Coherent harmonic excitation frequency

Harmonic Generation. Nonlinear frequency conversion, especially harmonic generation, is important for the development of sources of coherent light at frequencies not otherwise accessible by efficient lasers, in particular the blue, violet, and UV frequencies needed for dense data storage. Harmonic generation is also useful for nonlinear spectroscopic studies, which probe excited states in materials (34). 

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. 

Among other methods of creating and observing optical manifestations of coherent superpositions of non-degenerate magnetic sublevels (an elegant analysis may be found in [4]), the most widely used method is that of resonance of beats. The effect appears when the frequency fli of harmonic modulation of the excitation rate... 

The sum in Equation 3.41 is a geometric series whose elements become unity, and add constructively, when kdl2 = mir, where m is an odd integer. This condition defines the relationship between SAW wavelength. A, and transducer periodicity, d, for coherent addition, as shown in Figure 3.19. The IDT excites odd harmonics at odd multiples of the synchronous frequency f = m/i. 

It is instructive to compute the time correlation function in the simple case that the ground and excited state potentials are harmonic but differ in their equilibrium position and frequency. This is particularly simple if the initial vibrational state is the ground state (or, in general, a coherent state (52)) so that its wave function is a Gaussian. We shall also use the Condon approximation where the transition dipole is taken to be a constant, independent of the nuclear separation, but explicit analytical results are possible even without this approximation. A quick derivation which uses the properties of coherent states (52) is as follows. The initial state on the upper approximation is, in the Condon approximation, a coherent state, i /,(0)) = a). The value of the parameter a is determined by the initial conditions which, if we start from a stationary state, are that there is no mean momentum and that the mean displacement (x) is the difference in the equilibrium position of the two potentials. In general, using m and o> to denote the mass and the vibrational frequency... 

The high intensity and coherence of laser radiation can lead to more elaborate photon scattering processes than those involved in the conventional Raman effect. The simplest example is second harmonic generation (hyper-Rayleigh scattering) and the associated hyper-Raman effect in which two laser photons of frequency interact simultaneously with the molecule to produce a scattered photon at frequency (hyper-Rayleigh), or at XiOi.-tO (Stokes hyper-Raman) or at (antiStokes hyper-Raman). As illustrated in figure 1.3, these processes involve two virtual intermediate excited states. 

The second volume of Laser Spectroscopy covers the different experimental techniques, necessary for the sensitive detection of small concentrations of atoms or molecules, for Doppler-free spectroscopy, laser-Raman-spectroscopy, doubleresonance techniques, multi-photon spectroscopy, coherent spectroscopy and time-resolved spectroscopy. In these fields the progress of the development of new techniques and improved experimental equipment is remarkable. Many new ideas have enabled spectroscopists to tackle problems which could not be solved before. Examples are the direct measurements of absolute frequencies and phases of optical waves with frequency combs, or time resolution within the attosecond range based on higher harmonics of visible femtosecond lasers. The development of femtosecond non-collinear optical parametric amplifiers (NOPA) has considerably improved time-resolved measurements of fast dynamical processes in excited molecules and has been essential for detailed investigations of important processes, such as the visual process in the retina of the eye or the photosynthesis in chlorophyl molecules. 

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. 

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