Phase-modulated pulses

The procedure to combine any two phase modulated pulses is straightforward and is going to be discussed below. For the kth step of the two pulses (denoted by the two indices a and b), their amplitudes and phases can be described by A a, Wka and A b, respectively. The vector sum (denoted... 

The probability for two-photon excitation, 2 using phase-modulated pulses at frequency co -A+ coo, where cog is the carrier frequency, can be calculated from [2]... 

As a simple model for a self-phase-modulated pulse, we consider a linearly chirped pulse with a fixed envelope function. The corresponding complex field amplitude is given by... 

The main advantage of the phase-modulated pulse is its capability of having very broad spectrum in a controlled manner. A preliminary experiment of four-wave mixing in dye solutions has been tried in our group using a broad-band chirped pulse produced in an optical fiber, and confirmed the achievement of subpicosecond resolution time much shorter than the pulse width, though T2 is too short to be observed. 

FIGURE 30 Temporal variation of (a) intensity, (b) phase, and (c) frequency produced by a medium with a positive nonlinear refractive index, (d) Spectrum of a self-phase-modulated pulse. The asymmetry results from a rise time that was 1.4 times faster than the full time. [Part (d) reproduced from Reintjes, J. (1984). Nonlinear Optical Parametric Processes in Liquids and Gases, Academic Press, Orlando, FL.]... 

FIGURE 31 Pulse compression produced by a self-phase-modulated pulse and a pair of diffraction gratings. The dispersion of the gratings causes the lower-frequency components of the pulse to travel a longer path than that of the higher-frequency components, allowing the back of the pulse to catch up to the front. 

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]. 

Another class of selective pulses that deserves a comment refers to the so called multifrequency pulses. These are amplitude or phase modulated pulses capable of acting simultaneously at different frequencies. To illustrate how this can be done, let us consider the pulse described by (4.2.9) without phase modulation, and add an extra amplitude modulation of cos(Acot),... 

WoUenhaupt M, Prakelt A, Sarpe-Tudoran C, liese D, Bayer T, Baumert T (2006) Femtosecond strong-field quantum control with sinusoidtilly phase-modulated pulses. Phys Rev A 73 063409... 

Valdmanis J A and Fork R L 1986 Design considerations for a femtosecond pulse laser balancing self phase modulation, group velocity dispersion, saturable absorption, and saturable gain IEEE J. Quantum. Electron. 22 112-18... 

The fluorescent lifetime of chlorophyll in vivo was first measured in 1957, independently by Brody and Rabinowitch (62) using pulse methods, and by Dmitrievskyand co-workers (63) using phase modulation methods. Because the measured quantum yield was lower than that predicted from the measured lifetime, it was concluded that much of the chlorophyll molecule was non-fluorescent, suggesting that energy transfer mechanisms were the means of moving absorbed energy to reactive parts of the molecule. 

In order to implement the phase-tunable DDS, the phase wheel is also shifted according to phase modulation and phase cycling. The digital signal carrying the amount of the additional phase shift is given to DDS (I) by the pulse programmer. 

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])...

Siegel et al. showed that enhancement of the CT can also be obtained using hyperbolic secant (HS) pulses to invert selectively the STs [74], Unlike the DFS waveform, whose frequency sweep is generated by a constant rf-pulse phase while modulating the amplitude, the HS pulse utilizes both amplitude and phase modulation, yielding an enhancement exceeding that obtained by DFS or RAPT [61, 74, 75]. Most recently, the pulse sequence called wideband uniform-rate smooth truncation (WURST) [76] was introduced to achieve selective adiabatic inversion using a lower power of the rf-field than that required for the HS pulses [77,78]. One of its applications involved more efficient detection of insensitive nuclei, such as 33S [79]. 

The study confirmed that the action of the precursors of the main pulse has to be carefully considered in the ultrashort intense laser pulse interactions. Nevertheless, a regime of rather stable propagation [34] of a laser pulse of tens of femtoseconds was found in a broad window of the laser intensity/medium density diagram, in which (1) the ionization occurs in one or a few optical cycles, avoiding effects of self-phase modulation and defocusing for most of the... 

Fig. 10.13. 2D J-resolved NMR spectrum of santonin (4). The data were acquired using the pulse sequence shown in Fig. 10.12. Chemical shifts are sorted along the F2 axis with heteronuclear coupling constant information displayed orthogonally in F . Coupling constants are scaled as J/2, since they evolve only during the second half of the evolution period, t /2. 13C signals are amplitude modulated during the evolution period as opposed to being phase modulated as in other 13C-detected heteronuclear shift correlation experiments.

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