mode pattern extends over both cavities such that it follows a whispering-gallery-type mode at both ends, whereas a big coupling spot forms at the closest contact of the two microcavities. The pattern of such a "rounded bow tie" mode allows the mode to have a high-Q factor. This mode pattern minimizes the leakage of light at both ends of the microcavities as the pattern at both ends is similar to the whispering gallery mode.

Quasiattractors in coupled maps and coupled dielectric cavities.

We study the origin of attracting phenomena in the ray dynamics of coupled optical microcavities. To this end we investigate a combined map that is composed of standard and linear map, and a selection rule that defines when which map has to be used. We find that this system shows attracting dynamics, leading exactly to a quasiattractor, due to collapse of phase space. For coupled dielectric disks, we derive the corresponding mapping based on a ray model with deterministic selection rule and study the quasiattractor obtained from it. We also discuss a generalized Poincaré surface of section at dielectric interfaces.

Terahertz beat frequency generation from two-mode lasing operation of coupled microdisk laser.

We propose a coupled microdisk laser as a compact and tunable laser source for the generation of a coherent continuous-wave terahertz radiation by photomixing. Using the Schrödinger-Bloch model including the nonlinear effect of active medium, we find single-mode and two-mode lasings depending on the pumping strength. We explain the transitions of lasing modes in terms of resonant modes that are the solutions of the Schrödinger-Bloch model without active medium and nonlinear interaction. In particular, a two-mode lasing is shown to generate a terahertz oscillating frequency originating from the light beating of two nearly degenerated resonant modes with different symmetries.

On-manifold localization in open quantum maps.

A quantized chaotic map exhibiting localization of wave function intensity is opened. We investigate how such patterns as scars in the Husimi distributions are influenced by the losses through a number of numerical experiments. We find the scars to relocate on the stable or unstable manifolds depending on the position of the opening, and provide a classical argument to explain the observations. For asymmetrically introduced openings mode interaction contributes to determine the localization patterns. We finally show examples of similar localization in a simulated dielectric microcavity.

Designing coupled microcavity lasers for high-Q modes with unidirectional light emission.

We design coupled optical microcavities and report directional light emission from high-Q modes for a broad range of refractive indices. The system consists of a circular cavity that provides a high-Q mode in the form of a whispering gallery mode, whereas an adjacent deformed microcavity plays the role of a waveguide or collimator of the light transmitted from the circular cavity. As a result of this very simple, yet robust, concept we obtain high-Q modes with promising directional emission characteristics. No information about phase space is required, and the proposed scheme can be easily realized in experiments.