Second-order NLO properties

One of the more interesting applications of non-linear optical effects is the generation of the second harmonic. This phenomenon results when a laser beam passes through a material having second-order NLO properties (hence, composed by non-centrosymmetric molecules) the light emitted has a frequency double that of the incident radiation (or the wavelength has been halved). 

It is also worth noting that, due to their dipolar and conjugated donor-acceptor nature, all these amino-terminated Group 6 metaUacumulenes exhibit a strong negative solvatochromic effect and they show significant second-order NLO properties [68]. 

Where is the bulk second order NLO property, N is the number of molecules and / the local field factors. Erom this equation it can be readily seen that the target must be for molecules with a high f] in order to achieve high bulk activity, although in practice the relationship is not quite so simple. 

The other common technique used for determination of second-order NLO properties is second harmonic generation. In an SHG measurement a laser beam at frequency co illuminates a sample and coherent light at twice the frequency (2co) is generated and detected. These measurements can be performed on a wide range of sample types including powders in addition to those mentioned above for the LEO measurements. SHG is therefore a very useful method for... 

Recent advances in optical technology have created great interest in the construction of second-order nonlinear optical (NLO) devices for frequency conversion and electrooptic modulation. Although inorganic substances such as LiNbO possess strong second-order NLO properties and... 

Second order NLO properties including SHG arise from the second order NLO susceptibility x tensor in the relationship for the bulk polarization, P, such that (2-3)... 

Many of the different susceptibilities in Equations (2.165)-(2.167) correspond to important experiments in linear and nonlinear optics. x<(>> describes a possible zero-order (permanent) polarization of the medium j(1)(0 0) is the first-order static susceptibility which is related to the permittivity at zero frequency, e(0), while ft> o>) is the linear optical susceptibility related to the refractive index n" at frequency to. Turning to nonlinear effects, the Pockels susceptibility j(2)(- to, 0) and the Kerr susceptibility X(3 —to to, 0,0) describe the change of the refractive index induced by an externally applied static field. The susceptibility j(2)(—2to to, to) describes frequency doubling usually called second harmonic generation (SHG) and j(3)(-2 to, to, 0) describes the influence of an external field on the SHG process which is of great importance for the characterization of second-order NLO properties in solution in electric field second harmonic generation (EFISHG). 

Before we examine how second- and third-order N LO effects are related to nonlinear polarization, we briefly examine an important symmetry restriction on second-order NLO properties. From Eq. (5), we can see that P(E) = P(0) + xmE + x E2 + x i)E3+... and P -E) = P(0) - x 1)E + xp)E2 - x Eh... we can also see from Fig. 11.1 that P(E) + P(-E) if%(2) + 0. In a centra symmetric material, P(E) is necessarily equal to P(-E) and, therefore, P(0), and other even-order terms must be zero. Therefore, for second-order effects to be observed in a molecule or material, the molecule or material must be non-centrosymmetric. However, no such requirement applies to odd-order processes, such as third-order effects [Fig. 11.1 shows P(E) = P(-E) for a material with only linear and cubic susceptibilities non-zero]. 

However, as far as interplay of conductivity and second-order NLO in hybrid molecular materials is concerned, very few studies are available (534, 535). As previously mentioned, both conducting and second-order NLO properties are formally connected to the same concept of charge transfer, though intermole-cular in conductors but intramolecular in compounds exhibiting second-order optical nonlinearity. Attempts to associate the [Ni(dmit)2] anion with cationic cyanine dyes known to exhibit second-order optical non-linearity such as DAMS+ (4-dimethylamino-l-methylstibazolium), DAMP+ (4-dimethylamino-1-methylpyridinium) and NOMS+ (4 -nitro-l-methylstibazolium) (Scheme 28)... 

In the literature however, other related parameters, besides x are often used to describe the macroscopic second-order NLO properties of materials. The SHG nonlinear coefficient d and the linear electro-optic coefficient r are the parameters commonly used for second-harmonic generation and the Pockels effect respectively [3, 5]. They are related to x according to Eqs. (4) and (5). 

Disperse Red 1 (DRl) used for photoassisted poling in polymers, the back thermal reaction advantageously allows one to end up with materials containing the most stable fmws-isomers. In any case, the back reaction can be induced by light and plays an important role in both orientation and disorientation processes. Photoassisted poling does not necessarily require a stable photoisomer, as shown for azo compounds, which are very efficient. On the contrary, photoswitching of second-order NLO properties makes sense only when the photoisomer is thermally stable. 

This paper reviews experimental work done on the NLO properties of photochromes other than azo derivatives, which have been described in the preceding chapters of this book. In the first part, the molecular second-order NLO polarizabilities will be given the NLO properties of the materials will indeed depend on these values. In the second part, photoassisted poling of different photochromes in polymer matrices will be described. The photo-switching of second-order NLO properties of poled polymers or crystals will then be described in the third section. Both second and third parts will end with some applications of these optical phenomena. We will conclude with the prospectives of these materials in NLO. 

In this equation, po is the permanent dipole moment of the molecule, a is the linear polarizability, 3 is the first hyperpolarizability, and 7 is the second hyperpolarizability. a, and 7 are tensors of rank 2, 3, and 4 respectively. Symmetry requires that all terms of even order in the electric field of the Equation 10.1 vanish when the molecule possesses an inversion center. This means that only noncentrosymmetric molecules will have second-order NLO properties. In a dielectric medium consisting of polarizable molecules, the local electric field at a given molecule differs from the externally applied field due to the sum of the dipole fields of the other molecules. Different models have been developed to express the local field as a function of the externally applied field but they will not be presented here. In disordered media,... 

FIG. 10.3 Light-induced activation of second-order NLO properties based on aggregation of photomerocyanine (right). This product is obtained from photochromic nitro-BIPS type spiropyran (left) (from ref. 53). 

Recently, a mixed-substituent polyphosphazene (polymer V) was synthesized and the second-order NLO properties were investigated (17). The nitrostilbene/trifluoroethoxy ratio was approximately 36 64. Due to the low glass transition temperature of V (T - 25 C), the second harmonic signal decayed to zero within a few minutes. However, polymer V is a prototype which offers many opportunities for further tailoring the molecular structure of polyphosphazenes to generate an optimum combination of NLO and physical properties (17). 

The electro-optic and optical devices based on CPs can be classified into three categories those based on second order NLO properties those based on third order NLO properties those based on properties other than NLO CP-based lasers. The driving forces behind the development of these devices are discussed elsewhere. 

SYMMETRY BASED APPROACH TO THE EVALUATION OF SECOND ORDER NLO PROPERTIES OF CARBON NANOTUBES... 

Evaluation of Second Order NLO Properties of Carbon Nanotubes... 

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