Chirp positive

Figure 41. Selective bond breaking of H2O by means of the quadratically chirped pulses with the initial wave packets described in the text. The dynamics of the wavepacket moving on the excited potential energy surface is illustrated by the density, (a) The initail wave packet is the ground vibrational eigen state at the equilibrium position, (b) The initial wave packet has the same shape as that of (a), but shifted to the right, (c) The initail wave packet is at the equilibrium position but with a directed momentum toward x direction. Taken from Ref. [37]. (See color insert.)...

Fig. 3.14. Left transient reflectivity change of Te obtained with transform limited, negatively chirped, and positively chirped pulses. Right coherent phonon amplitude as a function of the pulse chirp. Adapted from [42]...

I accosted her, but received no answer. A second and a third appeal on my part were equally ineffectual. Losing patience at what appeared to me intolerable rudeness, I brought my mouth into a position full in front of her mouth so as to intercept her motion, and loudly repeated my question, Woman, what signifies this concourse, and this strange and confused chirping, and this monotonous motion to and fro in one and the same Straight Line ... 

Fig. 2. Left Dissociation yield U for a positive chirp ( + ), no chirp ( 0 ), and negative chirp experiment (gray, left scale) and theory (light gray, right scale). Right The dissociation yield U is a steep function of negative chirp experiment (bars, left scale) and theory (open circles, right scale).

For the positively chirped (PC) pulses and small detuning, relaxation does not hinder a coherent population transfer. Moreover, under these conditions the relaxation favors more efficient population transfer with respect to the system with frozen nuclear motion. 

In order to demonstrate the efficiency and robustness of the formulations presented in Sect. 5.2 and 5.3, three practical applications are considered here. In the first part of this section, we consider the complete excitation of a wavepacket from a nonequilibrium displaced position, which is directly related to the idea of bond-selective breaking, as explained in the Introduction . This is demonstrated numerically by taking diatomic molecules LiH and NaK as examples. In the second part, we consider the complete pump-dump control and creation of a localized wavepacket using quadratic chirping within the pump-dump mechanism. The bond-selective photodissociation of the H20 molecule is discussed in the third part of this subsection as an example of a multidimensional system. 

By manipulating the timing of the pump and/or dump pulses as demonstrated above, a target wavepacket with the central momentum and position desired can be generated by appropriately designed quadratic chirping. These wavepackets can serve as initial states for other processes. 

First, we present the dynamics of the initial wavepacket a. Initially the system stands at the equilibrium position of the electronic ground X. The temporal evolution of the wavepacket Pe generated in the electronic excited state is shown in the left-hand column of Fig. 5.9. Apparently, tp originates in the Frank-Condon (FC) region, which is located at the steep inner wall of the electronically excited A state. The repulsive force of the potential l 0 the drives e(t) downhill toward the saddle point and then up the potential ridge, where Pe(t) bifurcates into two asymptotic valleys, with Ye = 0.495 in channel f. The excitation achieved using this simple quadratically chirped pulse is not naturally bond-selective because of the symmetry of the system. The role played by our quadratically chirped pulse is similar to that of the ordinary photodissociation process, except that it can cause near-complete excitation (see Table 5.1 for the efficiency). This is not very exciting, however, because we would like to break the bond selectively. 

As demonstrated above, bond-selective dissociation can be achieved with high efficiency by using an initial displaced-position and/or a directed-momentum wavepacket. The latter wavepacket can be prepared via the sequence of quadratically chirped pulses or by using semiclassical optimal control theory [34,35],... 

The Wigner distributions of harmonics obtained with laser intensity of 1 x 1015 W/cm2 are shown in Fig. 8.3. In this case, the harmonics are negatively chirped at the leading edge of the chirp-free pulses as shown in Fig. 8.3a. So the positively chirped laser pulses can compensate for the negative harmonic chirp, as shown in Fig. 8.3b. 

Fig. 8.3. Wigner distribution of harmonics after propagating through a 0.7-mm long neon medium of density 2 x 1018 cm 3. Laser intensity applied is 5 x 101BW/cm2. The laser intensity and laser pulse duration used in four different cases are a 1 x 101BW/cm2, chirp-free 25 fs, b positively chirped 35 fs from a, c 5 x 1015 W/cm2, chirp free 25fs, and d negatively chirped 100fs from c...

Fig. 8.8. Harmonic spectra from Ne driven by femtosecond laser pulses with different laser chirp at the gas jet position of z = —18 mm. The sign of the pulse duration refers to the sign of applied laser chirp...

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