Problem of ultrashort-pulse diffraction

Abstract

The problem of delta-shaped pulse of light diffraction from the aperture in the plane screen is formulated and solved in general form for the plane wave. Two examples are considered: diffraction from the slit and from the circular aperture. The analytical solution is given for the ifiuminated zone of the space behind the aperture and for the shadow.The temporal response is show to consist of the direct wave and that scattered from the aperture edges. At large distances from the screen the Fourier transform of the solution coincide with well-known results for the plane monochrome wave.

New approach to the analysis of ultrashort pulse diffraction (Invited Paper)

“…Application of this formula to the field behind the screen revealed [12,13,14] that it comprised only two components: V(P,t)= VG(P,t)+VB(P,t) -VG ('t) is the part of incident plane wave cut out of the initial one by the aperture; this part propagates in space without any change of its form, its transverse amplitude distribution is proportional to T(x, y); -VB ('t) is the wave excited by the edge of the aperture (or any other spatial heterogeneity of its transparency).…”

“…For the reaction of elementary area of the aperture (that resembles a sort of space-temporal Green function for the Kirchhoffproblem) we got the following formula (see [12] for example) zo ir z01 h(r,t) = --8(t--r/c)+----I 1+-8(t-r/c). r cr rj…”

“…The most popular diffraction problem of the elementary physical optics is that of the plane wave diffraction from the circular aperture of a radius. Solution of this problem using 8 -wave approach was given in [12,14] and contained only Position of observation points: P1 is before the screen, P2 is in the illuminated zone out of z-axis, P3 is at z-axis, P4 is in the shadow.…”

“…However, it seems to be handy for the description of short pulses propagation. Moreover, it was shown in [12,14] that the method can clarify some features of diffracted wave that can give a key to a fine experiment realization.…”

“…The technique based on 8 -wave ideas proposed in our previous publications [12,13,14]. Those papers demonstrated the simplicity of interpretation of spatial and temporal form of the diffracted wave transformation using the pulse approach.…”