Professor Mark Csele's Homebuilt Lasers Page

Lasing Mechanisms

Boltzmann Distributions and Population Inversions

Every system has thermal energy. In the case of a gas, consider gas atoms confined to a cylinder. Thermal energy manifests itself as atoms colliding with each other and bouncing off the cylinder walls (this is the gas pressure). Thermal energy also excites atoms raising them to higher energy levels. The resulting distribution of energy is governed by Boltzmann's Law, one of the fundamental laws of thermodynamics. Boltzmann's law predicts the population of atoms at a given energy level. It predicts an exponential drop in populations of higher energies as follows:

Boltzmann Distribution, Copyright John Wiley & Sons, 2004

(Diagram Copyright John Wiley & Sons, 2004, used with permission)

Such a system is said to be at thermal equilibrium and the population of atoms at any given energy level is governed solely by temperature. If the temperature of the entire system were raised the distribution would shift and more atoms would reach higher energies however the population of a lower level will always exceed that of a higher level. This situation occurs in an incandescent lamp where electrical energy heats a tungsten filament. Many atoms at high energies drop to a lower energy state and in doing so emit a photon of light (the difference in energy between the upper energy state and the ower energy state for the transition). Still, there is a higher population of atoms at the lower energy state than the upper state.

Consider now a situation where energy is injected into such a system to cause a population of atoms at a higher energy level to be greater than that of a lower level. Such a non-equilibrium condition is required for lasing action. Energy may be selectively injected to pump an upper energy level from which transitions occur to a lower level (and in doing so photons of light are emitted). This is the process of Pumping in which the injection of energy into an atomic system brings about a Population Inversion where the population of a high energy level exceeds the population of a lower level (in this case, the two levels involved are the lasing levels - the ones actually involved in the production of laser light).

HeNe Level Pumping A prime example of this type of activity occurs in the ubiquitous helium-neon laser. Helium is electrically excited. Excited helium atoms then collide with neon atoms and in doing so transfer energy to them. Neon atoms are then pumped, selectively, to an upper energy level from which lasing transitions can occur. It is no accident that helium is used in a HeNe laser: helium has an excited energy level very close to a level of neon used as a pump. Incidentally, the neon never ionizes (loses an electron). Neon atoms in the HeNe laser remain neutral, they just acquire more energy (in the Bohr model of the atom, simply rising to a higher orbit).
(Diagram Copyright John Wiley & Sons, 2004, used with permission)



Stimulated Emission

Here is one of those funny quantum-mechanics concepts. If a photon of light at an energy of, say E2 is fired into a cell containing atoms at ground state, it is likely that it will be absorbed and, in the process, pump the atom to a higher energy state. If an atom is already in a high energy state though, and a photon of the correct wavelength comes along is can stimulate the excited atom to emit a photon of the exact same wavelength and phase as the incident photon, leaving two photons exiting this process. In essence, the original photon is amplified by this process called stimulated emission. Of course the atom which emits the photon loses its energy in the process and must either be pumped to an excited state again or it will re-absorb another photon. This is why population inversion is required: if inversion is not maintained that atoms will absorb, rather that emit, photons of light.

Stimulated Emission

(Diagram Copyright John Wiley & Sons, 2004, used with permission)


This is the basic principle of the laser: amplification by stimulated emission. It is bizarre in that the entire process occurs without interaction in the classical sense - the incident photon does not collide with the excited atom, apparently proximity alone triggers the stimulated emission.

From a quantum mechanical standpoint population inversion is required for laser action - if the upper lasing level does not have a higher population than the lower lasing level stimulated emission will not occur. If the lower level did have a higher population then photons would be absorbed by the lower energy atoms causing (upward) excitations rather than emission of light - this is certainly not the desired effect!

