Modeling of space-time focusing of localized nondiffracting pulses

Abstract

In this paper we develop a method capable of modeling the space-time focusing of nondiffracting pulses. The new pulses can possess arbitrary peak velocities and, in addition to being resistant to diffraction, can have their peak intensities and focusing positions chosen a priori. More specifically, we can choose multiple locations (spatial ranges) of space/time focalization; also, the pulse intensities can be chosen in advance. The pulsed wave solutions presented here can have very interesting applications in many different fields, such as free-space optical communications, remote sensing, medical apparatus, etc.

Engineering the Optical Vacuum: Arbitrary Magnitude, Sign, and Order of Dispersion in Free Space Using Space–Time Wave Packets

“…We first confirm the predicted normal and anomalous second-order GVD for ST wave packets in free spacein contradistinction to the anomalous GVD associated solely with TPFs. ,, We plot in Figure a–c measurements for three superluminal ST wave packets at θ = 50° ( ṽ ≈ 1.19 c ). ,,, Note that these superluminal group velocities do not violate relativistic causality in any way, as examined in detail recently in refs and . Indeed, the group velocity is the speed of the peak of the wave packet, which is not the carrier of information .…”

“…To date, most work on ST wave packets in free space has focused on propagation invariance, whether for X-waves, sideband ST wave packets such as focus-wave modes, − or baseband ST wave packets − ,, (according to the classification in ref ). Our work reported here is part of an ongoing effort regarding the control over the axial evolution of ST wave packets, which encompasses axial spectral encoding (producing a prescribed axial evolution of the pulse spectrum along the propagation axis), and accelerating or decelerating wave packets whose group velocity varies axially . Here, the temporal profile of the freely propagating ST wave packet is dictated by incorporating an effective GVD in free space.…”

Gaussian beams diffracting in time

“…from well-established knowledge about monochromatic light beams, and establishes a basis for the study of their nonlinear propagation at the high intensities involved in their intended applications. We also offer a new perspective of the family of LWs [7], of which TD beams is a broad subset, and of the luminal TD pulses in [3], stimulating ongoing research in modeling LWs for applications [13]), the design of more sophisticated waves, as the nonparaxial tilted-phase-front beams recently introduced in [14], or their transformation by (paraxial) optical systems.…”

The Complex Charge Paradigm: A New Approach for Designing Electromagnetic Wavepackets

“…They range from nondiffracting modes, such as Bessel, Mathieu, Weber, Airy, and nonparaxial accelerating beams, [ 1–13 ] to so‐called “space‐time” wavepackets [ 14–30 ] whose propagation invariance arises from prespecified correlations between spatial and temporal frequency components of each mode in the wavepacket. Besides displaying a host of intriguing physical phenomena like self‐healing [ 31–34 ] and superluminal and subluminal travel, [ 35–39 ] propagation‐invariant waves can potentially lead to greater speed and precision in scientific and industrial processes, such as particle manipulation, [ 40–45 ] laser micromachining, [ 46–49 ] communications, [ 50,51 ] and novel imaging techniques. [ 52–54 ] Beyond these propagation‐invariant modes and the standard focused beams, there are still more classes of electromagnetic waves, including beams carrying topological charge, [ 55–57 ] beams containing intricate structures like vortex and field‐line loops, [ 58–65 ] and autofocusing beams.…”

“…They range from nondiffracting modes, such as Bessel, Mathieu, Weber, Airy, and nonparaxial accelerating beams, [1][2][3][4][5][6][7][8][9][10][11][12][13] to so-called "space-time" wavepackets [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] whose propagation invariance arises from prespecified correlations between spatial and temporal frequency components of each mode in the wavepacket. Besides displaying a host of intriguing physical phenomena like self-healing [31][32][33][34] and superluminal and subluminal travel, [35][36][37][38][39] propagation-invariant waves can potentially lead to greater speed and precision in scientific and industrial processes, such as particle manipulation, [40][41][42][43][44][45] laser micromachining, [46]…”