The Why's and Wherefore's of Refraction

How does strong light interact with transparent refracting material such as water droplets? A research project by Prof. H.M. Lai and Prof. K. Young of the Department of Physics to study this phenomenon won an 'excellent' rating by the Research Grants Council, an honour it shared with seven other CUHK research projects. A total of only 13 projects have been so rated in Hong Kong.

Events That Raised Interest in the Subject

Although funding from the Research Grants Council (RGC) was only applied for in the late 1980s, the two researchers became interested in the subject about 20 years ago, when both as new lecturers in the department became aware of a Bell Labs experiment which showed that a strong beam of laser shone perpendicularly onto a liquid surface did not push the surface in, but instead drew it upwards. This contradicted all conventional notions of radiation pressure, and was all the more strange since electromagnetism was supposed to have been completely understood for over a century. A chance visit by Prof. Sir Rudolph Peierls, head of the physics department at Oxford, pointed the way to a new approach. The critical issue, which the investigators recognized, is that the molecules re-arrange themselves in the presence of light energy, and a complete solution can be found for moderately long pulses of light passing through transparent refracting material.(1) W.M. Suen worked on this problem for his M.Phil. thesis, and has since obtained his Ph.D. from Caltech in general relativity, become tenured in Washington University, and in 1995 won the Outstanding Young Researcher Award from the Overseas Chinese Physicists Association in the United States. He is currently an associate professor in the University's Department of Physics for one term.

The early work on laser interaction with bulk liquids foreshadowed later investigations into interaction with microdroplets. The next major development came about through yet another chance visit, this time by Prof. Richard Chang of Yale University, in the mid-1980s. There was then much interest in what happens when an intense laser pulse runs into fog -- a collection of transparent microdroplets. Since this problem involves precisely the force exerted by light on a transparent liquid, the group at CUHK was one of the few that had the knowledge to solve it, and research results agreed precisely with experiments using single microdroplets.(2)

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 electromagnetic field can form a resonance. This is analogous to the vibrations of a violin string -- if the round trip path between the two 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 world record in miniaturization. Moreover, since wavelength is proportional to circumference, this technique allows monitoring of the droplet size, e.g., the size of diesel fuel droplets in internal combustion engines.

Fig. 1Fig. 2

However, there is one major difference between the resonances on a violin string and the optical resonances in a microdroplet. In the latter, the laws of electromagnetism dictate that a tiny part of the electromagnetic energy will 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 important contributions. Some of the subsequent work was also supported by a Croucher Foundation grant.

The formalism is applicable to many systems that lose energy to the environment. It turns out that gravitational waves emitted from black holes constitute one such system, formally very analogous to electromagnetic waves emitted from microdroplets -- even though the length scales differ by a factor of a billion. The researchers at CUHK, together with W.M. Suen, have achieved a much clearer understanding of the behaviour of such waves, which are expected to be detected within the next decade.(4)

Future Research in the Field

The new approach opens up many research directions. In June 1995, Ching, Leung, Suen and Young were awarded another RGC grant to study waves in open systems in general, while Leung and Lai were awarded an RGC grant to study specific optical phenomena in microdroplets. Both are the outgrowths of the original project awarded in 1988. Speaking of this long-term project, both Prof. Lai and Prof. Young feel that future developments will depend principally on the younger members of the team. As regards themselves, the project has been gratifying not only because of the scientific results, but also because it has provided opportunities for a home-grown team to be nurtured.

References

  1. H.M. Lai, W.M. Suen & K. Young, Phys. Rev. Lett., 47, 177 (1981); Phys. Rev., A25, 1755 (1982).
  2. H.M. Lai, P.T. Leung, K.L. Poon & K. Young, J. Opt. Soc. Am., B6, 2430 (1989).
  3. E.S.C. Ching, H.M. Lai & K. Young, J. Opt. Soc. Am., B4, 1995 (1987).
  4. E.S.C. Ching, P.T. Leung, W.M. Suen & K. Young, Phys. Rev. Lett., 74, 2414 (1995).


From left: W.M. Suen, H.M. Lai, P.T. Leung, K. Young, E.S.C. Ching, S.Y. Liu and S.S. Tong

Prof. Kenneth Young is a theoretical physicist. He obtained his BS and Ph.D. from the California Institute of Technology in 1969 and 1972 respectively, and joined CUHK in 1973. His research interests cover a wide range of subjects including high energy physics, optical physics, electrodynamics, meteorology, etc. He is a professor of physics and is serving concurrently as a pro-vice-chancellor of the University, and dean of the Graduate School. Prof. Hon-Ming Lai obtained his B.Sc. from CUHK in 1967 and Ph.D. from Dartmouth College in the United States in 1971. He joined CUHK as lecturer in 1974. He is a theoretical physicist with research interests in plasma physics, electrodynamics, and optical physics. He is a professor in the Department of Physics and is serving concurrently as chairman of the department.