Spin conservation in high-order-harmonic generation using bicircular fields

We present an alternative theoretical model for a recent experiment [A. Fleischer et al., Nature Photon. 8, 543 (2014)] which used bichromatic, counter-rotating high-intensity laser pulses to probe the conservation of spin angular momentum in high-order-harmonic generation. We separate elliptical polarizations into independent circular fields with definite angular momentum, instead of using the expectation value of spin for each photon in the conservation equation, and we find good agreement with the experimental results. In our description the generation of each individual harmonic conserves spin angular momentum, in contrast to the model proposed by Fleischer et al. Our model also correctly describes analogous processes in standard perturbative optics.

Figure 1

Existence regions for the different harmonics predicted by model 2 compared to numerical simulations for (a) right-circular and (b) left-circular harmonics. The ellipses are drawn with arbitrary widths at the half-maximum-intensity ranges in ellipticity defined by Eq. (14). We display only the lowest-order channel for each harmonic order and helicity, though higher-order channels are also present which partly overlap with the ones displayed. The background spectra are two-dimensional numerical simulation results for a flat-top pulse of 20 cycles of the fundamental with $7\frac{1}{2}$ cycles of sinusoidal on- and off-ramp. We use a model potential for argon at equal driver intensities of $7\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$.

Figure 2

Dependence of the harmonic energies for the (a) right- and (b) left-circularly polarized harmonics, as a function of the relative detuning $\delta /\omega ={\omega }^{\prime }/\omega -1$ between the right- and left-circular components of the elliptically polarized fundamental driver, as per Eq. (17). We numerically integrate the SFA dipole [15, 16], and we use a flat-top pulse of 20 cycles of the fundamental with $2\frac{1}{2}$ cycles of sinusoidal on- and off-ramp. We take equal intensities of $2\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ in the drivers, with $\alpha ={35}^{\circ }$, and an S-type ground state with an argon-like $I_p$ of $15.6\mathrm{eV}$.

Figure 3

Channel (1,2), where an elliptical driver at frequency ${\omega }_1$ and a left-circular driver at frequency ${\omega }_2$ produce a left-circular harmonic at frequency ${\omega }_1+2{\omega }_2$, can be understood as a simple four-wave mixing process. It can thus be treated perturbatively, and it will occur at much lower intensities. By decomposing the elliptical driver as a superposition of circular polarizations, as in Eqs. (2) and (10), one obtains an allowed process with a right-circular ${\omega }_2$ driver, and a forbidden process with three left-circular drivers which has too much angular momentum for a single harmonic photon.