# Description of a pulse train

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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.

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 )

// // 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 )

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

(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.

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

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

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

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

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

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.

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

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)

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

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