Stokes wave

This is not the case for stimulated anti-Stokes radiation. There are two sources of polarization for anti-Stokes radiation [17]. The first is analogous to that in figure B1.3.3(b) where the action of the blackbody (- 2) is replaced by the action of a previously produced anti-Stokes wave, with frequency 03. This radiation actually experiences an attenuation since the value of Im x o3 ) is positive (leading to a negative gam coefficient). This is known as the stimulated Raman loss (SRL) spectroscopy [76]. Flowever the second source of anti-Stokes polarization relies on the presence of Stokes radiation [F7]. This anti-Stokes radiation will emerge from the sample in a direction given by the wavevector algebra = 2k - kg. Since the Stokes radiation is... 

As the time scale of the Raman scattering event ( 3.3 x 10 14 s for a vibration with a Stokes wave number shift of 1000 cm 1 excited in the visible) is much shorter than that of the fastest conformational fluctuations, an ROA spectrum is a superposition of snapshot spectra from all the distinct conformations present in a sample at equilibrium. Since ROA observables depend on absolute chirality, there is a cancellation of contributions from enantiomeric structures arising as a mobile structure explores the range of accessible conformations. Therefore, ROA exhibits an enhanced sensitivity to the dynamic aspects of biomolecular structure. In contrast, conventional Raman band intensities are blind to chirality and so are generally additive and therefore less sensitive to conformational mobility. Ultraviolet circular dichroism (UVCD) also demonstrates an enhanced sensitivity to the dynamics of chiral structures ... 

From Eq. (3.6-4) we immediately recognize that in stimulated Raman scattering processes where only one input laser field with frequency is employed, a coherent Stokes wave is generated for those Raman modes which have the highest ratio between differential Raman cross section and linewidth F. The latter corresponds to the dephasing time T2 of the physical system, F = l/Tj, and reflects the damping of the system. 

The amplitudes of the high-order harmonics very strongly depend on the amplitude of the basic waves. For Stokes waves, for example, the amplitude of the n-th harmonic is proportional to the n-th power of the amplitude of the basic wave. Therefore, even weak damping of dm-scale basic waves due to films can lead to strong nonlinear depression of the bound waves ( cascade effect), the latter effect can result in a maximum of the damping in the mm-scale wavelength range. 

This is not the case for stimulated anti-Stokes radiation. There are two sources of polarization for anti-Stokes radiation [H]. The first is analogous to that in figure B1.3.3(bl where the action of the blackbody (-CO2) is replaced by the action of a previously produced anti-Stokes wave, with frequency co. This radiation actually... 

There are several comprehensive reviews [4] of theories of stimulated Raman processes and of salient experiments. For our purpose, we need only consider that when intense laser radiation (at frequency coo) is incident on a Raman-active medium, there is exponential growth of the spontaneous Stokes wave (at frequency 0)3) given by... 

Here, Na and Nb are populations in the lower and upper states of the Raman transition, da/dq is the rate of change of polarizability with normal coordinate, no and ns are the refractive indices at o)o and 0)s5 r is the Raman linewidth and y the reduced mass. Eq. (1) describes a Stokes Raman laser producing coherent radiation at 0)3. In this brief and simplified description, we may consider that the strong pump and Stokes waves generate a coherent material excitation at 0)r. This oscillation causes variations in the refractive index which then modulate and scatter the incident laser radiation (o)o) thus producing sidebands or many orders of coherent Stokes and anti-Stokes radiation at frequen-... 

Since an oscillating dipole moment is a source of new waves generated at each molecule, (3.5) shows that an elastically scattered wave at the frequency co of the incident wave is produced (Rayleigh scattering) as are inelastically scattered components with the frequencies co — cOn Stokes waves) and superelastically scattered... 

If the incident laser intensity /l becomes very large, an appreciable fraction of the molecules in the initial state Ei is excited into the final state Ef and the intensity of the Raman-scattered light is correspondingly large. Under these conditions we have to consider the simultaneous interaction of the molecules with two EM waves the laser wave at the frequency [Pg.162]

The Raman medium is taken as consisting of N harmonic oscillators per unit volume, which are independent of each other. Because of the combined action of the incident laser wave and the Stokes wave, the oscillators experience a driving force F that depends on the total field amplitude E... 

