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Space-time coupling in femtosecond pulse shaping and its effects on coherent control
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10.1063/1.3058478
/content/aip/journal/jcp/130/3/10.1063/1.3058478
http://aip.metastore.ingenta.com/content/aip/journal/jcp/130/3/10.1063/1.3058478

Figures

Image of FIG. 1.
FIG. 1.

Typical pulse shaper in geometry using a pixelated SLM at the symmetry plane of the setup. In most experiments the shaper’s output waveform is focused by an additional focusing element to the sample of interest.

Image of FIG. 2.
FIG. 2.

(a) Space-time coupling as a function of focal length given a constant frequency-to-space mapping of 6.807 THz/mm; the gratings have 300 lines/mm (dash-dotted curve), 600 lines/mm (dotted curve), 800 lines/mm (dashed curve), and 1200 lines/mm (solid curve), respectively. The arrows indicate the space-time coupling constant for the Littrow geometry, i.e., . (b) Angle of incidence and diffraction angle at the center frequency as a function of focal length.

Image of FIG. 3.
FIG. 3.

Top row and bottom row at five positions within the Rayleigh length of the focusing element.

Image of FIG. 4.
FIG. 4.

(a) Top row and bottom row at five positions within the Rayleigh length of the focusing element. (b) Spectral intensity and (c) temporal intensity as a function of for .

Image of FIG. 5.
FIG. 5.

(a) Top row and bottom row at five positions within the Rayleigh length of the focusing element. (b) Spectral intensity and (c) temporal intensity as a function of for .

Image of FIG. 6.
FIG. 6.

Spatial offset as a function of the delay time for (a) a linear phase and (b) a double-pulse modulation. The solid lines result from Eq. (12). (c) Measured and simulated beam profile for a sinusoidal phase.

Image of FIG. 7.
FIG. 7.

Top row: experimentally measured and bottom row: simulated space-frequency distributions as a function of transverse coordinate and frequency . [(a) and (e)] Unshaped pulse, [(b) and (f)] linear phase with , [(c) and (g)] double pulse with , and [(d) and (h)] sinusoidal phase with .

Image of FIG. 8.
FIG. 8.

Spatial offset in the focus of a 400 mm lens as a function of the delay time for a (a) linear phase, (b) double-pulse modulation, and (c) sinusoidal phase. The solid lines are derived from Eq. (13).

Image of FIG. 9.
FIG. 9.

Top row: experimentally measured; bottom row: simulated space-frequency distributions as a function of transverse coordinate and frequency . [(a) and (e)] Unshaped pulse [(b) and (f)] linear phase with , [(c) and (g)] double pulse with , and [(d) and (h)] sinusoidal phase with .

Image of FIG. 10.
FIG. 10.

Measured (top row) and simulated (bottom row) spectra at the center of the focal plane, i.e., at , as a function of time delay and frequency . [(a) and (d)] Linear, [(b) and (e)] double pulse, and [(c) and (f)] sinusoidal phase modulation.

Image of FIG. 11.
FIG. 11.

Spatially resolved second harmonic spectrum of a double pulse with a time delay of . (a) Measurement and (b) analytical solution, Eq. (25).

Image of FIG. 12.
FIG. 12.

Spatially resolved second harmonic spectrum for a sinusoidal phase modulation. (a) Measurement and (b) analytical solution, Eq. (26).

Image of FIG. 13.
FIG. 13.

The three constants (a) , (b) , and (c) as a function of time delay in a double logarithmic plot. Spectral intensity for two different time delays, namely, (d) 400 fs and (e) 1400 fs.

Image of FIG. 14.
FIG. 14.

(a) Rubidium V-type three-level system. (b) Spatially resolved population distribution after interaction with a Gaussian-shaped bandwidth-limited pulse with a maximum fluence of . Ground state: black solid curve; lower excited state: red dotted curve; and upper excited state: blue dashed curve.

Image of FIG. 15.
FIG. 15.

Spatially resolved final population of the Rb three-level system after excitation with (a) a downchirped pulse and (b) an upchirped pulse , respectively. (c) and (d) show the difference between the simulations in (a) and (b) and the corresponding ones without space-time coupling. Ground state: black solid curve; lower excited state: red dotted curve; and upper excited state: blue dashed curve.

Image of FIG. 16.
FIG. 16.

Spatially resolved final population of the Rb three-level system. The top row [(a) and (b)] shows simulations with space-time coupling and the center row [(c) and (d)] the difference with respect to simulations without space-time coupling. The bottom row [(e) and (f)] shows the spatially varying spectral intensity as a function of and the two horizontal dashed lines indicate the two resonance frequencies. For the left column the time delay is 51.7 fs and for the right column the time delay is 53.3 fs.

Image of FIG. 17.
FIG. 17.

(a) Ground and excited state potential curves of . (b) Spatially resolved population in the ground (solid curve) and the excited state (dashed curve) after the interaction with a bandwidth-limited pulse.

Image of FIG. 18.
FIG. 18.

Spatially resolved population in the ground (solid curve) and in the excited state (dashed curve) of after interacting with a double pulse. (a) Time delay 720 fs and relative phase 0 and (b) time delay of 560 fs and relative phase of 2.3 rad. The differences with respect to simulations neglecting space-time coupling are shown in (c) and (d).

Tables

Generic image for table
Table I.

Experimental parameters.

Generic image for table
Table II.

Simulation parameters.

Generic image for table
Table III.

Spatially averaged population for a pulse with no and with space-time coupling. Final populations calculated from spatially averaged fields with and with no space-time coupling. Populations for the maximum field at .

Generic image for table
Table IV.

Spatially averaged population for a pulse with no and with space-time coupling. Final populations calculated from spatially averaged fields with and with no space-time coupling.

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/content/aip/journal/jcp/130/3/10.1063/1.3058478
2009-01-16
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Space-time coupling in femtosecond pulse shaping and its effects on coherent control
http://aip.metastore.ingenta.com/content/aip/journal/jcp/130/3/10.1063/1.3058478
10.1063/1.3058478
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