1. INTRODUCTION

During the past few decades, the development of high power laser facilities and pulse power devices has enabled the creation and study of matter in the high energy density (HED) regime, defined by energy densities greater than ${10}{^5}\;{\rm J}\;{{\rm cm}^{- 3}}$ and pressures in excess of 1 Mbar [1–3]. This regime includes, for example, the hohlraum plasmas of the National Ignition Facility (NIF), planetary cores, and radiatively heated foils (Fig. 1) [4]. More recently, the advent of ultra-high power lasers [5] has made it possible to access the more elusive plasma regime defined as ultra-high energy density (UHED), characterized by three orders of magnitude higher energy densities (${\gt} {10}{^8}\;{\rm J}\;{{\rm cm}^{- 3}}$). This is the regime that characterizes the center of stars and the compressed inertial confinement fusion (ICF) capsules driven by the world’s largest lasers.

 

Fig. 1. Plasma parameter space showing the typical parameters of plasmas generated by irradiating NW targets with femtosecond pulses of relativistic intensity relative to other high energy density plasmas. The black lines show the approximate limit of the region commonly accepted as high energy density (HED), ${\gt} {1} \times {{10}^5}\;{\rm J}\;{{\rm cm}^{- 3}}$ and that defined as ultra-high-energy density (UHED), ${\gt} {1} \times {{10}^8}\;{\rm J}\;{{\rm cm}^{- 3}}$. Adapted from [4] with permission from Springer Nature.

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The creation of matter at these conditions in the laboratory is of great interest for ICF and for the realization of laser-driven inertial fusion energy (IFE) [6–10], for generating intense sources of x-rays and high energy particles [11,12], and to further the understanding of atomic physics in extreme environments [13–15]. However, until recently, the creation of a large volume of UHED matter in the laboratory was limited to the central hot spot of the spherically imploded capsule in ICF experiments. This requires the use of high energy lasers [16,17], which typically fire a few shots per day. Such low repetition rates are a roadblock for applications such as gamma-ray radiography, neutron imaging, and radiation damage tests of materials. An alternative approach is to heat the material using today’s petawatt class lasers that are capable of firing at multi-Hz repetition rates [18,19]. These higher repetition rate lasers reach intensities approaching ${{10}^{22}}\;{\rm W}$ ${{\rm cm}^{- 2}}$, which drive highly relativistic electron oscillations. For the a $\lambda = {800}\;{\rm nm}$ laser, an intensity (${I_L}$) just above ${2} \times {10}^{{18}}\;{\rm W}\;{{\rm cm}^{- 2}}$ is required to make electrons oscillate with a quiver momentum ${m_ec}$, where ${m_e}$ is the electron rest mass, and $c$ is the speed of light.

In terms of the laser strength parameter, ${a_{o}} = {({7.3} \times {{10}^{- 19}}\;{[\lambda ({\unicode{x00B5}{\rm m}})]^2}\;{I_L}\;({\rm W}\;{{\rm cm}^{- 2}}))^{1/2}}$, relativistic electron motion requires ${a_{o}} \gt {1}$. These lasers can produce relativistic plasmas with interesting properties and exciting applications, such as accelerating electrons to multi-GeV energy [20,21], producing beams of light ions with several tens of MeV [22,23] and heavy ions in excess of 1 GeV energy [24], and generating intense flashes of high energy photons [25]. However, heating sizable UHED plasma volumes by irradiating solid slab and foil targets is a challenge that even many of today’s most powerful lasers fall short of achieving. In such conventional solid target heating scenarios, a significant fraction of the incoming light is reflected, preventing it from heating the target.

The transition into the UHED regime has barely been achieved by hittng these solid targets with electrons accelerated by the most powerful lasers currently available. Moreover, the heated plasma depth is small, typically about 1 micrometer [26–30]. For example, heating with 400 J pulses of 0.8 ps duration achieved a 5 keV surface temperature, decreasing to 0.6 keV at 1.3 µm depth [30]. Recently, irradiation of Cu foils with high contrast $\lambda = {400}\;{\rm nm}$ pulses of ${2} \times {{10}^{21}}\;{\rm W}\;{{\rm cm}^{- 2}}$ intensity heated uniform plasmas to a temperature of ${\sim}{3}\;{\rm keV}$ up to a depth of 1 µm [31]. Homogeneous heating by the 400 nm wavelength laser pulses was attributed to the generation of the MeV electrons, with favorable conditions becoming trapped and undergoing refluxing in a few microns’ thick targets [31].

Alternatively, exposing arrays of large aspect ratio aligned nanostructures to intense high-contrast femtosecond laser pulses, even at low energies like the Joule-level, offers a distinctive combination of almost complete optical absorption and greatly enhanced light penetration into near-solid density targets. This enables volumetric heating of the material deep into the UHED regime. Increased absorption has also been achieved using other types of structured targets, as evidenced by enhanced x-ray emission from gratings [32–36], “smoked” targets [37], nanospheres and nanoparticles [38–40], laser induced periodic surface structures [41], and “velvet” nanowire (NW) targets [42–45]. In particular the irradiation of arrays of 0.8–1-µm-long Ni NWs with picosecond laser pulses was demonstrated to increase absorption and produce up to 50 times greater ${\sim} {1}\;{\rm keV}$ photon emission than a flat target [42]. Irradiation of Au NW arrays showed a 20-fold increase in soft x-ray emission [38]. A review of plasmas created by intense irradiation of targets with nanostructure features in general has been published [46].

 

Fig. 2. PIC simulation and spectra from plasma generated by femtosecond pulse irradiation of a vertically aligned array of 55 nm diameter Ni nanowires irradiated at an intensity of ${5} \times {{10}^{18}}\;{\rm W}\;{{\rm cm}^{- 2}}$ by a $\lambda = {400}\;{\rm nm}$, 66.6 fs FWHM duration laser pulse. (a) PIC simulations of the penetration of the laser beam electric field in an array of 15-µm-long Ni wires with an average atomic density of 12% solid density. Times are measured with respect to the peak of the laser pulse. The laser field is in units of TV/m. (b) Computed impinging (red contour) and reflected (blue contour) laser intensity. (c) Computed electron density evolution in units of critical density (${n_{{\textit ecr}}} = {6.8} \times {{10}^{21}}\;{{\rm cm}^{- 3}}$). (d) Single-shot x-ray spectra comparing the emission from an irradiated array of a 5-µm-long Ni NW (red trace) to that from a flat, polished Ni target (blue trace). The NW target plasma spectrum is dominated by a He-like Ni line emission. The only line observed in the flat target plasma spectra is the Ni-${\rm K}\alpha$ line. The inset is a scanning electron microscope image of the NW array. Adapted from [4] with permission from Springer Nature.

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Nevertheless, high aspect ratio aligned nanostructures surrounded by empty spaces are unique and of particular interest. They allow for the deep penetration of the ultrafast optical laser pulse energy into the material, where light is trapped and practically totally absorbed [Figs. 2(a)–2(c)], significantly exceeding the absorption from solid flat targets. This results in volumetric heating to significant depths [4]. The energy absorption in nanowire arrays was measured to increase as a function of the effective target area, which is a function of the total nanowire area interacting with the laser and the nanowire number density [47]. High aspect ratio NWs present a greatly increased effective absorption area to the laser beam. This allows the laser electric field to pull a much larger number of electrons from the NW surfaces, which are accelerated in the voids to gain relativistic quiver energies, resulting in nearly full absorption. Using laser pulses of only 0.5 J energy [4], electron densities nearly one hundred times greater than the typical critical density $n_{\textit{ecr}}$, multi-keV temperatures, and extraordinarily high degrees of ionization (e.g., 52 times ionized Au) were achieved. The electrons ripped off the NW surface by optical field ionization acquire high kinetic energy and collide with the NWs, rapidly heating the material to extreme temperatures and causing the nanostructures to explode and rapidly fill the voids [Figs. 2(a) and 2(c)]. This forms a continuous critical electron density layer that prevents further coupling of laser energy into the material. However, the use of sufficiently short laser pulses allows for very efficient coupling of the laser pulse energy deep into the NW array, heating to multi-keV temperatures a volume of near-solid density material several microns in depth. This novel volumetric heating approach opens access to the UHED plasma regime using table-top, Joule-class sub-hundred-femtosecond lasers that can operate at a high (multi-Hz) repetition rate [18,19], thereby advancing the prospects of various applications.

