Radiation generation occurs fundamentally due to the acceleration of charged particles. As laser-plasma interactions have been shown to produce highly relativistic charged particles and extremely high field strengths, it is natural to expect significant radiation emission. Although fundamentally the same physical process, depending on the phenomenological character of the interaction and spectral properties of the radiation, it is usually categorized in some way; e.g. synchrotron radiation, THz radiation, transition radiation, or Thomson scattering to name but a few. Interest in sources of the full spectrum of radiation emission stems from its multiplicity of applications across the technical disciplines, homeland security, healthcare, and even in humanities subjects, such as the probing of great works of art by soft x-rays.

Betatron Radiation

Fig. 1: Betatron oscillations generate bright photon beams into the x-ray region.The various curves represent the spectral brightness of various sources as a function of photon energy. The thick blue curve represents recent HERCULES results, thin blue curve, various third generation synchrotrons, thin green, second generation synchrotrons and thick green, previous work by collaborators using a petawatt power, picosecond duration laser.

X-rays have revolutionized medicine, science and technology. Bright, coherent ultrashort flashes of X-rays can take movies of proteins, pathogens and nanostructures, giving insight into their workings. Despite the demand, only a few dedicated Synchrotron facilities exit worldwide, partially due the size and cost of conventional accelerator and wiggler technology. Together with the researchers from the Imperial College (London) we have shown that X-rays of a quality similar to 3rd generation Synchrotrons can be obtained in a university scale laboratory, on a spatial scale of millimeters rather than tens of metres of conventional light sources, using a 100 Terawatt laser focused into a gas (Fig. 1). This scheme has recently demonstrated high quality beams of electrons. We demonstrated, that the plasma wave that accelerates the electrons can also wiggle them (Fig. 2A). Operating in the non-linear regime, this yields a high quality X-ray beam, which is spatially coherent, emanates from a micron-sized source, has 10-100 keV photon energy, milliradian divergence, ten femtosecond duration and a peak brightness comparable to 3rd generation Synchrotrons. The laser-plasma wiggler is a simple scheme that could revolutionize photon science, offering university scale laboratories access to X-ray sources with properties currently only achievable with multi $100 million machines.

 CUOS investigators have demonstrated that a laser driven plasma can simultaneously serve as both particle accelerator and wiggler, producing high quality beams of X-rays, with mrad divergence, µm source size, tens of keV critical energy and peak brightness of up to 1022 ph/s/mrad2/mm2/0.1%BW (S. Kneip, et al. ,”Nature Physics 6, 980 (2010).). Extensive numerical modeling was carried out; Electron trajectories obtained with the particle-in-cell code OSIRIS were post-processed to yield the characteristics of the betatron radiation. Simulated X-ray beam profile, spectrum, brightness, oscillation amplitude and K-parameter agree well with the experiments. The measured radiation is spatially coherent, opening up a multitude of applications, such as phase contrast and lensless imaging, previously only possible with large conventional light sources (Fig.2) (S. Kneip, et al.  Appl. Phys. Lett. 99, 093701 (2011).). The concept of the laser plasma wiggler has the potential of making novel radiation sources more compact, economical and abundant, and thus impacting progress all across science and technology.

Betatrons radiation and applications

Fig. 2 (A) Mechanism of betatron radiation generation in plasma bubble; (B) laser wakefield betatron source of x-rays is strongly collimated ( divergence <10 mrad) and can resolve micron features [Kneip et al.,  Nature Physics 2010]; (C) betatron source of x-rays at UM is spatially coherent and allows phase contrast imaging [Kneip et al., Appl. Phys. Lett. 2011]; (D) absorption radiography of MicroSD card.

