When high-power CW laser energy is radiated to the gas, the molecules or atoms in it will be ionized, forming a high-temperature and high-particle density plasma environment composed of electrons, ions, and neutral particles [1]. Under the conditions of Stark broadening, the electrons in the xenon lamp and mercury lamp with higher pressure undergo active free–free transition in the process of reverse bremsstrahlung radiation [2], producing highly bright and stable light with a stronger UV distribution [3, 4], which is widely used in many fields such as semiconductor measurement, material characterization, and hyperspectral imaging [5–7].

Since the photon energy is comparable to the excitation and ionization potentials of most gases, multiphoton absorption and cascade ionization are considered to be important mechanisms for plasma generation by laser–gas interactions [8], but even with xenon, which has the lowest thermal conductivity and ionization energy among all non-radioactive rare gases [9], the laser energy required to produce plasma is enormous. On the other hand, once the plasma is generated, the center of higher temperature and high-electron density is formed. At this time, the local thermodynamic equilibrium of the plasma [10] can be maintained by injecting lower energy to achieve long-term stable luminescence. The plasma in this state absorbs the energy of laser light through inverse bremsstrahlung [11, 12] to balance the energy loss generated by radiation and other processes, and this energy is far less than the breakdown threshold of gas.

In this work, a xenon lamp was selected as the object to generate plasma, and xenon in the lamp was pre-ionized by DC high-voltage ignition to form an initial plasma discharge channel, in which some atoms in the gas were transferred from the ground state to the excited state, obtaining more energy. Before pre-ionization, we focused the laser between the two electrodes of the lamp to maintain the continuous emission of the plasma generated by pre-ionization. Through preliminary maintenance experiments with the existing pressurized xenon lamps in the laboratory, a xenon lamp bulb with a charge pressure of 12 atm, which was the easiest to maintain, was selected. The threshold power of the laser required to maintain the plasma at this charging pressure was studied with the help of different lens combinations, and the regularity of the plasma maintenance process was analyzed in combination with the characteristics of the focused beam.

In the literature [13], a spherical heat transfer model was developed for a focused laser beam, and the effect of plasma temperature on the laser power required for the equilibrium process was investigated from the perspective of laser absorption by the plasma. At a constant pressure P, the absorption coefficient μ ω T k exists in a rising process due to the increase in plasma temperature T caused by laser injection; subsequently, the electron and ion density n decreases with the increase in temperature T and the absorption coefficient also decreases, as shown in Eqs 1, 2, where Θ T k was the heat flux potential, which varied monotonically with temperature. Corresponding to the absorption of the laser by the plasma, there exists a threshold power P 0 enabling the plasma to enter a steady state, that is, a local thermodynamic equilibrium state, and when the plasma is unable to maintain this state, that is, the injected laser energy does not allow the plasma to reach the desired temperature, the ionization becomes so weak that the absorption of the laser can even be neglected. P 0 ≈ 2 π Θ T k μ ω T k , (1) P   ∼   n T = c o n s t a n t . (2)

The aforementioned combination was simulated and compared with the focused beam characteristic parameters fitted after CCD measurement, and the results are shown in Table 1. It can be observed that the NA obtained by simulation and actual measurement data fitting was not much different, and the difference in the beam waist radius was also basically maintained at the same level. The difference was caused by the aberration of the optical path and the diffraction of the beam during the actual beam propagation [19]. With the increase in NA, the threshold power tended to decrease gradually. In order to analyze this reason, we first carried out simulation analysis on the selected combinations. The simulated data and the photographs recorded by the camera verified that some combinations showed obvious deviation from the simulation curve of ω 0 in Figure 3A due to the existence of aberration. Other combinations met the characteristics of Gaussian beam propagation, that is, with the increase of NA, the beam waist radius gradually decreased. It was worth noting that in the actual beam transmission, the beam waist radius cannot be ideally reduced with the increase in NA; as obtained in the simulation, as shown in Figure 3A, after NA was greater than 0.15, the change slope of the measurement curve was smaller than that of the simulation curve, which will directly affect the threshold power density of the laser at the focal point.

We studied the threshold power affected by the beam waist radius and Rayleigh length for eight combinations with small aberrations and no excessive energy loss (this energy loss is mainly reflected in the shading of the laser energy by the experimental device) and established its relationship with the threshold power, as shown in Figure 3B, with the beam waist radius as the independent variable. The threshold power density represents the average distribution of laser energy at the focal plane and was numerically equal to the ratio of the threshold power to the focal plane area, which showed an opposite trend to the threshold power with ω 0 , and this relationship can be better explained by the variation of the plasma luminescence size with the laser focusing NA in Figure 3D. If the NA was small, that is, ω 0 and Z 0 is large, although the plasma size was larger at this time, but its longitudinal dimension was still less than the Rayleigh length of the focused laser, and the threshold power density at this time reflects the power conditions that should be met when the plasma was lit; as NA increases, Z 0 decreases to the same scale as the plasma length, the power density at the luminous edge still met the value required in the first case, and the power density at the focal plane was in a rising stage due to the decrease of ω 0 ; this process continued until the Rayleigh length was smaller than the plasma length, that is, the case of large NA, and the power density beyond the Rayleigh length still met the threshold power density for maintaining the plasma under this condition, which also meant that the plasma needed more energy to maintain, and the maintenance power that should be continuously decreasing becomes stable and appears to increase. In addition, this trend was further increased by the fact that the decrease in ω 0 tends to level off with increasing NA during the actual transmission. In summary, we believed that a certain threshold power density was necessary for the formation of a stable plasma; this value was in the approximate range of 1,500–2,000 W/mm², but the required laser power was also influenced by the Rayleigh range and the relative length of the plasma size when analyzed from the point of view of plasma maintenance. This was also better verified by combination 4 (circled in Figures 3B,C), that is, ①+④, which had a lower threshold power due to its larger Rayleigh length than the combination in the same ω 0 conditions.

We adopted the method of combining simulation and experimental measurement to study the continuous and stable luminescence process of the laser-maintained xenon plasma at a fixed pressure. The following main conclusions were drawn for this process.

In the selection of optical path, the lens should be chosen from a lens group with small aberration and large energy transmission to obtain a focused beam, the poor focusing effect mainly occurred in the case of large NA, and ZEMAX in this process can play a preliminary screening role. In addition, the beam waist radius decreased with increasing NA, and the elevated power density was to some extent conducive to the reduction of the threshold power, but as the Rayleigh length also decreased along with it, the reduced energy concentration region reduced the plasma size, while the mismatch between the two sizes can make the plasma maintenance require higher power, and the threshold power no longer decreased or even appeared to increase slowly, and the two factors, ω 0 and Z 0 , each played a major role in maintaining the laser threshold of the plasma in different NA ranges.