Maximization of a frequency splitting on continuous exceptional points in asymmetric optical microdisks.

We study a systematic formation of continuous exceptional points (EPs) in a fully-asymmetric optical microdisk. A parametric generation of chiral EP modes is investigated by analyzing asymmetricity-dependent coupling elements in an effective Hamiltonian. It is shown that given the external perturbation, the frequency splitting around EPs is scaled by the fundamental "strength" of EPs [J. Wiersig, Phys. Rev. Res.4, 023121 (2022)10.1103/PhysRevResearch.4.023121] multiplied by the extra responding strength of the newly added perturbation. Our finding demonstrates that the sensitivity of EP-based sensors can be maximized by carefully examining the continuous formation of EPs.

Bloch theorem dictated wave chaos in microcavity crystals.

Universality class of wave chaos emerges in many areas of science, such as molecular dynamics, optics, and network theory. In this work, we generalize the wave chaos theory to cavity lattice systems by discovering the intrinsic coupling of the crystal momentum to the internal cavity dynamics. The cavity-momentum locking substitutes the role of the deformed boundary shape in the ordinary single microcavity problem, providing a new platform for the in situ study of microcavity light dynamics. The transmutation of wave chaos in periodic lattices leads to a phase space reconfiguration that induces a dynamical localization transition. The degenerate scar-mode spinors hybridize and non-trivially localize around regular islands in phase space. In addition, we find that the momentum coupling becomes maximal at the Brillouin zone boundary, so the intercavity chaotic modes coupling and wave confinement are significantly altered. Our work pioneers the study of intertwining wave chaos in periodic systems and provide useful applications in light dynamics control.

Strong interlayer coupling and stable topological flat bands in twisted bilayer photonic Moiré superlattices.

The moiré superlattice of misaligned atomic bilayers paves the way for designing a new class of materials with wide tunability. In this work, we propose a photonic analog of the moiré superlattice based on dielectric resonator quasi-atoms. In sharp contrast to van der Waals materials with weak interlayer coupling, we realize the strong coupling regime in a moiré superlattice, characterized by cascades of robust flat bands at large twist-angles. Surprisingly, we find that these flat bands are characterized by a non-trivial band topology, the origin of which is the moiré pattern of the resonator arrangement. The physical manifestation of the flat band topology is a robust one-dimensional conducting channel on edge, protected by the reflection symmetry of the moiré superlattice. By explicitly breaking the underlying reflection symmetry on the boundary terminations, we show that the first-order topological edge modes naturally deform into higher-order topological corner modes. Our work pioneers the physics of topological phases in the designable platform of photonic moiré superlattices beyond the weakly coupled regime.

Far-Field Correlations Verifying Non-Hermitian Degeneracy of Optical Modes.

An experimental verification of an exceptional point (EP) in a stand-alone chaotic microcavity is a tough issue because as deformation parameters are fixed the traditional frequency analysis methods cannot be applied any more. Through numerical investigations with an asymmetric Reuleaux triangle microcavity (ARTM), we find that the eigenvalue difference of paired modes can approach near-zero regardless of nonorthogonality of the modes. In this case, for a definite verification of EPs in experiments, wave function coalescence should be confirmed. For this, we suggest the method of exploiting correlation of far-field patterns (FFPs), which is directly related to spatial mode patterns. In an ARTM, we demonstrate that the FFP correlation of paired modes can be used to confirm wave function coalescence when an eigenvalue difference approaches near zero.

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.

Rayleigh scatterer-induced steady exceptional points of stable-island modes in a deformed optical microdisk.

A formation of second-order non-Hermitian degeneracies, called exceptional points (EPs), in a chaotic oval-shaped dielectric microdisk is studied. Different symmetric optical modes localized on a stable period-3 orbit coalesce to form chiral EPs. Unlike a circular microdisk perturbed by two scatterers (CTS), our proposed system requires only one scatterer to build chiral EPs. The scatterer positions for counterpropagating EP modes are far distant from one another and almost steady against varying scatterer sizes in contrast to the CTS case. Our results can contribute to establishing a more solid platform for EP-based-device applications with flexibility and easy feasibility in obtaining EPs.

Augmentation of absorption channels induced by wave-chaos effects in free-standing nanowire arrays.

