The Measurement of Ultrashort Laser Pulses

Transcription

1 The Measurement of Ultrashort Laser Pulses To spectrometer SHG crystal Fresnel biprism beamsplitter Cylindrical lens Etalon Oppositely tilted pulses Lens Prof. Rick Trebino Input pulse Georgia Tech & Swamp Optics Atlanta, GA USA

2 The vast majority of humankind s greatest discoveries have resulted directly from improved techniques for measuring light. Microscopes led to biology. Telescopes led to astronomy. Spectrometers led to quantum mechanics. X-ray crystallography solved DNA. The Michelson interferometer led to relativity. And technologies, from medical imaging to GPS, result from light measurement!

3 So what is the frontier of light measurement? Ultrafast! In the 1960s, researchers began generating laser pulses nanoseconds long shorter than could be measured. It s now routine to generate femtosecond pulses. 10fs laser pulse Computer clock cycle Camera flash 1 minute One month Age of pyramids Human existence Age of universe femtosecond 1 picosecond Time (seconds) So how do you measure the pulse itself? You must use the pulse to measure itself. But that isn t good enough. It s only as short as the pulse. It s not shorter.

4 The Dilemma In order to measure an event in time, you need a shorter one. To study this event, you need a strobe light pulse that s shorter. Photograph taken by Harold Edgerton, MIT But then, to measure the strobe light pulse, you need a detector whose response time is even shorter. And so on So, now, how do you measure the shortest event?

5 A light pulse has intensity and phase vs. time (or frequency). Its electric field can be written: Intensity, I(t) Time Phase, (t) Alternatively, in the frequency domain: Spectrum, S( ) Frequency Spectral phase, ( ) We need to measure the (temporal or spectral) intensity and phase.

6 time The phase determines the pulse s frequency (i.e., color) vs. time. Example: Linear chirp The instantaneous frequency: Phase, (t) Frequency, (t) time time Gaussian-intensity linearly chirped pulse Light electric field Time

7 One-Dimensional Phase Retrieval It s more interesting than it appears to ask what we lack when we know only the pulse spectrum S( ). Recall: Spectrum, S( ) Frequency Spectral phase, ( ) Obviously, what we lack is the spectral phase ( ). Retrieving it is called the 1D phase retrieval problem. Even with extra information (constraints), it s impossible. Interestingly, this follows from the Fundamental Theorem of Algebra. E.J. Akutowicz, Trans. Am. Math. Soc. 83, 179 (1956) E.J. Akutowicz, Trans. Am. Math. Soc. 84, 234 (1957)

8 Using the Event to Measure Itself Pulse to be measured Crossing beams in a nonlinear-optical crystal, varying the delay between them, and measuring the signal pulse energy vs. delay yields the Intensity Autocorrelation, A( ). Beam splitter The signal field is E SHG sig (t, ) E(t) E(t- ). So crystal the signal intensity is I(t) I(t- ) E(t ) SHG crystal Detector Variable delay, E(t) E sig (t, ) The Intensity Autocorrelation: () A ItI t dt

9 Autocorrelation of a Complex Pulse As the pulse become more complex, its autocorrelation becomes simpler. Retrieving the intensity from the autocorrelation is fundamentally impossible! This problem is also equivalent to the onedimensional phase-retrieval problem! Coherent artifact The autocorrelation approaches a broad background plus a narrow coherent artifact.

10 Coherent artifacts also occur in multi-shot autocorrelations of unstable pulse trains. This type of autocorrelation trace occurs for all types of unstable pulse trains. In the 1960s, researchers mistook the coherent artifact for their actual pulse s autocorrelation and vastly under-estimated their pulse lengths. Unfortunately, this still happens today!

11 Most modern techniques measure only the coherent artifact! Nonrandom train plus random components fs fs fs The SPIDER technique retrieves nonrandom pulse trains well. But for random, longerpulse trains, SPIDER yields the much shorter, nonrandom component of the pulse train the coherent artifact. These techniques cannot distinguish a stable train of short pulses from an unstable train of much longer pulses.

12 The Spectrogram of a Waveform E(t) It s the spectrum of the product: E(t) g(t- ): (, ) Etgt ( ) ( )exp( i t) dt 2 Light electric field Example: Linearly chirped Gaussian pulse g(t- ) Et () g(t- ) gates out a piece of E(t), centered at. 0 Time (t) The spectrogram yields the color and intensity of E(t) at the time,.

13 Spectrograms for Linearly Chirped Pulses Negatively chirped Unchirped Positively chirped Frequency Frequency Time Delay 1 0 Like a musical score, the spectrogram visually displays the frequency vs. time (and the intensity, too).

14 Frequency-Resolved Optical Gating (FROG) Unknown pulse FROG is simply a spectrally resolved Autocorrelator autocorrelation a spectrogram. Beam splitter E(t ) Nonlinear-optical medium Camera Detector Spectrometer Variable delay E(t) E sig (t, ) E(t) E(t ) Use any fast nonlinear-optical medium. SHG is the most sensitive, but its traces are symmetrical and so have an ambiguity in the direction of time. Third-order nonlinearities, however, do not.

