1. Introduction

Biological systems are rich in structure at the micro- and nano-level and investigations of structure-function relationships continue to provide exciting insights [1]. Scientific capabilities to image these structures have been on an explosive growth [2], particularly in the x-ray regime, with tremendous strides made in terms of both spatial and temporal resolution [3, 4, 5, 6]. Ultrafast x-ray pulses driven by table-top intense lasers in the visible-infrared regime have now become available. The crucial factor that controls the x-ray luminosity is obviously the laser energy absorption. The absorption process has been modelled using a plethora of mechanisms, some with wide applicability, and some restricted to specific laser and target irradiation conditions. It is however widely accepted that a hot dense plasma, which is the source of the ultrashort x-ray pulses, energetic electrons and ions, absorbs a significant amount of laser light via collective mechanisms, with plasma-wave excitation as the basic step [7, 8]. The plasma wave of frequency ω_p equals the frequency ω of the light wave in a process of linear resonance (analogous to a driven linear harmonic oscillator) and eventually gives off the energy to the plasma electrons via ‘wave-breaking’ [9]. The resulting ‘hot’ electrons are the prime carriers of the bulk of the absorbed laser energy and can radiate out photons with energies up to the hard x-ray regime or result in the generation of mega-electron-volt (MeV) energy ion beams. However, during the illumination of a target by an intense laser, the plasma frequency exceeds several times the laser frequency in a time-scale much faster than the laser-period and hence the frequency-matching condition ω_p = ω necessary for linear resonance is only satisfied in a specific location of the plasma density gradient, thus making linear resonance less efficient.

Recently, an attempt has been made to unify the various absorption mechanisms with the proposal that under intense femtosecond laser illumination, the self-consistent electrostatic potential experienced by an electron localized in the laser-interaction zone becomes strongly an-harmonic due to modulations in the plasma density and sharp vacuum-plasma interfaces. As the electron is driven along the intensity-gradient at the rising edge of the incident laser pulse, its position-dependent frequency Ω[r(t)] in the anharmonic potential may match the laser frequency ω. Under such circumstances, anharmonic resonance (AHR) occurs and the laser energy is transferred to the electron, as shown in the schematic in Fig. 1. Simulations show that this AHR is expected to be universal and aided by plasma inhomogeneities and density gradients [8, 10, 11, 12, 13, 14]. Here, we provide the first conclusive evidence for the AHR absorption mechanism. Interestingly, it turns out that the micro- and nanostructures that are naturally found in a bacterial system prove to be great facilitators of the AHR process. We report how density modulations created by micron-scale bacteria doped with silver-chloride nanoparticles result in a 10⁴-fold enhancement in the hard x-ray emission, compared to a plain solid target.

 

Fig. 1 (a) Schematic of the experimental as well as simulation setup. (b) Schematic of AHR for an electron in a potential well, with (blue) and without (green) a density modulation. The dashed line represents the condition Ω[r(t)]/ω = 1, where AHR occurs. The potential well with the density modulation is deeper due to a higher plasma frequency and the electron needs to make several excursions in order to meet the resonance criterion, as indicated by the classical electron trajectories. In other words, the electron is more localized in the deeper potential well, resulting in a higher degree of absorption of the laser energy.

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2. Experiment

We used a femtosecond laser source (40 fs, 800 nm) focused with an f/3 off-axis parabolic mirror at a 45° angle of incidence to a 17 μm diameter focal spot on the target. The nanosecond prepulse contrast was 5 × 10⁻⁶. The target was rastered such that every laser pulse was incident on a different spot on the target. The x-ray measurements were carried out with a thallium-doped sodium-iodide scintillation detector coupled with conventional electronics under pile-up free conditions (<1 count per 10 pulses). A magnet electron spectrometer [20], which has a dispersing magnet of strength 0.1 T and is capable of detecting electrons in the energy range (0.1 – 7.0) MeV, was positioned along the target-normal direction at a distance of 80 cm from the target. The dispersed electron trace was obtained on a Fujifilm BAS-SR2025 image plate over a total of 100 laser shots.

