An optical response of one-dimensional string made of dipoles with a periodically varying density excited by a spot of light moving along the string at the superluminal (sub-luminal) velocity is theoretically studied. The Cherenkov radiation in such system is rather unusual, possessing both transient and resonant character. We show that under certain conditions, in addition to the resonant Cherenkov peak another Doppler-like frequency appears in the radiation spectrum. Both linear (small-signal) and nonlinear regimes as well as different string topologies are considered.

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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.

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