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. In this Letter, we report the formation of a chiral EP in a gradient-index cavity designed by conformal transformation optics. Here, the mirror symmetry of the cavity is broken solely by its gradient index profile, and the parameter space is constructed with coordinate transformation parameters. We unveil the chirality, nonorthogonality, and complex-square-root topology near the chiral EP, which can be explained by the non-Hermitian model Hamiltonian.

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. We numerically show that so-designed cavities are also able to support high-Q whispering gallery modes with directional far-field emission patterns. We verify such characteristics by using a phase space representation (called the Poincaré Husimi function) of the intracavity wave function.

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. With this quadratic signal pair, we could reconstruct the photoacoustic signal without suffering from the initial phase drift that usually occurs in a conventional interferometric system. The performance of the proposed system is verified by imaging human hairs embedded in a polydimethylsiloxane resin block. The system's lateral and axial resolutions are measured to be 84 and 86 µm at a 1.5 mm depth of a PDMS resin block, respectively. The experimental result is good enough to distinguish the hairs staggered in depth.

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. The evolution of the beam in the LOF was analyzed by using the Gaussian ABCD matrix method. To confirm the idea experimentally, 17 LOF samples were fabricated and analyzed theoretically and also experimentally. The results show that it is feasible in designing the LOF to be more suitable for specific or dedicated applications. Applications in physical sensing and biomedical imaging fields are expected.

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.

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. The fiber-optic probe for the combined system was homemade with a lensed single-mode fiber (SMF) and a large-core multimode fiber (MMF). The compact and robust common probe is capable of obtaining both the PA and the OCT signals at the same position without any physical contact. Additionally, the MMF of the probe delivers the short pulses of a Nd:YAG laser to efficiently excite the PA signals. We experimentally demonstrate the feasibility of the proposed dual-modal system with a phantom made of a fishing line and a black polyethylene terephthalate fiber in a tissue mimicking solution. The all-fiber-optic system, capable of providing complementary information about absorption and scattering, has a promising potential in minimally invasive and endoscopic imaging.

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. The emission characteristics of the other high-Q resonance modes, on the other hand, are governed by usual ray-wave correspondence. We experimentally demonstrate that the TSO emission mode can be lased without selective excitations by devising a half-moon shaped highly deformed cavity. And we also show that the emission characteristics of the TSO lasing modes are well explained by numerical ray and wave analyses.

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. A numerical analysis of the boundary element method shows that the far-field pattern of the resonance agrees well with that of the experiment.

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. Also, the pattern can be interpreted as a linear combination of nearly degenerate eigenstates in the circular dielectric microcavity. Applying this analysis to a spiral-shaped microcavity, we generate quasiscarred patterns for n=2 and n=3.

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. Through a spectral analysis of the time evolution of the light field, the competition between these lasing modes is discussed.

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.

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 ). Linear stability analysis, by assuming the time-delayed perturbation, varies as e(lambdat) where lambda is the eigenvalue, gives the boundaries of the stability islands and critical feedback gains ( K(c) ) for both Rössler oscillators and Lorenz oscillators. We also found that the stability island are found when the delay time is about tau= (n+ 1 / 2 ) T , where n is an integer and T is the average period of the chaotic oscillator. It is shown that these analytical predictions agree well with the numerical results. For the dynamic case, we investigate Rössler oscillator with periodically modulated delay time. Stability regimes are found for parameter space of feedback gain and modulation frequency in which it was impossible to be stabilized for a fixed delay time. We also trace the detailed routes to the stability near the island boundaries for both cases by investigating bifurcation diagrams.

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.

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.

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.

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.