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Photon-Photon Collision Using Extreme Lasers

A special issue of Photonics (ISSN 2304-6732). This special issue belongs to the section "Optical Interaction Science".

Deadline for manuscript submissions: 20 April 2025 | Viewed by 6623

Special Issue Editor


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Guest Editor
Department of Applied Physics, University of Salamanca, 37008 Salamanca, Spain
Interests: intense lasers, at the petawatt and multi petawatt level; interaction of matter with those extreme fields; quantum vacuum; quantum nonlinearities; vacuum birefringence; sark matter in quantum vacuum driven by strong fields; femtosecond lasers; nuclear fusion with lasers

Special Issue Information

Dear Colleagues,

Photon–photon collision is a fundamental physical process that has been studied since the very inception of quantum mechanics. Moreover, it is a very famous process, thanks to the Star Wars lightsabers; however, those sabers are fictional and cannot be formulated in real-life scenarios because the collision of two visible photons has a negligibly small, or non-zero, cross section.

When the energies of photons are large enough, an electron–positron pair can be generated in a process that is the reverse motion of electron-position annihilation which generates a pair of photons. For that process to occur, the photon mass has to be comparable or greater than the electron mass. Consequently, the energy of photons is too low for a real pair generation in lasers (infrared, visible, ultraviolet or even soft X-ray).

The impossibility of pair generation in the optical or soft X-ray domain does not imply that the physics of this domain is completely known. The cross section is so small that it seems impossible to obtain any kind of measurement. However, in recent decades, several advancements have been achieved in laser technology, and now the record peak intensity is beyond 1023 W/cm2; it is anticipated that in the coming years it will be possible to achieve the intensity of 1024 W/cm2 . This intensity means an extraordinary concentration of energy, comparable to the density of water, if we can transform all the mass into pure energy.

Such extraordinary progress provides an impetus for the growth of photon–photon collision experiments in the near future. This Special Issue of Photonics calls for papers that address a wide array of questions concerning the development of these experiments:

  • What is the best scenario for these experiments? For example, is two counterpropagating petawatt lasers an optimized scenario? Can optical petawatt pulses colliding with soft X-ray lasers (as the XFEL lasers) be an alternative?
  • What is the best laser? What is the best pulse length? Is intensity the only relevant parameter?
  • Is it possible to develop PW or multi-PW lasers specifically tailored for this purpose?

The advantage of working in low energies for the onset of the electron–positron pair creation is that the vacuum will not be broken with the appearance of new pairs; at the same time, the extreme lasers tension will provide the quantum vacuum with an unprecedented strength. This may be relevant for two reasons. One, to directly measure the vacuum response due to electron–positron virtual pairs in the nonlinear regime. There are two models to describe this response, one presented by Max Born and Leopold Infeld in 1934, and another presented by Werner Heisenberg and Hans Heinrich Euler in 1936. The peculiarity is that they do not coincide in the second-order terms. Although the Heisenberg–Euler model seems to be most popularly accepted by the community, clean experimental evidence of which model is the rightly nonlinear, if any, has not been obtained yet. Moreover, certain kinds of dark matter can modify the response of the quantum vacuum and result in a modification of the photon–photon scattering by adding new couplings beyond the particle physics standard model. In this context, we invite papers that address the following areas:

  • Designing laser experimental configurations that can differentiate between these two models;
  • The present status of ongoing experiments, either in the commissioning or designing phase, and new experimental problems/solutions found;
  • Ultrahigh sensitivity detectors specifically designed for that purpose, such as X-ray ultraprecise polarizers, and single photon detectors;
  • Techniques developed for other purposes that can be of interest in photon–photon quantum vacuum experiments;
  • Experiments using existing lasers and experimental configurations that would need further laser developments;
  • Possibilities to obtain information on the properties of certain kinds of dark matter,the most suitable dark matter candidates that can be seen in such extreme photon bath, advantages of photon fields that cannot generate electron/positron pairs and would mask a hypothetical dark matter signature;
  • Comparison with other techniques studying dark matter which also use lasers but not such extreme lasers, and possibilities of combinations and synergies.

