Lasers are optical amplifiers, optical oscillators, and in a way, the most sophisticated light source ever invented. Not only are lasers extremely useful, but they are also champions of magnitude: While different laser types cover the electromagnetic spectrum from radiation (<10 nm) over the visible spectrum to far infrared light (699 μm), their individual output band can be as narrow as a few µHz. Their high temporal and spatial coherence lets them cover hundreds of meters in a tight beam of lowest divergence as a perfectly sinusoidal, electromagnetic wave. Some lasers reach peak power outputs of several exawatts, while their beams can be focused down to the smallest spot sizes in the hundreds and even tens of nanometers. Laser is the acronym for Light Amplification by Stimulated Emission Of Radiation, which suggests that it makes use of a phenomenon called stimulated emission, but well, how exactly do they do that? It’s time to look the laser in the eye (Disclaimer: don’t!).

The Optical Amplifier

When we talk about the amplification of electrical signals, we are typically not too concerned about whether or not the amplified signal is actually the original signal – just amplified. The minuscule flow of electrons in a bus line may transport a signal, but this signal is not bound to that exact representation. We can send it through a transformer, optocoupler or piezo-transducer and, if we do it right, it just won’t matter. We are really ok if an amplified signal is a good, enlarged copy, as long as the copy retains the subset of properties of the original signal we are interested in.

Light is however indeed bound to its inherent representation as an electromagnetic wave. To understand how light is amplified – or copied – we need to look at the different properties of light both as a wave and as a particle. As a wave, it’s really not much more than synchronized oscillations of electric and magnetic fields propagating through space. To amplify it, we would want to somehow increase the amplitude of this oscillation while leaving its temporal course, such as its phase and frequency, intact. As a particle, however, a photon of a certain wavelength, direction, and polarization – all we can do is add more. So, if take this photon and we add another photon with this very same properties – a copy so to speak – we will see that the amplitude of our electromagnetic wave also doubles. It is amplified.

Since all we can do to amplify light, an optical amplifier must contain some kind of photon xerox — only this one really needs to leave the numbers intact. In lasers, this task of copying photons is done by special atoms (or molecules) inside the optical amplifier. They are called the active laser medium, and in a Helium-Neon laser, for example, it’s the Neon gas. All it needs is a container, an energy source, and some kind of windows for light to enter and exit. This contraption is the key element of every laser, from laser diodes over CO2 laser tubes to fiber lasers.

How To Make A Photon

Most photons we see in everyday life originate from a process called spontaneous emission. Atoms and molecules can be stimulated to transition to higher energy states than their ground state, in which the outer electrons leave their regular orbits and transition into more energetic states. If this state of excitation is long-lived (metastable), they may stay in this state for quite a while, but always keep a certain tendency to translate back to a lower energy state. Sooner or later, they will do so – spontaneously – while emitting a photon of a certain frequency in a random direction and with a random phase. This is called spontaneous emission, and the frequency of the emitted photon depends on the energy differential between the high (E₂) and low energy state (E₁). Compact fluorescent lamps, as well as incandescent lamps with a halogen filling, make use of this phenomenon.

How To Copy A Photon

Now, if a photon of this exact frequency f₂₁, collides with such an excited atom, it can stimulate the atom to transition back to the low energy state right away, before it has time to do so spontaneously. The electromagnetic field of this original photon causes the atom to turn into an electrical dipole and oscillate with the external field. This deep interaction causes the emitted, new photon to take on the same phase and direction as the original one, which makes it practically a copy. Regarding most of the special properties of lasers, such as high monochromaticity, coherence and diffraction limited divergence angle, this quantum mechanical interaction is pretty much the bottom of the barrel.

However, inversely to stimulated emission, incoming photons can also run into atoms of the laser medium that are in the low-energy ground state. These photons will be absorbed, exciting the atom to the corresponding high-energy state. Unless another photon collides with the same atom soon enough to cause a stimulated emission, this atom is likely to spontaneously fall back to its ground state. It will still release a photon, but the photon released in a spontaneous emission can have any direction or phase and won’t align with the absorbed photon’s direction or phase, which results in an attenuation of incoming light.

Population Inversion

With a large number of atoms of the gain medium, the actual amplification process becomes a statistical sum of collisions. If there is a higher concentration of atoms in a low energy state than in the high energy state, we will experience a net loss of photons and thus, an attenuation of light. If the number of excited atoms is larger than the number of low energy atoms, we will experience a net gain. This overbalance of excited atoms is called the population inversion, and it is a basic requirement for optical amplification.

