6 Nonlinear Optics at Liquid^Liquid Interfaces PIERRE-FRANCOIS BREVET Laboratoi
6 Nonlinear Optics at Liquid^Liquid Interfaces PIERRE-FRANCOIS BREVET Laboratoire d’Electrochimie, De ´ partement de Chimie, Ecole Polytechnique Fe ´ de ´ rale de Lausanne, Lausanne, Switzerland I. INTRODUCTION Processes at interfaces are ubiquitous in nature. They occur in respiration or photosynth- esis reactions, for example, and one of the elementary steps in these mechanisms often involves the transfer of charged species across the interface. As a result, any experimental studies attached to the investigation of these transfer reactions entail the development of a surface sensitive technique. For charged species transfer reactions, the methodology of choice has long been derived from standard electrochemistry, since the transfer of a charged particle across an interface gives rise to a current which is amenable to detection by conventional electrochemical techniques [1]. The field of liquid–liquid electrochemistry has greatly benefited from these general ideas [2–4]. A major drawback of this approach, though, is that the distinction between the different transferring species is not an easy matter. This is an important problem in many aspects relevant to biological processes, as the transfer of an electron across the interface is often coupled to the simultaneous transfer of an ion. More selective techniques have been devised, and the most successful rely on spectroscopy principles. Indeed, the signature of a transferring species may be obtained from its absorption or emission spectrum and therefore UV-visible absorption and fluor- escence spectroscopy have been employed extensively [5–10]. The use of other techniques like resonance Raman spectroscopy has also been reported [11,12]. Nevertheless, linear optical techniques have no intrinsic surface specificity and therefore require an optimized optical configuration to gain surface specificity. The geometry of choice in this case is the total internal reflection (TIR) geometry whereby the light impinges onto the interface from the medium of highest refractive index n1, usually the organic phase, with an angle of incidence larger than the critical angle given by arcsinðn2=n1Þ. The electromagnetic wave present in the low-index phase (index n2) is thus an evanescent wave for which the pene- tration depth is only of the order of 100 nm. This depth is only a fraction of the diffusion layer in mass transport limited processes but is still far greater than the Debye screening length and therefore precludes any studies addressing the problem of adsorption or double layer effects at interfaces. This is clearly a major limitation, circumvented only on rare occasions [13,14]. This problem has led to the development of nonlinear optical techniques that do have a much more reduced probing depth at the interface owing to symmetry rules. The simplest nonlinear techniques are the three wave mixing techniques, namely sum 123 Copyright © 2001 Marcel Dekker, Inc. frequency and difference frequency generation (respectively SFG and DFG) whereby two fundamental photons of frequency !1 and !2 are converted into one photon at the fre- quency !1 þ !2 in SFG or !1 !2 in DFG [15]. In the simple case where a single funda- mental frequency is used, two photons at the frequency ! are converted into one photon at the frequency 2!. The technique is called second harmonic generation (SHG) and is probably the one that is the most widely used because of the simplicity of the experimental arrangement. Although originally applied in surface science to study molecular adsorption on clean surfaces under high-vacuum conditions, the field has rapidly expanded to other domains [16,17]. The first study of liquid–liquid interfaces has been reported by S. G. Grubb et al. in 1988 for the orientation of compounds at the water–carbon tetrachloride interface [18]. Subsequently, the structure and the dynamics of liquid interfaces have been the focus of interest and the problem of charge transfer reactions across the polarized liquid–liquid interfaces has only been addressed recently [19,20]. The present review intends to cover the work reported on nonlinear optics at liquid– liquid interface since the first report of S. G. Grubb et al. [18]. The theoretical aspects of nonlinear optics are first introduced in Section II. The experimental results covering the molecular structure of liquid interfaces are presented in Section III, followed by a section devoted to the dynamics and the reactivity at these interfaces. Section V focuses on new aspects where spherical interfaces with radii of curvature of the order of the wavelength of light are investigated. Section VI presents the field of SFG. II. THEORETICAL APPROACHES A. General Theoretical Framework The problem is restricted in this section to SHG only and hence to a single monochromatic electromagnetic wave impinging at the interface between two dielectric media. This is the general framework describing SHG at both air–liquid and liquid–liquid interfaces. The light source is taken as a well-defined monochromatic harmonic plane wave and is char- acterized by its wave vector kð!