Third Harmonic Generation in

Here we recall fundamental formulas leading to x ) (-3q co,co,(i)) determination. For the purpose of simplicity we will start considerations with nonabsorbing media and generalize it after to absorbing ones. 

Third harmonic generation produced in n successive nonlinear optical media by a laser beam with frequency (O can be considered as resulting in a superposition of n nonlinear emissions from each nonabsorbing medium separately (THG in a plane parallel slab). Harmonic generation in a nonlinear medium (2) (cf. Fig. 6) can be described in term of source (bound 

Arrows show harmonic wave vectors at 3 Electric fields are perpendicular to the figure plane. 

Remark In the linear media, if = n (for instance in vacuum), the direction of propagation of fundamental and harmonic waves is the same. 

Each bound wave is associated with 4 free waves propagating in 1, 2, 3 media cf. Fig determined by boundary conditions (continuity of 

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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. 

Naumov, A. N., Sidorov-Biryukov, D. A., Fedotov, A. B., and Zheltikov, A. M. 2001. Third-harmonic generation in focused beams as a method of 3D microscopy of a laser-produced plasma. Opt. Spectrosc. 90 778-83. 

Saeta, P. N., and Miller, N. A. 2001. Distinguishing surface and bulk contributions to third-harmonic generation in silicon. Appl. Phys. Lett. 79 2704—06. 

Ward, J. R, and New, G. H. C. 1969. Optical third harmonic generation in gases by a focused laser beam. Phys. Rev. 185 57-72. 

Figure 2. Hystereses curves for third harmonic generation in PDN6S vs temperature at two different fundamental wavelengths. At 1.9 /mi there is a change of intensity of about a factor of two whereas at 1.06 /mi there is a change of intensity of about six due to resonance effects.

Fig. 4. Measurement sequence of third-harmonic generation in solution. A THG experiment of fused silica in vacuum yields the calibration of the whole setup. The same fused silica plate measured in air leads to the air contribution, which is afterwards taken into account in the THG measurements of the various sample concentrations...

Similar as for third-harmonic generation, in the rotational average of the second-order hyperpolarizability yf0FWM = y(-co,co,-co,coj) the indices with... 

F. Theberge, Q. Luo, W. Liu, S.A. Hosseini, M. Sharifi, S.L. Chin, Long-range third-harmonic generation in air using ultrashort intense laser pulses, Applied Physics Letters 87, 081108 (2005)... 

L. Berge, S. Skupin, G. Mejean, J. Kasparian, J. Yu, S. Frey, E. Salmon, J. P. Wolf, Supercontinuum emission and enhanced self-guiding of infrared femtosecond filaments sustained by third-harmonic generation in air, Physical Review E 71, 016602 (2005)... 

Kajzar, F. and J.Messier, Third-harmonic generation in liquids. Phys. Rev. A (1985)322352-2363. 

Another potential application of fully converted polydiacetylenes is based upon their unusual non-linear optical properties. Sauteret et al. found that the third order susceptibilities of TCDU and TS increases by about a factor of 600 upon polymerization and become comparable to those of inorganic semiconductors like GaAs or germanium. This is a consequence of the increase of n-electron delocalization upon polymerization. Polymeric diacetylenes can therefore be used as efficient elements for third harmonic generation. In Ref. this effect has been employed for tripling the frequencies of 1.89 pm and 2.62 pm radiation. 

Churikov, V. M., and Hsu, C. C. (2000). Optical control of third harmonic generation in azo-doped polymethylmethacrylate thin films. Appl. Phys. Lett. 77, 2095-2097. 

De Dominicis, L., Botti, S.. Asilyan. L., Ciardi. R.. Fantoni, R.. Tenanova, M.L., Fiori, A.. Orlanducci, S., Appolloni. R. Second and third harmonic generation in single walled carbon nanotubes at nanosecond time scale. Appl. Phys. Lett.. 85, 1418-1420 (2004)... 

Dias, A.R., Garcia, M.H., Rodrigues, J.C., Petersen, J.C., Bjpmholm, T., Geisler, T. Third-harmonic generation in organometallic ruthenium(II) derivatives containing coordinated p-substituted benzonitriles. 1. Mater. Chem. 5, 1861-1865 (1995)... 

Eerretti, A., Lami, A., Villani, G. Third-harmonic generation in mixed-valent Ru-pyrazine chains a theoretical study. J. Phys. Chem. A 101, 9439-9444 (1997)... 

One aspect of Eq. (90) deserving comment is its amenability for the identification of resonances. Three-photon resonances are manifest in the first and second terms, through the appearance of the factor (Euo — 3to — zTu) two-photon resonances (Euo — 2to — iTu) are featured in the second and fourth, and single-photon resonances (Euo — to — iTu) are seen in each of the first six. Since exploitation of the latter kind of resonance is in practice usually avoided because of the competing linear absorption with which it is associated, it is the two- and three- photon resonances that are of the most interest. Under suitable conditions, third-harmonic generation in either of those cases is driven largely by just two of the contributions to Eq. (90). Other contributions, signifying... 

Jian Zhang (1991) Laser-induced Continuum Structure and Third Harmonic Generation in One- and Two-valence Electron Atoms PhD thesis. University of Southern California... 

The experiments on second- and third-harmonic generation in the reflection geometry demonstrate a giant enhancement of nonlinearities of the bireffingent PS films. The effect cannot be explained in terms of effective medium approximation and is apparently related to strong local fields in nanostructured solids (Fig. 3). 

The Hubbard model, which has played a significant part in the earlier development of nonlinear optical response theory of molecules, has been revived by Shehadi et al.203 to explain the properties of small bridged metallic polymers. The Hubbard-Peierls hamiltonian has also been used by Shuai et al.,204 in conjunction with a symmetry adapted density matrix renormalization group formulation, to calculate a number of properties, including third harmonic generation in trans-octatetraene. 

Fig. 25.12 Transmitted amplitudes for a sample of two aluminum plates 5 mm thick bonded together by an adhesive epoxy layer of 30-50 pm thickness. The amplitudes of the second and the third harmonic generated in transmission through (a) a weak...

J. Zhang, P Lambropoulos, Laser-induced continuum structure and third-harmonic generation in sodium Theory and calculations, Phys. Rev. A 45 (1992) 489. 

Theory and experimental demonstration of optical third-harmonic generation in cholesteric liquid crystal [11]. 

Xu, C. Kondo, T. Sakakura, H. Kumata, K. Takahashi, Y. Ito. R. Optical third harmonic generation in layered perovskite-type material (CioH2iNH3)2Pbl4. Solid State Cornmun. 1991, 79, 245. 

FIGURE 49.2. Schematics of experimental arrangement for measuring values of oriented polymers by the second-harmonic generation. The same arrangement can be used for the measurements ox via third-harmonic generation. In the case of the third-harmonic generation the measurement is usually carried out in a vacuum. 

Soboleva fV et al (2005) Second- and third-harmonic generation in birefringent photonic crystals and microcavities based on anisotropic porous silicon. Appl Phys Lett 87(24) 241110-241113 Timoshenko VY et al (2003) Anisotropy of optical absorption in birefiingent porous silicon. Phys Rev B 67(11) 113405... 

Third-harmonic generation in liquid crystals is clearly not forbidden by symmetry. It has in fact been observed in a number of liquid crystals by Goldberg and Schnur. However, their attempt to... 

III. THEORY OF THIRD-HARMONIC GENERATION IN CHOLESTERIC LIQUID CRYSTALS... 

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