INDEX third-harmonic generation

The two important consequences of the third-order optical nonlinearities represented by x are third-harmonic generation and intensity dependence of the refractive index. Third-harmonic generation (THG) describes the process in which an incident photon field of frequency (oj) generates, through nonlinear polarization in the medium, a coherent optical field at 3a>. Through x interaction, the refractive index of the nonlinear medium is given as n = nQ+n I where n describes intensity dependence of the refractive index ana I is the instantaneous intensity of the laser pulse. There is no symmetry restriction on the third-order processes which can occur in all media including air. 

The index ms indicates that j s transforms according to the mixed symmetry representation of the symmetric Group 54 [33]. 7 5 is an irreducible tensor component which describes a deviation from Kleinman symmetry [34]. It vanishs in the static limit and for third harmonic generation (wi = u>2 = W3). Up to sixth order in the frequency arguments it can be expanded as [33] ... 

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. 

While the above discussion clearly highlights the importance of including solvent effects in the calculations, the calculated properties cannot be compared directly with experimental results. This is mainly caused by the many different conventions used for representing hyperpolarizabilities and susceptibilities. However, the calculated properties can be combined with appropriate, calculated Lorentz/Onsager local field factors to obtain macroscopic susceptibilities that can be compared with experimental results. For water, we used this to calculate the refractive index and the third harmonic generation (THG) and the electric field-induced second harmonic (EFISH) non-linear susceptibilities. The results are collected in Table 3-11. 

The first contribution to the polarization induces a modification of the wave propagation in the material, for both its amplitude and phase, but without any frequency change. This phenomenon is known as the optical Kerr effect, by analogy with the magneto-optic and electro-optic Kerr effects where the medium refractive index varies proportionally with the square of the applied magnetic or electric static field. The second contribution corresponds to the third harmonics generation (THG). 

I i Intensity of incident light, 1 sample path length, 1 c coherent length, n, refractive index If phase matching condition A k =0 does not hold, I decreases, i.e., 1 m depends on the incident angle 0. m = 2 second harmonic generation (SHG) m=3 third harmonic generation (THG)... 

The tensors and 7 constitute the molecular origin of the second-and third-order nonlinear optical phenomena such as electro-optic Pock-els effect (EOPE), optical rectification (OR), third harmonic generation (THG), electric field induced second harmonic generation (EFI-SHG), intensity dependent refractive index (IDRI), optical Kerr effect (OKE), electric field induced optical rectification (EFI-OR). To save space we do not indicate the full expressions for and 7 related to the different second and third order processes but we introduce the notations —(Ajy,ui,cj2) and 7(—a , o i,W2,W3), where the frequency relations to be used for the various non-linear optical processes which can be obtained in the case of both static and oscillating monochromatic fields are reported in Table 1.7. 

P( P(-o> w,0) P(0 -fa>,w) Y( - Y(-2(i) (i>,tD,0) Y(-o) (i>,0,0) Second harmonic generation (SHG) Electrooptic Pockels effect Optical rectification Third harmonic generation DC electric-field-induced SHG Intensity-dependent refractive index Optical Kerr effect Coherent anti-Stokes Raman pSHG pEOPE pOR. yTHG. EFISH oj DC-SHG. JlDRI or. yOKE. yCARS... 

The third order nonlinear optical properties of the functionalized polymers have been studied by optical third harmonic generation and by four wave mixing. The four wave mixing experiments performed at 1. 064 pm fundamental wavelength reveal index grating writing through trans-cls isomerization via a two photon process. This process can be used for all optical orientation of chromophores, as it will be discussed later. 

Third-harmonic generation (THG), in which a fundamental beam at frequency 0) is converted to frequency 3a), is a technique frequently used to measure to, w, cS) of organic molecules or polymers. This technique is rather accurate and sensitive even to small y (-3a> o>, w) values. Only electronic effects contribute to THG. Therefore, thermal or stray-light effects, which can be troublesome in measurements based on the intensity-dependent refractive index, do not contribute to o), to, w). However, important slower contributions to... 

The first term in constant phase of E(r. z) that arises from the refractive index of the medium through which the beams propagate. The second term vanishes because of conservation of momentum in the harmonic generating medium. The third term is the Gouy phase, which changes by (n — m) n as the beams pass through a focal point. 

---