Resonant enhancement of generation of harmonics

We develop a Floquet based formalism which describes a process of the generation harmonics of in an atom driven by a laser field. Using this formalism, we show that several harmonics are strongly enhanced in the spectrum when the laser frequency is such that a multiphoton resonance occurs between the initial state and a quasienergy state. We illustrate these findings by a numerical calculation of the harmonics generation in the potassium and rubidium atoms driven by a laser in the near-infrared energy range. The present formalism is also applicable when the initial state is a coherent superposition of several field-free atomic states.

Figure 1

(Color online) Harmonics spectra of potassium from the ground $4s$ state for laser frequencies $\omega =0.709\mathrm{eV}$ [(red) solid line], $\omega =0.689\mathrm{eV}$ [(green) dashed line], and $\omega =0.719\mathrm{eV}$ [(blue) short dashed line]. Peak strength of the EM field $F_0=0.005\mathrm{a.u.}$

Figure 2

(Color online) Intensities of the third [(red) solid line], fifth [(green) dashed line], seventh [(blue) short dashed line], and ninth [(magenta) dotted line] harmonics for potassium as functions of the driving laser frequency. Peak strength of the EM field $F_0=0.005\mathrm{a.u.}$

Figure 3

(Color online) Left panel: intensities of the third [(red) solid line)] and fifth [(green) dashed line] harmonics for potassium as functions of the driving laser frequency. Peak strength of the EM field $F_0=0.005\mathrm{a.u.}$ Right panel: the same for seventh [(red) solid line] and ninth [(green) dashed line] harmonics.

Figure 4

(Color online) Harmonics spectra of Rb from the ground $5s$ state for laser frequencies $\omega =0.624\mathrm{eV}$ [(red) solid line], $\omega =0.614\mathrm{eV}$ [(green) dashed line], and $\omega =0.634\mathrm{eV}$ [(blue) short dashed line]. Peak strength of the EM field $F_0=0.005\mathrm{a.u.}$

Figure 5

(Color online) Intensities of the third [(red) solid line], fifth [(green) dashed line], and seventh [(blue) short dashed line] harmonics of rubidium as functions of laser frequency. Peak strength of the EM field $F_0=0.005\mathrm{a.u.}$