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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. 1.

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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

1.

Direct creation of a frequency comb

2.

The dream: a purely dispersive mechanism, creates the soliton

The reality: needs an amplitude modulation

3.

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.


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:


w

2w

3w

4w

W

5w

Direct creation of a frequency comb

4w

5w

3w

2w

w

LASER

Pulse duration

tRT

Mode bandwidth

Number of pulses

CEO?

CEP?


Direct creation of a frequency comb


Ultrashort laser sources

1.

Direct creation of a frequency comb

2.

The dream: a purely dispersive mechanism, creates the soliton

The reality: needs an amplitude modulation

3.

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.


Phase

Phase

Phase

modulation

modulation

modulation

A purely dispersive mechanism, creates the soliton

dispersion

FIBER

dispersion

dispersion

dispersion

Dispersion

Phase

modulation

LASER


A purely dispersive mechanism, creates the soliton

Electric field

amplitude

Nonlinear index leads to

phase modulation

(a)

time

z = v4t

z = v3t

z = v1t

z = v2t

distance z


A purely dispersive mechanism, creates the soliton

Electric field

amplitude

(b)

Upchirped pulse in

Negative dispersion

medium

time

z = v2t

(slow)

z = v1t

(fast)


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)


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:


PHASE MODULATION

DISPERSION


PHASE MODULATION

DISPERSION


Characteristic field:

Characteristic time:

Normalized distance:

Equation in the retarded frame

Solitons: solutions of the eigenvalue equation


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.


Phase

Phase

Phase

modulation

modulation

modulation

A purely dispersive mechanism, creates the soliton

dispersion

FIBER

dispersion

dispersion

dispersion

Dispersion

Phase

modulation

LASER


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, 75:013824 (2007).


The magic wand of saturation

Starts mode-locking

Changes the group velocity

Couples intracavity pulses

in amplitude

in phase?

Interacts with CEP!

Ultrashort laser sources

1.

Direct creation of a frequency comb

2.

The dream: a purely dispersive mechanism, creates the soliton

The reality: needs an amplitude modulation

3.

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.


Gain pressure at the

bottom of the dam;

saturates as the dam fills up

and the flow released

balances the influx

Saturation

Gain Medium

Gain saturation is what stabilizes a laser.


time

Saturation

Absorption saturation

Gain saturation

Stabilizes

Starts mode-locking

I

0


Saturation starts mode-locking

The ideal “saturation absorption” curve:

Pulse energy


Saturation changes the group velocity

I

z

z = vgt

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

GAIN

ABSORBER

ABSORBER


A

B

t1

z

t2

t3

t4

t5

t =- z/c

t = z/c

t

Saturation changes the group velocity, and

couples intracavity pulses in amplitude

Application: creating two pulse trains of exactly the same repetition rate.


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


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

Repetition rate versus cavity length,

and other repetition rate mysteries

MQW with equal spacing of λ/2

MQW with a non-periodic structure


Repetition rate versus cavity length

E1 E2

Modeling

MQW

E’1E’2

Propagation axis z

MQW

z-ct

z-ct

Time


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


Slow versus fast saturable absorber

The ultrafast: Kerr lensing and Kerr deflection

The magic wand of saturation

Starts mode-locking

Changes the group velocity

Couples intracavity pulses

in amplitude

in phase?

Interacts with CEP!

Ultrashort laser sources

1.

Direct creation of a frequency comb

2.

The dream: a purely dispersive mechanism, creates the soliton

The reality: needs an amplitude modulation

3.

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.


The ultrafast: Kerr lensing and Kerr deflection

n = n0 + n2I

Kerr deflection

Kerr Lensing

lossy

ideal

lossy

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


The ultrafast: Kerr lensing and Kerr deflection

H. W. Kogelnik and T. Li,

“Laser beams and resonators", Appl. Opt.,

5: 1550-1567, (1966)

Cavity analysis: classical textbooks


1

-

fNL

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:

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).


1 0

0

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

The deflection matrix is therefore simply:

n2I

For details see ?????????????

This may be an interesting research topic


y

x

d

A third ultrafast cavity perturbation:

Kerr astigmatism modification

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-8:373--379 (1972).


Ultrashort laser sources

1.

Direct creation of a frequency comb

2.

