1. 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…

2. Ultrashort laser sources1.
Direct creation of a frequency comb 2.
The dream: a purely dispersive mechanism, creates the soliton 3.
The reality: needs an amplitude modulation
Saturable absorption, Kerr lensing or Kerr deflection 4.
Ideal laser medium versus ideal amplifier medium 5.
Two pulse/cavity lasers 6.
The OPO: from the theoretician dream to the
experimentalist nightmare.

3. Direct creation of a frequency comb
A perfectly regular frequency comb is formed by nonlinear optics:
w, 2w, 3w, 4w, 5w, ...
But they are not in phase.
If they can be put in phase, a pulse train with zero CEO is created.
Reference:

4. tRT Direct creation of a frequency comb 5w 4w 3w 2w w LASER CEO? CEP?
Pulse duration
tRT
Mode bandwidth
Number of pulses
CEO?
CEP?
Pulse duration (for square spectrum) : x \lambda/4c = 390 as
CEO = 0
CEP changes with propagaton in air w 2w 3w 4w 5w W

5. Direct creation of a frequency comb

6. Ultrashort laser sources1.
Direct creation of a frequency comb 2.
The dream: a purely dispersive mechanism, creates the soliton 3.
The reality: needs an amplitude modulation
Saturable absorption, Kerr lensing or Kerr deflection 4.
Ideal laser medium versus ideal amplifier medium 5.
Two pulse/cavity lasers 6.
The OPO: from the theoretician dream to the
experimentalist nightmare.

7. FIBER LASER A purely dispersive mechanism, creates the soliton
dispersion
FIBER
Phase
modulation
Phase
modulation
dispersion
Phase
modulation
dispersion
dispersion
Dispersion
Phase
modulation
LASER

8. (a) Nonlinear index leads to phase modulation time z = v4t z = v3t
A purely dispersive mechanism, creates the soliton
Electric field
amplitude
Nonlinear index leads to
phase modulation
(a)
time
z = v4t
z = v3t
z = v2t
z = v1t
distance z

9. (b) Electric field amplitude Upchirped pulse in Negative dispersion
A purely dispersive mechanism, creates the soliton
Electric field
amplitude
(b)
Upchirped pulse in
Negative dispersion
medium
time
z = v2t
(slow)
z = v1t
(fast)

10. e(t,0) eik(t)d e(t,0) Propagation in the time domain PHASE MODULATION
A purely dispersive mechanism, creates the soliton
Propagation in the time domain
PHASE MODULATION
E(t) = e(t)eiwt-kz
n(t) or
k(t)
e(t,0) eik(t)d
e(t,0)

11. e(DW,0) e(DW,0)e-ik(DW)z Propagation in the frequency domain
A purely dispersive mechanism, creates the soliton
Propagation in the frequency domain
DISPERSION
n(W) or
k(W)
e(DW,0)
e(DW,0)e-ik(DW)z
Retarded frame and taking the inverse FT:

12. PHASE MODULATION
DISPERSION

13. PHASE MODULATION
DISPERSION

14. Equation in the retarded frame
Characteristic field:
Characteristic time:
Normalized distance:
Solitons: solutions of the eigenvalue equation

15. A purely dispersive mechanism, creates the soliton
The soliton as a “canal wave”
Recreation of the observation of John Russell for
the 150th anniversary of his observation in 1834.

16. FIBER LASER A purely dispersive mechanism, creates the soliton
dispersion
FIBER
Phase
modulation
Phase
modulation
dispersion
Phase
modulation
dispersion
dispersion
Dispersion
Phase
modulation
LASER

17. A purely dispersive mechanism, creates the soliton
The elements of soliton control in the laser
Tuning the wavelength, the mode and the CEO
L. Arissian and J.-C. Diels, “Carrier to envelope and dispersion control
in a cavity with prism pairs”, Physical Review A, 75: (2007).

18. Ultrashort laser sources1.
Direct creation of a frequency comb 2.
The dream: a purely dispersive mechanism, creates the soliton 3.
The reality: needs an amplitude modulation
Saturable absorption, Kerr lensing or Kerr deflection
The magic wand of saturation
Starts mode-locking
Changes the group velocity
Couples intracavity pulses
in amplitude
in phase?
Interacts with CEP! 4.
Ideal laser medium versus ideal amplifier medium 5.
Two pulse/cavity lasers 6.
The OPO: from the theoretician dream to the
experimentalist nightmare.

