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Abstract
Radiographic imaging using X-rays is a tool for basic research and applications in industry, materials science, and medical diagnostics. In this article, we present a novel approach for the generation of X-rays using a vacuum-free microplasma by femtosecond fiber laser. By tightly focusing a laser pulse onto a micrometer-sized solid density near-surface plasma from a rotating copper target, we demonstrate the generation of Cu K-photons (8-9 keV) with high yield ∼ 1.6 × 109 phot/s/2π, and with a source size diameter of approximately 10 microns. Femtosecond fiber laser allows working with a high repetition rate (∼2 MHz) and moderate energy levels (10-40 µJ), ensuring the effective quasi-continuous generation of X-ray photons. Furthermore, we introduce a hybrid scheme that combines the tightly focusing laser-plasma X-ray generator with an online control unit for microplasma size source based on the back-reflected second harmonic generated in the laser-induced microplasma. The compactness and high performance of this vacuum-free femtosecond fiber laser microplasma X-ray source makes it a promising solution for advanced radiographic applications. Our preliminary results on the creation of a microfocus X-ray source provide insights into the feasibility and potential of this innovative approach.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The development of new-generation X-ray sources, combining high-contrast spectral bright radiation, stability, micron-sized emitters, and compactness, has continued to grow over the past decades. This growth can be attributed largely to the use of X-ray sources for imaging and related developments in biology, medicine, and materials science. Specifically, this pertains to phase-contrast X-ray imaging, which is sensitive to the phase shift caused by an object placed in the path of X-ray radiation and makes it possible to reveal details that only slightly differ in absorption. Consequently, the phase contrast X-ray technique can image weakly absorbing materials, such as carbon-based materials or biological objects. The key parameter for observing phase contrast is the source coherence, which is determined by the X-ray source size. In this regard, polychromaticity results in a reduction of the final contrast obtained during imaging experiments. Hence, monochromatic X-ray sources emitting a high photon flux are used for phase-contrast imaging, and a microfocus X-ray source is necessary [1]. An important characteristic of the microfocus X-ray tube is the requirement to stabilize the displacement of the focal spot during the study, necessitating research under conditions where high accuracy of the focal spot position is crucial during prolonged sample exposure [2]. The primary advantages of working with microfocus X-ray tubes are the resolution corresponding to the micron or submicron range.
Femtosecond lasers make it possible to produce laser-plasma sources of X-ray radiation, such as brightness K-characteristic lines and broadband Bremsstrahlung emission. Moreover, the efficiency of generating monochromatic laser-plasma X-rays can be compared with the simultaneously generated broadband backlighter based on Bremsstrahlung emission [1]. The effective source size is larger than the optical focal spot and is limited by beam pointing stability conditions. Typically, the observed X-ray source size is found to be 2–3 times larger than the laser focal spot [1]. To maximize the image contrast, a high spatial coherence of the X-ray source is required, along with a small size of the X-ray source. It was stated that the imaging contrast decreases when the X-ray source size is increased, and the imaging contrast is higher for increasing the distance between the object and the detector [3]. Furthermore, as stated in [4], the imaging contrast depends on the laser intensity due to the relationship between the plasma spot size emitting X-ray photons and the laser intensity that affects the target.
The role of the surface state in increasing the coupling of input light into laser-produced plasma, resulting in enhanced X-ray yield, is well known. In this regard, the influence of roughness on the X-ray yield holds special significance [5]. Even with a polarized light field and irrespective of the angle of incidence, higher yields are observed in the case of a rough target. This suggests the need to consider other mechanisms, such as surface electromagnetic waves, that could enhance laser-plasma coupling.
Recent trends indicate that high-energy lasers traditionally used for plasma X-ray sources production can be conveniently and effectively replaced by high-average-power and high-repetition-frequency laser radiation. This approach aims to increase the brightness of the generated X-rays [6]. A recent study demonstrated that laser-produced plasma, driven by double-pulsed femtosecond laser pulses at a repetition rate of 100 kHz in an ambient air environment, can serve as an effective broadband X-ray source using a rotating disk target [7]. Meanwhile, the problem of creating a new-generation laser-plasma microfocus X-ray source with controlled size in real time remains unresolved. To address this issue, the use of the second harmonic as a monitoring tool for the long-term stability of the X-ray source size can be effective. In the geometry of the normal incidence of a femtosecond laser beam on the target surface, the generation of the second harmonic is prohibited in the plane wave approximation. However, for tightly focused beams, the existence of a longitudinal component of the electric field allows for the generation of the back-reflected signal of the second harmonic [8]. Additionally, the laser-induced local field on the rough structure of the metal surface can lead to an effective generation of the second harmonic through resonant excitation of surface-plasmon-polariton modes [9]. Furthermore, plasmon-polariton surface waves can exist in femtosecond laser-induced plasma [10].