The dream: a purely dispersive mechanism, creates the soliton

The reality: needs an amplitude modulation

3.

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.


Ideal laser medium versus ideal amplifier medium

Long lifetime media

Short lifetime media

Crystalline host lasers

Dye laser, semiconductor lasers

Ti:sapphire, alexandrite, forsterite etc…

High gain, low power

Low gain, high power

“Soliton” type operation possible, but

strong tendency to Q-switching

Operation dominated by gain, loss modulation

“robust” operation

Average power independent of repetition rate

 High energy/pulse with long cavities

Pulse energy independent of repetition rate

> 1 nJ/pulse difficult (VECSL)

(

Degenerate self optimizing cavity

Couder, Bartolemy 1994

Ideal amplifier


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


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)‏

…)


Ultrashort laser sources

1.

Direct creation of a frequency comb

2.

The dream: a purely dispersive mechanism, creates the soliton

The reality: needs an amplitude modulation

3.

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.


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)


  • Two pulse/cavity lasers for a

  • better understanding of the mode-locked laser operation

E

TIME

E

5 mm

FREQUENCY

2 m

Is a mode-locked laser really

a periodic modulation to the cw wave?

The lone bullet in the resonator:

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?


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


D

D

DL

LASER

GAIN

Dn

n

DL

L

=

The principle of Intracavity Phase Interferometry

M2

DL

SOLUTION: go to an FM station!

This is what IPI is

Review in J. Phys. B, 42:183001 (2009)

LASER

M1

Michelson interferometer

determines the position of M2

through intensity measurement

I

DL

In presence of noise:

listening to Chopin with an AM radio


Fourier Transform

0.16 Hz

f01

f02

Frequency

Frequency (Hz)

Intracavity Phase Interferometry (IPI)

Interference of

two pulse trains

LASER

CAVITY

1

2


0.2

0.1

0.85

0.86

0.88

0.89

0.87

Time (seconds)

DL(pm)

0.01

0.02

-0.04

-0.03

-0.02

-0.01

Dn

DL

=

n

L

Example of data

D

Expanded scale

(measurement)

Fourier transform

D(Dn)=


z

z

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

signal

With amplitude noise (and small n2):

This is like listening to Chopin with an AM radio

This is what IPI is

SOLUTION: go to an FM station!


PPLN

D1

D2

Measurement of n2

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) = 2 10-19cm2/W

2

Delay

Repetition rate detector

Ti:sapphire

EOM

Beat

Note

detector

BS


Requires a … z-scan

No scan required

Intensity measurements on continuous beam

Requires single shot determination of the intensity

Frequency measurement

Intensity measurement

Amplitude noise sensitive

Not affected by amplitude noise

OPO tunable

Dispersion of n2

Measurement of n2 --- IPI vs z-scan

Z-scan

I P I

Single intensity difference provides n2

(larger dynamic range)


saturable

absorber

dye jet

TGG

IPI applied to magnetometry

Resolution:

10 nT or Faraday rotation of 8x10-9rad

Extracavity pump

Femtosecond temporal resolution

Intracavity probe

d

G

TGG =

Terbium Gallium Garnet


: 2

Delay

gate

M

1

Periodic

excitation

Periodic displacements: detecting ultrasound phonons.

Laser

cavity

D

d

Phonon or vibration

excited on mirror

D

BEAT NOTE

Time

After

excitation


The VECSEL approach

SAM

VECSEL

Advantages:

  • High power in a small package

  • No problems with Q-switching

INTRA-CAVITY

EXTRA-CAVITY

53


D

SA

X

Reference

arm

P

Sensing

element

Fiber implementation of IPI


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


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


Ultrashort laser sources

1.

Direct creation of a frequency comb

2.

The dream: a purely dispersive mechanism, creates the soliton

The reality: needs an amplitude modulation

3.

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.


The OPO: from the theoretician dream to the

experimentalist nightmare.

Parametric gain

Population inversion 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


Ip

Ip

TIME

TIME

G

A

I

N

G

A

I

N

TIME

TIME

Parametric gain

Population inversion gain


OPO

Pump cavity

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


The intracavity pumped OPO:

an experimentalist nightmare


The intracavity pumped OPO:

an experimentalist nightmare


OPO

Pump cavity

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


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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