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Abstract
Higher brightness UV light sources based on laser-sustained plasma (LSP) finds critical applications in high-resolution optical inspection and measurement. An annular beam focused with a low F-number is proposed for the first time to investigate its effect in realizing high-brightness LSP compared with Gaussian beams. We experimentally verified that the annular laser beam sustained a nearly laterally symmetric plasma with a longitudinal length less than 600 µm plasma length, where the length-width ratio was four times smaller than that driven by a TEM00 Gaussian beam. Theoretical analysis further explored that the annular beam's transmission path could limit the plasma's longitudinal growth, like a “reservoir”. Furthermore, the “reservoir” effect is favorable for effectively increasing the plasma temperature and the effective power ratio of UV from 8% to 15%. This work paves a novel way of generating high-brightness UV sources by spatial manipulation of infrared pumping beam.
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1. Introduction
Gas discharge technology is widely used in high-resolution optical inspection and measurement as a major light source. With the development of high-power laser technology, the gas discharge has moved into the optical field [1]. Continuous optical discharge (COD) was first theoretically predicted and experimentally realized in 1970 by Raizer et al. [2,3]. The continuous wave (CW) laser beam is focused on an initial plasma formed in the gas (usually Argon or Xenon) by an arc discharge. After the electrodes have been de-energized, the plasma can only be sustained by absorbing laser power. Hence COD is known as laser-sustained plasma (LSP) [4]. The minimum average laser power at which the plasma can be sustained without disappearing is also known as the LSP laser threshold [1]. Early LSP was usually based on a 10.6 µm high-power CO2 laser [1], which absorbed laser power through the inverse bremsstrahlung process between electrons and ions to sustain the plasma. However, the absorption based on the inverse bremsstrahlung process leads to excessively high LSP laser thresholds, limiting the practical application of LSP. With the development of near-infrared (NIR) lasers, NIR high-power lasers are used to sustain plasma through bound-bound electronic transitions. The bound-bound electronic transitions increase as the pressure of the gas (Argon or Xenon) raises, resulting in the increase of laser absorption by the plasma. Therefore, the application of high-power NIR lasers reduce the LSP laser threshold and make LSP widely available. For example, LSP is a broad-spectrum light source with high spectrum brightness, widely used in imaging and measurement fields. The LSP-based light source proposed by S. Horne et al. provides a flat spectrum from the deep UV band to IR band (170 nm to 800 nm), with a spectral radiance of approximately 10 $mW/({m{m^2} \cdot nm \cdot sr} )$, 5-10 times higher than that of a high-brightness Xenon arc lamp [5]. With the current development of semiconductor processes, higher brightness of light sources in the UV band is a critical element for high-resolution optical inspection and measurement. It is possible to generate high-brightness UV light by means of free-electron lasers and synchrotron radiation. However, these approaches need to be based on large scientific installations, hence difficult to apply in industrial production [6,7]. As a broad-spectrum light source with high spectral brightness, LSP is also used to generate high-brightness UV light. Compared to the above-mentioned methods, LSP-based UV light sources show clear advantages for industrial applications due to the much more compact structure.
For UV light sources, brightness is the most important parameter and the brightness of an LSP-based UV light source depends on the size and brightness of the plasma. To reduce the size of the plasma, KLA Tencor researchers have designed an LSP lightbox called “Sirius”. The system uses an ellipsoidal reflector to focus the laser beam, making the plasma smaller and brighter [8]. The beam focusing parameter F-number affects the shape and stability of LSP plasma. The F-number is defined by $F = f/d$, where f is the focal length of the focusing system and d is the beam diameter. The laws of plasma size evolution at different Gaussian beam F-numbers (3 to 15) were studied by V.P. Zimakov et al. from A. Ishlinsky Institute for Problems in Mechanics [9]. They found that the plasma length increases gradually as the F-number increases. However, at 6 < F < 10, the bistable phenomenon of “long plasma” and “short plasma” is generated by plasma refraction, and after F > 10, the plasma length drops sharply. The LSP with different F numbers was studied by Z. Szymanski et al. and the lowest F number was F = 1.06, and these results show that the plasma shape strongly depends on the focusing geometry [10–12]. An annular beam based LSP with F = 7 was studied by X. Chen et al [13,14]. The laser in their work was an unstable resonator whose output beam had an annular shape similar to a TEM01 mode profile. This demonstrates that the annular beam could be used to sustain the plasma in the same way as a Gaussian beam. Another study from V.P. Zimakov et al. found that the increase in LSP spectrum brightness is due to the increase in plasma length with increasing laser power [15]. The plasma temperature does not change and therefore the power fraction in the UV spectrum band does not change. This raises the difficulty of reducing the size of the plasma while at the same time increasing the LSP spectrum brightness. In addition, the plasma in LSP usually has an elliptical shape with a relatively high length-width ratio, making the subsequent optical design and beam shaping of LSP-based light sources more difficult.
