Third harmonic generation nonlinear optical materials

Third Harmonic Generation Nonlinear Optical Materials... 

The unique properties of liquid crystals have also provided opportunity for study of novel nonlinear optical processes. An example involves the ability to modify the pitch of cholesteric liquid crystals. Because a pseudo-wave vector may be associated with the period of pitch, a number of interesting Umklapp type phasematching processes (processes in which wave vector conservation is relaxed to allow the vector addition to equal some combination of the material pseudo-wave vectors rather than zero) are possible in these pseudo-one-dimensional media. Shen and coworkers have investigated these employing optical third harmonic generation (5.) and four-wavemixing (6). 

This paper is a tutorial overview of the techniques used to characterize the nonlinear optical properties of bulk materials and molecules. Methods that are commonly used for characterization of second- and third-order nonlinear optical properties are covered. Several techniques are described briefly and then followed by a more detailed discussion of the determination of molecular hyperpolarizabilities using third harmonic generation. 

LeBozec and co-workers have reported nonlinear behavior in a series ofterpyri-dyl and dipicolinic acid complexes, with further studies on these complexes by Maury and co-workers [83, 84]. Their research was on new molecular materials for optoelectronics, with studies based on octupolar nonlinear optical molecules showing that molecular quadratic hyperpolarizability values were strongly influenced by the symmetry of the complexes [85]. Other studies on organic-lanthanide complexes with nonlinear optics have also reported second- and third-harmonic generation behavior with simultaneous multiphoton absorption properties [50]. Such studies have shown the importance of coordination chemistry as a versatile tool in the design of nonlinear materials. 

The most widely employed material characterization techniques in third-order nonlinear optics are third-harmonic generation (THG) [21], degenerate four wave-mixing (DFWM) [22], Z-scan [6], and optical limiting by direct two-photon absorption (TPA) and fluorescence spectroscopy induced by TPA [23]. All of them will be discussed in the following. Further measurement techniques such as electric-field induced second-harmonic generation (EFISH) [24], optical Kerr... 

In the third-harmonic generation, the third-order susceptibility leads to a nonlinear polarization component which oscillates at the third-harmonic frequency of the incident laser beam. This leads to a light wave at the third-harmonic frequency of the fundamental wave. As optical frequencies are involved and since the output frequency is different from the input frequency only the electronic nonlinearities can participate without any contributions from thermal or orientational effects. Because one needs fast nonlinearities for all-optical signal processing, the main interest is directed towards the fast electronic nonlinearities. Therefore and also due to its simplicity, third-harmonic generation is a very attractive method to characterize newly developed materials. 

In the Third-Harmonic Generation (THG) experiment an input beam at frequency w is incident into the nonlinear sample and an optical signal oscillating at frequency 3w is generated through the nonlinear interaction inside of the material. This is described by w, w, w) ... 

Applications of second order nonlinear optical materials include the generation of higher (up to sixth) optical harmonics, the mixing of monochromatic waves to generate sum or difference frequencies (frequency conversion), the use of two monochromatic waves to amplify a third wave (parametric amplification) and the addition of feedback to such an amplifier to create an oscillation (parametric oscillation). 

In Eqs. 1 and 2. the indices i, j. k. and I refer to the coordinate system of the bulk material and molecule, respectively. Illustrated in Fig. 1 are the linear and nonlinear polarizations with respect to electric field. The Fourier decomposition of this nonlinear polarization comprising components of zero frequency, the fundamental frequency, the second-harmonic frequency, the third-harmonic frequency, etc., is shown in Fig. 2. The effects up to the second order, which are easily observed experimentally, are called the optical rectification. P(0) linear electro-optic effect P((u) second-harmonic generation P(2a>), and third-harmonic generation P(3co). 

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