
Elements with Angular Dispersion 105
or, using the wavelength dependence of the index of refraction, and taking into
account that, for the Brewster prism, tan α = 1/n(ω
):
d
2
d
2
ω
=
h
nc
λ
2πc
λ
2
d
2
n
dλ
2
λ
+ b
λ
3
πc
2
dn
dλ
2
λ
. (2.83)
The stability of the cavity requires that R > L and that the coefficients a and b
be positive. In the visible range, most glasses have a positive GVD (k
> 0or
d
2
n/dλ
2
> 0). Therefore, in a cavity with a single prism as sketched in Fig. 2.23,
the GVD is adjustable through the parameter h, but always positive.
The calculation applies to a simple solid state laser cavity as sketched in the
inset of Fig. 2.23, with a