Ultrashort Laser Pulse Phenomena, 2nd Edition

38 Fundamentals

per unit travel distance and unit spectral width. From Eq. (1.138) we find for the

corresponding quantity

τ

p

Lλ

= 2π

c

λ

2



|k





|. (1.140)

For BK7 glass at 620 nm, k





≈ 1. 02 ×10

−25

s

2

/m, and the GVD as introduced

above is about 500 fs per nm spectral width and m propagation length.

1.2.5. Complex Dielectric Constant

In general, the dielectric constant, which was introduced in Eq. (1.72) as a real

quantity, is complex. Indeed a closer inspection of Eq. (1.71) shows that the finite

memory time of matter requires not only , χ to be frequency dependent but also

that they be complex. The real and imaginary part of ˜, ˜χ are not independent

of ...