Laser Gain

Assuming we've generated population inversion (by pumping energy into the lasing medium to excite upper lasing levels) laser gain may now occur. Laser gain (or optical gain) is a measure of how well a medium amplifies photons by stimulated emission. Consider a single photon travelling down a laser tube and stimulating an excited atom to emit a photon of the same frequency and phase ... this is laser gain. Thinking of the 'stream of photons' travelling down the tube as an electromagnetic wave we can see that the power of the wave increases if the rate of stimulated emissions exceeds that of spontaneous emissions (again, refer to the Quantum page for a backgrounder on atomic emission). As the wave travels further down the tube the power increases as a function of length. The power increase, mathematically, is exp(gx) where g is termed the optical gain coefficient of the laser medium and x the distance down the tube. No surprises, the power increases exponentially as the wave travels down the tube (since one photon stimulates another giving us two, then those two stimulate two more so we get four, then those four ... we rapidly get amplification)

The fact that we have gain does not automatically imply laser output: this gain must first overcome any and all losses in the system. Some losses, like that of the percentage of the light in the laser cavity extracted as the output beam (through the output coupler), are controllable while others, like losses at tube windows or due to absorption in the laser medium, are usually not. So, stimulated emissions must occur at a rate sufficient to give the laser enough gain to overcome total loss in the system. At that point, laser output may occur and an output beam will be seen.

The ramifications of this for a laser constructor are simple: the longer the lasing medium, the more power will increase per pass down the tube. When attempting to lase a weak transition, like many gases have, a longer tube will allow a larger power increase per pass through the tube. This may be important when considering losses in the laser (such as those caused by the cavity mirrors or tube windows) and how to overcome them ... but more on that later.

Although we like to think of lasing transitions as a discrete process occurring at exactly one precise energy (e.g. between two defined energy levels E2 to E1) this is not true. For practical purposes energy levels are not so sharp as we might think. Several effects can broaden the energy levels. In some types of lasers (e.g. dye) the energy levels are _so_ broad that we speak of them in terms of energy bands. This means that each lasing transition does not occur at one exact, precise wavelength. Laser gain is realized as a Gaussian curve with a centre wavelength at which maximum gain occurs.

Optical Gain curve for a laser transition, Copyright John Wiley & Sons, 2004

In a perfect world, any input to a laser medium would result in pumping-up the upper energy levels and hence lasing action would result however there are a number of obstacles to be overcome. First and foremost is absorption of photons. The lasing medium produces output via an energy transition from the upper level to the lower level. The emitted photons can, however, be absorbed by atoms at the lower level to pump them back up to the upper level. This is absorption. Clearly for laser action we need more stimulated emission of photons than absorption (or re-absorption) at the same transition. Absorption depends on the medium itself and the lifetime of a particular energy level. If the lower level has a relatively long lifetime atoms in that (lower) energy state stay there longer giving them a good chance of absorbing photons. On the other hand if the lower level has a short lifetime atoms in that state decay quickly to another state where they will not absorb the newly emitted photons in the laser. CW gas lasers invariably have the later situation. In the HeNe laser, atoms in the lower state rapidly decay to yet a third state where they stay until they collide with the walls of the tube and enter the ground state. This rapid decay in energy _is_ accompanied by emission of light at about 600nm but this light is spontaneous emission and is seen as a red line in the spectrum of the tube emission as viewed through a spectroscope (i.e. if you view the pink glow coming from the length of the tube you'll see it there). Again, no surprises, atoms at the lower level must emit the energy somewhere when making the transition to a yet lower energy level. This, BTW, shows that the HeNe laser involves four energy levels in the active lasing atom (i.e. the Neon atom): The ground state, the upper lasing level, the lower lasing level, and the middle state called a metastable state from which it returns to ground state only to begin the process again by being pumped by collision with energetic He atoms (More on this below).

Laser Gain (or optical gain), that g number, factors in absorption across energy levels in the laser medium since this effect is part-and-parcel of the quantum package - one cannot simply separate the stimulated emission rate from the absorption rate as they are both characteristics of that medium.

Three and Four Level Lasers

Lasers are classed by the number of actual atomic energy levels involved in the lasing process. In a three-level system energy injected into the gain medium pumps atoms to the pump level. From there atoms decay to the upper lasing level usually by emitting heat, not photons. This upper level often has a long lifetime so a healthy population of atoms builds in that level and population inversion, required for laser action, ocurs. Lasing transitions now occur between that upper and the ground state emitting laser light in the process. In a four-level system an intervening level exists between the upper and ground states. Atoms making a laser transition to the lower state decay further to the ground state usually by emitting heat (although, for example, the argon ion laser does this decay by emitting a UV photon).

