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How do you focus regular light to make it a laser beam?

Category: Physics
Published: April 17, 2014

A laser beam is not just focused light. A laser beam is coherent light. Furthermore, you can't create a laser beam by cleverly focusing regular light, no matter how hard you try. You create a laser beam using stimulated emission. Stimulated emission is what causes the light in a laser beam to be coherent, and coherence is what makes a laser beam so much more useful than regular light. In fact, the word "laser" is actually an acronym that stands for "Light Amplification by Stimulated Emission of Radiation"1.

red laser beam
A laser beam is coherent light, not focused light. Public Domain Image, source: Christopher S. Baird.

What is coherence? In the simplest picture, you can visualize a beam of light as a bundle of many little sine waves traveling through space. In this picture, coherence means that all the respective peaks of the various sine waves are lined up in space, and continue to stay lined up as the waves travel. By the phrase "lined up", we mean that if you were able to take a snapshot at a certain time of the different wave components in a light beam, you would find that all the first peaks are at the same location in space, all the second peaks are at the same distance, etc. In order for the peaks to stay completely aligned everywhere, a few things have to happen:

1. The waves have to have approximately the same wavelength (temporal coherence)
If one wave has its consecutive peaks separated by a distance of 600 nanometers, and another wave has its peaks separated by a distance of 830 nanometers, then it should be obvious that if you line up one pair of peaks, you cannot line up any of the other pairs of peaks. Ideally, if all the wave components had exactly the same wavelength (and the other criteria listed below were met), then all the peaks could be lined up perfectly, forever. Such a situation is actually physically impossible. It would take an infinitely long beam of light in order to have all the wave components have exactly the same wavelength (the proof of this statement is not obvious and requires Fourier analysis). Despite the fact that an exactly single-wavelength beam of light is physically impossible, we can get very, very close. In fact, having a light beam that is very close to single-wavelength (called "monochromatic") is one of the main reason lasers are so useful. Using monochromatic light can allow us to measure or trigger a very specific response in a material (e.g. spectroscopy, laser cooling).

2. The waves have to be in phase (spectral coherence)
The phase of a wave describes what part of a sine wave's cycle exists at a certain reference point. Two waves that are 180° out of phase will have one wave peaking at the same point in space that the other wave is bottoming out. Therefore, even if two waves have the same wavelength, if one wave is shifted forward a bit relative to the other wave, their peaks will not be aligned. The phase of the various waves in a beam must be the same in order for their peaks to be aligned and for the beam to be spectrally coherent. The stable phase of a coherent beam can be very useful. The phase of a wave tends to shift when it interacts with a material, so using a beam with a stable phase allows us to measure the phase shift due to the material, and therefore learn something about the material (e.g. ellipsometry).

3. The waves have to be locally traveling in the same direction (spatial coherence)
If you take one wave traveling north and another wave traveling north-east, then their peaks can not be lined up. Only if a beam has its waves at each point traveling in the same direction can the peaks line up. Note that some people restate this principle as "all the rays of light are parallel". Such a statement is over-simplified to the point of being wrong. If a coherent beam of light such as a laser beam consisted of completely parallel beams, then such beams would not spread out as they travel. In reality, beams always spread away from straight line motion as they travel through space (we call it "diffraction"). You may not notice the divergence of a laser beam with your naked eye, but it is there. Rather than saying all the rays of light in a coherent beam are parallel, a more accurate statement would be that the wave components at a certain point in space are parallel in a single coherent beam, but are not parallel from point to point. Also, if two waves are traveling in different directions, but otherwise meet all the other criteria for being jointly coherent, we treat the two waves as completely separate beams, and their combination leads to interference patterns. For a coherent beam that has a very large beam-width compared to its wavelength, the diffraction is very small, so that all of the waves at different locations are very close to parallel. Such beams can be useful for pointing or scanning (e.g. laser printing, 3D laser scanning, bar code scanning, laser guidance of missiles, lidar).

4. The waves have to be the same polarization (polarization coherence)
The polarization of a light wave describes the direction in space that its electric field is oscillating. If one wave has its electric field oscillating up and down, and another wave has its electric field oscillating side to side, then their peaks cannot be lined up because the peaks exist in different directions. The different wave components in a light beam have to have their electric fields pointing in the same direction in order to have their peaks line up and for the beam to be coherent. Polarized light is useful because we can learn something about an object that the light hits by the way the object changes the polarization of the light (e.g. polarimetry).

If all the above criteria are met, then the peaks are all aligned everywhere and they stay aligned as time progresses. The beam is therefore completely coherent. (Note that perfect coherence is physically impossible, but many beams such as laser beams can come very close to being perfectly coherent). Regular light, such as from an incandescent light bulb or from a fire, is incoherent. The light from a fire contains different light waves that are not the same frequency, are not in phase, are not traveling in the same direction, and are not in the same polarization state. Focusing incoherent light, such as by using a glass lens, does not make the light waves have the same frequency, the same phase, the same local direction, or the same polarization. Therefore, focusing incoherent light does not make it coherent like a laser beam. Focusing light just concentrates the energy of the light into a smaller area.

The phenomenon of stimulated emission in a laser is very useful because it produces light that is usually temporally, spectrally, spatially, and polarizationally coherent. Stimulated emission means that an electron is in an excited state when a bit of light (a photon) comes along and knocks the electron down to the unexcited state, causing it to emit another bit of light (another photon) in the process. In the act of knocking the electron down, the original photon causes the new photon to be coherent with it. The process repeats in domino fashion; each time a new photon being added to the beam that is coherent with the original photons. Stimulated emission is not as exotic as it may sound and in fact happens a lit bit all the time. The hard part in designing a working laser is getting stimulated emission to be the main way an electron de-excites. In a regular chunk of matter, an excited electron most often de-excites by colliding with other electrons or atoms, thereby loosing its energy to heat, or by spontaneously emitting a bit of non-coherent light. Designing a laser therefore involves making the stimulated emission transition of the excited electron very probable, and making the other transition possibilities less probable.

Note that stimulated emission is not the only way to make coherent beams. For high frequency waves such as visible light, stimulated emission is the most effective way of creating coherent beams. But for low frequency waves such as radio waves, coherent beams are much easier to create simply by driving a sine-wave electrical current into an antenna. The waves that are created by an antenna that is driven at a single frequency, such as those that carry radio station broadcasts, are coherent. Such broadcast radio waves are technically not laser beams, because they are not created by stimulated emission, but they have all the useful coherence properties of laser beams. A police officer's radar speed gun is a lot more similar to a presentation laser pointer than most people realize. Both are handheld devices that shoot out a beam of coherent electromagnetic waves. Neither one uses focusing to create the beam's coherence.

1Note: I personally find the word "amplified" in the name "Light Amplification by Stimulated Emission of Radiation" to be redundant. Stimulated emission is, by definition, an amplification process. Much more important is the fact that stimulated emission leads to coherence. A more accurate name for a laser would be "Light Coherence by Stimulated Emission of Radiation". But I guess the acronym "lcser" does not roll off the tongue as well as the acronym "laser".

Topics: coherence, electromagnetism, laser, laser beam, light, light beam, stimulated emission, wave, waves