  Pulse self-compression is a simple and economical method for improving the
peak power of ultra-intense laser pulses. By solving a modified nonlinear
Schrodinger equation considering the fifth-order susceptibility, we found that
self-compression appeared even in normally dispersive medium owing to the
negative fifth-order susceptibility inducing a mass of negative frequency
chirp. Furthermore, negatively pre-chirped pulses allow for self-compression at
lower intensity, avoiding medium damage. We numerically analyze the optimal
choice of pre-chirp, input intensity, and medium length. A proof-of-principle
experiment successfully proves the above theoretical findings. It is expected
that petawatt or even exawatt laser pulses with 25 fs/15 fs transform limited
pulse duration can be self-compressed to about 9.9 fs/7.6 fs in normally
dispersive medium, such as fused silica glass plate.
