Chirped laser pulses

The laser parameters should be chosen so that a and p can make the nonadiabatic transition probability V as close to unity as possible. Figure 34 depicts the probability P 2 as a function of a and p. There are some areas in which the probabilty is larger than 0.9, such as those around (ot= 1.20, p = 0.85), (ot = 0.53, p = 2.40), (a = 0.38, p = 3.31), and so on. Due to the coordinate dependence of the potential difference A(x) and the transition dipole moment p(x), it is generally impossible to achieve perfect excitation of the wave packet by a single quadratically chirped laser pulse. However, a very high efficiency of the population transfer is possible without significant deformation of the shape of the wave packet, if we locate the wave packet parameters inside one of these islands. The biggest, thus the most useful island, is around ot = 1.20, p = 0.85. The transition probability P 2 is > 0.9, if... 

A negative chirped pulse is shown in Figure 6.4c. Experiments and theoretical studies on coherent control of ultrafast electron dynamics by intense chirped laser pulses will be discussed in Sections 6.3.2.3 and 633.2. 

N. V. Vitanov and B. Girard. Adiabatic excitation of rotational ladder by chirped laser pulses. Phys. Rev. A, 69(3) 033409 (2004). 

Figure 10. Temporal development of the population in the 2 fig state during interaction with up- and down-chirped laser pulses ( 3500 fs2). The chirped pulse profile is shown as a dotted line.

In this sense, the control of electronic transitions of wavepackets using short quadratically chirped laser pulses of moderate intensity is a very promising method, for two reasons. First, only information about the local properties of the potential energy surface and the dipole moment is required to calculate the laser pulse parameters. Second, this method has been demonstrated to be quite stable against variations in pulse parameters and wavepacket broadening. However, controlling of some types of excitation processes, such as bond-selective photodissociation and chemical reaction, requires the control of wavepacket motion on adiabatic potential surfaces before and/or after the localized wavepacket is made to jump between the two adiabatic potential energy surfaces. 

By combining the control of electronic transitions of wavepackets using quadratically chirped laser pulses with semiclassical optimal control [34,35] on a single adiabatic surface, we should be able to establish an effective methodology for controlling the dynamics of large-dimensional chemical and biological systems. 

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. 

The temporal characteristics of chirped laser pulses can be quantitatively analyzed in terms of linear chirp coefficient and pulse duration. The linear chirp coefficient, a, is defined as the second derivative of the temporal... 

Fig. 8.4. a Linear chirp coefficient and b pulse duration of chirped laser pulses with respect to the grating detuning of a pulse compressor... 

A. The Dressed Schrodinger Equation for Chirped Laser Pulses... 

Since this effective Hamiltonian will be parameterized by the laser amplitude and its frequency, it will be relevant for processes with chirped laser pulses. 

The models we have discussed so far correspond to continuous (CW) lasers with a fixed sharp frequency and constant intensity. They can be easily adapted to the case of pulsed lasers that have slowly varying envelopes. They can furthermore have a chirped frequency—that is, a frequency that changes slowly with time. For periodic (or quasi-periodic) semiclassical Hamiltonians, the Floquet states are the stationary states of the problem. Processes controlled by chirped laser pulses include additional time-dependent parameters (the pulse... 

We first derive the time-dependent dressed Schrodinger equation generated by the Floquet Hamiltonian, relevant for processes induced by chirped laser pulses (see Section IV.A). The adiabatic principles to solve this equation are next described in Section IV.B. 

The topology will allow us to classify all the possibilities of complete population transfer by adiabatic passage for a three-level system interacting with two delayed pulses, as it was done for the two-level system interacting with a chirped laser pulse. 

The recent availability of ultrafast and intense mid-IR laser pulses has opened the way of controlling nuclear motion in the electronic ground state by multiphoton vibrational excitation. In order to access higher vibrational levels, anharmoni-cities have to be taken into account. This is commonly done by using chirped laser pulses, which change the instantaneous frequency during their duration,... 

As follows from the second dispersion-theory approximation, the distance Tcompr at which the duration of a chirped laser pulse reaches its minimum is defined by the dispersion-spreading length L i p of a wave packet ... 

The LICS, produced by an idealized Continuous-Wave (CW) laser (steady amplitude and single-frequency laser), can differ substantially from the structure produced by a pulsed laser, since the AC Stark shifts produce time-dependent detunings relative to one- and two-photon resonance. The time-dependent pulse and frequency effects in population trapping in LICS have received attention in theoretical works [93]. Using numerical approaches, as well as approximate analytical solution, it was shown that the trapped population in realistic atomic systems can be sufficiently decreased, to the point when no population remains in the system, by the increase in laser energies. Furthermore, the use of properly chirped laser pulses not only helps to increase the trapped population but also makes the system more stable against increases in the pulse energy. 

E. Paspalakis, M. Protopapas, P.L. Knight, Population transfer through the continuum with temporally delayed chirped laser pulses. Opt. Commun. 142 (1997) 34. 

Fig. 11. Optical setup to create linearly chirped laser pulses.

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