Ultrashort Laser Pulse Phenomena, 2nd Edition

Focusing Elements 91

cross-correlation does not differ from the width of the autocorrelation which is

measured without the lens in the interferometer arm. Figure 2.14(b) shows the

position of the peak of the cross-correlation as function of  f and the corre-

sponding r, respectively. For comparison, the delay associated with chromatic

aberration alone is also shown (dashed curve).

2.4.3. Achromatic Doublets

The chromaticity of a lens was found to be the cause for a radial dependence

of the time of arrival of the pulse at the focal plane, as was shown by Eq. (2.38).

Therefore one should expect achromatic optics to be free of this undesired pulse

lengthening. To verify that this is indeed the case, let us consider the doublet

shown in Figure 2.15.

The thicknesses of glass traversed by the rays in the media of index n

1

and

n

2

are L

1

and L

2

and are given by:

L

1

= d

1

−

r

2

2



1

R

1

−

1

R

2



(2.50)

and

L

2

= d

2

−

r

2

2



1

R

2

−

1

R

3



(2.51)

R

1

n

2

r

0

Phase front

L

1

L

2

d

3

F

R

3

Pulse front

r

d

1

d

2

n

1

R

2

f

Figure 2.15 Ray tracing in an achromat (Adapted from Bor [23]).