A relatively modest intensities of ${5} \times {{10}^{18}}\;{\rm W}\;{{\rm cm}^{- 2}}$ (normalized vector potential ${a_{0}} = {0.76}$, $\lambda = {400}\;{\rm nm}$) have been demonstrated to be sufficient to volumetrically heat near-solid density plasmas to multi-KeV energies to depths of several µm [4]. A single-shot spectrum in the 1.5–1.75 Å region of a plasma created by irradiating an array of aligned Ni NWs 55 nm in diameter and separated by 135 nm at this intensity, is shown in Fig. 2(d). Strong emission from the 2p–1s ($\lambda = {1.588}$ Å) and intercombination lines of He-like Ni (${{\rm Ni}^{+ 26}}$) are observed. This spectrum differs greatly from the spectrum corresponding to a polished flat target irradiated at the same conditions, which only shows a line emission from the Ni ${\rm K}\alpha$ line at 1.658 Å [shown with 10 X magnified scale in Fig. 2(d)]. The ${\rm K}\alpha$ emission is produced mainly by high energy electrons, while the generation of the He-like ion transitions requires a hot thermal plasma to generate and excite the highly stripped ions. Remarkably, the He-like line emission from the NW target exceeds the intensity of the ${\rm K}\alpha$ line at this irradiation intensity. In contrast, in experiments with Cu foils, the emission from the ${\rm K}\alpha$ lines was only surpassed at irradiation intensities ${\gt}\;{2} \times {{10}^{20}}\;{\rm W}\;{{\rm cm}^{- 2}}$ [48]. In this 7–8 keV spectral region, the aligned Ni NW target produced more than a 50 times larger x-ray flux [4]. Similarly, a near-solid density Au plasma with a very high degree of ionization was created by irradiating an array of 80 nm diameter Au wires 5 µm in length. The Au NW spectra (see Fig. 2 in [4]) displayed strong Au M-shell emission, with unresolved 4–3 lines from ions ranging from Co-like (${{\rm Au}^{+ 52}}$) to Ga-like Au (${{\rm Au}^{+ 48}}$). The spectra showed dramatic increases of up to 100 times in the emission in the 2.3 keV to 2.75 keV photon region with respect to flat solid targets irradiated by the same laser pulses.

2. LASER NANOSTRUCTURES INTERACTION

A. Laser Energy Penetration Depth

A key parameter for determining the volume of the heated plasma and the deposited energy density is the energy penetration depth into the array. Experiments at a moderate relativistic intensity of ${4} \times {{10}^{19}}\;{\rm W}\;{{\rm cm}^{- 2}}$ showed heating to multi-keV temperatures over depths of several µm [49]. The He-$\alpha$ line emission from a buried NW segment of a selected tracer material was monitored to measure the energy penetration depth. This requires growing NW arrays with segments composed of different materials [Figs. 3(a) and 3(b)].

 

Fig. 3. (a) Schematic diagram of segmented Ni-Co nanowire array. The top Ni segment ranges in length from 1 to 6 µm. The nanowires are 55 nm in diameter and the array has 13% solid density. (b) Scanning electron microscope (SEM) image with energy-dispersive spectroscopic elemental composition measurement, indicating the concentration of Ni (blue) and Co (red). (c) Example spectra showing the He-like lines’ dominance over the ${{\rm K}\,\alpha}$ lines for the two elements, as recorded with a von Hamos spectrometer. (d) Simulated spectra corresponding to the three arrays with different Ni wire segment lengths. (e) Measured and simulated (Co He-$\alpha$)/(Ni He-$\alpha$) line ratios as a function of the Ni nanowire segment length. Adapted from [49]. © The Authors, some rights reserved, exclusive licensee AAAS. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC) http://creativecommons.org/licenses/by-nc/4.0/.

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Fig. 4. PIC simulations of the integrated electron and ion kinetic energy density distribution in an array of 55 nm diameter Ni NWs irradiated at an intensity of ${4} \times {10}^{{19}}\;{\rm W}\;{{\rm cm}^{- 2}}$. Each frame corresponds to a different time with respect to the peak of the laser pulse. The laser pulse impinges into the array from the top at normal incidence. Adapted from [49]. © The Authors, some rights reserved, exclusive licensee AAAS. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC) http://creativecommons.org/licenses/by-nc/4.0/.

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The element in the top segment of the NWs was Ni ($Z = {28}$). Cobalt ($Z = {27}$), a neighboring element in the periodic table, having similar mass and ionization energy, was selected as the buried tracer element to facilitate a similar plasma dynamic to take place along the NWs. The selection of contiguous elements in the periodic table also allowed the characteristic spectral lines of both materials (e.g., the He-like lines) to be recorded within the same spectral window of a single crystal spectrometer [Fig. 3(c)]. The emission from He-like Co ions was observed for targets with up to 4 µm of Ni on top. When the thickness of the top Ni layer reaches 5 µm, the Co lines are observed to decrease in intensity to the level of the bremsstrahlung and radiative recombination continuum. This demonstrates, in agreement with simulations, that the energy required to heat the plasmas to the level necessary to ionize Co ions to the He-like stage penetrates at least 4-µm deep into the near-solid density material.

Figure 4 shows 3-D particle-in-cell (PIC) simulation maps of the kinetic energy density in a Ni nanowire array irradiated at an intensity of $4 \times {10^{19}}\;{\rm W}\,{{\rm cm}^{- 2}}$, computed at four different times during the plasma evolution. The energy density and pressure for hot electron gases are given by integrals of the energy and momentum-velocity product, weighted by the distribution function. The energy density can be calculated directly from the particle data from the PIC simulation [49].

The plasma dynamics leading to the energy density distribution in Fig. 4 is as follows. The strong electric field of the laser pulse strips electrons from the NW surfaces by optical field ionization, creating ionization states up to $Z = {18}$. The electrons are rapidly accelerated into the inter-wire gaps. As the hot electron population deposits its energy deep into the NW cores, more highly ionized ions are produced. The freed electrons are accelerated toward the substrate, and a large return current through the NWs re-stablishes a charge balance. A resulting strong quasi-static self-generated azimuthal magnetic field pinches the NWs into an extremely dense, hot plasma [50–52]. An energy density of ${22}\;{\rm GJ}\;{{\rm cm}^{- 3}}$ and a pressure of 125 Gbar are computed to be quickly reached within the wires near their tips (${+}{4}\;{\rm fs}$ frame in Fig. 4), where the electron density surpasses ${{10}^{24}}\;{{\rm cm}^{- 3}}$. As long as the plasma in the inter-wire gaps remains underdense the laser pulse continues to propagate deep into the array. As the NW expands, the inter-wire gaps become filled with supercritical-density plasma that is homogenized by collisions. This creates a uniform plasma layer several µm thick in which the atoms are ionized up to the He-like stage. The NW tips disintegrate first, as observed in the earliest frame of Fig. 4 (${+}{4}\;{\rm fs}$), and the gaps fill with plasma. Subsequently, the expansion of the wires continues to progressively close the inter-wire gaps along the length of the wires (${+} {44}\;{\rm fs}$ and ${+}{124}\;{\rm fs}$ frames in Fig. 4) until the plasma fills the whole target cross section in which the energy density reaches ${\sim}{1}\;{\rm GJ}\;{{\rm cm}^{- 3}}$ and the pressure reaches 7 Gbar (${+}{304}\;{\rm fs}$ frame in Fig. 4). The plasma thermalizes and the electron temperature reaches ${\sim} {14}\;{\rm keV}$ over the plasma volume with an average electron density surpassing ${3} \times {{10}^{23}}\;{{\rm cm}^{- 3}}$. Even higher plasma densities could be achieved by increasing the irradiation intensity, using arrays with higher wire filling factors, employing arrays of a higher $Z$ material or by a combining of these parameters.

B. Interactions at Highly Relativistic Intensities

A further increase in intensity has resulted in an unprecedented degree of ionization for dense laboratory plasmas [53]. Electron beam ion traps (EBIT) have been successfully used to ionize Au atoms up to the Ne-like stage (${{\rm Au}^{69 +}}$) by collisions of ions with a high energy electron beam while trapped in a potential well [54,55]. However, in EBIT plasmas the densities are typically over 10 orders of magnitude lower than the solid density. Stripping heavy atoms in solid materials of most of their electrons requires extreme conditions that exist in astrophysical plasmas but that are difficult to create in the laboratory [56–58].

Dense plasmas with high degrees of ionization have been achieved with laser pulses, with energy ranging from several hundred Joules to kilojoules. For example, experiments conducted at the Laboratory of Laser Energetics with the OMEGA laser to heat a reduced scale “hot” hohlraum using 9 kJ pulses of a nanosecond duration revealed strong L-shell gold emission with an average charge state of Ti-like Au (${{\rm Au}^{57 +}}$) and an inferred temperature of 6.5 keV at an electron density of ${{10}^{21}}\;{{\rm cm}^{- 3}}$ [58]. This density is still orders of magnitude below solid density. In contrast, irradiation of an aligned Au NW array with ultra-high contrast femtosecond second-harmonic laser pulses of only 10 joules energy focused to an intensity of ${3} \times {{10}^{21}}\;{\rm W}\;{{\rm cm}^{- 2}}$ (${a_o} = {21}$) generated near-solid density plasmas in which atoms were stripped of up to seventy-two electrons to reach a N-like state (${{\rm Au}^{72 +}}$) [53]. Figure 5 shows L-shell emission spectra corresponding to an array of 100 nm diameter Au NWs with an average density corresponding to 15% of solid density irradiated with ultra-high contrast (${\gt}{{10}^{12}}$) $\lambda = 400\;{\rm nm}$ pulses of ${\sim} {45}\;{\rm fs}$ duration from a frequency doubled Ti:Sapphire laser [18]. The emission from the Ne-like Au transition at 10,527 eV and lines corresponding to higher ionization stages up to N-like Au (${{\rm Au}^{72 +}}$) are observed. The average charge state is centered at Al-like ${{\rm Au}^{66 +}}$.

