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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.

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Presentation on theme: "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."— Presentation transcript:

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 e RT

2 Electric field Time Electric field Frequency RT av f 0 e RT p Description of a pulse train p = e (i + 1) - e (i ) A train of functions

3 // Electric field Time // RT Coherence e Electric field Frequency Coherence RT b av f 0 RT p p = e (i + 1) - e (i ) Description of a pulse train A train of pulses

4 Electric field Frequency Coherence RT b av f 0 RT p p = e (i + 1) - e (i ) Description of a pulse train The mode comb p

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

6 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

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

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

9 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 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 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

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

13 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 spectrum analyzer on a 100 KHz scale) Q-switched-mode-locked train

14 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


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