From the above, it is evident that obtaining a minimum-sized laser-plasma spot is a key challenge. In this study, we report on the generation of the characteristic K-photons (8-9 keV) from Cu target through laser-plasma interactions of a tightly focused femtosecond fiber laser beam with a micrometer-sized solid density near-surface plasma from a rotating Cu target. We demonstrate that the advantages of tens of microjoules energy and high repetition rate of fiber laser pulses, which are used for effective quasi-continuous generation of X-ray photons, can be beneficial for achieving desirable properties such as X-ray spectral brightness, ultra-small source size, and apparatus compactness. Furthermore, we present a hybrid scheme that combines a laser-plasma X-ray generator operating in tightly focusing mode with an on-line control unit for a microplasma size source based on an image of the back-reflected second harmonic of the laser igniting microplasma. Preliminary results on the creation of a microfocus X-ray source have recently been published in [11].
2. Experimental setup
The experiments were performed using a femtosecond ytterbium fiber laser ANTAUS-10W-40u/250 K (Avesta-Project, Russia). The laser emitted radiation at a wavelength of 1030 nm with an average power up to 20 W and pulse duration 280fs. The frequency rate varied from 200 kHz to 2.5 MHz, maximum pulse energy varied from 40 µJ (for 500kHz) to 8 µJ (for 2.5 MHz); M2 is 1.2. The laser pulse energy was monitored by a calibrated photodetector that registered a laser beam reflected from a thin quartz plate (∼4%). Additionally, a beam expander was placed into the beam path to enlarge the size of the laser beam to 4 mm (1/e2 level). Moreover, a half-wave plate was used for controlling the laser pulse polarization. To avoid retroreflection of the laser beam, a Faraday isolator was placed within the beam path. Focusing of the laser beam was achieved using a microscopic objective (PAL-20-NIR-HR-LC00) with a focal length of 10 mm and efficient NA∼0.2. The focused laser beam was directed onto the surface of a copper cylinder that was both rotating (∼5000 rpm) and moving cyclically in a vertical direction at a constant speed of 50 mm/min. The cylinder had a diameter of 44 mm and a thickness of 8 mm. The side surface of the target was polished to a roughness not exceeding 0.5 µm and was mounted on the shaft of a motor. A single vertical pass over the target surface led to the formation of micro-craters through ablation, resulting in a uniformly modified surface within ∼10 seconds. The axial runout of the rotating surface on the shaft did not exceed 2 µm. This target movement procedure enabled continuous operation with a single copper cylinder for more than 7 hours. To prevent particle deposition on the focusing optics, a system was assembled to blow air (or Helium) into the interaction region. Ablated particles were carried away by the airflow passing through a narrow tube and subsequently removed by a vacuum suction. The experimental setup is presented in Fig. 1
Fig. 1. Experimental setup. a) Laser pulse facility diagram. b) 3D model of the target assembly. c) SEM image of the target surface. 1 is the femtosecond laser system, 2 is the Faraday isolator, 3 is the half-wave plate, 4 is the quartz plate, 5 is the photodetector, 6 is the beam expander, 7 is the dichroic mirror, 8 is the focusing lens, 9 is the blowing system, 10 is the Cu target placed on a 5-axis motorized stage, 11 is the sample (tungsten carbide ball), 12 is the CCD X-RAY camera, or X-Ray scincilator, or X-Ray spectrometer, 13 is the CCD cameras, 14 is the beam splitter, 15 is the CCD camera XCAM1080PHA on motorized stage, 16 is the fiber spectrometer on motorized stage. Orange line is laser beam with wavelength 1030 nm, green line is second garmonic (515 nm), purple line is X-ray radiation.
For the applied laser pulse parameters (relatively low energy and intensity of 1014W/cm2) and the configuration of the experimental setup (using a rotating copper target), the use of a vacuum environment was deemed unnecessary. X-ray radiation generated under laser-plasma interaction was detected by an X-123 spectrometer (Amptek, USA) and a single-channel scintillation detector SCSD-4 (Radikon, Russia), positioned 20 cm away from the target.
The X-ray flux N2 in the photon energy range E > 3 keV was calculated from the expression (1)
where N1 is the number of quanta recorded by the scintillation detector, R2 is the distance from the target to the input “eye” of the Radikon scintillation detector, T is the transmittance of the filters, R1 radius of the diaphragm at the detector entrance apertureTo accommodate high radiation fluxes, attenuating filters made of copper or aluminum were positioned in front of the detectors. The focus position relative to the target was determined by monitoring the intensity of X-ray radiation. For monitoring the laser-induced microplasma size we created the image transfer system for online control. The system collects the backreflected second harmonic signal on the CCD camera matrix (XCAM1080PHA; ToupTek Photonics Co., China) with a spatial resolution. The optical system achieved a spatial resolution of 0.3 µm/pixel. Simultaneously, the spectrum of the second harmonic was measured by the USB4000 spectrometer (Ocean Optics, USA). For this purpose, the 50:50 beam splitter was mounted into the optical path. The rotating target was placed on a motorized 5-axis stage. The movement of the multiaxis stages was controlled using the Duet2WiFi stepper motor controller. The investigated samples were also placed on a motorized 3-axis motorized stage and controlled using a similar controller. The full experiment was fully automated using LabVIEW. X-ray signal intensity, X-ray source size (based on the second harmonic signal), second harmonic spectrum, and second harmonic signal intensity were recorded simultaneously. The maximum duration of the experiment was approximately 7 hours. Additionally, two CCD cameras were placed inside the interaction chamber for controlling the movement of the rotating copper target.
