Collinear phase matching

When 2o3 approaches resonance, X undergoes strong (>10 ) enhancement. For efficient THG, collinear phase-matching is necessary, that is, the refractive index n(3co) = n(co) in order to yield a maximum effective interaction length. With focused incident radiation, THG can be observed only in negatively dispersive media. Tunability is achieved by varying the incident frequency 03. 

Gas phase CARS spectroscopic Investigations are typically carried out using collinear phase matching and very narrowband pump and probe lasers of linewidth 0.1 cm or less to achieve high spectral resolution. As Illustrated in Fig. 1, CARS is implemented quite differently when applied to combustion diagnostics. 

If the pump is an extraordinary wave, collinear phase matching can be achieved for some angle 0 against the optical axis, if rip(0), defined by (5.119), lies between no(cop) and n icop). 

Fig. 5.119a,b. Optical parametric oscillator (a) schematic diagram of experimental arrangement (b) pairs of wavelengths (Ai, X2) for idler and signal wave for collinear phase matching in LiNbOs as a function of angle 0 [5.290]... 

Knowing the characteristics of linear wave propagation, we can then discuss the nonlinear optical effects in a cholesteric liquid crystal. In Sec. Ill, we shall consider the problem of third-harmonic generation along the helical axis in such a medium. Emphasis is on the derivation of collinear phase-matching conditions. 

We have shown theoretically and experimentally that third-harmonic generation can be collinearly phase matched in cholesteric liquid crystals. Phase matching is achieved since the momentum mismatch between the fundamental and the third harmonic is compensated by the lattice momentum which is present due to the periodicity of the helical structure of the cholesteric medium. Many different phase-matching conditions exist. Analogous to electron-electron interaction in a periodic lattice,... 

The condition (5.119) for collinear phase-matching can only be fulfilled if the dispersion, i.e., the dependence of the refractive index n(A) on the wavelength A can be neglected. This is true for gases and vapors at sufficiently low pressures where n 1. 

In the gas phase, dispersion may be negligible, making collinear phase matching possible (see Figure 2A). However, the BOXCARS approach is often preferred because it allows spatial discrimination between the input and output beams. Additional spatial discrimination may be achieved using a three-dimensional form called folded BOXCARS (see Figure 2F). 

It is possible to find nonlinear crystals where the phase-matching condition (7.17) for collinear phase matching can be fulfilled if one of the three waves propagates as extraordinary wave and the others as ordinary waves through the crystal in a direction e specified by (7.19) and (7.17) [7.76]. 

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