Pulse shaping chirping

Figure 1. Temporal profiles and relative intensities of the generated SH pulses calculated for several values of focusing strength m = L/b, and ratio LjL, = 40 for (a) uniform (periodically-poled) nonlinear media and (b) linearly chirped (aperiodically-poled) quasi-phasematched grating with AA = 0.2 /um (d = 10.3 ) The fundamental pulse shape (grey...

SH pulses, although the presumption that the SH pulses have a hyperholie seeant temporal profile is quite approximate. Correct accounting of the SH pulse shape would improve the accuracy of the model even further. Significantly, the model reported in references is not able to descrihe such a dependence for the reasons discussed above. Although our analysis has assumed fundamental pulses with no frequency chirp, it is possible to extend the present model to describe SHG with chirped fundamental pulses. 

In Reference [43], the effect of pulse-shape has been also addressed by applying to a 30 fs pulse a quadratic phase chirp whose group delay dispersion is 630 fs, thereby stretching the pulse-duration to 120 fs. The dominant ro-vibrational states in this PD process by a 795nm laser are the Vj = 9, = 3 states (states with = 3... 

As a method to control wavepackets, alternative to the use of ultra-short pulses, I would like to propose use of frequency-modulated light. Since it is very difficult to obtain a well-controlled pulse shape without any chirp, it is even easier to control the frequency by the electro-optic effect and also by appropriate superposition of several continuous-wave tunable laser light beams. 

This means that for a one-photon chirping process, if we choose the pulse shape A(f), giving the Rabi frequency... 

An adiabatic pulse is a special type of shaped pulse where either a frequency or a phase sweep occurs during the pulse duration. Adiabatic pulses are discussed in detail in section 5.3.1. So far the simulations involving the Bloch module have not considered the exact time related frequency sweep of a shaped pulse yet it is this factor that determines if each point in the pulse shape obeys the adiabatic condition. Using an adiabatic chirp pulse Check its 4.3.33 and 4.3.3.6 will examine various aspects of adiabatic pulses starting with the time evolution and the graphical representation of the amplitude and phase modulation. 

Load the file ch5318.cfg. Open the Bloch module (Utilities Bloch module) and determine the necessary pulse power for a 50 ms CHIRP pulse pO 50 ms, N 300, Start 0, Step 5 and Offset 0 (Calcuiate RF profile). Clicking the X, y and z buttons in the button panel, determine the point where the x and y intensity is 0 and the z-profile is -1. Use the waveform analysis tool to inspect the pulse shape pO 50m, spO 210 Hz and Offset 0 (Calculate I Waveform analysis) and then calculate the excitation profile for N 61, Start -1500 and Step 50 (Calculate I Excitation profile). Repeat the calculation for a pulse power of 160 Hz and compare the results. 

The values of (E) are dependent on a priori known values of Ev and R (EV ), and only very weakly dependent on Fpuiae (except for the ability to use 7 puise to select either (E)+ or (E ) and the pulse shape (duration, chirp, etc.). 

Further advances in the field of coherent chemistry will require improved time resolution and tunability of the laser sources in the experiments [434]. Shorter laser pulses with a pulse duration of less than 20 fs will be appropriate. The optimum control technique will be achieved by specially tailored femtosecond pulse shapes [435-439], determined by sophisticated calculations using the theories of coherent chemistry [440-444]. Finally, more elaborate polarization and multipulse excitation schemes, including chirped and ultra-short pulses, will be needed. 

The fact that such an experimental window for coherent control in liquids does actually exist was verified in experiments on the selective multiphoton excitation of two distinct electronically and structurally complex dye molecules in solution (Brixner et al. 2001(b)). In these experiments, despite the failure of single-parameter variation (wavelength, intensity or linear chirp control), adaptive femtosecond pulse shaping revealed that complex laser fields could achieve chemically selective molecular excitation. These results prove, first, that the phase coherence of complex molecules persists for more than 100 fs in a solvent environment. Second, this is direct proof that it is the nontrivial coherent manipulation of the excited state and not of the frequency-dependent two-photon cross sections that is responsible for the coherent control of the population of the excited molecular state. 

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... 

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.)...

Figure 6.4 Shaped femtosecond laser pulses from quadratic spectral phase modulation of an 800 nm, 20 fs FWHM input pulse, shown as dashed line in the right column. The assignment of quantities is the same as in Figure 6.3. The three cases correspond to different chirp parameters of (a) 4>2 = ISOOfs, (b) ( 2 = 3000fs, and (c) = -3000fs. ...

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