3. Results and discussion
3.1 Dependence of X-ray emission on pulse repetition rate and energy
The X-ray photon flux was optimized by varying key parameters of the femtosecond fiber laser radiation, including energy, and repetition rate. Measurements were performed to investigate the dependence of the X-ray radiation yield on the laser pulse repetition rate, ranging from 500 kHz to 2.5 MHz, while maintaining a maximum average power of 20 W. Due to the power limitation of the laser system at 20 W, an increase in pulse repetition rate resulted in a proportional decrease in pulse energy, ranging from 40 µJ to 8 µJ.
It is demonstrated that, at a fixed power of 20 W, the X-ray radiation yield of (1.6 ± 0.5)x 109 photons/s in 2π is achieved for a laser pulse frequency of 2 MHz. Than it starts to fall for a following repetition rate increase. The rise of the X-ray signal exhibited a near-linear relationship within the repetition rate range of 500 kHz to 1.2 MHz (refer to Fig. 2(a)). Subsequently, at a range of 1.6-2.0 MHz, the signal saturated before entering a decreasing trend within the range of 2.0-2.5 MHz. The obtained photon flux aligns with existing knowledge derived from femtosecond laser systems operating at frequencies up to 1 kHz, with laser pulse energies in the order of millijoules [12].
Fig. 2. (a) Dependence of X-ray emission on laser pulse repetition rate at a fixed power of 20 W. (b) Dependence of X-ray emission on laser pulse repetition rate at a fixed energy of 10 µJ
The dependence of X-ray emission on the repetition rate (or energy) of laser pulses is governed by two interrelated processes. On one hand, an increase in repetition rate leads to a higher number of interactions with the target, resulting in an increased X-ray yield. On the other hand, the energy of each laser pulse decreases. The tight focusing employed in the experiments causes the vacuum intensity to exceed 100 TW/cm2, leading to air ionization. Ionization of the surrounding gas significantly impacts the development of self-action processes, causing energy loss, defocusing, and scattering on the laser-induced plasma [13–15].
According to the [15] ionization losses in air at vacuum intensity of 100 TW/cm2 do not exceed 1%. This also follows from calculations performed in [13].
It should be noted that with increasing repetition rate of laser pulses the concentration of micro-particles in the near-surface region of the interaction zone increases which is attributed to a significant rise in the ablation rate. Consequentially, a two-component medium comprising microparticles suspended in air is formed, complicating the evaluation of ionization losses – a phenomenon that necessitates separate theoretical analysis. The accumulation of ablated particles within the zone of impact is associated with a reduced threshold for medium ionization and an amplified concentration of ionized electrons within the focal region, engendering additional energy losses due to ionization, as well as contributing to the defocusing of the beam.
Following the general ideas this increase in particle concentration can cause scattering and energy losses of the laser pulse delivered to the target [16–18]. The settling time of ablated particles varies from hundreds of nanoseconds to tens of microseconds, depending on the initial energy density [16]. Consequently, with an increase in laser pulse repetition rate, the influence of the ablated particles plume intensifies, further affecting the development of self- action and scattering processes of the incident laser radiation.
In order to better determine the role of repetition rate, we fixed the energy level at 10 µJ while varying the repetition rate of the laser pulses. It was found that the X-ray emission exhibits a power-law dependence on the repetition rate of the incident pulses, with an exponent of 3.7 in the range of 200 kHz to 1.2 MHz, and then saturates (Fig. 2(b)).
The nonlinear in X-ray yield with increasing repetition rate of the incident pulses at a constant target scanning rate may be attributed to a reduction in the spatial and temporal separation between the incident pulses. At a target rotation velocity of 5000 rpm and a repetition rate of 500 kHz, the spatial separation between influencing pulses on the target is approximately 4 µm. While at a repetition rate of 1.4 MHz, it becomes approximately 2.2 µm, and in case of 2 MHz, it decreases to 1 µm. Thus, varying the repetition rate of the incident pulses results in overlapping inter-pulse distances, forming micro-craters where laser radiation is localized. Laser surface modification of the target also leads to the generation of local fields and resonances, stimulating an growth of the absorption energy and increase of the local intensity and X-ray emission [19]. Because the laser plasma/nanoparticle ablation plume coexist after 0.5–1.0 µs laser impact, each subsequent laser pulse interacts with the plume [17], [18]. It should be noted that the influence of pulse overlap has been studied in previous works [18], [20], and it has been found that there is an optimal distance between pulses where X-ray yield is maximized. The observed saturation of the X-ray depending on the laser pulse repetition rate can be correlated with an increase in the concentration of microparticles in the near-surface аrеа of the target. Consequently, the observed plateau in X-ray yield as a function of the laser pulse repetition rate can be correlated with the elevated concentration of microparticles in the near-surface region. This accumulation precipitates a diminution in the ionization threshold of the medium, an enhancement in the density of ionized electrons within the beam waist, and subsequent augmentation in energy dissipation due to ionization. Additionally, these conditions induce beam defocusing, which ultimately contributes to the clamping effect [16–18,21].
