Fourth-harmonic generation

Figure 1. Block diagram showing component layout for both the laboratory apparatus and the mobile unit Y, Nd YAG laser S and F, second and fourth harmonic generation crystals, respectively ...

Figure 2.20 The spectral range covered by the fundamental radiation of a Ti-sapphrre laser and the various harmonic generation processes second, third, and fourth harmonic generation (SHG, THG, and FHG, respectively) (courtesy of Quantronix).

Lasers and LEDs. Dye lasers pumped by Ar ion, Cu ion and frequency doubled Nd YAG solid state lasers. LEDs operating at 635-652, diode lasers at 635 (AlGalnP), 652 (InGaAlP) and 730 mn (AlGaAs). Solid state pulsed lasers, (e.g. Nd YAG, Nd YLF) operating at second, third and fourth harmonic generation. 

As shown in Fig. 7 we compared the frequency of the cesium Di line at 895 nm with the 4th harmonic of the methane stabilized He-Ne laser operating at 3.4 pm (/ = 88 THz). The laser that creates the frequency comb, the fourth harmonic generation and the HeNe laser are identical with the systems shown in Fig. 4. However, the HeNe laser was stabilized to a methane transition in this experiment and was used as a frequency reference instead of the Cs fountain clock. The frequency of this laser has been calibrated at the Physikalisch Technische Bundesanstalt Braunschweig/Germany (PTB) and in our own laboratory [51] to within a few parts in 1013. 

For pico- and femtosecond studies, time-resolved measurements require powerful pulsed laser systems operated in conjimction with effective detection techniques. Relevant commercially available laser systems are based on Ti sapphire oscillators, tunable between 720 and 930 nm (optimum laser power around 800 nm). For nanosecond work, Nd iYAG (neodymium-doped yttrium-alumi-num-gamet) (1064 nm) and ruby (694.3 nm) laser systems are commonly employed. For many applications, light pulses of lower wavelength are produced with the aid of appropriate nonlinear crystals through second, third, or fourth harmonic generation. For example, short pulses of 2=532, 355, and 266 nm are generated in this way by means of Nd " YAG systems. Moreover, systems based... 

Finally, fhe application of higher order nonlinear optical processes such as third-harmonic generation (Berkovic 1995 Tsang 1995) or fourth-harmonic generation (Lee et al. 1997) could provide even more detailed interface information. For example, in the case of fourth-harmonic generation the induced polarization is given by Pj 4u>) = j k,l,m,nx]tL Ek u>)Ei co)Em u>)E io), i.e., the hyperpolarizability is a tensor of rank 5. Hence if is possible fo resolve up to five-fold surface symmetries. However, the absolute values are... 

The Nd YAG rod is a few centimetres long and contains 0.5 to 2.0 per cent by weight of Nd. In pulsed operation the peak power of each pulse is sufficiently high for generation of second, third or fourth harmonics at 533 nm, 355 nm and 266 nm, respectively, using suitable crystals. 

The compounds K5Nb3OFi8 and Rb5Nb3OFi8 display promising properties for their application in electronics and optics. The compounds can be used as piezoelectric and pyroelectric elements due to sufficient piezo- and pyroelectric coefficients coupled with very low dielectric permittivity. In addition, the materials can successfully be applied in optic and optoelectronic systems due to their wide transparency range. High transparency in the ultraviolet region enables use of the materials as multipliers of laser radiation frequencies up to the second, and even fourth optical harmonic generation. 

As was proven later by Bishop [19], the coefficient A in the expansion (73) is the same for all optical processes. If the expansion (73) is extended to fourth-order [4,19] by adding the term the coefficient B is the same for the dc-Kerr effect and for electric field induced second-harmonic generation, but other fourth powers of the frequencies than are in general needed to represent the frequency-dependence of 7 with process-independent dispersion coefficients [19]. Bishop and De Kee [20] proposed recently for the all-diagonal components yaaaa the expansion... 

In addition to the fourth-order response field Tfourth, the probe light generates two SH fields of the same frequency 211, the pump-free SH field Eq(2 Q), and the pump-induced non-modulated SH field non(td> 211). The ground-state population is reduced by the pump irradiation and the SH field is thereby weakened. The latter term non(td, 211) is a virtual electric field to represent the weakened SH field. Time-resolved second harmonic generation (TRSHG) has been applied to observe E on (td, 211) with a picosecond time resolution [20-25]. The fourth-order field interferes with the two SH fields to be detected in a heterodyned form. 

Characterization of Molecular Hyperpolarizabilities Using Third Harmonic Generation. Third harmonic generation (THG) is the generation of light at frequency 3co by the nonlinear interaction of a material and a fundamental laser field at frequency co. The process involves the third-order susceptibility x 3K-3 , , ) where —3 represents an output photon at 3 and the three s stand for the three input photons at . Since x(3) is a fourth (even) rank tensor property it can be nonzero for all material symmetry classes including isotropic media. This is easy to see since the components of x(3) transform like products of four spatial coordinates, e.g. x4 or x2y2. There are 21 components that are even under an inversion operation and thus can be nonzero in an isotropic medium. Since some of the terms are interrelated there are only four independent terms for the isotropic case. 

A block diagram of an experimental set-up is shown in Fig. 5 [31]. The UV light generated from an excimer laser of ArF, KrF and XeF (X = 193, 248 and 352 nm, respectively) at 10 Hz is usually used as a pump laser, which is linearly polarized with a polarizer. Another pump laser of fundamental to fourth harmonics of an NdiYAG laser (X = 1064, 532, 355, and 266 nm) at 10 Hz can be used. These light beams are introduced into an ultrahigh vacuum (UHY) chamber through a synthesized-quartz... 

A photon wavelength of 266.2 nm is used in the experiments reported here, the fourth harmonic of a special neodymium laser system which can generate powerful ultra-violet pulses of a joule or more. " Experimental conditions are (see also table 1) molecular beam density at the interaction volume, 6x 10 molecules cm laser energy, 0.3 J per pulse (4x 10 photons per 10 ns pulse, i.e., 30 MW) laser repetition rate, one pulse per minute and flight path length, 5.63 cm. 

Implementing the algorithm sketched above in the computer symbolic manipulation program FORM, as exemplified in Appendix A, and applying the method to the second-harmonic-generation (SHG) process, which is described by the interaction Hamiltonian Hi given by (55), one can easily calculate subsequent terms of the series (92). Restricting the calculations to the fourth-order terms, we get... 

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... 

Further features are evident when the relative magnitudes of the dipole difference d and the transition dipole p ° are considered. One immediately striking feature is the observation that the second, fourth, sixth, and eighth terms all disappear if d = 0, leaving only terms associated with virtual excitation routes. [Note that no such routes were manifest in the second-harmonic result. If d = 0 then the entire expression Eq. (85) becomes zero—any process involving an odd number of photons has to entail at least one 00 or uu segment in the interaction sequence.] In the third-harmonic case, in particular, both terms associated with two-photon resonances disappear—in other words, there can be no two-photon resonance enhancement of third-harmonic generation under such circumstances. If, however, d p °, then the even terms of Eq. (90)... 

Variations of the above apparatus are used in a number of laboratories. Several experiments utilize a type II KDP crystal to generate the third harmonic at 353 nm instead of the fourth harmonic at 264 nm. To obtain a higher repetition rate at a sacrifice in temporal resolution, the glass laser can be replaced with a mode-locked neodymium YAG laser. 

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