ultrashort laser sources nonlinear optics needs high intensities, and non-thermal effects ideal...
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Ultrashort laser sources
Nonlinear optics needs high intensities, and non-thermal effects
Ideal excitation: ultrashort pulses
Enjoy the theory, but…
…getting your hands dirty is something else!
Blessed the feeble minded, for they are theoreticians…
Ultrashort laser sources
The dream: a purely dispersive mechanism, creates the soliton
The reality: needs an amplitude modulation
Saturable absorption, Kerr lensing or Kerr deflection
Two pulse/cavity lasers
Direct creation of a frequency comb
The OPO: from the theoretician dream to the experimentalist nightmare.
Ideal laser medium versus ideal amplifier medium
1.
2.
3.
4.
5.
6.
Direct creation of a frequency comb
A perfectly regular frequency comb is formed by nonlinear optics:
But they are not in phase.
If they can be put in phase, a pulse train with zero CEO is created.
Reference:
Direct creation of a frequency comb
LASER
Pulse duration
RT
Mode bandwidth
Number of pulses
CEO?
CEP?
Direct creation of a frequency comb
Ultrashort laser sources
The dream: a purely dispersive mechanism, creates the soliton
The reality: needs an amplitude modulation
Saturable absorption, Kerr lensing or Kerr deflection
Two pulse/cavity lasers
Direct creation of a frequency comb
The OPO: from the theoretician dream to the experimentalist nightmare.
Ideal laser medium versus ideal amplifier medium
1.
2.
3.
4.
5.
6.
A purely dispersive mechanism, creates the soliton
Phase
modulationdispersion
Phase
modulationdispersion
Phase
modulation
dispersion
Phasemodulation
dispersion
Dispersion
FIBER
LASER
A purely dispersive mechanism, creates the soliton
time
Electric fieldamplitude
distance z
z = v1tz = v2tz = v4t z = v3t
Nonlinear index leads to phase modulation
(a)
time
Electric fieldamplitude
z = v1t(fast)
z = v2t(slow)
A purely dispersive mechanism, creates the soliton
(b)
Upchirped pulse inNegative dispersionmedium
Propagation in the time domain
PHASE MODULATION
n(t)or
k(t)
E(t) = (t)eit-kz
(t,0) eik(t)d (t,0)
A purely dispersive mechanism, creates the soliton
DISPERSION
n()or
k()() ()e-ikz
Propagation in the frequency domain
Retarded frame and taking the inverse FT:
A purely dispersive mechanism, creates the soliton
PHASE MODULATION
DISPERSION
PHASE MODULATION
DISPERSION
Equation in the retarded frame
Characteristic field: Characteristic time:
Normalized distance:
Solitons: solutions of the eigenvalue equation
Recreation of the observation of John Russell forthe 150th anniversary of his observation in 1834.
The soliton as a “canal wave”
A purely dispersive mechanism, creates the soliton
A purely dispersive mechanism, creates the soliton
Phase
modulationdispersion
Phase
modulationdispersion
Phase
modulation
dispersion
Phasemodulation
dispersion
Dispersion
FIBER
LASER
The elements of soliton control in the laser
Tuning the wavelength, the mode and the CEO
Gain medium
Dispersiontuning
GVDtuning
Mode frequencytuning
Wavelengthtuning
L. Arissian and J.-C. Diels, “Carrier to envelope and dispersion control in a cavity with prism pairs”, Physical Review A, 75:013824 (2007).
A purely dispersive mechanism, creates the soliton
Ultrashort laser sources
The dream: a purely dispersive mechanism, creates the soliton
The reality: needs an amplitude modulation
Saturable absorption, Kerr lensing or Kerr deflection
Two pulse/cavity lasers
Direct creation of a frequency comb
The OPO: from the theoretician dream to the experimentalist nightmare.
Ideal laser medium versus ideal amplifier medium
1.
2.
3.
4.
5.
6.
The magic wand of saturation
Starts mode-lockingChanges the group velocity
Couples intracavity pulses in amplitudein phase?
Interacts with CEP!
Gain MediumGain saturation is what stabilizes a laser.
Saturation
Gain pressure at the bottom of the dam;saturates as the dam fills upand the flow released balances the influx
Saturation
Gain saturation Absorption saturation
Stabilizes Starts mode-locking
time
I
0
Saturation starts mode-locking
The ideal “saturation absorption” curve:
Pulse energy
Saturation changes the group velocity
zz = vgt
I
Saturable gain
Saturable absorption
Saturation changes the group velocity
Application creating two pulse trains of exactly the same repetition rate.