Working with such extreme experimental conditions is extraordinarily difficult. Laser technology employs beyond 10 PW peak power, but existing lasers are often too complex because they are designed to be as multipurpose as possible. For this goal, is it necessary to understand the optimized laser (or lasers) configuration, especially when pump–probe scenarios are taken into account. This also represents a detection challenge because it is going to be a very weak source with a lot of possible noise sources. This Special Issue welcomes papers that focus on optimizing the experimental scenarios:

  • The best achievable laser or lasers combinations, best frequency combination, and possibility of using multiple beam lasers as alternatives;
  • Advantages of using an X-UVV or soft X-ray probe;
  • Repetition rate and data management necessary for correct signal conclusive identification inside a huge background noise produced by the extreme laser photons;
  • Measurement of the vacuum birefringence or the photon–photon scattering;
  • Difficulties present in the experimental set up, such as extreme vacuum needs, large vacuum volumes, and sources of noise;
  • Extreme effects from residual electrons, such as radiation reaction, Thompson emission, and pair cascading. Analysis of their characteristic patters in order to reduce the signal-to-noise ratio.

Extreme lasers are now considered as a new alternative to explore photon–photon collisions in the domains where photon energy is so low that pair creation is impossible. However, such a high density of photons can stress the quantum vacuum and induce nonlinear responses, which again become important mechanisms that must to be taken into account while studying elementary particles and dark matter. Papers analyzing or proposing scenarios on how to study these changes, describing the best laser configurations and highlighting the potential experimental difficulties are welcome in this Special Issue.

Precise measurement of photon–photon collisions requires extremely demanding interdisciplinary experiments. Thus, we invite submissions of papers that from a diverse range of fields to shed light on this rather intricate mechanism using varying techniques, including artificial intelligence to extract a weak signal from a noise environment. To conclude, photon–photon scattering means to detect a few scattered photons per pulse—in the best case—out of a background of maybe 1020 photons generated with a multi-petawatt laser.

Prof. Dr. Luis Roso
Guest Editor

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Keywords

  • ultraintense lasers
  • photon-photon collisions
  • extreme vacuum
  • single photon counting
  • Breit-Wheeler process
  • radiation reaction
  • petawatt and exawatt lasers
  • vacuum birefringence
  • QED Lagrangian
  • born-infeld lagrangian
  • dark matter searches with laser light
  • extreme laser technology
  • relativistically driven electrons
  • thomson scattering from laser driven electrons

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Published Papers (2 papers)

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28 pages, 10257 KiB  
Article
Thomson Scattering and Radiation Reaction from a Laser-Driven Electron
by Ignacio Pastor, Luis Roso, Ramón F. Álvarez-Estrada and Francisco Castejón
Photonics 2024, 11(10), 971; https://doi.org/10.3390/photonics11100971 - 17 Oct 2024
Viewed by 898
Abstract
We investigate the dynamics of electrons initially counter-propagating to an ultra-fast ultra-intense near-infrared laser pulse using a model for radiation reaction based on the classical Landau–Lifshitz–Hartemann equation. The electrons, with initial energies of 1 GeV, interact with laser fields of up to [...] Read more.
We investigate the dynamics of electrons initially counter-propagating to an ultra-fast ultra-intense near-infrared laser pulse using a model for radiation reaction based on the classical Landau–Lifshitz–Hartemann equation. The electrons, with initial energies of 1 GeV, interact with laser fields of up to 1023 W/cm2. The radiation reaction effects slow down the electrons and significantly alter their trajectories, leading to distinctive Thomson scattering spectra and radiation patterns. It is proposed to use such spectra, which include contributions from harmonic and Doppler-shifted radiation, as a tool to measure laser intensity at focus. We discuss the feasibility of this approach for state-of-the-art and near-future laser technologies. We propose using Thomson scattering to measure the impact of radiation reaction on electron dynamics, thereby providing experimental scenarios for validating our model. This work aims to contribute to the understanding of electron behavior in ultra-intense laser fields and the role of radiation reaction in such extreme conditions. The specific properties of Thomson scattering associated with radiation reaction, shown to be dominant at the intensities of interest here, are highlighted and proposed as a diagnostic tool, both for this phenomenon itself and for laser characterization in a non-intrusive way. Full article
(This article belongs to the Special Issue Photon-Photon Collision Using Extreme Lasers)
Show Figures

