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中文摘要：
基于瑞利一索末菲衍射积分，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C^2倍，其轴上谱线宽度增加（1＋C^2）^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。
英文摘要：
Based on the Rayleigh-Sommerfeld diffraction integral and complex analytical signal representation, the free space propagation equation and its Fourier spectrum for ultrashort chirped pulsed Gaussian beams are derived, and the far-field analytical electric field and spatial intensity are presented. The effects of chirp parameter on the spatiotemporal and spectral properties are illustrated with analytical formulas and numerical calculation results. It is found that if the chirp parameter C is relatively small, the on-axis spectral blueshifts increase by C^2 times, the onaxis spectral bandwidth increases by （1 ＋ C^2）^1/2 times, and the off-axis spectral redshifts also increase considerably. On-axis intensity increases with increasing chirp parameter for relatively small values of the pulse duration, and transversal intensity distribution is concentrated near to the propagation axis. The transversal intensity distribution remains nearly unchanged with increasing chirp parameter for relatively large values of the pulse duration. The sign of chirp parameters has no effect on the spectral distribution and transversal intensity distribution.
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