Analytical description of resonances in Fabry–Perot and whispering gallery mode resonators
Aigars Atvars
Abstract
Whispering gallery mode optical resonators have attracted attention due to their simplicity and applicability for sensing. In this paper, analytical formulas are provided that describe resonance conditions in optical resonators. Basic terms (resonance wavelengths and frequencies, free spectral range, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Q</mml:mi></mml:math> -factor, summation principle of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Q</mml:mi></mml:math> -factors of various processes, finesse, etc.) are introduced. A description of interference of an infinite number of waves of progressively smaller amplitudes and equal phase differences is given. A description of a Fabry–Perot resonator with nonequal reflection coefficients is also given as well as analysis of all-pass and add-drop optical filters. The presented description of resonators will help to analyze the effects of optical resonators, interpret the results of experiments, and guide the development of novel applications of microresonators.