Plenty of issues on quantal features in chaotic systems have been raised since chaos was accepted as one of the intrinsic properties of nature. Through intensive studies, it was revealed that resonance spectra in chaotic systems exhibit complicated structures, which is deeply concerned with sophisticated resonance dynamics. Motivated by these phenomena, we investigate light absorption characteristics of chaotic nanowires in an array. According to our results, a chaotic cross-section of a nanowire induces a remarkable augmentation of absorption channels, that is, an increasing number of absorption modes leads to substantial light absorption enhancement, as the deformation of cross-section increases. We experimentally demonstrate the light absorption enhancement with free-standing Si-nanowire polydimethylsiloxane (PDMS) composites. Our results are applicable not only to transparent solar cells but also to complementary metal-oxide-semiconductor (CMOS) image sensors to maximize absorption efficiency.

Lowest threshold lasing modes localized on marginally unstable periodic orbits in a semiconductor microcavity laser.

The lowest threshold lasing mode in a rounded D-shape microcavity is theoretically analyzed and experimentally demonstrated. To identify the lowest threshold lasing mode, we investigate threshold conditions of different periodic orbits by considering the linear gain condition due to the effective pumping region and total loss consisting of internal and scattering losses in ray dynamics. We compare the ray dynamical result with resonance mode analysis, including gain and loss. We find that the resonance modes localized on the pentagonal marginally unstable periodic orbit have the lowest threshold in our fabrication configuration. Our findings are verified by obtaining the path lengths and far-field patterns of lasing modes.

Lasing of scarred mode near above threshold in a semiconductor microcavity laser.

We study a lasing of mode groups in a fully chaotic rounded D-shape InGaAsP semiconductor microcavity laser when an electrode is smaller than a cavity (inward gap). Although there are numerous unstable periodic orbits supporting resonances, a mode group localized on period-5 unstable periodic orbit is more competitive than the others for our laser configuration of the inward gap. By means of theoretical and numerical analyses with ray and wave dynamics, we show that the analyses well agree with our experimental results.

Extremely high Q and unidirectional laser emission due to combination of the Kolmogorov-Arnold-Moser barrier and the chaotic sea in a dielectric microdisk.

Emission characteristics of an oval-shaped microcavity laser are studied. In experiments, modes localized on periodic orbits emit unidirectionally with a narrow in-plane divergence angle of about 12 deg. The origin of high directionality is elucidated by means of classical ray dynamics. Wave calculations show that the Q-factors of the resonances are higher than 108. We explain this extraordinary high Q-factor in relation with a dynamical barrier region where Kolmogorov-Arnold-Moser curves significantly obstruct leakages of resonances.

Pair of Exceptional Points in a Microdisk Cavity under an Extremely Weak Deformation.

One of the interesting features of open quantum and wave systems is the non-Hermitian degeneracy called an exceptional point, where not only energy levels but also the corresponding eigenstates coalesce. We demonstrate that such a degeneracy can appear in optical microdisk cavities by deforming the boundary extremely weakly. This surprising finding is explained by a semiclassical theory of dynamical tunneling. It is shown that the exceptional points come in nearly degenerated pairs, originating from the different symmetry classes of modes. A spatially local chirality of modes at the exceptional point is related to vortex structures of the Poynting vector.

Unidirectional emission of high-Q scarred modes in a rounded D-shape microcavity.

We propose a deformed microcavity laser, where a high-Q mode group emits unidirectionally. The cavity comprises three circular arcs and one linear section. To minimize diffraction effects from the boundary, three circular arcs and one linear section are tangentially connected. By adjusting the sizes and the positions of the two sub-circular arcs, unidirectionality is maximized. In an experiment with an InP based InGaAsP semiconductor microcavity laser, a lasing mode group localized on aperiod-7 unstable periodic orbit emits unidirectionally. In our resonance calculation, a high-Q factor is confirmed.

Separatrix modes in weakly deformed microdisk cavities.

Optical modes in deformed dielectric microdisk cavities often show an unexpected localization along unstable periodic ray orbits. We reveal a new mechanism for this kind of localization in weakly deformed cavities. In such systems the ray dynamics is nearly integrable and its phase space contains small island chains. When increasing the deformation the enlarging islands incorporate more and more modes. Each time a mode comes close to the border of an island chain (separatrix) the mode exhibits a strong localization near the corresponding unstable periodic orbit. Using an EBK quantization scheme taking into account the Fresnel coefficients we derive a frequency condition for the localization. Observing far field intensity patterns and tunneling distances, reveals small differences in the emission properties.