However, with an overbalance of excited atoms, such a two level system becomes highly unstable – it’s practically impossible to maintain. To achieve a population inversion in a stable system, optical amplifiers and lasers make use of more than two excitation levels of the involved atoms. For example, by exciting atoms from the ground state E₁ to an excitation state E₃, a population inversion between E₃ and an intermediate energy state E₂ can occur even if more low energy atoms are present in the ground state E₁. As long as atoms transition from E₂ to E₁ – for example by a secondary spontaneous emission – at the same rate as atoms are lifted up from E₁ to E₃, the light amplification process at f₃₂ can happen.

Pump it

To achieve the primary excitation of the laser medium to just the right high energy state, we need a mechanism to lift its atoms up there. This action is called pumping. Different types of lasers use different pumping methods, but besides keeping it going in an efficient and feasible way, it has little effect on the stimulated emission process itself. In some cases, the pumping itself is done by secondary light sources, such as discharge tubes or light emitting diodes. In other cases, the pumping is a well-designed bucket-chain of electrons and atoms or molecules passing on energy from a high voltage source to the atoms of the laser medium.

The first laser ever built, the ruby laser, uses photons emitted from a Xenon flash tube to excite chromium ions suspended in a synthetic sapphire. Other crystal lasers, such as Nd:YAG lasers, can be pumped by either arc lamps (or flashes), typically Xenon or Krypton, or more efficiently by light emitting diodes. Generally, diode pumped solid state lasers (DPSSL) use photons emitted from semiconductor diode junctions to pump various laser media.

CO2 lasers use electron collisions to induce a molecular oscillation in N₂ molecules, which then pass on their energy and excite the CO₂ laser medium. Helium-Neon lasers utilize electron collision to excite Helium atoms, which then collide with and excite the laser medium Neon. Except for CO₂ lasers, which are still commonly used in laser cutters, the intricate pumping mechanisms that involve special gas mixtures and high voltages are more and more replaced by diode-based solid state alternatives.

The Optical Oscillator

While the optical amplifier may already be called a laser in a way, most optical amplifiers will not lase on their own. Any amount of photons that is going to be amplified while passing through the amplifier is bound to leave the amplifier very quickly — with light speed — and gone they are. On their way, they will not necessarily experience enough collisions with the atoms of the laser medium to achieve any reasonable lasing action. To make things worse, the optical amplifier amplifies light in all directions, which makes it a CFL tube at best. There are a few tricks to overcome this: One is, to give the optical amplifier a very, very long and narrow shape so that the only photons passing along this long axis of the amplifier will be amplified. Another way can be to increase the density of the gain medium. And eventually, mirrors can be installed on both ends of the optical amplifier to conveniently increase the effective length of the amplifier.

Because high-density gain mediums come with other challenges, such as high breakdown voltages for gaseous mediums, mirrors (and oftentimes long tubes) are the way to go here. Using mirrors, you can also create what is called an optical oscillator. Similar to a mass on a spring, an elastic string, or an LC-oscillator, they oscillate in resonance with a certain frequency. An optical oscillator is even easier to set up, since the main material you need is a chunk of space, with two mirrors on each end to prevent the light from exiting and getting absorbed. In this optical cavity, photons, light or electromagnetic waves (depending on how you look at it) can bounce back and forth between the two mirrors, superimposing to a standing wave.

You may have seen this before, it looks like a standing wave on a string. An optical oscillator behaves very similarly: The modes of this optical cavity are solely dependent on the propagation speed of the wave, in this case lightspeed, and the length of the cavity L. The modes — or resonance frequencies — that fit into our cavity depend mostly on the length of the cavity. If we choose the cavity to be long in comparison to the wavelengths we are interested in, in the hundreds of nanometers for visible light, the frequency response of this cavity shows many tightly and evenly spaced modes. If we choose the length of the cavity to be shorter, the spacing f_s between the modes increases. This spacing is an important factor for the power output of industrial multimode lasers, which therefore typically have much longer cavities than for instance diode lasers in optical drives that rely on single frequency operation.

However, all oscillators are subject to losses, and we need to overcome them to keep any oscillation going. In lasers, this is done by — you may have guessed it — the optical amplifier. The optical amplifier goes right in between the mirrors, and if it’s strong enough to overcome the losses of your system, mostly the small amount of absorption in the mirrors, this system will oscillate.