 

Fig. 5. L-shell emission spectra corresponding to an array of 100 nm diameter Au NWs with an average density of 15% of solid (red) and for a solid Au foil (blue) irradiated with high contrast 400 nm laser pulses of femtosecond duration focused to an intensity of ${3} \times {{10}^{21}}\;{\rm W}\;{{\rm cm}^{- 2}}$. Radiation from transitions corresponding to ionization stages up to N-like Au (${{\rm Au}^{72 +}}$) are observed. Reproduced from [53] with permission from Springer Nature.

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The use of the second harmonic increases the critical electron density by a factor of four to a relativistic critical density approaching ${1} \times {{10}^{23}}\;{{\rm cm}^{- 3}}$ [59,60], increasing the ionization rate. In addition, the second-harmonic generation process greatly increases the contrast, suppressing pre-pulses that prevent the early formation of a large scale pre-plasma that would reduce the deposition of energy into the bulk of the target [4,61]. The energy penetration depth in these Au targets was measured by monitoring the He-$\alpha$ line emission from a Ni tracer buried underneath a variable amount of Au, and the results were compared with those obtained from irradiating solid density slab targets. In the case of solid targets, He-like Ni line emission was still visible underneath a 1 µm thick solid Au layer but faded under 1.5-µm-thick Au layer. A much larger laser energy penetration in the NWs arrays was demonstrated monitoring the He-$\alpha$ line from Ni NWs buried under segments of Au NWs of different length in a dual composition array of 100 nm diameter wires with 15% of solid density. The emission from the He-like Ni lines was still visible under 8 µm of Au, revealing the significantly larger volume of the NW plasmas. For the NW plasmas the average computed energy density approaches ${\sim} {100}\;{\rm GJ}\;{{\rm cm}^{- 3}}$, corresponding to an UHED regime virtually unexplored in laboratory plasmas. Moreover, this was achieved using femtosecond laser pulses of only 10 J energy, which can be generated by high repetition rate lasers.

Figure 6 shows the results of 3-D relativistic PIC simulations that assist in determining the mechanisms by which the energy is deposited deep into these NW targets at the irradiation conditions of Fig. 5 [53]. The electric field propagation (a)–(c), the electron density in units of ${n_{{\textit ecr}}}$ ${\sim} 7 \times {10^{21}}\;{{\rm cm}^{- 3}}$ (d)–(f), and the degree of ionization (g)–(i) are shown for three different times with respect to the peak of the laser pulse: ${-}{30}\;{\rm fs}$, 0 fs, and ${+}{1000}\;{\rm fs}$. Initially, the laser electric field propagates in the inter-wire gap along the length of the wire, accelerating electrons produced by optical field ionization toward the substrate. As the laser intensity increases, the large electric field at the NW tips drives optical field ionization up to Ne-like ${{\rm Au}^{69 +}}$. The return electron current that flows through the wires generates a quasi-static magnetic field that pinches the nano-wires to reach peak electron densities in excess of 1000 ${n_{{\textit ecr}}}$. Electron collisions rapidly heat the nanowire tips that explode by the time the peak of the laser pulse arrives [Fig. 6(e)], filling the gaps with an overdense plasma with density ${\gt} {15}$ times the critical density. At this point, the laser can no longer propagate into the NW array. However, the laser still heats up a thin surface layer, depositing a majority of the energy in a thin slab of overdense plasma, which reaches a peak electron energy density of ${\gt}{1000}\;{\rm GJ}\;{{\rm cm}^{- 3}}$ (see Extended Data Fig. 3 in [53]).

 

Fig. 6. 3-D PIC simulation of the evolution of an array of a 100 nm diameter Au NW irradiated at an intensity of ${3} \times {{10}^{21}}\;{\rm W}\;{{\rm cm}^{- 2}}$ obtained using periodic boundary conditions. (a)–(c) Driving electric field, (d)–(f) electron density, and (g)–(i) particle ionization state distribution at three different times: 30 fs preceding the peak of the laser pulse, at the peak of the laser pulse, and ${+}{500}\;{\rm fs}$ following. The electron density is plotted in units of ${n_{\textit{ecr}}}$ (${7} \times {{10}^{21}}\;{{\rm cm}^{- 3}}$ for $\lambda = 400\;{\rm nm}$) and only for densities ${\gt}{15} \,{n_{{\textit ecr}}}$. Reproduced from [53] with permission from Springer Nature.

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Energetic electrons expelled from this upper layer travel along the length of the wires, releasing their energy into the array and ionizing atoms throughout the entire volume up to the N-like stage. The average degree of ionization, Al-like (${{\rm Au}^{68 +}}$), is lower than in the solid-density plasma, but in the NW case, the plasma depth is nearly an order of magnitude larger, in agreement with experiments. A steady-state ionization balance indicates that an electron temperature in excess of 10 keV is required to reach such a high degree of ionization. However, since the plasma is highly transient, it is inferred that the electron temperature must be at least several tens of keV. In an accompanying 3-D PIC simulation for solid-density Au slab targets irradiated by the same laser pulses, the ionization of atoms to high charge states at ${+}{500}\;{\rm fs}$ after the peak of the laser pulse is computed to penetrate only ${\sim}{2}\;{\unicode{x00B5}{\rm m}}$, in accordance with the ${\lt} {1.5}\;{\unicode{x00B5}{\rm m}}$ inferred from spectral measurements. The laser energy is absorbed mainly by collisionless processes with electrons and ions within the skin depth [62]. Energetic electrons generated within the skin depth transports the energy deeper into the solid density target, where current filaments give rise to Weibel instabilities [63].

Combined with a relativistic factor of $\gamma = {15}$, the use of second-harmonic generation increases the critical density to ${{10}^{23}}\;{{\rm cm}^{- 3}}$, leading to an increase collision frequency that results in atoms being ionized up to N-like (${{\rm Au}^{72 +}}$) and in a higher average charge of ${{\rm Au}^{69 +}}$. The irradiation of arrays of NWs results in lower density plasmas that have a much larger volume. 3D PIC simulations reveal that the mechanism of energy deposition deep into the NW target differs from that at lower irradiation intensities and is dominated by energetic electrons accelerated near the target surface. A further increase in ionization to He-like (${{\rm Ag}^{+ 77}}$) could be achieved combining a further increase of the laser irradiation intensity to ${\gt}\;{1} \times {{10}^{22}}\;{\rm W}\;{{\rm cm}^{- 2}}$ (${a_o} = {34}$) with a larger spot size, as discussed in the Outlook and Future Directions sections.

3. APPLICATIONS

A. X-ray Generation

The combination of high temperature at near-solid density with volumetric heating in NW arrays offers advantages for the efficient conversion of laser light into x-ray pulses of picosecond duration. Intense ultra-short bursts of x-ray radiation are essential for a variety of applications, including ICF backlighters [64,65], fundamental studies of matter at extreme conditions [66], and probing ultra-fast changes in material with high spatial and temporal resolution [67,68]. Dense plasmas produced by the laser irradiation of solids with intense short-pulse lasers are emitters of intense x rays [32,33]. However, the conversion efficiency (CE) of the optical laser energy into x rays is limited by several factors. These include the incomplete absorption of the laser pulse energy and the rapid hydrodynamic expansion of the thin plasma layer generated at the surface of the solid, which cools the plasma at a faster rate than the radiative cooling time. Efforts to increase the x-ray conversion efficiency have focused on addressing these two factors using structured targets. Targets investigated include micro-lithographic gratings [32,33,69,70], nanometer size dielectric spheres or ellipsoids [38,43], “smoked” clustered surfaces [33,37,42], nanoporous arrays [71,72], and nanowire arrays [4,42,44,72–82]. Arrays of large aspect ratio nanowires have led to the largest overall increases in x-ray conversion efficiency with respect to solid targets, reaching conversion efficiencies of up to 20% for Au nanowire arrays [82].

The increased x-ray yield from the NW arrays has been attributed to increased absorption [42–44,75], to a larger number of heated atoms [37], and to an increased hydrodynamic time-to-radiative cooling time ratio that effectively allows the plasma to cool radiatively before hydrodynamic cooling occurs [73]. The radiative cooling time ${\tau _{{\rm rad}}}$ is here defined as the time needed to radiatively dissipate the thermal energy of the plasma, and the hydrodynamic cooling time is ${\tau _{{\rm hydro}}} = \Delta L/{C_s}$, where $\Delta L$ is the plasma size and ${C_s}$ is the acoustic velocity. Tailoring the plasma to attain a radiative cooling time shorter than the hydrodynamic cooling time can result in an order of magnitude increase in the conversion efficiency from optical to picosecond x rays. This condition requires a large electron density, ${n_e}$, in combination with a large plasma size such that

The high ${n_e}$ in the nanowire arrays, on the order of 100 times the critical density, along with volumetric heating (large $\Delta L$) in large aspect ratio nanowires, meets this condition. Irradiation of Au NW arrays with ultra-high contrast (${\gt}{{10}^{12}}$) relativistic laser pulses resulted in ${\sim} {20}\%$ CE of optical laser light into ${\rm h}\nu \gt {1}\;{\rm keV}$ x rays in ${4}\pi$ sr [Fig. 7(a)] [73].

