arXiv subjects

Sunghwan Rim

Publications and source records attributed to Sunghwan Rim.

18 recordsLinked to original sources

arXiv2020

Circle-shaped Transformation Cavity via Center-Shift Möbius Transfomation

Circle-shaped transformation cavities of shifted center are the most simple transformation cavities in the sense that they have only spatial index variation without boundary shape deformation. For these cavities, we analyze the characteristics of conformal whispering gallery modes according to center-shift coordinate transformation. For this study, we use an alternative scheme for designing a transformation cavity without using a shrinking parameter that is needed to satisfy total internal reflection condition. It is observed that the isotropic emission of whispering gallery modes in the uniform index circular cavity changes to the bi-directional emission of conformal whispering gallery modes as the center-shift increases. Also, using a purity factor that quantitatively measures in RV space the degree of intactness for the internal wave pattern of resonant modes in transformation cavities compared with corresponding whispering gallery mode in uniform disk cavity, we show that the conformal whispering gallery modes in the circle-shaped transformation cavity has not only directionality but also high persistence for characteristics of whispering gallery modes.

physics.optics↗

arXiv2020

Whispering gallery modes in triple microdisks of triangular configurations

We study whispering gallery modes in triple microdisks of equilateral and isosceles triangular configurations. The characteristic properties of resonant modes in three microdisks on vertices of an equilateral triangle are explained by discrete rotational symmetry of the triangle. The avoided crossings of resonant modes in three microdisks on vertices of an isosceles triangle are also studied in terms of a combination of single and coupled microdisks. Finally, we propose the matrix models which well explain the resonant modes in triple microdisks.

physics.optics↗

arXiv2019

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.

physics.optics↗

arXiv2011

Dynamics of Morphology-Dependent Resonances by Openness in Dielectric Disk for TE polarization

We have studied the dynamics of morphology-dependent resonances by openness in a dielectric microdisk for TE polarization. For the first time, we report that the dynamics exhibits avoided resonance crossings between inner and outer resonances even though the corresponding billiard is integrable. Due to the avoidance, inner and outer resonances can be exchanged and $Q$-factor of inner resonances is strongly affected. We analyze the diverse phenomena aroused from the dynamics including the avoided crossings.

physics.optics↗

arXiv2010

Outer Resonances and Effective Potential Analogy in Two-Dimensional Dielectric Cavities

Outer resonances are studied as one type of quasinormal modes in two-dimensional dielectric cavities with refractive index $n>1$. The outer resonances can be verified as the resonances which survive only outside the cavity in the small opening limit of the dielectric disk. We have confirmed that the outer resonances universally exist in deformed cavities irrespective of the geometry of cavity and they split into nearly degenerate states in slightly deformed cavity. Also we pointed out that the effective potential analogy is inapplicable to the description of outer resonances. Since most outer resonances in the dielectric cavities have quite high leakages, they would affect to the broad background in the density of states. Especially, for TE polarization case, relatively low-leaky outer resonances exist and it presents the possibility that they can interact with the inner resonances and affect lasing modes.

physics.optics↗

arXiv2009

An efficient finite element method applied to quantum billiard systems

An efficient finite element method (FEM) for calculating eigenvalues and eigenfunctions of quantum billiard systems is presented. We consider the FEM based on triangular $C_1$ continuity quartic interpolation. Various shapes of quantum billiards including an integrable unit circle are treated. The numerical results show that the applied method provides accurate set of eigenvalues exceeding a thousand levels for any shape of quantum billiards on a personal computer. Comparison with the results from the FEM based on well-known $C_0$ continuity quadratic interpolation proves the efficiency of the method.

nlin.CD↗

arXiv2008

Resonances in a circular dielectric cavity

We study resonance distributions in a circular dielectric cavity. It is shown that the decay-rate distribution has a peak structure and the details of the peak are consistent with the classical survival probability time distribution. We also investigate the behavior of the complex resonance positions at the small opening limit. At the large $n$ limit, the real part of complex resonance positions approaches the solutions with different $m$ of Dirichlet problem with a scale $n^{-2}$ and the imaginary part goes zero as $n^{-2m}$ for TM and $n^{-2(m+1)}$ for TE polarization, where $m$ is the order of the resonance.

physics.optics↗

arXiv2005

Scarred Resonances and Steady Probability Distribution in a Chaotic Microcavity

We investigate scarred resonances of a stadium-shaped chaotic microcavity. It is shown that two components with different chirality of the scarring pattern are slightly rotated in opposite ways from the underlying unstable periodic orbit, when the incident angles of the scarring pattern are close to the critical angle for total internal reflection. In addition, the correspondence of emission pattern with the scarring pattern disappears when the incident angles are much larger than the critical angle. The steady probability distribution gives a consistent explanation about these interesting phenomena and makes it possible to expect the emission pattern in the latter case.

nlin.CD↗

arXiv2005

Chaos Synchronization of delayed systems in the presence of delay time modulation

We investigate synchronization in the presence of delay time modulation for application to communication. We have observed that the robust synchronization is established by a common delay signal and its threshold is presented using Lyapunov exponents analysis. The influence of the delay time modulation in chaotic oscillators is also discussed.

