How do you study a laser firing for one-quadrillionth of a second?

I’m grateful to Mukund Thattai, at the National Centre for Biological Sciences, Bengaluru, for explaining many of the basic concepts at work in the following article.

An important application of lasers today is in the form of extremely short-lived laser pulses used to illuminate extremely short-lived events that often play out across extremely short distances. The liberal use of ‘extreme’ here is justified: these pulses last for no more than one-quadrillionth of a second each. By the time you blink your eye once, 100 trillion of these pulses could have been fired. Some of the more advanced applications even require pulses that last 1,000-times shorter.

In fact, thanks to advances in laser physics, there are branches of study today called attophysics and femtochemistry that employ such fleeting pulses to reveal hidden phenomena that many of the most powerful detectors may be too slow to catch. The atto- prefix denotes an order of magnitude of -18. That is, one attosecond is 1 x 10-18 seconds and one attometer is 1 x 10-18 metres. To quote from this technical article, “One attosecond compares to one second in the way one second compares to the age of the universe. The timescale is so short that light in vacuum … travels only about 3 nanometers during 1 attosecond.”

One of the more common applications is in the form of the pump-probe technique. An ultra-fast laser pulse is first fired at, say, a group of atoms, which causes the atoms to move in an interesting way. This is the pump. Within fractions of a second, a similarly short ‘probe’ laser is fired at the atoms to discern their positions. By repeating this process many times over, and fine-tuning the delay between the pump and probe shots, researchers can figure out exactly how the atoms responded across very short timescales.

In this application and others like it, the pulses have to be fired at controllable intervals and to deliver very predictable amounts of energy. The devices that generate these pulses often provide these features, but it is often necessary to independently study the pulses and fine-tune them according to different applications’ needs. This post discusses one such way and how physicists improved on it.

As electromagnetic radiation, every laser pulse is composed of an electric field and a magnetic field oscillating perpendicular to each other. Of these, consider the electric field (only because it’s easier to study; thanks to Maxwell’s equations, what we learn about the electric field can be inferred accordingly for the magnetic field as well):

Credit: Peter Baum & Stefan Lochbrunner, LMU München Fakultät für Physik, 2002

The blue line depicts the oscillating electric wave, also called the carrier wave (because it carries the energy). The dotted line around it depicts the wave’s envelope. It’s desirable to have the carrier’s crest and the envelope’s crest coincide – i.e. for the carrier wave to peak at the same point the envelope as a whole peaks. However, trains of laser pulses, generated for various applications, typically drift: the crest of every subsequent carrier wave is slightly more out of step with the envelope’s crest. According to one paper, it arises “due to fluctuations of dispersion, caused by changes in path length, and pump energy experienced by consecutive pulses in a pulse train.” In effect, the researcher can’t know the exact amount of energy contained in each pulse, and how that may affect the target.

The extent to which the carrier wave and the envelope are out of step is expressed in terms of the carrier-envelope offset (CEO) phase, measured in degrees (or radians). Knowing the CEO phase is crucial for experiments that involve ultra-precise measurements because the phase is likely to affect the measurements in question, and needs to be adjusted for. According to the same paper, “Fluctuations in the [CEO phase] translate into variations in the electric field that hamper shot-to-shot reproducibility of the experimental conditions and deteriorate the temporal resolution.”

Ignore all the symbols and notice the carrier wave – especially how its peak within the envelope shifts with every next pulse. The offset between the two peaks is called the carrier-envelope offset phase. Credit: HartmutG/Wikimedia Commons, CC BY-SA 3.0

This is why, in turn, physicists have developed techniques to measure the CEO phase and other properties of propagating waves. One of them is called attosecond streaking. Physicists stick a gas of atoms in a container, fire a laser at it to ionise them and release electrons. The field to be studied is then fired into this gas, so its electric-wave component pushes on these electrons. Specifically, as the electric field’s waves rise and fall, they accelerate the electrons to different extents over time, giving rise to streaks of motion – and the technique’s name. A time-of-flight spectrometer measures this streaking to determine the field’s properties. (The magnetic field also affects the electrons, but it suffices to focus on the electric field for this post.)

This sounds straightforward but the setup is cumbersome: the study needs to be conducted in a vacuum and electron time-of-flight spectrometers are expensive. But while there are other ways to measure the wave properties of extreme fields, attosecond streaking has been one of the most successful (in one instance, it was used to measure the CEO phase at a shot frequency of 400,000 times per second).

As a workaround, physicists from Germany and Canada recently reported in the journal Optica a simpler way, based on one change. Instead of setting up a time-of-flight spectrometer, they propose using the pushed electrons to induce an electric current in electrodes, in such a way that the properties of the current contain information about the CEO phase. This way, researchers can drop both the spectrometer and, because the electrons aren’t being investigated directly, the vacuum chamber.