3.2 Spectral characterization of the X-ray source
One of the key parameters for applied research is the fraction of characteristic X-ray radiation (Cu Kα,β) in the overall recorded spectrum. Therefore, we measured the X-ray spectra and estimated the fraction of Cu Kα,β in the overall recorded spectrum. A typical X-ray spectrum is shown in Fig. 3(a), consisting of bremsstrahlung radiation and characteristic lines Cu Kα (∼8 keV) and Cu Kβ (∼9 keV). It is important to note that X-ray radiation with photon energies up to 7 keV is effectively absorbed in air, as shown in Fig. 3(a). Variation in the repetition rate at a fixed energy demonstrates that the fraction of Cu Kα,β increases from 10% to 25% with an increase in repetition rate from 500 kHz to 1.4 MHz (Fig. 3с). With further repetition rate increase, the fraction of Cu Kα,β saturates. Similar to the overall X-ray yield, this dependence is attributed to competing processes of intensity enhancement due to processes as mentioned above.
Fig. 3. (a) X-ray emission spectrum at a laser pulse repetition rate of 2 MHz and energy of 10 µJ, where the blue line represents the original spectrum, the black line represents the spectrum accounting for air absorption, and the red dashed line represents the exponential approximation of the Bremsstrahlung spectrum. (b) Normalized X-ray emission spectrum from an X-ray tube (black line) and laser-plasma source (red line). (c) Ratios of the spectral brightness of characteristic lines to the total spectral brightness at energy of 10 µJ and frequency of 2 MHz.
A comparison of X-ray spectra obtained with laser-plasma sources and those generated in an X-ray tube was also conducted (see Fig. 3(b)). In comparison with the X-Ray tube, for the similar conditions of the X-ray flux, a significant portion of the Bremsstrahlung spectrum from the laser-plasma source is concentrated at lower energies, which allows for easy filtration if necessary (e.g., using thin foils). Performing such an operation with an X-ray tube would be much more challenging. It should be noted that the contrast in Cu Kα,β at 8 keV for the laser-plasma source is approximately 15, which is more than twice the contrast of Cu Kα,β for an X-ray tube.
By approximating the Bremsstrahlung spectrum, it is possible to determine the temperature of hot electrons. The estimation of the intensity on the target was performed using a known expression that relates the intensity of a femtosecond laser pulse I to the temperature of hot electrons Th. This expression has been verified by us for intensities on the order of 1014W/cm2 during the target interaction in the microchannel formation regime [22]:
Thus, based on the temperature of hot electrons obtained from the approximation of the Bremsstrahlung spectra, it is possible to determine the laser pulse intensity on the target. We believe that this approach is also valid for the generation of X-ray pulses in the target interaction regime with a developed (modified by laser pulses) surface. Under optimal conditions (repetition frequency of 2 MHz, laser pulse energy of 10 µJ, power 20 W), the electron temperature is determined to be 1.7 ± 0.2 keV. According to Eq. (2), the intensity on the target is estimated to be (3.5 ± 0.5) ·1014 W/cm2, which is higher than the corresponding intensity estimate on the target for Gaussian beam focusing (in vacuum) – 2.5·1014 W/cm2.
This may also indicate an increase in the intensity on the target due to the mechanisms described above.
3.3 Monitoring of the X-ray source using second harmonic generation
In the context of the task related to the creation of a microfocus source, where X-ray generation is accompanied by ablation and surface modification processes on the target, it is necessary to real-time monitor not only the X-ray photon flux but also the size of the microplasma X-ray source. This is due to the need for periodic adjustment of the focus position with respect to the target, as the laser ablation process leads to a reduction in the diameter of the copper disk. This process results in both a decrease in the X-ray photon flux and an increase in the size of the X-ray source. To address this, the use of a nonlinear optical process of second harmonic generation (SHG) accompanying X-ray photon generation has been proposed. Thus, the interaction of intense femtosecond laser radiation with a solid-state target in the plasma formation regime can be accompanied by the generation of the second harmonic back reflected from the target [8]. The intensity of the second harmonic (SH) nonlinearly depends on the intensity of the laser radiation I: SH ∼ Iγ [23–25]. The second harmonic and the hot electrons responsible for X-ray generation occur in the same region of the hot plasma. This allows the use of the second harmonic image to characterize the X-ray generation region and, accordingly, estimate the size of the X-ray source.
