High-resolution Interferometric Diagnostics for Ultrashort Pulses

7. LATERAL SHEARING INTERFEROMETRY FOR HIGH-HARMONIC GENERATIONσkT (µm−1 )0.250.20.150.1φ2,kT (µm2 )0−20−40−60(a)−80(b)−5 0 5 −5 0 5gas jet z (mm)gas jet z (mm)Figure 7.22: Properties of the 25 th harmonic extracted from simulation (red line) and experiment(blue); (a) far-field width; (b) on-axis phase curvature.broad angular spectrum. In the phase, several effects are at play. For z ≈−5, the near cancellationof the intensity-dependent phase by the laser wavefront produces a near-zero phase curvature inboth the near- and far-fields. One possible cause of the disagreement between theory and experimentin this region is deviations of the laser beam profile from Gaussian. With increasing z , thenear-field becomes more curved as the laser curvature decreases, and this initially (-5 – -2 mm)leads to curvature of the far-field. However, the relationship between the on-axis curvatures in thenear- and far-fields is nonmonotonic. Rather for a Gaussian profile,φ 2,kT = −φ 2,rσ −42,r + φ2 2,r(7.15)i.e. the absolute value of the far-field curvature initially increases with increasing near-field curvature,but then reaches a maximum before asymptotically decreasing to zero. This is observedfor z > −2 in Fig. 7.22(b). An additional effect is the propagation from the generation plane to themeasurement plane which produces a phase curvature −(0 − z )/(2qk L ) i.e. a linear increase withz .Another trend evident in both simulation and theory is the dependence of the amplitude andphase profiles on the harmonic number. This is presented in Fig. 7.23 at z = −1.5 mm. Generally,the amplitudes become broader with increasing harmonic number. This can be attributed to the182