Harmonic generation, higher

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. 

We believe that our model can be extended even further to accurately describe other nonlinear optical interactions such as sum and difference frequency mixing, as well as higher-order harmonics generation. 

Molecular crystals are among the most efficient second- and higher-harmonic generating materials. An external electric field E, upon interacting with a molecule, will induce a dipole moment p. If the field is strong, the response may not be linear, in which case the components of p can be developed in increasing powers of E as described by the expansion (i = 1, 2, 3)... 

Sun, C. K. 2005. Higher harmonic generation microscopy. Microsc. Tech. 95 17-56. 

In summary, nonlinear optical imaging methods, such as TPM, allow for an order of improvement in the signal simply by utilization of 10 times shorter pulses. The enhancement is even more dramatic for higher-order nonlinearities, such as third harmonic generation where two orders of magnitude increase is expected. These improvements, however, rely on successful measurement and elimination of phase distortions. 

B. Higher Harmonics Generation in Field-Induced Birefringence by a Suspension of Rigid Dipoles Zero Bias Field... 

Figure 10 shows a typical measured homodyne waveform and the corresponding numerical fit (solid lines). The measured THz waveform exhibits both the fundamental ECDL difference frequency (Fig. 10(a)) and higher harmonics - predominantly the third harmonic (Fig. 10(b)). Multiple harmonic generation in THz photo-mixers has been previously reported [103], By fitting the observed waveform to a sum of harmonic sinusoidal functions, the amplitude and phase of the THz electric field can be determined separately for the fundamental and third harmonic. The solid line shows a numerical fit to the data. The fundamental extracted frequency, 0.535 THz, compares well to the expected frequency based on the frequency difference of the two ECDL. The extracted E field amplitudes and phases are 3.37 x 10 4 and 2.17 radians for 0.535 THz (Fig. 10(a)) and 5.61 x 10-5 and 3.94 radians for the 1.605 THz third harmonic, respectively (Fig. 10(b)). 

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