Figure 1

Figure 1
<p>Schematic representation of the studied process. Initially, the laser and the electron bunch are counter-propagating. The laser moves towards the positive Z-axis, and the electron bunch moves initially in the opposite direction. The upper figure shows the initial position with the electron bunch centered at <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mn>00</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> and the laser pulse peak at <math display="inline"><semantics> <mrow> <mi>z</mi> <mo>=</mo> <mo>−</mo> <mn>24</mn> <msub> <mi>λ</mi> <mn>0</mn> </msub> </mrow> </semantics></math> (19.2 <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>). Neglecting the interaction before this point is a reasonable assumption. Since the electron’s initial speed is very close to <span class="html-italic">c</span>, the electron would cross the laser pulse close to <math display="inline"><semantics> <mrow> <mi>z</mi> <mo>=</mo> <mo>−</mo> <mn>12</mn> <msub> <mi>λ</mi> <mn>0</mn> </msub> </mrow> </semantics></math>. However, for extreme intensities, as we will describe, the trajectory of the electrons will be significantly modified.</p>
Full article ">Figure 2
<p>Schematic representation of the TS radiation pattern. Electrons driven exclusively by the laser polarization radiate mainly in the YZ plane (<b>a</b>). However, electrons driven by the laser magnetic field radiate mostly in the XY plane (<b>b</b>). Comparing Thomson radiation along these two planes provides relevant information on RR-induced dynamics. The YZ pattern, driven by the laser electric field, corresponds to even harmonics of the fundamental frequency. The XY radiation, due to coupling with the laser magnetic field, also shows strong even harmonics. Relativistic distortion of these donut shapes is not depicted for simplicity.</p>
Full article ">Figure 3
<p>Spectral location of the Thomson scattered main peak (i.e., <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mi>norm</mi> </msub> <mo>=</mo> <msub> <mi>ω</mi> <mi>peak</mi> </msub> <mo>/</mo> <msub> <mi>ω</mi> <mn>0</mn> </msub> </mrow> </semantics></math>), X-polarization, spectra averaged for an electron sample aimed at the central part of the <math display="inline"><semantics> <msub> <mi>TEM</mi> <mn>00</mn> </msub> </semantics></math> laser pulse, including RR, as a function of <math display="inline"><semantics> <msub> <mi>θ</mi> <mi>s</mi> </msub> </semantics></math>. Scattering is computed in the YZ plane. Notice the extremely fast increase in the (blue-shifted) peak frequency with the scattering angle as the angle approaches <math display="inline"><semantics> <mi>π</mi> </semantics></math> (this corresponds to light scattered counter-propagating with respect to the laser).</p>
Full article ">Figure 4
<p>Integrated spectral power, X-polarization in red and the other orthogonal quadrature in blue, averaged for an electron sample aimed at the central part of the <math display="inline"><semantics> <msub> <mi>TEM</mi> <mn>00</mn> </msub> </semantics></math> laser pulse, including RR, as a function of the scattering angle. Scattering plane is YZ. Notice that for a scattering angle of <math display="inline"><semantics> <mrow> <mi>π</mi> <mo>/</mo> <mn>2</mn> </mrow> </semantics></math>, the light is nearly completely polarized along the X-axis, and notice how the two orthogonal contributions become more balanced as the scattering angle approaches <math display="inline"><semantics> <mi>π</mi> </semantics></math>.</p>
Full article ">Figure 5
<p>Schematic representation of the angles where the TS spectra have been calculated. Labels (<b>a</b>–<b>i</b>) refer to the directions of observation of the spectra shown in the next figure.</p>
Full article ">Figure 6
<p>Averaged TS spectra including RR for several scattering angles in the YZ plane; see main text for details. (<b>a</b>–<b>i</b>) Scattering angles are, respectively, <math display="inline"><semantics> <mrow> <mn>64</mn> <mi>π</mi> <mo>/</mo> <mn>128</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>72</mn> <mi>π</mi> <mo>/</mo> <mn>128</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>80</mn> <mi>π</mi> <mo>/</mo> <mn>128</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>88</mn> <mi>π</mi> <mo>/</mo> <mn>128</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>96</mn> <mi>π</mi> <mo>/</mo> <mn>128</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>104</mn> <mi>π</mi> <mo>/</mo> <mn>128</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>120</mn> <mi>π</mi> <mo>/</mo> <mn>128</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>126</mn> <mi>π</mi> <mo>/</mo> <mn>128</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mn>127</mn> <mi>π</mi> <mo>/</mo> <mn>128</mn> </mrow> </semantics></math>. Observe that the last one, (<b>i</b>), corresponds to scattering almost perfectly counter-propagating to the laser pulse. The colors red and blue are the same as in the previous figure, with quadrature <math display="inline"><semantics> <msub> <mi>q</mi> <mn>1</mn> </msub> </semantics></math> in red (polarization along the electric field) and quadrature <math display="inline"><semantics> <msub> <mi>q</mi> <mn>2</mn> </msub> </semantics></math> in blue.</p>
