Introduction to lasers pdf

The coverage starts with. This textbook provides an introductory presentation of all types of lasers. It contains a general description of the laser, a theoretical treatment and a characterization of its operation as it deals with gas, solid state, free-electron and semiconductor lasers. This expanded and updated second edition of the book presents a. In this book emphasis is laid on laser including its operation, different types, properties like coherence and monochromaticity, beam propagation, theoretical treatment of atom?

In a very short time, lasers advanced from research interest to increasingly useful, commercially available tools for material processing, precision measurements, surgery, communication, and even entertainment.

This book provides the background in theoretical physics necessary to understand engineering applications. It summarises relevant theories of geometrical optics, physical optics, quantum optics,. The only introductory text on the market today that explains the underlying physics and engineering applicable to all lasers Although lasers are becoming increasingly important in our high-tech environment, many of the technicians and engineers who install, operate, and maintain them have had little, if any, formal training in the.

This book is the result of more than ten years of research and teaching in the field of quantum electronics. The purpose of the book is to introduce the principles of lasers, starting from elementary notions of quantum mechanics and electromagnetism. Because it is an introductory book, an effort has. This text is designed to fill the gap between brief reviews of lasers provided in modern physical optics texts and the thorough, graduate-level texts on lasers an quantum mechanics.

For those students who may not want to invest a substantial amount of their elective time in extensive course work in. Home Introduction To Laser Physics.

Introduction to Laser Physics. Introduction to Laser Physics by K. Introduction to Laser Physics by Koichi Shimoda. Laser Physics by Peter W. Milonni,Joseph H. Introduction to Laser Spectroscopy by Halina Abramczyk. Basics of Laser Physics by Karl F. Introduction to Laser Technology by C. Figure 3 illustrates spontaneous a and stimulated b emission with the two coherent waves that result from the latter case. The primary problem in achieving stimulated laser emission is that, under normal conditions of thermodynamic equilibrium, the population, or number of atoms or molecules at each energy level, is not favorable to stimulated emission.

Because of the tendency of atoms and molecules to spontaneously drop to lower energy levels, the number at each energy level decreases as the energy increases. In other words, virtually all of the atoms or molecules are in the ground state for a visible-wavelength energy transition. Examine spontaneous absorption and emission, as well as stimulated emission resulting in energy level transitions with this interactive tutorial. These fundamental processes represent important concepts necessary in understanding laser operation.

The reason that stimulated emission is difficult to achieve becomes apparent when considering the likely events surrounding the decay of an electron from an exited state with the subsequent and spontaneous emission of light. The emitted light could easily stimulate emission from another exited atom, but so few are available that the emission more likely will first encounter an atom in the ground state, and will be absorbed instead Figure 3 c.

Because the number of atoms in an exited state is so miniscule in relation to the number in the ground state, the emitted photon has a much greater probability of being absorbed, rendering stimulated emission insignificant when compared to spontaneous emission at thermodynamic equilibrium.

The mechanism by which stimulated emission can be made to dominate is to have more atoms in the excited state than in the lower energy state, so that emitted photons are more likely to stimulate emission than to be absorbed. Because this condition is the inverse of the normal equilibrium situation, it is termed a population inversion. As long as there are more atoms in the upper energy level than in the lower, stimulated emission can dominate, and a cascade of photons results.

The first emitted photon will stimulate the emission of more photons, these subsequently stimulate the emission of still more, and so on. The resulting cascade of photons grows, resulting in the amplification of emitted light.

If the population inversion terminates the ground state population becomes dominant , spontaneous emission will again become the favored process. At the time of Einstein's proposal, most physicists believed that any condition other than thermodynamic equilibrium was unstable and could not be sustained.

It was not until after World War II that serious consideration was given to methods of producing the population inversions necessary to sustain stimulated emission. Atoms and molecules can occupy many energy levels, and although some transitions are more likely than others due to rules of quantum mechanics and for other reasons , a transition can occur between any two levels.

The minimum requirement for stimulated emission and amplification, or laser action, is that at least one higher energy level must have a greater population than a lower level. A population inversion can be produced through two basic mechanisms, either by creating an excess of atoms or molecules in a higher energy state, or by reducing the population of a lower energy state.

A system can also be chosen that is unstable in the lower level, but for continuous laser operation, attention must usually be paid to both populating the higher level and depopulating the lower level.

