Invited paper Fourier-transform heterodyne spectroscopy of liquid and solid surfaces

Fourier-transform heterodyne spectroscopy is a simple but powerful technique to study narrow line shapes and small frequency shifts. We review the technique and its application to the study of hydrodynamic fluctuations. We introduce a simple scheme for obtaining the full spectrum of light scattered from liquid and solid surfaces. Using this scheme we obtained a spectral resolution of 200 μHz. Two applications of the technique, one involving the detection of counter-propagating capillary waves, the other measurement of the epitaxial crystal-growth speed of a crystalline silicon interface, are presented. PACS: 07.65; 68.10; 68.35 In many experiments one is interested in determining changes in a certain physical quantity. This requires measurement of the quantity with respect to a reference value. When it is not possible to measure the quantity directly or to have a reliable reference one can still do accurate differential measurements. For example, if one is interested in measuring the small frequency shift of an electromagnetic wave due to a scattering process, one must either measure, to a very high degree of accuracy, the frequencies of each of the incident and scattered waves to determine the frequency difference, or one can measure directly the beat frequency of the two waves. In the second method the difference in frequency of the two waves is directly measured. Differential measurements can be carried out even if the reference (the incident electromagnetic wave) fluctuates and require a smaller relative accuracy than absolute measurements. In radio and radio-frequency technology differential techniques have been applied extensively. Beating at optical frequencies was first demonstrated in the classic Zeeman splitting experiment of Forrester et al. in 1955 using a mercury lamp as a light source [1]. With the advent of lasers, lightbeating spectroscopy has become an important tool for measuring optical lineshapes and small frequency shifts with a resolution on the order of several Hertz [2]. The technique was first used for the study of the output of lasers by monitoring intermode beats [3]. Today beating spectroscopy is an invaluable tool in many fields including quasi-elastic light scattering studies of macromolecules and critical phenomena of fluids [4], surface wave light scattering studies of the viscoelastic properties of fluid interfaces [5], and velocimetry of fluids [6,7]. In this paper we are mainly concerned with light scattering from interfacial fluctuations in fluids, in particular from capillary waves on liquid surfaces (also called ripples or ripplons) [8], which result from the interplay between thermal fluctuations and interfacial tension. Consider a light beam striking the interface between two media with different indices of refraction. At a smooth and sharp interface, the beam is reflected and refracted. If the interface is rough, the incident light is scattered; if, in addition, the roughness is time-dependent, the scattered light has a different frequency spectrum from that of the incident light. Thus, by analyzing the spectrum of the light scattered from a fluctuating fluid interface, one can obtain information on the dynamics of the interface. The first attempts at measuring the capillary wave spectra of methanol and isopropanol were made by Katyl and Ingard using a Fabry-P érot interferometer as a scanning optical filter [9]. Since the resolution of the interferometer was too low to resolve the capillary wave peaks, only a broadening of the incident light spectrum was observed. Using a differential light-beating technique, one year later, Katyl and Ingard were able to observe the capillary wave peaks of methanol [10]. At the same time Bouchiat et al. measured capillary wave spectra of ether and glycerine using a light-beating technique, and obtained the dispersion of the capillary waves [11,12]. Since then lightbeating or heterodyne spectroscopy has been widely used to study capillary waves on a great variety of fluid interfaces [13–16]. The beat signal can be processed in the time domain to get an intensity correlation function or in the frequency domain to get the power spectrum. The intensity correlation function is typically obtained with an autocorrelator [17]; the power spectrum is obtained using a scanning electric filter [18], or by performing a Fourier transform on the intensity correlation function. One can also get the power spectrum more directly by performing a Fourier transform on the beat signal [17]. Recent advances in computer technology have made this frequency-domain analysis more convenient and cost-effective than conventional time-domain analysis using autocorrelators. Combined with a heterodyne detection