Phase matching directions

Biaxial crystals offer the possibiUty of coincidence of the phase matching direction with one of the optic axes. This highly desirable situation, called non-critical phase matching, is quite tolerant of divergence of the incident beam from the most efficient phase matching direction. 

The femtosecond (fs) laser system consists of a TiiSapphire laser and a regenerative amplifier pumping two independent optical parametric amplifiers that provide laser pulses of around 100 fs duration over a very broad range of wavelengths (250-2000 nm). The signal is detected in the transmitted phase-matching direction lc = k3 + k2 — ki and recorded by a spectrometer with spectral resolution = 2 nm. The spectra are measured by scanning over the... 

Two types of phase-matching exist for SHG Type I, where the two fundamental photons are of the same polarization, and Type II, where they are orthogonally polarized. The phase- matching direction and one of the principal vibration directions of the crystal may be coincident in biaxial and uniaxial (birefringent) crystals. This situation, called noncritical phase-matching, is quite... 

Figure 3 (a) Time sequence of the (stimulated) three-pulse photon echo experiment. The times ti, t2, and t3 represent the time coordinates used in the response functions [Equations (7)—(12)] while r, T, and t measure the delay times with respect to the peak positions of the light pulses. For 5-shaped light pulses, both sets of times would be equivalent, (b) The so-called box configuration, (101) which allows the spatial separation of the third-order polarization generated in the —ki + k2 + kj and the +ki — k2 + k3 phase matched directions. 

Figure 4 Distribution of all six possible time orderings, labeled (ijk), onto the four quadrants spanned by time coordinates r and T (shown for the — k + k2 + k3 phase matching direction). 

Figure 5 (a) Stimulated photon echo signal of the azide ion (N3 ) in D2O at 2043 cm-1 as a function of r and T for the — kj + k2 + k3 (gray surface) and the +ki — k2 + k3 (white surface) phase matching directions, (b) Representative traces for four selected values of T. The solid lines represent a global fit of all the scans to the model correlation function Equation (20). (From Ref. 41.)... 

As an example, we show how to extract the three-pulse photon echo (3PPE) polarization P3p(t) from Eq. 9.52. The polarization in any other phase-matching direction can be found in the same manner. Specifically, we search for the contribution to the total polarization P t) which is proportional to exp ik3pr, where... 

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