20120214 optical pulse_measurement_wei-yi

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20120214 optical pulse_measurement_wei-yi

  1. 1. Introduction optical pulsemeasurement & Fiber clearWei-Yi TsaiInstitute of Photonics TechnologiesNational Tsing Hua University, TaiwanFeb,14, 2011
  2. 2. NTHUOutline Defined of ultrafast Mathematic introduce definition Correlation & Convolution Pulse measurement methods Field autocorrelation Cross correlation Intensity autocorrelation Homework 2
  3. 3. NTHUDefined of ultrafast What is ultrafast ? The range of ultrafast ?‘’ ultrashort’’ refers to the femtosecond(fs) to picosecond(ps)range.3Milli- Micro- Nano- Pico- Femto- Atto-Time(s) 10e-3 10e-6 10e-9 10e-12 10e-15 10e-18frequency 1kHz 1MHz 1GHz 1THz 1PHz 1EHz
  4. 4. NTHUGoal of pulse measurement4* ( )1( ) Re{ ( ) } { ( ) ( ) }, ( ) ( )2o o oj t j t j t j tE t a t e a t e a t e a t a t e         -10 -8 -6 -4 -2 0 2 4 6 8 10-1-0.8-0.6-0.4-0.200.20.40.60.81X: 0.5811Y: 0.6262( )t( )a tIt is straightforward to get carrier frequency by spectrometer,we focus on measuring the complex envelope function
  5. 5. NTHUDifficult The laser pulse duration cannot be easily measured byoptoelectronic methods, since the response time ofphtodetector and oscilloscopes are at best of the order of200(fs)5(Shang-Da Yang, Ultrafast Optics, Lecture slide 05)
  6. 6. NTHUDefinition For a given power spectrum , the pulse is : Transform-limited (TL), if Chirped, if is nonlinear62( )A ( ) 0  ( ) -10 -8 -6 -4 -2 0 2 4 6 8 10-1-0.8-0.6-0.4-0.200.20.40.60.81-10 -8 -6 -4 -2 0 2 4 6 8 10-1-0.8-0.6-0.4-0.200.20.40.60.81Chirped TL
  7. 7. NTHUPulse measurement method Because the pulses are so short that no existing electronicsare capable of resolving them, so the common approach isto measure the ultrashort pulse by itself Auto-correlation Cross-correlation7*12 1 2( ) ( )f a t a t dt *( ) ( )f a t a t dt 
  8. 8. NTHUOutline Defined of ultrafast Mathematic introduce Correlation & Convolution Pulse measurement methods Field autocorrelation Cross correlation Intensity autocorrelation FAQ8
  9. 9. NTHUField autocorrelation9(Shang-Da Yang, Ultrafast Optics, Lecture slide 05)
  10. 10. NTHUField autocorrelation trace formula1001( ) ( ) 1 Re{ ( ) }jFA outI P G e      11 01 ( ) cos( ( ))GG R       when1*( )1 12( ) ( )( ) ( )( )Gja t a tG G e Ca t    Is the normalized field autocorrelation function of ( )a t
  11. 11. NTHUExample A TL pulse with two smallside lobes11(Shang-Da Yang, Ultrafast Optics, Lecture slide 05)
  12. 12. NTHUHow to retrieve G1 from the field autocorrelation Perform Fourier transform for trace: Extract the component centered at : Shift to the baseband: Perform inverse Fourier transform:12{ ( )}FA FAI F I , 0( ) ( )oFA FAI I     0,0 , 0( ) ( )FA FAI I       1,01( ) { ( )}FAG F I  11 0( ) 1 ( ) cos( ( ))FA GI G       (Shang-Da Yang, Ultrafast Optics, Lecture slide 05)
  13. 13. NTHULimitation FA function is nothing but power spectrum of the fieldenvelope a(t): As a result NO spectral phase information , then we cannotdistinguish transform-limited pulse withlong chirped pulse with and evenincoherent noise1321{ ( )} ( )F G A ( ) ( )TLI t ( ) 0  ( )chirpI t22( )2   ( )noiseI t
  14. 14. NTHULimitation14-5 -4 -3 -2 -1 0 1 2 3 4 500.511.522.53Temporal intensity profileTime tIntensity(a.u)-5 -4 -3 -2 -1 0 1 2 3 4 500.20.40.60.811.21.41.61.82Field autocorrelation trace-5 -4 -3 -2 -1 0 1 2 3 4 501234567Temporal intensity profileTime tIntensity(a.u)-5 -4 -3 -2 -1 0 1 2 3 4 500.20.40.60.811.21.41.61.82Field autocorrelation trace
  15. 15. NTHULimitation15-5 -4 -3 -2 -1 0 1 2 3 4 500.10.20.30.40.50.60.70.8Temporal intensity profileTime tIntensity(a.u)-5 -4 -3 -2 -1 0 1 2 3 4 500.20.40.60.811.21.41.61.82Field autocorrelation trace11 0( ) 1 ( ) cos( ( ))FA GI G R        
  16. 16. NTHUlimitations NO pulse asymmetry information, for16( ) ( )FA FAI I  (Shang-Da Yang, Ultrafast Optics, Lecture slide 05)
  17. 17. NTHUOutline Defined of ultrafast Mathematic introduce Correlation & Convolution Pulse measurement methods Field autocorrelation Cross correlation Intensity autocorrelation FAQ17
  18. 18. NTHUField-Cross-correlation18(Shang-Da Yang, Ultrafast Optics, Lecture slide 05)
