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Nonlinear optical effect in the soft x-ray region by two-photon ionization of He +

Nonlinear optical effect in the soft x-ray region by two-photon ionization of He +. CLEO/QELS2002 May 22, 2002. Kenichi Ishikawa* 、 Katsumi Midorikawa Laser Technology Laboratory, RIKEN, Japan

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Nonlinear optical effect in the soft x-ray region by two-photon ionization of He +

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  1. Nonlinear optical effect in the soft x-ray region by two-photon ionizationof He+ CLEO/QELS2002 May 22, 2002 Kenichi Ishikawa*、Katsumi Midorikawa Laser Technology Laboratory, RIKEN, Japan *Present address : Department of Quantum Engineering & Systems Science, Graduate School of Engineering, University of Tokyo ishiken@q.t.u-tokyo.ac.jp Phys. Rev. A 65, 043405 (2002)

  2. Nonlinear Optical Effect The material response to anapplied optical field depends on the field strength in a nonlinear fashion Göppert-Mayer Theory 1931 Winter RF 1959 Franken et al. (2nd-order harmonic) Visible 1961 Kaiser and Garrett (Two-photon excitation) Kobayashi et al. VUV 1998 Descamps et al. XUV 2001 High-order harmonic generation ？ Soft X-ray ？

  3. High-order harmonic generation High-order harmonics of a Ti:Sapphire laser CLEO2002 CMQ3 27HG (30nm, 41.85eV) → 〜300nJ, < 30fs focused to an area of 10mm2 by a soft x-ray mirror He2+ 5×1013W/cm2 Motivation：to propose a system for the experimental observation of a nonlinear optical effect in a soft x-ray range using such an intense pulse. E = 0 2p 27HG (30nm, 41.85eV) 40.8 eV Two-photon ionization of He+ 1s He+

  4. Three conditions The two-photon ionization probability must be • High. • Quadratic in soft x-ray intensity. • Linear in pulse duration. Not evident at high intensity and ultrashort pulse duration. Numerical simulation

  5. Field of the soft x-ray pulse Model Time-dependent Schrodinger equation • Numerical method • Alternating direction implicit (Peaceman-Rachford) method • He2+ Yield • evaluated as the number of electrons absorbed by the mask function at the outer radial boundary.

  6. He2+ yield vs. Peak intensity gaussian 30fs-27th harmonic pulse “analytical” means, s = 2.9×10-52 cm4s • Saturation can be seen at I > 1013 W/cm2. • Not due to the decrease of the He+ population. • Due to the ac-Stark effect. (Haberland 1987) • The two-photon ionization probability is sufficiently high to be observed experimentally. • The yield is approximately proportional to (Intensity)2.

  7. The He2+ yield is sufficiently high if we use the 27HG. 5.6×10-5 at I = 2×1013W/cm2 3.3×10-4 at I = 5×1013W/cm2 Ac-Stark effect → Saturation ↓Nevertheless… The yield is approximately quadratic in intensity for the case of the 27HG. Two-photon ionization probability ( He2+ Yield ) Two-photon ionization probability by a Gaussian pulse with a duration (FWHM) of 30 fs

  8. Three conditions The two-photon ionization probability must be • High. • Quadratic in soft x-ray intensity. • Linear in pulse duration. OK OK

  9. If the pulse duration is > 5 fs, the yield is proportional to the duration. Application such as the pulse duration measurement by autocorrelation If the pulse duration is < 5 fs, the linearity breaks down. Excitation of the 2p level due to energy uncertainty. He2+ yield vs. Pulse duration of a gaussian 27th harmonic pulse with a peak intensity of 5×1013 W/cm2.

  10. Three conditions The two-photon ionization probability IS • High! • Quadratic in soft x-ray intensity! • Linear in pulse duration! (> 5fs) Attractive candidate for experimental observation of a nonlinear optical effect in the soft x-ray domain.

  11. Quantum effect • The final yield depends on • Time interval between the two pulses • Relative phase of the two pulses Two-photon ionization by a double pulse Double pulse : Intensity = 5×1013 W/cm2、Pulse duration = 1 fs • 27HG → The final He2+ yield is NOT twice as large as that after the first pulse.

  12. Dependence on the relative phase Electric field of the double pulse • Single pulse • independent of f1 • Double pulse • The yield oscillates with f1 - f2. Pulse width = 1 fs, Interval = 4.14824 fs    Single pulse: F2(t)=0

  13. Dependence on the time interval Electric field of the double pulse The period (0.1 fs) of the dipole moment oscillation corresponds to the energy difference between 1s and 2p. Dipole moment after single pulse (He+: superposition of 1s and 2p) Pulse width = 1 fs 0.1 fs 0.1 fs The relation between the phase of the dipole moment induced by the 1st pulse and the phase of the 2nd pulse causes an oscillation in the He2+ yield.

  14. Conclusions • The two-photon ionization of He+ by a 27th harmonic pulse of a Ti:Sapphire laser is an attractive candidate for experimental observation of a nonlinear optical effect in the soft x-ray domain. • High probability • Yield quadratic in pulse intensity • Yield linear in pulse duration (> 5 fs) • When the pulse duration is < 5 fs, the He2+ yield is NOT linear in pulse duration. The yield by a double pulse oscillates with the pulse interval. Phys. Rev. A 65, 043405 (2002)

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