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Abstract
Laser-sustained plasma (LSP) featured by high radiance in the ultraviolet (UV) spectral range is found to be powerful in high resolution inspection and spectroscopy applications. In this paper, we demonstrate significant enhancement of UV radiance in LSP excited by a high power focused annular laser beam of small F-number. A two-dimensional refractive index distribution in the plasma region is established to obtain the propagation path of the annular beam. Subsequently, the spatial distribution of the annular beam power density is calculated to establish the quantitative relationship between laser power and plasma dimension. Theoretical analysis of a “reservoir” effect constructed by the annular beam is carried out. Abrupt plasma dimension change is observed when the laser power exceeds the “reservoir” boundary. The new model is then validated by experiments. LSP with the highest reported UV radiance to our knowledge has been achieved. This work paves what we believe is a novel way of generating high radiance UV sources by spatial manipulation of excitation laser beam.
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1. Introduction
A dense plasma can be sustained by absorbing the power of laser at temperature up to $2 \times {10^4}$K and the continuous optical discharge (COD) was first realized in 1970 by Raizer et al. [1,2], also known as the laser-sustained plasma (LSP). One of the implementation methods of LSP is to generate the initial plasma of low density in the high-pressured noble gas (usually xenon or argon) by using the common arc discharge in a closed bulb. Subsequently, the laser is focused on the plasma and provides the power for its maintenance instead of electric current [3]. Readily available high-power near-infrared (NIR) lasers are used to sustain plasma through bound-bound electronic transitions with high absorption rate [4], making LSP light sources widely used as a miniaturized broadband light source. Such light source has been applied to broadband spectroscopy and imaging research [5,6], especially in UV band [7].
For LSP-based UV light sources, the spectral radiance determined by plasma size and total UV radiation power is an important parameter. The laser focusing parameter F-number defined as F = f/d is used to describe the effect of laser focusing characteristics on LSP, where f is the focal length and d is the beam diameter. Z. Szymanski simulated the plasma sustained by the Gaussian laser in the F-number range of 1.06 to 8.4, demonstrating that the plasma shape strongly depends on the focusing geometry [8]. V. P. Zimakov et al. showed that the F-number of Gaussian beam greater than 6 would lead to the increase of plasma length and instability of plasma [9,10]. Y. Hu et al. carried out experimental research on Gaussian beam in the range of F-number from 3.5 to 15. The results showed that the decrease of F-number can reduce the growth of plasma length caused by the increase of laser power [11]. However, the geometric size limitations of optical components make it difficult to reduce the F-number below 3 simply by using lenses. To further reduce the F-number, KLA has designed an LSP lightbox called “Sirius”. The system uses an ellipsoidal reflector to focus the laser beam, making the LSP smaller and brighter [12]. A. K. Mikhail et al. used two laser beams with an angle of 60 degrees to effectively reduce the F-number and sustained a small-sized plasma [13,14]. In our previous work, we shaped the Gaussian beam into an annular beam and focused it on the center of the Xenon lamp with an ellipsoidal reflector [15]. The annular beam with an F-number less than 1 was found to have the “reservoir” effect, reducing the size of the plasma. A one-dimensional refractive index distribution in the plasma region was established to illustrate that the laser beam type can affect the plasma size. However, the refractive index distribution perpendicular to the optical axis was not considered. The quantitative relationship between laser power and plasma size has not been established. The effective laser power range of the “reservoir” effect lacked theoretical analysis and experimental verification.
In this article, we construct an annular beam with a minimum F-number of 0.6. As is shown in Fig. 1, the refractive index distribution in the plasma region causes the deflection of the incident annular beam. The deflected annular beam then constructs a high-power density region. Such region confines the LSP in the form of a “reservoir”. A two-dimensional refractive index distribution in the plasma region is established. The Eikonal equation is used to analyze the propagation path of the annular beam in the plasma region. The spatial distribution of the annular beam power density is calculated to establish the quantitative relationship between laser power and plasma dimension. Theoretical analysis indicates that the “reservoir” effect can suppress the size growth of plasma within hundreds of watts of laser power. Abrupt plasma dimension change is observed when the laser power exceeds the “reservoir” boundary. The new model is validated by experiments. Moreover, an LSP setup with the highest reported UV radiance to our knowledge has been achieved.