This oscillation is called lasing, and it is really nothing more than electromagnetic waves bouncing back and forth between the mirrors, experiencing resonance from the cavity and recovering their losses when they pass through the amplifier. To make use of them, usually only one of the mirrors is highly reflective, typically 99.9 % or more. The other mirror, the output coupler, is partly transmissive and allows for a small amount, about 1%, of radiation to exit the cavity. Of course, the amplifier also has to compensate for this amount.

How The Laser Starts Lasing

Once we’ve put everything together, our optical cavity with the output coupler and the optical amplifier, we will want to turn it on. The pump medium will start elevating the laser medium to its high energy level, but there is no light inside the cavity to be amplified yet. Still, even with no incoming radiation, some of the excited atoms in the laser medium will randomly translate to a lower energy state, emitting a photon of just the right wavelength, but with random phase and into a random direction. We need only a few of them with the right phase to be directed along the axis of the optical cavity to get the avalanche going. These initial photons will bounce back and forth between the mirrors of the cavity, getting amplified each time, and the laser starts lasing.

Multimode Lasers

Optical cavities support all modes that fit in between the reflectors, so the exact number of wavelengths of light a laser produces depends mostly on the bandwidth of the optical amplifier. If its bandwidth is narrow, it may cover only a single mode of the optical cavity. If its bandwidth is large, multiple modes of the cavity can be amplified, and because this usually allows for a higher utilization of the pump mechanism, it naturally comes with a higher efficiency. Most industrial high power lasers actually don’t emit only a single frequency, but many. This is possible even though the gain medium operates at a very specific frequency defined by its excitation states, and comes by certain side effects depending on other characteristics of the gain medium. In gas mediums, the collisions of photons with atoms or molecules can shorten the decay time, which — following the statistics of these collisions — shapes the bandwidth of the amplifier to a bell curve. Also, Doppler effects due to the fast movement of gas atoms can further broaden the gain curve. There are many secondary imperfections in the various processes of pumping and stimulated emission that are used productively in multimode lasers.

Pulsed lasers

By pulsing a laser, a larger peak power output can be achieved than what continuous operation would make possible. This can, for example, be done electronically, or through a spark gap circuit, and with shorter pulses, higher peak power output values can be obtained. However, limitations in power output and pulse widths limit the usefulness of this approach.

Multimode lasers offer the possibility of achieving extremely short pulses at a very high momentary power output simply by combining the phase-locked modes of the optical cavity. By combining a series of equally spaced modes in the frequency domain, the interference of the modes causes the output to become a series of pulses in the time domain.

The phenomenon of beat, an acoustic interference of sound, where two tones of slightly off frequency create a perceived pulsation of the volume, is very similar. The more modes are superimposed, the shorter and more intense the pulse becomes, and in multimode lasers, they can be as short as a few femtoseconds (10^-15 s) while producing several exawatts (10¹⁸ W) of peak power.

To achieve this, the modes of the optical cavity need to be tight enough spaced to fit as many as possible into the bandwidth of the optical amplifier. Also, the optical amplifier should have a large enough bandwidth to amplify more than a single frequency.

A Primer On Laser Optics

We still left out a few interesting features hidden in the internal optics of lasers, which are mostly the reflectors. First, the reflectors don’t need to be external, they can be evaporation deposited directly onto the polished windows of the optical cavity. Still, to make the output frequency of the laser tunable – which can be easily achieved by slightly changing the length of the cavity – it is practical to adjustably mount at least one of the mirrors externally. If one or both mirrors are mounted externally, some lasers will be equipped with Brewster windows, which is really just a window with its surface cut to a special angle.

This angle – the Brewster angle – is an angle where only light of a certain, linear polarization experiences can losslessly pass without reflections while all other polarizations are reflected away from the cavity and filtered from the beam. This minimizes reflections and polarizes the laser beam.

Also, the reflectors must not be plain. In some applications, it is advantageous to use concave or a mix of concave and plain or even convex reflectors. Now the beam exiting the output coupler is not parallel anymore, but can be converted into a parallel beam of any diameter by using simple optics.

I hope you enjoyed this very close look at the inner workings of lasers and optical amplifiers. There’s still a lot of engineering to get from here to just throwing a piece of plywood into a laser cutter, writing data in an optical drive, or exposing a photomask for silicon wafer production. Nevertheless, we have even seen impressive DIY builds of ruby lasers, CO2 lasers, and TEA lasers. DIY or industrial grade, they all share the same core principle, a quantum mechanical avalanche of cloned photons.