Simple single-lens equivalent systems for graded-index (GRIN) lenses in inhomogeneous medium obtained using matrix optics are proposed in this letter. Due to its simplicity, the equivalent optical system enables quick analysis of the imaging properties of GRIN lens rod immersed in inhomogeneous medium. This facilitates the optical analysis of complicated optoelectronics systems in inhomogeneous medium utilizing GRIN lens rods.

The spontaneous emission rate of two interacting excited atoms near a dielectric interface is studied using the photon closed-orbit theory and the dipole image method. The total emission rate of one atom during the emission process is calculated as a function of the distance between the atom and the interface. The results suggest that the spontaneous emission rate depends not only on the atomic-interface distances, but also on the orientation of the two atomic dipoles and the initial distance between the two atoms. The oscillation in the spontaneous emission rate is caused by the interference between the outgoing electromagnetic wave emitted from one atom and other waves arriving at this atom after traveling along various classical orbits. Each peak in the Fourier transformed spontaneous emission rate corresponds with one action of photon classical orbit.

The formulas of the quantum electrodynamics have been applied to calculate the spontaneous emission rate of excited atom in dielectric microcavity. The results exhibit damping oscillating patterns which depend sensitively on the scaling parameter and geometrical structure. Compared with the case that the emitting atom is immersed in dielectric, the spontaneous emission rate is depressed obviously and the center or the mean value of the oscillations is intimately related to the real refractive index of the local position where the atom is. In order to explain this phenomenon, we utilize the closed-orbit theory to deal with the classical trajectories of the emitted photon, and extract the corresponding frequencies of the oscillations by Fourier transform. It is found that the oscillations can be represented in terms of the closed-orbits of the photon motion constrained in dielectric microcavity, thus providing another perspective on the spontaneous emission of atom sandwiched by dielectric slabs.

Gauge block measurement by using optical interferometry in Korea Research Institute of Standards and Science (KRISS) is described. A partially modified commercial Twyman-Green type gauge block interferometer equipped with three frequency stabilized lasers which are coupled into one single mode optical fiber, is used for the measurement of gauge blocks of nominal length up to 250 mm. Fringe scanning Fourier transform method is used to obtain the excess fraction value from the interference fringes. The temperature inside the interferometer is stabilized within +-4 mK for three hours. The standard uncertainty (k=1) of measurement is 29 nm for a 250-mm gauge block.

Using Gutzwiller's periodic orbit theory, we study the quantum level density of a spherical billiard in the presence of a magnetic flux line added at its center, especially discuss the influence of the magnetic flux strength on the quantum level density. The Fourier transformed quantum level density of this system has allowed direct comparison between peaks in the level density and the length of the periodic orbits. For particular magnetic flux strength, the amplitude of the peaks in the level density decreased and some of the peaks disappeared. This result suggests that Aharonov-Bohm effect manifests itself through the cancellation of periodic orbits. This phenomenon will provide a new experimental testing ground for exploring Aharonov-Bohm effect.

The limitation of paraxial condition of paraboloid refracting system in performing fractional Fourier transform acts like an aperture, which makes the system different from ideal systems. With aperture expanded as the sum of finite complex Gaussian terms, a more practical approximate analytical solution of fractional Fourier transform of Gaussian beam in an apertured paraboloid refracting system is obtained and also numerical investigation is presented. Complicated and practical fractional Fourier transform systems can be constructed by cascading several apertured paraboloid refracting systems which are the simplest and the most basic units for performing more precise transform.