Third harmonics generation

In the third-harmonic generation process, three photons with the same frequency to mix and generate a new photon with a frequency 3co. This nonlinear optical process. 

Using different techniques such as Maker fnnges and z-scan, the THG in thin-film [194, 212-215] and bulk ZnO [216, 219, 223] has been measured. For a c-axis-oriented ZnO sample, where the optical axis is along the surface normal, by using a p-polarized incident beam (pmP3m configuration), it is possible to explore only the component. As the THG may also occur in air, which has a large coherence 

The third harmonic power as a function of the incidence angle 0 is given by [194] 

This has been experimentally confirmed by direct measurements of SHG power in nanocrystalline ZnO thin films, which has been shown to be several orders of magnitude weaker than the THG power [217]. 

In thin films of nanostructured ZnO ( 200 nm thick) grown by PLD, a significant enhancement of% compared to the epitaxially grown ZnO films has been observed with THG efficiencies as high as 1.3% at Xa, = 1250 nm, corresponding to = (1.4 0.7) X 10 esu [217]. This enhancement has been attributed to the reduced dimensionality due to nanocrystalline structure, which has been shown to enhance also the second-order nordinearities as discussed above. Such high efficiency of nonlinear optical conversion creates a potential for nanostructures ZnO thin films to be used in nonlinear optical devices. 

Electric field-induced second harmonic generation EFISH (-2co co,co,0) 

The term third harmonic generation, THG, refers to the generation of a light beam that consists of photons having three times the energy of the photons of the input beam. THG can be easily detected and is, therefore, widely employed in the third-order nonlinear characterization of newly developed materials [28]. THG is a four-photon process, in which three incident photons with angular frequency co create a photon with frequency 3 u. The off-resonant THG process can be represented by a transition between virtual excited states, as shown by the dashed lines in Fig. 3.4. 

In the case of THG, the third-order susceptibility corresponds to a nonlinear polarization component, which oscillates at the third harmonic frequency of the incident laser beam. Regarding the simphfied case of an isotropic solution, only the element ) third-order susceptibility tensor creates 

For THG measurements, pulsed laser systems operating at infrared wavelengths (typically 1064, 1850, 1907 or 2100 nm) are used. Most commonly, is ob- 

Thin polymer sheets allowing unhindered passage of a low-intensity light beam of a given non-resonant wavelength can act as lenses if a high-intensity beam is passed through them. This is a consequence of the intensity dependence of the refractive index n [see Eq. (3-27)]. 

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Sipe J E, Moss D J and van Driel H M 1987 Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals Phys. Rev. B 35 1129-41... 

Question. Show that the third term in Equation (9.11) results in the generation of radiation of frequency 3v when radiation of frequency v is incident on a crystal capable of third harmonic generation. 

Because the second term in the brackets contains 3v in the sine function, radiation at a frequency which is three times that of the incident radiation is generated. This is referred to as third harmonic generation. The first term in brackets indicates that some radiation of unchanged frequency also results. 

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] ... 

We note that 02 4 vanishs if two of the four the frequency arguments Wq, wi, u>2, W3 become zero. For the case that three frequency arguments are equal (third harmonic generation) both mixed-symmetry effective frequencies w 2 vanish. The coefficients Amsi Bms, etc. 

Table 1 Coefficients for 7[ (a ) for third harmonic generation (THG), degenerate four wave mixing (DFWM), electric field induced second harmonic generation (ESHG), and Kerr effect in methane at the experimental geometry rcH = 2.052 a.u. A CCSD wavefunction and the t-aug-cc-pVDZ basis were used. (Results given in atomic units, the number in parentheses indicate powers of ten.)...

A similar convergence is found for the third harmonic generation process at the lower of the two frequencies, 671.5 nm. At the higher frequency, 476.5 nm, the Taylor approximations for the third harmonic generation hyperpolarizability converge only very slowly, even with a tenth-order Taylor approximation a one-percent accuracy is not obtained. This accuracy, however, is still achieved with a [1,2] Fade approximant calculated from the dispersion coefficients up to sixth order. 

If we compare results obtained with the same basis sets with the three coupled cluster models CCS, CC2 and CCSD, we find similar trends as observed in Refs. [22,45] The CCS model underestimates strongly the static hyperpolarizabilities and their dispersion. The results are usually of similar quality as those obtained with SCF. For methane, the CCS static hyperpolarizabilities are intermediate between the SCF and the CCSD values obtained in the same basis set. In Ref. [45] the CCS percentage dispersion contribution to the third harmonic generation (THG) hyperpolarizability of methane was found to be slightly smaller than for SCF, both underestimating significantly the dispersion obtained with the correlated coupled cluster models CC2 and CCSD. Accordingly the CCS dispersion coeflBcients listed in Table 3 are substantially smaller than the respective CCSD results obtained in the same basis sets. 

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...

Schaller, R. D., Johnson, J. C Wilson, K R., Lee, L. F., Haber, L. H. and Saykally, R. J. (2002) Nonlinear chemical imaging nanomicroscopy from second and third harmonic generation to multiplex (broad-bandwidth) sum frequency generation near-freld scanning optical microscopy. 

C. P. J., Wilson, K. R., Muller, M. and Brakenhoff, G. J. (1998) Characterization of femtosecond pulses focused with high numerical aperture optics using interferometric surface-third-harmonic generation. Opt. Commun., 147, 153-156. 

Geisler, T. Pedersen, K. Petersen, J. C. Third-harmonic Generation in Substituted Oligo-phenylene Vinylenes and Organic Square Planar Nickel Complexes. In Notions and Perspectives of Nonlinear Optics Keller, O., Eds. World Scientific Singapore, 1996 pp 580-585. 

Figure 5. Vibration diagrams depicting the effect of air on optical third harmonic generation from a thin solid. (See text for further discussion.)...

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). 

If any of the frequencies (w, 2m or 3w in third harmonic generation or similar frequency combinations in three wave mixing experiments) pproach the region of intense absorption situated around 16000 cm appreciable changes in the values of are expected... 

Third-order susceptibilities of the PAV cast films were evaluated with the third-harmonic generation (THG) measurement [31,32]. The THG measurement was carried out at fundamental wavelength of 1064 nm and between 1500 nm and 2100 nm using difference-frequency generation combined with a Q-switched Nd YAG laser and a tunable dye laser. From the ratio of third-harmonic intensities I3m from the PAV films and a fused quartz plate ( 1 thick) as a standard, the value of x(3) was estimated according to the following equation derived by Kajzar et al. [33] ... 

Where P is the polarisation and the others the linear (1) and non-linear, second (2) and third order (3) terms. Examples of important second order effects are frequency doubling and linear electro-optic effects (Pockles effect), third order effects are third-harmonic generation, four-wave mixing and the quadratic electro-optic effect (Ken-effect). 

Canioni, L., Rivet, S., Sarger, L., et al. 2001. Imaging of Ca2-t intracellular dynamics with third harmonic generation microscope. Opt. Lett. 26 515. 

Millard, A. C., Wiseman, P W., Fittinghoff, D. N., et al. 1999. Third harmonic generation microscopy by use of a compact femtosecond fiber laser source. Appl. Opt. 38 7393. 

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