The remarkable analogy between optical and mechanical phenomena was fully developed in Hamilton's ingenious optico-mechanical theory that played a fundamental role in the development of ideas in quantum physics. Thanks to the development of modern laser cavities, not only eigenvalues but also eigenfunctions have been analogously explored by using solid-state lasers for 2D quantum harmonic oscillator and semiconductor lasers for 2D quantum billiards. Optical resonators with the same isomorphism clearly confirm that the level degeneracies in 2D mesoscopic quantum systems generally lead to the wave functions with intensities concentrated on classical periodic orbits. The emergence of the ray geometry from the coherent wave in optical resonators is still an open and fascinating issue of active research in recent years. The attractive interest comes partly from the fundamental questions of light-matter interaction and ray-wave correspondence, and partly from numerous applications, such as cavity spectroscopy, optical pattern formation, single-photon emitters and ultralow threshold lasers.