Frequency fourth-harmonic

Raman excitation. and I2s are the high-frequency and low-frequency components of the pump light pulse. A probe pulse of frequency 12 interacts with the coherence to present the optical response of the fundamental frequency 12 + C0fsl2. (c) Fourth-order coherent Raman scattering, the optical response of the second harmonic frequency 212 + co 2I2 is modulated by the vibrational coherence. 

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. 

The results are presented in Table 3.68 which is divided into frequencies derived using the harmonic approximation and anharmonic data taking account of the fourth-order polynomial description of the PES. It appears that the SCF harmonic frequencies are barely altered at all by BSSE. In fact, the only harmonic frequency to be affected is the v, stretch, v(FH), which is increased by 12 cm at the MP2 level when the BSSE is included. When the treatment is expanded to include anharmonicity, there is again virtually no effect on either frequency from BSSE. However, MP2 calculations do show significant changes account of superposition error raises the v frequency by 32 cm and lowers v(F-N) by a... 

In the past fifth harmonic generation has been investigated with powerful fixed frequency solid state (Nd-YAG or Nd-Glass) and gas (XeCl, KrF) lasers . In one of these experiments input powers of more than 300 MW (mode-locked Nd-YAG fourth harmonic, X=266.1 nm) provide, for example, conversion efficiencies of 10 to 10 . Since the pulse power of most dye laser systems is lower by one or two orders of magnitude nonresonant fifth-order frequency mixing of this radiation would produce intensities below a useful level. 

The dynamics of populations of the electronic states in a 4,4 -bis(dimethylamino) stilbene molecule (two-photon absorption) was studied against the frequency, intensity, and shape of the laser pulse [52]. Complete breakdown of the standard rotating wave for a two-photon absorption process was observed. An analytical solution for the interaction of a pulse with a three-level system beyond the rotating wave approximation was obtained in close agreement with the strict numerical solution of the amplitude equations. Calculations showed the strong role of the anisotropy of photoexcitation in the coherent control of populations that can affect the anisotropy of photobleaching. The two-photon absorption cross section of an ethanol solution of a trans-stilbene and its derivatives exposed to radiation of the second harmonic of a Nd YAG laser (532 nm) of nanosecond duration has been detected [53]. In experiments, the method based on the measurement of the photochemical decomposition of examined molecules was used. The quantum yield of the photoreaction (y266) of dyes under one-photon excitation (fourth harmonic Nd YAG laser 266 nm) was detected by absorption method. 

The mode spacing Avm is locked to the cesium clock frequency vcs in such a way that vcs = m - Avm- Therefore the frequency difference N Ay between N comb modes is precisely known. The fourth harmonics of a stabilized HeNe laser at k = 3.39p m is now compared with the frequency of a mode of the frequency comb. The beat frequency fc between 4/HeNe nd the mode frequency f is measured by a frequency counter. A dye laser at 486 nm is frequency doubled and excites the two-photon transition 15-25 of the hydrogen atom. Its frequency is locked to the doubled frequency of a diode laser, which is in turn locked to a mode of the frequency comb. The dye laser frequency is not exactly 7 times the HeNe laser frequency /, but differs from 7/ by —2A/. A frequency divider chain (see Fig. 14.59) generates from / and 1 f — lAf the frequency 4/—A/, which is just half of the sum /-f7/ —2A/. This frequency, which corresponds to a wavelength of 851 nm, is compared with that of a mode of the frequency comb. The difference frequency fc2 is measured by a counter. 

By force constants, we refer to derivatives of the electronic energy with respect to internal geometrical parameters of a molecule (Table 1). llie harmonic force constants are the second derivatives evaluated at an equilibrium structure, while higher derivatives may be put in the category of anharmonic force constants. From harmonic constants, harmonic frequencies are immediately obtained, and, typically, the harmonic frequencies are at least accurate enough to be used in making zero-point correaions to stabilities. Given harmonic constants and the lowest one or two orders of anharmonic force constants (third and fourth derivatives), transition frequencies of small polyatomics can often be extracted. Usually, this involves a perturbative treatment of the anharmonic parts of the potential in a produa basis of harmonic oscillator functions. 

Several well-characterized crystals for frequency doubling or frequency sum up to 0.25 pm which corresponds to the fourth harmonic of the YAG laser frequency (1.053 pm), are proposed by crystal manufacturers with outstanding conversion efficiencies. This upper frequency limitation around 0.25 pm results from the onset of absorption above this frequency and concomitant heating in practically all efficient doubling crystals there are similar limitations towards the mid- and far-IR spectrum because of strong absorption bands there due to IR active lattice modes (phonons, vibrations) and one resorts here to other nonlinear processes and coupling schemes. 

Avj (K, co) is the so called anharmonic shift of the fundamental frequency of mode k, the computationally most demanding part of the calculations, requiring the evaluation of the numerical third and fourth derivatives of the PES and the treatment of the Fermi resonances. The anharmonic shifts can be seen as corrections with respect to the harmonic frequencies, in most cases not exceeding 5%, but are very important when vibrational frequencies need to be computed with a high accuracy, or even for a qualitative analysis for example, for a C-H stretching mode typically at about 3000 cm", an anharmonic correction... 

From the separate lines of Eqs. 13-12 and 13-13 real and imaginary components of impedance at first (fundamental), second, third, and fourth harmonics can be calculated from the known voltage signal parameters and measured frequency-dependent current. The values for the Aaracteristic total capacitance C V ) and conductance G(f,j.) of the circuit can be computed. Comparison of the experimental and calculated frequency-dependent data for each harmonic serves as a diagnostic criterion that the system can indeed be represented by a simple parallel G C combination. Poor fit between the experimental and the calculated frequency-dependent impedance or current functions implies that a more complicated kinetic mechanism is responsible for the measured impedance characteristics. 

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