Objective In the implosion process of laser inertial confinement fusion (ICF), several requirements are proposed for the uniformity of the target irradiation and various beam-smoothing techniques, including spectral dispersion smoothing (SSD) , have been developed and applied. According to different physical processes, different physical parameters are adopted in different periods to further improve the focal spot smoothing effect. Considering OMEGA as an example, the main pulse generated by its front end is divided into two parts, corresponding to SSD. In the initial part of the pulse, high-frequency multifrequency phase modulation is used to achieve a wide bandwidth output to obtain a better smoothing effect. The relatively narrow spectral width output can smooth the main pulse and suppress the stimulated Brillouin scattering. Finally, the initial part of the pulse and the main pulse form a complete pulse output through the beam combination. The modulation requirements of the pulse light in the main pulse front end of the OMEGA device differ at different time points. However, the pulse light in the main pulse front end of the OMEGA device is realized by splicing time and space; the optical system is relatively complex. Therefore, it is necessary to implement a scheme that can achieve different modulations at different time points, changing the corresponding spectral width. The scheme can meet different spectral width requirements of different time points in the pulse light without beam-splitting modulation. Methods This study investigates the specific phase modulation technology. The specific phase modulation function is obtained by integrating original phase change function of the target. It is essential that the modulation depth of the specific phase modulation function is a time-varying function. The spectrum width can be changed at any time using a specific phase modulation function to modulate the phase of the pulse light. Based on phase modulation spectrum theory, the spectrum characteristics of the laser with a specific phase modulation are analyzed. Using an arbitrary waveform generator (AWG) for digital pulse shaping, two output channels of AWG are used to output specific phase-modulated electrical signal and pulse shaping signal, respectively. After amplifying the two signals of two output channels of AWG using two electric amplifiers, the pulse shaping signal is connected to the bias modulator to shape the output of the continuous wave (CW) laser into the pulse optical input phase modulator. Additionally, a specific phase-modulated electrical signal is loaded onto the phase modulator. The modulation spectrum of 250-ps signal light at different time points in 3 ns is obtained by changing the relative time difference of two electrical signal outputs using AWG. The experimental results are consistent with the theoretical simulation. Results and Discussions To obtain a modulation output with gradually increasing spectral width, phase modulation function f(1) (t) is obtained by integrating the target phase change function phi(1)' (t) (Fig. 1) . Under the modulation of f(1) (t) , the spectrum (Fig. 6) of the pulse light increases slowly at first. Then, the spectrum width significantly increases as the modulation depth increases, vibrating in a zigzag pattern. The oscillation amplitude of the experimental results is relatively large due to the influence of the measurement accuracy of the spectrometer. Since the signal light has a certain time width, the broadening of the spectrum appears delay and tailing at the beginning and end of the experiment, respectively. If the sampling interval is constant and the signal pulse width is reduced, the oscillation amplitude of the spectrum width with time will increase. However, if the pulse width of the signal light remains unchanged and the sampling interval is reduced, the zigzag oscillation will be smoother. If the pulse width of the signal light is reduced and the sampling interval is reduced, the spectrum width of the signal light changes with increasing oscillation, and it is closer to the absolute value of the phase change function vertical bar phi(1)' (t)vertical bar . To obtain a modulation output with gradually decreasing spectral width, the phase modulation function f(2) (t) is obtained by integrating the target phase change function phi(2)' (t) (Fig. 2) . Under the modulation of f(2) (t), the spectral width (Fig. 7) of the signal light increases rapidly at first, reaches the maximum value, and then decreases in zigzag oscillation. The experimental results are consistent with the results of the simulation. At the tail of the f(2) (t) modulation function, the modulation is smaller, and the modulation change is weaker in the pulse width of the signal light. The analysis and experiment show that the spectrum width decreases rapidly in tail time. Conclusions This study proposes a method of specific phase modulation function. The corresponding time-varying phase modulation function is designed, and its physical process is analyzed. The phase modulation under the function can effectively realize the change in signal light spectral width with time. The experimental results show that under the effect of the designed phase modulation function, the spectral width of the signal light increases or decreases with time. It is consistent with the results of the simulation and verifies the feasibility of the real-time dynamic control of the spectrum. In practical applications, a higher power amplifier can achieve higher modulation voltage output and wider spectrum width adjustment. The research of the specific phase modulation can provide theoretical reference to improve the time domain-smoothing performance, realize dynamic control of spectral width, and improve the control ability of high-power lasers.