19. Saturation
Gain saturation is what stabilizes a laser.
Gain Medium
Gain pressure at the
bottom of the dam;
saturates as the dam fills up
and the flow released
balances the influx

20. Saturation
Absorption saturation
Gain saturation
Stabilizes
Starts mode-locking
time I

21. Pulse energy Saturation starts mode-locking
The ideal “saturation absorption” curve:
Pulse energy

22. Saturation changes the group velocityz
z = vgt
Saturable gain
Saturable absorption

23. 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
GAIN
ABSORBER
ABSORBER

24. t1 A B z t t = z/c t =- z/c t2 t3 t4 t5
Saturation changes the group velocity, and
couples intracavity pulses in amplitude
Application: creating two pulse trains of exactly the same repetition rate. t1 A B z t
t = z/c
t =- z/c t2 t3 t4 t5

25. (… Saturation changes the group velocity, and
couples intracavity pulses in amplitude
and phase
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

26. 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

27. Repetition rate versus cavity length,
and other repetition rate mysteries
MQW with equal spacing of λ/2
MQW with a non-periodic structure
Period of λ/2

28. Repetition rate versus cavity length
E E2
Modeling
MQW
E’ E’2
Propagation axis z
MQW
z-ct
z-ct
Time

29. …) Repetition rate versus cavity length,
and other repetition rate mysteries
Nanostructures, the CEO and the CEP
The position of the standing wave determines the magnitude of the
interaction with a structure < l, therefore the change in group velocity.
For details see: “group-phase_velocity_coupling.pdf” …)
More material on the coupling in amplitude and phase between two
Intracavity pulses in: two_pulse_walzing_in_a_laser_cavity.pdf

30. Ultrashort laser sources1.
Direct creation of a frequency comb 2.
The dream: a purely dispersive mechanism, creates the soliton 3.
The reality: needs an amplitude modulation
Saturable absorption, Kerr lensing or Kerr deflection 4.
Ideal laser medium versus ideal amplifier medium
The magic wand of saturation
Starts mode-locking
Changes the group velocity
Couples intracavity pulses
in amplitude
in phase?
Interacts with CEP! 5.
Two pulse/cavity lasers
Slow versus fast saturable absorber
The ultrafast: Kerr lensing and Kerr deflection 6.
The OPO: from the theoretician dream to the
experimentalist nightmare.

31. The ultrafast: Kerr lensing and Kerr deflection
n = n0 + n2I
Kerr deflection
lossy
ideal
lossy
Both mechanisms can provide the ideal “saturation absorption” curve:

32. The ultrafast: Kerr lensing and Kerr deflection
Cavity analysis: classical textbooks
H. W. Kogelnik and T. Li,
“Laser beams and resonators", Appl. Opt.,
5: , (1966)

33. 1 0 1 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:
1 0 1 -
fNL
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).

34. n2I The ultrafast saturable loss: Kerr deflection 1 0
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
The deflection matrix is therefore simply:
n2I
For details see ?????????????
This may be an interesting research topic

35. A third ultrafast cavity perturbation: Kerr astigmatism modificationx d
1 d
0 1
Propagation matrix:
The ABCD matrix should be calculated in the plane xz and yz.
The crystal thicknesses are
(at Brewster angle)
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: (1972).

36. Ultrashort laser sources1.
Direct creation of a frequency comb 2.
The dream: a purely dispersive mechanism, creates the soliton 3.
The reality: needs an amplitude modulation
Saturable absorption, Kerr lensing or Kerr deflection 4.
Ideal laser medium versus ideal amplifier medium 5.
Two pulse/cavity lasers 6.
The OPO: from the theoretician dream to the
experimentalist nightmare.

37. ( … Ideal laser medium versus ideal amplifier medium
Short lifetime media
Long lifetime media
Dye laser, semiconductor lasers
Crystalline host lasers
Ti:sapphire, alexandrite, forsterite etc…
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
Pulse energy independent of repetition rate
> 1 nJ/pulse difficult (VECSL)
Average power independent of repetition rate
 High energy/pulse with long cavities ( …
Degenerate self optimizing cavity
Couder, Bartolemy 1994
Ideal amplifier

38. Cavity Ray Path

39. Cavity mode can be defined by 2 apertures
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

40. Advantages for the 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)‏ …)

41. Ultrashort laser sources1.
Direct creation of a frequency comb 2.
The dream: a purely dispersive mechanism, creates the soliton 3.
The reality: needs an amplitude modulation
Saturable absorption, Kerr lensing or Kerr deflection 4.
Ideal laser medium versus ideal amplifier medium 5.
Two pulse/cavity lasers – a most powerful probe 6.
The OPO: from the theoretician dream to the
experimentalist nightmare.

