Transition to the Relativistic Regime in High Order Harmonic Generation

Experiments and computer simulations on the generation of high order harmonics from steep plasma gradients using intense femtosecond laser pulses are presented. Qualitative changes in the harmonic emission take place when the intensities are increased above ${10}^{19}\mathrm{W}/{\mathrm{cm}}^2$ and/or the plasma scale length is varied. Good agreement between experimental and calculated spectra makes it possible to clearly distinguish between nonrelativistic and relativistic mechanisms of harmonic generation.

Figure 1

Experimental schematic for HOHG.

Figure 2

Harmonic spectra from glass (a) and polystyrene (b)–(d) recorded at $5\times {10}^{18}\mathrm{W}/{\mathrm{cm}}^2$ (a),(b) and $2\times {10}^{19}\mathrm{W}/{\mathrm{cm}}^2$ (c),(d). Dashed curve: transmission of a 170 nm aluminum film.

Figure 3

Electron density (top), spectra of the transverse current (middle), and harmonic spectra (bottom) for $p$-polarized excitation with $a_0=0.3$. The circles (bottom left) represent the spectrum calculated for a harmonically oscillating mirror with $s_0/\lambda =0.06$. The dashed lines indicate the critical surface (middle) and ${\omega }_p$ (bottom). Red dotted lines represent ${\omega }_p(x)$.

Figure 4

Calculated dependence of the 4th and 5th harmonic energy on the plasma scale length (a). Parameters as in Fig. 3. Experimental dependence of harmonic energy on the plasma scale length (b): filled circles and squares correspond to the experimental results at $I=2\times {10}^{19}\mathrm{W}/{\mathrm{cm}}^2$; open circles and triangles represent experimental results with $I=2\times {10}^{17}\mathrm{W}/{\mathrm{cm}}^2$ from [12].

Figure 5

Harmonic spectra for $p$-polarized excitation and $L/\lambda =0.02$. Solid lines represent the calculated normalized harmonic spectra. The filled circles correspond to the experimental energy conversion efficiency.