Narrowing behavior of chirped pulses with small Fresnel number in focusing systems

Based on the diffraction integral and Fourier transform, the fields of chirped pulses passing through a thin lens are derived. Influences of Fresnel number and chirp parameter on the transverse intensity distributions of the chirped pulses at focal plane are illustrated with numerical results. Also, effect of pulse duration on the intensities is investigated. It is found that the width of transverse intensity distribution of the chirped pulses decreases with increasing the chirp parameter and the narrowing behavior presents more obvious with smaller Fresnel number. A physical explanation for the narrowing behavior is given on the basis of a simplified form of the field expression.