Ultrashort Laser Pulse Phenomena, 2nd Edition

Problems 57

is equivalent to τ

G0

= w

0

r/(Lc). For r = w with w ≈ Lλ/(πw), cf. Eq. (1.182),

the pulse duration becomes τ

G0

≈ λ/(πc). Obviously, these effects become only

important if the pulses approach the single-cycle regime.

1.8. PROBLEMS

1. Verify the c

B

factors of the pulse duration–bandwidth product of a Gaussian

and sech pulse as given in Table 1.1.

2. Calculate the pulse duration ¯τ

p

defined as the second moment in Eq. (1.49)

for a Gaussian pulse and compare with τ

p

(FWHM).

3. Consider a medium consisting of particles that can be described by

harmonic oscillators so that the linear susceptibility in the vicinity of a

resonance is given by Eq. (1.153). ...