Quadratic phase modulation

Quadratic phase modulation using the spectral phase modulation function... 

In the following, we describe two prominent types of spectral phase modulation, each of which plays an important role in coherent control. Both types, namely sinusoidal (Section 6.2.1) and quadratic (Section 6.2.2) spectral phase modulation, are relevant for the experiments and simulations presented in this contribution. We provide analytic expressions for the modulated laser fields in the time domain and briefly discuss the main characteristics of both classes of pulse shapes. 

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. ...

Besides the phase of the fundamental mode, strictly speaking, the preferred phase, many other characteristics have been studied in [226]. Because a large mismatch was chosen, they have lacked any trend, but an interesting oscillatory behavior has been discovered for the initial two-mode coherent state. Within each period, the phase-matched second-harmonic and second-subharmonic generation processes can be prepared. The model of an ideal Kerr-like medium [223] have been considered for a comparison with cascaded quadratic non-linearities. It follows that these nonlinearities exhibit not only self-phase modulation in the fundamental mode but also a cross-phase modulation of the modes that can be considered for a nondemolition measurement. 

Chapter 3 is devoted to pressure transformation of the unresolved isotropic Raman scattering spectrum which consists of a single Q-branch much narrower than other branches (shaded in Fig. 0.2(a)). Therefore rotational collapse of the Q-branch is accomplished much earlier than that of the IR spectrum as a whole (e.g. in the gas phase). Attention is concentrated on the isotropic Q-branch of N2, which is significantly narrowed before the broadening produced by weak vibrational dephasing becomes dominant. It is remarkable that isotropic Q-branch collapse is indifferent to orientational relaxation. It is affected solely by rotational energy relaxation. This is an exceptional case of pure frequency modulation similar to the Dicke effect in atomic spectroscopy [13]. The only difference is that the frequency in the Q-branch is quadratic in J whereas in the Doppler contour it is linear in translational velocity v. Consequently the rotational frequency modulation is not Gaussian but is still Markovian and therefore subject to the impact theory. The Keilson-... 

The heptane water and toluene water interfaces were simulated by the use of the DREIDING force field on the software of Cerius2 Dynamics and Minimizer modules (MSI, San Diego) [6]. The two-phase systems were constructed from 62 heptane molecules and 500 water molecules or 100 toluene molecules and 500 water molecules in a quadratic prism cell. Each bulk phase was optimized for 500 ps at 300 K under NET ensemble in advance. The periodic boundary conditions were applied along all three directions. The calculations of the two-phase system were run under NVT ensemble. The dimensions of the cells in the final calculations were 23.5 A x 22.6 Ax 52.4 A for the heptane-water system and 24.5 A x 24.3 A x 55.2 A for the toluene-water system. The timestep was 1 fs in all cases and the simulation almost reached equilibrium after 50 ps. The density vs. distance profile showed a clear interface with a thickness of ca. 10 A in both systems. The result in the heptane-water system is shown in Fig. 3. Interfacial adsorption of an extractant can be simulated by a similar procedure after the introduction of the extractant molecule at the position from where the dynamics will be started. 

Linear materials are used primarily for high-speed modulation of the intensity, amplitude, phase, frequency, or direction of a light beam. Quadratic materials are used principally for light valves and shutters. 

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