Three and Four Level Lasers, Copyright John Wiley & Sons, 2004

(Diagram Copyright John Wiley & Sons, 2004, used with permission)


Four-level lasers are by far the most common. In the helium-neon laser, for example, the pump level is in helium, while the upper and lower lasing levels are in neon. It is also possible, in some lasers such as metal-vapour lasers, to pump directly to the upper lasing level (i.e. there is no pump level). In this case atoms are excited to the upper lasing level where they make a transition to the lower lasing level, finally decaying to ground state. These are particularly efficient systems since they lack an energy loss when atoms in the pump level decay to the upper lasing level (which, in most cases, shows up as heat in the laser).

Lasing Thresholds

In any medium there will be losses due to scattering, absorption by impurities, and losses caused by the cavity and tube walls itself. As well, to be practical, we will purposely extract a portion of the laser beam within the laser and use that as our output beam. In a practical laser such as a HeNe we might extract 1% of the light in the cavity as a beam. That really means a loss of 1%. Obviously we must have enough gain inside the laser medium to allow us to overcome all losses in the laser as well as allow us to extract our output beam and _still_ allow laser action to continue. Given all losses we can calculate a minimum gain which still allows laser action. This is the threshold gain of the laser medium. Although some elements of the laser cannot be controlled (say, perhaps, losses due to impurities) we can control the amount of power we extract through the output coupler - the partially reflecting mirror at the front of the laser. It should be evident that there is a limit on how low the reflectivity of the two cavity mirrors can be for a given laser medium. Remember that regular aluminum mirrors have a reflectivity of only about 85% ... indeed many lasers such as the HeNe lack the gain needed to allow such huge losses. This explains why dielectric or dichroic mirrors are used for many lasers. These mirrors use multiple thin-film layers to interfere with incoming light and reflect it. Such mirrors can have reflectivities of up to 99.999%! They are not easy to make, though, and require high-vacuum thin-film coating apparatus to produce. This also explains why laser mirrors are so expensive as opposed to the common metalized (e.g. aluminum) variety.

Of course we can't forget about the length of the laser medium. Obviously the longer the tube, the higher the amplification and hence higher losses may be tolerated. Take the argon gas laser as an example. Short argon lasers (30cm) absolutely require dielectric cavity mirrors but there are many reports of longer lasers (1 metre or more) lasing with inexpensive aluminum mirrors, especially on the strongest transitions (514nm and 488nm). Many of the weaker transitions simply do not have the gain to lase without dielectric mirrors (unless you've got a 10 metre tube and I've never seen one that long - can't imagine attempting to align the mirrors on that one - ouch). The stronger transitions, though, may well tolerate 15% or more losses in the mirrors. Theoretically one could build a HeNe 2m long and use aluminum mirrors but this is hardly practical! For the amateur laser constructor though, using a longer tube may still allow construction using cheaper components.

Some lasers have HUGE gains - so high that light is amplified to a useable level in a single pass down the tube. Such lasers are termed superradiant and will operate without feedback (i.e. no cavity mirrors). Nitrogen lasers are usually superradiant. It may be noted though that including a single, rear, cavity mirror in this type of laser boosts power output and creates a beam with better characteristics (less dispersion). Other lasers such as copper-vapour lasers require very little feedback to lase. An uncoated microscope slide reflects 8% of incident light and makes a good output coupler for such a laser. Nitrogen-laser pumped dye lasers frequently have enough gain to operate superradiantly as well.

Note also that there is a threshold on the pumping rate that must be reached for lasing action to occur. Until the pump rate (the rate of input power) is sufficient to allow population inversion - higher populations at the upper lasing level than the lower lasing level - laser gain will not occur. After that threshold is reached (and population inversion is achieved) we still require that gain exceed total loss in the laser so pumping power must still be increased. Eventually, gain will exceed loss and laser output will begin - the output increasing with pump rate (i.e. pump power). This is easily seen with diode lasers in which a certain minimum current must be reached before any laser output is seen. After that point any increase in drive current leads to an increase in laser output (up to a point ... there are physical limits on this as well and they usually involve the medium and how much power it will take per unit volume before saturating or overheating).

