ultrashort laser sources

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…


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

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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:


LASER

Pulse duration

RT

Mode bandwidth

Number of pulses

CEO?

CEP?









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A purely dispersive mechanism, creates the soliton

Phase

modulationdispersion

Phase


Phase

modulation

dispersion

Phasemodulation

dispersion

Dispersion

FIBER

LASER


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)


(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)


DISPERSION

n()or

k()() ()e-ikz

Propagation in the frequency domain

Retarded frame and taking the inverse FT:


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”



Phase


Phase


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).










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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









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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


Kerr Lensing Kerr deflectionn = n0 + n2I

lossy

lossy

ideal

Both mechanisms can provide the ideal “saturation absorption” curve:


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).








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Ideal laser medium versus ideal amplifier medium4.

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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

…)





Two pulse/cavity lasers – a most powerful probe



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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








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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

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).

ultrashort laser sources

Documents

dispersive mechanism

ideal laser medium

frequency combthe opo

kerr lensing

kerr deflection

frequency comba

theoretician dream

ideal amplifier medium1