Introduction to Basic Laser Physics
ROBERT J. SCHECHTER
Table Of Contents
THEORY AND DESIGN OF LASERS
SPECIALIZED TECHNIQUES IN LASER DESIGN
|Laser light differs from “ordinary” light in several important
ways. These differences are a direct result of the manner in which
laser light is generated.|
Light is that portion of the electromagnetic spectrum in the so-called visible region. Electromagnetic radiation of longer wavelength consists of infrared radiation, microwaves, and radio waves. Radiation of shorter wavelength includes ultraviolet rays, x-rays, and gamma rays.
All electromagnetic radiation (EMR) travels at the same speed (in a vacuum)—the “speed of light.” Given that the speed of a wave equals the product of its wavelength multiplied by its frequency, and given also that the speed of all types of electromagnetic radiation is the same, the wavelength and frequency of all EMR are inversely related. The larger (or longer) the wavelength, the lower the frequency is. Thus, light may be referred to in terms of its frequency or its wavelength: the higher the frequency (or the shorter the wavelength), the “blue-er” the color becomes. The amount of energy in light (or any EMR) is directly related to its frequency, with blue light having more energy than red light.
White light (which is a mixture of all the colors) is composed of EMRs of varying wavelengths traveling in all directions (Fig. 1). Light of one color is said to be monochromatic and composed of only one wavelength (or of a small range of wavelengths). However, the light waves are not in phase. Although the light waves may be of the same wavelength, each wave will not be at its peak at the same time (Fig. 2). Laser light is composed of one wavelength traveling in one direction. Each wave is in phase or “in step” as well, with each component wave reaching its peak and trough at the same time (Fig. 3). Such light is said to be coherent; this is one of the important characteristics of laser light.
|THEORY AND DESIGN OF LASERS|
|Modern physics recognizes that light has certain characteristics of a wave, yet
has certain properties of a stream of particles as well. A “particle
of light” is called a photon.|
When a light beam (or any other EMR) interacts with matter, energy may be transferred. Classical physics, however, was incorrect in its descriptions of this energy transfer. The error was in assuming that energy was continuous (i.e., that energy could exist in any desired amount). Albert Einstein proposed that light energy could exist only in discrete units, called quanta. (For this explanation of the “photoelectric effect”—and not for the theory of relativity—Einstein was awarded the Nobel Prize in physics.) Using this quantum theory, the previously inexplicable experimental results relating to light energy could be successfully explained and predicted.
According to quantum theory, an electron or a photon, for example, can exist at one energy level or at a higher level but at nothing in between. This physical principle, discovered early in the twentieth century, provides the theoretical basis for laser operation. Thus, the laser could have been invented several decades earlier than 1960, when the first ruby laser was produced.
When light is passed through certain kinds of materials, the photons may excite electrons around certain atoms into the next higher energy level. However, the photon must be of exactly the right energy—the difference in energy between the two electron levels. (Actually, there are often several higher energy levels possible, but we simplify the discussion by assuming that there is only one.)
Energy is required to elevate the electron into the next electron energy level. Ordinarily, most atoms in the material have their “elevatable” electrons in the lower energy level. Any photon of the “right” energy can “bump” the electron into the higher energy level (Fig. 4). At some time in the future (of the order of a hundred millionth of a second!), the electron falls spontaneously back to its lower energy level. As it does so, it releases its excess energy in the form of a photon of light. This photon is of exactly the same energy (the same frequency, wavelength, and “color”) as the photon that “bumped” the electron up originally (Fig. 5). This process is called spontaneous emission. The emitted photons go off in all directions. Although they are all of the same “color,” they are not unidirectional, and they are not in phase (not coherent). (For our purposes, they are useless.)
When light of the right energy is transmitted through a medium such as the one just discussed, photons are absorbed as electrons are “bumped” into higher energy levels. The light beam is weakened by its passage through the material (see Fig. 4). Later, the absorbed photons are re-emitted as the electrons fall down to the lower energy level, but these re-emitted photons are released in random directions and, within certain constraints, at random times.
The situation is different if an entering photon strikes an electron at its higher energy level. In this case, the photon can “knock” the electron off its perch, so to speak, back to the lower energy level. As the electron falls, it emits a photon. Thus, whereas only one photon struck the atom, two photons leave it—the original photon plus the emitted photon (Fig. 6). The second photon is traveling in the same direction as the first and is in phase with it. This process is called stimulated emission and is the basis for laser light. In fact, the term laser is an acronym for light amplification by the stimulated emission of radiation.
Thus, whether an incoming beam of light is weakened or augmented by its passage through matter depends on the proportion of atoms in that material that have their “elevatable” electrons in the higher energy level. If most atoms do not have electrons in the higher level, the light beam is weakened. If most atoms do have electrons in the higher level, stimulated emission occurs and the light beam is augmented as it emerges.
