Second nonlinear optics

The first term, the linear part containing the polarizability a, will be extended by the first nonlinear optical term including the first hyperpolarizability P (second-order polarization), the second nonlinear optical term containing the second hyperpolarizability y (third-order polarization), and so on. The most important nonlinear optical effects are based on the first hyperpolarizability P because with increasing order of the hyperpolarizabilities the effects are getting weaker (P 1/E > y l/E etc.). 

The most significant symmetry property for the second-order nonlinear optics is inversion synnnetry. A material possessing inversion synnnetry (or centrosymmetry) is one that, for an appropriate origin, remains unchanged when all spatial coordinates are inverted via / —> - r. For such materials, the second-order nonlmear response vanishes. This fact is of sufficient importance that we shall explain its origm briefly. For a... 

The second-order nonlinear optical processes of SHG and SFG are described correspondingly by second-order perturbation theory. In this case, two photons at the drivmg frequency or frequencies are destroyed and a photon at the SH or SF is created. This is accomplished tlnough a succession of tlnee real or virtual transitions, as shown in figure Bl.5.4. These transitions start from an occupied initial energy eigenstate g), pass tlnough intennediate states n ) and n) and return to the initial state g). A fiill calculation of the second-order response for the case of SFG yields [37]... 

The focus of the present chapter is the application of second-order nonlinear optics to probe surfaces and interfaces. In this section, we outline the phenomenological or macroscopic theory of SHG and SFG at the interface of centrosymmetric media. This situation corresponds, as discussed previously, to one in which the relevant nonlinear response is forbidden in the bulk media, but allowed at the interface. 

Figure Bl.5.5 Schematic representation of the phenomenological model for second-order nonlinear optical effects at the interface between two centrosynnnetric media. Input waves at frequencies or and m2, witii corresponding wavevectors /Cj(co and k (o 2), are approaching the interface from medium 1. Nonlinear radiation at frequency co is emitted in directions described by the wavevectors /c Cco ) (reflected in medium 1) and /c2(k>3) (transmitted in medium 2). The linear dielectric constants of media 1, 2 and the interface are denoted by E2, and s, respectively. The figure shows the vz-plane (the plane of incidence) withz increasing from top to bottom and z = 0 defining the interface.

Given the interest and importance of chiral molecules, there has been considerable activity in investigating die corresponding chiral surfaces [, and 70]. From the point of view of perfomiing surface and interface spectroscopy with nonlinear optics, we must first examhie the nonlinear response of tlie bulk liquid. Clearly, a chiral liquid lacks inversion synnnetry. As such, it may be expected to have a strong (dipole-allowed) second-order nonlinear response. This is indeed true in the general case of SFG [71]. For SHG, however, the pemiutation synnnetry for the last two indices of the nonlinear susceptibility tensor combined with the... 

The applications of this simple measure of surface adsorbate coverage have been quite widespread and diverse. It has been possible, for example, to measure adsorption isothemis in many systems. From these measurements, one may obtain important infomiation such as the adsorption free energy, A G° = -RTln(K ) [21]. One can also monitor tire kinetics of adsorption and desorption to obtain rates. In conjunction with temperature-dependent data, one may frirther infer activation energies and pre-exponential factors [73, 74]. Knowledge of such kinetic parameters is useful for teclmological applications, such as semiconductor growth and synthesis of chemical compounds [75]. Second-order nonlinear optics may also play a role in the investigation of physical kinetics, such as the rates and mechanisms of transport processes across interfaces [76]. 

Heinz T F 1991 Second-order nonlinear optical effects at surfaces and interfaces Noniinear Surfaoe... 

Reider G A and Heinz T F 1995 Second-order nonlinear optical effects at surfaces and interfaces recent advances Photonio Probes of Surfaoes ed P Halevi (Amsterdam Elsevier) pp 413-78... 

Hohifeld J, Conrad U, Muller Wellershoff S S and Matthias E 1998 Femtosecond time-resolved linear and second-order reflectivity of metals Nonlinear Optics in Metals ed K H Bennemann (Oxford Clarendon) pp 219-67... 

Campagnola P J, Wei M D, Lewis A and Loew L M 1999 High-resolution nonlinear optical imaging of live cells by second harmonic generation Biophys. J. 77 3341-9... 

Nonlinear Optical Devices. A transparent, optically active, sol—gel-derived organic—inorganic glass has been synthesized (68). This hybrid consists of a 2,4-dinitroaminophenylpropyl-triethoxysilane covalently bound to a siUcon alkoxide-derived siUca network. This hybrid exhibits a strong electric field-induced second harmonic signal and showed no signs of crystallization. 

Only certain types of crystalline materials can exhibit second harmonic generation (61). Because of symmetry considerations, the coefficient must be identically equal to zero in any material having a center of symmetry. Thus the only candidates for second harmonic generation are materials that lack a center of symmetry. Some common materials which are used in nonlinear optics include barium sodium niobate [12323-03-4] Ba2NaNb O lithium niobate [12031 -63-9] LiNbO potassium titanyl phosphate [12690-20-9], KTiOPO beta-barium borate [13701 -59-2], p-BaB204 and lithium triborate... 

Fig. 1. Representative device configurations exploiting electrooptic second-order nonlinear optical materials are shown. Schematic representations are given for (a) a Mach-Zehnder interferometer, (b) a birefringent modulator, and (c) a directional coupler. In (b) the optical input to the birefringent modulator is polarized at 45 degrees and excites both transverse electric (TE) and transverse magnetic (TM) modes. The appHed voltage modulates the output polarization. Intensity modulation is achieved using polarizing components at the output.

Serious attempts to use LB films in commercial appHcations include the use of lead stearate as a diffraction grating for soft x-rays (64). Detailed discussion on appHcations of LB films are available (4,65). From the materials point of view, the abiHty to build noncentro symmetric films having a precise control on film thickness, suggests that one of the first appHcations of LB films may be in the area of second-order nonlinear optics. Whereas a waveguide based on LB films of fatty acid salts was reported in 1977, a waveguide based on polymeric LB films has not yet been commercialized. 

Frequency-dependent polarizability a and second hyperpolarizability y corresponding to various third-order nonlinear optical processes have been... 

Fig. 8. Examples of some of the donor-acceptor substituted TEEs prepared for the exploration of structure-property relationships in the second- and third-order nonlinear optical effects of fully two-dimensionally-conjugated chromophores. For all compounds, the second hyperpolarizability y [10 esu], measured by third harmonic generation experiments in CHCI3 solution at a laser frequency of either A = 1.9 or 2.1 (second value if shown) pm is given in parentheses. n.o. not obtained...

Acentricity greatly enhances the y-value (see 92 vs 91 and 90 or 101 vs 99 and 100, Fig. 8). Such a trend had been predicted for certain ranges of compounds by theory [137] however when the first hyperpolarizability, which determines second-order nonlinear optical properties, is maximized, y is predicted to be zero [138]. 

Microscopy methods based on nonlinear optical phenomena that provide chemical information are a recent development. Infrared snm-frequency microscopy has been demonstrated for LB films of arachidic acid, allowing for surface-specific imaging of the lateral distribution of a selected vibrational mode, the asymmetric methyl stretch [60]. The method is sensitive to the snrface distribntion of the functional gronp as well as to lateral variations in the gronp environmental and conformation. Second-harmonic generation (SHG) microscopy has also been demonstrated for both spread monolayers and LB films of dye molecules [61,62]. The method images the molecular density and orientation field with optical resolution, and local qnantitative information can be extracted. 

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