If too many atoms or molecules accumulate in the lower energy level, the population inversion will be lost and laser action will stop. The most common approach for producing a population inversion in a laser medium is to add energy to the system in order to excite atoms or molecules into higher energy levels. Simply adding energy by thermally agitating the medium is not sufficient under thermodynamic equilibrium to produce a population inversion, because heat only increases the average energy of the population, but does not increase the number of species in the excited state relative to that in the lower state.

The ratio of the number of atoms at two energy levels 1 and 2 under thermodynamic equilibrium is given by the following equation :.

As demonstrated by the equation, at thermodynamic equilibrium, N 2 can be greater than N 1 only if the temperature is a negative number. Before the research describing maser and laser action was published, physicists referred to a population inversion as a negative temperature , which was symbolic of their view that any condition other than thermodynamic equilibrium was unlikely to be sustained.

To produce the required population inversion for laser activity, atoms or molecules must be selectively excited to specific energy levels. Light and electricity are the excitation mechanisms of choice for most lasers. Either light or electrons can provide the energy necessary to excite atoms or molecules to selected higher energy levels, and the transfer of energy is not required to directly promote electrons to a specific upper level of the laser transition.

Some approaches can be rather complex, but these often produce better-performing lasers. One frequently utilized approach excites an atom or molecule to a higher energy level than required, after which it drops to the upper laser level. Indirect excitation can be employed to excite atoms in a surrounding gas mixture, which then transfer their energy to the atoms or molecules responsible for producing the laser action.

As previously discussed, the amount of time spent by an atom or molecule in an excited state is critical in determining whether it will be stimulated to emission and participate in a cascade of photons, or lose its energy through spontaneous emission. Excited states commonly have lifetimes of only nanoseconds before they release their energy by spontaneous emission, a period that is not lengthy enough to likely undergo stimulation by another photon. A critical requirement for laser action, therefore, is a longer-lived state that is suitable for the upper energy level.

Such states do exist for certain materials, and are referred to as metastable states see Figure 4. The average lifetime before spontaneous emission occurs for a metastable state is on the order of a microsecond to a millisecond, quite a lengthy period of time on the atomic timescale. With lifetimes this long, excited atoms and molecules can produce significant amounts of stimulated emission. Laser action is only possible if the population builds up faster than it decays in the upper energy level, maintaining a population larger than that of the lower level.

The longer the spontaneous emission lifetime, the more suitable a molecule or atom is for laser applications. The maser that Charles Townes demonstrated in advance of the first laser was significant because it required the creation of a population inversion in order to function, and therefore proved to many skeptical physicists that such an inversion could be produced.

His system was a two-level maser, utilizing only the upper and lower energy levels. Townes employed a novel approach in his ammonia molecule system to produce the population inversion - a molecular beam technique that separated the excited ammonia molecules from ground-state molecules. The ground-state molecules were discarded, and the separated excited molecules constituted the required population inversion. Other, more efficient, means have now been developed for masers, and practical lasers require the utilization of three, four, or more energy levels.

This tutorial explores metastable states for both three-level and four-level laser systems. The simplest functional energy-level structure for laser operation is a three-level system, which is illustrated in Figure 4 a. In this system, the ground state is the lower laser level, and a population inversion is created between this level and a higher-energy metastable state. Most of the atoms or molecules are initially excited to a short-lived high-energy state that is higher than the metastable level.

From this state they quickly decay to the intermediate metastable level, which has a much longer lifetime than the higher energy state often on the order of times longer. Because each atom's residence time in the metastable state is relatively long, the population tends to increase and leads to a population inversion between the metastable state and the lower ground state which is continuously being depopulated to the highest level.

Stimulated emission results from the fact that more atoms are available in the upper excited metastable state than in the lower state where absorption of light would most likely occur. Although the three-level laser system works for all practical purposes, as exemplified by Maiman's first laser, a number of problems limit the effectiveness of this approach.

The central problem occurs because the lower laser level is the ground level, which is the normal state for most atoms or molecules. In order to produce the population inversion, a majority of ground state electrons must be promoted to the highly excited energy level, requiring a significant input of external energy.

In addition, the population inversion is difficult to sustain for an appreciable time, and therefore, three-level lasers must be operated in pulsed mode rather than continuously. Lasers utilizing four or more energy levels avoid some of the problems mentioned above, and therefore are more commonly utilized. Figure 4 b illustrates a four-level scenario. The energy level structure is similar to that in the three-level system, except that after the atoms drop from the highest level to the metastable upper state, they do not drop all the way to the ground state in a single step.

