Hermite–Gaussian beams, as a typical kind of higher-order mode laser beams, have attracted intensive attention because of their interesting properties and potential applications. In this paper, a full vector wave analysis of the higher-order Hermite–Gaussian beams upon reflection and refraction is reported. The explicit analytical expressions for the electric and magnetic field components of the reflected and refracted Hermite–Gaussian beams are derived with the aid of angular spectrum representation and vector potential in the Lorenz gauge. Based on the derived analytical expressions, local field distributions of higher-order Hermite–Gaussian beams reflection and refraction at a plane interface between air and BK7 glass are displayed and analyzed.

A generic new data processing method is developed to accurately calculate the absolute optical path difference of a low-finesse Fabry-Perot cavity from its broadband interference fringes. The method combines Fast Fourier Transformation with nonlinear curve fitting of the entire spectrum. Modular functions of LabVIEW are employed for fast implementation of the data processing algorithm. The advantages of this technique are demonstrated through high performance fiber optic temperature sensors consisting of an infrared superluminescent diode and an infrared spectrometer. A high resolution of 0.01 °C is achieved over a large dynamic range from room temperature to 800 °C, limited only by the silica fiber used for the sensor.

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