The Stokes wave is amplified if the gain g exceeds the losses /. The amplification factor g depends on the square of the laser amplitude Ei and on the term (da/dq). Stimulated Raman scattering is therefore observed only if the incident laser intensity exceeds a threshold value that is determined by the nonlinear term (daij/dq)o in the polarization tensor of the Raman-active normal vibration and by the loss factor / =... 

According to (3.26), the driving term in the wave equation (3.28) for an anti-Stokes wave at 0 = is given by... 

For small amplitudes of the anti-Stokes waves, we can assume that the molecular vibrations are independent of and can replace qy by its solution (3.25). This yields an equation for the amplification of "a that is analogous to (3.29) for Es... 

Despite the enormous intensities of stimulated Stokes and anti-Stokes waves, stimulated Raman spectroscopy has been of little use in molecular spectroscopy. The high threshold, which, according to (3.30), depends on the molecular density N, the incident intensity I a and the square of the small polarizability term (daij/dq) in (3.27), limits stimulated emission to only the strongest Raman lines in materials of high densities N. 

Because of the nonlinear interaction discussed in Sect. 3.3.1, new Stokes and anti-Stokes waves are generated (Fig. 3.16d). The waves co and C02 produce a large population density of vibrationally excited molecules by stimulated Raman scattering. These excited molecules act as the nonlinear medium for the generation of... 

In a similar way, a Stokes wave with frequency cOg = 2co2 — co i is generated by the incident waves at coi and C02 (Fig- 3.16d). Since four waves are involved in the generation of the anti-Stokes wave, CARS is called 3. four-wave parametric mixing process (Fig. 3.17). 

The higher frequency coj, > twi, ci>2 of the anti-Stokes waves allows one to use filters that reject the incident light as well as fluorescence light. 

Figure 1 illustrates the sequential Stokes interaction within the droplet. Unlike the incident pump at which is localized mainly at the focal spot, the field of the 1st Stokes with >2 shift is distributed around the interface. Thus the pumping length of this 1st Stokes wave is 2ta while that of the incident wave is only a fraction of a. When several I s are included, the density of MDR s is such that at least one MDR exists within the Raman gain profile at X2S to provide the necessary feedback for the Stokes wave at X2s" processes then repeat for the nth-order Stokes... 

Phase-modulation broadening of the incident and Stokes waves has been reported from liquid and solid optical fibers. Phase modulation is associated with the real part of which is known to be large for CS2- Self... 

The 1st Stokes spectrum from CS2 droplets was also noted to be asymmetrically broadened. For the Stokes wave, phase modulation can be induced by... 

If the medium is initially in its ground state, the scattered wave is at a lower frequency (longer wavelength) than the incident wave, and the medium is excited to one of its internal energy levels during the interaction. In this situation the frequency shift is termed a Stokes shift, in analogy to the shift to lower frequencies that is observed in fluorescence (which was explained by Sir George Stokes), and the scattered wave is termed a Stokes wave. The incident (laser) and scattered (Stokes) frequencies are related by... 

Stimulated scattering processes that involve Stokes waves arise from third-order nonlinear interactions with nonlinear polarizations of the form... 

When pump depletion is negligible, the intensity of the Stokes wave is given by... 

Photon number is conserved in stimulated scattering interactions, with one photon being lost in the pump wave for every one created in the Stokes wave. The energy created in the Stokes wave is smaller than that lost in the pump wave by the ratio cos/coi, termed the Manly-Rowe ratio, and the difference in photon energy between the pump and Stokes waves represents the energy given to the medium. 

When the energy in the Stokes wave becomes comparable to that in the incident laser pump, depletion occurs and the gain is reduced. In principle, every photon in the incident pump wave can be converted to a Stokes photon, giving a maximum theoretical conversion efficiency of... 

FIGURE 20 (a) Generation of a Stokes wave in singie-pass stimulated Raman scattering, (b) Generation of a Raman-Stokes wave in a Raman laser oscillator. 

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