Study on stress-optical coefficients for analyzing character of oscillating quartz crystal resonators

A dynamic photoelastic method (probe light beam modulation method) is a practical system for investigating quartz crystal resonators which are oscillating in the resonant frequency. This method has been applied to analyze the behavior of AT cut and NS-GT cut quartz crystal resonators in previous studies. When we analyze the character of an oscillating quartz crystal resonator by using optical methods we have to note that a quartz crystal has birefringence (double refraction). Then, if stress distributions of the resonator will be measured by the probe light beam modulation method, stress-optical coefficients C´(x, Ω) are very important factors. These coefficients are function of resonator´s cut angles from an original quartz crystal and an incident angle of probe light beam to a surface of the quartz crystal resonator. A specific vibrating stress σ´_b of the quartz crystal resonator can be detected separately, from unwanted spurious stresses and vice versa, when the incident angle of the probe light beam is chosen at an adequate direction