Abstract
We present a model for quasi-phase matching (QPM) in high-order harmonic generation (HHG). Using a one-dimensional description, we analyze the time-dependent, ultrafast wave-vector balance to calculate the on-axis harmonic output versus time, from which we obtain the output pulse energy. Considering, as an example, periodically patterned argon gas, as may be provided with a grid in a cluster jet, we calculate the harmonic output during different time intervals within the drive laser pulse duration. We find that identifying a suitable single spatial period is not straightforward due to the complex and ultrafast plasma dynamics that underlies HHG at increased intensities. The maximum on-axis harmonic pulse energy is obtained when choosing the QPM period to phase match HHG at the leading edge of the drive laser pulse.
Highlights
High-order harmonic generation (HHG) is an extremely nonlinear optical process that provides coherent radiation in the extreme ultraviolet spectral region on an ultrafast time scale
To demonstrate QPM for HHG in experiments using the schemes mentioned above, the selection of a fixed-periodic structure for maximizing the total high-order harmonic (HH) output is usually based on an unproven assumption, namely, that the quasi-phase matching period has to be chosen equal to twice the coherence length calculated for the time-instance where the intensity of the drive laser pulse is maximum
We show that the maximum harmonic pulse energy is obtained when choosing the QPM period for phase matching in the leading edge of the drive laser pulse, rather than at the peak
Summary
High-order harmonic generation (HHG) is an extremely nonlinear optical process that provides coherent radiation in the extreme ultraviolet spectral region on an ultrafast time scale. To demonstrate QPM for HHG in experiments using the schemes mentioned above, the selection of a fixed-periodic structure for maximizing the total high-order harmonic (HH) output is usually based on an unproven assumption, namely, that the quasi-phase matching period has to be chosen equal to twice the coherence length calculated for the time-instance where the intensity of the drive laser pulse is maximum (at peak intensity). This is based on the argument that the nonlinearly induced dipole moment of the individual atoms is the highest at that time [14]. We show that the maximum harmonic pulse energy is obtained when choosing the QPM period for phase matching in the leading edge of the drive laser pulse, rather than at the peak
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