There is an urgent need for an effective method to continue to increase the brightness of the LSP-based UV light source, while reducing the size of the plasma and sustaining a near-symmetrical shape. Here we propose a LSP source driven by a low F-number annular beam, for the first time to our knowledge. Interestingly, the low F-number annular beam transmitted in the plasma has a “reservoir” effect with the increase of laser power. The “reservoir” effect limits the growth in plasma size while increasing the core temperature of the plasma instead. This approach not only effectively increases the power fraction in the UV band, but also reduces the size of the plasma and sustains a nearly symmetrical shape, which can effectively increase the brightness of LSP-based UV light source. As the power fraction in the UV band increases, the utilization of annular beam helps the LSP to improve the IR-to-UV conversion efficiency. Nearly symmetrically shaped, high brightness UV sources generated by LSP source driven by a low F-number annular beam will potentially simplify the design of subsequent optical systems. In this paper, an annular beam at F = 0.4 is constructed at the focal point by designing a conical lens set and an ellipsoidal reflector. We systematically measured the laser threshold power of LSP and characterized the plasma geometry and spectrum. Specifically, the length-width ratio of the plasma and the spectrum fraction of the LSP UV band (λ<400 nm) were studied. Compared with LSP driven by Gaussian beams at F = 3.5 and F = 5, it was found that the length-width ratio of the plasma was closer to 1 and the fraction of the UV-band (λ<400 nm) of the spectrum was higher for LSP driven by annular beams at low F-numbers. We found that by using an annular beam at a low F-number, we can obtain an LSP light source with a nearly-symmetrical plasma shape, a length of less than 0.6 mm, and a higher spectrum fraction in the UV band. We then used the Saha equation and Eikonal equation to analyze the transmission of an annular beam in a plasma, which explains the experimental phenomenon from the beam propagation perspective in the plasma refractive index distribution.
2. Experimental setup
The experimental setup for an ordinary LSP is generally shown in Fig. 1(a), where a lens with focal length f focuses a Gaussian beam with beam diameter d between the electrodes of a Xenon lamp (OSRAM, XBO 150 W/OFR) to achieve LSP. The central wavelength of the continuous fiber laser (JPT, CW-500W) is 1.08 µm. The maximum power is up to 500 W. The output Gaussian beam quality factor M2 is measured to be less than 1.3 and the collimator output beam diameter is about 10 mm. To study the effect of different F numbers on LSP, two lenses with f = 35 mm (Thorlabs, LA4052-B) and 50 mm (Thorlabs, LA4148-B) are used to achieve LSP using the Gaussian beam with a beam diameter of 10 mm at F = 3.5 and F = 5, respectively. To reduce the F-number, a set of conical lenses (Thorlabs, AX2520-B) is used to convert a Gaussian beam with a beam diameter of 10 mm into a toroidal beam with an outer diameter of 15 mm and an inner diameter of 3.48 mm, as shown in Fig. 1(b). Then a lens with f = 30 mm (Daheng Optics, GCL-010819) is utilized to achieve LSP at F = 2. To further reduce the F-number, an elliptical reflector (OptoSigma, TCEA-148C-28) and a concave lens with f = -150 mm (Thorlabs, LF1547-B) are used instead of a convex lens with f = 30 mm. The laser source is placed at the focal point f2 of the equivalent elliptical reflector, and the annular beam will be focused between the Xenon lamp electrodes, i.e., at the focal point f1 of the elliptical reflector. In this way, it is possible to realize LSP at F = 0.4, as shown in Fig. 1(c). Figure 1(d) shows the annular beam near the focus point of Fig. 1 (b). The annular beam is focused between the two electrodes to sustain the plasma. The annular beam in Fig. 1(c) is deflected by 90 degrees and is also focused between the two electrodes. Figure 1(d) also shows the variation of the beam cross section for the annular beam near the focus point [16–18]. Figure 1(e) shows the detail optical design in the dashed box in Fig. 1(c). The process of generating the annular beam is introduced [19]. It can be noticed that the laser beam appears hollow in the middle and turns into an annular beam under the action of the conical lens set. It subsequently diverges through the concave lens and converges through the ellipsoidal reflector.
