II Laser operation In this section, we discuss how do the laser elements (pump, medium and resonator) work? Consider the following figures; In the above figure ( 3 )

Step (1) An energy from an appropriate pump is coupled into the laser medium. The energy is sufficiently high to excite a large number of atoms from the ground state Eo to several excited states E3. Then the atoms spontaneously decay and back to the ground state Eo. But some of them back by a very fast (radiationless) decay from E3 to a very special level E2.

Step (2) The level E2 labeled as the upper laser level, has a long lifetime. Whereas most excited levels in atom decay with lifetime of order 10-8 sec. Level E2 is metastable, with a typical lifetime of order of 10-3 sec. So that the atoms being to pile up at this metastable level (E2), which functions as a bottleneck. N2 grows to a large value, because level E2 decays slowly to level E1 which labeled by lower laser level and level E1 decays to the round state rapidly, so that N1 cannot build to a large value. The net effect is the population inversion (N2>N1) between the laser levels E1 and E2.

When the population inversion has been established, a photon of resonant energy (h=E2-E1) passes by one of the N2 atoms, stimulated emission can be occurred. Then, laser amplification begins. Note carefully that a photon of resonant energy (E2-E1) can also stimulate absorption from E1 to E2. Then the light amplification occurs and there is a steady increase in the incident resonant photon population and lasing continues. Step (3)

Step )4)

One of the inverted N2 atoms, which dropped to level E1 during the stimulated emission process, now decays rapidly to the ground state Eo. If the pump is still operating the atoms is ready to repeat the cycle, there by insuring a steady population inversion and constant laser beam output. Figure (3) shows the same action of figure (2(.

In (a) the laser medium is situated between the resonator (two mirrors) in which most of the atoms are in the ground state (black dots). In (b) An external energy (pumping) raising most of the atoms to the excited levels (as E3). The excited states are shown by circles. During this pumping process, the population inversion is established. In (c) the light amplification process is initiated, in which many of the photons leave through the sides of the laser cavity and are lost. Since the remainder (seed photons) are directed along the optical axis of the laser.

In (d) and (e) As the seed photons pass by the inverted N2 atoms, stimulated emission adds identical photons in the same direction, providing an ever increasing population of coherent photons that bounce bake and forth between the mirrors. In (f) A fraction of the photons incident on the mirror (2) pass out through it. These photons constitute the external laser beam.

Characteristic of Laser Light Monochromaticity. The light emitted by a laser is almost pure in color, almost of a single wavelength or frequency. Although we know that no light can be truly monochromatic, with unlimited sharpness in wavelength definition, laser light comes far closer than any other available source in meeting this ideal limit. The monochromaticity of light is determined by the fundamental emission process where atoms in excited states decay to lower energy states and emit light. In blackbody radiation, the emission process involves billions of atoms and many sets of energy-level pairs within each atom. The resultant radiation is hardly monochromatic, as we know.

If we could select an identical set of atoms from this blackbody and isolate the emission determined by a single pair of energy levels, the resultant radiation, would be decidedly more monochromatic. When such radiation is produced by non-thermal excitation, the radiation is often called fluorescence. Figure 1 shows such

Figure (1) fluorescence and its spectral content for a radiative decay process between two energy levels in an atom. (a) Spontaneous decay process between well-defined energy levels. (b) Spectral content of fluorescence in (a), showing line shape and linewidth. an emission process. The fluorescence comes from the radiative decay of atoms between two well-defined energy levels E2 and E1. The nature of the fluorescence, analyzed by a spectrophotometer, is shown in the lineshape plot, a graph of spectral radiant existence ( ) versus wavelength.

Note carefully that the emitted light has a wavelength spread about a center wavelength 0 , where 0 = c/0 and 0 = (E2 - E1)/h . While most of the light may be emitted at a wavelength 0 , it is an experimental fact that some light is also emitted at wavelengths above and below 0 , with different relative existence, as shown by the lineshape plot. Thus the emission is not monochromatic, it has a wavelength spread given by 0 2 , where is often referred to the linewidth. When the linewidth is measured at the half maximum level of the lineshape plot, it is called the FWHM linewidth, that is, full width at half maximum

In the laser process, the linewidth shown in figure (1) is narrowed considerably, leading to light of a much higher degree of monochromaticity. Basically this occurs because the process of stimulated emission effectively narrows the band of wavelengths emitted during spontaneous emission. This narrowing of the linewidth is shown qualitatively in figure (2). To gain a quantitative appreciation for the monochromaticity of laser light, consider the data in table (1), in which the linewidth of a high quality He-Ne laser is compared to the linewidth of the spectral output of a typical sodium discharge lamp and to the linewidth of the very narrow cadmium red line found in the spectral emission of a low-pressure lamp. The conversion from to n is made by using the approximate relationship. where Vl0=C.

