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Description of a pulse train

To the change in phase between successive pulses. corresponds a frequency::. t RT. j e. Electric field. Time. Description of a pulse train. The “ideal” mode-locked laser emits a train of identical pulses: . The change in phase from pulse to pulse is a measurable quantity,

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Description of a pulse train

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  1. To the change in phase between successive pulses corresponds a frequency:: tRT je Electric field Time Description of a pulse train The “ideal” mode-locked laser emits a train of identical pulses: The change in phase from pulse to pulse is a measurable quantity, independent of the duration of the individual pulse in the train.

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

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

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

  5. Tuned cw laser: the mode spacing varies with frequency Unequally spaced teeth D l counter 2Ln(l)/c (a) l 200 Mode locked laser comb: Spectro. Rep. Rate - 101 884 000 Hz D fixed teeth spacing. 100 counter 700 800 900 Fixed number Wavelength [nm] Mode-locking = Laser Orthodontist

  6. Evolution of a single pulse in an ``ideal'' cavity How unequally spaced modes lead to a perfect frequency comb 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 equidistant?

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

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

  9. Evolution of a single pulse in an ``ideal'' cavity How unequally spaced modes lead to a perfect frequency comb 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? 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

  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 high power system Tuning a laser oscillator Single pulse characterization at high repetiton rate: SPIDER

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