Coulomb imaging is a technique for showing aspects of molecular geometry such as bond lengths and angles.
The name of the method derives from the concept of a Coulomb explosion and is named after the physicist Charles-Augustin de Coulomb, who gave us Coulomb's law. This law defines the force of attraction or repulsion between two electrically charged particles, just as Newtons' law does for the gravitational force. In place of masses, it uses the electrical charges, which with the separation of the two charged particles, allows the force to be determined. If the charges are given by Q1 and Q2 and the separation is R, then the force is proportional to Q1xQ2/R2.
The law predicts that if we put two like charges together they will repel each other and "explode" apart. If we calculate the energy released in the explosion, it is easy to show (using simple calculus), that it is proportional to 1/R. Therefore, if we can measure the kinetic energy of the explosion products we can deduce the initial separation of the charged particles.
This phenomenon is particularly useful if the charged particles are the atomic ions created by removing many electrons from a molecule, as this allows us to determine the geometry of the molecule before the explosion with some precision. In other words, it allows us to produce an image the molecule before the explosion.
The aims of the project
In the lab at Waterloo and at the Advanced Laser Light Source (ALLS) in Montreal we are studying the way molecules behave when placed in intense laser radiation.
Read an introductory article about Coulomb imaging
New ways to see matter or “blowing molecules apart with laser light and imaging them using position sensitive detection, to creating the worlds smallest and fastest flash photograph”.
We are constantly searching for new ways to see the world around us in better detail and by now we are used to seeing individual atoms on a surface as imaged by an electron microscope. Coulomb imaging is a way of looking at individual gas molecules, which we might be modifying with light so that they react with other molecules or a surface. A Coulomb explosion is a very simple phenomenon in which two or more charged objects (ions) placed close together repel each other with the electrostatic or Coulomb force. The force between any two ions is proportional to the product of the charges, and inversely proportional to the square of the distance between the charges (this is just the familiar inverse square law). Things become even simpler after the explosion, because the final kinetic energy of the ions is just proportional to the product of their charges and inversely proportional to the initial separation. This means that if we know the charge state of the ions we can measure their kinetic energy (by measuring their velocity) and then work out their initial separation. If there are more than two ions it gets a little bit more complicated, we have to measure the direction of the ions in order to find the magnitude of their velocities, then we can determine the initial separation and the geometry of the group of ions.
In order to use Coulomb imaging to see a molecule (to check if we have successfully bent a straight molecule of straightened a bent one) we must ionize all of the atoms in the molecule first and then detect the ions after the explosion. This is where the intense laser comes in, it can produce an electric field which is stronger than the attraction between the electrons and the atoms and so ionize them. The ions are accelerated toward a detector by an electric field and if we measure the position and time when the ions hit the detector we can measure their velocity vectors, this is where a PSD (position sensitive detector) comes in.
It might seem that any detector should measure position, but the standard detector of ions does not. This detector consists of a pair of MCPs (Micro-Channel Plates). These are thin glass plates around 1mm thick and 40mm diameter which consist of many invisible holes of micrometer size which connected one face to the other, the holes or channels are at an angle to the thickness and so when an ion hits the front of one of the holes electrons are emitted from the MCP material and a high field placed across the MCPs draws them to the back of the plate. On the way they collide again with the channel wall and emit more electrons, creating an electron avalanche. In this way a single ion can release a short burst of perhaps 106 electrons which can be observed as a voltage spike on an oscilloscope, giving information about the timing of an ion arrival event but not its position.
In order to get the positional information a so called position sensitive anode is required. There are several types of detector currently available. There are charged couple devices (CCDs), which are basically a television camera placed behind a phosphor screen, itself behind the MCPs. The CCD camera can see a spark of light emitted when a cloud of electrons hit the phosphor screen. Unfortunately, although this method is capable of detecting many spatial events at the same time, it is difficult to get timing information as well and both are essential. This difficulty is due to the way the chip, which controls the CCD, reads out the information by scanning across the detector from top to bottom, rather like the way a picture is projected on a television screen. No individual event time can be recorded during the time it takes to make the scan, which is relatively slow. A popular commercially available PSD, which can determine the time and position of an event, is the so-called delay line anode. When a cloud of electrons hit the wound wire, it sends a signal which travels in both directions. These signals take a short but measurable time (as short as a few hundred picoseconds) to travel to the ends of the wires where their times are recorded. The times are compared and the position determined from a simple formula:
To make a 2D detector, a second delay line is wound orthogonally to the first and four times are measured. This system is accurate to micrometer resolution and can detect several ions arriving in a short time of each other, which is important if we are going to measure the complete energy released in the Coulomb explosion. A drawback of the system is that it requires expensive timing equipment and more importantly, if two ions arrive at the same time their positions are unknown because the pair of timing signals are indistinguishable. Additionally, adding to this ‘dead time’, is a dead time which occurs if an electron cloud hits the detector after the first burst, but while the signal from the first event is still winding its way to the timers, ie: the second event occurs between the signal and one of the timers. This is a somewhat difficult problem to surmount, but these detectors are currently being extensively used across the world. A third kind of detector, which is being used at Waterloo, is the so-called backgammon anode. This is so named because it looks like a backgammon board with interconnecting electrodes. These electrodes divide the charge cloud from an event in the X direction and the rectangular electrodes, which form a capacitor with the big wedge behind them (the rectangular electrodes are drawn transparent so that the wedge electrodes are visible) and then divide the charge again in the Y direction. The position of an event is given by the ratio of the pulse heights as measured on an oscilloscope, where
Because the four pulses appear at the same time, the timing of an event is trivial. This kind of anode still has the dead time problem if two events occur at the same time, but not the additional dead time problem because there is no traveling pulse. Best of all, it can plug into a four channel oscilloscope, and so does not require expensive dedicated timing equipment.