E. coli cells are ellipsoidal in shape (∼ 1.8 μm × 0.7 μm) [21]. Each cell also possesses numerous flagella, 25 nm in diameter and (10–20) μm in length from the cell exterior [21]. DH5α strain of E. coli bacteria was grown overnight in a suspension culture in minimal media. We used both dead and alive (chemically fixed and UV-attenuated) bacterial cells. Though the effect is similar, most of the experiments were carried out with fixed and attenuated cells to avoid bio-hazard. Fixation was carried out using a mixture of 4% paraformaldehyde and 2.5% gluteraldehyde solutions, followed by an exposure to UV dose (250 mJ of 280–300 nm UV). The fixed E. coli cells were spread on a polished glass and dried. The cells remained structurally unaffected under a vacuum of 10⁻⁵ torr for hours. A profilometer scan showed that the bacterial coatings were uniform with height variations between (1–2) μm, which is equivalent to (2–3) layers of E. coli cells. The fixation process sheds the flagella and therefore only the ellipsoidal structure of the cells was exploited in the experiment. E. coli has no known subcellular structures. Hence, we assume that the majority of the 0.7 femtolitre volume is filled with optically uniform cytoplasm. For the purpose of this work, these cells can also be viewed as microparticles with well-defined sizes that are filled with low-Z atoms.

Silver-chloride (AgCl) nanoparticle-doped bacterial cells were prepared by suspending the E. coli cells, first in 10 mM Ca(NO₃)₂ solution at pH = 4, followed by incubation in 1 mM AgNO₃ solutions for about 2 hours, before fixation. E. coli cells act like nanofactories, producing rich nanoparticulate structures for the right protocol [22]. The TEM image (Fig. 4(a)) shows that the nanoparticle diameters were ≃ (22 ± 6) nm. X-ray diffraction pattern (not shown here) of the isolated nanoparticles extracted from the cells, matched with AgCl, strongly suggesting that these were AgCl nanoparticles. We speculate that AgNO₃ was absorbed in the cells and underwent ion-exchange reactions in the cells to form AgCl nanoparticles. The mass ratio of the Ag in the cells was found to be about 5% using x-ray fluorescence measurements. At this level of doping the cells are not lysed and ellipsoid structure of the cell is intact.

3. Results

As shown in Fig. 2, the spectrum for a polished uncoated glass target shows a hot electron temperature of (343 ± 14) keV, whereas the bacteria-coated glass target shows a hot electron temperature of (400 ± 4) keV under otherwise identical conditions. In addition, the integrated hot electron yield for the bacteria-coated target is nearly 70 times higher than that for the un-coated glass target. These hot-electron energy measurements are consistent with our earlier studies [15], which showed a 100-fold enhancement in hard x-ray bremsstrahlung emission from bacteria-coated targets compared to plain glass targets at a modest intensity of ∼ 10¹⁶ W/cm².

 

Fig. 2 (a) Experimentally measured hot electron spectra at an incident laser intensity of 3 × 10¹⁸ W/cm² for an uncoated glass target and a bacteria-coated target, under otherwise identical conditions. The hot electron temperatures are indicated on the plot. The integrated hot electron yield for the bacteria-coated target is 67 times that for the uncoated plain glass target. The data were collected over 100 laser shots. The low-energy cutoff is 250 keV. The inset shows the electron traces on the image-plate in the electron spectrometer. (b) The results of 2D PIC simulations considering ellipsoidal particles (simulating bacterial cells) of size 0.7 μm × 1.8 μm, placed on a plain solid substrate at an incident laser intensity of 10¹⁸ W/cm². The low-energy energy is 250 keV, as in the experiment.

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Laser-plasma generation with micro-particulate biological targets is very different from other ‘tailored’ targets hitherto used in laser-plasma studies. In earlier studies, it was shown that a plain solid target coated with nano-particles enhanced local electromagnetic fields by the “lightning rod effect”, leading to enhanced hot electron generation and x-ray emission [16]. The local electric-field enhancement in micron-sized bacterial cells, however, is rather small (a factor of 2–3) [15], compared to metallic nanostructures. In addition, the bacterial cells are not sufficiently large for efficient Mie focusing of the incident field [17], nor are they highly regular (as in a grating, for example) for the surface-plasmon mechanism to play a major role [18]. At laser intensities of ∼ 10¹⁸ W/cm², temperatures of about ∼ 185 keV have been observed in previous measurements [19, 7], attributed to resonance absorption or vacuum heating, depending on experimental conditions. These temperatures are significantly less than the observed electron temperature of ∼ 400 keV.

