Fresnel biprism beam-splitter

Cylindrical lens

Oppositely tilted pulses

Input pulse

Etalon

To spec-trometer

SHG crystal

Lens

Georgia Tech & Swamp Optics Atlanta, GA USA

Prof. Rick Trebino

The Measurement of Ultrashort Laser Pulses

The vast majority of humankind’s greatest discoveries have resulted directly from improved techniques for measuring light.

Spectrometers led to quantum mechanics.

The Michelson interferometer led to relativity.

Microscopes led to biology.

Telescopes led to astronomy.

X-ray crystallography solved DNA.

And technologies, from medical imaging to GPS, result from light measurement!

So what is the frontier of light measurement? Ultrafast!

So how do you measure the pulse itself?

1 minute10fs laser

pulse Age of universe

Time (seconds)

Computer clock cycle

Camera flash

Age of pyramids

One month

Human existence

10-15 10-12 10-9 10-6 10-3 100 103 106 109 1012 1015 1018

1 femtosecond 1 picosecond

In the 1960s, researchers began generating laser pulses nanoseconds long—shorter than could be measured. It’s now routine to generate femtosecond pulses.

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.

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.

But then, to measure the strobe light pulse, you need a detector whose response time is even shorter.

So, now, how do you measure the shortest event?

Photograph taken by Harold Edgerton, MIT

The Dilemma

And so on…

Its electric field can be written:

Alternatively, in the frequency domain:

We need to measure the (temporal or spectral) intensity and phase.

A light pulse has intensity and phasevs. time (or frequency).

Spe

ctra

l ph

ase,

(

)

FrequencySpe

ctru

m, S

()

Pha

se,

(t)

Time

Inte

nsity

, I(t)

The instantaneous frequency:Example: Linear chirp P

hase

, (t)

time

time

Freq

uenc

y,

(t)

time

The phase determines the pulse’s frequency (i.e., color) vs. time.

Time

Ligh

t ele

ctric

fiel

d

Gaussian-intensity linearly chirped pulse

One-Dimensional Phase Retrieval

E.J. Akutowicz, Trans. Am. Math. Soc. 83, 179 (1956)E.J. Akutowicz, Trans. Am. Math. Soc. 84, 234 (1957)

Retrieving it is called the 1D phase retrieval problem.

It’s more interesting than it appears to ask what we lack when we know only the pulse spectrum S().

Obviously, what we lack is the spectral phase ().

Even with extra information (constraints), it’s impossible.

Recall:

Spe

ctra

l ph

ase,

(

)

FrequencySpe

ctru

m, S

()

Interestingly, this follows from the Fundamental Theorem of Algebra.

Using the Event to Measure Itself

SHG crystal

The Intensity Autocorrelation: ( )A I t I t dt

SHGcrystal

Pulse to be measured

Variable delay,

Detector

Beamsplitter

E(t)

E(t–)

Esig(t,)

The signal field is Esig(t,) E(t) E(t-).So the signal intensity is I(t) I(t-)

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().

Autocorrelation of a Complex PulseAs 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 one-dimensional

phase-retrieval problem!

Coherent artifact

The autocorrelation approaches a broad background plus a narrow coherent artifact.

Coherent artifacts also occur in multi-shot autocorrelations of unstable pulse trains.

This type of autocor-relation 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!

Most modern techniques measure only the coherent artifact!

The “SPIDER” technique retrieves nonrandom pulse trains well.

But for random, longer-pulse trains, SPIDER yields the much shorter, nonrandom compon-ent 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.

Non

rand

om tr

ain

plus

ra

ndom

com

pone

nts

fs

fs

fs

The Spectrogram of a Waveform E(t)

The spectrogram yields the color and intensity of E(t) at the time, .

It’s the spectrum of the product: E(t) g(t-):

Example: Linearly chirped Gaussian pulse

( )E t

Time (t)0

2

( , ) ( ) ( ) exp( )E t g t i t dt

g(t-)

g(t-) gates out a piece of E(t), centered at .

Ligh

t ele

ctric

fiel

d

Spectrograms for Linearly Chirped Pulses

Like a musical score, the spectrogram visually displays the frequency vs. time (and the intensity, too).

Freq

uenc

yFr

eque

ncy

Time

Delay

Negatively chirped Unchirped Positively chirped

1

0

Autocorrelator

Nonlinear-optical medium

Unknown pulse

Variable delay

CameraSpec-

trometer

Beamsplitter

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.

FROG is simply a spectrally resolved autocorrelation—a spectrogram.

Frequency-Resolved Optical Gating (FROG)

E(t)

E(t–)Detector

Esig(t,) E(t) E(t)

Properties of the Spectrogram/FROG

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!

The gate need not be—and should not be—much shorter than E(t).

Time (ps)

Inte

nsity

10-1-30

0

30

Phas

e (r

ad)

Temporal Intensity and PhaseSimulated FROG trace with 1% additive noise

Wav

elen

gth

(nm

) TBP=95

430

420

410

400

390

380

-1000 -500 0 500 1000-1 0 1-1 0Delay (ps)

No coherent artifact!