X-ray Production using the Lambda-cubed Laser

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The conventional x-ray tube that has been around for more than a century works on the principle of driving electrons from a cathode into an anode material. The repulsion these electrons exhibit for each other limits the brightness of such tubes, the number of x-rays that can be emitted from a given area in a given amount of time.  These same materials, on the other hand, are replete with their own electrons and need only a driver to push the electrons with weakly relativistic velocities in order to emit x-rays.  When we focus our ultrafast laser light onto materials we make a very bright x-ray source with application to phase contrast imaging, crystal diffraction and time resolved x-ray studies. Such as source was used to make the image above.  In this source the relativistic lambda cubed laser is focused onto various metals, semiconductors, and dielectrics to generate x-rays both in a vacuum vessel and in the open laboratory with an small flow of helium gas. The chart to the right shows the spectra and efficiency of a number of these sources.

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In addition to the short duration of the x-rays from these laser-solid interaction (between 100fs and a few ps) the sources also have small lateral dimensions. This gives them sufficient coherence to produce images with enhanced edges due to phase contrast. In the image below the wings of a damselfly are shown with the effects of diffraction from their fine support structure. The fine structure of materials in another target of our research.  Owing to their very short wavelength, x-rays can probe both the well-ordered atomic structure of materials such as the silicon crystal whose diffraction is shown below and the defects in materials as is illustrated by the crack that was imaged by femtosecond-laser based x-rays.

Papers on hard x-ray generation can be found at:

  • Bixue Hou, John A. Nees, Aghapi Mordovanaki, Marc I. Wilcox, Wolfgang Theobald, Gérard A. Mourou, L. M. Chen, Jean-Claude Kieffer, Andrzej Krol, C. C. Chamberlain “Hard x-ray generation from solids driven by relativistic intensity in the wavelength-cubed regime”, Applied Physics B 83 81-85 (2006).
  • B. Hou, J. Nees, W. Theobald, G. A. Mourou, L-M Chen, J-C Kieffer, A. Krol, C. C. Chamberlain, “Dependence of hard x-ray yield on laser pulse parameters in the lambda-cubed regime,” Appl. Phys. Lett. 84, 13 2259-61 (2004).

Non‐linear Thomson Scattering

Another mechanism for radiation generation is non-linear Thomson back-scattering of the electron beam from intense electromagnetic radiation. In Thomson scattering, an electron, initially at rest, oscillating in a laser field experiencing non-relativistic motion emits radiation at the laser frequency. As the laser intensity increases, the Lorentz force due to the magnetic field begins to become significant, and hence the motion of the electron becomes more complicated. The radiation spectrum starts to pick up higher harmonics of the laser frequency, which gives rise to `non-linear’ Thomson scattering. As the intensity increases further, the relativistic motion of the electron in the direction of the laser propagation results in a Doppler-shift of the fundamental frequency, in addition to increasing the spectral power in the harmonics of the down-shifted frequency. If the electron is  initiated with a relativistic momentum counter-propagating with respect to the laser pulse, then it gains a Doppler upshift. For a very relativistic electron with Lorentz factor, and a lower laser intensity, the upshift in frequency scales as ω10= 4γ2.  Hence, a 400 MeV electron beam, as produced regularly by the HERCULES laser, would upshift a 1 eV photon to 2~MeV.

For a higher laser intensity, there is a slight down-shift of the up-shifted frequency, as the laser accelerates the electron beam against its motion. However, the normalized laser field strength parameter and the normalized betatron (wiggler) parameter are almost interchangeable in the description of Thomson scattering for a relativistic electron colliding with a laser pulse. Hence, as the strength parameter increases, the photon spectrum tends towards a synchrotron-like broad spectrum, extending to much higher photon energies than the shifted fundamental. This more than compensates for the down-shift discussed above, meaning that extremely high photon energies extending into the 10 MeV range could result from a 400 MeV beam and an ultra-intense laser pulse. The relationship between non-linear Thomson scattering and inverse Compton scattering deserves a mention at this point. In inverse Compton scattering, a photon scatters from an electron through a quantum mechanical interaction. For non-linear Thomson scattering, strictly speaking the electrons emit a radiation field due to oscillation in the laser field in a purely classical process. Consideration of quantum effects only really becomes important for photon energies approaching the beam energy.