The researchers used fused silica, a material with a wide band-gap, for the electrodes. The band-gap is the amount of energy a material’s electrons need to be imparted so they can ‘jump’ from the valence band to the conduction band, turning the material into a conductor. The band-gap in metals is zero: if you placed a metallic object in an electric field, it will develop an internal current linearly proportional to the field strength. Semiconductors have a small band-gap, which means some electric fields can give rise to a current while others can’t – a feature that modern electronics exploit very well.

Dielectric materials have a (relatively) large band-gap. When it is exposed to a low electric field, a dielectric won’t conduct electricity but its internal arrangement of positive and negative charges will move slightly, creating a minor internal electric field. But when the field strength crosses a particular threshold, the material will ‘break down’ and become a conductor – like a bolt of lightning piercing the air.

Next, the team circularly polarised the laser pulse to be studied. Polarisation refers to the electric field’s orientation in space, and the effect of circular polarisation is to cause the electric field to rotate. And as the field moves forward, its path traces a spiral, like so:

A circularly polarised electric field. Credit: Dave3457/Wikimedia Commons

The reason for doing this, according to the team’s paper, is that when the circularly polarised laser pulse knocks electrons out of atoms, the electrons’ momentum is “perpendicular to the direction of the maximum electric field”. So as the CEO phase changes, the electrons’ directions of drift also change. The team used an arrangement of three electrodes, connected to each other in two circuits (see diagram below) such that the electrons flowing in different directions induce currents of proportionately different strengths in the two arms. Amplifiers attached to the electrodes then magnify these currents and open them up for further analysis. Since the envelope’s peak, or maximum, can be determined beforehand as well as doesn’t drift over time, the CEO phase can be calculated straightforwardly.

(The experimental setup, shown below, is a bit different: since the team had to check if their method works, they deliberately insert a CEO phase in the pulse and check if the setup picks up on it.)

The two tips of the triangular electrodes are located 60 µm apart, on the same plane, and the horizontal electrode is 90 µm below the plane. The beam moves from the red doodle to the mirror, and then towards the electrodes. The two wedges are used to create the ‘artificial’ CEO phase. Source: https://doi.org/10.1364/OPTICA.7.000035

The team writes towards the end of the paper, “The most important asset of the new technique, besides its striking simplicity, is its potential for single-shot [CEO phase] measurements at much higher repetition rates than achievable with today’s techniques.” It attributes this feat to attosecond streaking being limited by the ability of the time-of-flight spectrometer whereas its setup is limited, in the kHz range, only by the time the amplifiers need to boost the electric signals, and in the “multi-MHz” range by the ability of the volume of gas being struck to respond sufficiently rapidly to the laser pulses. The team also states that its electrode-mediated measurement method renders the setup favourable to radiation of longer wavelengths as well.

Featured image: A collection of lasers of different frequencies in the visible-light range. Credit: 彭嘉傑/Wikimedia Commons, CC BY 2.5 Generic.

Weyl semimetals make way for super optics

A Weyl semimetal is a crystal whose lattice has the uncommon ability to carry electrical energy at room temperature.

In 2015, materials scientists made an unexpected discovery. In a compound of the metals tantalum and arsenic, they discovered a quasiparticle called a Weyl fermion. A quasiparticle is a packet of energy trapped in a system, like a giant cage of metal atoms, that in some ways moves around and interacts like a particle would. A fermion is a type of elementary particle that makes up matter; it includes electrons. A Weyl fermion, however, is a collection of electrons that behaves as if it is one big fermion – and as if it has no mass.

In June 2017, physicists reported that they had discovered another kind of Weyl fermion, dubbed a type-II Weyl fermion, in a compound of aluminium, germanium and lanthanum. It differed from other Weyl fermions in that it violated Lorentz symmetry. According to Wikipedia, Lorentz symmetry is the fact that “the laws of physics stay the same for all observers that are moving with respect to one another within an inertial frame”.

Both ‘regular’ and type-II Weyl fermions can do strange things. By extension, the solid substance engineered to be hospitable to Weyl fermions can be a strange thing itself. For example, when an electrical conductor is placed within a magnetic field, the current flowing through it faces more resistance. However, in a conductor conducting electricity using the flow of Weyl fermions, the resistance drops when a magnetic field is applied. When there are type-II Weyl fermions, resistance drops if the magnetic field is applied one way and increases if the field is applied the other way.

In the case of a Weyl semimetal, things get weirder.

Crystals are substances whose atoms are arranged in a regular, repeating pattern throughout. They’re almost always solids (which makes LCD displays cooler). Sometimes, this arrangement of atoms carries a tension, as if the atoms themselves were beads on a taut guitar string. If the string is plucked, it begins to vibrate at a particular note. Similarly, a crystal lattice vibrates at a particular note in some conditions, as if thrumming with energy. As the thrum passes through the crystal carrying this energy, it is as if a quasiparticle is making its way. Such quasiparticles are called phonons.

