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.

Transformation cavities with a narrow refractive index profile.

Recently, gradient index cavities, or so-called transformation cavities, designed by conformal transformation optics, have been studied to support resonant modes with both high Q-factors and emission directionality. We propose a new, to the best of our knowledge, design method for transformation cavities to realize a narrower width of the refractive index profile, a great advantage in experimental implementations, without losing the benefits of conformal mapping. We study resonant modes with both high Q-factors and directional emission in newly designed transformation cavities, where the refractive index profile is 50% narrower than in previously proposed transformation cavities. By varying a system parameter with a fixed maximal value of the refractive index profile inside the cavity, the width of the refractive index profile narrows, the Q-factors become higher, and the near and far field patterns maintain their properties, namely, conformal whispering gallery modes and bidirectional emission, respectively.

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.

Optimization of conformal whispering gallery modes in limaçon-shaped transformation cavities.

Directional light emission from high-Q resonant modes without significant Q-spoiling has been a long standing issue in deformed dielectric cavities. In limaçon-shaped gradient index dielectric cavities recently proposed by exploiting conformal transformation optics, the variation of Q-factors and emission directionality of resonant modes was traced in their system parameter space. For these cavities, their boundary shapes and refractive index profiles are determined in each case by a chosen conformal mapping which is taken as a coordinate transformation. Through the numerical exploration, we found that bidirectionality factors of generic high-Q resonant modes are not directly proportional to their Q-factors. The optimal system parameters for the coexistence of strong bidirectionality and a high Q-factor was obtained for anisotropic whispering gallery modes supported by total internal reflection.

Designing arbitrary-shaped whispering-gallery cavities based on transformation optics.

A novel approach to designing anisotropic whispering gallery modes in gradient index cavities has been reported recently. These cavities, called transformation cavities, can support high-Q whispering gallery modes with directional emission. However, it is usually difficult to find the desired conformal mapping, and it may contain unwanted singularities inside. We show that arbitrary-shaped transformation cavities can be designed by virtue of a quasi-conformal mapping method without confronting such problems. Even though the quasi-conformal mapping method is exploited, we verify that the resulting mappings in our case are strictly conformal. As a demonstration, Q-factor, near field intensity, far field pattern, and phase space description of resonant modes formed in so-designed quadrupole-shaped transformation cavities are presented.

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.

Terahertz beat frequency generation from two-mode lasing operation of coupled microdisk laser.

We propose a coupled microdisk laser as a compact and tunable laser source for the generation of a coherent continuous-wave terahertz radiation by photomixing. Using the Schrödinger-Bloch model including the nonlinear effect of active medium, we find single-mode and two-mode lasings depending on the pumping strength. We explain the transitions of lasing modes in terms of resonant modes that are the solutions of the Schrödinger-Bloch model without active medium and nonlinear interaction. In particular, a two-mode lasing is shown to generate a terahertz oscillating frequency originating from the light beating of two nearly degenerated resonant modes with different symmetries.

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.

Experimental observation of the characteristic relations of type-I intermittency in the presence of noise.

Recently, it has been reported that the characteristic relation of type-I intermittency in the presence of noise is deformed nontrivially as the channel width epsilon changes from the positive region to the negative. In order to verify it experimentally as a real phenomenon, we study the characteristic relations both for epsilon<0 and for epsilon>0 in a simple inductor-resistor-diode circuit that is under noisy circumstances. The experimental results agree well with the theoretical expectation that the characteristic relations are proportional to epsilon(-1/4) for epsilon>0 and proportional to exp(alpha/epsilon/(3/2)) for epsilon<0.