42. 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)

43. 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
The lone bullet in the resonator:
FREQUENCY E
In a mode-locked laser, a wave packet of longitudinal dimension of mm,
travels back and forth in a resonator of the order of one or two meter
Why would this light bullet care whether its central wavelength would fit
as a sub-multiple of the cavity length?
5 mm
2 m

44. Is a mode-locked laser really a periodic modulation to the cw wave?
Does the light bullet care whether its central wavelength fits
as a sub-multiple of the cavity length?
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

45. Dn n = DL L The principle of Intracavity Phase Interferometry DL DL D
SOLUTION: go to an FM station!
This is what IPI is
LASER
Review in J. Phys. B, 42: (2009)
LASER D DL
GAIN M1 D
Michelson interferometer
determines the position of M2
through intensity measurement I Dn n = DL L DL
In presence of noise:
listening to Chopin with an AM radio

46. Intracavity Phase Interferometry (IPI)
Interference of
two pulse trains
Frequency
f02
f01
Fourier Transform
LASER
CAVITY
0.16 Hz
Frequency (Hz) 1 2

47. Example of data D Expanded scale (measurement) DL(pm)
0.87
0.86
0.85
0.88
0.89
0.1
0.2
Time (seconds) D
Expanded scale
(measurement)
DL(pm)
-0.01
0.01
-0.02
-0.03
-0.04
0.02
Fourier transform
D(Dn)= DL Dn L n =

48. Z-scan versus Intracavity Phase Interferometry (IPI)
Measurement of n2 is a measurement of phase
Most phase measurements convert the phase in intensity, hence sensitive to amplitude noise
Example: zscan D z
signal
With amplitude noise (and small n2):
This is like listening to Chopin with an AM radio z
SOLUTION: go to an FM station!
This is what IPI is

49. Measurement of n2 BS D(n2) = 2 10-19 cm2/W 2 Delay EOM Ti:sapphire
1. External pumping, with pump cavity ½ length or signal cavity.
EOM: Pockel’s cell to induce an intensity difference I1-I2 between the two OPO pulses
Optimum resolution from 0.16 Hz bandwidth:
D(n2) = cm2/W 2
Delay
Repetition rate detector D1
EOM
Ti:sapphire
PPLN
Beat
Note
detector D2 BS

50. Measurement of n2 --- IPI vs z-scan
Requires a … z-scan
No scan required
Single intensity difference provides n2
Requires single shot determination of the intensity
Intensity measurements on continuous beam
Frequency measurement
Intensity measurement
(larger dynamic range)
Not affected by amplitude noise
Amplitude noise sensitive
OPO tunable
Dispersion of n2

51. IPI applied to magnetometry
Resolution:
10 nT or Faraday rotation of 8x10-9rad
Extracavity pump
Femtosecond temporal resolution
Intracavity probe
saturable
absorber
dye jet
TGG d G
TGG =
Terbium Gallium Garnet

52. D Periodic displacements: detecting ultrasound phonons. : 2 gate M
Delay 1 M
Periodic
excitation
Laser
cavity D d
Phonon or vibration
excited on mirror D
BEAT NOTE
Time
After
excitation

53. The VECSEL approach Advantages: High power in a small package
No problems with Q-switching
INTRA-CAVITY
SAM
EXTRA-CAVITY
VECSEL 53 53

54. Fiber implementation of IPID P X
Sensing
element
Reference
arm SA

55. The route to the phase sensing by IPI
has numerous bifurcations
Start
cw magnetometer
Laser gyro
Fresnel drag
Electro-optical coefficient
Phase
sensor
Optical accelerometer
Nonlinear index
measurement
RF magnetometer
Phonon visualization
Nanomechanics vizualization
Three dimensional nanoscope

56. The route to the phase sensing by IPI
is a multiple lane highway.
Extracavity
Pumped
OPO
Intracavity
Pumped
OPO
Ti:sapphire
+ saturable
absorber dye
Dye laser
Fiber
mode-locked
laser
VCSEL
pumped
OPO
PHASE
SENSOR

57. Ultrashort laser sources1.
Direct creation of a frequency comb 2.
The dream: a purely dispersive mechanism, creates the soliton 3.
The reality: needs an amplitude modulation
Saturable absorption, Kerr lensing or Kerr deflection 4.
Ideal laser medium versus ideal amplifier medium 5.
Two pulse/cavity lasers 6.
The OPO: from the theoretician dream to the
experimentalist nightmare.

58. 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, because
the gain has a long lifetime
The signal pulse (at ws) only gains
energy as long as the pump is present
No fluorescence!
Fluorescence noise
Amplified spontaneous emission
No amplified spontaneous emission
Group velocity affected by saturation
Control of group and phase
Velocities intertwined

59. Population inversion gain Parametric gain
TIME Ip
TIME Ip
TIME G A I N
TIME G A I N

60. The OPO: a (theoretical) dream for IPI
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
Advantages: controllable crossing point, high power
Disadvantage: instabilities
Cure: SHG
Instabilities in Intracavity Pumped Optical Parametric Oscillators and Methods of Stabilization}
Andreas Velten, Alena Zavadilova, Vaclav Kubecek, and Jean-Claude Diels
Applied Physics B 98:13-25 (2009)
SHG
OPO
Pump cavity

61. The intracavity pumped OPO:
an experimentalist nightmare

62. The intracavity pumped OPO:
an experimentalist nightmare

65. 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
Advantage: same stability as extracavity pumped
Disadvantage: Each OPO pulse is pumped only once/2 round-trips.
Not enough pump energy available
SHG
OPO
Pump cavity

66. 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: , (2010).