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基于瑞利-索末菲衍射积分,使用复解析信号法推导出了啁啾脉冲高斯光束在自由空间中的传输方程及其傅里叶谱,给出了远场的光场和空间光强的解析式,研究了啁啾参数C对脉冲光束传输的影响。结果表明,当啁啾参数C较小时,随啁啾参数增加,其轴上光谱蓝移增加C2倍,其轴上谱线宽度增加(1+C2)1/2倍。随衍射角增大,轴外光谱红移比无啁啾参数时快。脉冲宽度较小时,啁啾参数增大,轴上光强增大,横向光强分布越集中于传输轴附近;脉冲宽度较大时,啁啾参数增大对横向光强的影响减小。啁啾参数的正负号不影响横向光强分布和光谱分布。
Based on the Rayleigh-Sommerfeld diffraction integrals, the propagation equation of chirped pulsed Gaussian beam in free space and its Fourier spectrum are deduced by complex analytic signal method, and the optical field and spatial light intensity in the far field are given Analytical formula, the chirp parameter C on the pulsed beam transmission. The results show that when chirp parameter C is small, the on-axis spectral shift increases C2 times and the on-axis spectrum width increases by (1 + C2) 1/2 times as the chirp parameter increases. With the increase of the diffraction angle, the off-axis spectral redshift is faster than the non-chirp parameter. When the pulse width is small, the chirp parameter increases, the light intensity on the axis increases, and the lateral light intensity distribution concentrates on the transmission axis. When the pulse width is larger, the influence of the chirp parameter on the transverse light intensity decreases when the pulse width is larger. The sign of the chirp parameter does not affect the lateral intensity distribution and spectral distribution.