Resonant mode calculation method for extremely large-scale optical ring resonators.

To analyze the resonant modes of optical devices such as optical gyro-sensors and semiconductor lasers, Maxwell's equations need to be solved. Widely used numerical methods are the finite element method (FEM) and the finite-difference time-domain (FDTD) method. However, when optical systems are significantly larger than the operating wavelength, applying these methods becomes practically infeasible due to the exponential increase in computational resources and simulation time.

Chiral exceptional point in transformation cavity.

Unlike the ideal circular whispering gallery cavities, those without mirror symmetry intrinsically support resonant modes exhibiting chirality which indicates an imbalance between clockwise and counterclockwise wave components. In extreme cases, nearly degenerate pairs of copropagating modes can be found around the chiral exceptional points (EPs) in parameter spaces. The chiral EPs have been studied in various schemes; however, most attention has been focused on the cases with piecewise constant or periodic refractive index profiles.

A robust scheme for unidirectional emission from a hybrid whispering gallery cavity system based on transformation optics.

Using the transformation cavity, a gradient index cavity designed by transformation optics, we propose a hybrid resonator system to extract unidirectional narrow-beam emission from high-Q whispering gallery modes by embedding a transformation cavity inside a deformed uniform index cavity that exhibits unidirectional narrow-beam emission. For effective mode coupling between the transformation cavity and enclosing cavity, the embedded transformation cavity is designed to have bidirectional evanescent emission, which enables most of the emission from the transformation cavity to be laterally incident on the rim of the enclosing deformed cavity. Consequently, ultrahigh-Q resonances of this system can provide a sharp free-space light output, which is difficult to achieve by embedding a homogeneous disk cavity instead of the transformation cavity.

Birefringent whispering gallery cavities designed by linear transformation optics.

It was reported that whispering gallery cavities designed by conformal transformation optics can support high-Q resonant modes with emission directionality. Intrinsically, these cavities have gradient index profiles implementing conformal mappings in physical space. In this paper, using the linear coordinate transformation, we propose another design scheme of whispering gallery cavities with (piecewise-) homogeneous, anisotropic index profile.

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.

Noncontact photoacoustic imaging based on optical quadrature detection with a multiport interferometer.

A noncontact photoacoustic imaging method based on optical quadrature detection is proposed. The photo-induced acoustic signal is detected by an optical method without contacting the specimen. By utilizing the intrinsic phase difference of a multiport optical interferometer, the quadrature signal of a conventional interferometric signal could be obtained.

Analysis of Design and Fabrication Parameters for Lensed Optical Fibers as Pertinent Probes for Sensing and Imaging.

A method for adjusting the working distance and spot size of a fiber probe while suppressing or enhancing the back-coupling to the lead-in fiber is presented. As the optical fiber probe, a lensed optical fiber (LOF) was made by splicing a short piece of coreless silica fiber (CSF) on a single-mode fiber and forming a lens at the end of the CSF. By controlling the length of the CSF and the radius of lens curvature, the optical properties of the LOF were adjusted.

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.

An All-Fiber-Optic Combined System of Noncontact Photoacoustic Tomography and Optical Coherence Tomography.

We propose an all-fiber-based dual-modal imaging system that combines noncontact photoacoustic tomography (PAT) and optical coherence tomography (OCT). The PAT remotely measures photoacoustic (PA) signals with a 1550-nm laser on the surface of a sample by utilizing a fiber interferometer as an ultrasound detector. The fiber-based OCT, employing a swept-source laser centered at 1310 nm, shares the sample arm of the PAT system.

Chaos-assisted tunneling in a deformed microcavity laser.

We investigate the impact of local dynamics on chaos-assisted tunneling in a highly deformed microcavity whose classical ray dynamics exhibits a small measure of trapezoidal-shaped orbit (TSO) stability islands in a main chaotic sea. These two classically completely decomposed regions in phase space can support resonance modes of their own respectively. Using numerical ray and wave analyses, we show that the emission characteristics of the TSO resonance mode are determined by local ray dynamics near TSO islands.

Directional single mode emission in a microcavity laser.

