Interaction between negative and positive index medium waveguides

The coupling between negative and positive index medium waveguides is investigated theoretically in this paper. A coupled mode theory is developed for such a waveguide system and its validity is verified. Interesting phenomena in the coupled waveguides are demonstrated, which occur in the case when the negative index medium waveguide in isolation guides its mode backward. A new type of coupled mode solution that varies exponentially with the coupling length is found in the special case when the propagation constants of two individual waveguides are nearly the same. A coupler operating in this case is insensitive to the coupling length, and its coupling efficiency can reach 100% as long as the coupling length is long enough. However, when the propagation constants of the two individual waveguides differ greatly, the coupled mode solution is still a periodic function of the coupling length, but the coupled power is output backward. In addition, the modes in the composite waveguide system are also studied using the coupled mode theory, and their fundamental properties are revealed.Comment: 7 page

A novel view of plane wave expansion method in photonic crystals

We propose a method derived from the simple plane wave expansion that can easily solve the interface problem between vacuum and a semi-infinite photonic crystal. The method is designed to find the complete set of all the eigenfunctions, propagating or evanescent, of the translation operators $\{{\bf T_R} \}$, at a fixed frequency. With these eigenfunctions and their eigenvalues, the transmitted and reflected waves can be determined. Two kinds of applications are presented for 2D photonic crystals. The first is a selection rule for determine the normal direction of the vacuum-photonic crystal interface to achieve the highest attenuation effect at a gap frequency. The second is to calculate the transmittance and reflectance for a light incident from vacuum to an semi-infinite photonic crystal. As an example we recalculate a system studied previously by K. Sakoda et al. and get results in agreement with theirs

VR-Face: An Operator Assisted Real-Time Face Tracking System

In this paper, a model-based face analysis and synthesis system is presented. The system, named VR-Face, tracks and estimates one's 3D head motion in real time, and represents the estimated motion with a pre-rendered 3D texture-mapped head model. Initially, a user has to identify two eyes and one nostril on the screen for tracking. In this way, the background can be complex, and even dynamic. When the system fails to follow up one's head motion, it prompts the user with a box indicating the original face position to recover itself from tracking errors. The overall performance, including both analysis and synthesis, is above 25 frames/sec on a PC with a 400MHz Pentinum II-MMX CPU. The system has been demonstrated under different lighting conditions with different low-price PC cameras

Real-Time 3-D Head Motion Estimation in Facial Image Coding

A simple procedure that uses only three feature points to infer 3-D head motion from consecutive video frames is presented. In this procedure, a feature triangle formed using the three feature points is automatically calibrated, and an iterative method that simulates steepest descent method is applied to estimate one's head motion. A pre-diction algorithm is adopted in occasional cases where the estimated result is not acceptable. This procedure has been applied to live video with an update rate of 7 frames/sec (250 frames/sec without feature extraction) on a Pentium-II 233MHz PC, independent of cameras and users