Degenerate four-wave mixing nonlinear optics

Before going into the details of various materials and their third-order NLO properties, it would serve well to have an idea of the characterization techniques used for their study. To study the effect of the real part of third-order susceptibility, Z-scan measurements, degenerate four-wave mixing (DFWM), optical heterodyne detection of optical Kerr effect (OHD-OKE), and differential optical Kerr effect (DOKE) detection are employed. For the study of TPA, techniques such as nonlinear transmission (NLT) method, two-photon excited fluorescence (TPEF) method, and Z-scan measurements are used. The observables from the above-mentioned techniques vary depending on the inherent limitations of the technique. The nature of the light source employed like the central wavelength of the laser. 

The third-harmonic generation method has the advantage that it probes purely electronic nonlinearity. Therefore, orientational and thermal effects as well as other dynamic nonlinearities derived from excitations under resonance condition are eliminated (7). The THG method, however, does not provide any information on the time-response of optical nonlinearity. Another disadvantage of the method is that one has to consider resonances at oj, 2w and 3o> as opposed to degenerate four wave mixing discussed below which utilizes the intensity dependence of refractive index and where only resonances at a) and 2a) manifest. 

Nonlinear optical studies were carried out using a combination of nonlinear absorption, self-focusing and degenerate four wave mixing measurements. The measurements were made using a Quantel Nano-Pico system that permits operation at either 10 ns or 100 ps pulse lengths at 1064 nm. The 10 ns pulses were TEM mode and temporally smoothed to a near gaussian (H). 

In a recent communication we reported that the third order nonlinear optical susceptibility of Pt, Pb, and H2 tetrakis(cumylphenoxy)phthalocyanines was large and varied substantially with the metal substituent. (1) The structure of these compounds is shown in Fig. 1. The susceptibility was measured by degenerate four-wave mixing at 1.064 pm, a wavelength far from the main absorption bands of phthalocyanines near 650 nm. The nonlinear susceptibility of the Pt phthalocyanine was about a factor of 9 larger than that of the Pb phthalocyanine and a factor of 45 larger than the metal free compound. 

Poly(3-alkyl-a-thiophene) systems show significant third-order nonlinear susceptibilities ( ) Though, oligothiophenes have been studied for their third-order susceptibilities, accurate third-order optical nonlinearity data obtained by degenerate four-wave mixing or electric-field-induced second harmonic generation (EFISH) are difficult to attain reliably on samples with poor solubility characteristics (92MM1901). 

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 degenerate four wave mixing (DFWM) experiment the third-order susceptibility 3)(-tt>,tt>,-CL>,CL>) with degenerate frequencies can be determined [22]. This nonlinear susceptibility is directly proportional to the nonlinear refractive index n2, which is used to describe optically induced refractive index changes. An advantage of this technique is the possibility to record the temporal shape of the third-order nonlinear optical signal. 

Under the influence of an optical pump, the molecular angular distribution described by Equation 12.4 can be considerably modified. In turn, this results in modification of the X ijkl tensor components. Further, we discuss the influence of a polarized pump beam on third-order nonlinear phenomena such as third harmonic generation (THG) [(described by (-3a),ft>,w,a>) coefficient], electric field induced second harmonic generation (EFISH) [x / kl -2(0, (o, o), 0)] and degenerate four-wave mixing (DFWM) X kl ... 

In the case of degenerate four-wave mixing, i.e. m = m + u> — u>, a nonlocal may support nonlinear optical activity and thus intensity dependent contributions to optical rotation and circular dichroism [4, 13, 17-19]. In analogy to Eq. (8) we can include nonlinear optical activity phenomena by writing [4]. 

Four-Wave Mixing is the optical process where the nonlinear interaction between three beams generates a fourth beam. When the frequencies of the input waves are different, new frequencies are generated. The case of equal frequencies is called degenerate four-wave mixing (DFWM). 

Tlie usual experimental techniques developed to study the optical Kerr effect in materials have already been described in a preceding chapter of this book. We only mention here the methods which have especially been used for nanocomposite materials as colloidal solutions or thin films Degenerate four-wave mixing (DFWM) and optical phase conjugation, which provide the modulus of x only and may be completed by Interferometry techniques to get its phase as well, optical limiting, optical Kerr shutter, and z-scan, which is probably the most common technique used in recent years due to its ability to provide simultaneously the nonlinear refraction and absorption coefficients of the same sample point [118],... 

Powell, C.E., Humphrey, M.G., Morrall, J.P., Samoc, M., Luther-Davies, B. Organometallic complexes for nonlinear optics. 33. Electrochemical switching of the third-order nonlinearity observed by simultaneous femtosecond degenerate four-wave mixing and pump-probe measurements. J. Phys. Chem. A 107, 11264-11266 (2003)... 

The temporal response of the third-order nonlinear optical susceptibility in poly(PTS) crystal was determined by time-resolved degenerate four-wave mixing (DFWM) by Carter and coworkers. The excited lifetime T ws measured to be 1.8 0.5 ps at 652 nm in the resonant region. The values of phase relxation time T2 measures by Hattori and Kobayashi for a cast film of poly(3BCMU) were 30 and 90 fs for the respective incident... 

---