Enhancing strong-field-induced molecular vibration with femtosecond pulse shaping

This work investigates the utility of femtosecond pulse shaping in increasing the efficiency of Raman excitation of molecules in the strong-field interaction regime. We study experimentally and theoretically the effect of pulse shaping on the strength of nonresonant coherent anti-Stokes Raman scattering in iodine vapor at laser intensities exceeding ${10}^{13}$ W/cm${}^2$. We show that unlike the perturbative case, shaping strong nonresonant laser pulses can increase the signal strength beyond that observed with the transform-limited excitation. Both adiabatic and nonadiabatic schemes of excitation are explored, and the differences of their potential in increasing the excitation efficiency are discussed.

Figure 1

Temporal profile of TL (dashed lines) and shaped (solid lines) femtosecond pulses with the electric field amplitude (black single lines) and phase (red double lines). (a) Linearly chirped pulse with ${\alpha }^{\prime }=50000$ fs${}^2$; (b) sinusoidal phase modulation with $A=1.65$, $T=334$ fs.

Figure 2

Raman spectrum at ${\omega }_p-{\omega }_S$ for TL pulses (black dashed line) and shaped pulses (red solid line). All Raman transitions (rotationally broadened into bands) and their strengths are indicated according to thermal Boltzmann distribution at $100{}^{\circ }$C: initial states $v=0$ (white area), $v=1$ (gray area), and $v=2$ (black area). (a) Linearly chirped pulses with ${\alpha }^{\prime }=50000$ fs${}^2$; (b) sinusoidal phase modulation with $A=1.65$, $T=334$ fs.

Figure 3

Vibrational excitation schemes of iodine molecules, discussed in this work. (a) Pump and Stokes pulses are off-resonance with the excited electronic $B$ state and generate vibrational coherence between $|v_0\rangle$ and $|v_f\rangle$ in the ground $X$ manifold, which is probed after a variable time delay $\Delta \tau$. (b), (c) Pump and Stokes pulses are resonant with a single-photon electronic transition $X\leftarrow B$.

Figure 4

Raman excitation probability as a function of Stokes intensity. The excitation schemes are as follows: TL pulses (black solid line), pump and Stokes pulses linearly chirped (blue dashed line), pump and Stokes pulses shaped with a sinusoidal phase mask (red dotted line).

Figure 5

Raman excitation probability as a function of Stokes wavelength. (Left) Both pump and Stokes intensities are set to ${10}^{12}$ W/cm${}^2$. (Right) Both intensities are set to ${10}^{13}$ W/cm${}^2$. Line assignment is the same as in Fig. 4.

Figure 6

(Left) Raman excitation probability as a function of Stokes intensity. The excitation schemes are as follows RAP (purple dashed line), STIRAP (orange dotted line), piecewise STIRAP (green dash-dotted line), and TL pulses (black solid line). (Right) Schematic view of the intensity profiles of pump (blue dashed line) and Stokes (red solid line) pulses used in the calculations of RAP (top), STIRAP (middle), and piecewise STIRAP (bottom).

Figure 7

Raman excitation probability as a function of Stokes wavelength in two cases of resonant excitation schemes shown in Fig. 3 [left, Fig. 3b; right, Fig. 3c]. Line assignments are as in Figs. 4 and 5. The target manifold is extended to $v=6,...,17$ in order to account for all Raman transitions at the given pump and Stokes wavelengths. Both intensities are set to ${10}^{13}$ W/cm${}^2$.

Figure 8

Experimental setup. (a) Collinear CARS geometry with spatial filtering. (b) Use of polarizing optics and spectral filtering to separate CARS signal from the excitation pulses.

Figure 9

Fluorescence spectrum of iodine due to strong pump and Stokes excitation. (a) Detected signal in the wavelength range from 482 to 522 nm stemming from TPA of Stokes (blue dashed), TPA of pump (green dotted), and TPA of mixed pump and Stokes (black solid). CARS signal is shown on top of the fluorescence curve (red shaded area). (b) Fluorescence spectrum in the range from 350 to 700 nm.

Figure 10

Detected spectrum with strong pump and Stokes fields and a weak probe field (red dotted line), output spectrum in the absence of probe pulses (blue dashed line), CARS signal derived as the difference of the two spectra (black solid line). Pump and Stokes pulses are (a) TL, (b) modulated with a sinusoidal phase, (c) linearly chirped.

Figure 11

Comparison of CARS intensity with different excitation schemes Pump and Stokes pulses are TL (black solid line), linearly chirped (blue dashed line), or shaped with a sinusoidal phase mask (red dotted line). (a) CARS spectrum, (b) CARS signal as a function of the probe time delay, and (c) the corresponding Fourier spectra.

Figure 12

CARS intensity as a function of Stokes intensity with $I_p=5\times {10}^{13}$ W/cm${}^2$. Line assignments are the same as in Fig. 11.

Figure 13

CARS intensity as a function of the pump-Stokes time delay, implemented with TL pulses in the far off-resonance excitation scheme of Fig. 3a.

Figure 14

Near-resonance CARS. (a) CARS intensity as a function of pump-Stokes time delay for TL pulses (black solid line) and oppositely chirped pulses with ${\alpha }_{S,p}^{\prime }=\pm 10000$ fs${}^2$ (blue dashed line) and ${\alpha }_{S,p}^{\prime }=\pm 25000$ fs${}^2$ (red dotted line). (b) CARS intensity as a function of pump-Stokes time delay and (c) as a function of pump intensity with $I_S=4\times {10}^{12}$ W/cm${}^2$ for TL pulses (black solid line) and same-sign linearly chirped pulses with ${\alpha }_{S,p}^{\prime }=-10000$ fs${}^2$ (blue dashed line) and ${\alpha }_{S,p}^{\prime }=-25000$ fs${}^2$ (red dotted line).