The mode structure of microcrystal and microdroplet lasers

The work horse of optics is the ray picture – i.e., the short-wavelength limit of Maxwell’s wave equations. In the form of the paraxial approximation, it is also the backbone of conventional optical resonator theory. Without such approximations, one is forced to resort to numerical solutions of the full wave equations, which in general reduces resonator design to trial-and-error. An exception are those few systems for which exact solutions can be obtained due to their symmetric, separable geometry. Short-wavelength (or quasiclassical) approximations appear to be as important for light as they certainly are for electrons, and hence it is somewhat surprising that classical concepts such as “diffusion” familiar from condensed matter physics have not played a significant role in optical resonator design until recently. That is so because the engineer often has the freedom to choose geometries for which either the ray picture is simple or the wave equation is separable (up to small perturbations). This is a luxury that we do not usually have with optical systems that occur in nature – specifically self-assembled dielectric microresonators formed from materials as diverse as aerosol droplets or microcrystallites. We study these optical cavities since they exhibit properties that are desirable for artificially patterned micro-optical devices as well. Because of this, the ray picture with its explanatory and predictive power is again of value. However, ray and wave properties combine in new ways when diffraction and interference compete with (a) ray chaos, induced by unconventional resonator geometries, and (b) the openness of the system due to its coupling to the environment. Among the pioneering experiments in microcavity optics were spectroscopy and imaging of liquid microdroplets falling in air[2]. If they contain a suitable organic dye, excitation by a pump beam can cause these droplets to act as extremely efficient lasers. The feedback required for lasing is provided by long-lived modes whose emission properties are found to depend sensitively on the shape of the droplet. To understand these “morphology-dependent resonanaces”, ray optics is an excellent framework: firstly, the droplets’ diameter of 30− 100 μm is much larger than optical wavelengths; furthermore, the mechanism by which the light is trapped in the droplets is total internal reflection at