Laser Diode Threshold, Diagram Copyright John Wiley & Sons, 2004
(Diagram Copyright John Wiley & Sons, 2004, used with permission)

Cavities

The laser cavity is composed of the two mirrors surrounding the gain medium. Usually one mirror (the rear) is totally reflecting and the front mirror partially. The portion of the light that passes through the output coupler makes the laser beam while another portion is reflected back into the gain medium to be further amplified. In commercial lasers the rear mirror is almost always a dielectric mirror designed to reflect as much light as possible back into the gain medium. Such a mirror may have twenty or more alternating thin dielectric films (such as magnesium fluoride, cerium oxide, or similar dielectric material). A regular aluminized mirror reflects only about 80% of incident light (absorbing 20%). That represents a huge loss in a laser and may not allowe lasing of weak transitions (like most gas lasers have). Even 'enhanced' aluminum mirrors only hit 90% reflectivity. Dielectric mirrors also have the peculiar trait of being reflective at only one band of wavelengths. HeNe mirrors (which are always dielectric) reflect red light very well but actually transmit blue. I have a YAG laser in which the mirrors reflect IR light at 1064nm quite well but transmit the entire visible spectrum - the mirrors are competely colourless. This is used to advantage in this type of laser since it allows a visible red HeNe beam to be fired through the YAG laser itself so as to act as a targeting laser (allowing the target to be identified before the YAG pulse obliterates it!).

The output coupler must also be selected with respect to the ratio of how much light is reflected to how much is transmitted. High transmission ratios represent a high loss to the laser. Many gas lasers use output couplers with transmissions between 1% and 5% (and bear in mind that this is a lot lower than the loss from even the best aluminum mirrors). It should be evident from these figures why high performance dielectric mirrors are required for most lasers to work - taking more that a few percent of intra-cavity light at the output coupler represents a huge loss in the system. If loss it too high (i.e. greater than the gain of the system), the laser will not work. This hopefully clarifies a common misconception that by increasing the % transmission of an output coupler will allow higher powers to be produced ... on the contrary, it will usually case the laser to stop operating!

BTW, This is one of the biggest limitations affecting amateur laser constructors. If a high gain laser is built (e.g. N2) inexpensive and readily available aluminum mirrors may be used however is a low-gain laser is built the amateur must procure a set of suitable dielectric mirrors which will work for the wavelength range of the laser chosen. One can use mirrors which are 'close' ... HeNe mirrors, for example, reflect best at 632.8nm in the red but reflect reasonably well (>95%) over a wider range covering the orange through near-IR region of the spectrum allowing use in mercury-ion lasers as well (which have a red laser line). Of course there is another problem with this in that many mirrors are not flat but rather concave and so the distance between the mirrors must match this (mirrors from a 30cm long HeNe will likely not work in a 1m long mercury-ion laser).

Many cavity configurations are possible including the use of plane (flat) mirrors and/or concave mirrors. Flat mirrors are the easiest to obtain however a cavity built with two flat mirrors is very difficult to align. Flat mirrors work well in short lasers with a large diameter gain medium (e.g. YAG, N2, etc) but not with long gas lasers with small bores (e.g. Argon). Concave mirrors may be used and make cavity alignment much easier but focal lengths must be chosen so that light is trapped _within_ the cavity. As an example, if a cavity consists of one flat and one concave mirror the concave mirror must have a focal length longer than the distance between the mirrors in order to ensure light within the cavity does not escape. If two concave mirrors are used, their focal lengths muct be greater than half the distance between the mirrors. Geometric optics formulae must be used to ensure the cavity is stable and will resonate.

For the amateur laser constructor, obtaining suitable mirrors in the correct focal length can sometimes be impossible (unless you are willing to pay dearly for a custom-built mirror). For these reasons many amateurs, when building a low-gain laser, choose cavities built around mirrors which may be scrounged from scrapped commercial lasers.

