0198506961.pdf

8.5 Calibration in laser spectroscopy 173

very high time resolution and for creating pulses of extremely high peak
intensity (by compressing a high-energy pulse into a very short time).
The frequencyfrepis measured by directing some of the laser light
onto a photodiode (see Fig. 8.16). The femtosecond laser does not pro-
duce a sufficiently wide spread in frequencies for the specific scheme
illustrated in Figs 8.15 and 8.16. This is obtained by sending the output
of the femtosecond laser along a special highly-dispersive optical fibre, as
indicated schematically in Fig. 8.16. The combination of the femtosec-
ond laser and this special fibre produces radiation with the frequency
spectrum in eqn 8.24, that spans a large spectral range, e.g. from 520 nm
to 1170 nm in the work of Udemet al. (2001), equivalent to a frequency
range of 300 THz. Forfrep= 1 GHz this range of values corresponds to
n=2.5to6× 106.
After the frequency comb has been generated, the next stage is to
determine the offsetf 0 by an ingenious method devised by Professor
Theodor H ̈ansch and co-workers, namely a comparison, or self-referenc-
ing, of the frequency of lines from different parts of the frequency comb.
This is achieved by sending the light (from the low-frequency wing of
the comb) through a frequency-doubling crystal; in this nonlinear opti-
cal medium some radiation is generated at the second harmonic of the
input frequency. The light emerging from the crystal has frequency com-
ponents 2(n′frep+f 0 ), wheren′is an integer (the reason for introducing

PD1 PD2

PD3

‘Unknown’

frequency

Diffraction

grating

Diffraction

grating

Doubling

crystal

Femtosecond

laser Fibre

counter counter counter

control

Fig. 8.16The experimental arrangement for the measurement of an optical frequency using a frequency comb from a fem-
tosecond laser. Photodiode 1 measures the frequency interval between the laser modes,frepin eqn 8.24, andfrepis maintained
constant by electronic feedback from the frequency counter to the laser (the laser cavity length is kept fixed by adjusting the
position of a mirror with a piezoelectric actuator). Photodiode 2 measures the beat frequency between modes in the low- and
high-frequency wings of the comb (see Fig. 8.15). Photodiode 3 measures the frequency difference between one mode of the
comb and the unknown laser frequency as in eqn 8.26. The diffraction gratings spread out the light so that only the relevant
part of the frequency comb falls onto the detector, as explained in the text. Figure courtesy of Dr Helen Margolis, National
Physical Laboratory; after Margoliset al. (2003).