For online monitoring of the X-ray generation process, an optical setup was assembled, which includes a microscope that magnifies the second harmonic image onto a CCD camera. Simultaneously, monitoring of the second harmonic spectrum was recorded using a fiber spectrometer (see Fig. 1(A)-(b)). The second harmonic signal is well distinguished from the copper emission spectrum in the same spectral range (510, 515, 521 nm) due to the different divergence of the second harmonic radiation and plasma emission (Fig. 4).
Fig. 4. Second harmonic spectrum (black line) and copper plasma emission (red line) at 2 MHz and an energy of 10 µJ.
To verify the proposed approach, it was demonstrated that the amplitude of the second harmonic signal is directly related to the change in X-ray photon flux. For this purpose, joint measurements of X-ray emission and the second harmonic amplitude were conducted as a function of laser pulse energy and average power, respectively, within the frequency range of 500 kHz to 2 MHz. As shown in Fig. 5(b), for a given laser pulse repetition rate, the X-ray yield monotonically depends on the amplitude of the second harmonic. Moreover, both the amplitude of the second harmonic signal and the X-ray photon flux nonlinearly depends on the average laser radiation power (P2.8) until saturation is reached (see Fig. 5(a)). It is worth noting that the dependence of the second harmonic signal amplitude on the X-ray photon flux is nearly linear, both at the frequency of 500 kHz and at 2 MHz (Fig. 5(b)).
Fig. 5. (a) Dependence of X-ray photon flux (black spheres) and second harmonic intensity (blue spheres) on the average power of laser pulses at a fixed frequency of 2 MHz. Black line represents a power-law approximation of the initial region of the dependence. (b) Dependence of second harmonic intensity on X-ray photon flux at frequencies of 500 kHz and 2 MHz.
Considering the dependence of X-ray emission and second harmonic generation efficiency on laser pulse energy in the range of energy/power values (2-7 µJ/4-13 W, for a pulse repetition rate of 2 MHz), it is worth noting that both dependencies exhibit a similar power-law behavior of P2.8 (see Fig. 5(a)). However, at higher energies (7-11 µJ), deviations from the power-law dependence are observed. These deviations are attributed to the influence of air ionization and the ablation plume, which can lead to defocusing and an increase in the beam size on the target. Thus, the intensity of the second harmonic can serve as an indicator of X-ray generation.
Furthermore, images of the second harmonic generation region were obtained using a CCD camera. Based on the acquired data, profiles were reconstructed and fitted with a Gaussian function (see Fig. 6(a)). Such measurements were conducted in the repetition rate range of 500 kHz to 2.2 MHz at a fixed power of 20 W, as shown in Fig. 6(b). The size of the microplasma X-ray source was calculated based on the 1/e2 level. It should be noted that the temporal dynamics of the size variation of the second harmonic generation region correlates with the dynamics of the X-ray signal. To perform absolute spatial calibration after the measurements, the target was replaced with a ruler with a known division, and the magnification was estimated from the image captured by the camera, which was approximately 8× in this setup. The resulting diameter of the source under optimal conditions - 2 MHz, 20 W, and 10 µJ - is determined to be 8.5 ± 1.6 µm (at the 1/e2 level). The error is calculated based on measurements from more than 10,000 images.
Fig. 6. Profile of the second harmonic at 2 MHz, 20 W, 10 µJ (black line) and its Gaussian profile approximation (red line). Microplasma size is indicated at the 1/e2 level and measures 8.5 µm (a). Dependence of the microplasma diameter at the 1/e2 level on the frequency of laser pulses at a fixed power of 20 W (b).
Figure 6(b) presents the dependence of the plasma source size, obtained using the second harmonic method, on the repetition rate at a fixed power of 20 W. This dependence exhibits a weak linear trend of decreasing source size with increasing repetition rate, which can likely be attributed to the following processes. As the repetition rate increases, the laser energy and vacuum intensity decrease, leading to a reduction in beam defocusing in air, which should significantly decrease the source size. However, ablated micro-particles surrounding the target, which have not settled before the next pulse arrives at higher frequencies, lower the ionization threshold of the medium, resulting in beam defocusing even at lower energies.
3.4 Measurement of the X-ray source size using the edge method
To validate the proposed method of the laser induced microplasma size, independent measurements of the X-ray source size were conducted using the edge method and compared with the results obtained from the second harmonic technique. In order to determine the size of the X-ray microplasma spot, a methodology based on measuring the geometric unsharpness at the edge of a test object was employed. In practice, several similar methods based on this principle are used, commonly referred to as the “edge illumination method” in the literature [26–28]. In X-ray phase-contrast imaging the contrast does not only rely on the absorption of the sample, but is also produced by the phase shift that X-rays experience when passing through different regions of the sample. In this study, the calculation of the focal spot size was based on the British standard [27]. A tungsten carbide ball with a diameter of 550 µm was used as the test object, with a detector pixel size of 9 µm and a magnification factor of M = 12.5. The intensity profile for calculating the focal spot size is shown in Fig. 7. The 0% and 100% levels correspond to the average background value and the object, respectively. The segment AB of the profile was approximated by a linear function, and the points (D and C) of the intersection with the 0% and 100% levels were determined. The focal spot size was then calculated using the relationship $f = \overline {DC} /({M - 1} )$, where $\overline {DC} $ is the distance along the x-axis between points D and C in Fig. 7. As a result, the focal spot size of the X-ray source was determined to be approximately 14 µm in both the horizontal and vertical directions, with a measurement error of approximately 1.5 µm.
