Multiphoton ionization of the calcium atom by linearly and circularly polarized laser fields

We theoretically study multiphoton ionization of the Ca atom irradiated by the second (photon energy $3.1$ eV) and third (photon energy 4.65 eV) harmonics of Ti:sapphire laser pulses (photon energy $1.55$ eV). Because of the dense energy level structure the second and third harmonics of a Ti:sapphire laser are nearly single-photon resonant with the $4s4p$ ${}^1{P}^o$ and $4s5p$ ${}^1{P}^o$ states, respectively. Although two-photon ionization takes place through the near-resonant intermediate states with the same symmetry in both cases, it turns out that there are significant differences between them. The photoelectron energy spectra exhibit the absence or presence of substructures. More interestingly, the photoelectron angular distributions clearly show that the main contribution to the ionization processes by the third harmonic arises from the far-off-resonant $4s4p$ ${}^1{P}^o$ state rather than the near-resonant $4s5p$ ${}^1{P}^o$ state. These findings can be attributed to the fact that the dipole moment for the $4s^2$ ${}^1{S}^e-4s5p$ ${}^1{P}^o$ transition is much smaller than that for the $4s^2$ ${}^1{S}^e-4s4p$ ${}^1{P}^o$ transition.

Figure 1

Relevant energy levels of Ca.

Figure 2

Relevant energy levels for ionization at the photon energy of $3.1$ eV. The energy detuning from the $4s4p$ ${}^1{P}^o$ bound state is $0.17$ eV.

Figure 3

(a) Ionization yield as a function of peak intensity by the linearly (solid) and circularly polarized (dashed) laser pulses at the photon energy of $3.1$ eV. (b) Ratio of the ionization yield by the circularly polarized laser pulse, $Y_{\mathrm{CP}}$, to that by the linearly polarized laser pulse, $Y_{\mathrm{LP}}$.

Figure 4

Photoelectron energy spectra by the linearly (solid) and circularly polarized (dashed) laser pulses at the photon energy of $3.1$ eV and the peak intensity of $5\times$${10}^{11}$ W/cm${}^2$.

Figure 5

(a) Comparison of the photoelectron energy spectra at the photon energy of $3.1$ eV. Solid line represents the result obtained from the complete atomic basis, while the dashed line represents the result from the atomic basis without the $4s4p$ ${}^1{P}^o$ state when solving the time-dependent Schrödinger equation. (b) Comparison of the populations of the $4s^2$ ${}^1{S}^e$ (circles) and $4s4p$ ${}^1{P}^o$ (squares) states as a function of time. The laser pulse is linearly polarized and the peak intensity is $5\times$${10}^{11}$ W/cm${}^2$.

Figure 6

Photoelectron angular distributions at the photon energy of 3.1 eV, corresponding to the (a) first, (b) second, (c) third, and (d) fourth ATI peaks in Fig. 4. The laser pulse is linearly polarized and the peak intensity is $5\times$${10}^{11}$ W/cm${}^2$.

Figure 7

Relevant energy levels for ionization at the photon energy of $4.65$ eV. The energy detuning from the $4s5p$ ${}^1{P}^o$ bound state is $0.1$ eV.

Figure 8

(a) Ionization yield as a function of peak intensity by the linearly (solid) and circularly (dashed) polarized laser pulses at the photon energy of $4.65$ eV. (b) Ratio of the ionization yield by the circularly polarized laser pulse, $Y_{\mathrm{CP}}$, to that by the linearly polarized laser pulse, $Y_{\mathrm{LP}}$.

Figure 9

Photoelectron energy spectra by the linearly (solid) and circularly polarized (dashed) laser pulses at the photon energy of $4.65$ eV and the peak intensity of ${10}^{13}$ W/cm${}^2$. (a)–(d) represent the substructures.

Figure 10

Comparison of the photoelectron spectra at the photon energy of $4.65$ eV when the (a) $4s4p$ ${}^1{P}^o$, (b) $4s5p$ ${}^1{P}^o$, (c) $4s6p$ ${}^1{P}^o$, and (d) $3d4p$ ${}^1{P}^o$ states are artificially removed from the atomic basis when solving the time-dependent Schrödinger equation. The laser pulse is linearly polarized and the peak intensity is ${10}^{13}$ W/cm${}^2$.

Figure 11

Photoelectron angular distributions at the photon energy of 4.65 eV, corresponding to the (a) first, (b) second, (c) third, and (d) fourth ATI peaks in Fig. 9. The laser pulse is linearly polarized and the peak intensity is ${10}^{12}$ W/cm${}^2$.

Figure 12

Comparison of the photoelectron angular distributions by a linearly polarized laser pulse at the photon energy of $4.65$ eV when the $4s4p$ ${}^1{P}^o$, $4s5p$ ${}^1{P}^o$, $4s6p$ ${}^1{P}^o$, and $3d4p$ ${}^1{P}^o$ bound states of Ca are artificially removed from the atomic basis when solving the time-dependent Schrödinger equation. The peak intensity is ${10}^{12}$ W/cm${}^2$.