Dielectric materials, optical response

Optical properties are usually related to the interaction of a material with electromagnetic radiation in the frequency range from IR to UV. As far as the linear optical response is concerned, the electronic and vibrational structure is included in the real and imaginary parts of the dielectric function i(uj) or refractive index n(oj). However, these only provide information about states that can be reached from the ground state via one-photon transitions. Two-photon states, dark and spin forbidden states (e.g., triplet) do not contribute to n(u>). In addition little knowledge is obtained about relaxation processes in the material. A full characterization requires us to go beyond the linear approximation, considering higher terms in the expansion of h us) as a function of the electric field, since these terms contain the excited state contribution. 

Periodic oscillations in this dipole can act as a source term in the generation of new optical frequencies. Here a is the linear polarizability discussed in Exps. 29 and 35 on dipole moments and Raman spectra, while fi and x are the second- and third-order dielectric susceptibilities, respectively. The quantity fi is also called the hyperpolarizability and is the material property responsible for second-harmonic generation. Note that, since E cos cot, the S term can be expressed as -j(l + cos 2 wt). The next higher nonlinear term x is especially important in generating sum and difference frequencies when more than one laser frequency is incident on the sample. In the case of coherent anti-Stokes Raman scattering (CARS), X gives useful information about vibrational and rotational transitions in molecules. 

An applied electric field can be the electric held component of an electromagnetic wave, in which case electronic excitations or other optical responses may ensue. These are the topic of the next chapter. Here, the concern is with electrostatics, specihcally, the dielectric, or insulative, properties of materials. In an electrical conductor, an applied electric held, E, produces an electric current - ions, in the case of an ionic conductor, or electrons, in the case of an electronic conductor. Electrical conductivity has already been examined in earlier chapters. In insulating solids, the topic of the current discussion, the response to an applied electric held is a static spatial displacement of the bound ions or electrons, resulting in an electrical polarization, P, or net dipole moment (charge separahon) per unit volume, which is a vector quantity. In a homogeneous linear and isotropic medium, the polarization and electric held are aligned. In an anisotropic medium, this need not be so. The fth component of the polarization is related to the jth component of the electric held by ... 

So far, in the description of the interaction of light with matter, we have assumed that the response of the material to an applied optical field was independent of its magnitude. This approximation is valid when the electric field amplitude is negligible compared with the internal electric fields in atoms and molecules. However, when lasers are used as light sources, the intensity of the optical field is usually strong and can drive the electronic response of a dielectric into a nonlinear regime. This nonlinear optical response is described by a field-dependent susceptibility that can be written as... 

The macroscopic optical responses of a medium are given by its linear and nonlinear susceptibilities, which are the expansion coefficients of the material polarization, P, in terms of the Maxwell fields, 1 3]. For a dielectric or ferroelectric medium under the influence of an applied electric field, the defining equation reads... 

In the first part, emphasis will be put on the linear optical properties of dielectric media doped with noble metal nanoparticles. Indeed, the study of the linear response is definitely needed to further explore the nonlinear one. We will then introduce the fundamentals of the theoretical tools required to understand why and how people inquire into the third-order nonlinear properties of nanocomposite materials. In the second part, experimental results will be presented by first examining the different nonlinear optical phenomena which have been observed in these media. We will then focus on the nanoparticle intrinsic nonlinear susceptibility before analysing the influence of the main morphological factors on the nonlinear optical response. The dependence of the latter on laser characteristics will finally be investigated, as well as the crucial role played by different thermal effects. 

Figure 4a illustrates the spectral dependence of ellipsometric parameters and A for the hybrid sample Ag/APTES/Si. Experimental spectra were fitted by the optical response of one effective layer. According to model calculations for this sample, the thickness of the effective layer and APTES film was 5.3 and 11.5 nm, respectively. The spectral dependence of the dielectric function for the effective layer (Fig. 4b) possesses two features. The low-energy peak at 2.2 eV can be attributed to the residual material of the solution containing the P VP-coated Ag nanoparticles. The peak can be also contributed by the interparticle dipole-dipole couplings of nanoparticles on solid substrates. The peak at the 3.4 eV is related to the surface plasmon resonance of metal nanoparticles and corresponds to the absorption peak of Ag colloidal solution (Fig. 4b). In the spectra of hybrid samples Ag/DNA/APTES/Si, the peak at 4.5 eV originated from the contribution of DNA was additionally observed.

