1. 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.
Electric field
Time je
tRT
we summarize the essential notations and definitions.
Inside the laser typically, only one pulse circulate. A complex representation
of the field amplitude is particularly convenient in dealing with
propagation problems of electromagnetic pulses.

2. Description of a pulse train
A train of d-functions
tRT je
Electric field
Time
Electric field
nav jp
Frequency
f0=
1/tRT
2ptRT jp = je
(i + 1) -
(i )

3. // // Description of a pulse train A train of pulses tCoherence tRT je
Electric field // //
Time
Dn =1/tCoherence
Dnb =1/t
Electric field
nav
f0=
2ptRT jp
Frequency
1/tRT jp = je
(i + 1) -
(i )

4. jp Description of a pulse train The mode comb Dn =1/tCoherence
Dnb =1/t
Electric field
nav
f0=
2ptRT jp
Frequency
1/tRT jp = je
(i + 1) -
(i ) jp

5. (a) D D Tuned cw laser: the mode spacing varies with frequency
2Ln(l)/c D
counter
Unequally spaced
teeth
Mode-locking = Laser Orthodontist
700
800
900
100
200
(a)
Rep. Rate Hz
Wavelength [nm]
Mode locked laser comb:
fixed teeth spacing. D
counter
Fixed number
Spectro.

6. Two burning questions:
As a pulse circulates in the cavity,
Which mechanism makes the
does it evolve towards a steady state?
unequally spaced cavity modes
Evolution of a single pulse in an ``ideal'' cavity
equidistant?
How unequally spaced modes
lead to a perfect frequency comb

7. Evolution of a single pulse in an ``ideal'' cavity
Dispersion
Kerr-induced chirp
Kerr effect

8. How unequally spaced modes lead to a perfect frequency comb
Group delay
Phase delay
Cavity modes:
not equally spaced because nav = nav(w)
Unequally spaced modes, is contradictory to the fact that comb teeth are equally spaced.
A cavity with ONLY Kerr modulation generates the pulse train:
where
F.T.
where
dispersion

9. Two burning questions:
Which mechanism makes the
As a pulse circulates in the cavity,
unequally spaced cavity modes
does it evolve towards a steady state?
equidistant?
Evolution of a single pulse in an ``ideal'' cavity
How unequally spaced modes
lead to a perfect frequency comb
SAME
CONDITION

10. The choice of the optimum metrology method
for a given problem
The right tool for a given measurement: An overview
The pulse train

11. The right tool for a given measurement
An overview
THE PULSE TRAIN
TOOLS: Simple analog oscilloscope and frequency doubling crystal.
Electronic Spectrum analyzer
Spectrometer
What to look for?
Both fundamental and second harmonic: a straight line.
No sideband and higher harmonics
Continuous spectrum, central wavelength
MANY OPPORTUNITIES TO CHEAT WITH ANY METHOD
The more sophisticated the instrument, the easier it is for the manufacturer to cheat.
There is no point in taking an autocorrelation, frog of spider if the above conditions are not satisfied.

12. The right tool for a given measurement
An overview
THE PULSE TRAIN
Both fundamental and second harmonic: a straight line.
Electronic Spectrum analyzer

13. The right tool for a given measurement
An overview
THE PULSE TRAIN
What we should not see:
Modulation of the train on a ms scale
Q-switched-mode-locked train
(Shows as a sideband on spectrum
analyzer on a 100 KHz scale)

14. The right tool for a given measurement
An overview
THE PULSE OF A TRAIN
Do you want to tune the laser to get the shortest pulse?
TOOLS: Scanning autocorrelator, Intensity, interferometric, spatially encoded Spider
Tuning a laser oscillator
Tuning a high power
system
Single pulse characterization at high repetiton rate: SPIDER