The natural state of matter is that most electrons are at their lowest energy levels. One requirement for laser action is that most “elevatable” electrons must be at their higher energy level before the light enters the medium. Such a situation is called a population inversion.
To create a population inversion, energy must be supplied to the medium. In the case of solid (also referred to as solid-state) lasers, such as the ruby or the neodymium-yttrium-aluminum-garnet (YAG) laser, energy may be supplied in the form of external flashes of light (by surrounding the solid crystal with a helical flash tube). In the case of gas lasers (e.g., argon, krypton), external energy may be supplied in the form of an electric current passing through the gas.
These, then, are the two possible fates of a beam of light (of the appropriate wavelength) that passes through the solid or gas of a laser (the laser cavity or resonant cavity). If most electrons are not in the higher energy level, the light beam is weakened by a net loss of photons absorbed in “bumping up” the electrons to the higher energy level. If most electrons are already at their higher energy level (a population inversion), the light beam is augmented. Its photons strike energized electrons, causing them to fall to their lower energy level; for each electron “knocked down,” a photon is released and added to the original light beam. It is almost as if a chain reaction occurs, exponentially increasing the strength (the number of photons) of the light beam.
The energy of the emitted laser beam can be increased still further by causing the light beam to traverse the material multiple times. This is accomplished by placing a mirror over each end of the crystal or gas tube so that the distance between them is an even multiple of the laser light's wavelength. The light is reflected back and forth. If external energy continues so that a population inversion is present, the beam is amplified.
Photons produced by stimulated emission travel in the same direction as, and are in phase with, the original photons that caused their emission. As this coherent light beam continues to bounce back and forth between the two mirrors, it becomes more and more intense.
With the two mirrors like this, of course, no laser light would ever emerge from the apparatus. In the construction of a laser, therefore, one mirror must be only partially reflecting. The laser light emerges from this end.
For example, let us suppose that the partially reflecting mirror reflects only 80% of the light that hits it. If the laser beam undergoes a net amplification of, say, 30% on each round trip between the mirrors, the beam can be weakened by the 20% loss factor and still continue to increase in strength as it bounces between the mirrors. A laser beam may be emitted as long as the system is working.
Some electrons at the higher energy level decay spontaneously, undergoing spontaneous emission rather than stimulated emission. However, these photons are emitted randomly in all directions. Because they do not strike the mirrors at a right angle, as do photons released by stimulated emission, they are not be added to the beam. The only photons remaining in the beam after a few back-and-forth reflections are those in the coherent laser light.
Solid or gas lasers may emit continuously if the “exciting” energy is applied continuously. This output is limited in part by the heat generated in the lasing medium. If the “exciting” energy is supplied in brief pulses, laser output of higher energy levels (in pulses) can be obtained.
Listed next are the characteristics of the emitted laser beam:
There is still no satisfactory verb in the English language to describe just what ophthalmologists do with lasers. The verb “to lase,” is intransitive, that is, it cannot take an object to show what is affect by the “lasing.” Thus, although a laser can lase, an ophthalmologist cannot.
|SPECIALIZED TECHNIQUES IN LASER DESIGN|
|Recently, it has become desirable to produce beams of even higher power
from solid-state lasers, such as the neodymium-YAG. Power increases like
this can be achieved by using the techniques of Q-switching or mode-locking.|
Light from a pulsed solid-state laser, such as the ruby laser, does not emerge as a single flash, but rather as a series of extremely brief ones. This occurs because of the way the laser operates. For example, we may consider the ruby laser, in which the population inversion is being generated by a helical flash tube surrounding the ruby crystal. As soon as enough excited electrons are present in the crystal, stimulated emission occurs and the electrons are de-excited. The light from the helical flash tube then re-excites the electrons, and another stimulated emission (and laser flash) occurs. This continues for as long as light from the flash tube is on, typically about a thousandth of a second.
The “Q” in Q-switching is taken from the phrase quality factor, which is related to the ratio of energy storage to energy dissipation in the laser medium. A laser with a high Q is storing energy well, whereas one with a low Q is storing energy poorly.
Q-switching is a method by which the Q factor of a laser apparatus can be changed at a selected moment. It is a method to prevent laser action from starting until a very large percentage of the electrons are in the excited state. What Q-switching involves in theory is temporarily to block one of the mirrors. Thus, no laser action can occur even though electrons are being stimulated into their higher energy levels. When the mirror is “unblocked,” reflection occurs and an enormous amount of energy is released from the excited electrons present. The duration of Q-switched pulses is of the order of 10 to 50 billionths (10-9) of a second, termed nanoseconds.
Despite the theoretical purity of laser light, there are several factors that may serve to contaminate it. In the operation of a high-power solid laser, the output consists of a large number of waves of slightly different wavelengths.