 

Fig. 7. (a) X-ray (${\rm h}\nu \gt 1\;{\rm keV}$) CE for Au and Ni NW of different wire diameters compared to flat solid targets of the same material. $I = {4} \times {{10}^{19}}\;{\rm W}\;{{\rm cm}^{- 2}}$. Each point represents an average of 10 shots. The maximum measured single shot CE for 80 nm diameter wires exceeded 22% resulting in an increase of 35 times with respect to a polished flat target. Reproduced from Hollinger et al. [73] with permission. (b) Comparison of bremsstrahlung emission between an optically polished Cu flat (triangles) and Cu nanorods irradiated by ${{10}^{16}}\;{\rm W}\;{{\rm cm}^{- 2}}$. Adapted with permission from Fig. 4, Mondal et al, Phys. Rev. B 83, 035408 (2011) by the American Physical Society [44]. Single-shot water window spectra for (c) flat target, (d) 200 nm, (e) 500 nm diameter C nanowires, and (f) corresponding integrated lineouts. Reproduced with permission from [82].

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At higher photon energies in the 150–300 keV range x-ray measurements in Cu nanowires showed a 43-fold increase along with hot electron temperatures 11x higher compared to polished Cu foils when irradiated at an intensity of ${{10}^{16}}\;{\rm W}\;{{\rm cm}^{- 2}}$ [80]. The increase in x-ray yield was attributed to enhanced laser absorption due to the extremely high local electric fields around the nanowire tips [83,84]. Bremsstrahlung emission, recorded with a NaI scintillator coupled to a photomultiplier tube, is shown in Fig. 7(b). At low photon energy in the water window (2.33 nm to 4.40 nm), irradiation of plastic nanowire arrays at mildly relativistic intensities (${4} \times {{10}^{19}}\;{\rm W}\;{{\rm cm}^{- 2}}$) was found to enhance the x-ray emission by more than an order of magnitude compared to flat targets [82]. The CE was found to be as high as 0.5%/sr from targets with the longest NWs. Carbon Ly-$\alpha$, He-$\beta$, and He-$\alpha$ were measured for various C NW targets and compared to emission from a planar target, Figs. 7(c)–7(f). A recent study [85] measured hard x-ray flashes from a C nanotube plasma exceeding ${{10}^{10}}$ photons per Joule with an efficiency of ${{10}^{- 3}}$.

The duration of the x-ray pulse emission was measured to be longer in the NW arrays as compared with flat solid targets. In the case of Ni nanowires irradiated at an intensity of up to ${{10}^{17}}\;{\rm W}\;{{\rm cm}^{- 2}}$ a pulse duration of ${\sim}{25}\;{\rm ps}$ FWHM was measured for photon energies ${\gt} {150}\;{\rm eV}$, compared to ${\lt} {6}\;{\rm ps}$ for a flat target [42]. Spectrally and time resolved measurements of the emission from Ni NW arrays irradiated at highly relativistic intensity of ${3} \times {{10}^{21}}\;{\rm W}\;{{\rm cm}^{- 2}}$ were recently conducted at ALEPH laser facility at Colorado State University. The He-like Ni line emission duration was measured to be 12 ps. In contrast, solid-density foils, where the hydrodynamic expansion cools the plasma more rapidly, emitted for 4 ps.

B. Giant Magnetic Fields in Laser Produced Plasmas

Large magnetic fields were discovered in laser-produced plasmas as early as the 1960s, and several mechanisms that induce currents in plasma were investigated since, the most common being resonance absorption, ponderomotive push, and instabilities [86–88]. Among the most examined in recent times, and relevant to the present context, is the Weibel instability, initially proposed for plasmas where there is a temperature anisotropy [63]. As proposed by Weibel, the anisotropy induces counter-streaming currents in the plasmas, which suffer growing spatial separation and break up when aided by internal fluctuations, resulting in localized magnetic fields. In the context of this review, this pertains to the transport of relativistic electrons where, as explained earlier, fast electrons are pumped into the NWs or planar portions of a target by an ultra-high intensity laser pulse interacting with the nanostructure at the surface. These electrons form giant mega ampere pulses and induce large return currents in the NW/planar target plasma. The interaction of these two currents results in filamentation of the electrons and the localization of the giant magnetic fields (GMFs) [63,89–91]. The filamentation occurs at the skin depth scale of a few nanometers in a dense plasma, and the separation grows by an inverse cascade. In contrast, a new route has recently been pointed out, where the radiative loss at the boundary of the electron beam in the plasma (essentially the same scale as the laser irradiated spot size) can seed an instability, causing magnetic field generation [92,93]. The time evolution of the magnetic field has been shown to be ultrashort and provides a way of measuring the conductivity of the hot, dense plasma created by the fast electrons themselves [94–96]. The combination of micrometer spatial resolution with femtosecond time scales has shown the turbulent features of the magnetic field, mimicking similar evolution in astrophysical scenarios [93,96,97].

The ultra-large fluxes of the electrons in the nanostructures are simulated to cause the highest magnitude GMFs and magnetic pressures ever known on the earth [50]. High current fast electron beams and their energy deposition in a supersolid density nuclear fuel core are of interest for the fast ignition scheme of laser fusion. In this scheme, beams of a few MeV electrons must transport some 100 megaampere currents to the core of a compressed ICF target. Filamentation can severely hinder this process. In a bulk, moderately dense plasma, filamentation lengths are typically a few microns for beams generated with $\lambda = {1}\;{\unicode{x00B5}{\rm m}}$ laser irradiation (${n_{{\textit ecr}}} = {10^{21}}\;{{\rm cm}^{- 3}}$) [98]. These contradictory scenarios have stimulated extensive investigation of the fast electron transport under different laser and target conditions. It is therefore interesting to compare the cases of solid fused silica (FS) with that of the FS covered with an array of C nanotubes (CNTs) [Figs. 8(a) and 8(b)].

 

Fig. 8. 2-D spatial profile of the magnetic fields 3 ps after irradiation at the rear side of (a) CNT-FS sandwich target and (b) only FS, at an intensity of $({2 - 4}) \times {{10}^{18}}\;{\rm W}\;{{\rm cm}^{- 2}}$. (c) 3-D spatial profile of (a) clearly showing central hollow and local magnetic field peaks as high as 370 MG, in contrast with only 30 MG for FS alone. (d) 3-D plot of the current density of the CNT-FS target, derived from the magnetic field profile shown in (a). (e) Temporal evolution of the rear-side magnetic fields for the CNT-FS and the FS only targets (enhanced five times for comparison) captured at an intensity of $({2 - 4}) \times {{10}^{18}}\;{\rm W}\;{{\rm cm}^{- 2}}$. Time constants are represented by $\tau$. The inset shows the SEM image of the target. The average nanotube spacing is ${\sim}{50}\;{\rm nm}$, and the average diam. is ${\sim}{10}\;{\rm nm}$. Reproduced with permission from Figs. 3 and 1, Chatterjee et al., Phys. Rev. Lett. 108, 235005 (2012) [99] by the American Physical Society. (f) Temporal magnetic field evolution at the front side of the Si NWs and silica. The inset is a schematic of the experiment. TGT: sketch of the Si NW target showing NWs on the glass substrate. SEM image of the Si NW target shows that the average nanowire is ${\sim}{60}\;{\rm nm}$. Reprinted from P. Singh, G. Chatterjee, A. D. Lad, et al., “Efficient generation and guiding of megaampere relativistic electron current by silicon nanowires,” Appl. Phys. Lett. 100, 244104 (2012) [100] with the permission of AIP Publishing.

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The CNTs have been demonstrated to show successful transport of high flux, relativistic electron pulses over millimeter distances [Fig. 8(e)], ${\sim}\;{100}$ times larger than the typical filamentation lengths of a few microns [99]. In another study [Fig. 8(f)], Si-NW-coated surfaces have caused a 30 times enhancement of the electron flux through a 100 µm distance [100]. The current densities estimated from the GMF field measurements of up to 370 MG [Figs. 8(a)–8(c)] in the case of a 1-mm-long carbon nanotube are ${{10}^{12}}\;{\rm ampere}\;{{\rm cm}^{- 2}}$ [Fig. 8(d)]. In both these studies, the electron spectrometers placed at the target’s rear recorded fluxes orders of magnitude larger than those from plane targets. The magnetic and electric field configurations induced by the surface currents in the nanostructures are reasons for the electron guiding, as elaborated below.

C. Relativistic Electron Transport through Nanostructured Targets and the Role of Self-Generated Giant Magnetic Fields

The transport of large fluxes of fast electrons involves complex physics and impacts many phenomena and applications such as the generation of synchrotron radiation. The self-generated GMFs play a crucial role not only in the interaction between the forward hot electron and the return thermal currents but also in the divergence/confinements of electrons at different spatial locations inside the target and at the surfaces. Self-generated GMFs have also been shown to pinch and collimate electron beams [101]. In experiments and 2D PIC simulations on 12-µm-long 100 nm OD and 40 nm ID CNTs, collimation of fast electrons is shown to be achieved by a push-pull process, where they are pushed outwards by the magnetic field at the surface of the CNT but are pulled back by the surface electrostatic field (Fig. 9), leading to the guiding of fast electrons along the wall of the CNT. Similar conclusions were reached in another study on a metallic nanobrush target adhered to a Cu foil [102] and on conical nanolayer targets [103].

