Quantum Goos-H\"{a}nchen shift and tunneling transmission at a curved step potential

We study the quantum Goos-H\"{a}nchen (GH) shift and the tunneling transmission at a curved step potential by investigating the time evolution of a wave packet. An initial wave packet is expanded in terms of the eigenmodes of a circular step potential. Its time evolution is then given by the interference of their simple eigenmode oscillations. We show that the GH shift along the step boundary can be explained by the energy-dependent phase loss upon reflection, which is defined by modifying the one-dimensional (1D) effective potential derived from the 2D circular system. We also demonstrate that the tunneling transmission of the wave packet is characterized by a free-space image distant from the boundary. The tunneling transmission exhibits a rather wide angle divergence and the direction of maximum tunneling is slightly rotated from the tangent at the incident point, which is consistent with the time delay of the tunneling wave packet computed in the 1D modified effective potential

Synchronization of Chaotic Oscillators due to Common Delay Time Modulation

We have found a synchronization behavior between two identical chaotic systems^M when their delay times are modulated by a common irregular signal. ^M This phenomenon is demonstrated both in two identical chaotic maps whose delay times are driven by a common^M chaotic or random signal and in two identical chaotic oscillators whose delay times are driven by^M a signal of another chaotic oscillator. We analyze the phenomenon by using^M the Lyapunov exponents and discuss it in relation with generalized synchronization.^MComment: 5 pages, 4 figures (to be published in PRE

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 lima\c{c}on-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.Comment: 13 pages, 6 figure

Dependence of far-field characteristics on the number of lasing modes in stadium-shaped InGaAsP microlasers

We study spectral and far-field characteristics of lasing emission from stadium-shaped semiconductor (InGaAsP) microlasers. We demonstrate that the correspondence between a lasing far-field emission pattern and the result of a ray simulation becomes better as the number of lasing modes increases. This phenomenon is reproduced in the wave calculation of the cavity modes.Comment: 7 pages, 3 figure

Ultrathin, polarization-independent, and focus-tunable liquid crystal diffractive lens for augmented reality

Despite the recent advances in augmented reality (AR), which has shown the potential to significantly impact on our daily lives by offering a new way to manipulate and interact with virtual information, minimizing visual discomfort due to the vergence-accommodation conflict remains a challenge. Emerging AR technologies often exploit focus-tunable optics to address this problem. Although they demonstrated improved depth perception by enabling proper focus cues, a bulky form factor of focus-tunable optics prevents their use in the form of a pair of eyeglasses. Herein, we describe an ultrathin, focus-tunable liquid crystal (LC) diffractive lens with a large aperture, a low weight, and a low operating voltage. In addition, we show that the polarization dependence of the lens, which is an inherent optical property of LC lenses, can be eliminated using birefringent thin films as substrates and by aligning the optical axes of the birefringent substrates and LC at a specific angle. The polarization independence eliminates the need for a polarizer, thus further reducing the form factor of the optical system. Next, we demonstrate a prototype of AR glasses with addressable focal planes using the ultrathin lens. The prototype AR glasses can adjust the accommodation distance of the virtual image, mitigating the vergence-accommodation conflict without substantially compromising the form factor or image quality. This research on ultrathin lens technology shows promising potential for developing compact optical displays in various applications.Comment: 23 pages, 9 figure