Phase-modulated pulses coherent

Soliton ring fiber lasers can be also realized with active mode locking by polarization modulation [11.77], or by additive-pulse mode locking (APM). In the latter technique the pulse is split into the two arms of an interferometer and the coherent superposition of the self-phase modulated pulses results in pulse shortening [11.55]. 

Fig. 5 Radio frequency pulse sequences for measurements of Sj and Si in DSQ-REDOR experiments. The MAS period rR is 100 ps. XY represents a train of 15N n pulses with XY-16 phase patterns [98]. TPPM represents two-pulse phase modulation [99]. In these experiments, M = Nt 4, N2+ N3 = 48, and N2 is incremented from 0 to 48 to produce effective dephasing times from 0 to 9.6 ms. Signals arising from intraresidue 15N-13C DSQ coherence (Si) are selected by standard phase cycling. Signal decay due to the pulse imperfection of 15N pulses is estimated by S2. Decay due to the intermolecular 15N-I3C dipole-dipole couplings is calculated as Si(N2)/S2(N2). The phase cycling scheme can be found in the original figure and caption. (Figure and caption adapted from [45])...

Figure 2 Pulse sequences and coherence pathway diagrams for the phase-modulated split-t) (A) STMAS and (B) triple-quantum MAS NMR, showing the generic sequences with the specific values for Mg being r=24/31, r —O, r"=7/31 and s=12/31, s =0, s"— 9/3 and (C) numerical simulations of the relative sensitivity of the ST and MQ experiments as a function of the ratio between the RF field strength and the quadrupolar coupling...

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 6.10 Ultrafast efficient switching in the five-state system via SPODS based on multipulse sequences from sinusoidal phase modulation (PL). The shaped laser pulse shown in (a) results from complete forward design of the control field. Frame (b) shows die induced bare state population dynamics. After preparation of the resonant subsystem in a state of maximum electronic coherence by the pre-pulse, the optical phase jump of = —7r/2 shifts die main pulse in-phase with the induced charge oscillation. Therefore, the interaction energy is minimized, resulting in the selective population of the lower dressed state /), as seen in the dressed state population dynamics in (d) around t = —50 fs. Due to the efficient energy splitting of the dressed states, induced in the resonant subsystem by the main pulse, the lower dressed state is shifted into resonance widi die lower target state 3) (see frame (c) around t = 0). As a result, 100% of the population is transferred nonadiabatically to this particular target state, which is selectively populated by the end of the pulse.

V. Coherent Control with Phase-Modulated Femtosecond Laser Pulses... 

V. COHERENT CONTROL WITH PHASE-MODULATED FEMTOSECOND LASER PULSES... 

Fig. 5a-d Pulse sequences and coherence transfer pathways for 3QMAS NMR experiments a amplitude-modulated z-filter acquisition scheme b phase-modulated shifted-echo experiment for spin 1=3/2 E and AE represent the echo and antiecho pathways. Split-tii c z-filter d shifted-echo acquisition schemes for spin 7=3/2. ( ) represents the phase of pulse n... 

Fig. 11 a-d Pulse sequences and coherence transfer pathways for the 2D STMAS experiment a two-pulse sequence as described by Gan b amplitude modulated z-filter acquisition scheme c phase-modulated shifted-echo experiment d split-ti shifted-echo experiment. The values of k, k and k" are chosen to refocus the second-order quadrupolar broadening at the end of the period... 

Few two-dimensional experiments naturally produce phase modulated data sets, but if gradient pulses are used for coherence pathway selection it is then quite often found that the data are phase modulated. In one way this is an advantage, as it means that no special steps are required to obtain frequency discrimination. However, phase modulated data sets give rise to spectra with phase-twist lineshapes, which are very undesirable. So, it is usual to attempt to use some method to eliminate the phase-twist lineshape, while at the same time retaining frequency discrimination. 

The electric field envelope of the femtosecond pump pulse which is short compared to the period of the oscillations in Fig. 15.3 (b) covers a frequency range much broader than the energy spacing of individual levels of the low-frequency mode. In other words, the pump spectrum overlaps with several lines of the vibrational progression depicted in Fig. 15.1 (b). As a result, impulsive dipole excitation from the Vqd = 0 to 1 state creates a nonstationary superposition of the wavefunc-tions of low-frequency levels in the Vqd = 1 tate with a well-defined mutual phase. This quantum-coherent wavepacket oscillates in the Vqd = 1 state with the frequency Q of the low-frequency mode and leads to a modulation of O-H stretching absorption which is measured by the probe pulses. In addition to the wavepacket in the Vqd = 1 state, impulsive Raman excitation within the spectral envelope of... 

The spectral width Aty can be further increased by focusing the laser pulses into a special optical fiber, which consists of a photonic crystal (Fig. 9.88) where by self-phase modulation the spectrum is considerably broadened and extends over one decade (e.g., from 1064 nm to 532 nm) (Fig. 9.89). This corresponds to a frequency span of 300 THz [1327] It was found by interference experiments, that the coherence properties were preserved in this broadened spectmm, i.e. the nonlinear processes in the optical fiber did not destroy the coherence of the original frequency comb. 

Phase-modulated coherent pulse such as due to self-phase modulation has a common feature with incoherent light in that it has broad band-width whose reciprocal is much shorter than the light duration. It, therefore, is expected to play the same role as incoherent light in some nonlinear transient spectroscopy. This expectation has also been confirmed by preliminary theoretical and experimental study. 

---