标题： 平坦三维介质谐振器光谱的迹公式应用 显示英文标题

标题： Application of a trace formula to the spectra of flat three-dimensional dielectric resonators

摘要： 扁平三维圆形介质谐振器的长度谱是通过微波实验确定的。 它们与基于有效折射率近似的二维模型得到的半经典迹公式进行了比较，发现有很好的一致性。 有必要考虑有效折射率的色散以进行二维近似。 此外，实验长度谱与迹公式预测之间的微小偏差被归因于有效折射率近似的系统误差。 总之，本文中开发的方法使得迹公式可以应用于二维介质谐振器，也可用于现实中的扁平三维介质微腔和激光器，从而能够根据经典周期轨道来解释它们的光谱。 显示英文摘要

摘要： The length spectra of flat three-dimensional dielectric resonators of circular shape were determined from a microwave experiment. They were compared to a semiclassical trace formula obtained within a two-dimensional model based on the effective index of refraction approximation and a good agreement was found. It was necessary to take into account the dispersion of the effective index of refraction for the two-dimensional approximation. Furthermore, small deviations between the experimental length spectrum and the trace formula prediction were attributed to the systematic error of the effective index of refraction approximation. In summary, the methods developed in this article enable the application of the trace formula for two-dimensional dielectric resonators also to realistic, flat three-dimensional dielectric microcavities and -lasers, allowing for the interpretation of their spectra in terms of classical periodic orbits.