Þ and its electric field vector Eð!Þ. On impinging at the interface between the two media from medium 1, the wave is refracted into medium 2 and reflected back into medium 1 according to the usual laws of linear optics (see Fig. 1) [21]. In particular, the Snell–Descartes law holds for the angles of incidence, reflection, and refraction at the fundamental frequency. The fundamental electromagnetic wave induces a polarization wave in the medium while traveling, as a result of the action of the electric field Eð!Þ on all the particles constituting the dielectric medium. At optical frequencies ranging between 1013 and 1015 Hz, only the electronic motion is of interest and the polarization is reduced to its electronic part. In most cases, one can assume that the polarization oscillates at the exciting frequency. However, for large field amplitudes, one has to include the nonlinear components oscillating at harmonic frequencies owing to the nonlinear response of the electrons of the material to the excitation field. The first-order nonlinear contribution varies quadratically with the excitation field and therefore contains a contribution oscillat- ing at the second harmonic frequency of the exciting field. Introducing the electronic susceptibility tensor ð2Þð2!; !; !Þ characterizing the materials, this component is given by [15,22]: PNLð2!Þ ¼ 0Kð2Þð2!; !; !Þð2Þð2!; !; !Þ : Eð!ÞEð!Þ ð1Þ Copyright © 2001 Marcel Dekker, Inc. where 0 is the vacuum permittivity. The quantity Kð2Þð2!; !; !Þ arises from the definition of the polarization and accounts in particular for the degeneration of the fundamental electric field. For SHG, Kð2Þð2!; !; !Þ ¼ 1=4, but for SFG, Kð2Þð2!; !; !Þ ¼ 1=2 [22,23]. Solving the wave equation in the medium, it appears that the component of the nonlinear polarization as given in Eq. (1) acts as a source for an electromagnetic wave propagating at twice the fundamental frequency within the medium. The properties of the nonlinear polarization source induced in the medium are found in the susceptibility tensor ð2Þ ð2!; !; !Þ that possesses the symmetry properties of the material it describes. In particular, for liquids, the susceptibility tensor possesses the property of inversion symmetry. This symmetry operation transforms the co-ordinates (x; y; z) of any point in the medium into the co-ordinates (x; y; z). As a result, dropping the frequency dependencies for clarity, the nonlinear polarization is transformed as: PNL ¼ 0Kð2Þð2ÞEE ¼ 0Kð2Þð2ÞðEÞðEÞ ¼ PNL ð2Þ using the inversion symmetry operation on the vectors, a relationship only fulfilled if the susceptibility tensor ð2Þð2!; !; !Þ vanishes altogether. This property for the susceptibility tensor describing liquids is the origin of the surface specificity of the SHG process at the interface between two centrosymmetrical media [24–26]. For liquids, the susceptibility tensor vanishes except at interfaces where the inversion symmetry operation transforms any point in Liquid 1 into a point in Liquid 2. The nonvanishing surface tensor, written as ð2Þ S ð2!; !; !Þ with a subscript, still possesses the remaining symmetry properties of the interface and in particular the isotropy within the surface plane. As a result, from the initial 27 ð2Þ S;IJK components, only four survive, three only being independent: ð2Þ S;XZX ¼ ð2Þ S;XXZ, ð2Þ S;ZXX, and ð2Þ S;ZZZ, the normal to the interface being taken along the ^ Z Z axis with the ^ X axis in the interface plane. The surface nonlinear polarization PNL S ð2!Þ is localized at the interface and is usually described as a nonlinear polarization sheet. This approximation holds because the thickness corresponding to the physical region of the FIG. 1 Geometry for the SHG process at the interface between two centrosymmetrical materials. The nonlinear polarization is a sheet of polarization in the plane of the interface located at the origin of the Z axis. Copyright © 2001 Marcel Dekker, Inc. interface where the bulk properties of one liquid change to the bulk properties of the other liquid is much smaller than the wavelength of light. Within this formalism, the problem can be treated with the help of the laws of linear optics yielding for the SH intensity ISHG [15,22,27,28]: ISHG ¼ !2 80c3 Re ffiffiffiffiffiffi ffi 2! 1 q Re2 ffiffiffiffiffi ! 1 p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2! m cos 2! m p 2 jj2ðI!Þ2 ð3Þ where ! 1 and uploads/Finance/ nonlinear-optics-at-liquid-liquid-interfaces.pdf
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