Full article ">Figure 7
<p>Projection of a sample trajectory onto the XZ plane, including RR. The electron is initially located at <math display="inline"><semantics> <mrow> <mi>z</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, moves from right to left, strongly interacts with the laser pulse around <math display="inline"><semantics> <mrow> <mi>z</mi> <mo>/</mo> <msub> <mi>λ</mi> <mn>0</mn> </msub> <mo>=</mo> <mo>−</mo> <mn>12</mn> </mrow> </semantics></math>, and gets deflected, eventually becoming a free electron. The center of the laser pulse was initially at <math display="inline"><semantics> <mrow> <mi>z</mi> <mo>/</mo> <msub> <mi>λ</mi> <mn>0</mn> </msub> <mo>=</mo> <mo>−</mo> <mn>24</mn> </mrow> </semantics></math> and propagates from left to right along the Z axis.</p>
Full article ">Figure 8
<p>Time evolution of the relativistic <math display="inline"><semantics> <mi>γ</mi> </semantics></math> factor (<b>a</b>) and the normalized velocity (<b>b</b>) for the sample trajectory in <a href="#photonics-11-00971-f007" class="html-fig">Figure 7</a>. The significant reduction in the <math display="inline"><semantics> <mi>γ</mi> </semantics></math> factor (i.e., the electron energy) due to RR is evident, along with substantial perturbations in <math display="inline"><semantics> <msub> <mi>v</mi> <mi>x</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>v</mi> <mi>z</mi> </msub> </semantics></math>. Color code in (<b>b</b>): red, green, and blue correspond to <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>x</mi> </msub> <mo>/</mo> <mi>c</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>y</mi> </msub> <mo>/</mo> <mi>c</mi> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>z</mi> </msub> <mo>/</mo> <mi>c</mi> </mrow> </semantics></math>, respectively.</p>
Full article ">Figure 9
<p>Radiated electric field at the detector in the time domain (<b>a</b>) and a close-up (<b>b</b>) displaying the spike structure under the radiated pulse envelope. The scattering plane is YZ. The electric field component parallel to the X axis is shown in red, while the other component is in blue. In (<b>b</b>), the component along the scattering vector is also displayed in green and is negligible compared to the other components.</p>
Full article ">Figure 10
<p>Asymptotic momentum components for counter-propagating 1 GeV electrons, including RR. (<b>a</b>–<b>c</b>) correspond respectively to the asymptotic distributions of <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mi>x</mi> </msub> <mo>/</mo> <mi>m</mi> <mi>c</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mi>y</mi> </msub> <mo>/</mo> <mi>m</mi> <mi>c</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mi>z</mi> </msub> <mo>/</mo> <mi>m</mi> <mi>c</mi> </mrow> </semantics></math>. The sample contains 4096 electrons randomly distributed up to <math display="inline"><semantics> <mrow> <msub> <mi>ρ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.25</mn> <msub> <mi>w</mi> <mn>0</mn> </msub> </mrow> </semantics></math>, with <math display="inline"><semantics> <mrow> <msub> <mi>w</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>4</mn> <mo> </mo> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>. The laser is in the <math display="inline"><semantics> <msub> <mi>TEM</mi> <mn>00</mn> </msub> </semantics></math> mode, X polarized, with a peak intensity of <math display="inline"><semantics> <mrow> <mn>5</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>22</mn> </msup> <mspace width="0.166667em"/> <msup> <mrow> <mi mathvariant="normal">W</mi> <mo>/</mo> <mi>cm</mi> </mrow> <mn>2</mn> </msup> </mrow> </semantics></math>.</p>
Full article ">Figure 11
<p>Asymptotic kinetic energy for counter-propagating 1 GeV electrons with RR. The sample includes 4096 electrons randomly distributed up to <math display="inline"><semantics> <mrow> <msub> <mi>ρ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.25</mn> <mo>×</mo> <msub> <mi>w</mi> <mn>0</mn> </msub> </mrow> </semantics></math>, with <math display="inline"><semantics> <mrow> <msub> <mi>w</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>4</mn> <mo> </mo> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>. The laser is in the <math display="inline"><semantics> <msub> <mi>TEM</mi> <mn>00</mn> </msub> </semantics></math> mode, X polarized, with a peak intensity of <math display="inline"><semantics> <mrow> <mn>5</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>22</mn> </msup> <mspace width="0.166667em"/> <msup> <mrow> <mi mathvariant="normal">W</mi> <mo>/</mo> <mi>cm</mi> </mrow> <mn>2</mn> </msup> </mrow> </semantics></math>. A strong reduction in kinetic energy is predicted under these conditions with RR. Contour plots of iso-energy show an approximate circular symmetry around the laser propagation axis.</p>
Full article ">Figure 12
