Local field effects nonlinear optics

Sipe JE, Boyd RW (2002) Nanocomposite materials for nonlinear optics based on local field effects, in optical properties of nanostructured random media, 82nd edn. Springer, Berlin, pp 1-19... 

P. Ye and Y. R. Shen, Local field effect on linear and nonlinear optical properties of... 

A final point worth mentioning is the effect of local fields on the optical nonlinearities of strongly QC nanostructures. These arise from embedding QD s in a medium of different dielectric constant (2). One requires to know how the field intensity inside the particle varies at saturation in excitonic absorption. This has been approached theoretically by defining a local field factor f such that Em = f Eout (2). The factor f depends on the shape of the QD and the dielectric constant of the QD e = + E2 relative to that of the surrounding medium. Here... 

A more general framework to treat local field effects in linear and nonlinear optical processes in solution has been pioneered, among others [45], by Wortmann and Bishop [46] using a classical Onsager reaction field model (see the contribution by the Cammi and Mennucci for more details). Such a model has not been extended to treat vibrational spectra. 

In my view, this book contains the most in-depth and broad-based discussion of molecular nonlinear materials yet available. While it does not in itself discuss all the issues (there is relatively little on molecular crystals or on local-field effects), the combination of theoretical and experimental presentations makes the book of unique value to any investigators in the general of molecular nonlinear optics. 

The contributions to the fifth-order nonlinear optical susceptibility of dense medium have been theoretically estimated by using both the local-field-corrected Maxwell-Bloch equations and Bloembergen s approach. In addition to the obvious fifth-order hyperpolarizability contribution, the fifth-order NLO susceptibility contains an extra term, which is proportional to the square of the third-order hyperpolarizability and which originates purely from local-field effects, as a cascaded contribution. Using as model the sodium 3s 3p transition system, it has been shown that the relative contribution of the cascaded term to the fifth-order NLO susceptibility grows with the increase of the atomic density and then saturates. 

A more general framework to treat local field effects in linear and nonlinear optical processes in solution has been pioneered, among others [206], by Wortmann and... 

While the linear absorption and nonlinear optical properties of certain dendrimer nanocomposites have evolved substantially and show strong potential for future applications, the physical processes governing the emission properties in these systems is a subject of recent high interest. It is still not completely understood how emission in metal nanocomposites originates and how this relates to their (CW) optical spectra. As stated above, the emission properties in bulk metals are very weak. However, there are some processes associated with a small particle size (such as local field enhancement [108], surface effects [29], quantum confinement [109]) which could lead in general to the enhancement of the fluorescence efficiency as compared to bulk metal and make the fluorescence signal well detectable [110, 111]. 

In the weak coupling limit, as is the case for most molecular systems, each molecule can be treated as an independent source of nonrlinear optical effects. Then the macroscopic susceptibilities X are derived from the microscopic nonlinearities 3 and Y by simple orientationally-averaged site sums using appropriate local field correction factors which relate the applied field to the local field at the molecular site. Therefore (1,3)... 

In an organic molecule, the nonlinear optical effect originates from nonlinear polarization of the molecules. The polarizability of a molecule is the ability of a charge in the molecule to be displaced under the driving of the electric field. Under an intense optical field, induced polarizability p can be expressed as a polynomial function of local field strength e, [34] ... 

Wortmann, R. and Bishop D.M., Effective polarizabilities and local field corrections for nonlinear optical experiments in condensed media. J.Chem.Phys. (1998) 108 1001—1007. 

In tune with the above introductory remarks, we have arranged this review in the following way Section II deals with the oriented gas model that employs simple local field factors to relate the microscopic to the macroscopic nonlinear optical responses. The supermolecule and cluster methods are presented in Section III as a means of incorporating the various types of specific interactions between the entities forming the crystals. The field-induced and permanent mutual (hyper)polarization of the different entities then account for the differences between the macroscopic and local fields as well as for part of the effects of the surroundings. Other methods for their inclusion into the nonlinear susceptibility calculations are reviewed in Section IV. In Section V, the specifics of successive generations of crystal orbital approaches for determining the nonlinear responses of periodic infinite systems are presented. Finally,... 