Fig. 1. Schematic diagram of LSP experimental setup at different F. (a) LSP driven by Gaussian beam; (b) LSP driven by annular beam at F = 2; (c) LSP driven by annular beam at F = 0.4; (d) annular beam near the focus point; (e) generation of annular beam. CLS: conical lenses set.
3. Results and discussion
3.1 LSP driven by annular beam at F = 0.4
Using the annular beam and ellipsoidal reflector, LSP with a laser threshold of 280 W was achieved at F = 0.4. Figure 2 shows the LSP achieved using the device in Fig. 1(c) with the action of the annular laser at 290 W, 295 W, 300 W, 305 W, and 310 W. Figure 3(a) shows the measurement setup used in the experiment. The CCD (WinCamD-LCM-UV-S1) and spectrometer (Ocean, Maya 2000 Pro) are placed at the focal plane of the ellipsoidal reflector to observe the shape and spectrum of the plasma, respectively. The LSP is located at the focal point of the ellipsoidal reflector. The shape of the plasma is measured by the CCD through a lens with f = 75 mm (Thorlabs, AX4275-UV). The distance from the plasma to the lens is 120 mm, and the distance from the CCD to the lens is 203 mm, thus the horizontal magnification is 1.7. It can be found that the volume of the LSP increases slightly with the increase of laser power, and the brightness of the core region increases significantly.
Fig. 2. Plasma image in CCD when F = 0.4 and laser power increases to (a) 290 W; (b) 295 W; (c) 300 W; (d) 305 W; (e) 310 W. The color bar reflects the intensity level of plasma.
The length and width of the LSP were measured by CCD, as shown in Fig. 3, where the inset shows the original imaging results. We define the full width at half maximum (FHWM) of the plasma along the laser direction as the length of the plasma (the dashed line in the inset), and the FHWM of the plasma perpendicular to the laser direction as the width of the plasma (the solid line in the inset). As shown in Fig. 3, the length of plasma is 569 µm and the width is 463 µm. The plasma is nearly symmetrical shape with a length-width ratio of only 1.2. This nearly symmetrical shape with a length-width ratio close to 1 benefits the subsequent optical design and beam shaping of LSP-based light sources.
Fig. 3. (a) Measurement setup of plasma size and spectrum;(b) original plasma image in CCD; (c) length (the dashed line in the Fig. 3(b)) and (d) width (the solid line in the Fig. 3(b)) of LSP measured from CCD.
3.2 LSP under different F numbers
With the change of F-number, the characteristics of LSP such as laser threshold, plasma length, and the length-width ratio will change significantly. As shown in Fig. 4, the laser threshold of LSP driven by Gaussian beam at F = 3.5 is 50 W, the spot radius at the focal point is 4.82 µm. The laser threshold of LSP driven by Gaussian beam at F = 5 is 50 W, the spot radius at the focal point is 6.88 µm. The laser threshold of LSP driven by annular beam at F = 2 is 140 W, the spot radius at the focal point is 9.95 µm. The laser threshold of LSP driven by annular beam at F = 0.4 is 280 W, the spot radius at the focal point is 12.25 µm. It can be found that the LSP threshold increases with the decrease of the F-number. Since the LSP threshold varies widely for different F-numbers, we use the difference between laser power and LSP threshold power, ΔP, as a reference to study the plasma length as well as the length-width ratio for different F-numbers at different laser powers. As shown in Fig. 5(a), it can be found that the length of the plasma increases with the increase of power. In addition, the length of the plasma decreases with the decrease of the F-number. At F = 5 and ΔP = 30 W, the length of the plasma can reach 1.3 mm. In contrast, at F = 0.4 and ΔP = 30 W, the length of the plasma is only 0.592 mm. Furthermore, as shown in Fig. 5(b), the length-width ratio of the plasma decreases significantly as the F-number decreases, and the length-width ratio of the plasma is only 1.2 for F = 0.4. This plasma with a length-width ratio close to 1 has a significant advantage in the subsequent further processing when used as a light source.
