Description of a pulse train

The “ideal” mode-locked laser emits a train of identical pulses:

To the change in phase between successive pulses

corresponds a frequency::

The change in phase from pulse to pulse is a measurable quantity,independent of the duration of the individual pulse in the train.

Ele

ctri

c fi

eld

Time

eRT

Ele

ctri

c fi

eld

Time

Ele

ctri

c fi

eld

FrequencyRT

avf0

eRT

p

RT

Description of a pulse train

p = e(i + 1) - e(i )

A train of functions

//

Ele

ctri

c fi

eld

Time//

RT

Coherence

e

Ele

ctri

c fi

eld

Frequency

Coherence

RT

b

av

f0RT

p

p = e(i + 1) - e(i )

Description of a pulse train

A train of pulses

Ele

ctri

c fi

eld

Frequency

Coherence

RT

b

av

f0RT

p

p = e(i + 1) - e(i )

Description of a pulse train

The mode comb

p

700 800 900

100

200 (a)

Rep

. Rat

e -

101

884

000

Hz

Wavelength [nm]

Mode locked laser comb:

fixed teeth spacing. D

counter

Fixed number

Spectro.

Unequally spaced teeth

Tuned cw laser: the mode spacingvaries with frequency

2L

n()

/c

D

counter

Mode-locking = Laser Orthodontist

Two burning questions:

As a pulse circulates in the cavity,

does it evolve towards a steady state?Which mechanism makes the

unequally spaced cavity modes

equidistant?

Evolution of a single pulse in an ``ideal'' cavity

How unequally spaced modes

lead to a perfect frequency comb

Evolution of a single pulse in an ``ideal'' cavity

Dispersion

Kerr effect

Kerr-induced chirp

How unequally spaced modeslead to a perfect frequency comb

Phase delayGroup delay

Cavity modes: not equally spaced because nav = nav()

Unequally spaced modes, is contradictory to the fact that comb teeth are equally spaced.

where

where

dispersion

A cavity with ONLY Kerr modulation generates the pulse train:

F.T.

Two burning questions:

As a pulse circulates in the cavity,

does it evolve towards a steady state?

Which mechanism makes theunequally spaced cavity modes

equidistant?

Evolution of a single pulse in an ``ideal'' cavityHow unequally spaced modes

lead to a perfect frequency comb

SAME

CONDITION

The choice of the optimum metrology method for a given problem

The right tool for a given measurement: An overview

The pulse train

TOOLS: Simple analog oscilloscope and frequency doubling crystal.

The right tool for a given measurement

Electronic Spectrum analyzer

Both fundamental and second harmonic: a straight line.

Spectrometer

What to look for?

No sideband and higher harmonics

Continuous spectrum, central wavelength

THE PULSE TRAIN

An overview

The right tool for a given measurement

THE PULSE TRAIN

An overview

Both fundamental and second harmonic: a straight line.

Electronic Spectrum analyzer

The right tool for a given measurement

THE PULSE TRAIN

An overview

What we should not see:

Modulation of the train on a s scale

(Shows as a sideband on spectrumanalyzer on a 100 KHz scale)

Q-switched-mode-locked train

TOOLS: Scanning autocorrelator, Intensity, interferometric, spatially encoded Spider

The right tool for a given measurement

THE PULSE OF A TRAIN

Do you want to tune the laser to get the shortest pulse?

Tuning a laser oscillator Tuning a high power system

An overview

Single pulse characterization at high repetiton rate: SPIDER