Control over the Refractive Index

Photodissociation is but one of many processes that are amenable to control. A host of other processes that have been studied are discussed later in this book, such as asymmetric synthesis, control of bimolecular reactions, strong-field effects, and so forth. Also of interest is control of nonlinear optical properties of materials [203],i particularly for device applications. In this section we describe an application of thfrj bichromatic control scenario discussed in Section 3.1.1) to the control of refractive indices. riff 

The real and imaginary parts of the refractive index n quantify the scattering and absorption (or amplification) properties of a material- The refractive index is besfl derived from the susceptibility tensor y of the material, defined below, whi j describes the response of a macroscopic system to incident radiation [212], Spe fically, an incident electric field E(r, t), where r denotes the location in the medium, tends to displace charges, thereby polarizing the medium. The change in dmd(r, the induced dipole moment, from point r to point r + dr is given in terms of th polarization vector P(r, t), defined as 

It is customary to relate the polarization to the external field by defining a susceptibility x(t) tensor via the relation 

The term is a complex tensor whose real part relates to light scattering and whose imaginary-part describes absorption or amplification of light. In the wealc-field (linear) domain it is independent of the field E(r, t). As the field gets stronger, % may become dependent on the field, in which case we say that / has nonlinear contributions. Below, for convenience, we suppress the spatial dependence of %. 

To see the relationship to the refractive index, we focus on the case where the tensor y reduces to a scalar. This is the case, for example, if fire electronic response of the medium is isotropic, in which case x(co) reduces to a scalar x(co), or where the field is, for example, along the laboratory-z axis and only the single yzz o) component is of interest. In the former case, the complex refractive index n(co) is given by 

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Examination of Eq. (6.21) shows that y(a>) is comprised of two terms that are proportional to c, 2 and that are associated with the traditional contribution to the susceptibility from state 11 ) and E2) independently, plus two field-dependent terms, proportional to a -j = c cje co /eia), which results front the coherent excitation of both II ) and E2) to the same total energy E = Ex + to) = E2+ to2. As a consequence, changing au alters the interference between excitation routes and allows for coherent control over the susceptibility. As in all bichromatic control scenarios, this control is achieved by altering the parameters in the state preparation in order to affect c1,c2 and/or by varying the relative intensities of the two laser fields. Note that control over y(ciy) is expected to be substantial if e(a>j)/e(cOj) is large. However, under these circumstances control over yfro,) is minimal since the corresponding interference term is proportional to e(a>t)/e(cQj). Hence, effective control over the refractive index is possible only at one of co( or >2. 

For optical fibers, improved control over the stracture of the thin films in the preform will lead to fibers with improved radial gradients of refractive index. A particnlar challenge is to achieve this sort of control in preforms created by sol-gel or related processes. 

Here we show that an application of bichromatic control (Section 3.1.1) allows us to control both the real and imaginary parts of the refractive index. In doing so we consider isolated molecules [213, 214], or molecules in a very dilute gas, where collisional effects can be ignored and time scales over which radiative decay occurs can be ignored. 

The term controlled index means that the refractive index can be made smaller than that of the bulk precursor by controlling the microstructure via the porosity. When silica is deposited, for example, the film index n can be varied over a wide range (7) from n = 1.1 to 1.5. This process control makes sol-gel coatings interesting for many optical, electronic, and sensor applications, but the evolution of the microstructure during film formation is not well understood, in spite of efforts to survey the variables (8, 9). This chapter reviews the important factors determining the microstructure of dip-coated films and explores at length two of them, evaporation and surface tension. 

The term controlled index means that the refractive index can be made smaller than that of the bulk precursor by controlling the microstructure via the porosity. When silica is deposited, for example, the film index n can be varied over a wide range [7] from n= 1.1 to 1.5. This... 

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