In a ring cavity or in a linear cavity
GAIN
ABSORBER
ABSORBER
GAIN
t1
AB
z
t t = z/ct =- z/c
t2
t3
t4
t5
Saturation changes the group velocity, andcouples intracavity pulses in amplitude
Application: creating two pulse trains of exactly the same repetition rate.
Application: creating two pulse trains of exactly the same repetition rate.
It works… with a flowing dye jet
What happens if you substitute MQW for the liquid dye jet?
It is a whole new parenthesis.
(… Nanostructures, the CEO and the CEP
Saturation changes the group velocity, andcouples intracavity pulses in amplitudeand phase
Nanostructures and the CEO.
2 pulse/cavity linear cavity, mode-locked by saturable absorbers.
Beat note bandwidth unusually broad????
TEST: RECORD REPETITION RATE VERSUS CAVITY LENGTH
Period of λ/2
MQW with equal spacing of λ/2
Repetition rate versus cavity length,and other repetition rate mysteries
MQW with a non-periodic structure
Repetition rate versus cavity length
Modeling
Propagation axis z
E1 E2
E’1 E’2
MQW
MQW
z-ctz-ct
Tim
e
…)
Nanostructures, the CEO and the CEP
The position of the standing wave determines the magnitude of theinteraction with a structure < , therefore the change in group velocity.
For details see: “group-phase_velocity_coupling.pdf”
More material on the coupling in amplitude and phase between twoIntracavity pulses in: two_pulse_walzing_in_a_laser_cavity.pdf
Repetition rate versus cavity length,and other repetition rate mysteries
Ultrashort laser sources
The dream: a purely dispersive mechanism, creates the soliton
The reality: needs an amplitude modulation
Saturable absorption, Kerr lensing or Kerr deflection
Two pulse/cavity lasers
Direct creation of a frequency comb
The OPO: from the theoretician dream to the experimentalist nightmare.
Ideal laser medium versus ideal amplifier medium
1.
2.
3.
4.
5.
6.
The magic wand of saturation
Starts mode-lockingChanges the group velocity
Couples intracavity pulses in amplitudein phase?
Interacts with CEP!
Slow versus fast saturable absorber
The ultrafast: Kerr lensing and Kerr deflection
The ultrafast: Kerr lensing and Kerr deflection
Kerr Lensing Kerr deflectionn = n0 + n2I
lossy
lossy
ideal
Both mechanisms can provide the ideal “saturation absorption” curve:
The ultrafast: Kerr lensing and Kerr deflection
Cavity analysis: classical textbooks H. W. Kogelnik and T. Li, “Laser beams and resonators", Appl. Opt.,5: 1550-1567, (1966)
1 0 1- 1fNL
The ultrafast saturable loss: Kerr lensing
The beam waist should not be in the middle of the crystal
Analysis: write the ABCD matrix of the cavity, starting from the nonlinear lens
Multiply by the nonlinear lens matrix:
For details: J.-C. Diels and W. Rudolph, “Ultrashort laser pulse phenomena,Fundamental, techniques on a fs time scale”, 2nd Edition, Chapter 5,Section 5.5 “Cavities” (Elsevier, 2006).
The ultrafast saturable loss: Kerr deflection
Analysis: write the ABCD matrix of the cavity, starting from the nonlinear element
Multiply by the nonlinear deflection matrix.
At Brewster angle, the deflection from beam axis is proportional to n2I
n2I
1 0
0 n2IThe deflection matrix is therefore simply:
For details see ?????????????
This may be an interesting research topic
1 d0 1
Propagation matrix:
A third ultrafast cavity perturbation: Kerr astigmatism modification
The ABCD matrix should be calculated in the plane xz and yz.
The crystal thicknesses are
(at Brewster angle)
yx
d
Different ABCD (and stability condition) in the xz and yz planes.The difference is intensity dependent.
H.~W. Kogelnik, E.~P. Ippen, A.~Dienes, and C.~V. Shank.“Astigmatically compensated cavities for cw dye lasers.”IEEE Journal of Quantum Electron., QE-8:373--379 (1972).
Ultrashort laser sources
The dream: a purely dispersive mechanism, creates the soliton
The reality: needs an amplitude modulation
Saturable absorption, Kerr lensing or Kerr deflection
Two pulse/cavity lasers
Direct creation of a frequency comb
The OPO: from the theoretician dream to the experimentalist nightmare.