Chirality of a resonance in the absence of backscatterings.

Chirality of a resonance localized on an islands chain is studied in a deformed Reuleaux triangular-shaped microcavity, where clockwise and counter clockwise traveling rays are classically separated. A resonance localized on a period-5 islands chain exhibits chiral emission due to the asymmetric cavity shape. Chirality is experimentally proved in a InGaAsP multi-quantum-well semiconductor laser by showing that the experimental emission characteristics well coincide with the wave dynamical ones.

Avoided level crossings in an elliptic billiard.

In an elliptic billiard, we find avoided level crossings taking place over wide ranges, which are of a Demkov type for generations of eigenfunctions localized on an islands chain and its pair unstable periodic orbit. For a proof of the existence of avoided level crossings, first, we show that the quantized eigenvalue of the unstable periodic orbit, obtained by the Einstein-Brillouin-Keller quantization rule, passes the eigenvalues of bouncing-ball modes localized on the unstable periodic orbit after Demkov type avoided level crossings so that pairs of bouncing-ball modes are sequentially generated. Next, by using a perturbed Hamiltonian, we show that off-diagonal elements in Hamiltonian are nonzero, which give rise to an interaction between two eigenfunctions. Last, we verify that the observed phenomenon is Fermi resonance: that is, the quantum number difference of two normal modes equals the periodic orbits, where eigenfunctions are localized after an avoided level crossing.

Resonant torus-assisted tunneling.

We report a new type of dynamical tunneling, which is mediated by a resonant torus, i.e., a nonisolated periodic orbit. To elucidate the phenomenon, we take an open elliptic cavity and show that a pair of resonances localized on two classically disconnected tori tunnel through a resonant torus when they interact with each other. This so-called resonant torus-assisted tunneling is verified by using Husimi functions, corresponding actions, Husimi function distributions, and the standard deviations of the actions.

Energy shell structure in a dielectric elliptic microcavity.

An energy shell structure depending on eccentricity is analyzed in a dielectric elliptic microcavity. Through the analysis, it is explicated that the energy shell structure is governed by classical constant actions of periodic orbits. For clarification, the relation between dominances of the periodic orbits and bifurcation behaviors are obtained and the length spectra based on eigenvalues computed by a numerical method are compared with the exact lengths of the periodic orbits obtained by analytic calculations. By matching effective wave numbers obtained from the periodic orbit lengths to exact wave numbers of stationary states in closed and open cavities, we find deviations provoked from the openness. We show that these deviations are caused by additional phase factors in the Einstein-Brillouin-Keller quantization.

Unidirectional emission from a cardioid-shaped microcavity laser.

We find unidirectional emission in a cardioid-shaped microcavity laser. When a deformation parameter is well adjusted, rays starting around a period-5 unstable periodic orbit emit unidirectionally. To confirm the emission direction, we fabricate a laser by using an InGaAsP semiconductor and investigate emission characteristics. When the laser is excited by current injection with a dc current, resonances localized on the period-5 unstable periodic orbit emit unidirectionally.

Fermi resonance in dynamical tunneling in a chaotic billiard.

We elucidate that Fermi resonance ever plays a decisive role in dynamical tunneling in a chaotic billiard. Interacting with each other through an avoided crossing, a pair of eigenfunctions are coupled through tunneling channels for dynamical tunneling. In this case, the tunneling channels are an islands chain and its pair unstable periodic orbit, which equals the quantum number difference of the eigenfunctions. This phenomenon of dynamical tunneling is confirmed in a quadrupole billiard in relation with Fermi resonance.

Mechanism of Q-spoiling in deformed optical microcavities.

It was reported that Q spoiling in a chaotic microcavity is caused by chaos [PRL, 75, 2682 (1995)] and chaos-assisted tunneling [Nature 385, 45 (1997)]. However, even when a cavity is slightly deformed not to exhibit a broad chaotic region in phase space, high Q modes are spoiled. We find that Q spoiling in this region is caused by the transition of a whispering gallery mode (WGM) to a scarred resonance when a WGM interacts with its pair quasi-normal mode through an avoided resonance crossing. We prove that this transition induces Q spoiling in a quadrupole dielectric microcavity by showing that Q factors obtained from the Husimi functions depending on resonance deformation during the transition agree well with those obtained from the complex eigenvalues.