Quickfire Question: How do Fiber Optics work?

When you stick something in water - something like a pencil or a ruler is best since they are straight, you can see the object appear to bend at the surface of water.  This is due to the differences in refractive index between the water and the air.

All materials have a refractive index, because of the way that they interact with light. The vacuum, free space, has a refractive index "n" of 1, and all normal materials (negative refractive index is something I can cover another time!) have a refractive index higher than one. To give a couple of examples, for air, n is 1.0008, for water n is 1.330, for most ordinary glass, n is 1.51 and for diamond, n is 2.417. 


In a previous post, I mentioned Snell's Law,  this simple law relates the angles of incidence and refraction, and the refractive indices of the materials.

For something passing from a low refractive index to a high one at any angle, we can see that the light gets through, but what about the other way? If we try to calculate snell's law for certain angles, we see that the formula can't produce a result. At a very particular angle known as the critical angle, light can no longer escape from a high index material to a low one, and the light reflects from the surface.


This reflection is known as Total Internal Reflection. You can see total internal reflection when swimming underwater in a pool - look at the water's surface at a shallow angle, and it looks like a mirror.

This principle of total internal reflection is used in fiber optics to keep the light inside the fiber. A simple fiber optic is made of two materials - a core, with a high refractive index and a cladding with a low refractive index. Because of the TIR effect, light continuously reflects from the boundary, and is carried along the fiber.


There are a number of different sorts of optical fibre. Multimode fibers are generally wide compared to the wavelength of light, and as a result light can bounce at different angles (modes). some light may pass straight along the core, and some may bounce a lot from the edges. This causes the light to spread out. When the core is much narrower, then we may have a Monomode fibre, where the light can only pass in a straight line through the core (the mathematics of this are more complicated). As a result, the light does not spread out (due to reflections anyway!). The kind of fiber described above is known as a step index fibre, because the core immediately jumps from high to low index in the cladding. However one may also have a graded index fibre where the refractive index drops slowly towards the edge.


FIber optics are used in a broad range of applications, from telecommunications, to lighting applications, sensor applications and are commonly used for imaging in surgery. There are many other issues, complexities and types of fibres which build on the basic background introduced here.

Light and the Age of the Universe: George Gamow

In my discussions on the Cosmic Microwave background, I realised I had made a horrible omission: a guy called George Gamow. While I do not wish to take any of the well deserved credit from the winners of the Nobel Prizes, Gamow was one of those names who was sadly lost in history. He had actually predicted the CMB, or something like it, back in 1948. Here is a nice little article about it.

http://www.bookofjoe.com/2006/10/george_gamow_wi.html

Quickfire Question: How do LEDs work?

LEDs, or Light Emitting Diodes are very common devices used in a wide variety of applications from some street signage, power indicators, transmitters in remote controls and even LED torches. They are very efficient devices, which much like sodium lamps, convert most of the current passing through them into light, with very little loss as heat, but how do they work?

All LEDs are made from semiconductor materials - materials which have conducting properties somewhere between insulators (like glass) and conductors (like metals). Semiconductors can be carefully constructed to perform a variety of applications, such as diodes, which only allow current to pass through in one direction, to transistors - which either allow current to pass, or stop it, depending on the voltage at a "gate", solar cells and much more elaborate structures ranging from logic circuits all the way up to computer chips.

Like the previously mentioned diodes, LEDs only allow current to pass through in one direction, and when the current passes through, light is emitted. There are a couple of ways that LEDs can be constructed, I will concentrate on the simplest.

Semiconductors can be "doped" with other materials, which can either donate electrons (n-type semiconductors), or can accept electrons (p-type semiconductors). The former have extra electrons which can flow through the semiconductor from the negative to the positive terminal, and the latter have "holes" which are like positively charged electrons, that flow from the positive to the negative terminal. When the two meet they can recombine, and release energy in the form of light.

By varying the dopants, we can manipulate the wavelength of light that is emitted. Other methods of varying the colour are more elaborate, and involve the use of quantum tunneling, different sorts of junctions, and even adding additional materials. As we can see, the spectrum of conventional LEDs tends to be very pure:

producing a very limited spread of colour in each LED, however the addition of other chemicals such as phosphors, can "down convert" high frequency light such as blue, and re-emit that light in a broader spread of wavelengths. This is a common method of producing white LEDs.

More recently another type of LED has been developed, known as an Organic LED, or OLED. In place of inorganic materials such as Indium and Gallium, OLEDs use carbon based chemicals (hence organic) that emit light. The semiconductor properties of these materials are similar, though the emission is somewhat different, having a much broader spectrum. Some of the details and issues surrounding OLEDs will be covered in a later post.