2. Modeling and simulation
A refractive index distribution model in the plasma region needs to be established to analyze the propagation path of annular beams in the plasma region. For a closed xenon lamp, the relationship between the atomic number density N and the pressure p in the initial state satisfies the Ideal Gas Law.
where T is the temperature and R is the ideal gas constant. For the determined pressure, N can be represented as a function of T. For the plasma area, if only the first-order ionization is considered, the electron density ne equals to the ion density n+ and the neutral particle density equals to N minus n + . According to the Saha ionization equation, electron density can be represented as a function of temperature.
Fig. 2. Simulation results of (a) the refractive index distribution in the plasma region; (b) laser transmission path of the annular beam; (c) the fraction of laser power in different F-number ranges of the annular beam.
The annular beam in the experiment can be regarded as a collection of rays with F-numbers between 0.6 and 1.6. Relevant research has shown that the eikonal equation is suitable for analysis in the field of plasma science [17]. Therefore, the laser beam transmission path inside the plasma for rays with different F-numbers is calculated using the Eikonal equation on the Oyz plane [18].
The normalized laser power density distribution along the Y = 0 axis can be calculated by dividing the laser power by the area size of a single region within S1 to S4. As is shown in Fig. 3(a), the power density in S1 and S2 regions is similar, which will result in the plasma size growing from S1 region to cover S2 region at relatively small laser power increments. However, the power density difference between S2 and S3 regions is nearly three times, which creates a “reservoir” resulting in relatively large laser power increments before the plasma size covers S3. Based on the previous experimental results, the power required to maintain the plasma in the S1 region is approximately 280W, and the corresponding power density can be calculated. Assuming that the laser power density required to sustain a plasma in each region is same, the power required to sustain a plasma in each region can be calculated. Figure 3(b) shows the simulation results of the relationship between laser power and plasma length. The variation of plasma size with laser power is represented by the red line in the figure. Within the range of hundreds of watts of laser power growth marked by the reservoir area, the growth in plasma length with increasing laser power will be suppressed. Abrupt plasma dimension change is observed when the laser power exceeds the “reservoir” boundary. The spatial distribution of the annular beam power density suppresses the plasma size, making the power increment absorbed by the plasma tend to rise in the plasma temperature, thus improving the spectral radiance.
Fig. 3. Simulation results of (a) normalized laser power density along the Y = 0 axis and (b) the relationship between laser power and plasma length.
Based on the simulation process, the impact of the “reservoir” effect on the LSP spectral radiance can be summarized as follows. The spatial distribution of refractive index in the plasma region results in only the rays with F-number below the critical value could reach the plasma core area. The low F-number rays construct the laser power density distribution along the Z-axis. Therefore, the growth of plasma length with the increase of laser power is nonlinear. Within a certain range of laser power, the growth of plasma length is suppressed. The plasma will tend to increase temperature rather than plasma size, which is beneficial for improving the spectral radiance of LSP.
