Recently, high-pressure CO₂ laser amplifiers have become an important research direction for chirped pulse amplification, multi-stage MOPA (master oscillator power amplifier) oscillator amplifier, and high-energy laser systems because of their large gain volume, wide gain line width, smooth gain spectrum, and the ability to output TW lever pulse near 10 μm. These amplifiers have important applications in laser isotope separation, laser-driven particle acceleration, laser-induced nuclear fusion, etc. When the gas pressure is higher than 10 bar, the gain spectrum is quasi-continuous with a bandwidth of more than 1 THz, which can amplify picosecond pulses. However, the periodic frequency modulation of the gain spectrum generated by rotating energy-level spacing limits the amplification effect. In the time domain, a single input pulse splits into a series of pulses, which affects pulse extraction and energy amplification. Limited by the high-voltage pulse discharge pumping technology, the pressure cannot be infinitely increased to eliminate pulse splitting. The difference in quality of isotopes shifts the frequency of the central spectral line such that several discrete spectra are mixed into a smooth continuous spectrum, overcoming the periodic spectral modulation of the gain spectral line and amplifying picosecond pulses without generating secondary pulses.

The output characteristics of a long-wave infrared picosecond pulse, amplified using a CO₂ amplifier, were numerically simulated. By fully considering the transitions of regular, sequence, and hot bands, the pumping/relaxation dynamics of the laser energy level were modeled. Spectral data were mainly obtained from the latest version of the HITRAN 2016 database. To determine the optimal isotope ratio, analyze the amplified output of different bands, and compare the influence of pressure broadening on pure ¹²C¹⁶O₂ and mixed isotopes, we calculate the output characteristics of ¹²C¹⁶O₂, ¹²C¹⁶O¹⁸O, ¹²C¹⁸O₂, ¹³C¹⁶O₂, ¹³C¹⁶O¹⁸O, ¹³C¹⁸O₂ under different ratios of six isotopes, the molecular number ratio of ¹²C¹⁶O₂ , ¹²C¹⁶O¹⁸O, and ¹²C¹⁸O₂ is 1∶2∶1, at the four strong lines of 9R, 9P, 10R, and 10P bands and pure ¹²C¹⁶O₂ and ¹³C, ¹⁸O, both accounting for 50% at different pressures. Eventually, we simulated the output characteristics at 10 bar of the ultrashort pulse with a 0.3 ps pulse width, 1.466 THz bandwidth, and 0.01 J energy at 9 μm band passing through the gain medium^{where 13C and 18O account for 50% while 13C accounts for 0% and 18O accounts for 50%, and at 10 μm band passing through the gain medium where 13C and 18O account for 50% while 13C accounts for 100% and 18O accounts for 50%. The calculation results were analyzed and conclusions were drawn.}

When isotopes of 50% ¹³C and 50% ¹⁸O are added, no secondary pulse is generated; however, the output energy and peak power of the main pulse are the lowest. When the ratio of ¹³C to ¹⁸O is higher or lower than 50%, the output energy and peak power of the main pulse increased; however, the energy ratio of the main pulse decreased, and the number and energy ratio of the secondary pulses increased. This corresponds to the amplitude and modulation of the amplifier gain spectrum. Switching from the P- to the R-band has advantages: the peak power and energy ratio of the main pulse increase as well as the number of secondary pulses and their energy ratios decrease. The spectral line density of the R?band is 1.5 times that of the P-band. More gain overlaps result in higher gain and better smoothness. Increasing the gas pressure can increase the collision linewidth, gain overlap, output energy, and peak power; make the gain envelope smoother; and reduce the gain spectral modulation and pulse splitting. However, when no isotopes are added, the smoothing effect of pressure broadening on the gain spectrum is insignificant. Pulse splitting is completely suppressed only in the isotopic mixtures. When the ratios of ¹³C and ¹⁸O are 50% at 10 bar, the amplified energies of the 9 and 10 μm bands are close. At the 9 μm band, the gain spectrum range of ¹³C and ¹⁸O accounting for 50% is 0.533 THz wider than that of ¹³C accounting for 0% and ¹⁸O accounting for 50%; in contrast, at the 10 μm band, the gain spectrum range of ¹³C and ¹⁸O accounting for 50% is 0.094 THz wider than that of ¹³C accounting for 100% and ¹⁸O accounting for 50%. The pulse width of the six isotopes at 9 μm is reduced by 0.130 ps (28.14%), and the proportion of trailing energy is reduced by 46.37% compared with the three isotopes of ¹²C, while the pulse width of the six isotopes at 10 μm is reduced by 0.104 ps (23.26%) and the trailing energy proportion is reduced by 40.06% compared with the three isotopes of ¹³C (Fig. 7). Unlike Polyanskiy et al. who used the same seed passing through three isotopes of ¹²C with ¹⁸O accounting for 47% at the 9 μm band and obtained an amplified output pulse with a width of 0.5 ps, and energy tailing ratio of 25%, six isotope mixtures are used to expand the amplifier gain bandwidth, smooth the gain envelope, and obtain narrower pulse width and a lower tailing energy ratio after amplification.

In this study, numerical simulations were conducted to investigate the output characteristics of six isotopic CO₂ lasers with different proportions of CO₂ isotopes, as well as different wavelengths and gas pressures. The results show that, under the condition of 50% ¹³C and ¹⁸O atom ratios and a pressure of 5 bar, the gain modulation near 10.591 μm is 19.65%, and the gain modulation of the R-band is reduced by about 40% compared to the P-band, effectively suppressing the output of secondary pulses. Under a pressure of 10 bar, for a seed light with a pulse width of 0.3 ps and energy of 0.01 J, the laser pulse width is 0.332 ps with a tail energy ratio of 1.85% after amplification by six isotopes of ¹²C and ¹³C in the 9 μm band and 0.343 ps with a tail energy ratio of 3.77% after amplification by six isotopes of ¹²C and ¹³C in the 10 μm band. Compared with the simulation results by Polyanskiy et al. who used three isotopes of ¹²C to amplify the same seed laser in the 9 μm band, the pulse laser width and tail energy ratio are reduced by 0.168 ps and 23.15%, respectively. The calculations and analyses in this study provide a reference for parameter selection for high-pressure isotopic CO₂ lasers.