Basic Optics: The principles of imaging - lenses and pinholes

We are all familiar with imaging - everything we see results from the imaging of the world on to our retina. Cameras image the world onto a film or a CCD, usually through a lens. Projectors display images on a screen, but how and why does imaging work.

If we imagine the light either bouncing, or being emitted from an object. That light passes through a hole, and then on to a screen. How do we know whether an image will form? For a large hole, like the one in the following picture, the light from any point on the object, on the right hand side ( I have chosen a picture of Darwin) may land on several points on the screen. As a result, the image will appear bright (because plenty light gets through the hole) but blurry (because the light from a point can hit a larger area on the screen.

The more we shrink the hole down, the more the light from the object is limited on the screen - however the less light gets through, so we have a much more sharply defined object, but it's also much darker.

Finally, if we introduce a lens into the larger hole, the light is bent so that (if the object and image are in the right places) all the light passing through the hole will land at the same point on the screen, and so we now have a bright object in good focus.

For a pinhole, it does not matter where the object and screen are, the image will always be in focus, however for a lens it does. There is a simple formula which tells us where the object and image are, depending on the focal length of the lens. The focal length is the distance at which an object at infinity is focussed. So for example when you hold a magnifying glass to focus the sun on to a point, it is the distance from the paper at which the spot is smallest and hottest. The formula that tells us where the object and image are is:

S1 and S2 are the object and image distances. It doesn't matter which way round, though the magnification will be affected by the different possible object and image distances.

This is a very simplified formula though, and depends on a number of considerations being true. The formula relies on what is known as the paraxial approximation - all the rays of light must be passing fairly close to the optical axis - a straight line passing out from the centre of the lens, perpendicular to the lens. if the rays pass close to the edge of the lens, or at a steep angle to the lens, then the image may be distorted, causing a number of optical aberrations (spherical aberrations, coma, field curvature). Also it ignores the different refractive indices of different wavelengths of light. In the same way as light is bent as it passes through a prism or a raindrop, and split up into different colours, the light of different colours passing through a lens may be focussed in different places. This is called chromatic aberration - and may often be seen towards the edges of lenses or pictures.

Light and the Age of the Universe - The Discovery and Analysis of the CMB

Discovery of the Cosmic Microwave Background

The Comic Microwave Background was discovered pretty much by accident by Arno Penzias and Robert Wilson who were working for Bell Laboratories, looking for signals from radio waves reflected from balloons. In the course of their experiments, they had to eliminate all noise sources such as radio broadcasts, and even a "white dielectric substance" left on the inside of the detector horn by a family of pigeons who had taken nest there. Once they had got rid of and accounted for every bit of noise they could, they noticed that there was a constant microwave hiss, from every direction, day and night - they had discovered the Cosmic Microwave Background.

The antenna where they made this discovery is now a national monument in the US:

They still did not know what they had found however, but when a friend of theirs told them about a still unpublished paper by Jim Peebles talking about the possibility of finding a signal like theirs, and what it would mean, they began to realise the significance of their discovery. The papers by Peebles and his colleagues, and the paper published by Penzias and Wilson were published together in Astrophysical Journal Letters. Penzias and Wilson won the 1978 Nobel Prize for their work.

The Cosmic Background Explorer

It was thought from early on after the discovery, that there would be small anisotropies (differences depending on direction) in the CMB, but ground based measurements were not good enough to measure them. It was not until the COsmic Background Explorer (COBE) was launched in 1989 that these anisotropies were first observed.

These fluctuations were very small, just one part in 10,000 of the average temperature. The resolution was still relatively low however, and so there was still much detail to be found. One additional important piece of evidence however came out of this - the match between the theoretically predicted Black Body curve based on the Big Bang model, and the experimental curve. The two matched precisely:

These results earned another Nobel Prize, but this time for the principal investigators on the COBE project; George Smoot and John Mather. The CMB wasn't the only thing that COBE was analysing however, and there were other important experiments and discoveries made. A good outline of the COBE satellite's other results can be found here.

The Wilkinson Microwave Anisotropy Probe (WMAP)

The next satellite to look at the CMB was WMAP. This time dedicated to the analysis of the CMB. After the success of COBE, WMAP was designed to not only view the CMB at higher resolution and sensitivity, but also to look at other features of the CMB such as polarization in order to give a better understanding of the early universe. There are a number of interesting results from WMAP, which will continue to operate until (currently) September 2010, and more details can be found here.

A brief summary of some of the WMAP results

• The universe is 13.73 billion years old (the most accurate figure we have))
• The universe is very flat (Euclidean)
• Around 23% of the universe is dark matter.
• The anisotropies appear to be random (though there are some hints of deviations from simple randomness which could give further clues into the early nature of the universe)

The Future Exploration of the CMB

This article has provided only a brief outline of the discovery and analysis of the Cosmic Microwave background. There are a number of features that have not been discussed, such as doppler shift, polarization and so on, and there is still much work to be done in understanding the details of the CMB. Although WMAP only has a few months of life left, the European Planck observatory, which started to take measurements in 2009, and is expected to begin to release results in 2012.