Because the population inversion is not created between the ground state and the upper level, the number of atoms or molecules that must be elevated is dramatically reduced in this model. In a typical four-level laser system, if only one or two percent of the atoms or molecules reside in the lower laser level which is above the ground state , then exciting only two to four percent of the total to the higher level will achieve the required population inversion.

Another advantage of separating the lower laser level from the ground level is that the lower level atoms will naturally fall to the ground state.

If the lower laser level has a lifetime that is much shorter than the upper level, atoms will decay to the ground level at a rate sufficient to avoid accumulation in the lower laser level. Many of the lasers designed under these constraints can be operated in a continuous mode to produce an uninterrupted beam.

Actual working lasers are usually far more complex than the models described above. The upper laser level is often not a single level, but a group of energy levels that enables the required excitation energy to vary over a wide range during operation. The lower level may also consist of multiple levels, and if closely spaced upper levels each decay to a different lower level, a single laser may be operated on multiple transitions, producing more than one wavelength.

The helium-neon laser, for example, is most commonly utilized to emit a single red wavelength, but it can also be operated at other transitions to produce orange, yellow, green, and infrared radiation. Many other factors exist in the design of practical lasers, including the nature of the active media. Multiple gases or other combinations of molecular species are often employed to improve the efficiency of capturing and transferring the energy, or to assist in depopulating the lower laser level.

Before the landmark demonstration that masers and lasers could actually be produced, scientists had overlooked the fact that naturally occurring masers exist in outer space Figure 5. Even after Einstein's prediction of stimulated emission, a majority of physicists believed that producing a population inversion was so difficult that it was unlikely to occur in nature.

In effect, scientists apparently didn't seriously consider that matter could naturally exist in a state other than thermodynamic equilibrium. So-called cosmic masers include sources such as envelopes around red giant stars, comets, supernova remnants, and other star-forming molecular clouds.

In the gas cloud surrounding a hot star, the radiation emitted from the star can excite the gas molecules to higher energy levels, which then decay to a metastable state. As long as a suitable lower laser level exists, a population inversion can occur that will result in laser action. Although the process is identical to man-made masers or lasers, and large amounts of energy can be radiated, emission of stellar laser or maser energy is not restricted to a beam.

The radiation emitted by a cosmic maser travels outward in all directions just as the energy from any other interstellar hot gas cloud. The amplification of light by stimulated emission is a fundamental concept in the basic understanding of laser action.

This interactive tutorial explores how laser amplification occurs starting from spontaneous emission of the first photon to saturation of the laser cavity and the establishment of a dynamic equilibrium state. In addition to the creation of a population inversion, several other factors are required to amplify and concentrate light into a laser beam. Light from stimulated emission produced in a laser medium usually has a single wavelength, but must be extracted efficiently from the medium by some mechanism that includes amplification.

This task is accomplished in a resonant cavity , which reflects some of the emission back into the laser medium and, through multiple interactions, builds or amplifies the light intensity. For example, after the initial stimulated emission, two photons having the same energy and phase are each likely to encounter excited atoms, which will subsequently emit even more photons having the same energy and phase.

The number of photons produced by stimulated emission grows rapidly, and the increase is directly proportional to the distance the light travels in the laser medium.

Presented in Figure 6 is an illustration of the gain, or amplification, that occurs with increased path length in the resonant cavity due to the mirrors at each end. Figure 6 a shows the beginning of stimulated emission, which is amplified in Figure 6 b through Figure 6 g as the light is reflected from the mirrors positioned at the cavity ends. A portion of light passes through the partially reflecting mirror on the right-hand side of the cavity Figures 6 b,d, and f during each pass.

Finally, at the equilibrium state Figure 6 h , the cavity is saturated with stimulated emission. The degree of amplification achieved in a laser, expressed by the term gain , refers to the amount of stimulated emission a photon can generate as it travels a given distance.

For example, a gain of 1. This results in an amplification factor that increases with the path length of the laser cavity. The actual gain is far more complex and depends upon fluctuations in the population distribution between the upper and lower laser energy levels, among other factors. The important point is that the amount of amplification increases sharply with the distance traveled through the laser medium. In a laser constructed with a longitudinal resonant cavity, such as a ruby rod or a gas-filled tube, light traveling along the length of the laser medium generates far more stimulated emission than the light emitted perpendicular to the long axis of the cavity.