<p>Integrated spectral power: X-polarization in red and the orthogonal quadrature (q2) in blue, averaged over electron samples (typically 2048 or 4096 at each scattering angle) aimed at the central part of the <math display="inline"><semantics> <msub> <mi>TEM</mi> <mn>00</mn> </msub> </semantics></math> laser pulse, including RR, as a function of the scattering angle. The scattering plane is YZ. Notice the rapid increase in integrated power with the scattering angle.</p>
Full article ">Figure 13
<p>Averaged TS spectra. The scattering plane is YZ. Scattering angles for (<b>a</b>–<b>i</b>) are respectively <math display="inline"><semantics> <mrow> <mn>64</mn> <mi>π</mi> <mo>/</mo> <mn>128</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>68</mn> <mi>π</mi> <mo>/</mo> <mn>128</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>72</mn> <mi>π</mi> <mo>/</mo> <mn>128</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>76</mn> <mi>π</mi> <mo>/</mo> <mn>128</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>80</mn> <mi>π</mi> <mo>/</mo> <mn>128</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>84</mn> <mi>π</mi> <mo>/</mo> <mn>128</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>88</mn> <mi>π</mi> <mo>/</mo> <mn>128</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>92</mn> <mi>π</mi> <mo>/</mo> <mn>128</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mn>96</mn> <mi>π</mi> <mo>/</mo> <mn>128</mn> </mrow> </semantics></math>. A spectrum extending up to <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>/</mo> <msub> <mi>ω</mi> <mn>0</mn> </msub> <mo>≥</mo> <mn>3000</mn> </mrow> </semantics></math> is obtained for <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>96</mn> <mi>π</mi> <mo>/</mo> <mn>128</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 14
<p>Comparison of TS spectra (X-quadrature in red, q2-quadrature in blue) with (<b>a</b>) and without (<b>b</b>) RR. The scattering angle is <math display="inline"><semantics> <mrow> <mn>72</mn> <mi>π</mi> <mo>/</mo> <mn>128</mn> </mrow> </semantics></math>. The shape, amplitude, and power ratio of the two quadratures are altered by RR, which can help distinguish and detect RR signatures in the spectra. See more details in the main text.</p>
Full article ">Figure 15
<p>Projection of a sample trajectory onto the X-Z plane, including RR. The electron, initially at <math display="inline"><semantics> <mrow> <mi>z</mi> <mo>/</mo> <msub> <mi>λ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, moves from right to left, interacts strongly with the laser pulse around <math display="inline"><semantics> <mrow> <mi>z</mi> <mo>/</mo> <msub> <mi>λ</mi> <mn>0</mn> </msub> <mo>=</mo> <mo>−</mo> <mn>11</mn> </mrow> </semantics></math>, and is deflected nearly <math display="inline"><semantics> <msup> <mn>45</mn> <mo>∘</mo> </msup> </semantics></math> from its initial direction. Note the reversal in electron motion after deceleration (curly part moving towards the positive side of the <span class="html-italic">z</span>-axis).</p>
Full article ">Figure 16
<p>Time evolution of the relativistic <math display="inline"><semantics> <mi>γ</mi> </semantics></math> factor (<b>a</b>) and normalized velocity (<b>b</b>) for the trajectory shown in <a href="#photonics-11-00971-f015" class="html-fig">Figure 15</a>. The strong reduction in <math display="inline"><semantics> <mi>γ</mi> </semantics></math> due to RR is evident, along with substantial perturbations in <math display="inline"><semantics> <msub> <mi>v</mi> <mi>x</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>v</mi> <mi>z</mi> </msub> </semantics></math>, and to a lesser extent in <math display="inline"><semantics> <msub> <mi>v</mi> <mi>y</mi> </msub> </semantics></math>. Note that <math display="inline"><semantics> <msub> <mi>v</mi> <mi>z</mi> </msub> </semantics></math> reverses from counter-propagating to co-propagating at various points in the trajectory. In (<b>b</b>), the color code is as follows: red, green, and blue represent <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>x</mi> </msub> <mo>/</mo> <mi>c</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>y</mi> </msub> <mo>/</mo> <mi>c</mi> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>z</mi> </msub> <mo>/</mo> <mi>c</mi> </mrow> </semantics></math>, respectively.</p>
Full article ">Figure 17
<p>Radiated electric field at the detector in the time domain (<b>a</b>) and a close-up view (<b>b</b>) showing the structure of spikes under the radiated pulse envelope. The scattering plane is Y-Z. The electric field component parallel to the X-axis is shown in red, while the other component is shown in blue. In (<b>b</b>), the component along the scattering vector is also displayed (in green), which is negligible compared to the other components.</p>
Full article ">Figure 18
