Mapping of the surface profile of an asymmetric dielectric microcavity and identification of shape-sensitive internal modes

Abstract

In this thesis, I first present a non-destructive and non-contact highresolution optical technique for profiling soft or fluidic boundary of an opaque object. This technique utilizes the fact that the angle width, the angular separation between two adjacent intensity minima in the forward shadow diffraction, is inversely proportional to the projected width of the object in the same direction. An analytic formula for reconstructing the boundary shape is obtained for an object with two-fold symmetry in terms of the angle widths measured for various rotational angles of the object. The typical error in determining the object shape parameter is less than 0.2%, which corresponds to 20 nm of radial accuracy when applied to an object with a mean radius of 10 μm. I then apply the profiling technique to asymmetric liquid micro jet cavity and determine its surface profile in the accuracy enough to analyze the experimental results with theoretical concepts based on the one-to-one comparison between the experiments and with the numerical simulations. I found that the most dominant oscillation mode of our jet is the combination of quadrupolar and octapolar waves. The amplitudes of these two components are related by a certain quadratic relation, η2≃Bη1 2 ( η1 and η2 are amplitudes of quadrupolar and octapolar oscillation, respectively). The coefficient B is obtained as 0.42±0.08. I also survey the surface vibration of a microjet analytically by modifying Niels Bohrs non-linear hydrodynamical i treatment of the same problem, and find out that the expected value of B from this theory is nearly 0.41. The measured result and the theoretical prediction agree experimental error. With this information, fundamental intra quasi-mode positions can be predicted by simulation within experimental error. Moreover, I also confirm that numerical simulations show good agreement with spectroscopic experimental results for non-trivial features of quasi-mode dynamics such as avoided crossing gaps.