Perturbative analysis of optical microdisk cavities with boundary deformation

• Applicant: Professor Dr. Jan Wiersig
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
• Term: from 2015 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 282484332

• Final Report Year: 2020

Final Report Abstract

The general objective of the project “Perturbative analysis of optical microdisk cavities with boundary deformation” was to employ a perturbation theory and semiclassical methods to analyze several aspects of optical microdisk cavities with weak boundary deformations. Most of the goals of the project have been accomplished and further interesting results beyond the original plan have been obtained. The individual results are as follows: • The inverse problem for deformed microcavities has been introduced. It has been proven that for a given far-field intensity pattern, refractive index, and mode numbers the corresponding weak boundary deformation is unique and it has been shown how it can be calculated efficiently. • The frequency splitting for mode pairs in weakly deformed microdisks has been described by a semiclassical approach based on dynamical tunneling (resonance-assisted tunneling) between clockwise- and counterclockwise-propagating waves in raydynamical phase space. • Resonance-assisted tunneling between a given mode and the leaky region in phase space allows to accurately describe the effect of Q-spoiling in weakly deformed microdisks. • The perturbation theory has been applied to the problem of microdisks with surface roughness. Explicit and transparent formulas for the variance of the frequency splitting and the expectation values of the decay rates have been derived and successfully tested. • The semiclassical approach based on resonance-assisted tunneling and the perturbation theory have been used to locate second- and higher-order exceptional points (non-Hermitian degeneracies) in the parameter space of weakly deformed microdisks. • The perturbation theory for transverse-electric fields has been corrected. It has been demonstrated that the corrected version allows to describe the counterintuitive phenomenon of Q-factor enhancement due to a weak boundary deformation.

Publications

• Inverse problem for light emission from weakly deformed microdisk cavities. Phys. Rev. A, 94:013851, 2016
  M. Kraft and J. Wiersig
  
• Q spoiling in deformed optical microdisks due to resonanceassisted tunneling. Phys. Rev. E, 94:022202, 2016
  J. Kullig and J. Wiersig
  
• Frequency splittings in deformed optical microdisk cavities. Phys. Rev. A, 96:023848, 2017
  C.-H. Yi, J. Kullig, and J. Wiersig
  
• Optical microdisk cavities with rough sidewalls: A perturbative approach based on weak boundary deformations. Phys. Rev. A, 95:053815, 2017
  J. Wiersig and J. Kullig
  
• Exceptional points by coupling of modes with different angular momenta in deformed microdisks: A perturbative analysis. Phys. Rev. A, 98:023851, 2018
  J. Kullig, C.-H. Yi, and J. Wiersig
  
• Pair of exceptional points in a microdisk cavity under an extremely weak deformation. Phys. Rev. Lett., 120:093902, 2018
  C.-H. Yi, J. Kullig, and J. Wiersig
  
• Corrected perturbation theory for transverse-electric whispering-gallery modes in deformed microdisks. Phys. Rev. A, 99:063825, 2019
  M. Badel and J. Wiersig
  
• High-order exceptional points of counterpropagating waves in weakly deformed microdisk cavities. Phys. Rev. A, 100:043837, 2019
  J. Kullig and J. Wiersig