nlin.CD↗

arXiv2004

Periodic Phase Synchronization in coupled chaotic oscillators

We investigate the characteristics of temporal phase locking states observed in the route to phase synchronization. It is found that before phase synchronization there is a periodic phase synchronization state characterized by periodic appearance of temporal phase locking state and that the state leads to local negativeness in one of the vanishing Lyapunov exponents. By taking a statistical measure, we present the evidences of the phenomenon in unidirectionally and mutually coupled chaotic oscillators, respectively. And it is qualitatively discussed that the phenomenon is described by a nonuniform oscillator model in the presence of noise.

nlin.CD↗

arXiv2004

Resonance Patterns in a Stadium-shaped Microcavity

We investigate resonance patterns in a stadium-shaped microcavity around $n_ck R \simeq 10$, where $n_c$ is the refractive index, $k$ the vacuum wavenumber, and $R$ the radius of the circular part of the cavity. We find that the patterns of high $Q$ resonances can be classified, even though the classical dynamics of the stadium system is chaotic. The patterns of the high $Q$ resonances are consistent with the ray dynamical consideration, and appears as the stationary lasing modes with low pumping rate in the nonlinear dynamical model. All resonance patterns are presented in a finite range of $kR$.

nlin.CD↗

arXiv2004

Quasi-Scarred Resonances in a Spiral-Shaped Microcavity

We study resonance patterns of a spiral-shaped dielectric microcavity with chaotic ray dynamics. Many resonance patterns of this microcavity, with refractive indices $n=2$ and 3, exhibit strong localization of simple geometric shape, and we call them {\em quasi-scarred resonances} in the sense that there is, unlike the conventional scarring, no underlying periodic orbits. It is shown that the formation of quasi-scarred pattern can be understood in ter ms of ray dynamical probability distributions and wave properties like uncertainty and interference.

nlin.CD↗

arXiv2004

Origin of the Transition Inside the Desynchronized State in Coupled Chaotic Oscillators

We investigate the origin of the transition inside the desynchronization state via phase jumps in coupled chaotic oscillators. We claim that the transition is governed by type-I intermittency in the presence of noise whose characteristic relation is $ \propto \exp(α|ε_t -ε|^{3/2})$ for $ε_t -ε<0$ and $ \propto (ε_t -ε)^{-1/2}$ for $ε_t -ε>0$, where $ $ is the average length of the phase locking state and $ε$ is the coupling strength. To justify our claim we obtain analytically the tangent point, the bifurcation point, and the return map which agree well with those of the numerical simulations.

nlin.CD↗

arXiv2004

Generalized Phase Synchronization in unidirectionally coupled chaotic oscillators

We investigate phase synchronization between two identical or detuned response oscillators coupled to a slightly different drive oscillator. Our result is that phase synchronization can occur between response oscillators when they are driven by correlated (but not identical) inputs from the drive oscillator. We call this phenomenon Generalized Phase Synchronization (GPS) and clarify its characteristics using Lyapunov exponents and phase difference plots.

nlin.CD↗

arXiv2004

Characteristics of a Delayed System with Time-dependent Delay Time

The characteristics of a time-delayed system with time-dependent delay time is investigated. We demonstrate the nonlinearity characteristics of the time-delayed system are significantly changed depending on the properties of time-dependent delay time and especially that the reconstructed phase trajectory of the system is not collapsed into simple manifold, differently from the delayed system with fixed delay time. We discuss the possibility of a phase space reconstruction and its applications.

nlin.CD↗

arXiv2001

Mechanism of synchronization in a random dynamical system

The mechanism of synchronization in the random Zaslavsky map is investigated. From the error dynamics of two particles, the structure of phase space was analyzed, and a transcritical bifurcation between a saddle and a stable fixed point was found. We have verified the structure of on-off intermittency in terms of a biased random walk. Furthermore, for the generalized case of the ensemble of particles, \emph{a modified definition} of the size of a snapshot attractor was exploited to establish the link with a random walk. As a result, the structure of on-off intermittency in the ensemble of particles was explicitly revealed near the transition.

nlin.CD↗

arXiv1998

Correspondence between classical dynamics and energy level spacing distribution in the transition billiard systems

The Robnik billiard is investigated in detail both classically and quantally in the transition range from integrable to almost chaotic system. We find out that a remarkable correspondence between characteristic features of classical dynamics, especially topological structure of integrable regions in the Poincaré surface of section, and the statistics of energy level spacings appears with a system parameter $λ$ being varied. It is shown that the variance of the level spacing distribution changes its behavior at every particular values of $λ$ in such a way that classical dynamics changes its topological structure in the Poincaré surface of section, while the skewness and the excess of the level spacings seem to be closely relevant to the interface structure between integrable region and chaotic sea rather than inner structure of intergrable regoin.

chao-dyn↗

arXiv1998

Transitions to quantum chaos in a generic one-parameter family of billiards

Generic one-parameter billiards are studied both classically and quantally. The classical dynamics for the billiards makes a transition from regular to fully chaotic motion through intermediary soft chaotic system. The energy spectra of the billiards are computed using finite element method which has not been applied to the euclidean billiard. True generic quantum chaotic transitional behavior and its sensitive dependence on classical dynamics are uncovered for the first time. That is, this sensitive dependence of quantum spectral measures on classical dynamics is a genuine manifestation of quantum chaos.

chao-dyn↗