The oriented gas model was first employed by Chemla et al. [4] to extract molecular second-order nonlinear optical (NLO) properties from crystal data and was based on earlier work by Bloembergen [5]. In this model, molecular hyperpolarizabilities are assumed to be additive and the macroscopic crystal susceptibilities are obtained by performing a tensor sum of the microscopic hyperpolarizabilities of the molecules that constitute the unit cell. The effects of the surroundings are approximated by using simple local field factors. The second-order nonlinear response, for example, is given by... 

Another scheme to calculate and interpret macroscopic nonlinear optical responses was formulated by Mukamel and co-workers [112 114] and incorporated intermolecular interactions as well as correlation between matter and the radiation field in a consistent way by using a multipolar Hamiltonian. Contrary to the local field approximation, the macroscopic susceptibilities cannot be expressed as simple functionals of the single-molecule polarizabilities, but retarded intermolecular interactions (polariton effects) can be included. 

It is also important to realize that the nonlinear optical properties of a molecule in solution or in the solid state will differ from that of the isolated molecule due to polarization effects caused by the surrounding molecules. In theoretical calculations of molecules in die liquid phase, these effects may be modeled using for instance dielectric continuum models [33, 41, 42, 52, 56]. The use of such schemes for estimating the polarization of the solute by the solvent does not resolve the issue of local field factors. 

As the local electric field in the particles is enhanced at the SPR, the metal nonlinear optical response can be amplified as compared to the bulk solid one. Moreover, the intrinsic nonlinear properties of metals may themselves be modified by effects linked with electronic confinement. These interesting features have led an increasing number of people to devote their research to the study of nonlinear optical properties of nanocomposite media for about two decades. Tire third-order nonlinear response known as optical Kerr effect have been particularly investigated, both theoretically and experimentally. It results in the linear variation of both the refraction index and the absorption coefficient as a function of light intensity. These effects are usually measured by techniques employing pulsed lasers. 

Whatever the degree of approximation used in evaluating the effective nonlinear susceptibility of a composite medium, it can be seen in Eqs. (22), (23) or (27) that the result depends on the product of two complex quantities One linked with the medium morphology and composition (the local field factor), the other linked with the nonlinear optical properties of the metal inclusions themselves (the intrinsic third-order susceptibility, Xm ) - inasmuch as the own contribution of the host matrix to the whole nonlinear response still remains negligible. We will focus here on the second factor. It is noteworthy that very few theoretical work has been accomplished regarding the value of Xm for noble metal nanoparticles after the pioneering smdies of Flytzanis and coworkers [79, 80, 89, 90]. Moreover, as will be underlined below, their results may not be used in every experimental situation as they are. 

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... 

The sign and magnitude of the resulting thermal nonlinear refraction coefficient (which is, actually, a pure linear effect [219]) depend on the thermo-optical coefficient 9 /9r of the material. This coefficient has sometimes been assimilated to the one of the surrounding host only [132, 218], but we have recently shown that, due to local field enhancement at the SPR, they can be very different - even for weakly concentrated media exactly as for the pure electronic nonlinear properties as demonstrated in Section 3.2.4. Moreover, an absorptive thermo-optical effect, which is always disregarded in the literature, can occur parallel to the refractive one. These conclusions will be published soon. 

In this chapter we have shown that the third-order nonlinear optical response of metal/dielectric nanocomposite media varies in a complex manner with many parameters. These parameters are difficult to control independently in experimental investigations. We have distinguished the roles respectively played by the local field enhancement and the metal particle intrinsic nonlinearity. We have highlighted the influence of different parameters, and emphasized the significant finks between optical properties and thermal effects. 

Another approach has been proposed to enhance the optical nonlinearity of semiconductor nanoclusters based on surface plasmon resonance [99,100], In the proposed method, the semiconductor nanocluster is coated with metals such as silver. The local electric field inside the cluster can be enhanced because of the surface plasmon resonance of the metal particles. The local field enhancement effect on nonresonant xl3) of CdS clusters has already been demonstrated using the third harmonic generation technique [17, 84, 85]. In this case enhancement in the local field originates from the difference in dielectric properties between the clusters and the host. The proposed enhancement of x 3) of metal-coated semiconductor nanoclusters owing to surface plasmon resonance has not been demonstrated experimentally. 

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