Ultrashort Laser Pulse Phenomena, 2nd Edition

92 Femtosecond Optics

where d

1,2

is the center thickness of lens 1, 2. The inverse of the focal length of

the doublet lens is:

1

f

= (n

1

− 1)



1

R

1

−

1

R

2



+ (n

2

− 1)



1

R

2

−

1

R

3



. (2.52)

The condition of achromaticity

d

dλ

(1/f ) = 0 gives an additional relation between

the radii of curvature R

i

and the indices n

i

. The expression for the transit time in

glass in which we have inserted the chromaticity of the doublet is [23]:

T(r) =

d

1

c



n

1

− λ

dn

1

dλ



+

d

2

c



n

2

− λ

dn

2

dλ



+

λr

2

2c

d

dλ



1

f



.

(2.53)

Equation (2.53) indicates that, for an achromatic doublet for which the third term

on the right-hand side vanishes, the transit time has no more radial dependence.

The phase front and wave front ...