MadSci Network: Physics Query:

### Re: is it possible to compress light?

Date: Mon Mar 13 19:17:34 2006
Posted By: Michael Richmond, Faculty, Physics, Rochester Institute of Technology
Area of science: Physics
ID: 1141946199.Ph
Message:

Can one compress light? Well, I guess it depends on exactly what you mean by "compress". I think that the answer is "yes", and I'll try to explain below.

Under ordinary circumstances, light rays travel very far, very fast. If we are going to "compress" them, then we must first trap them so that they don't simply run away. One way to do that is to make a box lined with mirrors. If we shine a light inside the box, the light rays will bounce back and forth between the mirrors.

Now, each light ray consists of electric and magnetic fields. These fields do carry energy, so we can associate energy with each light ray. If you look in a textbook, you'll find several ways that one can express this energy. In you consider light to be made up of little individual particles, or photons, then the energy of each one is just its frequency times a number called Planck's constant. High-frequency photons (like ultraviolet or X-rays) have more energy each than low- frequency photons (like infrared or radio waves).

So, suppose that we have a single photon bouncing around endlessly in our box. The energy of that photon will be its frequency times Planck's constant. For a single photon of visible light, that's a very small amount of energy. One photon of yellowish light, of wavelength 550 nm and frequency 5.45x10^(14) Hz, has about 3.6x10^(-19) Joules of energy. That's very little, when you consider that a single Joule is about enough energy to lift an apple upwards from your waist to your mouth.

We can compress the light by moving the sides of the box inwards. For example, suppose that our box was originally 2 meters long by 2 meters wide by 2 meters high. If we push the sides inward so that the length decreases from 2 meters to 1 meter, then the photon will be forced to bounce a smaller distance as it goes back and forth between the mirrors. Does that increase the energy of the photon? Yes! But that energy doesn't come for free; it comes from us. As we push the sides of the box inwards, the photon is constantly bouncing off the interior of the sides. It exerts a small force on each mirror as it bounces, always pushing outward on the mirrors. We must overcome this tiny force of the photon when we push the sides together. The extra force we exert (F) as we move the mirrors together a distance (D) of 1 meter is equivalent to the energy (E) we spend: E = F times D. Fortunately for us, the force F is a teeny-tiny one, so the total energy we spend -- which is equal to the energy the photon gains -- won't be very large.

Another way to look at this process is that as we move the mirrors inwards, the walls move towards the photon. Under ordinary circumstances, when the walls were stationary, a photon of original frequency f would bounce off a wall and end up with exactly the same frequency. But if a photon of original frequency f bounces off a wall which is coming towards it, the reflected frequency is slightly higher. You can use the Doppler shift formula (applied twice) to figure out exactly what the new, higher frequency will be. And since the energy of the photon is related to its frequency, if the frequency increases, the energy increases.

So, in a theoretical sense, you can store energy by trapping light in a box and then compressing the box.

In a practical sense, however, this isn't a very efficient way to store energy. One problem is that we can't make perfect mirrors. After bouncing off the walls just 50 or 100 times -- which won't take very long at all -- photons will start to be absorbed by the walls, or lose a small amount of energy as they bounce. Any energy we put into the box will very quickly be converted from photons to heat inside the walls themselves. Another problem is that ordinary photons just don't have a high energy density: you can't store very much energy at all inside a reasonable volume. Regular AA-cell batteries contain much, much, much more energy than a battery-sized box full of photons; at least, that's the case under everyday circumstances.

So I don't think you'll find any companies ready to invest in photons as a medium for storing energy.

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