Modes

TE Modes for laser beams, Copyright John Wiley & Sons, 2004 Transverse modes describe the distribution of light energy in a laser medium. If a laser tube were cut directly in half, in the middle, and examined it is likely you'd find light energy built-up in certain areas and void in others. These modes are visible in the output beam of a laser by expanding the beam with a lens or concave mirror and resemble those shown. There are two numbers associated with each TE or transverse electromagnetic modes as they are called. TEM00 represents a perfect Gaussian beam in which intensity is highest at the center and tapers off in all directions equally. For many applications where a 'pure' beam is required it is important that the laser operate only in the TEM00 mode.
(Above diagram Copyright John Wiley & Sons, 2004, used with permission)

Large apeture gain media as well as certain cavity configurations often give rise to high-order modes such as TEM10 and TEM11 or higher. The number of dark stripes between light areas in the pattern corresponds to the subscript and there is no accepted system for determining which subscript comes first so that TEM21 is the same as TEM12.

Limiting Modes by using Intra-Cavity Apetures, Copyright John Wiley & Sons, 2004

(Diagram Copyright John Wiley & Sons, 2004, used with permission)

It might be noted from the above diagram that high-order modes are physically larger than low-order modes. This can be exploited to prevent a laser from oscillating in higher-order modes by placing an aperture of the proper size inside the cavity so that only the TEM00 mode will fit through it. Higher-order modes will be extinguished because the loss imposed on them by the aperture will be greater than the gain provided by the active lasing medium. For example our large lab laser, a Coherent Innova-90 argon rated at 7W CW, has an apeture disc provided which allows the user to select the size of hole inserted into the cavity. At a large apeture, TEM10 donut mode frequently shows up but insertion of a smaller apeture forces the laser to operate strictly in TEM00 mode - accompanied with a drastic loss in power! From the diagram it is evident that TEM11 mode occupies a larger volume in the gain medium (gas in the case of our argon laser) than the TEM00 mode does. The TEM11 mode can therefore interact with more of the excited laser medium and hence extract more power from the laser. Lasers oscillating in high-order modes usually produce more power than similar lasers limited to the TEM00 mode. Still, the beam purity of the TEM00 mode is often sought after, esp. for research applications and so despite power loss, it is still used.



Producing Fast Pulses

Q-Switching: Giant Pulse production

Q-Switching is a method for producing short, powerful pulses. It is used almost exculsively with optically-pumped solid-state lasers, usually a YAG. Q-Switching relies on the ability of the optical gain medium to store energy in the population inversion. Most gas and dye lasers have spontaneous lifetimes (The lifetime of an excited species before it spontaneously emits incoherent light - precluding the emission of stimulated emission) too short to allow an energy buildup in an upper lasing state. Carbon-dioxide gas lasers are one of the few exceptions as they _can_ be Q-Switched however this is rarely done as it lacks commercial applications.

Q-Switches block one of the mirrors until the lasing medium (the rod) builds-up a huge population in the upper level. At that point the cavity is made complete and lasing occurs in the form of one giant pulse. Q-Switching may be accomplished by mechanical means (such as a rotating mirror - used in some small military ruby lasers), Acousto-Optic (AO) switches which diffract light passing through them, Electro-Optic (EO) switches which change the polarization of the intra-cavity beam to match that of a polarizer also inserted into the cavity, and a dye cell which absorbs incident light until it saturates and bleaches allowing light to pass through.

The most popular configuration is in a YAG laser where an AO modulator is inserted directly into the optical cavity. The Q-switch is turned on or off by energizing it with 24-27MHz RF energy. With RF energy applied the Q-switch diffracts intra-cavity light spoiling the cavity so oscillation does not occur. When the RF energy is removed, the cavity is complete and the laser oscillates. Flashlamp-pumped YAG lasers can produce nanosecond pulses using this technique, CW YAG lasers (having lower gain) can produce pulses lasting 100's of nanoseconds. Note that the AVERAGE power of a Q-switched laser might well be low, depending on the firing rate, but the PEAK power is exceptionally high. These fast, intense pulses are useful for applications such as trimming precision resistors - the fast pulse vapourizes resistor material without heating surrounding material or substrate.

Cavity Dumping

In this method of producing very short pulses the laser cavity consists of two fully reflecting mirrors. The laser is allowed to lase, but with no output beam. To produce a pulse the intra-cavity light is _dumped_ via a mirror within the cavity to become the output beam. When the cavity is dumped, very high intra-cavity powers are suddenly dumped to produce a very short, very intense pulse of laser light. Since the cavity is now spoiled though, laser action stops immediately. The fast action of the dumping mirror can only be accomplished by EO or AO modulators. The pulse length produced depends on the length of the laser cavity. For a 30cm laser a pulse of 2nS is produced ... this is MUCH shorter than possible with Q-Switching.

