Presentation on theme: "Description of a pulse train"— 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 pulsescorresponds 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 fieldTimejetRTwe summarize the essential notations and definitions.Inside the laser typically, only one pulse circulate. A complex representationof the field amplitude is particularly convenient in dealing withpropagation problems of electromagnetic pulses.
2 Description of a pulse train A train of d-functionstRTjeElectric fieldTimeElectric fieldnavjpFrequencyf0=1/tRT2ptRTjp=je(i + 1) -(i )
3 // // Description of a pulse train A train of pulses tCoherence tRT je Electric field////TimeDn =1/tCoherenceDnb =1/tElectric fieldnavf0=2ptRTjpFrequency1/tRTjp=je(i + 1) -(i )
4 jp Description of a pulse train The mode comb Dn =1/tCoherence Dnb =1/tElectric fieldnavf0=2ptRTjpFrequency1/tRTjp=je(i + 1) -(i )jp
5 (a) D D Tuned cw laser: the mode spacing varies with frequency 2Ln(l)/cDcounterUnequally spacedteethMode-locking = Laser Orthodontist700800900100200(a)Rep. Rate HzWavelength [nm]Mode locked laser comb:fixed teeth spacing.DcounterFixed numberSpectro.
6 Two burning questions: As a pulse circulates in the cavity,Which mechanism makes thedoes it evolve towards a steady state?unequally spaced cavity modesEvolution of a single pulse in an ``ideal'' cavityequidistant?How unequally spaced modeslead to a perfect frequency comb
7 Evolution of a single pulse in an ``ideal'' cavity DispersionKerr-induced chirpKerr effect
8 How unequally spaced modes lead to a perfect frequency comb Group delayPhase delayCavity 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:whereF.T.wheredispersion
9 Two burning questions: Which mechanism makes theAs a pulse circulates in the cavity,unequally spaced cavity modesdoes it evolve towards a steady state?equidistant?Evolution of a single pulse in an ``ideal'' cavityHow unequally spaced modeslead to a perfect frequency combSAMECONDITION
10 The choice of the optimum metrology method for a given problemThe right tool for a given measurement: An overviewThe pulse train
11 The right tool for a given measurement An overviewTHE PULSE TRAINTOOLS: Simple analog oscilloscope and frequency doubling crystal.Electronic Spectrum analyzerSpectrometerWhat to look for?Both fundamental and second harmonic: a straight line.No sideband and higher harmonicsContinuous spectrum, central wavelengthMANY OPPORTUNITIES TO CHEAT WITH ANY METHODThe 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 overviewTHE PULSE TRAINBoth fundamental and second harmonic: a straight line.Electronic Spectrum analyzer
13 The right tool for a given measurement An overviewTHE PULSE TRAINWhat we should not see:Modulation of the train on a ms scaleQ-switched-mode-locked train(Shows as a sideband on spectrumanalyzer on a 100 KHz scale)
14 The right tool for a given measurement An overviewTHE PULSE OF A TRAINDo you want to tune the laser to get the shortest pulse?TOOLS: Scanning autocorrelator, Intensity, interferometric, spatially encoded SpiderTuning a laser oscillatorTuning a high powersystemSingle pulse characterization at high repetiton rate: SPIDER