Bulk Second Harmonic Generation

In 1996, Munn extended the microscopic theory of bulk second-harmonic generation from molecular crystals to encompass magnetic dipole and electric quadrupole effects [96] and included all contributions up to second order in the electric field or bilinear in the electric field and the electric field gradient or the magnetic field. This was accomplished by replacing the usual polarization of Refs. 72 and 84 by an effective polarization as well as by defining an effective quadrupole moment. Consequently, the self-consistently evaluated local electric field and electric field gradient were expressed in terms of various molecular response coefficients and lattice multipole tensor sums (up to octupole). In this... 

Wang H, Yan E C Y, Borguet E and Eisenthal K B 1996 Second harmonic generation from the surface of centrosymmetric particles in bulk solution Chem. Phys. Lett. 259 15-20... 

Unlike linear optical effects such as absorption, reflection, and scattering, second order non-linear optical effects are inherently specific for surfaces and interfaces. These effects, namely second harmonic generation (SHG) and sum frequency generation (SFG), are dipole-forbidden in the bulk of centrosymmetric media. In the investigation of isotropic phases such as liquids, gases, and amorphous solids, in particular, signals arise exclusively from the surface or interface region, where the symmetry is disrupted. Non-linear optics are applicable in-situ without the need for a vacuum, and the time response is rapid. 

As discussed in Section II.A, Eisenthal and coworkers have studied the related problem of isomerization at liquid-solid interfaces. They used time-resolved second harmonic generation to investigate the barrierless photoisomerization of malachite green at the silica-aqueous interface using femtosecond time-resolved second harmonic generation [26]. They found that the photoisomerization reaction proceeded but was an order of magnitude slower at the water-silica interface than in bulk solution. 

Cooper and Dutta [216] found that Li/Al LDHs intercalated with 4-nitro-hippuric acid could exhibit second harmonic generation, which is a frequencydoubling nonlinear optical process. This is due to a perpendicular monolayer packing of the guest in the interlayer, resulting in an ordered arrangement of dipoles and hence bulk dipole moment in the soUd. 

Optical second harmonic generation (SHG), which stems from the conversion of two photons of frequency to to a single photon of frequency 2(o, is an inherently surface-sensitive technique. Whereas no optical second harmonic wave is generated in the centrosymmetric bulk of a liquid, molecules participating in the asymmetry of the interface between two liquids (noncentrosymmetric environ-ment) contribute to SHG. Since the square root of SHG signal intensity, is proportional to the number N (per unit area), the molecular orientation (I) and the second order nonlinear polarizability of the SHG active species at the interface... 

One of the most important theoretical contributions of the 1970s was the work of Rudnick and Stern [26] which considered the microscopic sources of second harmonic production at metal surfaces and predicted sensitivity to surface effects. This work was a significant departure from previous theories which only considered quadrupole-type contributions from the rapid variation of the normal component of the electric field at the surface. Rudnick and Stern found that currents produced from the breaking of the inversion symmetry at the cubic metal surface were of equal magnitude and must be considered. Using a free electron model, they calculated the surface and bulk currents for second harmonic generation and introduced two phenomenological parameters, a and b , to describe the effects of the surface details on the perpendicular and parallel surface nonlinear currents. In related theoretical work, Bower [27] extended the early quantum mechanical calculation of Jha [23] to include interband transitions near their resonances as well as the effects of surface states. 

In the first study of its kind, second harmonic generation has been used to study potential induced reconstruction on Au(lll) and Au(100) by Kolb and coworkers [156]. These surfaces have been known to reconstruct in UHY when they are clean [153, 157], Surface reconstruction occurs when the surface atoms of a solid rearrange themselves in a structure different from that expected from simple termination of the bulk lattice. Various studies by cyclic voltammetry, electroreflectance spectroscopy and ex situ electron diffraction have suggested that flame-treated crystals form stable reconstructions in solution. Unfortunately, due to the lack of in situ probes, very little direct evidence for this reconstruction has been available. 

Figure 4.21 Optical second-harmonic generation in (a) a bulk crystal (b) a glass fiber (c) within the cavity of a semiconductor laser...

Nanometer scale domain configurations in fe bulk crystals pave the way for a new class of photonic devices. As an example, preliminary calculations show that a uv laser (A = 300 nm) based on second harmonic generation in LiTaC>3 crystal requires a periodic nanodomain superlattice with domain widths of around 700 nm. In addition, the current domain gratings in ferroelectric crystals are suitable only for quasi-phase-matched nonlinear interactions in the forward direction, where the pump and generated beams propagate in the same direction. Sub-micron ferroelectric domain gratings are the basis for a new family of devices based on backward nonlinear quasi-phase-matched optical interactions in which the generated beam travels in a reverse or another non-collinear direction to the incident beam. Non-collinear... 

Of the thirty-two crystal classes, twenty-two lack an inversion center and are therefore known as non-centrosymmetric, or acentric. Crystalline and polycrystalline bulk materials that belong to acentric crystal classes can exhibit a variety of technologically important physical properties, including optical activity, pyroelectricity, piezoelectricity, and second-harmonic generation (SHG, or frequency doubling). The relationships between acentric crystal classes and physical properties of bulk materials are summarized in Table 9.1.1. 

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