Fig. 5. LSP characteristics for different F-number (a) plasma length; (b) length-width ratio (the inset is LSP with different F numbers).
3.3 Spectrum analysis of LSP
The spectrum of the plasma can be measured by replacing the CCD with a spectrometer (Ocean, Maya 2000 Pro). Figure 6 is the normalized spectrum of plasma driven by annular beam at F = 0.4. The LSP spectrum at different laser powers and arc plasma were normalized to the peak point of the spectrum at the laser power of 310 W. Figure 6(a) shows the LSP spectrum for different laser powers and arc plasma spectrum in the range of 250∼1050 nm. Due to the radiation properties of Xenon, the spectrum of the Xenon plasma has a lower peak near 400 nm and a higher peak near 800 nm. It can be noticed that the spectrum around 400 nm of the LSP is significantly higher than that of the arc plasma. The reason for the difference is that the LSP is at a higher temperature than the arc plasma, thus generating more radiation at a shorter wavelength. Figure 6(b) shows the LSP spectrum for different laser powers and arc plasma spectrum in the range of 250∼400 nm. It can be found that the UV band spectrum of LSP (<400 nm) is significantly higher than the UV band spectrum of arc plasma, and the intensity of the UV band spectrum of LSP increases with the increase of laser power. The intensity of the LSP spectrum and arc plasma spectrum below 300 nm tends to be close to zero because the Xenon lamp used is an ozone-free Xenon lamp, and the UV light below 300 nm cannot penetrate the Xenon lamp.
Fig. 6. Normalized LSP spectrum for different laser powers when F = 0.4 and arc plasma spectrum between wavelength (a) 250∼1050 nm and (b) 250∼400 nm.
As shown in Fig. 7, the fraction of the LSP spectrum below 400 nm at F = 0.4 gradually increases with increasing laser power, from 12.2% at ΔP = 10 W to 15.3% at ΔP = 30 W. The fraction of the LSP spectrum below 400 nm is a ratio between spectral integration in the range of 250-400 nm and 250-1050 nm respectively. In comparison with the LSP at F = 5 and F = 3.5, it can be found that the fraction below 400 nm of the LSP spectrum at F = 5 and F = 3.5 is lower and does not increase with the increasing laser power; the fraction below 400 nm of the LSP spectrum at F = 0.4 is significantly higher and increases with the increasing laser power; The arc plasma has the lowest fraction of the spectrum below 400 nm, which is only 5.9%. This phenomenon indicates that the LSP at F = 5 and F = 3.5 did not increase the temperature with the increasing laser power, while the LSP at F = 0.4 increased the temperature with the increasing laser power and produced more radiation in the UV band. Referring to Fig. 5(a), it can be found that with the increase of laser power, the increase of plasma length at F = 5 and F = 3.5 is significantly more than that at F = 0.4, so it can be assumed that with the increase of laser power, the LSP at F = 5 and F = 3.5 is mainly reflected in the increase of plasma length, while the LSP at F = 0.4 is mainly reflected in the increase of core region temperature and thus the increase of the spectrum fraction of the UV band. With the increasing laser power at F = 0.4, the beam transmission path forms a closed absorption region within the plasma, which limits the increase of the plasma length.