High‐harmonic Generation 

When high-power optical laser pulses are reflected off a relativistically oscillating plasma surface, a broad, phase-locked harmonic spectra extending to multi-keV photon energies is produced in the specular direction [Tsakiris NJP 2006, Dromey PRL 2007]. This coherent high order harmonic x-ray generation (HOHG) results from an extension to Einstein’s prediction for the frequency upshift of light reflected off a perfect mirror moving close to the speed of light and has recently been shown to happen with unprecedented efficiency and brightness [Tsakiris NJP 2006]. Harmonic radiation extending up to 3.3Å, 3.8 keV (order n > 3200) for petawatt-class laser-solid interactions and the coherent nature of the harmonics is observed by the highly directional emission [Dromey PRL 2007]. When an intense laser pulse interacts with a sharp plasma-vacuum boundary, the electric field of the laser efficiently couples to the plasma surface. It is noted that a high laser contrast ratio is off utmost importance to the HOHG as is a very smooth target surface. The electrons respond by oscillating in phase to form a relativistic mirror oscillating at the laser frequency.

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Fig.6. The generation of attosecond pulses using harmonics from solid targets using high-contrast, ultra-high intensity laser pulses [TsakirisNJP 2006].

HOHG has recently become a popular research area as it is seen as a promising route for accessing the huge intensities required for probing the non-linear quantum electrodynamics properties of the vacuum [Schwinger PR 1951]. In principle, the focused harmonic radiation could have considerably higher peak intensity than the laser used for generation due to the increased focusability (shorter λ), the temporal compression of the pulses and the slow decay in conversion efficiency for pulse generation. The critical Schwinger limit for electron-positron pair production in vacuum (electric field~1016 Vcm-1) could be reached with refocused harmonics toI >1029 Wcm-2 from an incident laser pulse with I = 1022Wcm-2. The HOHG radiation forms high brightness attosecond pulse trains [Gordienko PRL 2004, Pukhov NP 2006, Tsakiris NJP 2006], which has potential applications including the probing of atomic and molecular transitions [Neutze Nature 2000].

In recent experiments we have measured the production of sub-nanometer, x-ray harmonic radiation (extending to 3.3 Å [3.8 keV]) from a high energy (> 200J) Petawatt class laser-solid (CH-film) interaction (see Figure). This corresponds to the most extreme non-linear optical process observed in the laboratory to date (harmonic order n > 3200). The coherent nature of the generated harmonics was verified by the highly directional beam emission, which for photon energy hν > 1 keV was emitted into a cone angle < 4°,significantly less than that of the incident laser cone (20°).

High-order harmonic generation (HOHG) using short pulse (<100 fs) infrared lasers focused to intensities surpassing 1018 Wcm2 onto a solid density plasma is a promising means of generating subfemtosecond (<10-15 s) pulses. Critical to the relativistic oscillating mirror mechanism is the steepness of the plasma density gradient at the reflection point, characterized by a scale length, which can strongly influence the harmonic generation mechanism. We have shown, that for intensities in excess of 1021 Wcm2, using HERCULES laser, an optimum density ramp scale length exists (Figure below) that balances an increase in efficiency with a growth of parametric plasma wave instabilities. We demonstrated that for these higher intensities the optimal scale length is c/w0, for which a variety of HOHG properties are optimized, including total conversion efficiency, HOHG divergence, and their power law scaling (F. Dollar, et al. , “Universal Scale Length for High-Order Harmonic Generation from Intense Laser Interactions,”Phys. Rev. Lett. 110, 175002 (2013)).

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 Figure. Experimental setup for HOHG observation. Spectra and Response corrected lineouts for (a) an ultrasharp density profile of λ/60, (b) a nominal λ/5 = c/w0 scale length, and (c) a longer 3λ/4 scale length. Note that the Al filter blocks light below 17.2 nm.

