大量程折射仪的分步求解算法

针对折射率m线法失效于对称金属包覆波导的大量程折射仪,本文根据模式色散方程和衰减全反射谱,提出了一种分步求解算法.首先将波导层为空气时的共振角度,由二分法及共振角处反射率之和应为最小,计算得到波导层的最优厚度.然后利用波导层最优厚度和波导层为样品时的共振角度,计算出样品的最优折射率.这种算法简单、迅速、误差小.以纯水为例,利用该算法所得结果与真实值一致.

Study on the multi-step algorithm for large-range refractometer

Based on the modal dispersion equation and attenuated total reflection spectrum, a multi-step algorithm for calculating the refractive index of analyte in symmetrical metal-cladding waveguide （SMCW） is proposed, and thus the large error generated by the utilization of m-line method to the SMCW-based large-range refractometer is avoided. Our algorithm is simple, quick and accurate. The calculation processes are as follow： the thickness of the guiding layer is obtained from the resonant angles when air is acted as guiding layer, then the refractive index of analyte is calculated from the obtained optimal thickness and the resonant angles when analyte is employed as guiding layer. The calculation mechanism of these two processes is that the approximate range can be given by dichotomy and the sum of reflectivity at all resonant angles should be minimal. Taking pure water as an example, the calculated refractive index agrees well with the actual one.