15 Properties of the Spectrogram/FROG The gate need not be and should not be much shorter than E(t). The spectrogram resolves the dilemma! It doesn t need the shorter event! It temporally resolves the slow components and spectrally resolves the fast components. No coherent artifact! Intensity Temporal Intensity and Phase -1 0 Time (ps) Phase (rad) Simulated FROG trace with 1% additive noise Spectrogram pulse retrieval is equivalent to the 2D Phase Retrieval Problem a well-behaved problem, which works because the Fundamental Theorem of Algebra fails for polynomials of two variables! Wavelength (nm) TBP= Delay (ps)

16 Properties of the Spectrogram/FROG Algorithms exist to retrieve E(t) from its spectrogram or FROG trace. The Solution! Set of E sig (t, ) that satisfy the nonlinear-optical constraint: E sig (t, ) E(t) E(t ) I (, ) E ( t, )exp( i t) dt FROG Set of E sig (t, ) that satisfy the data constraint: sig 2 The spectrogram uniquely and reliably determines the waveform intensity, I(t), and phase, (t), and, equivalently, S( ) and ( ).

17 SHG FROG Measurements of a 4.5fs Pulse Wavelength ( m) Intensity Measured Delay (fs) Delay (fs) 0 Time domain Time (fs) Retrieved Frequency domain Wavelength (nm) Agreement between the experimental and retrieved FROG traces provides a nice check on the measurement and the pulse-train stability. Baltuska, Pshenichnikov, and Weirsma, J. Quant. Electron., 35, 459 (1999). Thanks to FROG, ultrashort laser pulses are the best measured type of light on the planet! 1 Phase 0

18 For unstable trains, FROG has a coherent artifact but smartly ignores it! fs SHG FROG Delay Delay As expected, SHG FROG retrieves the nonrandom pulse train perfectly. fs For the random trains, SHG FROG retrieves the correct pulse lengths. fs More importantly, disagreement between measured and retrieved FROG traces reveals the instability.

19 Other FROG versions do even better. Delay Delay Delay Delay fs fs fs These FROG versions also reveal the instability. And they yield the structure!

20 Although FROG is not complex, it can be simplified. Beam splitter FROG Thin nonlinearoptical medium Camera Spectrometer Variable delay Camera GRating-Eliminated No-nonsense GRENOUILLE Observation of Ultrafast Incident Laser Light E-fields Fresnel biprism Thick nonlinear-optical medium

21 The Fresnel Biprism Crossing beams at a large angle maps delay onto transverse position. Input pulse Pulse #1 x = (x) Pulse #1 Pulse #2 Here, pulse #1 arrives earlier than pulse #2. Here, the pulses arrive simultaneously. Here, pulse #1 arrives later than pulse #2. Fresnel biprism Pulse #2 Delay range This yields a single-shot measurement of a pulse. Even better, it never misaligns.

22 The Thick Crystal Suppose broadband light with a large convergence angle impinges on an SHG crystal. The SH generated depends on the angle. And the angular width of the SH beam created varies inversely with the crystal thickness. Very thin crystal creates broad SH spectrum in all directions. Standard autocorrelators and FROGs use such crystals. Very Thin SHG crystal Thin SHG crystal Thin crystal creates narrower SH spectrum in a given direction and so can t be used for autocorrelators or FROGs. Thick crystal begins to separate colors. Very thick crystal acts like a spectrometer! Why not replace the spectrometer in FROG with a very thick crystal? Thick SHG crystal Very thick crystal

23 GRENOUILLE Beam Geometry Top view x Side view Cylindrical lens Fresnel biprism Thick SHG crystal (x) y Imaging lens Focusing lens x Camera y Is a complete single-shot FROG. Uses the standard FROG algorithm. Never misaligns. Is more sensitive. Measures spatio-temporal distortions.

24 Testing GRENOUILLE Compare a GRENOUILLE measurement of a pulse with a tried-and-true FROG measurement of the same pulse: Measured Retrieved Wavelength (nm) GRENOUILLE FROG Delay (fs) 1 0 Intensity Time domain Retrieved pulse GRENOUILLE FROG Frequency domain Time (fs) Wavelength (nm) 10 0 Phase (rad)

25 Spatio-Temporal Distortions Prism pairs and simple tilted windows cause spatial chirp. Prism pair Tilted window Input pulse Spatially chirped output pulse Input pulse Spatially chirped output pulse Gratings and prisms cause both spatial chirp and pulse-front tilt. Input pulse Angularly dispersed pulse with spatial chirp and pulse-front tilt Grating Input pulse Prism Angularly dispersed pulse with spatial chirp and pulse-front tilt

26 GRENOUILLE measures spatial chirp! Spatially chirped pulse Fresnel biprism SHG crystal - 0 Signal-pulse frequency + 0 Tilt in the otherwise symmetrical SHG FROG trace indicates spatial chirp! Frequency - 0 Delay + 0

27 GRENOUILLE measures pulse-front tilt. Tilted pulse front Fresnel biprism SHG crystal Zero relative delay is off to side of the crystal Zero relative delay is in the crystal center Untilted pulse front An off-center trace indicates the pulse front tilt! Frequency 0 Delay