<p>Three-dimensional asymptotic distributions of <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mi>x</mi> </msub> <mo>/</mo> <mi>m</mi> <mi>c</mi> </mrow> </semantics></math> (<b>a</b>), <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mi>y</mi> </msub> <mo>/</mo> <mi>m</mi> <mi>c</mi> </mrow> </semantics></math> (<b>b</b>), and <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mi>z</mi> </msub> <mo>/</mo> <mi>m</mi> <mi>c</mi> </mrow> </semantics></math> (<b>c</b>) as functions of the initial transverse position of the electrons. The panels show 4096 sample electrons, uniformly and randomly distributed up to <math display="inline"><semantics> <mrow> <msub> <mi>ρ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.25</mn> <msub> <mi>w</mi> <mn>0</mn> </msub> </mrow> </semantics></math>.</p>
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<p>Asymptotic distribution of <math display="inline"><semantics> <msub> <mi>E</mi> <mi>kin</mi> </msub> </semantics></math> projected onto the X-axis. The panel includes 4096 sample electrons, uniformly and randomly distributed up to <math display="inline"><semantics> <mrow> <msub> <mi>ρ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.25</mn> <mo>×</mo> <msub> <mi>w</mi> <mn>0</mn> </msub> </mrow> </semantics></math>. RR accounts for up to 98.5% loss of the initial kinetic energy for electrons near the center of the <math display="inline"><semantics> <msub> <mi>TEM</mi> <mn>00</mn> </msub> </semantics></math> mode laser axis.</p>
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<p>Averaged TS spectra. The scattering plane is YZ, and scattering angles for (<b>a</b>–<b>i</b>) are, respectively, <math display="inline"><semantics> <mrow> <mn>48</mn> <mi>π</mi> <mo>/</mo> <mn>128</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>56</mn> <mi>π</mi> <mo>/</mo> <mn>128</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>60</mn> <mi>π</mi> <mo>/</mo> <mn>128</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>64</mn> <mi>π</mi> <mo>/</mo> <mn>128</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>68</mn> <mi>π</mi> <mo>/</mo> <mn>128</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>72</mn> <mi>π</mi> <mo>/</mo> <mn>128</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>76</mn> <mi>π</mi> <mo>/</mo> <mn>128</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>80</mn> <mi>π</mi> <mo>/</mo> <mn>128</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mn>96</mn> <mi>π</mi> <mo>/</mo> <mn>128</mn> </mrow> </semantics></math>. An extremely broad spectrum, extending well beyond <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>/</mo> <msub> <mi>ω</mi> <mn>0</mn> </msub> <mo>≥</mo> <mn>15</mn> <mo>,</mo> <mn>000</mn> </mrow> </semantics></math>, is obtained for <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>96</mn> <mi>π</mi> <mo>/</mo> <mn>128</mn> </mrow> </semantics></math>.</p>
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<p>Visualization of the scattering process on a unit momentum sphere. Each point on the sphere’s surface represents the asymptotic direction of electron scattering; dot colors indicate asymptotic energy, with dark blue representing minimum and red representing maximum energy.</p>
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<p>Projection of a sample trajectory onto the XZ plane, including RR. The electron is initially located at <math display="inline"><semantics> <mrow> <mi>z</mi> <mo>/</mo> <msub> <mi>λ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, moves from right to left, strongly interacts with the laser pulse around <math display="inline"><semantics> <mrow> <mi>z</mi> <mo>/</mo> <msub> <mi>λ</mi> <mn>0</mn> </msub> <mo>=</mo> <mo>−</mo> <mn>10.5</mn> </mrow> </semantics></math>, and is deflected at an angle larger than <math display="inline"><semantics> <msup> <mn>90</mn> <mo>∘</mo> </msup> </semantics></math> with respect to its initial direction. The <math display="inline"><semantics> <msub> <mi>v</mi> <mi>z</mi> </msub> </semantics></math> (or <math display="inline"><semantics> <msub> <mi>p</mi> <mi>z</mi> </msub> </semantics></math>) component changes from counter-propagating to co-propagating. The thick gray line indicates the initial position of the electron bunch. For this extreme intensity, the electron trajectory is reversed.</p>
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<p>Time evolution of the relativistic <math display="inline"><semantics> <mi>γ</mi> </semantics></math> factor (<b>a</b>) and of the normalized velocity (<b>b</b>) for the sample trajectory in <a href="#photonics-11-00971-f022" class="html-fig">Figure 22</a>. The strong reduction in <math display="inline"><semantics> <mi>γ</mi> </semantics></math> due to RR is apparent, as well as the large perturbations on <math display="inline"><semantics> <msub> <mi>v</mi> <mi>x</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>v</mi> <mi>z</mi> </msub> </semantics></math>, and also to some extent on <math display="inline"><semantics> <msub> <mi>v</mi> <mi>y</mi> </msub> </semantics></math>. Note that <math display="inline"><semantics> <msub> <mi>v</mi> <mi>z</mi> </msub> </semantics></math> asymptotically reverses from counter-propagating to co-propagating. Color code in (<b>b</b>) is red, green, and blue corresponding to <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>x</mi> </msub> <mo>/</mo> <mi>c</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>y</mi> </msub> <mo>/</mo> <mi>c</mi> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>z</mi> </msub> <mo>/</mo> <mi>c</mi> </mrow> </semantics></math>, respectively.</p>