Light and the Age of the Universe - the Cosmic Microwave Background

Our main window to understanding the universe is light and the electromagnetic spectrum. Trapped here on earth, there is very little of the universe that we can actually touch and test with our own hands, but light provides an amazing tool. The Cosmic Microwave Background is perhaps on of the best methods we have of finding the age of the universe.

All objects that are in thermal equilibrium - that is, the matter and EM radiation in the objects are the same temperature - have what is known as a black body spectrum - EM radiation with properties that are a function of the temperature of that object only. That spectrum might be modified a little but atomic absorption and emission lines, but the fundamental black body spectrum will remain. The spectrum looks like the curves on this graph:

Each curve represents a black body emitter with a particular temperature, shown in Kelvin (roughly the temperature in degrees plus 273, where 0 is absolute zero). The Sun, indeed all stars have a black body spectrum. In the case of the sun, the surface, and black body temperature is about 6000K, so it looks not so dissimilar from the 5000K curve. You can see that the black body spectrum continues beyond the visible - indeed the IR part is what is responsible for heat from the sun. The earth has a black body spectrum of about 278K (5.5 Celsius), which peaks in the infra red.

So what does this have to do with the age of the universe? Well when the universe was a mere 400,000 years old, about 13.7 billion years ago, everything was very much closer together, though space was expanding rapidly, and so the universe was much hotter than it is now, so hot in fact that there were no atoms, there was just a sea or plasma of hydrogen and helium nuclei (and a bit of lithium) electrons, Electromagnetic radiation and other subatomic particles (earlier than this there weren't even nuclei, but that's earlier than we are interested in here). The universe was still too hot for the electrons to bind to the nuclei, and so photons were constantly being absorbed and re-emitted by the various charged particles that were around, and the universe was in a state of equilibrium between matter and radiation. This means there was a black body spectrum. Eventually, as the universe expanded electrons no longer had enough energy to constantly escape binding to the nuclei, and they finally bound, becoming hydrogen and helium atoms. There was still substantial interaction between matter and radiation, particularly in the form of scattering, such as Compton Scattering and Thompson Scattering. The universe continued to cool as it expanded further, and eventually cooled down to a temperature of about 4000K at which the scattering dropped off. The radiation at this point became decoupled from the matter in the universe, as the universe became transparent, though the shape of the spectrum remained imprinted on the light that passed on, and continued traveling through the universe.

In the intervening billions of years, space itself continued to stretch. Imagine drawing a wave on a balloon, and blowing up the balloon. You will see the wavelength becomes longer and longer. The same effect occurs to the radiation, but now the the very space of the universe is expanding, so photons that initially had a short wavelength, over time were stretched out so the wavelength was longer and longer, so long in fact, that the BB spectrum which peaked at 4000K now peaks at a temperature of just 2.725K - barely above absolute zero.

This temperature is the same in all directions, though there are tiny fluctuations, which resulted from small changes to the very uniform distribution of matter and energy in the early universe as we can see in the (Wilkinson Microwave Anisotropy Probe ) WMAP satellite image below. It is these tiny imperfections that seeded the collapse of the primordial matter into the stars and galaxies of the universe today.

By knowing the rate at which the universe is expanding, which we can measure from the red shift of other features of the universe such as distant stars, galaxies and quasars, and these initial temperatures (which we know from looking at hydrogen and helium in the lab) we can then deduce the age of the universe (in much the same way as we can determine how long a cup of water has been standing on a table for if we know it was boiling when it was put there)...

...13.7 billion years old.

Quickfire Question: How do incandescent (filament) bulbs work?

We are all familiar with incandescent bulbs, which have been until relatively recently been the most popular sort of bulb.

A voltage is placed across a metal filament held in an inert gas like argon, neon or nitrogen, in order to stop the gas from reacting with the filament and allowing the bulb to live longer. The filament has a high resistance to the current flowing through it, and this heats the filament, causing the atoms in the filament to vibrate. As the atoms vibrate, they then radiate energy in the form of light.

An important point that can be made here, is that all vibrating atoms and molecules will radiate somewhere on the electromagnetic spectrum. The hotter they are, the faster they vibrate, and thus the higher the energy (and frequency) the photons are that they emit.

A problem with this sort of lamp, is that they are very inefficient. Because the light is generated by heating, large amounts of energy is lost in unwanted heat. Also as the filament is heated, it slowly evaporates over time and eventually breaks, leading to a relatively short lifetime. It is mainly for these reasons that there is a move to using energy saving bulbs, which both have a longer life, and also produce the same amount of light for less energy input.