Due to the lack of spectral radiance measurement system, we could not make the direct measurement of the LSP brightness. Therefore, we estimated the average spectral radiance between 260 nm and 350 nm of the LSP driven by Gaussian beam as a reference. At a distance of 120 mm from the center of the Xenon lamp, a power meter (Thorlabs, S405C) is placed at the same height as the center of the Xenon lamp. The power meter target surface radius r = 5 mm, distance from the center of the Xenon lamp (at the plasma) R = 120 mm. The power meter reading Ppm. A 260-350 nm band pass filter with transmission efficiency 75% is placed between the lamp and the power meter. By spectral integration, the power between 260 nm and 350 nm is 56% of the total Ppm. Since R is much large than the plasma size, we can assume that the plasma radiates in 4π stereo angle uniformly. Hence the full UV range power emitted by the LSP is derived according to the following equation.
The average spectral radiance L of the LSP in the range of 260 nm to 350 nm is derived according to the following equation.
where P is the total power emitted by the plasma in the wavelength range from 260 to 350 nm, 4π indicates that the plasma radiates UV light into space at 4π stereo angles, A is the plasma cross-sectional area, and Δλ is the wavelength range corresponding to 260-350 nm (90 nm).The average spectral radiance (260-350 nm) of LSP estimated according to the above method are about 11.8 $mW/({m{m^2} \cdot nm \cdot sr} )$ at F = 5 and ΔP = 30 W, and about 23.5 $mW/({m{m^2} \cdot nm \cdot sr} )$ at F = 3.5 and ΔP = 30 W.
Different from the orthogonal setup in Gaussian beam illumination, the annular beam was arranged in a co-axial way with the fiber laser. Therefore, we could not directly measure Ppm. However, considering that the plasma size of the LSP driven by annular beam is much smaller as shown in Fig. 5, and the UV band fraction is much larger as shown in Fig. 7, the spectral radiance of the LSP driven by annular beam at F = 0.4 should be higher than that of the LSP driven by Gaussian beam at F = 3.5, i.e., 23.5 $mW/({m{m^2} \cdot nm \cdot sr} )$.
3.4 Beam transmission path in plasma at different F-numbers
It is known that the transmission of the beam in the plasma is refracted by the plasma refractive index distribution, and the electron refractive index plays a major role in the refractive index of the plasma, so the electron refractive index ${n_e}$ can be used to instead of the plasma refractive index n.
where e is the electron charge, $\lambda $ is the laser wavelength, ${n_e}$ is the electron density, m is the electron mass, and c is the speed of light. Therefore, we can assume a physical model of a cylindrical plasma with radius $r = 0.3\; mm$, length $l = 2\; mm$, as shown in Fig. 8(a), where the refractive index distribution is shown in Fig. 8(b) and Eq. (6). The minimum refractive index is located at the core of the plasma, i.e., at $r = 0$, where the electron density is highest and the refractive index is lowest. The plasma electron density in this paper was estimated from the following Saha equation.Fig. 8. (a) The plasma refractive index spatial distribution model; (b) The plasma refractive index profile along Y axis.
Then we calculated the laser beam transmission path inside the plasma for different F-number using the Eikonal equation on the Oxy plane [20–22], as shown below:
Fig. 9. The transmission path of different beams focused by different F-number in the plasma. (a) Gaussian beam at F = 3.5; (b) Gaussian beam at F = 5; (c) Annular beam at F = 2; (d) Annular beam at F = 0.4. The deflected beam is shown by the arrow lines. S1 and S2 are the laser region and the plasma absorption region, respectively.
Figure 9(a) shows the transmission path of the Gaussian beam at F = 3.5 inside the plasma; Fig. 9(b) shows the transmission path of the Gaussian beam at F = 5 inside the plasma; Fig. 9(c) shows the transmission path inside the plasma for an annular beam at F = 2. The annular beam has an outer ring F = 2 and an inner ring F = 8.6; Fig. 9(d) shows the transmission path inside the plasma for an annular beam at F = 0.4. The annular beam has an outer ring F = 0.4 and an inner ring F = 1. It can be found that as the F-number increases, the phenomenon of deflection of the laser beam transmission path becomes more obvious. At F > 2, the laser beam has no focus point within the plasma and a large laser region is formed. For the Gaussian beam at F = 3.5, the laser region is the region between two dark blue curves in Fig. 9(a); For the annular beam at F = 2, the laser region is the sum of the region between two green curves, and the region between two navy blue curves in Fig. 9(c). When F > 2, the beam is deflected by the plasma and will emit from the incident side. When F < 2, the beam intersects within the plasma and emits from the other side of the incident side, the laser beam has a focal point within the plasma. The two intersections of the red crossing lines and black crossing lines in Fig. 9(d) are the focal points of the corresponding beam. Taking the annular beam at F = 0.4 as an example, the laser region is the region between two black curves and two red curves in Fig. 9(d). It can be found that the laser region under the effect of the annular beam at F = 0.4 limits the length of plasma, like a “reservoir”, which is the reason why the growth of plasma length is not obvious with the increasing laser power. Thus, the main change in the plasma with increasing laser power is expressed in the increase of the temperature in the core region, which increases the fraction of the spectrum below 400 nm. In contrast, the laser transmission paths within the plasma at F = 3.5 and F = 5 do not have the same “reservoir” effect as at F = 0.4. Therefore, when the laser power increases, the plasma becomes longer rather than increasing the core temperature. Since the core temperature does not change significantly, the short wavelength radiation below 400 nm does not increase.
