Bulletin Spring‧Summer 1996

The Effect of the Liquid on the Light This work answered the question of what the light does to the liquid, but in many ways the other half of the problem — what the liquid does to the light — was more interesting. Light can suffer total internal reflection at the microdroplet interface, and become trapped in a closed path (Fig. 1). If the length of the closed path is an integral number of wavelengths, the e l e c t r oma g n e t ic f i e ld can f o rm a resonance. This is analogous to the vibrations of a violin string — i f the round trip path between the t wo clamped ends is an integral number of wavelengths, a standing wave, or resonance, is formed (Fig. 2). Many groups had observed these resonances spectroscopically, and realized their importance in nonlinear optics. In particular, optical feedback in these spherical systems has led to lasers about 1/100 mm in size, probably a wo r ld record in miniaturization. Moreover, since wavelength is proportional to circumference, this technique allows monitoring of the droplet size, e.g., the size of diesel f uel droplets in internal combustion engines. However, there is one major difference between the resonances on a violin string and the optical resonances in amicrodroplet. In the latter, the laws of electromagnetism dictate that a tiny part of the electromagnetic energy w i ll leak to the outside. When energy does not remain constant, many conventional tools of theoretical physics need to be modified. The CUHK group was able to give a precise definition of what is meant by a resonance in these circumstances, and to show that this leads to better understanding of many optical phenomena. 3 The most intriguing observation is that atomic and molecular life-times can be drastically reduced (and sometimes increased) when atoms and molecules are situated in a nontrivial environment such as a microdroplet or a cavity, even though they have no contact with the walls of the cavity. Emily Ching worked on this problem for her M.Phil, thesis, and the paper based thereon has become a standard reference. 3 Ching has since obtained her Ph.D. from Chicago University working on nonequilibrium nonlinear systems, in particular turbulence, and rejoined the department as a lecturer in 1995. Achievements of Research in Optical Interaction with Microdroplets With this set of tools in hand, the group felt that it was in a unique position to tackle a large number of phenomena in the area of optical interaction with microdroplets, and in 1988, Lai and Young obtained an RGC grant of HK$ 100,000 to work on these issues. P.T. Leung, then a Ph.D. student in the group, was a co-investigator; he has since become a lecturer in the Department of Physics. A variety of problems were tackled, and understood, including Brillouin scattering, the splitting of resonances, the precession of photon orbits, the degradation of resonances due to minor changes in shape. At the same time, Lai, Leung and Young realized that many of these issues are relevant to all quantum systems from which energy is lost to the environment — for which there is a dearth of standard mathematical tools. So, another thread of the project, possibly the more important one in the long run, is to generalize the standard tools of mathematical physics to such open systems. An important result, principally due to Leung's efforts, is that the resonances in many situations actually give a complete description of the system, in a precise mathematical sense. This generalizes the classic works of many, including Fourier, and Sturm and Liouville. Prof. S.Y. Liu of the University of Science and Technology of China, as well as a number of CUHK students ， all made 31