The Coulomb imaging apparatus requires a method for removing many electrons from a molecule rapidly compared to the speed with which a molecule can move (change shape). This is rather like setting the photographic exposure to a short time when photographing a moving subject. For instance, an exposure of a 1000th of a second (1ms) is a good speed for observing an athlete as they run by, or for that matter, a horse. In fact, the first attempt to image the motion of a moving object was carried out by Edward Muybridge over one hundred years ago and he was indeed able to observe the running action of a horse (at the time the subject of some controversy) by taking multiple photographs of a horse as it galloped by. Muybridge used an exposure of around 1ms. One hundred years later and after things have moved on, we now need an “exposure” of 0.000000000000005s or 5 femtoseconds to observe the running action of a molecule. This is because molecules vibrate and deform on a timescale of tens of femtoseconds. In principle making a 5fs or even sub-femtosecond (attosecond ) laser pulse is no more difficult than producing a 50fs pulse, which has been possible for some time, but in practice is a challenge.
There are many great things about laser light. We all learn at school that laser light is collimated so that it maintains an intense beam over a long distance and that it is a single colour, but equally important is that it produces light which consists of classically coherent waves, or in other words, the peaks and troughs of all the waves arrive at the same time and the wave goes on for ever (ironically this is different than quantum light, which we get from a common light bulb, where the wave is discontinuous). The colour isn’t so single either, which is very important for producing a short pulse; some lasing media can lase at more than one wavelength and some can lase at many wavelengths at once, ie: they have a wide bandwidth.
I recently designed a web applet to demonstrate the principle of producing an ultra-short laser pulse. The applet simply adds together a number of sine waves of slightly different wavelength, in such a way that their peaks are all aligned at one point in time, where the amplitude is the sum of all the individual amplitudes. As we move away from that point however the different wavelengths make the addition of the amplitudes decrease as the waves move out of phase (the peak of one wave may become aligned with the troughs of another). The student who implemented the applet was not convinced this would work and kept asking what we would have to do to the waves to get the short pulse. I had to keep saying, just add the waves together, and when the code was debugged he was surprised to see that it did indeed work. The applet just adds together a range of wavelengths and the user inputs (the bandwidth) as the waves are added in one by one. The amplitude at one point gets bigger and bigger and then falls off in time with different speeds depending on the bandwidth. A typical laser with 20nm bandwidth and a centre wavelength at 800nm will produce a 100fs laser pulse.
Unfortunately we can't just do this in the lab, adding together waves with a bandwidth of 200nm to achieve a 5fs laser pulse, because the medium which produces the current generation of ‘femtosecond’ laser pulses, titanium sapphire or Ti:sapphire, can not lase over such a large bandwidth. Some other means has to be found to stretch the bandwidth. A process called self phase modulation can come to the rescue. This process relies on the fact that the refractive index of a medium effects the speed with which a wave can travel and that the refractive index is increased when a high intensity laser pulse passes through it. The result is that at the front of the pulse the wave is moving more quickly than in the middle of the pulse (stretching the wavelength) and at the back of the pulse the wave is also moving more quickly than in the middle (compressing the wavelength). This happens for all of the waves in the laser pulse. In practice we can achieve this simply by focusing our 800nm laser into some material like sapphire, and what comes out is a white light pulse.
Adding in the bandwidth doesn’t immediately make the pulse short, however, because the newly created waves aren’t lined up. In order to align them we can use mirrors which have many layers, each of which reflects a part of the spectrum. The path differences between the different wavelengths, introduced by the layers, allows the light to be lined up in time and produce the shortest pulses.