Analytical estimates of attosecond streaking time delay in photoionization of atoms

We present estimates of the attosecond streaking delay in photoionization of atoms based on an analytical formula. In the derivation of the formula we use that the streaking delay depends on the propagation of the photoelectron over a finite range in space. We find that the analytical estimates agree well with results of ab initio calculations. Application of the formula provides insights into the influence of the streaking field on the field-free time delay in the analysis of streaking measurements.

Figure 1

Comparison of predictions of analytical formula for the field-free time delay $\mathrm{\Delta }{t}_{\mathrm{ff}}$, Eq. (8), with results extrapolated from ab initio calculations for hydrogen atom ($Z=1$) [10] as a function of propagation time.

Figure 2

Comparison of analytical estimates (solid lines) with results of ab initio calculations (circles, [10]) of the streaking delay in a hydrogen atom and helium ion. Parameters of the streaking field: peak intensity $I_s=1\times {10}^{12}{\mathrm{W}/\mathrm{cm}}^2$, wavelength ${\lambda }_s=800$ nm, and pulse duration of three cycles. In the analytical calculations, ionization of the photoelectron at the peak of the pulse and the most probable location of the electron in the initial state has been assumed.

Figure 3

Comparison of analytical predictions (solid lines) with results of ab initio calculations (symbols) for the streaking time delay in the case of photoionization of (a) helium (ab initio data from [10]) and (b) neon atom as a function of the XUV photon energy. Ab initio results from calculations using the present SAE potential (circles, [20]) and multielectron $B$-spline $R$-matrix calculations (diamonds, [22]) are shown. Streaking laser parameters are as in Fig. 2.

Figure 4

Absolute difference ${\mathrm{\Delta }}_{\mathrm{short}}$ as a function of the XUV photon energy for the contribution due to the short-range potential for (a) neon atom and (b) helium atom. Streaking laser parameters are as in Fig. 2.

Figure 5

Absolute difference ${\mathrm{\Delta }}_{\mathrm{phase}}$ for photoionization of (a) neon, (b) helium, and (c) hydrogen. Streaking laser parameters as in Fig. 2.

Figure 6

Absolute difference ${\mathrm{\Delta }}_{\log }$ for photoionization of (a) neon, and (b) helium. Streaking laser parameters as in Fig. 2.

Figure 7

Comparison of present analytical estimates (solid lines) for $\mathrm{\Delta }{t}_{\mathrm{CLC}}$ with those of an alternative analytical approximation (dashed lines, [12]). Streaking laser parameters as in Fig. 2.