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Back in 1885, von Lommel studied the diffraction of a circular opening. His study was one step further than the Airy diffraction model (describing patterns in the focal plane) because von Lommel’s model was able to describe what the light distribution before and after the focus is. Today’s extreme lasers have a flat-top profile whose diffraction pattern in the vicinity of the focus is very much reminiscent of von Lommel’s description. In the present chapter, we will compute, based on a Huygens–Fresnel integral method, the laser field distribution around the focus. This modelling is particularly important because the intensity distribution before and after the focal plane (where the Airy disk exists) is very relevant to many contemporary experiments and is key to the ionization of atoms and the dynamics of liberated electrons. For clarity, we are going to analyze three cases corresponding to three f-numbers: f/10, f/1.8, and f/1.1. Our computed results reveal the present-day significance of von Lommel’s pioneering results. They help us understand the light distribution in the entire focal region of an ultraintense laser pulse including the full vectorial fields, not just the focal plane.

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The Focus of an Ultraintense Laser Pulse

  • 章节

  • 发表日期：

    2026年

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  • Luis Roso,
  • Smrithan Ravichandran,
  • Anthony Raymond,
  • Seung-Whan Bahk,
  • Rohan Mahnot,
  • Elise Fiala,
  • Paulo Phillipe Marques,
  • Yinqi Fang,
  • Roberto Lera,
  • David Gutiérrez,
  • José Antonio Pérez-Hernández,
  • Robert Fedosejevs,
  • Wendell T. Hill

摘要

Back in 1885, von Lommel studied the diffraction of a circular opening. His study was one step further than the Airy diffraction model (describing patterns in the focal plane) because von Lommel’s model was able to describe what the light distribution before and after the focus is. Today’s extreme lasers have a flat-top profile whose diffraction pattern in the vicinity of the focus is very much reminiscent of von Lommel’s description. In the present chapter, we will compute, based on a Huygens–Fresnel integral method, the laser field distribution around the focus. This modelling is particularly important because the intensity distribution before and after the focal plane (where the Airy disk exists) is very relevant to many contemporary experiments and is key to the ionization of atoms and the dynamics of liberated electrons. For clarity, we are going to analyze three cases corresponding to three f-numbers: f/10, f/1.8, and f/1.1. Our computed results reveal the present-day significance of von Lommel’s pioneering results. They help us understand the light distribution in the entire focal region of an ultraintense laser pulse including the full vectorial fields, not just the focal plane.