Pulsed-beam propagation in lossless dispersive media I Theory

Pulsed Beam Expansion of Electromagnetic Aperture Fields

“…where ν = ν x = ν y is the oversampling parameter in (14) and the prime denotes a derivative with respect to the argument, i.e.,δ (t) = 1/jπt 2 . This type of windows gives rise to pulsed-quadratic beam waveobjects which exhibits frequency independent collimation (Rayleigh) distance and therefore are termed iso-diffracting [46].…”

“…The motivation to use these expansions lies in their mutual spectral-spatial (and temporal for time-dependent fields) localization and the capability to propagate the expansions' waveobjects in different complex environments. Such scalar and electromagnetic (EM) wave solutions have been obtained in anisotropic medium [8][9][10][11][12][13], dispersive medium [14][15][16][17], inhomogeneous medium [18][19][20][21][22] and for inverse scattering [23][24][25][26][27][28]. Several electromagnetic beam scattering and diffraction problems have been solved for rough surface scattering [29,30], dielectric interfaces [31,32], stratified media [33][34][35][36], and more.…”

Ultrashort, Strongly Focused Laser Pulses in Free Space

“…For isodiffracting pulses, all the frequency components have the same wavefront radius of curvature (Melamed & Felsen, 1998). For each traveling beam exp( ) jkR R ± that constitutes the expression of Eq.…”

Parameterization of the Tilted Gaussian Beam Waveobjects

“…This type of Gaussian beam waveobjects exhibits frequency independent collimation (Rayleigh) lengths for which reason we previously termed it to be isodiffracting [37]. This iso-diffracting feature makes such waveobjects highly suitable for UWB radiation representations [11,13,14,38].…”

“…This feature is significantly advantageous for propagation and scattering and results in simplified analytic expressions for the beam fields. Locality considerations have been utilized for solving beam-type waveobjects propagation in generic media profiles such as inhomogeneous [1][2][3], anisotropic [4][5][6][7][8][9][10][11], and for time-dependent pulsed beams, in dispersive media [12][13][14][15][16].…”