Comparing the data from both approaches, it can be observed that the method based on measuring unsharpness yields larger sizes (approximately 10 micrometers in diameter) for the X-ray source compared to the method based on second harmonic detection, specifically 14 ± 4 µm and 8.5 ± 1,6 µm, respectively. However, it should be noted that the size of the source determined using the second harmonic method is obtained from a relatively small number of laser pulses (close to 10), while the exposure required for obtaining the X-ray image takes about 5 minutes, corresponding to approximately 6*108 pulses. Thus, any fluctuations or instabilities occurring in the experimental setup will increase the size of the x-ray source measured using the unsharpness-based method. Therefore, we measured the positions of the “center of mass” of the second harmonic profile over a 5-minute time scale, as shown in Fig. 8. This, at the very least, increases the size of the source measured by the edge method to ∼ 11,5 µm. It is also worth considering that the instability in the position of the tungsten carbide ball is not taken into account in this case. Thus, taking into account the measurement errors, both methods yield comparable sizes for the X-ray source. Therefore, it can be concluded that the method based on on-line second harmonic measurement is applicable for estimating the size of the laser plasma X-ray source, based on femtosecond fiber laser focused on the metal target at I∼1014 W/cm2.
Fig. 8. Map of the “center of mass” position of the second harmonic signal over a period of 5 minutes.
The instability of the source position relative to the tungsten carbide ball is primarily attributed to the target material ablation, which causes a shift in the position of the X-ray source relative to the ball. It is assumed that at an energy density of a single laser pulse of about 30 J/cm2, the target is ablated at a rate of approximately 0.3 µm/pulse. Therefore, at a laser pulse repetition rate of 2 MHz, the target surface layer is removed by about 9 µm (Rayleigh length) in 5 minutes of laser exposure. This process is correspondingly accompanied by a decrease in the amplitude of the X-ray signal. Subsequently, the focus is adjusted based on X-ray flux (see Fig. 9).
Another factor that contributes to the increase in the size of the X-ray microplasma source is the possible defocusing of the laser beam due to the presence of ablated particles between the source and the object. This can also lead to the scattering of X-ray beams on these particles and, consequently, an increase in the diameter measured by the edge method. This is evidenced by the significant increase in the size of the X-ray source (up to 20 µm horizontally) measured by the edge method when the helium purge is turned off, with even more significant broadening in the vertical direction (up to 30-40 µm). This can be attributed to two factors. Firstly, helium has a higher ionization potential than air. Therefore, when helium is used for blowing, defocusing of the beam is reduced in the laser spot area, resulting in a smaller X-ray source size and an increase in X-ray emission due to reduced energy losses from ionization and a smaller beam size [21,29] Additionally, the helium flow significantly affects the ablated particles plume between the target and the sample, pushing it aside, which should also lead to a reduction in the apparent source size.
Finally, we measured the stability of the X-ray flux, as shown in Fig. 9. Due to target ablation, there is a gradual decrease in the signal amplitude due to the shifting of the focus away from the target surface (the target “wears away” with laser pulses). As a result, compensation for the linear trend is required, which can be done manually (jumps in Fig. 9), using proportional-integral-derivative (PID) control, or artificial intelligence (AI). However, a detailed description of this system is beyond the scope of this article.
Thus, the existing stability of the source parameters allows for conducting prolonged radiographic experiments. Additionally, the possibility of obtaining phase-contrast images was demonstrated using the example of measuring a plastic capillary with an outer diameter of 2.4 mm and an inner diameter of 1.7 mm. The X ray source-sample distance (SSD) was 2 cm and the X ray source-detector distance (SDD) was 20 cm. The magnification factor M = 10. The image was acquired with a 5-minute exposure on the Ximea XiRay11 detector. The X-ray projection of a fragment of the wall of the plastic capillary is shown in Fig. 10 (in the center). The intensity profile (Fig. 10, right), constructed from the acquired image, exhibits jumps at the boundaries between plastic and air, which is due to the phase-contrast effect. The edge illumination in Fig. 10 contains a combination of transmission and phase contrast, the latter mainly localized at the bound area of the plastic capillary.
Fig. 10. Rod sketch (left), X-ray image of a fragment of the wall of a plastic capillary (in the center), and intensity profile constructed along the dashed line (right). source-sample distance is 2 cm, source-detector distance is 20 cm, magnification factor is 10.