3. Experimental setup
To verify the simulation results, relevant experiments were conducted. The experimental setup for laser-sustained plasma is shown in Fig. 4(a). A CW fiber laser with a central wavelength of 1.08 µm is used to provide a collimated Gaussian beam. A pair of conical lenses are used to convert the Gaussian beam into a collimated annular beam. The simulation results of laser power density distribution before and after the conical lenses set are shown in Fig. 4(b). To further reduce the equivalent F-number of the focusing path, a concave lens and an elliptical reflector are used to focus the annular beam on the center of the xenon lamp, which coincides with the focal point of the elliptical reflector. The side of the elliptical reflector is perforated for measuring the characteristics of the plasma. The equivalent F-number is calculated based on the geometric size of the annular beam and the focal length of the elliptical reflector. An annular beam with the F-number of 0.6 for the outer edge and 1.6 for the inner edge is generated by the experimental setup. A homemade xenon lamp is used in the LSP experiments. The variation of the beam cross section of the annular beam near the convergence point is shown in Fig. 4(c). The experiment will verify the simulation results that the “reservoir” effect of the annular beam is beneficial for improving LSP spectral radiance.
Fig. 4. Schematic diagram of LSP experimental setup. (a) LSP driven by annular beam; (b) simulation results of laser power density distribution before and after CLS; (c) annular beam near the focus point. CLS: conical lenses set.
4. Results and discussion
4.1 Size analysis of LSP
The laser power increased from 342 W to 628 W, during which the size of the plasma was measured. The measurement setup for LSP size is shown in Fig. 5(a). A CCD is placed on the plane where the focal point of the elliptical reflector is located. A convex lens is placed at a distance of 200 mm from both the LSP and the CCD, thus the magnification is 1.0. To avoid the impact of laser scattering on the measurement results, a UV filter is placed to filter out the incident light with a wavelength above 400 nm. Figure 5(b) shows the original image captured by the CCD, where the Z-axis is the direction of laser incidence. The length and width of LSP can be calculated from the original image captured by the CCD. We define the full width at half maximum (FWHM) in the laser incidence direction as the length of the LSP, and the FWHM perpendicular to the direction of laser incidence as the width of the LSP. Figure 5 shows the plasma size measurement results corresponding to 568 W annular beam. The plasma length is 868 µm and the length-width ratio is 4.1.
Fig. 5. (a) Schematic diagram of measurement setup for plasma size and LSP spectrum. The results are presented in sections 4.1 and 4.2 respectively; (b) original image in CCD; (c) length (the dashed line in Fig. 5(b)) and (d) width (the solid line in Fig. 5(b)) of LSP measured from CCD.
The measurement results of plasma length are shown in Fig. 6. The quotient of laser power increment and plasma length change is defined as the length growth rate k, which is in the unit of µm/W. Note that within the laser power range of 447 W to 598 W, the growth rate of plasma length slows down. Abrupt plasma dimension change is observed when the laser power exceeds the “reservoir” boundary 598 W. Figure 7 shows the shape of LSP under different laser power. In the range of 447 W to 598 W, the size growth rate of the plasma is suppressed, which is beneficial for improving the spectral radiance of the LSP. This indicates that the experimental results have a “reservoir” effect zone covering hundreds of watts of laser power that is similar to the simulation results.
4.2 Spectrum analysis of LSP
The laser power increased from 342W to 638W, during which the spectrum of the plasma was measured with the setup in Fig. 5(a). Spectrometer calibrated with standard lamps within 250∼1150 nm was used to collect LSP spectrum. A cosine corrector was added to the spectrometer probe to reduce the impact of directionality on the measurement results. All spectra were normalized based on the maximum spectral value of the LSP at 638 W. Figure 8 shows the normalized spectrum of LSP under different laser power and their comparison with arc plasma. The results indicate that there are few differences in the intensity of the line radiation corresponding to the bound-bound transitions in the infrared band. However, the continuum radiation of the LSP generated by recombination and bremsstrahlung is significantly increased in the visible and ultraviolet bands as the laser power rises. The difference proves that in the annular beam laser sustained plasma experiment, a raise in the laser power could improve the temperature of the plasma, resulting in more continuum radiation at shorter wavelength. Figure 8(b) shows the spectrum of the LSP in the UV band (<400 nm). The fraction of the LSP spectrum in the UV band is calculated and displayed in Fig. 9 for quantitative comparison. The dashed line represents the arc plasma as a reference with the fraction value of 6.5%. It can be found that within the laser power range of 342 W to 638 W, the growth of laser power will lead to an increase in the fraction of the spectrum below 400 nm, which is beneficial for improving the spectral radiance of the LSP.