Full article ">Figure 24
<p>Radiated electric field at the detector in the time domain (<b>a</b>) and a close-up (<b>b</b>) displaying the structure of the spikes under the radiated pulse envelope. The scattering plane is YZ. The electric field component parallel to the X axis is displayed in red, the other one in blue. In (<b>b</b>), the component along the scattering vector is also displayed (in green), showing it to be negligible compared to the other components. Note the highly asymmetric shape of the electric pulse envelope in this particular case.</p>
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<p>Three-dimensional asymptotic normalized momentum components for counter-propagating 1 GeV electrons. (<b>a</b>–<b>c</b>) correspond respectively to the asymptotic distributions of <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mi>x</mi> </msub> <mo>/</mo> <mi>m</mi> <mi>c</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mi>y</mi> </msub> <mo>/</mo> <mi>m</mi> <mi>c</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mi>z</mi> </msub> <mo>/</mo> <mi>m</mi> <mi>c</mi> </mrow> </semantics></math>. The sample includes 4096 electrons randomly distributed up to <math display="inline"><semantics> <mrow> <msub> <mi>ρ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.25</mn> <mo>×</mo> <msub> <mi>w</mi> <mn>0</mn> </msub> </mrow> </semantics></math>, where <math display="inline"><semantics> <msub> <mi>w</mi> <mn>0</mn> </msub> </semantics></math> is 4 <math display="inline"><semantics> <mi mathvariant="sans-serif">μ</mi> </semantics></math>m. The laser is in the <math display="inline"><semantics> <msub> <mi>TEM</mi> <mn>00</mn> </msub> </semantics></math> mode, X polarized, with a peak intensity of <math display="inline"><semantics> <mrow> <msup> <mn>10</mn> <mn>23</mn> </msup> <mspace width="0.166667em"/> <msup> <mrow> <mi mathvariant="normal">W</mi> <mo>/</mo> <mi>cm</mi> </mrow> <mn>2</mn> </msup> </mrow> </semantics></math>. Close to the center of the laser <math display="inline"><semantics> <msub> <mi>TEM</mi> <mn>00</mn> </msub> </semantics></math> mode, RR accounts for up to 99 percent energy loss.</p>
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<p>Asymptotic velocity distribution (final velocity of the electrons) depicted over the unit sphere. The pink circle is the equator of the unit sphere and the gray circle crosses the unit sphere poles. The value of the final velocity is given by the color scale. The orange dotted ribbon indicates the multiple trajectories with asymptotic speeds that have been reversed, i.e., points towards the positive values of <span class="html-italic">z</span>.</p>
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<p>A comparison of TS spectra (X-quadrature in red, q2-quadrature in blue) with (<b>a</b>) and without (<b>b</b>) RR. The scattering angle is <math display="inline"><semantics> <mrow> <mn>28</mn> <mi>π</mi> <mo>/</mo> <mn>128</mn> </mrow> </semantics></math> in this case. The shape, amplitude, and power ratio of the two quadratures are altered by RR, which can help distinguish and detect RR signatures in the spectra. See more details in the main text.</p>
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9 pages, 874 KiB  
Article
Penrose Scattering in Quantum Vacuum
by José Tito Mendonça
Photonics 2024, 11(5), 448; https://doi.org/10.3390/photonics11050448 - 10 May 2024
Viewed by 4747
Abstract
This paper considers the scattering of a probe laser pulse by an intense light spring in a QED vacuum. This new scattering configuration can be seen as the vacuum equivalent to the process originally associated with the scattering of light by a rotating [...] Read more.
This paper considers the scattering of a probe laser pulse by an intense light spring in a QED vacuum. This new scattering configuration can be seen as the vacuum equivalent to the process originally associated with the scattering of light by a rotating black hole, which is usually called Penrose superradiance. Here, the rotating object is an intense laser beam containing two different components of orbital angular momentum. Due to these two components having slightly different frequencies, the energy profile of the intense laser beam rotates with an angular velocity that depends on the frequency difference. The nonlinear properties of a quantum vacuum are described by a first-order Euler–Heisenberg Lagrangian. It is shown that in such a configuration, nonlinear photon–photon coupling leads to scattered radiation with frequency shift and angular dispersion. These two distinct properties, of frequency and propagation direction, could eventually be favorable for possible experimental observations. In principle, this new scattering configuration can also be reproduced in a nonlinear optical medium. Full article
(This article belongs to the Special Issue Photon-Photon Collision Using Extreme Lasers)
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Figure 1