4. Conclusion
We implemented a new scheme of a microfocus X-ray laser-plasma source (X-ray yield is ∼1.6 × 109 phot/s/2π and size approximately 10 × 10 µm) based on a low-energy high repetition rate femtosecond fiber laser tightly focused (NA∼0.2) on a rotated coper target in combination with on-line control based on the second optical harmonic generated in the near-surface plasma. The yield is maximized for a repetition rate of 2 MHz and an average power of 20W. The optimal conditions (laser pulses repetition rate, laser pulse energy and spatial-temporal separation between the incident pulses) are determined by the balance between the laser pulse defocusing in the ablated plume for high frequencies and laser pulse self-action. The role of these processes could be reduced by blowing helium into the interaction zone. We revealed a nonlinear dependence between the repetition rate of incident laser pulses and the X-ray yield. The X-ray yield exhibited an increase as the repetition rate of the laser pulses increased, while the target scanning rate remained constant. The resulting size of the laser-plasma X-ray source minimum among known similar laser-plasma X-ray sources. The results obtained satisfy the requirements imposed on the source size for phase contrast measurements that was demonstrated in the performed test experiments.
The presented results give a first insight of the regimes of laser-plasma generation of X-ray generation under tight focusing of low energy, high repetition rate laser radiation at vacuum free conditions.
Funding
Ministry of Science and Higher Education of the Russian Federation (075-00963-23-01, 075-15-2021-1362).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. R. Toth, S. Fourmaux, T. Ozaki, M. Servol, J. C. Kieffer, R. E. Kincaid, and A. Krol, “Evaluation of ultrafast laser-based hard x-ray sources for phase-contrast imaging,” Phys. Plasmas 14(5), 053506 (2007). [CrossRef]
2. V. B. Bessonov, “Microfocus X-ray Tubes,” J. Russ. Univ. Radioelectron. 24(5), 6–21 (2021). [CrossRef]
3. M. Gambari, R. Clady, A. Stolidi, O. Utéza, M. Sentis, and A. Ferré, “Exploring phase contrast imaging with a laser-based Kα x-ray source up to relativistic laser intensity,” Sci. Rep. 10(1), 6766 (2020). [CrossRef]
4. S. Fourmaux and J. C. Kieffer, “Laser-based K α X-ray emission characterization using a high contrast ratio and high-power laser system,” Appl. Phys. B 122(6), 162 (2016). [CrossRef]
5. P. P. Rajeev, S. Banerjee, A. S. Sandhu, R. C. Issac, L. C. Tribedi, and G. R. Kumar, “Role of surface roughness in hard-x-ray emission from femtosecond-laser-produced copper plasmas,” Phys. Rev. A 65(5), 052903 (2002). [CrossRef]
6. A. Baguckis, A. Plukis, J. Reklaitis, V. Remeikis, L. Giniūnas, and M. Vengris, “Generation of plasma X-ray sources via high repetition rate femtosecond laser pulses,” Appl. Phys. B 123(12), 290 (2017). [CrossRef]
7. L. Rimkus, I. Stasevičius, and M. Vengris, “Compact High-Brightness X-ray Source Based on Irradiation of Solid Targets by Gigahertz and Megahertz Bursts of Femtosecond Laser Pulses,” Opt. InfoBase Conf. Pap. 1(8), ETh5A.3 (2022). [CrossRef]
8. N. G. Basov, V. Y. Bychenkov, O. N. Krokhin, M. V. Osipov, A. A. Rupasov, V. P. Silin, G. V. Sklizkov, A. N. Starodub, V. T. Tikhonchuk, and A. S. Shikanov, “Second Harmonic Generation in a Laser Plasma - Review,” Sov. J. Quantum Electron. 9(9), 1081–1102 (1979). [CrossRef]
9. G. S. Agarwal and S. S. Jha, “Theory of second harmonic generation at a metal surface with surface plasmon excitation,” Solid State Commun. 41(6), 499–501 (1982). [CrossRef]
10. V. M. Gordienko, S. A. Magnitskii, T. Y. Moskalev, and V. T. Platonenko, “Plasmon-polaritons on the surface of femtosecond laser-induced plasma,” SPIE Proc. 2770(126), 126–134 (1996). [CrossRef]
11. A. A. Garmatina, V. E. Asadchikov, A. V. Buzmakov, I. G. Dyachkova, Y. M. Dymshits, A. I. Baranov, D. V. Myasnikov, N. V. Minaev, and V. M. Gordienko, “Microfocus Source of Characteristic X-Rays for Phase-Contrast Imaging Based on a Femtosecond Fiber Laser,” Crystallogr. Rep. 67(6), 1026–1033 (2022). [CrossRef]