1.
2.
3.
Ideal laser medium versus ideal amplifier medium4.
5.
6.
Ideal laser medium versus ideal amplifier medium
Short lifetime media Long lifetime media
Dye laser, semiconductor lasers
Ti:sapphire, alexandrite, forsterite etc…
Crystalline host lasers
High gain, low power Low gain, high power
Operation dominated by gain, loss modulation “robust” operation
“Soliton” type operation possible, but strong tendency to Q-switching
Average power independent of repetition rate High energy/pulse with long cavities
Pulse energy independent of repetition rate > 1 nJ/pulse difficult (VECSL)
Ideal amplifier(Degenerate self optimizing cavityCouder, Bartolemy 1994 …
Cavity Ray Path
Couderc et. al. Setup
• Cavity mode can be defined by 2 apertures
• OR: Shape of pump defines cavity mode
• Useful for diode pumping
• Useful for VECSEL
• Use V shaped cavity with gain and MQW at focal length
• Gain diameter determined by pump• Absorber diameter determined by
best mode locking• Astigmatism may be a problem
(might lead to elliptical beam)
Advantages for the VECSEL
…)
Ultrashort laser sources
The dream: a purely dispersive mechanism, creates the soliton
The reality: needs an amplitude modulation
Saturable absorption, Kerr lensing or Kerr deflection
Two pulse/cavity lasers – a most powerful probe
Direct creation of a frequency comb
The OPO: from the theoretician dream to the experimentalist nightmare.
1.
2.
3.
Ideal laser medium versus ideal amplifier medium4.
5.
6.
5. Two pulse/cavity lasers
A better understanding of the mode-locked laser operation
The laser is more than a source: it is a powerful diagnostic tool
Intracavity Phase Interferometry as a linear and nonlinear probe
The two pulse/cavity laser as a two-level system (later)
5. Two pulse/cavity lasers for a better understanding of the mode-locked laser operation
Is a mode-locked laser really a periodic modulation to the cw wave?
TIME
E
FREQUENCY
EIn a mode-locked laser, a wave packet of longitudinal dimension of m, travels back and forth in a resonator of the order of one or two meter
5 m
2 m
Why would this light bullet care whether its central wavelength would fitas a sub-multiple of the cavity length?
The lone bullet in the resonator:
Is a mode-locked laser really a periodic modulation to the cw wave?
as a sub-multiple of the cavity length?Does the light bullet care whether its central wavelength fits
Yes, it does!
Because at each round-trip,
the Doppler shift at each reflection equals the mode shift.
The experimentalo proof is in the Intracavity Phase Interferometry
The principle of Intracavity Phase Interferometry
LASER
D
L
M1
M2
Michelson interferometerdetermines the position of M2
through intensity measurement
L
I
In presence of noise:
listening to Chopin with an AM radio
SOLUTION: go to an FM station!
This is what IPI is
LASER
D
L
GAIN
Review in J. Phys. B, 42:183001 (2009)
L L
Intracavity Phase Interferometry (IPI)
1 2
LASERCAVITY
Interference oftwo pulse trains
0.16 Hz
Frequency (Hz)
Frequency
f02
f01
Fourier Transform
D
Expanded scale (measurement)
Fourier transform
0.870.860.85 0.88 0.89
0.1
0.2
Time (seconds)
1430142514201415 1435 14400
0.2
0.4
0.6
0.8
1.
Beat frequency (Hz)
Spec
tral
inte
nsity
1Hz
1430142514201415 1435 14400
0.2
0.4
0.6
0.8
1.
Beat frequency (Hz)
Spec
tral
inte
nsity
1HzL L =
L(pm)-0.01 0.01-0.02-0.03-0.04 0.02
Example of data
Measurement of n2 is a measurement of phase
Most phase measurements convert the phase in intensity, hence sensitive to amplitude noise
Example: zscan
D
signal
z
z
With amplitude noise (and small n2):
Z-scan versus Intracavity Phase Interferometry (IPI)
