Total internal reflection-based biochip utilizing a polymer-filled cavity with a micromirror sidewall

A total internal reflection (TIR)-based biochip utilizing a polymer-filled cavity with a micromirror sidewall has been designed and fabricated. The implementation of the micromirror sidewall cavity facilitates precise alignment of the excitation light beam into the system. The incident angle of illumination can be easily modified by selecting polymers of different indices of refraction while optical losses are minimized. The design enables the hybrid, vertical integration of a laser diode and a CCD camera, resulting in a compact optical system. Brownian motion of fluorescent microspheres and real-time photobleaching of rhodamine 6G molecules is demonstrated. The proposed TIR-based chip simplifies current TIR optical configurations and could potentially be used as an optical-microfluidic platform for an integrated lab-on-a-chip microsystem.     

Numerical computations of integrals over paths on Riemann surfaces of genusN

This paper is a continuation of work by Forest and Lee [1,2]. In [1,2] it was proved that the function theory of periodic soliton solutions occurs on the Riemann surfaces ? of genusN, where the integrals over paths on ? play the most fundamental role. In this paper a numerical method is developed to evaluate these integrals. Predisely, the aim is to develop a computational code for integrals of the form $$\int\limits_\gamma {f(z)\frac{{dz}}{{R(z)}}, or} \int\limits_\gamma {f(z)R(z)dz,} $$ wheref(z) is any single-valued analytic function on the complex planeC, andR(z) is a two-valued function onC of the form $$R^2 (z) = \prod\limits_{k = 1}^{2N + \delta } {(z - z_0 (k)), \delta = 0 or 1,} $$ where {z ₀(k),1≤k≤2N+δ} are distinct complex numbers which play the role of the branch points of the Riemann surface ? = {(z, R(z))} of genusN?1+δ. The integral path γ is continuous on ?. The numerical code is developed in “Mathematica” [3].