Nd∶YAG with a uniform dopant of Nd³⁺ can generate gradient temperature distribution along laser propagation under high-power semiconductor diode lasers (LDs), which may cause a thermal lens effect, and thus reduce laser output power and beam quality. Regulating the gradient dopant of Nd³⁺ in Nd∶YAG is paid great attention to for improving the efficiency and beam quality. The traditional regulation method is to fabricate Nd∶YAG with gradient dopant by a unique dual-crucible technology from the Czochralski method. With the development of room temperature bonding technology, it is flexible to obtain designed gradient dopants of Nd³⁺ with specific sample thicknesses in a monolithic structure. We propose a numerical simulation method by establishing heat source equations. The temperature distribution in Nd∶YAG with uniform and gradient dopants of Nd³⁺ under kilowatt pump power is reported accordingly. We hope that the basic strategy can help design a new gradient doped Nd∶YAG monolithic gain media and understand the relationship between temperature distribution and Nd∶YAG with specific dopants along laser propagation.

Nd∶YAG is employed for numerical simulation of temperature distribution along laser propagation under high pump power. The aperture of Nd∶YAG is 10 mm×10 mm cut along the crystallographic axis [100]. In the case of bulk Nd∶YAG with a uniform dopant of Nd³⁺, the absorption coefficient is set as 5.78 cm^-1 with a bulk length of 8 mm to ensure over 99% absorption of the pump light after single path propagation. In the case of gradient Nd∶YAG, each segment has 1 mm thickness and various absorption coefficients. Meanwhile, a quarter geometric model is built to compare the temperature distribution in the central axis of bulk Nd∶YAG and gradient Nd∶YAG along laser propagation. The initial pump power is 1000 W and the pump pulse width time is 46 μs, with the repetition frequency of 1 kHz. The flat-top pump light is employed for temperature distribution calculation and heat source expression.

Following the pump energy of 46 mJ at 1 kHz, the temperature distribution along laser propagation in the central axis of bulk Nd∶YAG decreases from 185 to 26 ℃. The temperature is reduced to 106, 51, and 29 ℃ at the positions of 2, 4, and 6 mm in bulk Nd∶YAG, respectively. This indicates that the temperature close to the pump light is the highest in a bulk Nd∶YAG. By adjusting the absorption coefficient to 1.5, 2.1, 3.3, and 9.7 cm^-1 for each segment with 1 mm thickness in gradient Nd∶YAG, the constant distribution of temperature around 86.5 ℃ is obtained. The maximum temperature is 88.5 ℃ when the temperature difference between maximum and minimum value is 7.5 ℃. Additionally, by properly designing the sample thickness and absorption coefficient of the gradient Nd∶YAG, the total thickness can be shortened to 4 mm, which is beneficial for ultrashort pulse generation in microcavity.

A numerical simulation method by establishing heat source equations is proposed for temperature distribution evaluation in bulk Nd∶YAG and gradient Nd∶YAG. The temperature distribution in gradient Nd∶YAG shows a constant distribution of temperature around 86.5 ℃ under pump energy of 46 mJ at a repetition rate of 1 kHz. This confirms that the design of monolithic gain media such as gradient Nd∶YAG can help understand the temperature distribution along the central axis of Nd∶YAG along laser propagation.