References
- Berry, M. V., & Tabor, M. (1976). Closed orbits and the regular bound spectrum. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 349, 101–123.
- Bruno, O. P., & Reitich, F. (2001). Boundary-variation solution of eigenvalue problems for elliptic operators. Journal of Fourier Analysis and Applications, 7, 171–189.
- Cao, H., & Wiersig, J. (2015). Dielectric microcavities: Model systems for wave chaos and non-hermitian physics. Reviews of Modern Physics, 87, 61–111.
- Chakraborty, S., Bhattacharjee, J. K., & Khastgir, S. P. (2009). An eigenvalue problem in two dimensions for an irregular boundary. Journal of Physics A: Mathematical and Theoretical, 42, 195301.
- Dubertrand, R., Bogomolny, E., Djellali, N., Lebental, M., & Schmit, C. (2008). Circular dielectric cavity and its deformations. Physical Review A, 77, 013804.
- Harayama, T., & Shinohara, S. (2011). Two-dimensional microcavity lasers. Laser and Photonics Reviews, 5, 247–271.
- Itin, A. P., & Neishtadt, A. I. (2003). Resonant phenomena in slowly perturbed elliptic billiards. Regular and Chaotic Dynamics, 8, 59–66.
- Leonhardt, U. (2006). Optical conformal mapping. Science, 312, 1777–1780.
- Li, W., Reichl, L. E., & Wu, B. (2002).Quantum chaos in a ripple billiard. Physical Review E, 65, 056220.
- Reck, K., Thomsen, E. V., & Hansen, O. (2011). Solving the Helmholtz equation in conformal mapped ARROW structures using homotopy perturbation method. Optics Express, 19, 1808–1823.
- Ree, S., & Reichl, L. E. (1999). Classical and quantum chaos in a circular billiard with a straight cut. Physical Review E, 60, 1607–1615.
- Reichl, L. (2004). The transition to chaos: Conservative classical systems and quantum manifestations. New York, NY: Springer.
- Schinzinger, R. (2003). Conformal mapping: Methods and applications. Mineola, New York, NY: Dover Publications.
- Sieber, M. (1997). Semiclassical transition from an elliptical to an oval billiard. Journal of Physics A: Mathematical and General, 30, 4563–4596.
- Tureci, H., Schwefel, H., Stone, A., & Narimanov, E. (2002). Gaussian-optical approach to stable periodic orbit resonances of partially chaotic dielectric micro-cavities. Optics Express, 10, 752–776.
- Waalkens, H., Wiersig, J., & Dullin, H. R. (1997). Elliptic quantum billiard. Annals of Physics, 260, 50–90.
- Watson, G. N. (1966). A treatise on the theory of Bessel functions (2nd.ed.). Cambridge: Cambridge University Press.