Anomalous resonance-enhanced harmonic ellipticity in an elliptically polarized laser field

We investigate theoretically resonant harmonic generation in $\text{H}{\text{e}}^{+}$ from an elliptically polarized laser field. The results show that there are two anomalous resonance-enhanced harmonics and the intensities of the anomalous resonance-enhanced harmonics remain unchanged for different laser ellipticities which are approximately two orders of magnitude stronger than those of nonresonant harmonics. We illustrate that the first resonance-enhanced harmonic is due to the transition between the ground state and the first excited state and the second one is due to the transition between the ground state and the second excited state. Our results also show that the enhancements of the harmonic intensities are related to the continuous collisions of the electron with the parent ion due to multiphoton resonance. The two resonance-enhanced harmonic intensities decrease gradually and orders do not change with an increase of the laser intensity, which can be illustrated through the Stark effect. The ellipticities of the two resonance-enhanced harmonics are approximately equal to the selected driving laser ellipticities regardless of the $\pm$ sign under different driving laser ellipticities, which might provide an accessible route toward characterizing the polarization properties of the laser. Our results offer a way for the generation of quasimonochromatic circularly polarized EUV radiation with high intensity.

Figure 1

(a) Harmonic spectrum with different driving laser ellipticities for the laser intensity $2.0\times {10}^{14}\text{W/c}{\text{m}}^{\text{2}}$. (b) Harmonic intensity distribution as a function of the laser intensity and the harmonic order with ${\varepsilon }_D=0$. The colors indicate harmonic intensity. The upper panel and the lower panel indicate the intensities of the nonresonance and the resonance-enhanced harmonics with different laser intensity, respectively. (c) Stark shifts of the first excited state $2p$.

Figure 2

(a) Intensity and (b) ellipticity of the resonant (H21 and H23) and nonresonant (H31 and H37) harmonics for different driving laser ellipticities. The black dotted and gray dotted lines indicate ${\varepsilon }_D=0$ and ${\varepsilon }_H=0$, respectively.

Figure 3

The (a) $x$ and (b) $y$ components of the time-dependent dipole acceleration for different driving laser helicities. The blue solid line and the red dotted line represent the results of ${\varepsilon }_D=0.2$ (${\varepsilon }_D>0$) and ${\varepsilon }_D=-0.2$ (${\varepsilon }_D<0$), respectively.

Figure 4

(a) Ratio $r=|a_y\left(\omega \right)|/|a_x\left(\omega \right)|$ of the $x$ and $y$ components of the dipole acceleration in the frequency domain for different driving laser ellipticities. (b) Phase difference $\delta$ of the $x$ and $y$ components of the harmonics and (c) cosine value of $2\delta$ corresponding to (b) for the resonant (H21 and H23) and nonresonant (H31 and H37) harmonics for different driving laser ellipticities.

Figure 5

Time profile of the amplitude of the harmonics via the time-frequency analysis for the resonant (H21 and H23) and nonresonant (H31 and H37) harmonics with the driving laser ellipticity (a) ${\varepsilon }_D=0$, (b) ${\varepsilon }_D=0.2$, (c) ${\varepsilon }_D=0.4$, and (d) ${\varepsilon }_D=0.6$. The blue solid, red dashed, orange dash-dotted, and green dotted lines indicate H21, H23, H31, and H37, respectively. The yellow and the green arrows indicate the times that the time profiles of H31 and of H37 drop close to 0, respectively.