28 For measuring longer (1-20ps) pulses, GRENOUILLE can be further simplified. Fresnel biprism Thick nonlinear-optical medium Camera Camera Thick pentagonal nonlinear-optical medium

29 A pentagonal crystal combines the biprism and thick crystal into one optic. This yields relative delays up to ~30ps.

30 Pentagonal-Crystal GRENOUILLE Results Measured trace 1 Retrieved trace Wavelength (nm) Delay (ps) Delay (ps) 15 Intensity Intensity Time domain Phase (rad) 60 Phase (rad) Frequency domain Retrieved Spectrum GRENOUILLE Spectrometer Time (ps) Wavelength (nm)

31 What about ~1-nanosecond pulses? In the 1980s, researchers crossed tilted pulses to yield a much larger delay range (tens of ps) in single-shot autocorrelators. Pulse #1 x = (x) Here, pulse #1 arrives much earlier than pulse #2. Here, the pulses arrive simultaneously. Here, pulse #1 arrives much later than pulse #2. Pulse #2 Tilted pulses Delay range Wyatt and Marinero, 1981 But measuring a ns pulse would require one side of a ~1cm beam to precede the other by a meter a pulse tilt of ~89.99!

32 Generating Massive Pulse-Front Tilt The pulse-front tilt generated by an optic is proportional to the angular dispersion. Etalons yield ~100x more angular dispersion and hence also ~100x more pulse-front tilt than diffraction gratings: 89.99!

33 Doesn t the etalon s massive angular dispersion distort the pulse? f f f Focusing the etalon s output beam, as is done in spectrometers, maps angle to position, separating the colors and distorting the pulse badly. Etalon 2f Lens f 2f Imaging the etalon s output beam, as we do here, maps position at the etalon to position at the SHG crystal, maintaining temporal shape. Spectral-interferometry measurements confirm this result.

34 Nanosecond GRENOUILLE Setup To spectrometer SHG crystal Fresnel biprism beamsplitter Cylindrical lens Oppositely tilted pulses Lens (images horizontally and focuses vertically) Input pulse Etalon (with two clear edges on input face) Two oppositely tilted pulses emerge from the etalon and are imaged onto the SHG crystal horizontally.

35 The ns GRENOUILLE measures the intensity and phase of pulses up to several ns long. By tilting the pulses by >89.9º, we can generate ns delay ranges on a single shot! Pulse distorted by amplification Double pulse (from a Michelson) GRENOUILLE Nanosecond lasers are the least stable lasers in the world. Perhaps these new measurement devices will help engineers to improve them.

36 What GRENOUILLE Measures Intensity and phase vs. time QuickFROG pulse panel Measured FROG trace (spectrogram) Retrieved FROG trace (verification of measurement) Controls Spectrum and spectral phase FROG, GRENOUILLE and QuickFROG also measure the beam spatial profile. Autocorrelation Various other parameters, including spatial chirp and pulse-front tilt

37 The time has come for GRENOUILLE to replace the autocorrelator! M. Maier, et al., Phys. Rev. Lett., 17, 1275, Autocorrelators give us only a rough estimate of the pulse length. And they have many artifacts. Sadly, many ultrafast scientists still use this 1960s technology even today. Autocorrelator GRENOUILLE measures virtually everything about the pulse! And all without any alignment knobs! And it s less expensive. Swamp Optics GRENOUILLE Trebino, et al., Opt. Phot. News, 12, 22, 2001.

38 Another 1960s technology and what s become of it Recorded music Record player Cassette deck ipod Eight-track-tape player CD player Recorded-music technology has gone through at least five generations since the 1960s!

39 Another 1960s technology Slide rule Calculators Freeware on PocketPC Adding machine Calculator Calculators have gone through five generations, too! iphone calculator

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41 Swamp Optics GRENOUILLE won an R&D 100 award. This award is given to the 100 most technologically significant new products of the year.

42 GRENOUILLE also won a Circle of Excellence award. This award is given by SPIE and Photonics Spectra to the 25 top optics inventions of the year.

43 Swamp Optics products are wellknown to be the gold standard for laser-pulse measurement. They yield the pulse intensity and phase vs. time and frequency. They see through the coherent artifact and yield the correct pulse length even when instability is present (no other device can do this!). And they tell you if pulse-shape instability is present. They also measure the pulse s spatial profile, spatial chirp, and pulse-front tilt, all in real time. They operate single-shot or multi-shot. They re even very easy to align your beam into one. They re even inexpensive, starting at under US$10K.

44 Swamp Optics BOA Pulse Compressor won SPIE s Prism award. Only two knobs: one for GDD, another for wavelength Easy GDD scanning over a wide range Half the size of two-prism devices Zero spatio-temporal distortions Continuous GDD scanning Automatically aligned Inexpensive Only one prism, so it cannot misalign!

45 To learn more If you have an interesting pulsemeasurement problem, let us know! And if you read only one ultrashort-pulse-measurement book this year, make it this one! Swamp Optics manufactures FROGs and GRENOUILLEs to measure pulses from 4fs to 4ns! Starting at under $10K. gatech.edu