For a better understanding of the physical mechanism responsible for the observed enhancement in the hot electron generation, we performed fully-relativistic two-dimensional (2D) particle-in-cell (PIC) simulations. A plain solid substrate of dimensions 20λ × 5λ was used as the substrate, on which a number of ellipsoidal particles were placed adjacent to each other in order to simulate the bacterial cells. It is impossible to simulate the plasma formation from a complex system like biological cells but approximating the cell as an ellipsoidal particle is sufficient to derive key physics issues. At the intensities used in these experiments ionization and plasma dynamics dominate over all other aspects and the internal chemical structure of the cells is not a relevant feature. Typical bacterial cells are made up with 90% water, 3% lipid membrane that gives them the structure and the rest is protein and DNA. Since more than 90% of the atoms are H, C and O, for unraveling the physics of the laser-plasma it is sufficient to model the system as a low-Z (atomic number)-material packed in ellipsoidal shape of uniform plasma density.

The size of the ellipsoid was chosen to be 0.7 μm × 1.8 μm, similar to the bacterial cells used in the experiment. The system was illuminated by a Gaussian laser beam with parameters close to the experiment propagating in the y-direction and polarized along the x-direction. A uniform initial plasma density of 2n_c for the ellipsoids and 10n_c for the substrate (with stationary ions) was assumed, where n_c = 1.72 × 10²¹ cm⁻³ is the critical plasma density for the laser wavelength of 800 nm.

The hot electron spectra generated by the 2D PIC simulations with different numbers of ellipsoidal particles are shown in Fig. 2(b) and represent the high-energy component of the bi-Maxwellian hot electron distribution. For the plain solid substrate, the hot electron temperature is (290 ± 10) keV. The hot electron yield increases systematically as the number of ellipsoidal particles is increased. With nine ellipsoids, for example, the hot electron temperature is as high as ∼ 1 MeV and the integrated hot electron yield is about 25 times that of the solid substrate. A further increase in the number of ellipsoids in the simulation does not result in further enhancement since a maximum of nine ellipsoids could be contained within the focal region. Given the complexity of the morphology of the bacterial structures, our simple model of simulating bacterial cells by ellipsoidal particles gives a rather close reproduction of the experimental scenario.

4. Laser absorption by an anharmonically driven oscillator

Before we probe the mechanism responsible for the hot electron generation by following the dynamics of the electron motion driven by the laser, we present a brief overview of anharmonic resonance heating. As an example, consider a sphere of pre-ionized plasma of radius R with homogeneous charge density. It may mimic a few nano-meter interaction zone in front of a bacteria where laser interacts first. Initially, the center of the negatively charged electron sphere is assumed to coincide with the center of the positively charged immobile ion sphere. In this case form of the anharmonic potential is known [10, 11, 12] which simplifies our analysis. However, physical picture of AHR remains same for the other form of potential. For simplicity we consider electric field is linearly polarized along x and has the form E(t) = E₀ sin²(ωt/2n) cos(ωt) for t < nT; otherwise E(t) = 0; where T is the laser period, ω = 2π/T is the laser frequency, and n is the number of laser period. Effect of magnetic field of laser is neglected keeping intensity below 10¹⁸W/cm². However, PIC simulations are free from all these assumptions of the model. The equation of motion of the electron sphere can be written as $\ddot{\overrightarrow{x}}+g(r)\overrightarrow{x}/r=-\widehat{x}E(t)$, where r = |x| is the displacement of the electron sphere, and g(r) is the electrostatic restoring force which reads

