2.1 Ultrafast solid-state lasers - ETH - the Keller Group
2.1 Ultrafast solid-state lasers - ETH - the Keller Group
2.1 Ultrafast solid-state lasers - ETH - the Keller Group
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
90 <strong>2.1</strong>.4 Loss modulation [Ref. p. 134<br />
and passively mode-locked miniature <strong>lasers</strong> (Fig. <strong>2.1</strong>.7b) where a short laser crystal defines a simple<br />
monolithic cavity. The SESAM attached directly to <strong>the</strong> laser crystal <strong>the</strong>n formed one end-mirror<br />
of this laser cavity. As <strong>the</strong> laser cannot be pumped through <strong>the</strong> SESAM, <strong>the</strong> laser output needs to<br />
be separated from <strong>the</strong> collinear pump by a dichroic mirror. These examples suggest that <strong>the</strong>re is<br />
need for a device that combines <strong>the</strong> nonlinear properties of <strong>the</strong> SESAM with an output coupler.<br />
This has been demonstrated before for a passively mode-locked fiber laser [96Sha] and later also<br />
for <strong>solid</strong>-<strong>state</strong> <strong>lasers</strong> [01Spu1].<br />
<strong>2.1</strong>.4.4 Effective saturable absorbers using <strong>the</strong> Kerr effect<br />
<strong>2.1</strong>.4.4.1 Transverse and longitudinal Kerr effect<br />
The extremely rapid response and <strong>the</strong> broad bandwidth of <strong>the</strong> Kerr nonlinearity are very attractive<br />
for a mode-locking process. For high intensities, <strong>the</strong> polarization inside a dielectric medium does<br />
not proportionally follow <strong>the</strong> electric field anymore. This gives rise to an index change proportional<br />
to intensity. Off-resonance, this nonlinear optical effect is extremely fast, with estimated response<br />
times in <strong>the</strong> few-femtosecond range. The transverse and longitudinal effects resulting from <strong>the</strong><br />
intensity dependence are shown schematically in Fig. <strong>2.1</strong>.13. The transverse Kerr effect retards <strong>the</strong><br />
central and most intense part of a plane wave front and thus acts as a focusing lens, referred to as<br />
<strong>the</strong> Kerr lens. Along <strong>the</strong> axis of propagation, <strong>the</strong> longitudinal Kerr effect retards <strong>the</strong> center of an<br />
optical pulse, producing a red shift of <strong>the</strong> leading part of <strong>the</strong> pulse, and a blue shift in <strong>the</strong> trailing<br />
part. Consequently, <strong>the</strong> longitudinal Kerr effect has been named Self-Phase Modulation (SPM).<br />
Longitudinal Kerr effect:<br />
self phase modulation (SPM)<br />
n( z)= n2I<br />
( z)<br />
Transverse Kerr effect:<br />
Kerr lens<br />
n( xy , ) = n2I( xy , )<br />
Fig. <strong>2.1</strong>.13. The Kerr effect gives rise to an increase of <strong>the</strong><br />
refractive index with intensity, causing a retardation of <strong>the</strong><br />
most intense parts of a pulse (i.e. for n 2 > 0). In its longitudinal<br />
form, <strong>the</strong> Kerr effect causes Self-Phase Modulation<br />
(SPM) and in its transverse form, a nonlinear lens is formed<br />
in <strong>the</strong> central part of <strong>the</strong> beam profiles (i.e. Kerr lens).<br />
<strong>2.1</strong>.4.4.2 Nonlinear coupled cavity<br />
The longitudinal Kerr effect can also be used to produce <strong>the</strong> same effect as a fast saturable absorber.<br />
To do this, <strong>the</strong> phase nonlinearity provided by <strong>the</strong> longitudinal Kerr effect has to be converted<br />
into an effective amplitude nonlinearity. The earliest mode-locking schemes based only on SPM<br />
used a coupled cavity to convert SPM into SAM. In <strong>the</strong> soliton laser [84Mol], pulses compressed<br />
by SPM and anomalous dispersion in <strong>the</strong> coupled cavity are directly coupled back into <strong>the</strong> main<br />
laser cavity. This provides more gain for <strong>the</strong> center of <strong>the</strong> pulse. Pulses as short as 19 fs have been<br />
Landolt-Börnstein<br />
New Series VIII/1B1