Page 450 - Tunable Lasers Handbook

41 0 Paul Zorabedian

is the effective optical path length of the laser. The wavelength of the q’th mode
is given by h4 = 2Ltff/q. The peak wavelength of the filter passband is repre-
sented by hpk.
For the q’th mode to remain oscillating as the filter is tuned, h4 must track
hpk exactly. One way to fulfill this requirement is to change the cavity length by
ALeH as the filter is tuned by Ahpk so that

Dividing both sides of Eq. (72) by Le, and rearranging factors gives the follow-
ing condition for phase-continuous tuning:

This equation can be integrated to give

ln(Leffl) - ln(‘pk1]
(74)
In( eff2) In( A pk2)

The required accuracy with which the cavity length must track the filter is very
high. Assuming that the change in mode number must be I Aq I < % to avoid a
mode hop, then it is easy to show that tracking precision is specified by

The value of this quantity is 5 x 10-6 for a 1-pm wavelength and a 10-cm cavity.
The condition for phase-continuous tuning can also be expressed in terms of
optical frequency. Assume that the laser starts out oscillating in one longitudinal
mode that is coincident with the peak frequency of the filter: vq = vpk. Further
assume that the filter frequency is swept at a constant rate dvpk/dt. Tuning will be
phase continuous if the modes of the cavity are somehow swept at a rate identi-
cal to that of the filter:

This relation suggests that it should be possible to implement phase-continuous
tuning by applying a controlled chirp to the longitudinal modes without actually