Figure 3 shows temporal dynamics of an electron sphere (of total charge q_s = Ne, number of electrons N = 80000, and radius R = 10 nm) experiencing AHR in the potential corresponding to Eq. (1) when driven by a n = 10-cycle laser pulse of intensity I₀ ≈ 9.1 × 10¹⁶ W/cm² and wavelength 800 nm. Corresponding ponderomotive energy of an electron is U_p = I₀/4ω² ≈ 5.4 keV, plasma density is n_p = 10.95n_c, and ${\omega }_M/\omega =\sqrt{10.95/3}\approx 1.92$. The normalized excursion x/R, velocity v_x/c, and normalized frequency Ω[r(t)]/ω (in a) and the normalized absorbed energy per electron ε_abs/N/U_p (in b) are plotted with respect to the normalized time t/T. Initially, at t/T = 0, electron sphere is bound in the potential where x(0) = 0, v_x(0) = 0, and its energy is at a minimum negative value. Since potential is harmonic at its minimum, Ω/ω starts at ω_M/ω ≈ 1.92. As the laser field strength increases and oscillates with time, excursion and velocity also increase in rhythm with the field. Every time excursion increases (i.e., particle rides up in the potential) the dynamical frequency Ω/ω decreases, and around t/T ≈ 2.4, Ω/ω passes unity when x/R > 2.5. Although AHR occurs at this early time, the laser field strength on the electron sphere is not enough to overcome the attraction of the potential (see particle is still bound with negative energy). As a result particle comes back with reversal of the driving field, crosses the potential minimum (near t/T ≈ 2.8), and emerges on the other side of the potential. As it rides up, Ω/ω starts decreasing and crosses unity again around t/T ≈ 2.9 (near vertical dashed line) when its excursion becomes very large and absorbed energy becomes positive, i.e. particle becomes free aided by this efficient AHR. The fact that electron sphere becomes free from the potential and absorbed energy becomes positive at the same time when Ω(t)/ω = 1, clearly indicates AHR is indeed the mechanism behind this absorption. When particle becomes completely free, restoring force on the particle vanishes and Ω/ω drops to zero.

 

Fig. 3 Temporal dynamics of an electron sphere (of total charge q_s = Ne, number of electrons N = 80000, and radius R = 10 nm) experiencing AHR when driven by a n = 10-cycle linearly polarized (in x) laser pulse E(t) = E₀ sin²(ωt/2n) cos(ωt) for 0 < t < nT of intensity I₀ ≈ 9.1 × 10¹⁶ W/cm² and wavelength 800 nm. The normalized excursion x/R, velocity v_x/c, and the normalized frequency Ω[r(t)]/ω (in a) and the corresponding normalized absorbed energy per electron ε_abs/N/U_p (in b) are plotted (see text).

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It is important to mention that liberation of an electron from the potential through AHR as shown in Fig. 3 depends on the size and shape of the potential and the plasma density as well. Both higher plasma density and a bigger particle size (which lead to larger depth of the potential) will require higher intensity to liberate the electron from potential. Initial position of an electron in the potential also plays role. An electron which is initially located in the shallower part of the potential and near the line of resonance Ω/ω = 1 may experience AHR earlier and may be liberated much before than the electron which is located relatively deeper. Depending upon strength of the restoring field and the laser field, an electron which was initially freed by AHR may come back within the potential and finally leave through AHR again (i.e, occurrence of multiple AHR). These facts are demonstrated below.