The spectrogram resolves the dilemma! It doesn’t need the shorter event! It temporally resolves the slow components and spectrally resolves the fast components.

Properties of the Spectrogram/FROGAlgorithms exist to retrieve E(t) from its spectrogram or FROG trace.

2

( , ) ( , ) exp( )FROG sigI E t i t dt

The Solution!

Set of Esig(t,) that satisfy the nonlinear-optical constraint:

Esig(t,) E(t) E(t–)

Set of Esig(t,) that satisfy the data constraint:

The spectrogram uniquely and reliably determines the waveform intensity, I(t), and phase, (t), and, equivalently, S() and ().

SHG FROG Measurements of a 4.5fs Pulse

Baltuska, Pshenichnikov, and Weirsma,J. Quant. Electron., 35, 459 (1999).

Agreement between the experimental and retrieved FROG traces provides a nice check on the measurement and the pulse-train stability.

Thanks to FROG, ultrashort laser pulses are the best measured type of light on the planet!

Inte

nsity

Time (fs) Wavelength (nm)

Pha

se

Time domain Frequency domain

600 1000800-20 200

Wav

elen

gth

(m

)

Delay (fs) Delay (fs)

Measured Retrieved0.5

0.4

0.3-20 200 -20 200

10

0

SHG FROGDelay Delay

For unstable trains, FROG has a coherent artifact but smartly ignores it!

More importantly, disagreement between measured and retrieved FROG traces reveals the instability.

For the random trains, SHG FROG retrieves the correct pulse lengths.

As expected, SHG FROG retrieves the nonrandom pulse train perfectly.fs

fs

fs

Other FROG versions do even better.

These FROG versions also reveal the instability. And they yield the structure!

Delay DelayDelay Delay

fs

fs

fs

Although FROG is not complex, it can be simplified.

FROGThin

nonlinear-optical

medium

Variable delay

CameraSpec-

trometer

Beamsplitter

GRENOUILLE

Camera

Thick nonlinear-optical mediumFresnel biprism

GRating-Eliminated No-nonsense Observation of Ultrafast Incident Laser Light E-fields

Crossing beams at a large angle maps delay onto transverse position.

This yields a single-shot measurement of a pulse. Even better, it never misaligns.

Here, pulse #1 arrivesearlier than pulse #2.

Here, the pulsesarrive simultaneously.

Here, pulse #1 arriveslater than pulse #2.

Fresnel biprism

=(x)xInput

pulsePulse #1

Pulse #2

The Fresnel Biprism

Pulse #1

Pulse #2

Delay range

Very thin crystal creates broad SH spectrum in all directions.Standard autocorrelators and FROGs use such crystals.

VeryThinSHG

crystal

Thin crystal creates narrower SH spectrum ina given direction and so can’t be used

for autocorrelators or FROGs.

ThinSHG

crystal

Thick crystal begins to separate colors.

ThickSHG crystalVery thick crystal acts like

a spectrometer! Why not replace the spectrometer in FROG with a very thick crystal? Very

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.

The Thick Crystal

Is a complete single-shot FROG. Uses the standard FROG algorithm. Never misaligns. Is more sensitive. Measures spatio-temporal distortions.

GRENOUILLE Beam Geometry

Thick SHG

crystal

Imaging lensFresnel biprism

Cylindrical lens Camera

Top view

Side viewFocusing lens

x

y

(x)

y

x

Testing GRENOUILLE

Compare a GRENOUILLE measurement of a pulse with a tried-and-true FROG measurement of the same pulse:

Time domain Frequency domain

Inte

nsity

Time (fs)

GRENOUILLE

FROG

Retrieved pulse

-200 200 780 820Wavelength (nm)

0

10

0

Pha

se (r

ad)

Delay (fs)-300 0 300 -300 0 300

Wav

elen

gth

(nm

)

390400

410

390400

410

GRENOUILLE FROG

Mea

sure

dR

etrie

ved

1

0

Spatio-Temporal DistortionsPrism pairs and simple tilted windows cause spatial chirp.

Gratings and prisms cause both spatial chirp and pulse-front tilt.

Prism

Angularly dispersed pulse with

spatial chirp and

pulse-front tilt

Input pulse

Grating

Angularly dispersed pulse with spatial chirp and pulse-front tilt

Input pulse

Prism pair

Input pulse

Spatially chirped output pulse

Spatially chirped output pulse

Input pulse

Tilted window

GRENOUILLE measures spatial chirp!

-0

+0

SHGcrystal

Signal-pulse frequency

Delay

Freq

uenc

y

+0-0

Tilt in the otherwise symmetrical SHG FROG trace indicates spatial chirp!

Fresnel biprism

Spatially chirped

pulse

GRENOUILLE measures pulse-front tilt.

Zero relative delay is off to side of the crystal

Zero relative delay is in the crystal center

SHGcrystal

An off-center trace indicates the pulse

front tilt! Delay

Freq

uenc

y

0

Fresnel biprism

Untilted pulse front

Tilted pulse front

For measuring longer (1-20ps) pulses, GRENOUILLE can be further simplified.

