Half-cycle pulses

As the second example consider a train of half-cycle pulses, for example ... 

A laser field (cf Eq. (4.3)) consisting of one or several half cycle pulses takes the form... 

Figure 4.9 One (solid) and three half-cycle pulses (dashed) and their effects on the asymmetric stretching vibration of FHF. (a) Electric field (in atomic units) versus time (fs). The parameters are = 5.8 x 10" EJea and T = 10. (b) Modulus of the autocor-...

Frolov, A.M., Smith, V.H. Scaled-time dynamics of ionization of Rydberg Stark states by half-cycle pulses, J. Phys. B 1995,28, L449-56. 

Phase controlled A single pulse of variable time is produced per half-cycle. 

Pulse width modulation Each half-cycle of output is made up of pulses of varying duration but equal magnitude. 

There is also a great need for broadband reflection, i.e., the capability for a number of harmonic components to be reflected and/or focused all together. In particular, the XUV supercontinuum (25-40 nm) that has recently been demonstrated using a half-cycle polarization gating method requires broadband optics in its applications toward attosecond pulse char-... 

Pulse voltammetric techniques are of interest because of its reluctance to charging effects. Their application is made difficult by the influence of pulse width in the shape of voltammetric curves. For SQWV under usual conditions, the net current flowing during the anodic and cathodic half-cycles can be approached by (Ramaley and Krause, 1969) ... 

Symmetrically shifted pulses have been proposed as a means of solvent suppression. Symmetrically shifted pulses are symmetrically shifted laminar pulses that contain equal numbers of rectangular pulse components of the same phase at an offset frequency. The basis of the symmetrically shifted pulse family is the SS pulse which is conceptually equivalent to applying simultaneous ir/2 rectangular pulses with two separate, but in-phase, transmitters at offset frequency from the water. On a practical basis an SS pulse is obtained by a complete Itt cosine modulation of a single transmitter (see Fig. 15). An S pulse is half of an SS pulse (i.e. a half-cycle tt pulse) which results in a narrower null and a 180° phase inversion at the transmitter frequency. They are also the soft, continuous equivalent of binomial sequences. The SS and S pulses have broader excitation maxima than the sinusoidal profile of the JR sequence. The method has maximal excitation at an offeet frequency of second-order U-shaped water suppression. The exdtation profile is related to the maximum amplitude modulation and can be determined by numerical evaluation of the Bloch equations. Hence a new pulse shape must be used for each excitation window. The SS pulses give better water suppression than the JR sequence, but at the expense of poorer excitation of resonances closer to the water. Also, there is no phase inversion at zero frequency. The S pulse gives better excitation near the water frequency but with less water suppression. 

Let us now consider the prototypical case in which the electrode reaction O ne R exhibits reversible kinetics and the solution contains O, but not R, in the bulk. The solution has been homogenized and the initial potential E is chosen well positive of, so that the concentration profiles are uniform as the SWV scan begins. The experiment is fast enough to confine behavior to semi-infinite linear diffusion at most electrodes, and we assume its applicability here. These circumstances imply that we can invoke Pick s second law for both O and R, the usual initial and semi-infinite conditions, and the flux balance at the electrode surface, exactly as in (5.4.2)-(5.4.5). The final boundary condition needed to solve the problem comes from the potential waveform, which is linked to the concentration profile through the nemstian balance at the electrode. It is convenient to consider the waveform as consisting of a series of half cycles with index m beginning from the first forward pulse, which has m = 1. Then,... 

Figure 5. Concentrations of reaction products during an exhaust pulse of 3 s over Pt-Rh/ CeOj-Al Oj at 310°C with X-cycling during pulse. Influence of air plug (<->) and its compensation. A exhaust pulse with X. = 1 0.05,1 Hz B air plug followed by exhaust pulse with X = 1 0.05,1 Hz C air plug followed by exhaust pulse with X = 1 0.05, 1 Hz (asymmetric cycling 0.6 rich / 0.4 lean). The black arrows on top indicate the rich, the white arrows the lean half-cycles of which the exhaust pulse is composed. repre-...

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