Multiphoton and tunnel ionization by an optical field with polar asymmetry

A simplified form of multiphoton and tunneling ionization is applied to the problem of ionization of atoms by a bichromatic field consisting of the coherent superposition of a fundamental field and its second harmonic: E(t)=0.5[${\mathbf{E}}_{1}$ exp(-i\ensuremath{\omega}t)+${\mathbf{E}}_{2}$ exp(-2i\ensuremath{\omega}t)]+c.c. This superposition possesses a polar asymmetric average of the cube of the field, 〈${\mathit{E}}^{3}$〉=3/8(${\mathit{E}}_{1}^{2\mathrm{*}}$${\mathit{E}}_{2}$+${\mathit{E}}_{1}^{2}$${\mathit{E}}_{2}^{\mathrm{*}}$). Two limits of the adiabaticity parameter \ensuremath{\gamma} are considered, where \ensuremath{\gamma}=\ensuremath{\omega}(2mI${)}^{1/2}$/(\ensuremath{\Vert}e\ensuremath{\Vert}E) and I is the ionization potential. The case \ensuremath{\gamma}\ensuremath{\ll}1 corresponds to tunneling ionization by a quasistatic field. Here, the electron is released from the barrier with almost zero velocity at the moment when the magnitude of the field strength \ensuremath{\Vert}E\ensuremath{\Vert} is maximum. Subsequent oscillations of the free electron in the strong but adiabatically decreasing field yield some residual velocity. Polar asymmetry of the distribution of that velocity and 〈v〉 are calculated as a function of the phase shift, arg(${\mathit{E}}_{1}^{2}$${\mathit{E}}_{2}^{\mathrm{*}}$), between the squared fundamental field ${\mathit{E}}_{1}^{2}$ and its second harmonic ${\mathit{E}}_{2}$. The other case, \ensuremath{\gamma}\ensuremath{\gg}1, corresponds to multiphoton ionization by the combined fields where ${\mathit{n}}_{1}$\ensuremath{\Elzxh}\ensuremath{\omega}+${\mathit{n}}_{2}$2\ensuremath{\Elzxh}\ensuremath{\omega}\ensuremath{\approxeq}I. Interference of the amplitudes corresponding to opposite parities of the total number of quanta ${\mathit{n}}_{1}$+${\mathit{n}}_{2}$ with the same energy (${\mathit{n}}_{1}$+2${\mathit{n}}_{2}$)=const (\ensuremath{\approxeq}I/\ensuremath{\Elzxh}\ensuremath{\omega}) gives rise to the arg(${\mathit{E}}_{1}^{2}$${\mathit{E}}_{2}^{\mathrm{*}}$)-dependent polar asymmetry of emitted electrons. Recent experiments on arg(${\mathit{E}}_{1}^{2}$${\mathit{E}}_{2}^{\mathrm{*}}$)-sensitive effects in multiphoton ionization are discussed.

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