Equations 1 and 5 are fundamental to an understanding of the optical response of nanosized particles, since they directly relate the spectrum of the colloid to the dielectric function of the material. They are valid only for very dilute colloids [5]. For large volume fractions of nanoparticles in glasses, polymers or solutions, dipole coupling becomes important. A more general equation can be derived as follows [6]. 

The optical response of materials to the interaction of the electric dipole of light in a stationary state is given by Eq. (5.8), where the dielectric polarization of light, P, is expanded as a function of the electric field of light, E. 

Two types of Cu-nanoparticles-in-dielectric nanocomposites were produced through hydrogen reduction of Cu(II) Cu-zeolite and Cu-zeolite-silica. Amorphous silica was prepared by the sol-gel technique and served as optically transparent matrix incorporating zeolite microcrystals, The copper nanoparticles provide an optical response of the composite material due to the plasmon resonance band varied due to changes of matrix features. 

In the present work, we consider the two approaches for synthesis of nanoparticles designed for metal particles and being in the progress for ultraflne semiconductors. They allow to fabricate nanocomposites of the type nanoparticles-in-dielectrics with amorphous and crystalline matrices. The first one is based on the sol-gel technique producing dielectric silica films with nanoparticles incorporated within silica matrix [1]. Nanoparticles provide an optical response of the material due to the plasmon resonance [2] with variable spectral position and band shape. In the second approach nanoparticles are produced within the crystalline zeolite matrices which stabilize both the few-atomic clusters (e.g., Agg) and metal particles in the size range of 1-20 nm [3], Chemical routes of their synthesis admit easy control of size and optical properties. The metal nanoparticles in zeolites can be transformed into semiconductors without destroy of the zeolite matrix and with incorporation of zeolite microcrystals into transparent silica films. This construction... 

Nonlinear optics is primarily concerned with the response of a dielectric material to a strong electro-magnetic field. The polarization x thus induced in a molecule can be written as [1]. 

A number of exploitable effects exist, due to the non-linear response of certain dielectric materials to applied electric and optical fields. An applied field, E, gives rise to a polarization field, P, within any dielectric medium. In a linear material, the relationship between P and E may be characterized by a single (first-order, second-rank) susceptibility tensor... 

The relation between P and E defines the dielectric properties of the material. As the optical response of metals is in general non-local in space and in time and anisotropic, we have ... 

Maximum ON-state transmittance occurs when the refractive index of polymer ( p) matches with the ordinary refractive index ( ) of LC. During the film formation, it is possible that some fraction of LC dissolved in polymer matrix can have a profound effect mi the PDLC film properties. Therefore, determination of partition of LC between the polymer and LC phases is an important factor in evaluating the performance of PDLC films. The reorientation of LC portion in a PDLC composite film is responsible for the optical non-linearity and electro-optical properties of the device. The absorption of LC into an isotropic polymer results in the LC becoming a part of the polymer phase. In this state, reorientation of LC does not happen with an applied electric field, leaving less amount of LC behind for scattering of light. Therefore, selection of suitable concentration of LC in PDLC films is crucial in optimizing film properties. LC dissolved in polymer matrix alters refractive index, dielectric constant, viscosity etc. of the host polymer. As explained earlier, for best electro-optical responses, a polymer and LC material are chosen on the basis of... 

Deshmukh RR, Malik MK (2008b) Effects of the composition and nematic-isotropic phase transition on the electro-optical responses of unaligned polymer-dispersed liquid crystals. I. Composites of poly(methyl methacrylate) and E8. J Appl Polym Sci 108 3063-3072 Deshmukh RR, Malik MK, Parab SS (2012a) Dichroic dye induced nonlinearity in polymer dispersed liquid crystal materials for display devices. Adv Mater Res 584 79-83 Deshmukh RR, Parab SS, Malik MK (2012b) Effect of host polymer matrices on electro optical and dielectric behavior of polymer dispersed liquid crystal system. Adv Mater Res 584 531-535... 

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