Light emission is therefore concentrated along the length of the cavity even without the use of mirrors to confine its path to the lengthwise direction. Placing mirrors at opposite ends of a laser cavity enables the beam to travel back and forth, which results in increased amplification due to the longer path length through the medium. The multiple reflections also produce a narrowly focused beam an important laser characteristic , because only photons traveling parallel to the cavity walls will be reflected from both mirrors.

This arrangement is known as an oscillator , and is necessary because most laser materials have very low gain, and sufficient amplification can only be achieved with a long path length through the medium. A majority of current lasers are designed with mirrors on both ends of the resonant cavity to increase the path that light takes through the laser medium. The emission intensity grows with each pass of light until it reaches an equilibrium level that is established by the cavity and mirror design.

One cavity mirror reflects nearly the entire incident light, while the other the output mirror reflects some light and transmits a portion as the laser beam. In a laser that has low gain, the output mirror is chosen to transmit only a small fraction of the light perhaps only a few percent , and to reflect the majority back into the cavity. At equilibrium, the laser power is higher inside the cavity than outside, and varies with the percentage of light transmitted through the output mirror.

By increasing the transmittance of the output mirror, the difference in power between the inside and outside of the cavity can be reduced. However, as long as the output mirror reflects some portion of light back into the cavity, the power inside remains higher than in the emerging beam. A common misconception about lasers results from the idea that all of the emitted light is reflected back and forth within the cavity until a critical intensity is reached, whereupon some "escapes" through the output mirror as a beam.

In reality, the output mirror always transmits a constant fraction of the light as the beam, reflecting the rest back into the cavity.

This function is important in allowing the laser to reach an equilibrium state, with the power levels both inside and outside the laser becoming constant. Due to the fact that the light oscillates back and forth in a laser cavity, the phenomenon of resonance becomes a factor in the amplification of laser intensity. Depending upon the wavelength of stimulated emission and cavity length, the waves reflected from the end mirrors will either interfere constructively and be strongly amplified, or interfere destructively and cancel laser activity.

Because the waves within the cavity are all coherent and in phase, they will remain in phase when reflected from a cavity mirror. The waves will also be in phase upon reaching the opposite mirror, provided the cavity length equals an integral number of wavelengths.

Thus, after making one complete oscillation in the cavity, light waves have traveled a path length equal to twice the cavity length. If that distance is an integral multiple of the wavelength, the waves will all add in amplitude by constructive interference. When the cavity is not an exact multiple of the lasing wavelength, destructive interference will occur, destroying laser action. The following equation defines the resonance condition that must be met for strong amplification to occur in the laser cavity :.

The condition for resonance is not as critical as it might appear because actual laser transitions in the cavity are distributed over a range of wavelengths, termed the gain bandwidth. Wavelengths of light are extremely small compared to the length of a typical laser cavity, and in general, a complete roundtrip path through the cavity will be equivalent to several hundred thousand wavelengths of the light being amplified.

Resonance is possible at each integral wavelength increment for example ,, ,, ,, etc. Figure 7 illustrates a typical example in which several resonance values of N , referred to as longitudinal modes of the laser, fit within the gain bandwidth. Laser beams have certain common characteristics, but also vary to a wide degree with respect to size, divergence, and light distribution across the beam diameter.

These characteristics depend strongly upon the design of the laser cavity resonator , and the optical system controlling the beam, both within the cavity and upon output. Although a laser may appear to produce a uniform bright spot of light when projected onto a surface, if the light intensity is measured at different points within a cross section of the beam, it will be found to vary in intensity.

Resonator design also affects beam divergence, a measure of beam spreading as distance from the laser increases. The beam divergence angle is an important factor in calculating the beam diameter at a given distance.

In much of the previous discussion, the assumption has been that the mirrors at either end of a laser resonator cavity are planar, or flat. Conceptually this is the simplest configuration, but in practice it can be very difficult to accomplish. If the two mirrors are not precisely aligned, excessive light losses will occur that may cause the laser to stop operating.

Even a misalignment of a fractional degree, after several successive reflections, can result in significant light losses from the sides of the cavity. If one or both of the mirrors have a curved surface, the light losses due to misalignment can be reduced or eliminated.

Because of the focusing properties of the curved mirror, light is confined to the cavity even if the mirrors are not precisely aligned, or if the light is not emitted exactly along the cavity axis. There are a number of design variations that employ different combinations of plane and curved mirrors to ensure that the light is always focused back toward the opposite mirror. A configuration of this type is called a stable resonator because light that is reflected from one mirror to the other will continue to oscillate indefinitely if there are no other losses.