Wave-vector mismatch

Figure 4b depicts for the case bAk -0.3 (b is the confocal parameter of the gaussian and Ak is the linear plane-wave, wave-vector mismatch, Ak=3 (n -no )/c). One can see that bAk>0 results in... 

The parabolic equations derived in a slowly varying envelope approximation that describe the second harmonic generation (SHG) of ultrashort pulses in media with locally inhomogeneous wave-vector mismatch, have the form ... 

In regard to Equation (5.4), we have to note that without the above mentioned assumptions the nonlinearities will contain weighting factors that are proportional to the corresponding wave-vector mismatch and inversely proportional to refractive index, thus suggesting that the THG signal is sensitive to the refractive index interface(s) as well. In order to differentiate between contrast mechanisms in THG imaging of soft tissue materials it would be important to know the relationships of the corresponding linear and nonlinear optical parameters. A nonlinear optical... 

By solving the nonlinear wave equation, under the assumption of undepleted input beams, it is found that the intensity of the output wave at frequency 2w varies as a function of the interaction length inside of the sample, I, and the wave vector mismatch Ak [26] ... 

In this case the wave vector mismatch is defined as ... 

Wave-vector mismatch Difference between the wave vector of an optical wave and that of the nonlinear polarization that drives it. It is also called the phase mismatch. 

Here A, is the amplitude of the ith optical field, which may be either an incident field or a field generated in the interaction, and Ak, is the wave-vector mismatch between the fth optical field and the polarization that drives it and is given by... 

Nonlinear process Nonlinear polarization Wave-vector mismatch Plane-wave phase-matching condition... 

In the simplest situation, termed type I phase matching, the incident radiation is polarized as an ordinary or an extraordinary ray, depending on the properties of the nonlinear material, and the harmonic radiation is polarized orthogonally to the incident radiation as shown in Fig. 6a. The wave-vector mismatch is then given by... 

Just as for sum-frequency mixing, the generated intensity at low conversion efficiency grows as the product of the pump intensities at co and 0)2- In this situation a photon is created at both 0)3 and 0)2 for every photon annihilated at cl>. The wave-vector mismatch is AA = kieoy) — [k ct) ) — k co2), and the phase-matching condition is... 

Phase matching can be accomplished by using a mixture of gases with different signs of dispersion. In this situation each component makes a contribution to the wave-vector mismatch in proportion to its concentration in the mixture. The value of the wave-vector mismatch can be controlled by adjusting the relative concentration of the two gases until the appropriate phase-matching condition is met for either collimated or focused beams, as shown in Fig. 12. 

A more physical picture is that the grating vector K = lirlJA is used to compensate for the wave vector mismatch A)3 = 2 2/3,. The is also referred to as the... 

Both processes carry a wave vector mismatch M4 = k ( 1+ 3)- Since 2= and k =—k, we have AAt4= 0 (i.e., a perfectly phase-matched four-wave mixing process). However, the grating constant associated with (E2E ) is much smaller than that associated with ) as a result of the larger wave mixing angle. 

Here uis is the signal field radial frequency, ks is the signal wave vector, c is the speed of light, L is the sample pathlength, and Ak is the wave vector mismatch for generation of the signal. This mismatch arises due to the difference between the wavevector, ks, and the wavevector in the medium ... 

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