Hermite pulsed-beam expansion of well-collimated pulsed radiation

摘要

We present a novel expansion scheme for radiation from well- collimated pulsed aperture distributions. The basis functions are a new set of pulsed beams (PB), termed Hermite pulsed beams (HPB) as they are related to the time-harmonic Hermite Gaussian Beams. They are highly localized space-time wavepackets and form a biorthogonal set of for expansion of time-dependent radiation. This expansion is applicable only for well collimated fields since the HPB are only paraxial solutions of the time-dependent wave equation, but its validity can be extended by using the complex source technique. The expansion is based on a global matching of the HPB set to the entire aperture distribution and therefore should be contrasted with other new PB expansion schemes which are based essentially on local analysis. As expected, the representation is most efficient if the collimation properties of the HPB are matched to those of the entire aperture so that they exhibit the same far field properties (e.g. diffraction angle). We show that the relevant parameter is the collimation (Rayleigh) length and introduce criteria to find this parameter for a given pulsed source distribution. The properties of the expansion are explored via numerical examples.