Modelocking

This technique, used in research, can produce pulses of 1pS: 1000 times shorter than possible with cavity dumping. Often the laser is a YAG or a dye laser. In a Q-Switched or cavity dumped laser the energy is stored in the entire resonator. Modelocking compresses this energy into a tiny pulse which travels back-and-forth between the cavity mirrors. Each time the tiny pulse is reflected by the output coupler a pulse is produced. The result is a train of repeated, ultra-short pulses. To produce modelocking an EO modulator inside the cavity (the EO Q-Switch) opens only once per round trip closing at all other times. This allows only a single pulse to circulate around the cavity - and remember that this pulse is physically shorter than the cavity itself. The time between pulses is set by the round-trip time through the cavity. For a 30cm laser the pulses are emitted at 500MHz.



Non-Linear Optics

Second-Harmonic Light Generation

Imagine combining two infrared photons, each of energy 1eV, into a single photon of 2eV. The new photon would have a wavelength in the green portion of the spectrum with exactly half the wavelength of the original photons. This is exactly what second-harmonic generation (SHG) is. It can be done outside the laser by focussing an intense laser pulse onto a crystal - it was first demonstrated in this manner when a ruby laser in the deep red was focussed onto a quartz crystal to produce violet light. Usually, though, the SHG crystal is placed directly inside the cavity itself. High intra-cavity powers lead to better conversion efficiencies. Almost invariably, it is used with a YAG or similar solid-state laser (See the YAG page for practical details).

SHG requires a crystal which exhibits non-linear processes. Quartz works, with very low efficiency, but some materials like potassium titanyl phosphate (or KTP) exhibit very efficient conversion and KTP is the most common material used. The most common configuration is a Nd:YAG or Nd: YVO4 laser pumped either by an CW arc lamp or more commonly with an IR diode, with a KTP crystal inserted into the optical cavity between the mirrors. While the YAG normally produces light at 1064nm, the frequency-doubled output is green at 532nm. The cavity mirrors are usually designed to reflect almost 100% of the IR light while passing the green SHG light (the IR is required to keep the YAG lasing in the infrared). As well, a green filter is usually included in front of the laser to filter-out any remaining IR output leaving a pure, green laser beam.

As well as second harmonic generation, third and fourth harmonic generation is possible yielding UV output from the YAG ... this is widely used in research and photolithographic applications. In many cases these high-order harmonics are produced with multiple non-linear crystals

Output Parametric Oscillators (OPO)

OPO's do the opposite of SHG's in that they split a single photon of higher energy into two photons of lower energies (and hence longer wavelengths). The two photons need not be the same wavelength, but the total energies of the resulting photons equals the incoming photons.

OPO's are true oscillators and hence need a cavity like a laser does, but they do not exhibit stimulated emission like a laser does - they simply exhibit nonlinear optical phenomenon. The pump beam usually enters through one mirror and pumps the OPO crystal. A front mirror can be set to reflect the desired wavelength from which the beam emerges. OPOs are tunable since the wavelength produced depends on the angle of the crystal, which can be set mechanically. A common application is to use an Nd:YAG to pump a LiNbO3 OPO. This will produce tunable laser light in the infrared from 1.6um to over 5.0um by varying the angle. IR light in this range is useful for communications applications.



Further Reading ...

Fundamentals of Light and Lasers Fundamentals of Light and Lasers by Csele, 2004, John Wiley & Sons, ISBN 0-471-47660-9

Basic laser processes are covered in chapter 4, and cavities and optics (including longitudinal and transverse modes) in chapter 6.

The Laser Guidebook (Second Edition) by Hecht, 1992, McGraw-Hill, 1992 ISBN 0-07-027737-0. An essential book outlining the basic design of a host of differing laser systems.

Optoelectronics and Photonics, Principles and Practices by S.O. Kasap, 2001, Prentice Hall, ISBN 0-201-61087-6