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.

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.

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.

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.

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.

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.

Fermi resonance in optical microcavities.

Fermi resonance is a phenomenon of quantum mechanical superposition, which most often occurs between normal and overtone modes in molecular systems that are nearly coincident in energy. We find that scarred resonances in deformed dielectric microcavities are the very phenomenon of Fermi resonance, that is, a pair of quasinormal modes interact with each other due to coupling and a pair of resonances are generated through an avoided resonance crossing. Then the quantum number difference of a pair of quasinormal modes, which is a consequence of quantum mechanical superposition, equals periodic orbits, whereby the resonances are localized on the periodic orbits. We derive the relation between the quantum number difference and the periodic orbits and confirm it in an elliptic, a rectangular, and a stadium-shaped dielectric microcavity.

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.

Dependence of lasing threshold on Q factor in a deformed microcavity laser.

The relationship between lasing threshold and quality (Q) factor is investigated. When a deformed microcavity laser composed of a circular arc and an isosceles trapezoid is excited by current injection, various modes lase in ten emission directions. The lasing modes are classified into four groups, and the lasing threshold of each mode group is obtained according to emission spectra. The Q factor of each mode group is obtained from the resonance by comparing the far-field patterns of resonances with those of mode groups. Through the study, we find that the lasing threshold strongly depends on the Q factor.