Introduction to Pulse Measurement

In the 1960s, laser pulses broke the nanosecond barrier and became shorter than even the fastest electronics could measure—and the field of ultrashort-laser-pulse measurement was born. A simple, primitive pulse-measurement technique emerged, called intensity autocorrelation (see below).  It yielded only a rough measure of the pulse length (even then, it required an assumption about the pulse shape).  And it yielded no information about the pulse phase, or color. In other words, it provided a blurry black-and-white image of the pulse. Worse, for an unstable train of pulses, it yielded a narrow feature, called the "coherent artifact," which was often mistaken for the much longer pulse length  As a result, autocorrelations of unstable pulse trains always usually yielded a shorter pulse than was in fact present.

 

Yes, autocorrelation left much to be desired.  An interferometric version did better, but only slightly.

Schematic of an autocorrelator.  A pulse is split into two, one is variably delayed with respect to the other, and the two pulses are then crossed in a nonlinear-optical crystal, yielding a new light pulse whose intensity is given by the product of the two pulse intensities. If the two pulses overlap in time, some light is generated; if not, then no light is generated. The expression for the autocorrelation is shown at the upper right. In this and later figures, E(t) is the pulse electric field vs. time (indicative of the intensity and phase), and I(t) is the intensity vs. time.

Autocorrelations of stable and unstable trains of pulses, showing the coherent artifact.   Red indicates the pulse intensity, while blue indicates the phase. Notice that the autocorrelation does not depend at all on the phase (by design).  Also, structure in the intensity washes out in the autocorrelation. The relatively narrow feature in the autocorrelation of the unstable pulse train is the coherent artifact. Note that it's considerably shorter than the actual typical pulse in the train but is often confused for the actual pulse length.

Why measure the phase?

It wasn't until the 1990s that the problem was solved (by Rick Trebino—the founder of Swamp Optics--and several of his post-docs).  Interestingly, the solution was simple:  all that was required was to spectrally resolve the light pulse generated in an autocorrelator. The trick is in the pulse-retrieval mathematics, and Trebino invented a robust pulse-retrieval algorithm to retrieve the pulse from the spectrally resolved autocorrelation.  He called the technique Frequency-Resolved Optical Gating (FROG).  FROG succeeds in measuring the complete intensity and phase vs. time and frequency.

FROG-apparatus schematic. Spectrally resolving the nonlinear-optically generated pulse in an autocorrelator makes the difference.

Measured FROG trace (top left) of a 4.5fs pulse by Balthuska, Psheniknikov, and Wiersma.   Note that FROG also yields the pulse spectrum (green) and spectral phase (violet).  It requires no assumptions about the pulse shape.  And the "retrieved trace" (top right) confirms the measurement's accuracy, as well as the pulse train's stability.

So how does FROG do when measuring an unstable train of pulses?  Much better than autocorrelation!  There are various versions of FROG, depending on the nonlinear-optical process involved, such as SHG (second-harmonic generation), PG (polarization gating), and XFROG (cross-correlation).  But all retrieve the correct pulse length.  And most retrieve the structure in the pulse intensity and spectrum. No method ever devised does better in such a difficult measurement situation!

Unfortunately, numerous "new" techniques have emerged that fail miserably when confronted with trains of unstable pulses. This is unfortunate because there is no "stability meter" that can verify that a pulse train is stable, so this must be the job of the pulse-measurement technique.  Alas, alternative methods cannot distinguish between a stable train of short simple pulses and an unstable train of long complex pulses. It's difficult to imagine a more serious problem with a pulse-measurement device.

 

To appreciate this problem, we show below a demonstration of the performance of the so-called SPIDER technique for stable and unstable trains of pulses.  As you can see, it can significantly under-estimate the pulse length and pulse-train stability, and you'd never know it from the measurement.  The problem is that lasers are often unstable, and a pulse train must be considered guilty of instability until proven innocent.  Essentially all other methods perform similarly badly.

 

Measurements using such techniques are at worst wrong and at best unconvincing.

 

But not so for FROG.

So FROG is the only technique that actually can distinguish a stable pulse train from an unstable one.  This is remarkable in view of the fact that the FROG designs above necessarily average over many pulses.  Think about it:  a spectrometer will average over many pulses and also won't give any indication of whether the spectrum a of each pulse in the train was the same or not.  So it's pretty amazing that FROG can do this. It's because FROG over-determines the pulse by measuring a two-dimensional trace (in order to find one-dimensional quantities, like the intensity and phase), and this extra, redundant information turns out to be quite useful.

Of course, a single-shot method would be much better, as it would allow us to measure every pulse in the train.  Fortunately, FROG can be performed on a single-shot basis.  In particular, a simple, elegant version of FROG, called GRENOUILLE (the French word for "frog"), naturally operates single-shot. Even better, compared with a multi-shot FROG, GRENOUILLE is less expensive, more compact, much more robust, much easier to use, and virtually impossible to misalign.  It's shown below.

Multi-shot FROG tutorial

How does GRENOUILLE work?  First it replaces the usual beam splitter, variable-delay stage, and beam-recombining optics with a single simple optical element: a Fresnel biprism. A Fresnel biprism is simply a prism with a very large apex angle, which splits the beam in two and crosses them (see below).  Also, when the beams cross, the delay between them varies across the nonlinear-optical crystal.   Imaging the crystal onto a camera then generates all the required delays on a single shot, specifically, at different places in the crystal.  So the Fresnel biprism does precisely what all those other optics did, but much more simply.  Even better, unlike those complicated optics, it never misaligns.

