Advances in Imaging and Electron Physics, Vol. 103 by Peter W. Hawkes (Ed.)

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 positive aspects prolonged articles at the physics of electron units (especially semiconductor devices), particle optics at low and high energies, microlithography, snapshot technological know-how and electronic photo processing, electromagnetic wave propagation, electron microscopy, and the computing tools utilized in these kinds of domain names.

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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 spatial spectrum distribution obtained via (3a) is, therefore, The spatial and spectral widths of these distributions are b ( w ) = 21al/&, D < w >= 2/& (69) These widths change with the frequency as w-Il2 (a!

An example is given in (93) later. 3. The Real Field The real PB field is given by taking the real part of (80) [see (71)]. To clarify the structure of the real field we shall express it in terms of the real waveform f y (t) defined via (see (23)) Clearly, f,,( t ) decays as the parameter y increases: On the beam axis y = 0 and fy = f is strongest, but as the distance from the axis increases, y increases and the waveform f,,weakens. Substituting (87) in (81) and taking the real part, using also A(z) = AR i A I , the real PB field has the form + where y ( x , z ) is given in (83).

X with r(z)given in (79). B. Axial confinement along the beam axis is due to the pulsed behavior of f while transverse confinement is due to the fact that I’is complex and due to the property of analytic signals, which generally decay as the imaginary part of their argument befomes more negative. Since Im I’is positive definite, x . x in the argument of f has a 34 EHUD HEYMAN AND TIMOR MELAMED positive imaginary part which is quadraticallyproportional to the distance from the axis. The waveform of (80) is therefore strongest on the beam axis and weakens away from the+axis.

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