This is like listening to Chopin with an AM radio
SOLUTION: go to an FM station! This is what IPI is
BS
1. External pumping, with pump cavity ½ length or signal cavity.
Delay2
EOM Ti:sapphirePPLN
D1
D2
Repetition rate detector
BeatNotedetector
Measurement of n2
EOM: Pockel’s cell to induce an intensity difference I1-I2 between the two OPO pulses
Optimum resolution from 0.16 Hz bandwidth:
n2) = 2 10-19 cm2/W
Measurement of n2 --- IPI vs z-scan
I P I Z-scan
Single intensity difference provides n2
Requires a … z-scanNo scan required
Requires single shot determination of the intensityIntensity measurements on continuous beam
(larger dynamic range)Frequency measurement Intensity measurement
Not affected by amplitude noise Amplitude noise sensitive
OPO tunable Dispersion of n2
IPI applied to magnetometry
saturableabsorberdye jet
GTGG d
TGG = Terbium Gallium Garnet
Resolution: 10 nT or Faraday rotation of 8x10-9rad
Femtosecond temporal resolutionExtracavity pumpIntracavity probe
D BEAT NOTE
D
Laser cavity
Phonon or vibrationexcited on mirror
d
TimeAfter
excitation
Periodic displacements: detecting ultrasound phonons.
Periodicexcitation
gate Delay
1M
: 2
53
The VECSEL approach
VECSEL
SAM
EXTRA-CAVITY
INTRA-CAVITY
Advantages:
High power in a small package No problems with Q-switching
D
P
X
Sensingelement
Referencearm
SA
Fiber implementation of IPI
Three dimensional nanoscope
Start
Laser gyro cw magnetometer
Nonlinear index measurement
Phase sensor
Fresnel drag
Optical accelerometer
RF magnetometer
Electro-optical coefficient
Phonon visualization Nanomechanics vizualization
The route to the phase sensing by IPIhas numerous bifurcations
The route to the phase sensing by IPI is a multiple lane highway.
Dye laser
Ti:sapphire+ saturable absorber dye
Extracavity Pumped OPO
Intracavity Pumped
OPO
VCSELpumped
OPO
Fibermode-locked
laserPHASE
SENSOR
Ultrashort laser sources
The dream: a purely dispersive mechanism, creates the soliton
The reality: needs an amplitude modulation
Saturable absorption, Kerr lensing or Kerr deflection
Two pulse/cavity lasers
Direct creation of a frequency comb
The OPO: from the theoretician dream to the experimentalist nightmare.
1.
2.
3.
Ideal laser medium versus ideal amplifier medium4.
5.
6.
The OPO: from the theoretician dream to the experimentalist nightmare.
Population inversion gain Parametric gain
A fs signal pulse propagating through the gain medium extracts more and more energy from the medium as it grows, becausethe gain has a long lifetime
The signal pulse (at s) only gainsenergy as long as the pump is present
Fluorescence noiseAmplified spontaneous emission
Control of group and phase Velocities intertwined
Group velocity affected by saturation
No fluorescence!
No amplified spontaneous emission
TIME
Ip
TIME
Ip
TIME
GAIN
TIME
GAIN
Population inversion gain Parametric gain
How to make a laser with two pulses circulating independently in the cavity? 1. External pumping, with pump cavity ½ length or signal cavity.
Advantage: Stability – no feedback from OPO to pump
Disadvantage: high power needed (> 1nJ/pulse)
2. Intracavity pumping
OPOPump cavity
Advantages: controllable crossing point, high power
Disadvantage: instabilities Cure: SHG
SHG
Instabilities in Intracavity Pumped Optical Parametric Oscillators and Methods of Stabilization}Andreas Velten, Alena Zavadilova, Vaclav Kubecek, and Jean-Claude DielsApplied Physics B 98:13-25 (2009)
The OPO: a (theoretical) dream for IPI
The intracavity pumped OPO: an experimentalist nightmare
The intracavity pumped OPO: an experimentalist nightmare
Lasers for IPI: Optical Parametric Oscillators (OPO)
How to make a laser with two pulses circulating independently in the cavity?
2. Intracavity pumping where pump and OPO cavities have a commun multiple
OPOPump cavity
SHG
Advantage: same stability as extracavity pumped
Disadvantage: Each OPO pulse is pumped only once/2 round-trips.
Not enough pump energy available
IPI and intracavity pumped OPO’s: an field full of promises… and of stumbling blocks
For more details: Opo_and_NLloss.pdf
A. Velten, A. Zavadilova, V Kubecek, and J.-C. Diels. “Instabilities in intracavity pumped optical parametric oscillators and methods of stabilization.”Applied Physics B, 98:13–24, 2010.
"A. Velten, A, Schmitt-Sody and J.-C. Diels", "Precise intracavity phase measurement in an OPO with two pulses per cavity round-trip",Optics Letters, 35: 1181--1183, (2010).
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