Modelocked Modelocked Ti:sapphire Ti:sapphire Laser Laser
Lasers
A laser is an oscillator, all oscillators have1) Amplification/Gain2) Feedback
In a laserAmplification: stimulated emission in gain medium (gas, liquid solid)Feedback: mirrors (cavity)
LightAmplification byStimulatedEmission ofRadiation
Gain
Ener
gy OutputPartiallyTransmissive“Output coupler”
Gain by stimulated emission
Impossible to invert two 2 level system:
3-level systemrequires strong pump
Requires “inversion”greater population in upper state than lower stateotherwise absorption balances stimulated emission
Photon
Photon
Absorption
Photon
Stimulated Em
ission
4-level systembest
Pum
p
Fast relaxation
Slow relaxation
Lasi
ng
Pum
p
Fast relaxation
Slow relaxation
Lasi
ng
Fast relaxation
Resonator Stability
Need the resonator to be “stable”, i.e. the light stays in the cavity
Use ABCD matrices, resonator stable if round-trip matrix satisfies
stable conditionally stablerequires perfect alignment
unstable
20 14
A D+ +≤ ≤
Flat mirrors, just free space, A = D = 1, gives conditionally stable
Equality conditionally stable
Pulse generationA pulse forming mechanism is needed
otherwise lasers run “continuous wave” (CW)
Three types of pulsed operation
Gain switched (micro or millisecond pulses typically)
turn gain on and off (flash lamps, modulate pump)
Q-switched (nanosecond pulses
modulate cavity loss on times scales > round trip time
Modelocked (picosecond to femtosecond pulses
modulate cavity loss periodically at roundtrip time
Historical Progress in Ultrashort Pulses
Nd:glass
S-P DyeDye
CW Dye
Diode
Nd:YLF
Cr:YAG
Cr:liS(C)AFEr:fiber (telecom)Cr:forsteriteNd:fiber
Ti:sapphire
CPM
w/Amplification& Compression(Low Rep. Rate)
ColorCenter
1965 1970 1975 1980 1985 1990 1995
10
10
10
10
-11
-12
-13
-14
ADVANCES IN SHORT PULSE GENERATION
DyePuls
ewid
th(s
ec)
Year
Nd:YAG
Courtesy of E.P. Ippen
Modelocking
• Constructive interference between phase locked cavity modes 0 1 2 3 4 5
30 Modes (Random)
30 Modes (locked)
Inte
nsity
Time (ns)
Laser Cavity
How do you modelock?
• Active modelocking– Acoustooptic modulator, drive with RF– Minimum pulsewidth limited (ps’s)
• Saturable absorption– Use pulse to “gate” itself
• Pulse shortening rate increases with shortening of pulse• Often limited by processes that stretch pulse (dispersion)
– Real: finite population of absorbers• Dye molecules• Semiconductors• Finite relaxation time
– Effective: nonlinear phase shifts converted to amplitude• Nonlinear lensing + aperture• Nonlinear polarization rotation + polarizer• Essentially instantaneous
Kerr Lens Modelocking• Kerr Lens & Aperture gives
increased transmission at high intensity
• Increased transmission at high intensity = saturable absorption
• Short, intense pulse preferred in laser
• Kerr effect instantaneous• Not self starting
GaussianLaser Beam
High Intensity
Gaussian Beam =Gaussian Index Profile =Gradient Index Lens
GaussianLaser Beam
Low Intensity
Kerr Mediumn = n0 + n2I
Kerr Lens Modelocked Ti:sapphire
• Ti:sapphire has large bandwidth• Supports shortest pulses• Simple (amazingly)
M.T. Asaki, et al, Opt. Lett. 18, 977 (1993)
Output coupler High reflector
Pump
Ti:Sapphirecrystal
Prisms(Dispersion compensation)
Dispersion Compensation
High reflector
Prisms(
Elements in cavity have group velocity dispersion, velocity depends on frequency
In “visible”, red travels faster than blue (“normal” dispersion)Need to generate “anomalous” dispersion to counter act this
Blue lightis refractedmore than red
Red lighttravels throughtore glass thanblue light