# Modeling and Analysis of High-Power Ti:sapphire Laser Amplifiers-A Review
## 4 Summary and Future Outlook  
In summary, we have developed a pseudo-analytical method to simulate the amplification of laser pulses accurately and efficiently in the case of an overlap of two polarized orthogonal pulses by modifying the Frantz-Nodvik equation. The developed simulation model can imply a double-pass amplifier with multiple gain media, an overlapped pulse, and arbitrary input pulse shapes. Also, we introduced a square beam homogenizer with high sharpness and uniformity for a PW Ti:sapphire amplifier. The beam homogenizer using lens arrays is effective in improving the efficiency of the amplifier and in making compact high-power laser systems. We also pointed out the thermal effect as another essential consideration for developing high-power lasers. Using the differential Jones  
Figure 16: The focal lengths of the thermal lens, where the blue lines indicate the results of the conventional equations and red lines indicate the results obtained using the equations derived in this study, (**a–c**) is the case of [62; 63; 64], respectively.  
matrix, We derive the thermal effect on Ti:sapphire medium. The differential equation models are derived from considering the effects of amplification, intrinsic birefringence, and thermal birefringence. We confirmed the validity of the solution of the differential equation model by comparing it with the measured value of other high-power laser facilities. This review will help to develop high-power laser systems that are actively researched and developed, and the high-power lasers will be profitable in basic science and industrial applications. We are confident we have to focus on effective beam generation, higher repetition rate, and spatio-temporal quality enhancement beyond the generation of high-power pulses. The high-power laser system pursues a compact design for practical applications, so the research need for the high-power laser modeling and analysis will be even higher (Figure 17). Furthermore, the methods presented in this review can be applied to various anisotropic materials and may be useful for studying light modulation effects, and nonlinear effects.  
Figure 17: Results of the 2 PW laser system simulation; **(a)** Rendering image; **(b)** Residual pump energy changes and injection timing; **(c)** The intensity of the amplified pulse by time; **(d)** The spectral intensity of amplified beam and optical-compress condition; **(e)** The temporal shape of the optically compressed pulse; **(f)** The thermally induced OPD (Optical Path Difference) profile; **(g)** The expected focal length of the thermal lens effect; when pump energy of the final amplifier is 120 J, repetition rates is 8 Hz.  
**Author Contributions:** Investigation, J.J., S.C. and S.H.; writing-original draft preparation, J.J., S.C. and S.H.; writing-review and editing, T.J.Y., B.L.; supervision, T.J.Y., B.L.; project administration, T.J.Y.; funding acquisition, B.L., T.J.Y.  
**Funding:** This work was partially supported by Korea Institute for Advancement of Technology (KIAT), P0008763, \"The Competency Development Program for Industrial Specialist\" funded by the Ministry of Trade, Industry & Energy (MI, Korea). This work was partially supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (NRF-2018R1D1A3B07050578). This work was partially supported by the Industrial Strategic Technology Development Program, 20000495, \"Development of machine learning based alloy powder design and manufacturing platform using plasma high temperature reduction\" funded by the Ministry of Trade, Industry & Energy (MI, Korea).  
**Conflicts of Interest:** The authors declare no conflict of interest.