Okay, what about the thick crystal?  Pulse-measurement devices like autocorrelators are infamous for requiring ultra-thin crystals in order to generate the second harmonic for all the wavelengths in the pulse.  Now, we're doing the opposite!  It's because, for a FROG, we need to spectrally resolve the second harmonic, so why not take advantage of an SHG crystal's tendency to only generate a given second-harmonic wavelength in a given direction to also spectrally resolve the generated pulse?  See the figure below, which shows that the thick crystal, not only performs the usual autocorrelation, but also the spectral resolution (in place of a spectrometer) because the wavelength generated in such a crystal depends on angle.  How convenient!

Views of GRENOUILLE from the top and side.  In the (horizontal) x-direction, the Fresnel biprism maps delay onto transverse position at the crystal, which is then imaged onto horizontal position at the camera.   In the (vertical) y-direction, the crystal spectrally resolves the second-harmonic light generated in it. The lens afterward maps angle (and hence wavelength) onto vertical position at the camera.

GRENOUILLE measurements of a complex triple pulse. Note the excellent agreement between the GRENOUILLE measurement of the spectrum and the high-resolution spectrometer measurement of the same pulse.  Of course, unlike the spectrometer, GRENOUILLE also yields the phase.

So GRENOUILLE works well, and life is great; we can measure the temporal and spectral intensity and phase of ultrashort laser pulses better and more easily than we ever imagined.  But there's more to an ultrashort pulse than its temporal or spectral behavior.  There are some pesky spatial dimensions also.  Of course, we can easily measure the beam spatial profile.  But that's not enough.  The intensity and phase can vary in space, or, equivalently, the spatial profile can vary in time!  A pulse can have spatio-temporal distortions.

 

Below are schematics of the two most common spatio-temporal distortions in ultrashort laser pulses:  spatial chirp and pulse-front tilt.  Spatial chirp is fairly obvious (although Pink Floyd got it wrong on the back side of their famous Dark Side of the Moon album cover).  Pulse-front tilt is actually easy to understand, too.  Note that the part of the pulse that impinges on the near side of the diffraction grating in the figure below emerges first and so precedes the part of the beam that has to propagate all the way to the back edge of the grating.  Pulse-front tilt from a prism is a little trickier, but it involves the difference between phase and group delays.  Suffice it to say that propagation through a prism also tilts a pulse. And it turns out that all optics that introduce angular dispersion also introduce pulse-front tilt.  We've actually tilted a pulse by 89.999 degrees using an etalon.

Spatio-temporal distortions can be serious problems.  You can't focus such a distorted pulse very well, so the  intensity at a focus is greatly reduced.  The spatial resolution of a microscope using such a pulse is also greatly reduced.

 

Now, you're probably wondering:  most ultrafast lasers have angular-dispersive optics, like prisms and gratings, in them.  So wouldn't their output beams have a lot of these spatio-temporal distortions?  Well, not if the laser is properly aligned because the laser designer carefully compensates for them.  But that's only when the laser is perfectly aligned.  And we all know how easy it is to mis-align a laser.  So suffice it to say that all ultrafast laser pulses have some spatio-temporal distortions in them, no matter what the laser salesman says.  And if it doesn't when you buy it, it will someday when you breathe too close to the laser and mis-align it.

 

So, you're wondering, is it at least possible to measure spatial chirp and pulse-front tilt, so we can know when to re-align our laser or other optics in order to remove these effects?  Fortunately, the answer is yes, and, you guessed it, GRENOUILLE measures them both!

 

Below is a graphic that shows what happens when you send a spatially chirped pulse into a GRENOUILLE.  Note that the ordinarily symmetrical measured GRENOUILLE trace becomes tilted.  And the tilt is directly proportional to the spatial chirp.

And what about pulse-front tilt?  Yes, GRENOUILLE measures it, too!  A tilted pulse yields a measured GRENOUILLE trace that is displaced along the delay axis.  And the displacement is directly proportional to the pulse-front tilt.

In the next couple of figures, you can see examples of GRENOUILLE measurements of these distortions.

GRENOUILLE measurements of pulses with spatial chirp.  Note that GRENOUILLE can also measure the sign of the spatial chirp.

GRENOUILLE measurements of pulses with pulse-front tilt (and spatial chirp; when you have one spatio-temporal distortion, you usually have others, too). Note that GRENOUILLE can also measure the sign of the spatial chirp.

Learn even more about
FROG and GRENOUILLE.

So this concludes our introduction to pulse measurement.  As you can see, there's a lot to it.  But clever inventions and ideas have emerged, so it's now possible to do it very well.  Unfortunately, some not-so-clever ones have also emerged, so buyer beware!

 

In any case, once you've measured your pulse, you'll want to fix its problems.  As we mentioned above, the most common problem is temporal chirp, which can be fixed fairly easily using a pulse-compressor.  Alas, pulse-compressors involve prisms and gratings and so have a tendency to also introduce spatio-temporal distortions.  Check out our award-winning pulse-compressor, which doesn't.  Its design is fundamentally incapable of introducing such distortions!

Learn about
pulse compression.

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