Figure 1
<p>Geometry of Penrose scattering in vacuum: (<b>A</b>)—an intense light spring propagates in the <span class="html-italic">z</span> direction, with frequencies <math display="inline"><semantics> <msub> <mi>ω</mi> <mn>1</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>ω</mi> <mn>2</mn> </msub> </semantics></math>, its intensity rotates around the <span class="html-italic">z</span> axis; (<b>B</b>) a probe pulse with frequency <math display="inline"><semantics> <msub> <mi>ω</mi> <mi>i</mi> </msub> </semantics></math> propagates along the (negative) <span class="html-italic">x</span> direction and collides perpendicularly with the light spring; (<b>C</b>) scattered signals are emitted with frequencies <math display="inline"><semantics> <msub> <mi>ω</mi> <mo>±</mo> </msub> </semantics></math> and an angular spread dictated by the light spring structure.</p>
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<p>Representation of the radial integral <math display="inline"><semantics> <mrow> <mi mathvariant="script">I</mi> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> </semantics></math>, for <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>ℓ</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, with <math display="inline"><semantics> <mrow> <msub> <mi>J</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> in red, <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mn>12</mn> </msub> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> in dashed red. We have used <math display="inline"><semantics> <mrow> <msub> <mi>ℓ</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>14</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p>
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