One reason for this is that within a laser crystal many times larger than the wavelength of light there is more than one wavelength that can resonate back and forth. For laser operation, it is only necessary that a whole number of wavelengths can fit in the space between the mirrors. For example, if the length of the crystal is 10 m, then 100,000 waves of 100-μm wavelength can “fit.” However, 99,999 waves of a fractionally larger wavelength can also “fit,” and so on. Thus, multiple resonant wavelengths are possible in a typical laser.
A second reason for wavelength and/or resonance variability during the use of a solid-state laser is that as the laser operates, the crystal may become heated. This may result in a slight expansion, causing an increase in the length of the rod and thus an increase in the distance between the mirrors.
Ordinarily, these different modes of oscillation operate independently, in a situation known as a free-running mode. The large number of light waves with slightly different wavelengths, superimposed with random phases, may result in a long train of light waves with irregular amplitude.
Mode-locking is a method of controlling these slightly differing modes of emitted light. A layer of a suitable bleachable dye is placed in the path of the beam within the laser cavity. This dye is opaque to the light until the laser intensity builds sufficiently to saturate the dye and to change it for a brief instant from opaque to transparent. During that instant, the potential laser energy, which has been building up in the meantime in a manner analogous to the energy buildup of the Q-switched technique, is released.
The phases of all the modes are thus “locked together,” resulting in pulses in which all the modes combine to give a large resultant power. The duration of these pulses is of the order of tens of trillionths (10–12) of a second, termed picoseconds. These pulses are released as a series of half a dozen to a dozen short pulses (a pulse train). The time between each pulse corresponds to the time it takes the light to go back and forth between the mirrors in the laser cavity, typically about 8 billionths (10-9) of a second.
So, even though the distinction is made clinically between Q-switched and mode-locked lasers, the mode-locked technique is actually a form of Q-switching. Mode-locked and Q-switched lasers both have the common goal of producing high-power laser pulses. Although the energy levels of both types of lasers are approximately equal, the mode-locked laser pulse lasts only about one one-thousandth as long as that from a Q-switched laser. Since power is energy per unit time, the power of a mode-locked laser pulse is approximately one thousand times greater than that of a Q-switched laser pulse.
A Q-switched laser does not affect the relative phases of the components of the laser light; it releases a single burst of laser energy. In contrast, a mode-locked laser involves the additional feature of controlling the phase of the emitted beam. The beam from a mode-locked laser consists of a series of pulses, each pulse consisting of laser light in identical phase alignment.
In summary, mode-locking may be thought of as Q-switching plus phase-matching. Clinically, the output from a Q-switched laser consists of a single pulse lasting from 10 to 50 nanoseconds (10-9 second). The output of the mode-locked laser consists of a series of pulses, each 10 to 50 picoseconds (10–12 second) long; each series or train of pulses may last 10 to 100 nanoseconds.
All metallic elements are (at least fair) conductors of electricity. When metallic atoms are close together, their outermost free electrons are shared by all closely packed nuclei and are thus free to move in the metal. When an electric field is applied to such a material, the electrons feel an electrical “pressure,” or voltage. They move and constitute an electrical current. If such a metal is heated, atomic movement (electron-nucleus collisions) may be thought of as restricting electron flow and the electrical resistance increases. Elements that are electrical insulators have no such electrons free to roam in the solid and thus do not conduct electricity.
In between conductors and insulators is the class of elements known as semiconductors. Typical examples are germanium and silicon. The outermost orbits of these atoms contain four electrons. When large numbers of these atoms are brought together, they can form a crystalline solid in which each atom shares an electron with each of four nearest neighbors. At low temperatures, there are no free electrons and these materials do not conduct electricity. In contrast with conductors, however, as these materials are heated, electrons may break free and begin to become available to move under the influence of an electric field. Thus, (unlike the situation with metals) as the semiconductor is heated, its electrical resistance falls.
When an electron in a semiconductor moves away from its atom, it leaves behind a positively charged “hole” or vacancy. When an electric charge is applied to such a material, the free (negatively charged) electrons flow toward the positive terminal, and the (positively charged) “holes” flow toward the negative one. (Actually the “holes” are about three orders of magnitude heavier than the electrons and thus move more slowly under any given voltage.)
Electrons bound to their atoms usually are at their minimum possible energy level. Then they are said to be in the valance band. If enough energy is applied to these electrons, they may break free from their valence bonds and become promoted into a higher energy band called the conduction band. In the conduction band, these more energetic electrons can roam and create an electric current.
In a solid (unlike a gas), the atoms lie relatively close to each other, so close that the presence of one atom's electron fields has an effect on its neighbor's electrons. The electron energy levels become disturbed and the material ends up with energy states that are “smeared” into bands rather than discrete energy levels. In an energy band, the energy levels are so close together that they are in effect continuous.