 

Fig. 9. Formation of an ultra-dense nanowire Z-pinch. Longitudinal cross sections of magnetic field components (a) ${B_x}$ and (b) ${B_y}$ [in Giga-Gauss]. Laser propagation is from left to right. Longitudinal cross sections of electron density, ${n_e}$, in units of the critical electron density, at times: (c) $t = - {35}\;{{\rm T}_0}$, (d) $t = - {13}\;{{\rm T}_0}$, (e) $t = - {7}\;{{\rm T}_0}$, and (f) $t = {8}\;{{\rm T}_0}$. The inset in frame (c) shows a zoom of a periodic structure on the surface of the NW plasma. Cross sections of the electron density distribution in units of the critical electron density ${n_{{\textit ecr}}} = 7 \times {10^{21}}\;{{\rm cm}^{- 3}}$, averaged along the wire axis. The frame times are (g) $t = - {26}\;{{\rm T}_0}$, (h) $t = - {13}\;{{\rm T}_0}$, (i) $t = - {7}\;{{\rm T}_0}$, and (j) $t = {8}\;{{\rm T}_0}$. Reproduced with permission from Figs. 2, 4, and 5, Kaymak et al., Phys. Rev. Lett. 117, 035004 (2016) [50] by the American Physical Society.

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In an experimental and simulation study [104] at highly relativistic intensities (${a_o} = {21}$), nano and microwire electrons with energies of up to 60 MeV were observed to be guided via the self-induced giant magnetic and electric fields. In the experiments, pulses with only a moderate contrast (${{10}^{- 9}}$ at the 10s of the ps level) were used, indicating that the structures were perhaps robust enough to survive the prepulse levels.

D. Plasma Compression: Ultra-Dense Nanoscale Z-Pinch

Simulations show that NWs irradiated by femtosecond laser pulses of a highly relativistic intensity (${\sim}5 \times {10^{21}}\;{\rm W}\;{{\rm cm}^{- 2}}$) can drive a new kind of dense Z-pinch with nanometer-scale radial dimension and ultra-high plasma density, ${n_e} \gt 9 \times {10^{24}}\;{{\rm cm}^{- 2}}$ [50]. The 3-D PIC simulations demonstrate that the laser pulse drives a forward electron current in the area around the wires. The resulting charge separation induces return current densities of ${\sim} {0.1}$ Giga-amperes per ${\unicode{x00B5} \rm m}^2$ through the wires. In turn, this large return current generates a strong quasi-static azimuthal magnetic field surrounding the NW, whose strength reaches several Giga-gauss [Figs. 9(a) and 9(b)] [50]. The resulting Lorentz force compresses the NWs into extremely hot and dense plasmas where the electron density reaches values 1000 times larger than the critical density [Fig. 9(i)]. This density exceeds those in Z-pinches generated by large pulse power machines [105,106] and micro-capillary discharges [107] by more than 3 orders of magnitude.

E. Electron Acceleration

In laser–matter interactions at relativistic intensities, electrons are rapidly ripped from their parent atoms and accelerated to relativistic energies [108]. The resulting relativistic electron beams, in turn, drive processes such as proton acceleration [109–111], heavy ion acceleration [112–114], positron generation [115,116], and bright x-ray and gamma-ray beams [117–120]. All these processes depend upon a high charge, high energy electron distribution, and therefore the efficient coupling of the laser energy into electrons. Measurements and simulations of the hot electron distribution from structured targets, such as CNT [99], microchannel plates [121], wavelength-scale microwires [104,122,123], grating [124–127], and sub-wavelength nanowire [122,128–131], have all shown enhanced electron acceleration.

Grating targets irradiated at ${{\rm I}_L} \gt {10}^{{19}}\;{\rm W}\;{{\rm cm}^{- 2}}$ with ultra-high contrast pulses at incidence angles close to the resonant condition for surface plasmons demonstrate strong electron emission with energy spectra peaking at 5–8 MeV and with a total charge of ${\sim} {100}\;{\rm pC}$ [132]. Both these quantities are strongly increased with respect to a flat target. Experiments conducted with silicon NW arrays generated electron pulses in the 0.2–0.8 MeV energy range with a yield 30 times higher than that of a plane surface [128]. Irradiation of Si array targets at higher intensities, ${1} \times {{10}^{21}}\;{\rm W}\;{{\rm cm}^{- 2}}$, and accompanying PIC simulations showed a great increase in the number of electrons and their cutoff energy of (60–70 MeV) with respect to flat targets [104]. Another experiment conducted irradiating near-solid density arrays of aligned deuterated polyethylene (${{\rm CD}_2}$) NWs at ${I_L} \gt {1} \times {{10}^{21}}\;{\rm W}\;{{\rm cm}^{- 2}}$ with high contrast pulses also demonstrating greatly increased (22.4x) electron flux in comparison to foil targets of the same material, as well as a 3 times increase in the hot electron temperature [133]. PIC simulations show that electrons originating anywhere along the NW length are first driven toward the laser to reach a lower density plasma region near the tip of the nanowires, where they are accelerated to the highest energies. Electrons that reach this lower density plasma experience direct laser acceleration up to the dephasing length, where they outrun the laser pulse. The NW array cutoff energy was measured to reach ${\sim} {19}\;{\rm MeV}$ compared to ${\sim} {10}\;{\rm MeV}$ for a foil target [133].

F. Ion Acceleration

A direct consequence of electron acceleration is the acceleration of ions. Beams of energetic ions are of interest for hadron therapy [134], fast ignition nuclear fusion schemes [135–137], and other applications. Early experiments in laser-induced ion acceleration that were conducted irradiating bulk and foil targets with intense laser pulses resulted in the acceleration of ions to MeV per nucleon [138,139]. In the year 2000, ion beams with energies of several tens of MeV and various degrees of collimation were reported to arise from the so-called target normal sheath acceleration (TNSA) mechanism, where ions are accelerated in a large electrostatic field associated with the space charge buildup resulting from the displacement of electrons [140]. In TNSA, electrons that are accelerated to relativistic velocities by the laser field ${\rm J} \times {\rm B}$ force typically ionize the atoms in the rear surface of the target and propagate away, forming the space charge sheath in which the ions are accelerated. Highly ionized heavy ions (${{\rm Au}^{+ 51}}$ extending to ${{\rm Au}^{+ 61}}$) were accelerated up to 1.2 GeV by irradiating a double-layer target composed of a thin Au foil and a carbon nanotube foam at an intensity of ${1} \times {10}^{{22}}\;{\rm W}\;{{\rm cm}^{- 2}}$ [24]. Other ion acceleration mechanisms, including radiation pressure acceleration, also exist in which an ultra-short relativistic ion beam is generated from a thin foil with an ultra-intense electromagnetic wave [141].

The enhanced electron acceleration that takes place in the NW arrays results in the efficient acceleration of ions [142–144]. In turn, this process can lead to the generation of flashes of neutrons resulting from D-D nuclear fusion reactions caused by deuterons accelerated in ${{\rm CD}_2}$ NW arrays [142,145]. Figures 10(a)–10(c) show the computed spatio-temporal energy distribution of energetic deuterons in an array of 400 nm diameter ${{\rm CD}_2}$ NWs irradiated at an intensity of ${8} \times {{10}^{19}}\;{\rm W}\;{{\rm cm}^{- 2}}$ by laser pulses of 60 fs duration. The computed electron density reaches ${6.4} \times {{10}^{22}}\;{{\rm cm}^{- 3}}$. Measured ion spectra show deuteron energies up to 3 MeV [Fig. 10(e)] in comparison with only 0.5 MeV for flat ${{\rm CD}_2}$ targets [Fig. 10(d)].

 

Fig. 10. (a)–(c) 3D PIC simulation of energy distribution of energetic deuterons at different times, in an array of 400 nm diameter ${{\rm CD}_2}$ NW 16% of solid density irradiated at an intensity of ${8} \times {{10}^{19}}\;{\rm W}\;{{\rm cm}^{- 2}}$ by laser pulses of 60 fs duration. Times are measured with respect to the peak of the laser pulse. (d) Measured single-shot Thomson parabola ion energy spectra for a flat target (e) and for a ${{\rm CD}_2}$ NW target. Reproduced with permission from [145].

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Further increase of the laser intensity to ${3} \times {{10}^{21}}\;{\rm W}\;{{\rm cm}^{- 2}}$ produced well collimated high energy deuteron/proton beams propagating in the laser backward direction. The angular distribution of ions with energy ${\gt} {13}\;{\rm MeV}$ was measured to be highly directional and was contained within a 7.5° FWHM cone [Fig. 11(b)].

