By Peter W. Hawkes (Ed.)
Advances in Imaging and Electron Physics merges long-running serials--Advances in Electronics and Electron Physics and Advances in Optical & Electron Microscopy . The sequence gains prolonged articles at the physics of electron units (especially semiconductor devices), particle optics at low and high energies, microlithography, snapshot technology and electronic snapshot processing, electromagnetic wave propagation, electron microscopy, and the computing tools utilized in most of these domain names.
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Extra info for Advances in Imaging and Electron Physics, Vol. 103
C 2cz -ia! TO]. [ This expression describesa pulsed beam field (PB) that propagates along the z-axis. ]. It will be rederived in Section V as a direct solution of the time-dependent wave equation. 6. E. Frequency-Domain Interpretation It is instructive to understand the properties of the preceding solution in the frequency domain. The FD counterpart of the initial time-dependent field distribution (48) is [Indeed, (48) is immediately obtained by substituting (67) in the analytic inverse transform (21)].
The real field solutionsare given by (88) where the real signals fy (t) and 'Hf, (t) are given now by S,(r) and 'HSc(t)in (63), with 6 = ;TO y and y is given in (83). From the discussion in (63), the half-amplitude pulsewidth and the peak value of the wavepacket are TO 2 y and n-l (; TO y ) - ' , respectively. Thus, the waveform is shortest and strongest on the beam axis ( y = 0) and it decays as y increases away from the axis. Solving for y and substituting in (83) using (86a), we find for the half-amplitude beamwidth in the principal direction xi, + + + + D j ( z ) = DO, d m , DO, = 2dZZ, (94) where Doj is the width at the waist z = -arj.
These contributions emphasize radiation along the local physical directions. In accord with the time-harmonic field in (lo), we shall assume here that the source distribution has the short-pulse form (Fig. 7) UO(x0, t) = a[%, t - c-'+o(%)l (38) where a(%, t ) is a short temporal pulse and c-'@o(xo) is a delay function, both with slow spatial (XO) variations. It is then found that the dominant contribution to the plane-wave spectrum fro((, t) in (33) comes from the region of the stationary delay point xs((), defined by [see (1 l)] 6 = VO@O(Xs) (39) This condition defines the local radiation direction if a pulsed plane wave is locally matched to the source distribution (see Fig.
Advances in Imaging and Electron Physics, Vol. 103 by Peter W. Hawkes (Ed.)