We have also made measurements of ultra-high magnetic fields produced during intense laser interaction experiments with solids. We have shown that polarization measurements of high-order VUV laser harmonics generated during the interaction (up to the 25th order) suggest the existence of magnetic field strengths of 0.7 Gauss in the overdense plasma. This technique may be useful for laboratory studies of exotic highly magnetized astrophysical objects such as neutron stars.

Attosecond Pulses

In contrast to the attosecond sources from gas targets based on rescattering physics, Ultra-high intensity (>1018 W/cm2) relativistic laser interactions with solid targets have the potential of generating significantly brighter, higher energy x-rays with sub-attosecond (zeptosecond) duration. This approach could be the enabling technology needed to dramatically change the scope of attosecond applications beyond current capabilities.

As an ultra-intense laser pulse interacts with a plasma having a density scale-length less than the laser wavelength, high harmonics are generated. Under these conditions the laser’s electric field can efficiently couple to the critical density surface causing the electrons to oscillate in phase, effectively constituting a relativistic oscillating mirror. As shown in the Figure below, the position of this mirror surface is a temporal function of the incident optical laser cycle, thus the phase of the reflected light wave is modulated such that it is no longer purely sinusoidal.

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The two main driving terms are the electric field of the laser (at the laser frequency) and the ponderomotive force or light pressure (at twice the laser frequency), leading to the production of both odd- and even-order harmonics. The coherent oscillation of the plasma surface results in a well defined reflection plane that locks the phase of the entire harmonic spectrum and theoretically should produce a train of attosecond/zeptosecond x-ray pulses in a small reflected cone Furthermore, the large nonlinearity allows efficient coupling into the harmonic comb. Our recent experiments have demonstrated harmonic emission extending into the x-ray region with the largest conversion efficiencies (approaching 10-2) reported to date. The complementary characteristics of our high intensity, ultra-fast laser sources (Hercules and λ3) provide an unprecedented ability for exploring both x-ray and attosecond generation using this technique.

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Figure: Very intense lasers (i.e. > 1018Wµm2cm-2) make the critical surface oscillate as a “moving mirror”. The reflected light no longer has a sinusoidal waveform and consequently contains harmonics

In recent experiments we have measured the production of sub-nanometer, x-ray harmonic radiation (extending to 3.3 Å [3.8 keV]) from a high energy (> 200 J) Petawatt class laser-solid (CH-film) interaction (see Figure). This corresponds to the most extreme non-linear optical process observed in the laboratory to date (harmonic order n > 3200). The coherent nature of the generated harmonics was verified by the highly directional beam emission, which for photon energy hν > 1 keV was emitted into a cone angle < 4°, significantly less than that of the incident laser cone (20°). Such observations are only possible using a very high contrast laser pulse which is already available using HERCULES configured to operate with a double “plasma mirror”. The harmonic yield in these previous experiments was measured to have an n-(2.5−3) power law decay up to the 2500th-order, indicative of harmonic emission in the relativistic limit. Such measurements imply that the potential exists for producing attosecond pulses with conversion efficiencies as high as ~10-2(hν > 20eV) and ~10-5 (hν > 1 keV). Contrasting this with the best efficiencies reported for an optimized gas harmonic source of ~10-4 (hν > 20eV) and ~10-7 (hν > 100 eV), clearly indicates that the realization of such intense attosecond sources could revolutionize the breadth of attosecond science and potentially provide the extreme intensities needed to probe nonlinear QED.

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Figure: Relativistic high harmonic spectrum. The harmonic orders beyond 1000 are so closely spaced than the emission appears continuous.

We have also made measurements of ultra-high magnetic fields produced during intense laser interaction experiments with solids. We have shown that polarization measurements of high-order VUV laser harmonics generated during the interaction (up to the 25th order) suggest the existence of magnetic field strengths of 0.7 GGauss in the overdense plasma. This technique may be useful for laboratory studies of exotic highly magnetized astrophysical objects such as neutron stars.

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