Figure 4 shows temporal dynamics of two electron spheres of same size R = 10 nm with different number of electrons (and ions) N = 80000 (a,b, in left pannels) and N = 160000 (c,d, in right pannels) driven by 10-cycle laser pulse as in Fig. 3 at an intensity I₀ ≈ 1.82 × 10¹⁷ W/cm². Corresponding plasma densities are n_p = 10.95n_c, 21.9n_c, and ω_M/ω ≈ 1.92, 2.7. At t/T = 0, both spheres are bound in the potential where their x(0) = 0, v_x(0) = 0. Potential being much deeper for high density case, the electron sphere is more bound and starts at a more negative ε_abs compared to the electron sphere in the low density shallower potential. Correspondingly, Ω/ω also starts at different values, i.e., ω_M/ω ≈ 2.7, 1.92 respectively. The low density sphere (left pannels) passes AHR first time around t/T ≈ 2.45, ε_abs becomes positive with large |x/R| > 5. Note that, the low density system is same as in Fig. 3 but driven with higher peak intensity. Since field strength is now higher, sphere passes AHR earlier than Fig. 3. However, as the field strength approaches higher values, sphere is drawn back into the potential (in Fig. 3 sphere does not come back) where its energy decreases to a negative minimum, Ω/ω increases towards Ω_M/ω = 1.92 for t/T ≈ 3.5 – 3.8. From this time onwards, Ω/ω starts decreasing again and passes unity when t/T ≈ 4 (near vertical dashed line), ε_abs becomes permanently positive and sphere is set free forever through this AHR. Thus depending upon the peak laser intensity, an electron may undergo AHR at different times and also multiple times. Unequivocally, if an electron has to come out from the potential with ε_abs > 0, it must pass through AHR. The high density sphere (right pannels) also exhibits identical dynamical features of low density sphere, namely, its passage through AHR multiple times (e.g, t/T ≈ 4.4, and t/T ≈ 6) with ε_abs changing from negative to positive (electron goes bound to free state), then to a negative minimum (electron comes back from free to bound state), and finally negative to positive (electron becomes permanently free). The difference is that an electron in a more deeper potential (high density case) makes many excursions before it becomes free via AHR at a later time where instantaneous intensity is high compared to an electron in a relatively shallower potential (low density case) which faces AHR at an early time where instantaneous intensity is low although they are driven by same peak laser intensity. It results much higher energy (ε_abs/N ≈ 3U_p in d) for an electron experiencing AHR in a deeper potential compared (ε_abs/N ≈ 0.5U_p in b) to that an electron experiencing AHR in a shallower potential. This comparison is important as it explains why electrons from high density deeper potential will gain much higher energy than from a relatively shallower potential of a bacteria with relatively low plasma density (as already outlined in the schematic of Fig. 1). As elaborated further this is very important for understanding experiments with AgCl nanoparticles.

A simple model (with many assumptions) thus describes many important features of AHR phenomenon. PIC simulations are free from those assumptions of the simple model. Neither we are restricted to spherical shape of the target, nor we neglect the effect of laser pulse propagation and magnetic fields which make the problem multidimensional and thus close to reality.

 

Fig. 4 Temporal dynamics of two electron spheres of same size R = 10 nm with different number of electrons (and ions) N = 80000, 160000 (i.e., different plasma densities n_p = 10.95n_c, 21.9n_c, and ω_M/ω ≈ 1.92, 2.7) driven by 10-cycle laser pulse as in Fig. 3 at an intensity I₀ ≈ 1.82 × 10¹⁷ W/cm². Pannels (a,b) show low density case and (c,d) depict high density case. The normalized excursion x/R, velocity v_x/c, and the normalized frequency Ω[r(t)]/ω and the corresponding normalized absorbed energy per particle ε_abs/N/U_p are plotted as in Fig. 3. At t/T = 0, both spheres are bound in the potential where their x(0) = 0, v_x(0) = 0. Both the spheres undergo AHR two times (see text).

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5. AHR in E. Coli coated targets

In PIC simulations we identify AHR as the principal absorption mechanism experienced by an electron when its frequency Ω[r(t)] in the self-consistent anharmonic potential at a radial position r(t) at time t = t_r satisfies Ω[r(t_r)] = ω. Only at this time t_r (and near t_r), the laser-field energy is substantially transferred to the electrons. We calculated the restoring field $E_r^{\text{sc}}(t)$ on each electron in the radial direction and estimated ${\mathrm{\Omega }}^2[r(t)]=(e/m)d{E}_r^{\text{sc}}/dr$ numerically, by analogy with a harmonic oscillator, where the restoring field is $E_r^{\text{sc}}=(m/e){\mathrm{\Omega }}^{2}r$ and Ω is its constant eigenfrequency.