  19. 19. NTHUField-cross-correlationThe field cross-correlation function of and1901,( ) ( ) 2Re{ ( ) }jFx out s r xI P U U G e       1, 0 1,2 ( ) cos( ( ))tot x G xU G       *1, ( ) ( ) ( )x s rG a t a t C   ( )sa t ( )ra t2( )i iTU a t dt 
  20. 20. NTHUField cross-correlation For very short reference pulse20r st t 0 1,2 ( ) cos( ( ))tot s G xU a       1, 0 1,( ) 2 ( ) cos( ( ))FX tot x G xI U G       1, ( ) ( ) ( ) ( )x s sG a t t a     
  21. 21. NTHUField cross-correlation Perform Fourier transform for the trace Extract the component centered at Shift to the baseband2101,( ) 2Re ( ) jFX tot xI U G e    *1, ( ) ( ) ( )x s rG a t a t  { ( )} ( )FXFXF I I   * *0 0 0 0( ) [ ( ) ( ) ( ) ( )]s r s rA A A A               00, ( )FX oI   0*,0 , 0( ) ( ) ( ) ( )FX FX s rI I A A         
  22. 22. NTHUField cross-correlation The exact complex spectrum of the signal pulse can bederived by: If the complex spectrum of the reference pulse isknown Bandwidth of the reference pulse is broader than that of thesignal pulse22,0*( )( )FxsrIAA( )rA 
  23. 23. NTHUPoor signal-to-background contrast23Cross-correlation Field-autocorrelation01,( ) ( ) 2Re{ ( ) }jFx out s r xI P U U G e       (Assume: TL Gaussian, ),s r s rU U t t  -10 -8 -6 -4 -2 0 2 4 6 8 100.70.80.911.11.21.31.4cross-correlation-10 -8 -6 -4 -2 0 2 4 6 8 1000.20.40.60.811.21.41.61.82Field-autocorrelation
  24. 24. NTHUOutline Defined of ultrafast Mathematic introduce Correlation & Convolution Pulse measurement methods Field autocorrelation Cross correlation Intensity autocorrelation FAQ24
  25. 25. NTHUSecond harmonic generation (SHG)25NLOmaterial0 02-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1x 10-9-1-0.8-0.6-0.4-0.200.20.40.60.81-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1x 10-9-1-0.8-0.6-0.4-0.200.20.40.60.812 2( )j t j te e 22 ( )a a t 
  26. 26. NTHUIntensity autocorrelation (IA)26
  27. 27. NTHUFringe-resolved intensity autocorrelation …Intensity autocorrelation ……Intensity-field correlation ……Squared-field autocorrelation272 0 0( ) 1 2 ( ) 4 ( ) cos( ( )) ( ) cos(2 ( ))FRIA f gI G f g                2 2( ) ( )( )( )I t I tG RI t *2[ ( ) ( )] ( ) ( )( )2 ( )I t I t a t a tf CI t    * 22[ ( ) ( )]( )( )a t a tg CI t 
  28. 28. NTHUComparison between TL &chirped pulses of the same I(t)28(Shang-Da Yang, Ultrafast Optics, Lecture slide 05)
  29. 29. NTHUHow to retrieve G2 from the Intensity autocorrelation Perform Fourier transform for trace: Extract the component centered at : Remove the Dirac-function component Perform inverse Fourier transform:29{ ( )}FAIA FAIAI F I ,0 ( ) ( 0)FRIA FRIAI I   1,02 ( ) { ( )}FRIAG F I  (Shang-Da Yang, Ultrafast Optics, Lecture slide 05)
  30. 30. NTHUIntensity autocorrelation trace30-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1x 10-13012345678Ifria-2 -1.5 -1 -0.5 0 0.5 1 1.5 2x 1016-0.500.511.522.53x 10-132 ( )G -2 -1.5 -1 -0.5 0 0.5 1 1.5 2x 1016-0.500.511.522.53x 10-13X: 0Y: 2.755e-013
  31. 31. NTHUIntensity autocorrelation trace31-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1x 10-13012345678Intensity autocorrelation trace-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1x 10-13012345678Intensity autocorrelation trace2 ( )G 
  32. 32. NTHUDeconvolution factorI(t)1.41 1.54 132decR22( / )pt te 2sec ( / )ph t t ( / )pt tIf this factor is know, or assumed, the time duration (Intensity width)of a pulse can be measured using an Intensity autocorrelationThe deconvolution factor, defined as:/decR t  
  33. 33. NTHUlimitation , no pulse asymmetry information.332 2( ) ( )G G  (Shang-Da Yang, Ultrafast Optics, Lecture slide 05)
  34. 34. NTHUNoncollinear340(2)2 ( , ) ( ) ( ) ja t a t a t e      2(3)2 2( ) ( , ) ( ) ( ) ( )IAI a t dt I t I t G      (Shang-Da Yang, Ultrafast Optics, Lecture slide 05)
  35. 35. NTHUHomework 試著利用 一個Gaussian pulse 做field -auto-correlation,並畫出 .35FAI
  36. 36. NTHUFiber 材質種類36Single mode fiberPolarization maintain fiberDispersion compensate/increasing fiber
  37. 37. NTHUFiber adaptor37PC-PC APC-APC
  38. 38. NTHUFiber 分類 & Different fiber patch cord connectors.38PC APC
  39. 39. NTHUFiber clear Step1 先用棉花棒沾酒精 Step2 再用棉花棒沿著fiber頭的面積擦一次 Step3 最後用氮氣槍,把酒精吹乾39
  40. 40. NTHUFiber clear40PCAPC
  41. 41. NTHUEnd41Thanks for your listening

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