The spatial distribution of the illumination of dynamic apertures and its effect on the decay rate of the radiated localized pulses

Abstract

Various illumination schemes of dynamic apertures are investigated. The decay patterns of the generated ultra-wide bandwidth pulses are studied and compared to postulated diffraction lengths. It is shown that such definitions of the diffraction ranges characterize the propagation of the pulses in a broad sense. We emphasize the fact that to understand how a localized pulse decays we have to resort to the structure of its temporal and spatial spectral content. An exhaustive analysis of the depletion of the spectral components of the radiated localized pulses is presented.

Aperture synthesis of time-limited X waves and analysis of their propagation characteristics

“…The same approach has been used extensively in defining finite FWM excitations. 2,3,5,6 The latter approach has the advantage of providing a deeper insight into the spectral structure of the radiated LW pulses. Within such a framework, we have been able to demonstrate that the spectral depletion of LW pulses is essentially different from that of the usual quasimonochromatic pulses.…”

“…Instead, as the pulse travels away from the source plane, the sinusoidal term progressively introduces oscillations into the Gaussian windows ␦ (Ϫy 0 ) centered around all the significant spectral components. 3,[5][6][7] Since these oscillations increase with distance, the integration over yields smaller spectral contributions at the different frequencies. As a consequence, the integration over in Eq.…”

“…A large class of localized wave ͑LW͒ solutions to the scalar wave and Maxwell equations have been studied extensively. [1][2][3][4][5][6][7][8][9][10][11][12] A number of these pulsed wave solutions are finite-energy variants of the focus wave mode ͑FWM͒. 13,14 They are usually derived either as superpositions of infinite-energy FWM pulses, [8][9][10][11]14 or by time limiting various FWM-like excitations to construct finite-energy aperture fields.…”

“…13,14 They are usually derived either as superpositions of infinite-energy FWM pulses, [8][9][10][11]14 or by time limiting various FWM-like excitations to construct finite-energy aperture fields. [2][3][4][5][6][7] Alternatively, such LW pulses can be synthesized as superpositions over Bessel beams with appropriately chosen spectra. 15 Our approach is based mainly on the proven possibility of exciting Bessel beams from infinite apertures.…”

“…15 Our approach is based mainly on the proven possibility of exciting Bessel beams from infinite apertures. [1][2][3][4] It has been shown that a Bessel beam defined initially on an infinite plane ͑e.g., zϭ0͒ propagates under the effect of Huygens' operator in the positive z direction. [1][2][3][4] Any possible contributions from acausal ͑negative z-directed͒ components sum up to zero.…”