Triple harmonic generation

Triple harmonic generation (THG) has also been measured in liquid water (Kajzar and Messier (1985)64) where y(—3m m, m, m) was found to have a value of 1.29 x 10 14 esu at a frequency of 0.0428 au. This quantity should be of the same order as ye, defined above, and the fact that it is very much smaller than the overall y value from the EFISH experiment is an indication that the major contribution to the latter comes from the fl term. The most striking difference between the gas and liquid values is that fl and, consequently, the overall effective y have opposite signs in the two phases. 

In the discussion in Section 9.1.6 of harmonic generation of laser radiation we have seen how the high photon density produced by focusing a laser beam into certain crystalline materials may result in doubling, tripling, etc., of the laser frequency. Similarly, if a laser beam of wavenumber Vl is focused into a cell containing a material which is known to absorb at a wavenumber 2vl in an ordinary one-photon process the laser radiation may be absorbed in a two-photon process provided it is allowed by the relevant selection rules. 

Triple harmonic quantities are unbalanced ( uantities and can exist only on a system, which has a grounded neutral. The configuration of the windings of the source generating the harmonics, the system to which it is connected, and its grounding conditions, thus play a significant role in transmitting the harmonics to the whole system as discussed below ... 

In addition to the blueshifling of the optical absorbance of Q-state semiconductor particles, a linear optical effect, there are nonlinear optical effects demonstrated by Q-state semiconductors. Two types have been observed by MCs prepared in organized films. One is the third harmonic generation or frequency tripling (44). A... 

The fundamental component (aE) is linear in E and represents the linear optical properties discussed above. The second (jfiE-E) third ( yE-E-E) and subsequent harmonic terms are nonlinear in E and give rise to NTO effects. The / and values are referred to, respectively, as the first and second hyperpolarisabilities. The second harmonic term gives rise to second harmonic generation (SHG), the third results in frequency tripling effects, and so on. Importantly, since only the time-averaged asymmetrically induced polarisation leads to second-order NLO effects, the molecule and crystal must be non-centrosymmetric, otherwise the effects will cancel one another. Third-order effects, however, may be observed in both centrosymmetric and non-centrosymmetric materials. 

The dielectric tensor describes the linear response of a material to an electric field. In many experiments, and particularly in optical rheometry, anisotropy in is the object of measurement. This anisotropy is manifested as birefringence and dichroism, two quantities that will be discussed in detail in Chapter 2. The nonlinear terms are responsible for such effects as second harmonic generation, electro-optic activity, and frequency tripling. These phenomena occur when certain criteria are met in the material properties, and at high values of field strength. 

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. 

Tabic 4 shows results from [36] for the static and the second harmonic generation hyperpolarizabilities of CO at 694.3 nm. The electronic contributions were obtained from CC3/d-aug-cc-pVTZ calculations carried out at R q = 2.132bohr. These were approximately corrected for remaining basis set errors by adding the difference between CCSD/d-aug-cc-pVQZ and CCSD/d-aug-cc-pVTZ results for the same frequency and internuclear distance. For CO the triples correction for /3 (0) is 1.72 a.u. or =6%. At a wavelength of 694.3 nm the triples correction is already 2.35 a.u. or s7%. Thus, there is in tliis case a notable triples effect on the frequency dispersion. Since there is no information available about correlation contributions beyond CC3, it is difficult to assess the accuracy of these results. 

Tlie use of optical frequency conversion and optical parametric oscillation allows the generation of new frequencies from a source frequency [2, 3]. Second- and third-harmonic generation are particular cases of optical frequency conversion, where respectively, the original frequency is doubled or tripled. Optical frequency conversion and parametric oscillation devices are commonly used in laser technology [4-6]. 

At frequencies up to -150-200 GHz, solid-state sources such as YIG-tuned oscillators or Guim diode oscillators are now available with power outputs of up to 100 mW. The harmonic generation of such millimetre-wave sources is relatively efficient for doubling and tripling (>10-15%), but for higher harmonics the power drops rapidly ( (1 THz)< 0.1-10 pW). Nevertheless, harmonic generation was used as early as the 1950s to record the submillimetre wave spectra of stable molecules [33]- Harmonics from optimized solid-state millimetre-wave sources are now used to drive astronomical heterodyne receivers up to 900-1100 GHz... 

It is quite difficult to identify any one specific effect as the principal source of saturation phenomena for nonresonant harmonic generation. More likely it is a combination of a number of the competing nonlinear processes described above that determine the limiting intensities for these harmonics. So far, the best result for nonresonant tripling into the VUV has been obtained in Xe where with high-power picosecond pulses the conversion efficiency is 0.3%. ... 

The cascading effects in third harmonic generation with a buik a-quartz single crystal have been studied by Meredith The third harmonic frequency is obtained not only by a direct tripling of fundamental one but also by addition of fundamental w frequency with medium polarization at 2(o. There exists an additionai source polarization at 3w frequency given by... 

Third Harmonic Generation A frequency tripling of light in materials with nonlinear electric properties. 

Tables 1 and 2 and Figure 1 summarize a number of distinct nonlinear optical effects, in particular including those of third order arising from the combined influence of three frequencies, CO2, (Oy These effects are collectively called four-wave mixing, as three incident waves combine coherently to give a fourth resulting one of frequency o)i 0)2 o)y The radiation-induced polarization depends to third order on the electric field strength of the incident radiation, namely, on the triple product E(o)i) 2 ( (O2) E( ( 3). In the particular case where co = a)2 = o)y we may have third-harmonic generation, proportional to E (o)). Correspondingly, the intensity of the third harmonic radiation I(3oo) depends on P((jo),...

In the case of third harmonic generation, the frequencies of the input beams are the same (coi = CO2 = CO3) and the tripled beam has a frequency CO4 = 3coi. Therefore, for the THG process, Xyu should be invariant when the relative positions ofjkl indices change. Consequently, the number of independent elements of the susceptibility tensor for the THG process I is reduced to just four %xxxx, Xzzzz, Xxxzz, and Xzzxx-Furthermore, when Kleinman symmetry conditions are adopted for experiments performed far from the resonances, one would have x xzz = Xzzxx> resulting in only three independent elements [206]. 

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