Camera

Thick pentagonalnonlinear-optical medium

Camera

Thick nonlinear-optical mediumFresnel biprism

A pentagonal crystal combines the biprism and thick crystal into one optic.

This yields relative delays up to ~30ps.

Pentagonal-Crystal GRENOUILLE Results

0.2

0.4

0.6

0.8

1

Inte

nsity

Pha

se (r

ad)

Time domain

Time (ps)

60

Pha

se (r

ad)

-15 -10 -5 0 0

Inte

nsity

Wavelength (nm)

Retrieved Spectrum

796 802

GRENOUILLE Spectrometer

Frequency domain

Delay (ps)

397

398

399

400

401

402

Measured trace

Wav

elen

gth

(nm

)

-15 15

397

398

399

400

401

402

Delay (ps)

Retrieved trace

-15 15

In the 1980s, researchers crossed tilted pulses to yield a much larger delay range (tens of ps) in single-shot autocorrelators.

Here, pulse #1 arrivesmuch earlier than pulse #2.Here, the pulsesarrive simultaneously.Here, pulse #1 arrivesmuch later than pulse #2.

=(x)

xPulse #1

Pulse #2

What about ~1-nanosecond pulses?

Tilted pulses Delay rangeWyatt 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°!

Generating Massive Pulse-Front TiltThe 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 dif-fraction gratings: 89.99°!

Doesn’t the etalon’s massive angular dispersion distort the pulse?

Focusing the etalon’s output beam, as is done in spectrometers, maps angle to position, separating the colors and distorting the pulse badly.

Etalon Lens

f

f

Imaging the etalon’s output beam, as we do here, maps position at the etalon to position at the SHG crystal, maintaining temporal shape.

f

2f 2f

f

Spectral-interferometry measurements confirm this result.

Fresnel biprism beam-splitter

Cylindrical lens

Oppositely tilted pulses

Input pulse

Etalon (with two clear edges on input face)

To spec-trometerNanosecond

GRENOUILLE Setup

SHG crystal

Lens (images horizontally and

focuses vertically)

Two oppositely tilted pulses emerge from the etalon and are imaged onto the SHG crystal horizontally.

The ns GRENOUILLE measures the intensity and phase of pulses up to several ns long.

Pulse distorted by amplification Double pulse (from a Michelson)

By tilting the pulses by >89.9º, we can generate ns delay ranges on a single shot!

Nanosecond lasers are the least stable lasers in the world. Perhaps these new measurement devices will help engineers to improve them.

GRENOUILLE

What GRENOUILLE Measures

Measured “FROG trace” (spectrogram)

Retrieved “FROG trace” (verification of measurement)

Autocorrelation Various other parameters, including spatial chirp and

pulse-front tilt

Intensity and phase vs. time

Spectrum and spectral phase

Controls

QuickFROG “pulse” panel

FROG, GRENOUILLE and QuickFROG also measure the beam spatial profile.

The time has come for GRENOUILLE to replace the autocorrelator!

Swamp Optics’ GRENOUILLE

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

M. M

aier

, et a

l.,

Phy

s. R

ev. L

ett.,

17,

127

5, 1

966.

GRENOUILLE measures virtually everything about the pulse!

And all without any alignment knobs!

Trebino, et al., Opt. Phot. News, 12, 22, 2001.

And it’s less expensive.

Another 1960s technology and what’s become of it…

Record player

Eight-track-tape player

Cassette deck

CD player

iPod

Recorded-music technology has gone through at least five gener-ations since the

1960s!

Recorded music

Another 1960s technology…

Slide rule

Adding machine

Calculator

Freeware on PocketPC

iPhone calculator

Calculators

Calculators have gone through five generations, too!

Ad

Swamp Optics’ GRENOUILLE won an R&D 100 award.

This award is given to the 100 most technologically

significant new products of the year.

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.

Swamp Optics’ products are well-known to be the gold standard for laser-pulse measurement.They yield the pulse intensity and phase vs. time and frequency.

They operate single-shot or multi-shot.

They also measure the pulse’s spatial profile, spatial chirp, and pulse-front tilt, all in real time.

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’re even inexpensive, starting at under US$10K.

They’re even very easy to align your beam into one.

Swamp Optics’ BOA Pulse Compressor won SPIE’s Prism award. Only two knobs: one for GDD, another for wavelengthEasy GDD scanning over a wide rangeHalf the size of two-prism devices Zero spatio-temporal distortionsContinuous GDD scanningAutomatically alignedInexpensive

Only one prism, so it cannot misalign!

To learn more…

www.swampoptics.com

www.frog.gatech.edu

And if you read only one ultrashort-pulse-measurement

book this year, make it this one!

If you have an interesting pulse-measurement problem, let us know!

Swamp Optics manufactures FROGs and GRENOUILLEs

to measure pulses from 4fs to 4ns!

Starting at under $10K.