Design and optimization of zone plates for flying focus applications

TL;DR

This work tackles the challenge of limited peak intensity and short interaction lengths in flying focus schemes. It introduces a modulated width zone plate (MWZP) design, implemented via sinusoidal random modulation of zone widths and modeled with modified Fresnel integrals to realize a flying focus. Numerical results show that high-order foci (up to the 25th order) are suppressed by more than two orders of magnitude with a 200-zone MWZP, while maintaining an extended focal region exceeding 100 Rayleigh lengths and enabling tunable focal velocities, including subluminal, luminal, and superluminal regimes, depending on chirp. The MWZP is fabrication-friendly and holds promise for applications such as laser wakefield acceleration and photon acceleration, offering a path toward higher peak intensities in compact, zone-plate-based systems.

Abstract

Flying focus laser pulse technology, characterized by programmable velocity profiles and the ability to break the traditional link between focal spot motion and group velocity constraints, holds significant potential for revolutionary advances in high-intensity laser related fields. However,the flying focus generated with conventional approaches suffers from a low maximum intensity, as the energy is spread over a long distance, and the size of the focusing optics is also limited. Here, we propose a zone-plate-based flying focus scheme in which the zone widths are modulated by a sinusoidal random distribution. Numerical simulations show that the high-order foci produced by the modulated zone plate can be suppressed by more than two orders of magnitude. Meanwhile, the scheme sustains a high-intensity focal region extending over more than 100 Rayleigh lengths. Furthermore, the focal speed can be tuned over a wide range, including values exceeding the speed of light in vacuum. Owing to these advantages, the proposed modulated zone-plate scheme offers new possibilities for high-intensity laser physics and holds promise for applications such as laser wakefield acceleration, photon acceleration, and more.

Figures (8)

• Figure 1: The following are schematic diagrams illustrating: (a) a positively chirped laser beam and (b) a negatively chirped laser beam, both being focused by the MWZP. These setups result in the creation of an extended focal region. In the case of the positively chirped beam, the peak intensity travels (a) at a speed below the speed of light in the forward direction. Conversely, for the negatively chirped beam, the peak intensity can propagate (b) at a speed exceeding the speed of light in the backward directionSpatial_and_temporal_2019.
• Figure 2: The focal velocity of the flying focus pulse as a function of chirp parameter. A positively chirped pulse is limited to positive subluminal focal velocities, while a negatively chirped pulse can have either a positive or negative velocity. The specific cases simulated in the following sections are marked with a blue circle (focal velocity $+0.97\mathrm{c}$) and a red square (focal velocity $-\mathrm{1.0c}$).
• Figure 3: The comparison between FZP, GZP, and MWZP. (a) An FZP with 10 zones. (b) A GZP with 10 zones. (c) An MWZP with 10 zones. (d) The graph depicting the transmittance curve of the FZP as a function of its radius. (e) The graph showing the transmittance curve of the GZP versus its radius. (f) The graph representing the transmittance curve of the MWZP in relation to its radiusZHANG2018387.
• Figure 4: Simulated on-axis normalized diffraction intensity distribution $\mathrm{R}_{200}^{\mathrm{ZT}}(\mathrm{z})$ (in units of z/f) for (a) a chirped Gaussian pulse and (b) monochromatic plane wave propagation. The profiles compare the performance of an MWZP with 200 zones (black solid line) against a GZP (200 zones, red dashed line) and an FZP (200 zones, blue dotted line). (c) The normalized intensity of the MWZP $\mathrm{R}_{200}^{\mathrm{MWZP}}(\mathrm{z})$ at discrete high-order focal positions f/i (where i is an integer) is distinctly shown for both propagation cases.
• Figure 5: The primary focus intensity of MWZPs (black stars), GZPs (red dots), and FZPs (blue dots) as a function of the number of zones. Solid curves represent fits to the corresponding data. (a) The chirped Gaussian pulse case. (b) The plane wave case.