We refer to the core region of the plasma within the laser region, the purple region in Fig. 9, as the laser beam absorption region of the plasma. The laser beam absorption region of the plasma has the area ${S_2}$. The shaded region and the purple region in Fig. 9 are the laser beam region and have the area ${S_1}$. The area ${S_1}$ is divided by the area ${S_2}$, defined as the percentage of absorption area, ${\sigma } = \frac{{{{\boldsymbol S}_1}}}{{{{\boldsymbol S}_2}}}$. We compare the LSP threshold power with the inverse of the percentage of absorbed area ${{\sigma }^{ - 1}}$ at different F-numbers, as shown in Fig. 10. The black line is the LSP threshold at different F-numbers measured from the experiment. The red line is the calculated ${{\sigma }^{ - 1}}$ at different F-numbers. It can be found that the LSP threshold power variation at different F-numbers has obvious similarity with the ${{\sigma }^{ - 1}}\; $ variations at different F-numbers. The calculated results have a strong similarity to the experimental measurements. Therefore, we can consider that the laser threshold at different F-numbers is inversely proportional to the percentage of absorption area, ${\sigma }$. The “reservoir” effect of low F-number annular beam transmission within the plasma reduces the area within the initial plasma core that absorbs the laser, raising the laser threshold of the LSP. From another point of view, the “reservoir” effect constrains the energy in a smaller area, restricting the shape of the plasma and increasing the core temperature. Thus, by sustaining a near-symmetrical plasma shape with a low F-number annular beam, the power fraction in the UV spectrum band is increased, which helps to achieve higher brightness UV sources.
Fig. 10. Inverse of the percentage of absorbed area ${{\sigma }^{ - 1}}$ and LSP threshold power for different F-number beam.
4. Conclusions
In this paper, three different experimental setups were used to achieve LSP under the action of Gaussian beams with F = 5 and 3.5 and annular beams with F = 2 and 0.4, respectively. Laser thresholds of LSP, plasma lengths, and spectrum of the plasma were measured under the action of beams with different F-numbers, and the length-width ratio and the UV-band spectrum fraction of the plasma were studied and analyzed. The LSP achieved driven by an annular beam at F = 0.4 was found to have a plasma length of less than 0.6 mm, a length-width ratio close to 1, and a nearly doubled spectrum fraction in the UV-band compared to the Gaussian beam. This is since the transmission path of the laser beam with in the plasma is influenced by the refractive index of the plasma. Therefore, the transmission paths of Gaussian and annular beams within the plasma were analyzed using the Eikonal equation for different F-number, and it was found that the transmission path of the annular beam at low F-number limits the increase in the volume of the plasma, like a “reservoir”, which would cause plasma to tend to increase core temperature rather than the length when the laser power is increased. The demonstrated nearly symmetric high brightness UV light source driven by a low F-number annular beam could will potentially simplify the design of subsequent optical systems, such as optical imaging and spectroscopy.
Funding
National Key Research and Development Program of China (2022YFE0102300).
Acknowledgments
X. Yu is partially supported by the National Young Talents Program. F. Yu is partially supported by the Pioneer Hundred Talents Program, Chinese Academy of Sciences.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are available in Ref. [23].
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