Optical effects, nonlinear

The dielectric polarization P is related to the electromagnetic field E at optical frequencies by the material equation of the medium  

For anisotropic media, the coefficients x - and x - are, in general, second- and third-rank tensors, respectively. In practice, the tensor 

The following three-wave interactions in crystals with a square nonlinearity (x 5 0) are possible  

For efficient frequency conversion, the phasematching condition ki+k2= ks, where the 4, are the wave vectors for a i, a 2, and 03, respectively, must be satisfied. Two types of phase matching can be defined  

These can be represented with a shortened notation as follows  

There are a number of physical effects connected with the second- and third-order polarizabilities x and x - The most obvious of these is harmonic generation. For an optical radiation field of the form 

The relevant components of the susceptibility tensors are usually written 

The use of radiation with different frequencies gives rise to mixing and amplification processes, e.g. x i l i ( i + 2) 2) (sum) and 

Similar expressions also describe parametric processes in which the input beams are of unequal frequency and intensity. If coi is a high-power beam and CO2 a low-power beam then in the mixing process the power is transferred so that the coi intensity is decreased and the CO2 intensity increased in addition to the generation of coi CO2 co ). This process also transfers the amplitude and phase fluctuations of the low-power CO2 input to the high-power output. Thus a stable low-noise high-power beam can be generated. In this mode co is referred to as the idler frequency, since it is not of particular interest. 

Effects involving steady applied electric fields are described by the inclusion of zero-frequency terms. Thus the following and x terms occur  

The polarization is not truly a linear function of the electric field as we have assumed thus far. A more general relation can be written as 

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Figure Bl.5.5 Schematic representation of the phenomenological model for second-order nonlinear optical effects at the interface between two centrosynnnetric media. Input waves at frequencies or and m2, witii corresponding wavevectors /Cj(co and k (o 2), are approaching the interface from medium 1. Nonlinear radiation at frequency co is emitted in directions described by the wavevectors /c Cco ) (reflected in medium 1) and /c2(k>3) (transmitted in medium 2). The linear dielectric constants of media 1, 2 and the interface are denoted by E2, and s, respectively. The figure shows the vz-plane (the plane of incidence) withz increasing from top to bottom and z = 0 defining the interface.

Heinz T F 1991 Second-order nonlinear optical effects at surfaces and interfaces Noniinear Surfaoe... 

Reider G A and Heinz T F 1995 Second-order nonlinear optical effects at surfaces and interfaces recent advances Photonio Probes of Surfaoes ed P Halevi (Amsterdam Elsevier) pp 413-78... 

Optical parametric oscillators (OPOs) represent another tunable soHd-state source, based on nonlinear optical effects. These have been under development for many years and as of this writing (ca 1994) are beginning to become commercially available. These lasers may be tuned by temperature or by rotating a crystal. Models available cover a broad wavelength range in the visible and infrared portions of the spectmm. One commercial device may be tuned from 410 to 2000 nm. 

A wide variety of other nonlinear optical effects also have been demonstrated. According to equation 12, if two light beams having frequency CO and CO2 are combined in a material with a nonzero value of light waves of frequency + UJ2 and are produced. A combination of such effects, used... 

Fig. 8. Examples of some of the donor-acceptor substituted TEEs prepared for the exploration of structure-property relationships in the second- and third-order nonlinear optical effects of fully two-dimensionally-conjugated chromophores. For all compounds, the second hyperpolarizability y [10 esu], measured by third harmonic generation experiments in CHCI3 solution at a laser frequency of either A = 1.9 or 2.1 (second value if shown) pm is given in parentheses. n.o. not obtained...

Prasad P, Williams D (1991) Nonlinear optical effects in molecules and polymers. Wiley, New York... 

P.N. Prasad and D.J.Williams, Introduction to Nonlinear Optical Effects in Molecules Polymers. J. Wiley Sons, New York (1991). 

For the application of QDs to three-dimensional biological imaging, a large two-photon absorption cross section is required to avoid cell damage by light irradiation. For application to optoelectronics, QDs should have a large nonlinear refractive index as well as fast response. Two-photon absorption and the optical Kerr effect of QDs are third-order nonlinear optical effects, which can be evaluated from the third-order nonlinear susceptibility, or the nonlinear refractive index, y, and the nonlinear absorption coefficient, p. Experimentally, third-order nonlinear optical parameters have been examined by four-wave mixing and Z-scan experiments. 

Secondly, we describe the site-selective introduction of a functional molecule, tetrakis-5,10,15,20-(4-carboxyphenyl)porphyrin (TCPP), into the microphase separation structure of a diblock copolymer film of PS-fo-P4VP. Since porphyrin derivatives show various functionalities such as sensitization, redox activity, and nonlinear optical effect, a polymer nanodot array containing a porphyrin at a high concentration would be applicable to a light-harvesing and charge transporting nanochannel. 

It should be stressed that nonlinear optical effects (particularly optical parametric oscillation) are very demanding in terms of material quality. 

Paul W. Kruse and John G. Ready, Nonlinear Optical Effects in Hg Cd/Te... 

In the following sections we will first in Section 2 briefly discuss the necessary background to understand optical activity effects in linear and nonlinear optics and to illustrate the similarities and differences between both types. In Section 3 we present a more thorough analysis of nonlinear optical effects in second-harmonic generation, both from a theoretical and an experimental point of view. Section 4 deals with experimental examples that illustrate the usefulness of nonlinear optical activity in the study of chiral thin films and surfaces. Finally, in Section 5 we give an overview of the role of chirality in the field of second-order nonlinear optics and show that chiral molecules can be useful for applications in this field. 

Figure 9.3 Schematic illustration of second-order nonlinear optical effects, (a) Second-harmonic generation. Two light fields at frequency go are incident on medium with nonvanishing / 2. Nonlinear interaction with medium creates new field at frequency 2 go. (b) Frequency mixing. One light field at frequency GO and one at frequency go2 is incident on nonlinear medium. Nonlinear interaction with medium creates new field at frequency goi + go2. (c) electro-optic effect. Static electric field E (0) applied over nonlinear medium changes phase of an incoming light field.

In order to describe second-order nonlinear optical effects, it is not sufficient to treat (> and x<2) as a scalar quantity. Instead the second-order polarizability and susceptibility must be treated as a third-rank tensors 3p and Xp with 27 components and the dipole moment, polarization, and electric field as vectors. As such, the relations between the dipole moment (polarization) vector and the electric field vector can be defined as ... 

From the form of the polarization it is clear that in order to observe any nonlinear optical effect, the input beams must not be copropagating. Furthermore, nonlinear optical effects through the tensor y eee requires two different input frequencies (otherwise, the tensor components would vanish because of permutation symmetry in the last two indices, i.e., ytfl eee = Xijy ) For example, sum-frequency generation in isotropic solutions of chiral molecules through the tensor y1 1 1 has been experimentally observed, and the technique has been proposed as a new tool to study chiral molecules in solution.59,61 From an NLO applications point of view, however, this effect is probably not very useful because recent results suggest that the response is actually very low.62... 

Third-order nonlinear optical effect in polyarylenevinylene cast films prepared by via-precursor method... 

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