 

Fig. 11. (a) Setup to measure energy and angular distribution of deuterons/protons from a ${{\rm CD}_2}$ NW array accelerated in the laser backward direction using an array of filtered CR-39 detectors mounted in a semi-circle positioned at 10 cm from the target. (b) Angular distribution of ions with energy ${\gt} {13}\;{\rm MeV}$ contained in a 7.5° FWHM emission cone. The inserts are microscope images of ion traces in developed CR-39 detectors corresponding to different angles. The data were obtained with the 250-µm-Cu filter. (c) Angular distribution comparison between the nanowire and the solid density ${{\rm CD}_2}$ flat target. The measurement was conducted using 100-µm-Cu filters, with select ion energies ${\gt}{7.5}\;{\rm MeV}$. Adapted with permission from [142].

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The much larger flux from the NW target compared to a solid density ${{\rm CD}_2}$ flat target is shown in Fig. 11(c). At these highly relativistic intensities, the tip of the NWs rapidly explodes to form an overdense plasma prior to the arrival of the peak of the laser pulse. However, as the laser intensity approaches its peak value, the onset of relativistic transparency enables the ultra-short laser pulse to penetrate deep into the NW array. This, in turn, expands the region of interaction, producing the relativistic electron currents necessary to generate a substantial target normal sheath acceleration (TNSA) field of ${2} \times {{10}^{11}}\;{\rm V}\;{{\rm cm}^{- 1}}$ [Fig. 12(a)] at the target front. This field propels the front-side acceleration of deuterons to high energies. The PIC simulation in Fig. 12(b) shows a highly collimated deuteron beam in the laser backward direction. This is consistent with the experiment, which shows that the ions with the highest energy exhibit a minimal divergence of less than 10 deg FWHM. In addition to this TNSA field located in front of the NWs, which accelerates ions backward toward the laser, the simulations reveal the existence of an internal TNSA field within the NW array itself that drives ions radially. This radial quasistatic field that surrounds each NW is created by the laser-field-induced displacement of electrons from the NWs surfaces into the voids. Figure 12(c) displays the observable effect of the radial acceleration resulting from this internal TNSA field. At a significant depth into the NW array, these radially accelerated deuterons are also bent toward the ${{\rm CD}_2}$ substrate by an internal axial field.

 

Fig. 12. PIC simulations of ion acceleration in the nanowire array. (a) Electric field distribution in the nanowire axial (longitudinal) direction in an array of 200 nm diameter with 19% solid density ${{\rm CD}_2}$ NWs, 30 fs after the arrival of the peak of the 45 fs FWHM laser pulse to the NW tips. A TNSA field develops near the top of the array that accelerates ions in the laser backward direction. (b) Trajectories of deuterons from the exploding nanowire tips accelerated in the laser backward direction. (c) Trajectories of radially accelerated ions, which lead to D-D fusions. Reproduced with permission from [142].

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Furthermore, simulations forecast that using a thinner substrate would lead to the creation of an ion beam propagating in the forward direction. Electrons accelerated forward by the laser field traverse the thin substrate producing a quasi-static TNSA field at the back of the target. This field, which extends several microns, accelerates ions in the forward direction. Proton energies up to 20 MeV are predicted for a 1-µm-thick ${{\rm CD}_2}$ target substrate, which could be increased further by optimizing the NW parameters. For laser pulses at highly relativistic intensities, strong self-focusing is predicted to significantly increase the laser field magnitude on the axis. This results in a 2–3 times increase in the relativistic critical density and the relativistic gamma factor on the axis, leading to further enhancement of the plasma’s relativistic transparency along the laser axis. As a result, the laser intensity reaching the substrate is increased by almost an order of magnitude and is focused toward a very small sub-micrometer diameter central area from where highly collimated deuteron/proton beams emanate.

G. Micro-Scale Fusion and Neutron Generation

As demonstrated above, laser-irradiated nanostructure arrays act as micro-accelerators of high energy ions that can induce nuclear fusion reactions, producing high energy neutrons [145] and alpha particles [146]. Multi-kilojoule lasers drive spherical compressions where fusion reactions produce copious amounts of neutrons. However, they are currently limited by a low shot repetition rate, typically only one shot per hour. Recent advances in laser technology have enabled the production of fusion reactions with compact lasers that can be fired at much higher repetition rates. These advancements have significant implications for neutron pulse generation and for applications in neutron imaging and tomography, neutron scattering and diffraction for material structure and dynamics studies, as well as neutron and neutrino detector development. Experiments with compact femtosecond lasers have explored a variety of fusion target geometries and densities, including deuterated thin films [147], cryogenic ${{\rm D}_2}$ [148], deuterated clusters [149–153], and deuterated water jets [154].

 

Fig. 13. (a) Comparison of TOF neutron signals from a ${{\rm CD}_2}$ nanowire array target and a flat target. The flat target neutron signal (in red) was multiplied by 10 for clarity. The ratio of the average neutron yield of eleven nanowire shots to the average yield of six flat target shots at the same irradiation conditions yielded a value of 492. Adapted with permission from [145]. (b) The computed neutron number varies with the laser pulse energy. The trend of neutron production shifts from being supra-linear to more linear as energy increases. Reproduced with permission from [142].

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The ultra-fast irradiation of aligned NW arrays has the advantage of deeply penetrating the laser pulse into the NW, which leads to the acceleration of the electrons toward the substrate and radially from each nanowire, creating space charge fields. The deuterons near the tips are accelerated toward the laser by the field at the target front, while an internal radial TNSA field surrounding each of the NWs accelerates a larger number of ions radially. Experiments conducted at the ALEPH laser facility irradiating ordered ${{\rm CD}_2}$ NW arrays with femtosecond pulses at relativistic intensities demonstrated that 1.6 J pulses focused to an intensity of ${8} \times {{10}^{19}}\;{\rm W}\;{{\rm cm}^{- 2}}$ [145] accelerates deuterons to multi-MeV energies, resulting in microscale fusion. Up to ${2} \times {{10}^6}$ D-D fusion neutrons per joule were measured using an array of calibrated scintillator/photomultiplier detectors. Figure 13 shows the observation of a ${\sim}{500}$ times increase in the number of 2.45 MeV D-D neutrons produced as compared to the flat ${{\rm CD}_2}$ targets irradiated with the same laser pulses [145]. Later experiments at increased laser energies up to 8 J and intensities up to ${\sim}{3} \times {{10}^{21}}\;{\rm W}\;{{\rm cm}^{- 2}}$ generated up to ${1.2} \times {{10}^7}$ D-D fusion neutrons per shot [145]. By utilizing the deuteron momentum distribution obtained from the PIC code, the number of neutrons produced per deuteron was calculated by considering the stopping power of deuterons in the ${{\rm CD}_2}$ NWs and the substrate. The results show that at the lower irradiation intensities the increase in neutron creation with laser intensity exhibits a supralinear growth in agreement with experiments, which is linked to the rapid rise of the D-D fusion reaction cross section with increased deuteron energy. Nevertheless, as laser energy surpassed 5 J and the intensity reached a more highly relativistic intensity range, the relationship became nearly linear. In the experiment, up to ${1.2} \times {{10}^7}$ 2.45 MeV D-D fusion neutrons were detected. An experiment designed to reproduce these ${{\rm CD}_2}$ NW results was conducted at a different facility (CLAPA) using a lower intensity of ${3.8} \times {10}{\;^{19}}\;{\rm W}\;{{\rm cm}^{- 2}}$ on a larger spot size of 4.5 µm FWHM diameter. Measurements using a hybrid semiconductor pixelated detector covered with neutron converters reported a higher number of neutrons, ${2.4} \times {{10}^7}$ for 1 J of incoming laser energy [155].

H. Going to Longer Laser Wavelengths

We briefly discuss the possibility to leverage relativistic interaction between light and nanostructures by exploding high-intensity femtosecond laser pulses in the mid-infrared (mid-IR) spectrum (e.g., 3.9 µm wavelength). In the plasma generated by these lasers, electrons attain relativistic energies even at relatively modest intensities, thanks to the advantageous ${\lambda ^2}$ scaling of kinetic energy with laser wavelength. This lower intensity effectively suppresses optical field ionization and the formation of a pre-plasma during the initial phase of the laser pulse, facilitating more efficient vacuum heating of the plasma. To overcome the lower critical plasma density for long-wavelength radiation, flat targets can be substituted by NW arrays. Numerical simulations, which align with experimental results, indicate that approximately 80% of the incident laser energy can be absorbed, resulting in the creation of a long-lasting plasma with temperatures in the keV range and high charge states. This plasma boasts a density exceeding the critical value by more than three orders of magnitude.

Achieving high-density and finely tuned spatial gradients in plasmas when utilizing intensely relativistic, ultra-short laser pulses hinges on meeting stringent requirements for temporal contrast. A well-maintained temporal contrast is essential for efficient vacuum heating, where the laser energy is absorbed by the plasma, resulting in the generation of high-temperature, dense plasmas.