4.3 Spectral radiance analysis of LSP
Due to the lack of spectral radiance measurement system, we estimated the average spectral radiance between 260 nm and 350 nm of the LSP as a reference. A power meter with a target radius of r is placed at a distance of R from the LSP. To avoid the impact of laser scattering, a UV filter is placed to filter out the incident light with a wavelength above 350 nm. The power incident on the target area of the power meter Ppm can be calculated using the readings of the power meter and the transmittance curve of the filter. Note that the transmittance curve of the filter is measured using the Xenon lamp and the calibrated spectrometer with a cosine corrector to reduce the impact of directionality on the measurement results. R is much larger than the LSP size, so we can assume that the plasma radiates uniformly within 4π stereo angle. Therefore, the total power emitted by the LSP band between 260 nm and 350 nm can be estimated by the following equation.
The average spectral radiance L of the LSP in the range of 260 nm to 350 nm is estimated according to the following equation.
where P is the total power emitted by the LSP between 260 nm and 350 nm. 4π indicates that the plasma radiates uniformly within 4π stereo angle. A is the plasma cross-sectional area and Δλ is the wavelength range (90 nm). The average spectral radiance (260-350 nm) of LSP estimated according to the above method is about 169 $mW/({m{m^2}\cdot nm\cdot sr} )$ under 638W laser. By analyzing the measurement errors corresponding to the four key parameters (R, r, A, Ppm), the measurement error of the average spectral radiance in the wavelength range of 260 nm to 350 nm is less than 10 $mW/({m{m^2}\cdot nm\cdot sr} )$. As a reference, the average spectral radiance of arc plasma within the same wavelength range is only about 3 $mW/({m{m^2}\cdot nm\cdot sr} )$. LSP with the highest reported UV radiance to our knowledge has been achieved. Figure 10 shows the estimated plasma spectral radiance. The increase in the laser power could promote the growth in the spectral radiance of the LSP. By analyzing the relationship between plasma length-width ratio and the estimated spectral radiance, it can be noted that suppressing the increase of plasma length-width ratio with laser power will be beneficial for improving the estimated spectral radiance. The “reservoir” effect suppresses the plasma length-width ratio, making the power increment absorbed by the plasma tend to rise in temperature rather than simply increasing size, thus improving the spectral radiance. The experimental results support the simulation conclusion that the “reservoir” effect of the annular beam is beneficial for further improving the spectral radiance of the LSP.Fig. 10. Relationship between LSP length-width ratio and estimated plasma spectral radiance (260∼350 nm).
5. Conclusions
In this paper, a two-dimensional refractive index distribution in the plasma region is established to analyze the propagation path of the annular beam. By calculating the spatial distribution of laser power density, the relationship between laser power and plasma length is established. The conclusion of the simulation is within hundreds of watts of laser power, the growth of plasma length is suppressed. The plasma will tend to increase temperature rather than plasma size, which is beneficial for improving the spectral radiance of LSP. Abrupt plasma dimension change is observed when the laser power exceeds the “reservoir” boundary. The new model is then validated by experiments. An annular beam with 0.6 F-number is used to sustain the plasma. Based on the measurement results of plasma size and spectrum, as well as the estimated spectral radiance, it has been proved that the “reservoir” effect of the annular beam is beneficial for improving plasma UV spectral radiance. LSP with UV spectral radiance up to 169 $mW/({m{m^2}\cdot nm\cdot sr} )$ was realized, which is the highest reported UV radiance to our knowledge. This work paves a novel way of generating high radiance UV sources by spatial manipulation of excitation laser beam.
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 not publicly available at this time but may be obtained from the authors upon reasonable request.
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