12. L. Martín, J. Benlliure, D. Cortina-Gil, A. Haruna, and C. Ruiz, “Validation of a laser driven plasma X-ray microfocus source for high resolution radiography imaging,” Phys. Medica 82(February), 163–170 (2021). [CrossRef]
13. V. A. Aleshkevich, V. M. Gordienko, and B. G. Bravy, “Intensity delivery to the focal area with tight focusing of a femtosecond laser beam in a gas environment,” J. Opt. Soc. Am. B 40(5), 1031 (2023). [CrossRef]
14. R. Yamada, W. Komatsubara, H. Sakurai, K. Konishi, N. Mio, J. Yumoto, and M. Kuwata-Gonokami, “Simulation of nonlinear propagation of femtosecond laser pulses in air for quantitative prediction of the ablation crater shape,” Opt. Express 31(5), 7363 (2023). [CrossRef]
15. W. Hu, Y. C. Shin, and G. King, “Effect of air breakdown with a focusing lens on ultrashort laser ablation,” Appl. Phys. Lett. 99(23), 1–4 (2011). [CrossRef]
16. J. König, S. Nolte, and A. Tünnermann, “Plasma evolution during metal ablation with ultrashort laser pulses,” Opt. Express 13(26), 10597 (2005). [CrossRef]
17. S. Kraft, J. Schille, S. Mauersberger, L. Schneider, and U. Loeschner, “Pump-probe imaging for process control and optimization in high-speed laser micro machining,” in Proc.SPIE 11268, 54 (2020). [CrossRef]
18. J. Schille, S. Kraft, T. Pflug, C. Scholz, M. Clair, A. Horn, and U. Loeschner, “Study on X-ray Emission Using Ultrashort Pulsed Lasers in Materials Processing,” Materials 14(16), 4537 (2021). [CrossRef]
19. R. V. Volkov, S. A. Gavrilov, D. M. Golishnikov, V. M. Gordienko, P. M. Mikheev, A. B. Savel’ev, and A. A. Serov, “Generation of hot particles in femto-second laser-produced plasma with the use of solid-state modified targets,” Kvantovaya Elektron. 31(3), 241–246 (2001). [CrossRef]
20. H. Legall, C. Schwanke, J. Bonse, and J. Krüger, “The influence of processing parameters on X-ray emission during ultra-short pulse laser machining,” Appl. Phys. A 125(8), 570 (2019). [CrossRef]
21. A. A. Garmatina, B. G. Bravy, F. V. Potemkin, M. M. Nazarov, and V. M. Gordienko, “Intensity clamping and controlled efficiency of X-ray generation under femtosecond laser interaction with nanostructured target in air and helium,” J. Phys.: Conf. Ser. 1692(1), 012004 (2020). [CrossRef]
22. A. A. Garmatina, I. A. Zhvaniya, F. V. Potemkin, and V. M. Gordienko, “Generation of X-ray radiation from a plasma in a microchannel of a copper target located in the air under the action of soft-focused femtosecond laser pulses with an intensity of 100 TW cm -2,” Quantum Electron. 48(7), 648–652 (2018). [CrossRef]
23. D. von der Linde, H. Schulz, T. Engers, and H. Schüler, “Second Harmonic Generation in Plasmas Produced by Intense Femtosecond Laser Pulses,” IEEE J. Quantum Electron. 28(10), 2388–2397 (1992). [CrossRef]
24. R. S. Marjoribanks, L. Zhao, F. W. Budnik, G. Kulcsár, A. Vitcu, H. Higaki, R. Wagner, A. Maksimchuk, D. Umstadter, S. P. Le Blanc, and M. C. Downer, “Laser-plasma harmonics with high-contrast pulses and designed prepulses,” Laser Part. Beams 426(1), 342–347 (1998). [CrossRef]
25. V. M. Gordienko, I. A. Zhvaniya, and I. A. Makarov, “X-ray production and second-harmonic generation during femtosecond laser microdrilling,” Appl. Phys. A 120(2), 409–415 (2015). [CrossRef]
26. “GOST 22091.9-86 Pribory rentgenovskie. Metody izmereniia razmerov effektivnogo fokusnogo piatna /in Russian/. X-ray devices. The methods of effective focus spot size measurements,”.
27. “BS 6932, 1988 Edition, 1988 - Method for Measurement of the Effective Focal Spot Size of Mini-Focus and Micro-Focus X-Ray Tubes Used for Industrial Radiography,”.
28. “The European Standard EN 12543-5:1999. Non-destructive testing-characteristics of focal spots industrial X-ray systems for use in non-destructive testing, part 5: measurement if the effective focal spot size of mini and micro focus X-ray tubes.,”.
29. A. A Garmatina, M. M. Nazarov, P. A. Shcheglov, M. V. Chaschin, V. A. Aleshkevich, B. G. Bravy, V. M. Gordienko, and Panchenko V. Ya, “Effective line X-ray generation by chirped femtosecond laser pulses interaction with copper target at local helium flow,” Opt. Spectrosc. 130(4), 416 (2022). [CrossRef]