A Weyl semimetal is a crystal whose phonon is actually a Weyl fermion. So instead of carrying vibrational energy, a Weyl semimetal’s lattice carries electrical energy. Mindful of this uncommon ability, a group of physicists reported a unique application of Weyl semimetals on June 5, with a paper in the journal Physical Review B.

It’s called a superlens. A more historically aware name is the Veselago’s lens, for the Russian physicist Viktor Veselago, who didn’t create the lens itself but laid the theoretical foundations for its abilities in a 1967 paper. The underlying physics is in fact high-school stuff.

When light passes through a rarer medium into a denser medium, its path becomes bent towards the normal (see image below).

Credit: Wikimedia Commons
Credit: Wikimedia Commons

How much the path changes depends on the refractive indices of the two mediums. In nature, the indices are always positive, and this angle of deflection is always positive as well. The light ray coming in through the second quadrant (in the image) will either go through fourth quadrant, as depicted, or, if the denser medium is too dense, become reflected back into the third quadrant.

But if the denser medium has a negative refractive index, then the ray entering from the second quadrant will exit through the first quadrant, like so:

The left panel depicts refraction when the refraction indices are positive. In the left panel, the 'green' medium has a negative refractive index, causing the light to bend inward. Credit: APS/Alan Stonebraker
The left panel depicts refraction when the refraction indices are positive. In the left panel, the ‘green’ medium has a negative refractive index, causing the light to bend inward. Credit: APS/Alan Stonebraker

Using computer simulations developed using Veselago’s insights, the British physicist J.B. Pendry showed in 2000 that such mediums could be used to refocus light diverging from a point. (I highly recommend giving his paper a read if you’ve studied physics at the undergraduate level.

Credit: APS
Credit: APS

This is a deceptively simple application. It stands for much more in the context of how microscopes work.

A light microscope, of the sort used in biology labs, has a maximum zoom of about 1,500. This is because the microscope is limited by the size of the thing it is using to study its sample: light itself. Specifically, (visible) light as a wave has a wavelength of 200 nanometers (corresponding to bluer colours) to 700 nanometers (to redder colours). The microscope will be blind to anything smaller than these wavelengths, imposing a limit on the size of the sample. So physicists use an electron microscope. As waves, electrons have a wavelength 100,000-times shorter than that of visible-light photons. This allows electron microscopes to magnify objects by 10,000,000-times and probe samples a few dozen picometers wide. But as it happens, scientists are still disappointed: they want to probe even smaller samples now.

To overcome this, Pendry had proposed in his 2000 study that a material with a negative refractive index could be used to focus light – rather, electromagnetic radiation – in a way that was independent of its wavelength. In 2007, British and American physicists had found a way to achieve this in graphene, which is a two-dimensional, single-atom-thick layer of carbon atoms – but using electrons instead of photons. Scientists have previously noted that some electrons in graphene can flow around the material as if they had no mass. In the 2007 study, when these electrons were passed through a pn junction, a type of junction typically used between semiconductors in electronics, the particles’ path bent inward on the other side as if the refractive index was negative.

In the June 5 paper in Physical Review B, physicists demonstrated the same phenomenon – using electrons – in a three-dimensional material: a Weyl semimetal. According to them, a stack of two Weyl semimetals can be engineered such that the Weyl fermions from one semimetal compound can enter the other as if the latter had a negative refractive index. With this in mind, Adolfo Grushin and Jens Bardarson write in Physics:

Current [scanning tunnelling electron microscopes (STMs)] use a sharp metallic tip to focus an electron beam onto a sample. Since STM’s imaging resolution is limited by the tip’s geometry and imperfections, it ultimately depends on the tip manufacturing process, which today remains a specialised art, unsuitable for mass production. According to [the paper’s authors], replacing the STM tip with their multilayer Weyl structure would result in a STM whose spatial resolution is limited only by how accurately the electron beam can be focused through Veselago lensing. A STM designed in this way could focus electron beams onto sub-angstrom regions, which would boost STM’s precision to levels at which the technique could routinely see individual atomic orbitals and chemical bonds.

This is the last instalment in a loose trilogy of pieces documenting the shape of the latest research on topological materials. You can read the other two here and here.

Second star found to have magnetic-field flips also flips them fast

Tau Bootis A is a Sun-like white-dwarf star about 51 light-years from Earth. Its magnetic field changes polarity once every year as opposed to the 11 years it takes our Sun. While astronomers don’t really know why this is the case, they have a pretty interesting hypothesis: Tau Bootis A has a giant planet orbiting really close to it, and its gravitational field could be ‘dragging’ on the outer, convective layers of its host star to speed up its polarity reversals. Here’s an explanation of how this could work. It’s pretty fascinating that while we had the Sun’s cycle figured, just the second star we study that shows this behaviour defies most of our expectations.