These valance and conduction energy bands of a semiconductor are separated by a region of energy in which no allowed energy levels exist. This region is called the forbidden region, and its width is called the band gap. An electron in the conduction band has an energy greater than an electron in the valence band by an amount equal to the band gap.
If a large number of electrons is stimulated into the conduction band, it leaves a corresponding large number of holes in the valence band. Now, let us imagine that some photons strike these conduction band electrons. If these photons have an energy equal to or slightly greater than the band gap, they may cause the conduction electrons to drop back into the valence band. As they do so, they release photons of this same energy, which may then strike other stimulated electrons. It is easy to see how this would result in coherent amplification. If this medium is bracketed by a reflective surface at each end, laser output may be produced in a manner analogous to the situation in gas lasers.
This laser output is unlikely to occur in pure semiconductors because of additional factors impeding electron transitioning such as crystal momentum, lattice vibrations, and so forth. However, the behavior of these semiconductor materials may be modified by adding impurities into the structure. Adding some atoms of a different element is referred to as doping. Arsenic, for example, has five electrons in its outer valence shell. If we replace a semiconductor atom with arsenic, four of arsenic's electrons are used for the crystal bonding. The fifth electron, conversely, is relatively free to move in the crystal. Thus, addition of a different element that contains five electrons in its outer shell results in an excess of electrons, or negatively charged particles. Such a semiconductor is called an n-type semiconductor. Similarly, if we add an atom such as gallium, which has only three electrons in its outermost shell, we create an excess of positively charged “holes.” Such a conductor is called a p-type semiconductor.
The increasingly ubiquitous (in ophthalmology) diode laser is created when an n-type semiconductor is joined to a p-type semiconductor, forming a p-n junction (Fig. 7). When this happens, electrons flow from the excess electron n-type side to fill the holes in the excess hole p-type side (and it may be said that the holes flow from the p-type side to the n-type side). Eventually, an electric field is created that is strong enough to oppose any further electron migration and the situation stabilizes. However, one can stimulate this flow by connecting the n-type side to the negative terminal of a source of direct current, and the p-type side to the positive terminal. This causes further flow of electrons from the n-type side (and further flow of holes from the p-type side).
These electrons and holes may then recombine (with what amounts to a transition of the electrons back into the valence band and simultaneous production of photons of the appropriate energy.) The produced photons stimulate additional electron transitions back into the valence band (and additional photon production). Under the influence of the voltage applied to the p-n junction, electrons and holes are driven toward the junction, where they combine to release photons. As the voltage (forward bias) increases, more and more electrons from the n-type side and more and more holes from the p-type side are driven toward the junction. The increased number of electrons and “holes” combine to produce an increased number of photons. Thus the emitted light intensity becomes stronger. The region of the p-n junction where laser action takes place is only a micron or so wide.
One can design reflective surfaces at the ends of this “semiconductor sandwich” by polishing the two faces of the crystal. The crystal-air boundary provides a natural reflecting surface, and the natural cleavage face of the crystal also makes an excellent mirror. A reflecting surface at each end creates a resonant cavity, producing laser emission. By varying the direct current, the laser output may be easily modulated. Because emission results from transition between two energy bands, rather than between two discrete energy levels as in a gas laser, the emission is not quite so monochromatic as in a gas laser. The wavelength is related to the energy difference between the valence band and conduction band of that semiconductor.
The diode laser is extremely small. Because of its direct conversion of electricity into laser energy, it is highly efficient. The percentage of photons obtained with respect to the number of electrons crossing the junction is called the external quantum efficiency of the laser. It varies with temperature, being of the order of 50% or more at the temperature of liquid helium, for example, and still being about 15% at room temperatures. In terms of the percentage of laser power output with respect to the electrical power input, the efficiency can be as high as 10%. Because the stimulated emission arises from within the host material—and not from a small percentage of the active medium, as in other lasers—the diode laser is by far the most powerful for its size.
Many diode laser crystals have band gaps that correspond to wavelengths in the infrared region. Diode lasers that emit in the infrared may have limited clinical usefulness. Frequency doubling is a technique that allows these lasers to produce laser radiation in a perhaps more clinically desirable visible green, for example. Frequency doubling is possible only because of the high power densities of lasers, and is due to the manner in which light propagates through a solid medium. The nuclei and electrons of solids form dipoles, which are stimulated to oscillate and emit radiation themselves. Normally, the emitted radiation is the same as the incident radiation. However, with very high power levels nonlinear characteristics become significant. When this happens, oscillation occurs not only at the incident frequency but at harmonics. The strongest harmonic is at twice the incident frequency. With some additional engineering maneuvers, this harmonic can be channeled as the laser output. Solid state lasers that ordinarily “should” emit only in the infrared can thus be altered into lasers that emit in the visible green, for example.