For an unambiguous identification of AHR, we performed simulations with a smaller ellipsoid (0.25 μm × 0.4 μm) of density 10n_c. The laser was pulsed (10 cycles) with a peak intensity of 10¹⁸ W/cm². Figure 5 shows the evolution of velocities (v_x/c, v_y/c), the space-charge fields ( $E_x^{\text{sc}}/E_0$, $E_y^{\text{sc}}/E_0$), the driving field E_x/E₀ and the normalized frequency Ω[r(t)]/ω as a function of the normalized time t/T for two different electrons, which finally left the target in the direction of v_y < 0 (Fig. 5(a)) and along v_y > 0 (Fig. 5(b)), where y is the direction of laser propagation, E₀ is the laser electric field and T = 2π/ω is the laser cycle. After propagating in free space, the laser was made to interact with the target at t/T = 5.8, creating the space-charge fields $E_x^{\text{sc}}$ and $E_y^{\text{sc}}$ and resulting in a rapid initial increase of Ω. In the region t/T ≈ (6.0 – 6.5), the fields $E_x^{\text{sc}}$ and $E_y^{\text{sc}}$ as well as E_x were found to be strongly nonlinear (indicating the anharmonicity in the potential), leading to a prompt dephasing [10] of the velocity v with respect to E – in other words, $\overline{\mathbf{v}\cdot \mathbf{E}}\ne 0$. As the ratio Ω/ω decreased and passed through unity, AHR was found to occur and the electron trajectories demonstrated effective acceleration. The electron velocities along (a) v_y < 0 and (b) v_y > 0 resulted in a Doppler (a) blue-shift and (b) red-shift in the frequency of the driving field E_x, as evident from the (a) contraction and (b) dilation of the time-cycle of the driving field E_x (this is consistent with Ref. [10]). The velocity of electrons after the AHR was found to reach up to ≈ 0.6c (as shown in Fig. 5(b)), thus indicating that AHR is indeed responsible for the hot electron generation.

 

Fig. 5 Temporal dynamics of two electrons experiencing AHR at an incident laser intensity of 10¹⁸ W/cm². The velocity (v_x, v_y), the space-charge fields ( $E_x^{\text{sc}}$, $E_y^{\text{sc}}$), the driving field E_x and the normalized frequency Ω[r(t)]/ω are plotted with respect to the normalized time t/T, where ω is the laser frequency and T = 2π/ω is the laser cycle. The laser is incident at t/T ≈ 5.8 and creates the space-charge fields. The electron might leave the target either along (a) v_y < 0 or (b) v_y > 0, where y is the direction of laser propagation. This results in a Doppler (a) blue-shift or (b) red-shift in the frequency of the driving field E_x, as shown by the (a) contraction or (b) dilation of the time-cycle of the driving field E_x. AHR occurs when Ω/ω ≈ 1 around t/T ≈ 6.25 – 6.50.

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We also compute the absorbed energies as given in Fig. 6 for the electrons in Figs. 5(a) and 5(b). It is clear that individual ε_abs becomes positive only passing AHR near t/T ≈ 6.25 – 6.5. Before laser interacts with the target, total energy of each electron is zero since space-charge field (SCF) is not yet created and electron is at rest. As soon as laser starts interacting with the target, SCF and corresponding anharmonic potential are created. Each electron goes down in the potential, becomes bound for a while where total energy becomes negative (since kinetic energy is still less than the potential energy during this early time of interaction). As the laser field strength increases (note that peak of the laser field is expected near t/T = 7.5), kinetic energy of each electron increases and soon they are drawn to resonance around t/T ≈ 6.25 – 6.5 when their respective ε_abs becomes positive and electrons are permanently set free. In PIC simulations, initially, potential and space charge fields are zero. Here potential is self-consistently created and changes time to time during the interaction of the laser while in the model (Figs. 3 and 4) electrons move in a predefined fixed potential. As a result, in PIC simulations Ω/ω first increases from zero value (see Fig. 5) and reaches some maximum value as it becomes more bound (see Fig. 6(a) and 6(b)); whereas in the model (in Figs. 3 and 4) electron sphere starts from the bound state (with negative energy) where Ω/ω > 1. Sometimes due to multiple AHR (as shown in Fig. 4) electron sphere comes back into the potential, ε_abs becomes positive to negative with Ω/ω increasing towards Ω_M/ω and from that time onward dynamics of electron sphere is exactly similar to a PIC electron (see temporal evolution of ε_abs in Fig. 4 from last quarter of a period before the electron spheres finally leave through AHR are similar to PIC electrons in Fig. 6). It is interesting to note that the PIC electron in Fig. 6(b) goes much deeper in the potential and ends up with higher absorbed energy (approximately 4U_p) compared to the PIC electron in Fig. 6(a) with lesser amount of absorbed energy (approximately 1.25 U_p) which is also evident from higher v_x, v_y in Fig. 5(b) than that in Fig. 5(a). This further justifies the fact (already demonstrated by model calculations in Figs. 4(a) and (b)) that an electron liberated from deeper potential surface via AHR absorbs higher energy than an electron liberated from a shallow potential surface although they are driven by the same laser field. In spite of many differences between the model and PIC simulations, it is clearly exhibited that absorbed energy of an electron becomes positive and it becomes free only when the AHR condition Ω/ω = 1 is satisfied. From the comparison between the dynamical variables associated with PIC electrons and the electron sphere in the simple model it is unambiguously proven that AHR is indeed the mechanism behind the enhanced laser absorption in the bacteria coated target.

