Ultraviolet and deep-ultraviolet lasers offer short wavelengths and high photon energies. Thus, they are applicable to diverse fields such as fine processing, damage detection, and atomic spectral analysis. Deep-ultraviolet light-generation methods include synchrotron radiation, gas discharge lamps, excimer lasers, free-electron lasers, and nonlinear frequency conversion. Nonlinear frequency conversion uses nonlinear optical crystals to realize the output of deep-ultraviolet light via frequency doubling and frequency summing. Compared with other methods, it offers the advantages of low cost, simple structure, and continuous tuning. However, deep-ultraviolet lasers below 200 nm cannot be easily generated directly. Meanwhile, commonly used optical materials readily absorb deep-ultraviolet lasers, and the existing methods cannot offer both high efficiency and a wide tuning range.

By analyzing the coupled wave equation, the conversion efficiencies of the second, third and fourth harmonics in cascaded β?BBO crystals are discussed herein. The efficiency of nonlinear frequency conversion is positively correlated with the nonlinear polarization coefficient, and the nonlinear polarization coefficients of the third harmonic and above are much smaller than that of the second harmonic. Moreover, the shortest phase-matching range of the second harmonic of the β-BBO crystal is 409.6 nm, and the wavelength of deep-ultraviolet light is halted at 205 nm via direct frequency doubling. Therefore, we perform cascaded second-order nonlinear frequency conversion to achieve a high conversion efficiency for higher harmonics. The fundamental frequency light converges in the β-BBO crystal through the convex lens, and the second-harmonic wave perpendicular to the polarization direction of the fundamental frequency light is obtained. The two beams are collimated into parallel light using an off-axis parabolic mirror to avoid chromatic and spherical aberrations. After passing through a dual-wavelength waveplate (DWP), the polarization direction of the fundamental-frequency light rotates by 90°, the polarization direction of the second-harmonic wave remains unchanged, and the polarization direction of the fundamental-frequency light is the same as that of the second-harmonic wave. Subsequently, the fundamental frequency light and the second harmonic are converged in the second β-BBO crystal via an off-axis paraboloid mirror, whereas the third harmonic and fundamental frequency light are focused in the third β-BBO crystal via collimation and polarization adjustment, thus resulting in the fourth harmonic. Finally, a filter is used to filter the remaining wavelengths, and only the fourth harmonic is retained.

laser output wavelength, 650?1050 nm; fundamental frequency power P₀, 3.5 W; repeated frequency, 80 MHz; and pulse width, 150 ps. Additionally, fourth-harmonic crystal cooling to low temperature is performed to improve transmittance. The factors affecting the fourth-harmonic conversion efficiency are analyzed, and different crystal thickness conditions are simulated. The corresponding beam radius is calculated using the Rayleigh length formula, and a conversion-efficiency curve is obtained. The coupled wave equation is iterated step-by-step in the optical propagation direction using the Runge?Kutta method. Additionally, the beam radius and crystal thickness are obtained when the cascaded fourth-harmonic conversion efficiency is at its maximum. In practical application, the second-harmonic crystal length is 8.8 mm, the third-harmonic crystal length is 12.1 mm, the fourth-harmonic crystal length is 15.0 mm, and the laser radius is 33 μm (Fig. 5). The two-photon absorption coefficient of β-BBO crystal at 213 nm is 2.43 cm·GW^-1, and the two-photon absorptivity of 15 mm long crystal is 6%, based on the simulation parameters. Under the fundamental optical condition with an output wavelength of 650?1050 nm and P₀=3.5 W, the output power exceeds 100 mW in the range of 186?262.5 nm beyond the cascaded quadrupling frequency of the β-BBO crystal (Fig. 8). The maximum output power is 0.98 W at 227 nm, and the conversion efficiency is 28.6%. The results show that the cascaded output of the fourth harmonic of the deep-ultraviolet laser satisfies the requirements of wide tuning range and high conversion efficiency.

Based on an analysis of the coupled wave equation, the conversion efficiencies of the second, third and fourth harmonics in cascade β-BBO crystals are discussed. The effects of beam radius, crystal thickness, and crystal temperature on the harmonic conversion efficiency are investigated. Additionally, the second-, third-, and fourth-harmonic conversion efficiencies and the fourth-harmonic conversion power at each wavelength are simulated. A fourth-harmonic power output exceeding 100 mW is obtained in the range of 186?262.5 nm, and the maximum conversion efficiency reaches 28.6% at 227 nm. The feasibility of a wide-range tunable ultraviolet light source is verified theoretically, and a reliable light-source scheme is provided for ultraviolet Raman-spectrum detection.