Nonlinear optical coefficients

The physical properties of the expanded radialenes were greatly enhanced upon donor functionalization, leading to the stable derivatives 76-78 with fully planar conjugated rr-chromophores [110]. These compounds exhibit large third-order nonlinear optical coefficients, can be reversibly reduced or oxidized, and... 

Theoretical estimations and experimental investigations tirmly established (J ) that large electron delocalization is a perequisite for large values of the nonlinear optical coefficients and this can be met with the ir-electrons in conjugated molecules and polymers where also charge asymmetry can be adequately introduced in order to obtain non-centrosymmetric structures. Since the electronic density distribution of these systems seems to be easily modified by their interaction with the molecular vibrations we anticipate that these materials may possess large piezoelectric, pyroelectric and photoacoustic coefficients. 

By extension one may say that the power laws (5-7) which determine the magnitude of the linear and nonlinear optical coefficients are consequences of this strong electron-lattice coupling. We now make the conjecture that the time response of these coefficients is severely affected by the dynamics of the electron-lattice coupling in conjugated chains when two or more resonant chemical structures can coexist this is the case for many of the organic chains of Figure 2. 

Thus the ir-electron delocalization length Lj and the linear and nonlinear optical coefficients in ID conjugated systems reach their... 

I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, and R. Ito, Absolute scale of second-order nonlinear-optical coefficients, Journal of the Optical Society of America B 14(9), 2268-2294 (1997). 

J. Rams, F. Agullo-Rueda, J.M. Cabrera, Structure of high index proton exchanged LiNb03 waveguides with undegraded nonlinear optical coefficients, Appl. Phys. Lett. 71. 3356-3358 (1997). 

It is of particular interest from both NLO and chemical perspectives to understand how the polarizability changes in the evolution from an isolated atom to a molecule, a cluster of atoms or molecules, an extended array, and ultimately the bulk. Intuitively, one would expect that if the effective potential for the electron extends over several atomic sites, the polarizability and nonlinear optical coefficients might be larger. Indeed, the largest NLO coefficients have been found for semiconductors and unsaturated extended organic molecules both of which have highly delocalized electrons (2). 

In this paper, an overview of the origin of second-order nonlinear optical processes in molecular and thin film materials is presented. The tutorial begins with a discussion of the basic physical description of second-order nonlinear optical processes. Simple models are used to describe molecular responses and propagation characteristics of polarization and field components. A brief discussion of quantum mechanical approaches is followed by a discussion of the 2-level model and some structure property relationships are illustrated. The relationships between microscopic and macroscopic nonlinearities in crystals, polymers, and molecular assemblies are discussed. Finally, several of the more common experimental methods for determining nonlinear optical coefficients are reviewed. 

ZINDO57-58 is a semiempirical intermediate neglect of differential overlap/spectroscopy (INDO/S) based routine. It can be combined with an SOS method to calculate second-order nonlinear optical coefficients. ZINDO is parametrized to accommodate transition-metal calculations and is therefore suited for calculation on organometallic compounds. To achieve computational efficiency, some of the terms in Eq. (2) are replaced by empirical data or neglected. To see how the INDO/S does this, the closed-shell case will be examined.57 58 It is useful to introduce the following ... 

Table 9. Second-order nonlinear optical coefficients dijk (pni/V) and coherence lengths Ic (nm) of DAST. The reference value dQlll of (3 quartz is given for completeness. (Reprinted with permission from (U. Meier, M. Bosch, F. Pan and P. Gunter, (1998) J. Appl. Phys., 83, 3486). Copyright (1998), American Institute of Physics)...

Moreover, the nonlinear optical coefficients y and (3 are often expressed in the submultiple units cm and cm W" respectively. 

The possible variation of the material third-order susceptibility or nonlinear optical coefficients with particle size can originate from extrinsic effects, as the local field factor and metal concentration, or from intrinsic ones, that is from the size dependence of. Let us recall that, for Hache et al., the only size dependence of in the infraband contribution, due to quantum confinement... 

Dynamical Nonlinear Optical Coefficients from the SDMRG Method... 

X-ray data showed that the molecular arrangement in the crystal is drastically different for 2-(3,5-dimethyl-lH-l,2,4-triazolyl)-5-nitropyri-dine and 3,5-dimethyl-l-(4-nitrophenyl)-lH-l,2,4-triazole despite the same crystal space group. The difference in molecular arrangement influences the nonlinear optical coefficients for a blue light second-harmonic generation device (94BCJ1936). 

Society, Washington, DC, August 1994. Moderate-Sized Diffuse Gaussian Basis Sets for the Ab Initio Evaluation of Excited-State Energies and Nonlinear Optical Coefficients. 

Table 2. Nonlinear optical coefficients djj at the various wavelengths and calculated and measured convosion efficiencies.

In the non-depleted wave approximation the efficiency t] for frequency-doubling by conversion of a guided fundamental mode into a guided second-harmonic mode using the nonlinear optical coefficient djj is given by... 

We measured SHG efficiencies tjconv = P toipm ( pto inside of the film) for the conversion of a fundamental TEo-mode (X = 926 nm) into a second-harmonic TEi-mode of up to 6-10 3 (pto = 30W, nonlinear optical coefficient djj = 12.9 pm/V, beam width 0.5 mm, interaction length 2 mm) yielding a ncmnalized conversion efficiency of iJnorm = 0.5%W cm 2 (0.02%W ). This corresponds reasonable to the calculated conversion efficiency iJcalc - 2.2%W lcm if one considers the attenuation of the modes that was neglected in the theory. 

Rigid-Rod Transition Metal Acetylide Polymers 1171 Table 5.4 Third-order nonlinear optical coefficients for some Pt-polyynes [84]... 

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