 

Fig. 6 Temporal evolution of absorbed energies ε_abs for two PIC electrons shown in Fig. 5.

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Having found that AHR is responsible for an enhanced hot electron yield in bacterial targets, we envisaged that this effect will be further amplified if we could create additional density modulations on the target, leading to an increased anharmonicity in the self-consistent potential (as indicated in Fig. 1). Here, we demonstrate that we can control and further boost the hard x-ray emission by engineering density modulations that increase AHR by doping the bacteria with silver chloride (AgCl) nanoparticles. One would expect that the bremsstrahlung efficiency will be affected only marginally due to the presence of the high Z-metal because the bacterial layer is only 2–3 microns thick and the Ag-dopant mass is < 5%. However, the anharmonicity brought out by density modulations due to the presence of the AgCl nanoparticles would be significant and thus AHR would be more efficient. A comparison of the hard x-ray emission from Ag-doped bacterial targets with undoped bacterial targets at an incident laser intensity of 10¹⁶ W/cm² is shown in Fig. 7. Even when the solid angle of the detector was set such that there were barely measurable x-ray counts from the undoped bacterial target, the detector was flooded with x-ray emission from the Ag-doped bacteria and consequently a 12 mm lead block with a 1 mm aperture was placed in front of the detector to measure the x-rays under pile-up free conditions. The integrated hard x-ray yield from the doped bacterial target was found to be 85 times higher compared to that from the undoped bacterial target. The hot electron temperature (derived by fitting the x-ray spectrum to a bi-Maxwellian distribution) is (250±10) keV, compared to (57 ± 2) keV for an undoped bacterial target [15]. Hence, in comparison to a plain solid target, the Ag-doped bacterial target has an overall enhancement in hard x-ray yield by a factor as large as ≃ 10⁴.

 

Fig. 7 (a) A transmission-electron-microscope (TEM) image of the E. coli bacteria doped with AgCl nanoparticles, (22 ± 6) nm in size. (b) X-ray bremsstrahlung spectra at an incident laser intensity of 5 × 10¹⁶ W/cm² from a Ag-doped bacterial target as compared to an undoped bacterial target (enhanced by a factor of 10 for representation on the same scale). The hot electron temperature for the Ag-doped bacterial target is (250 ± 10) keV, compared to (57 ± 2) keV for the undoped bacterial target [15]. The integrated x-ray yield from the Ag-doped bacterial target is a factor of 85 higher than that from the undoped bacterial target. The data were acquired for over 10,000 laser shots. The low-energy cutoff in the experiment is 30 keV.