We report directional single mode emission in an InGaAsP semiconductor microcavity laser, which is composed of a circle and an isosceles trapezoid. When exciting a whole cavity, the laser generates a single mode without hopping in two directions over a wide range of continuous injection currents. In the emission spectrum, it is confirmed from the equidistant mode spacing that a scar mode becomes a single lasing mode above the lasing threshold.

Resonances near the classical separatrix of a weakly deformed circular microcavity.

We study localized resonance patterns of a weakly deformed circular dielectric microcavity. The dominant pattern among them is detected when the classical motion of the light is on the separatrix of the effective potential. In this case, the topological shape of the pattern is automatically determined by the refractive index of the microcavity n.

Lasing modes in a spiral-shaped dielectric microcavity.

The resonance patterns and lasing modes in a spiral-shaped dielectric microcavity are investigated through passive and active medium calculations. We find that the high-Q resonance modes are whispering-gallery-like modes, and these resonance modes can be easily excited as lasing modes. We also find that the quasi-scarred resonance mode, which shows strong directional emission beams from the cavity boundary, can be excited with selectively applied external pumping.

Unidirectional lasing from a microcavity with a rounded isosceles triangle shape.

We report that unidirectional lasing emission can be generated from a rounded isosceles triangular microcavity within a low nkD range, where n is the refractive index, k is the vacuum wave number, and D is the characteristic size of the microcavity. It is shown that unidirectional resonance modes have relatively high-Q values and in a nonlinear dynamic model appear as stationary lasing solutions with a low threshold. The formation of a whispering-gallery-type pattern along the rounded part on the symmetry axis is responsible for the unidirectionality of the resonances.

Quasiscarred 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 quasiscarred resonances in the sense that there is, unlike conventional scarring, no underlying periodic orbits. It is shown that the formation of a quasiscarred pattern can be understood in terms of ray dynamical probability distributions and wave properties like uncertainty and interference.

Effects of time-delayed feedback on chaotic oscillators.

We study the effects of time-delayed feedback on chaotic systems where the delay time is both fixed (static case) and varying (dynamic case) in time. For the static case, typical phase coherent and incoherent chaotic oscillators are investigated. Detailed phase diagrams are investigated in the parameter space of feedback gain ( K ) and delay time ( tau ).

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 that 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.

Chaotic behaviors of operational amplifiers.

We investigate nonlinear dynamical behaviors of operational amplifiers. When the output terminal of an operational amplifier is connected to the inverting input terminal, the circuit exhibits period-doubling bifurcation, chaos, and periodic windows, depending on the voltages of the positive and the negative power supplies. We study these nonlinear dynamical characteristics of this electronic circuit experimentally.

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.

Experimental observation of characteristic relations of type-III intermittency in the presence of noise in a simple electronic circuit.

We investigate the characteristic relations of type-II and -III intermittencies in the presence of noise. The theoretically predicted characteristic relation is that approximately exp[/epsilon/(2)] for a negative regime of epsilon and approximately epsilon(-nu) for the positive regime of epsilon (1/2 is the average laminar length and (1+epsilon) is the slope of the local Poincaré map around the tangent point. We experimentally confirm these relations in a simple electronic circuit.

Transition from phase synchronization to complete synchronization in mutually coupled nonidentical Nd:YAG lasers.

Using mutually coupled nonidentical continuous-wave Nd:YAG lasers, we experimentally confirmed the recently proposed transition route from phase synchronization to complete synchronization. As evidence of this transition we obtained the probability distribution of the intermittent synchronization time near the threshold of the complete synchronization transition.

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 and clarify its characteristics using Lyapunov exponents and phase difference plots.

Routes to complete synchronization via phase synchronization in coupled nonidentical chaotic oscillators.

We study the transition route to complete synchronization through phase synchronization in generic coupled nonidentical chaotic oscillators. Through numerical studies, two routes are found, i.e.

Sequential synchronization of chaotic systems with an application to communication.

We propose a hierarchically structured communication system by using sequentially synchronized chaotic systems. Sequential synchronization is attained by first feeding a noiselike signal to a variable of the first transmitter and its receiver simultaneously and then feeding a variable of the first transmitter and its receiver to a variable of the second transmitter and its receiver, respectively, for subsequent feedings of variables in sequence. When this is applied to communication, the hierarchical structure enables selective protection of information due to the sequential property.