In the case of near-infrared (near-IR) lasers commonly employed for relativistic laser-solid interactions, the demand for exceptional temporal contrast leads to the necessity of frequency, doubling the output radiation. The short wavelength requires a larger intensity to access the relativistic regime (e.g., $8.7 \times {10^{18}}\;{\rm W}\;{{\rm cm}^{- 2}}$ for $\lambda = 0.4\;{\unicode{x00B5}{\rm m}}$). Instead, when working with mid-IR laser frequencies, the required intensity decreases substantially (e.g., $9.1 \times {10^{16}}\;{\rm W}\;{{\rm cm}^{- 2}}$ for $\lambda = 3.9\;{\unicode{x00B5}{\rm m}}$), and the associated ionization rate is diminished. The reduction in the ionization rate is particularly noticeable when compared to laser sources operating in the visible or UV regions. These characteristics collectively alleviate the issue of pre-plasma formation and promote the achievement of well-defined spatial gradients in plasma density. Notably, mid-IR femtosecond driver pulses have proven advantageous in enhancing the efficiency of vacuum heating for solid targets during nonrelativistic interactions.

Experiments with a high-energy OPCPA laser system, which emits 90-femtosecond laser pulses at an idler wavelength of 3.9 µm were conducted at the Institute of Optics and Quantum Electronics, Friedrich-Schiller-University Jena [78]. These laser pulses with an energy of up to 25 mJ delivered a maximum peak intensity on target of approximately ${10^{17}}\;{\rm W}\;{{\rm cm}^{- 2}}$, resulting in a maximum value for the relativistic laser amplitude ${a_0} \approx 1.1$. The samples used in the experiments consisted of arrays of single-crystalline silicon nanowires (Si NWs) positioned on a silicon substrate. These nanowire arrays exhibit transparency across a wide spectral range spanning from 1.2 to 7 µm. Each individual nanowire had a length of 6 µm and a diameter of 200 nm. The gap or spacing between adjacent nanowires was approximately 100 nm. As a point of reference, a polished silicon wafer with a thickness of 500 µm was used.

The experiment has revealed a significant rise in the line emission from highly charged ions when using nanowire arrays, as opposed to a flat target. According to PIC simulations, a maximum temperature of ${\sim} 600\;{\rm eV}$ is attained within an approximately 1-µm-thick layer at the tip of the wires during the interaction with the laser pulse. After the laser pulse, the entire wire volume is heated almost homogeneously to approximately 50 eV. At the time of 300 fs after the peak of the laser pulse, the electron density in the NW volume reaches ${n_{e}}\sim 3 \times {10^{23}}\;{{\rm cm}^{- 3}}$ and the electron temperature thermalizes to ${\sim} {30}\;{\rm eV}$. Considering that the critical density at $\lambda = 3.9\;{\unicode{x00B5}{\rm m}}$ is $n_{\textit{ecr}} \approx 7 \times {10^{19}}\;{{\rm cm}^{- 3}}$, the simulations suggest that plasma as dense as ${n_e}\sim5 \times {10^3}{n_{\textit{ecr}}}$ is generated under the conditions of the experiment. Simulations also show that on a scale of ${\sim}{3}\;{\rm ps}$, the wires stay intact and high plasma density is maintained. As discussed in [78], this timescale is significantly longer than the femtosecond timescale of the wire explosion predicted for short-wavelength laser experiments [4,45,46]. Simulations indicate that at high values of ${a_0}$, the pinching of the electron current, propelled by a relativistically intense laser pulse along the wire, can efficiently heat electrons and boost plasma density [50]. This, in turn, significantly accelerates the hydrodynamic expansion of the plasma [4]. The amplitude of the fields responsible for the pinch effect scales with the laser wavelength as ${\lambda ^{- 1}}$. Furthermore, the number of forward-driven electrons is proportional to the critical density associated with the laser wavelength that scales as ${\lambda ^{- 2}}$. Simple estimates show that for long-wavelength laser sources, the laser-induced electron currents are too low to cause a significant pinching effect. Therefore, the unprecedentedly long lifetime of overdense plasma predicted under the condition of the experiment is due to the long laser wavelength.

The $\approx 1\;{\unicode{x00B5}{\rm m}}$ depth of the high-density and high-temperature plasma region is determined by the penetration depth of the laser pulses into the NW array which, in turn, is limited by the absorption. The simulations predict 76% absorption efficiency of the laser energy, which is concentrated mostly within the $\approx 1\;{\unicode{x00B5}{\rm m}}$ layer (for 20-mJ laser pulse energy) due to an extremely high ${n_e}/{n_{\textit{ecr}}}$ ratio.

4. NANOWIRE ARRAY TARGET FABRICATION

Targets consisting of both metallic and plastic (e.g. polyethylene) arrays of NWs can be fabricated [4,156]. The general technique consists of filling the pores of a template with the material of interest, followed by template dissolution. A critical drying process is used to preserve the NWs vertically aligned by avoiding their collapse, owing to surface tension. The pore diameter determines the NW diameter, and the density of pores sets the average density of the NWs. Anodic aluminum oxide (AAO) templates formed by electrochemical anodization of pure aluminum, which are commercially available with different pore densities, can be used with NW diameters of up to 200 nm. They consist of parallel arrays of holes surrounded by hexagonal cells of aluminum oxide that grow perpendicular to the metallic surface as the anodization advances, forming a structure that resembles a honeycomb [157,158]. For larger diameters (200 nm to 1000 nm), an ion track polycarbonate (PC) membrane, consisting of an arrangement of random distributed pores at different densities are used. The fabrication of metallic and deuterated polyethylene NW arrays is discussed in Supplement 1.

5. OUTLOOK AND FUTURE DIRECTIONS

The previous sections show that the interaction of intense laser pulses of ultra-short pulse duration with nanostructures have unique properties that include nearly full energy coupling, extreme electromagnetic fields, and efficient conversion into high fluxes of energetic photons and particle beams that open the door to applications in several areas. Some of these are discussed below.

A. Fusion Energy

An important scientific and technological challenge of great societal impact is the generation of clean energy by laser-driven fusion. Nuclear fusion is the process that powers the stars. Laser-driven fusion, known as inertial fusion energy (IFE), has the potential to safely produce practically inexhaustible carbon free energy from small footprint power plants. Nanostructured arrays irradiated with intense, ultra-short laser pulses represent a unique fusion platform, benefiting from the aforementioned increased laser coupling, volumetric heating and efficient local ion acceleration. The 2022 breakthrough demonstration of ignition at the National Ignition Facility (NIF) at Lawrence Livermore National Laboratory showed the viability of ICF for energy production [10]. IFE is the first and, so far, the only approach that has achieved energy gain. The NIF experiments demonstrated a capsule gain greater than unity [159], a burning fusion plasma [9,160], and the production of 3 MJ of fusion yield from 2 MJ of laser energy [10]. A subsequent 2023 experiment demonstrated a fusion energy output of 3.88 MJ and a target gain $({{\rm E}_{{\rm Fusion}}}/{{\rm E}_{{\rm Laser}}}) = {1.9}$. An ICF target can be thought of as an imploding rocket that is energized by a laser [161]. In the NIF experiment this was achieved using the laser indirect drive configuration in which the laser energy is converted to x rays in a high atomic number cylindrical radiation enclosure known as a hohlraum. The hohlraum contains, in the center, a spherical capsule with the nuclear fuel in the form of a deuterium-tritium (DT) ice layer. The x rays are absorbed within the spherical fusion capsule, which is surrounded by an ablator shell. In response to the ablation pressure, there is a rocket-like inward acceleration, which accelerates the shell to velocities $\ge {10^{- 3}}$ of the speed of light (300–500 km/s). The central DT vapor core reaches temperatures of 5–10 keV as a result of the combined effects of PdV work and alpha particle energy deposition. The heat flux from this hot central plasma ablates fuel from the inner surface of the shell, forming a low-density hot spot that is confined for a sub-nanosecond time by the up to ${1}\;{\rm Kg}\;{{\rm cm}^{- 3}}$ density shell. During this time fusion reactions occur, and alpha particle heating amplifies the fusion reaction rate. This process [162,163] can become intense enough to ignite the central hot spot. At this point, under the proper conditions of temperature, pressure, and confinement time [164,165], a thermonuclear burn wave is initiated [166] that propagates radially, igniting the surrounding dense fuel and creating a burning plasma that is sustained without an external energy source and producing fusion energy yields many times greater than the laser energy input.

Despite the major scientific and technical achievement of the breakthrough NIF experiments, significant challenges remain to scale to the gain and efficiency that is required for a power plant. An important metric is the product of the driver laser efficiency $\eta$ (laser output energy/input energy) and the target gain G. In the NIF experiments, where the laser is pumped inefficiently by flash lamps, $\eta$ is less than 1% and $\eta G \lesssim 0.02$. An IFE power plant will require $\eta {\rm G} \gt {10}$. Also, in the NIF experiment only about 1–2% of the laser pulse energy was transferred to the nuclear fuel in the form of inward kinetic energy. Approaches are required that can efficiently deliver greater energy to nuclear fuel and operate at a significantly higher repetition rate (1–10 Hz), while utilizing cost-effective targets suitable for mass production. A direct-drive scheme in which the laser beams directly compress and heat the capsule has also been investigated for decades [166,167]. Recent direct drive layer cryogenic target implosion experiments with the OMEGA laser at the Laboratory of Laser Energetics at the University of Rochester produced a hot spot pressure of 85 Gbar. Direct drive has the potential for increased efficiency but also has its own challenges.