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To justify whether the hot electron yield increases with the nanoparticle doping, further PIC simulations were carried out by placing nanoparticles on the surface of the ellipsoids. The ellipsoidal particles, representing the bacteria, were considered to have an electron density of 2n_c, doped with nanoparticles of density 20n_c and positioned on the substrate of density 10n_c to mimic the experimental conditions. The laser intensity was 10¹⁶ W/cm² as considered in the experiments, described in Fig. 7. While considering the nanoparticles in the simulation, the resolution of the computational grid was appropriately adjusted. Figure 8 shows the electron spectra with different numbers of nanoparticles placed at different locations on the surface of the ellipsoid. The maximum electron energy was found to increase further and the electron yield increased significantly even with one nanoparticle. AHR plays a very efficient role for the nanoparticle located close to the tip of the ellipsoid, since it interacts more efficiently for a relatively longer period of time, compared to the nanoparticles that are far away from the tip along the laser propagation direction. Consequently, even when 3–5 nanoparticles were considered on each ellipsoid in the simulation, it was found that most of the contribution came from a single nanoparticle near the tip of the ellipsoid and the other nanoparticles contributed relatively less due to the screening of the laser field. Note that a single nanoparticle of diameter 25 nm and density 20n_c contains nearly 3×10⁵ electrons and most of them may experience AHR almost simulatneously in the nearly same unattenuated laser field leading to higher yield even with one nanoparticle. The simulations indicated a 7–10 fold enhancement of the electron yield (at 200 keV) using a nanoparticle-doped ellipsoid, compared to an undoped ellipsoid. Assuming ∼ 10 ellipsoids (each with 3–5 nanoparticles) in the focal volume, we estimate a (70 – 100) fold enhancement of the yield, compared to the undoped bacterial target. Thus, in spite of the several simplifying assumptions, the PIC results attribute the experimentally observed near-80 fold enhancement in the hard x-ray yield to AHR. The experiments and analysis presented should be consistent with the use of other bacterial cells so long as their shape and initial densities are not too different. To check this, we also did experiments with Bacillus cells that are also ellipsoidal in shape. The x-ray emission and the hot electron generation from this system are also two orders of magnitude larger than that from the solid target. In fact the x-ray emission measured with the LactoBacillus cells is a few percent larger than that from the E.coli cells under similar conditions. The differences are attributable to the differences in the initial shape and size of the cells but the major effects of enhanced x-ray emission compared to the solid targets are fully consistent with the analysis presented here.

 

Fig. 8 Results of 2D PIC simulations for an incident laser intensity of 10¹⁶ W/cm², showing the hot electron spectra for several nanoparticles on the ellipsoid, representing the Ag-doped bacteria. The low-energy cutoff is 30 keV.

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It should be noted that the effect of local fields that contribute to the electrostatic potential computed in the PIC simulations is intrinsically included in the analysis presented here. The local fields not just contribute by increasing the intensity but also in enhancing the AHR heating.

Intense, femtosecond laser created plasmas are unique tabletop compact point-sources of pulsed energetic electrons, ions and x-rays. These emissions are of great importance to diverse scientific, technological and medical applications such as radiography [23], cancer therapy [24] and lithography [25]. Since the intense light is pulsed, the x-ray emission is also pulsed and is much brighter than conventional sources. One main issue in making these sources viable for application is to increase laser absorption such that the x-ray yield is high even at lower intensities. The lower the intensity required, the larger is the repetition rate of the lasers. Such an advance will add the crucially important feature of increasing the average luminosity of the x-rays. The present results offer such a paradigm to the laser produced plasma sources.

6. Conclusion

In conclusion, we present an interesting cross-disciplinary linkage between high-intensity laser science and biology, offering tremendous advantages in terms of enhanced laser-matter energy coupling. We provide the first conclusive evidence for the AHR absorption mechanism, facilitated by the engineered bacterial structures. This results in an overwhelming near-10⁴-fold enhancement in the hard x-ray emission from the Ag-doped bacterial target compared to a plain glass target. The significant enhancement in the hot electron as well as the hard x-ray yield should trigger additional investigations to choose optimal, readily-occurring biological structures in the nature around us. Although enhanced x-ray emission with artificially designed micro/nano-structures is feasible, the richness in the variety of well-reproducible easily-generated biological structures in large scales makes the present technique more amenable to various diverse applications. Such high-density laser-plasmas with attendant benefits of high yields of energetic particles and hard x-rays are expected to have manifold applications in biology, chemistry and condensed-matter sciences as well as in manufacturing technologies and medical therapies.