 

Fig. 14. Schematic diagram of a 2-D fusion reactor concept in which an array of intense femtosecond laser pulses (blue beams) irradiates a target composed of embedded nanorods to efficiently accelerate a stream of ions to 0.1–2 MeV energies. The yellow lines are the ion trajectories. Ions impinge on a fuel shell (gray). The same concept can also be implemented using a 3-D configuration. A cylindrical fuel shell is included for illustration purposes. Inspired by Fig. 1 from [168].

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As shown above, nanostructures can very efficiently couple laser energy into materials resulting in extreme energy densities [49]. Experiments and simulations have also demonstrated that the interaction of intense high contrast femtosecond laser pulses with high aspect ratio nanostructures result in the acceleration of ions to MeV energies, leading to nuclear fusion [142,145]. An initial demonstration of D-D fusion using arrays of aligned nanowires that accelerated deuterons to MeV energies [145] have been followed by the development of fusion energy concepts that relies on the efficient conversion of laser energy into ion kinetic energy and its subsequent deposition into fusible materials [168–170]. Figure 14 illustrates a fusion reactor concept developed by Marvel Fusion in which an array of intense ultra-short pulse lasers irradiates a target composed of embedded nanostructures to efficiently accelerate a converging stream of ions with energies ranging from 0.1 MeV to a few MeVs to match the peak of fusion cross sections. Each laser pulse can irradiate a large number of nanorods, each of which releases a large number of accelerated ions. The macro nano structured ion accelerator accelerates ions in about 500 fs using an array of about 1000 individual lasers. The design is envisioned to be capable of generating ionic implosion velocities and flow pressures that are orders of magnitude larger than those achieved with thermal ablation [168]. There are conceptual similarities between this scheme and the direct drive ICF approach, and it is postulated that potentially significantly larger energy densities can be achieved with higher coupling efficiency. Modeling suggests that ${\gt} {60}\%$ of the deposited laser energy can be converted into ion kinetic energy. It is envisioned that in this concept direct-drive-like fast fuel heating occurs on a timescale much shorter than the effective confinement time of the reactor. It is assumed that the fuel can be heated such that in situ fuel compression can be avoided. The laser systems required are based on solid-state laser technology that scale favorably in repetition rates with the wall-plug efficiencies required for IFE.

Of particular interest for fusion energy production are high activation energy aneutronic fuels like ${{\rm p}^{11}}{\rm B}$ [146,168]. Experiments have been conducted in which a boron nitride (BN) nanotube target created a proton beam with five times the maximum energy and two orders of magnitude higher flux of 1 MeV proton flux than a foil target of the same material [146]. In addition, a pBDT mixed fuel approach has also been proposed [169,171] in which boron-based chemical compounds are capable of chemically binding DT and where the boron is involved only marginally in the fusion reactions. The predominant role of boron is to avoid the need for cryogenic DT, simplifying the target and reducing costs. This nanostructure-based ion acceleration approach can also potentially find utility as a fast ignitor for targets compressed by nanosecond lasers [170]. Beyond IFE, it has also been suggested that the interaction of a new generation of lasers with ten petawatt peak power with nanostructures will give the opportunity to investigate nuclear reactions of interest for astrophysics [172].

B. Control of Instabilities by Nanostructures

A question arises on the ability of the NWs to transport large currents. The answer may lie in the understanding that the finite size of the nanostructures hinders the transverse interaction, opposing the Weibel instability and filamentation. An analytical and computational study of this problem sought to answer this by postulating that ripples in charge density caused by the NWs around their locations interfere with the fluctuations that cause the instability [173]. Under appropriate conditions (size of the nanostrutures and plasma temperature), the instability can be completely quenched, leading to suppression of filamentation and instabilities. Another interesting aspect of extreme contrast pulses (well above ${{10}^{- 10}}$) may run counter to the usual expectation that the NWs may be destroyed on the rising edge of the relativistic intensity pulse. Simulations described in Section 3.D have shown that the NW can, in fact, be compressed [50,51]. This raises the exciting possibility that the extreme contrast pulse can stabilize and excite the NWs producing the largest current densities, the largest magnetic magnitudes, and the highest magnetic pressures encountered only in stellar environments. This is of interest for applications that include IFE.

C. Synchrotron X-ray Emission

The interaction of highly relativistic beams with ordered nanowire arrays has been predicted to generate bright synchrotron emission [174–177]. This radiation is primarily driven by high energy electrons extracted from the nanowire array, which undergo collective betatron resonance in the copropagating laser field between the nanowires. This contrasts with the x-ray sources by the laser nanowire interactions discussed above in which the picosecond duration emission is dominantly by line radiation and bremsstrahlung. Synchrotron x-ray sources tend to be beam-like in nature, which increases their overall brightness. They have a duration similar to the laser pulse, in the case of interest here femtoseconds. For example, at intensities of ${{10}^{22}}\;{\rm W}\;{{\rm cm}^{- 2}}$, PIC simulations predict a conversion efficiency of 10% into x rays with photon energy ${\gt} {10}\;{\rm keV}$ and 6% into x-rays ${\gt} {1}\;{\rm MeV}$ for 36–50 nm diameter nanowires with a spacing of 1 µm [174]. The scaling of this effect is predicted to be ${\sim}{I_L}^{5/2}$ under optimal parameters [166]. At even higher intensities, ${8} \times {{10}^{23}}\;{\rm W}\;{{\rm cm}^{- 2}}$, 27% of the laser energy is predicted to be transferred into an x-ray pulse with a sub-femtosecond pulse width (${\sim}{440}\;{\rm as}$) and ultra-brilliant ${\sim}{{10}^{24}}$ photons ${{\rm s}^{- 1}}\;{{\rm mm}^{- 2}}\;{{\rm mrad}^{- 2}}$ per 0.1% BW at 15 MeV [176]. In an alternative experimental scheme, a laser wakefield accelerated electron beam was considered to co-propagate with the drive laser into an array of nanowires effectively creating an undulator, which generates a tunable (10–100 keV) beam of bright x rays [177].

With the current development of high-contrast lasers with intensities ${\gt}{{10}^{22}}\;{\rm W}\;{{\rm cm}^{- 2}}$, this will constitute an active field of research for laser driven ultra-bright x-ray source development. Over the next decade, results are expected to move from the domain of simulations to the experimental arena, potentially generating novel laser driven sources of directed x rays.

D. Extreme Degrees of Ionization

PIC simulations predict that irradiation of solid targets with similar intensity to those used to ionize gold to ${{\rm Au}^{+ 72}}$ (e.g., ${3 - 4} \times {{10}^{21}}\;{\rm W}\;{{\rm cm}^{- 2}}$, Section 2.B) but over a larger spot will create solid density plasmas in which atoms with an atomic number between $Z = {79}$ to $Z = {92}$ will be ionized up to He-like over even larger penetration depths (for the case of He-like Au see Extended Data Fig. 5 in [53]). This further increase in degree of ionization will result from the reduced plasma expansion rate associated with the larger plasma volume, which will make it possible to sustain an extremely hot plasma with a density close to the relativistic critical density for a longer time. The minimum spot size required to reach the He-like ionization state is estimated at 5 µm. These unprecedented degrees of ionization in solid density and near-solid density plasmas will create the opportunity to study the atomic physics of highly charged atoms in very high-density plasmas. This includes, for example, phenomena such as line broadening, line shifts, and continuum lowering. These unique plasmas might also enable the generation of beams of highly charged ions and more efficient x-ray sources.

E. Generation of Terabar Pressures

Another frontier enabled by the irradiation of nanostructure arrays with multi-Petawatt lasers is the generation of ultra-high pressures with relatively modest laser pulse energies. PIC simulations predict that laser irradiation at intensities ${\gt}{1} \times {{10}^{22}}\;{\rm W}\;{{\rm cm}^{- 2}}$ (${a_{o}} \gt {34}$) will generate unprecedented energy densities and pressures [49]. Figure 7 in [49] shows that an array of 400 nm diameter Au nanowires of 12% solid density irradiated at this intensity with a 30-fs duration pulse is predicted to reach a density of $2 \times 10^{25}\;{\rm cm}^{ - 3}$ during the nano-scale pinch compression phase, which corresponds to nearly 3200 times the critical density. Other laser-target configurations could reach 9000 times the critical densitiy, $6 \times 10^{25}\;{\rm cm}^{ - 3}$, during the nano-pinch [49]. Such extreme peak densities approach those obtained in the fusion hot spots created using megajoule laser energies in early experiments at NIF [178] but with temperatures that are potentially higher. The energy density within the nanowires is predicted to reach a peak value of ${2}\;{\rm TJ}\;{{\rm cm}^{- 3}}$, equivalent to a pressure of 7 Tbar near the end of the laser pulse. The expansion of the exploding nanowires is computed to potentially create a plasma layer in which the energy density is ${80}\;{\rm GJ}\;{{\rm cm}^{- 3}}$, equivalent to a 0.35 Tbar pressure, larger than that found in the solar interior. An extension of this prediction to intensities of ${1} \times {{10}^{23}}\;{\rm W}\;{{\rm cm}^{- 3}}$ showed that the expanded plasma following the z-pinch becomes relativistically transparent and compresses longitudinally by the oscillating component of the ponderomotive force, resulting in simulated pressures of 40 Tbar [52].