The data of table (1) show that the He-Ne laser is 10 million times more monochromatic than the ordinary discharge lamp and about 100,000 times more so than the cadmium red line. No ordinary light source, without significant filtering, can approach the degree of monochromaticity present in the output beam of typical lasers.

Figure (2) Qualitative comparison of linewidths for laser emission and spontaneous emission involving the same pair of energy levels in an atom. The broad peak is the line shape of spontaneously emitted light between levels E2 and E1 before lasing being. The sharp peak is the line shape of laser light between levels E2 and E1 after lasing beings. Table (1) comparison of linewidths

Light source Center Wavelength0 ( A0 )FWHMLinewidth 0 ( A0 )FWHM linewidth(HZ)Ordinary discharge lamp 5896 19X1010Cadmium low-pressure lamp 64380.0139.4X108Helium-neon laser 632810-77.5X103

Coherence. The optical property of light that most distinguishes the laser from other light source is coherence. The laser is regarded, quit correctly as the first truly coherent light source. Other light source, such as the sun or a gas discharge lamp, are at best only partially coherent.Coherence, simple stated, is a measure of the degree of phase correlation that exists in the radiation field of a light source at different location and different times. It is often described in terms of temporal coherence, which is a measure of the degree of monochromaticity of the light, and a spatial coherence, which is a measure of the uniformity of phase across the optical wavefront.

To obtain a qualitative understanding of temporal and spatial coherence, consider the simple analogy of water waves created at the center of a quite pond by a regular, periodic disturbance. The source of disturbance might be a cork bobbing up and down in regular fashion, creating a regular progression of outwardly moving crests and troughs, as in figure (3). Such a water wave filed can be side to have perfect temporal and spatial coherence. The temporal coherence is perfect because there is but a single wavelength; the crestto-crest distance remains constant.

As long as the cork keeps bobbing regularly, the wavelength will remain fixed, and one can predict with great accuracy the location of all crests and troughs on the pond's surface. The spatial coherence of the wave filed is also perfect because the cork is a small source, generating ideal waves, circular crests, and troughs of ideal regularity. Along each wave then, the spatial variation of the relative phase of the water motion is zero that is the surface of the water all along a crest or trough is in step or in one phase.

Perfect temporal coherence Perfect spatia coherence uniformity of phaseTemporal coherencephase difference time independent (temporal coherence Spatial coherence Figure (3) portion of a perfectly coherent water wave field created by a regularly bobbing cork at S. the wave field contains perfectly ordered wave fronts, C (crests) and T (troughs), representing water waves of a single wavelength

The water wave field described above can be rendered temporally and spatially incoherent by the simple process of replacing the single cork with a hundred corks and causing each cork to bob up and down with a different and randomly varying periodic motion. There would then be little correlation between the behavior of the water surface at one position and another. The wave fronts would be highly irregular geometrical curves, changing shape haphazardly as the collection of corks continued their jumbled, disconnected motions.

It does not require much imagination to move conceptually from a collection of corks that give rise to water waves to a collection of excited atoms that give rise to light. Disconnected, uncorrelated creation of water waves results in an incoherent water wave field. Disconnected, uncorrelated creation of light waves results, similarly, in an incoherent field.

To emit light of high coherence then, the radiating region of a source must be small in extent (in the limit, of course. a single atoms) and emit light of a narrow bandwidth (in the limited, with equal to zero). For real light sources, neither of these conditions is attainable. Real light sources, with the exception of the laser, emit light via the uncorrelated action of many atoms, involving many different wave lengths. The result is the generation of incoherent light. To achieve some measure of coherence with a non-laser source, two notifications to the emitted light can be made. First, a pinhole can be placed in front of the light source to limit the spatial extent of the source. Second, a narrow-band filter can be used to decrease significantly the linewidth of the light. Each modification improves the coherence of the light given off by the source-but only at the expense of a drastic loss of light energy.

In contrast, a laser source, by the very nature of its production of amplified light via stimulated emission, ensures both a narrow-band output and high degree of phase correlation. Recall that in the process of stimulated emission, each photon added to the stimulated radiation has a phase, polarization, energy, and direction identical to that of the amplified light wave in the laser cavity. The laser light thus created and emitted is both temporally and spatially coherent. In fact, one can describe or model a real laser device as a very powerful, fictitious point source located at a distance, giving off monochromatic light in a narrow cone angle. Figure 4 summarizes the basic ideas of coherence for non-laser and laser source.

For typical laser, both the spatial coherence and temporal coherence of laser light are far superior to that for light from other sources. The transverse spatial coherence of a single mode laser beam extends across the full width of the beam, whatever that might be. The temporal coherence, also called longitudinal spatial coherence, is many orders of magnitude above that of any ordinary light source. The coherence time tc of a laser is a measure of the average time interval over which one can continue to predict the correct phase of the laser beam at a given point in space. The coherence length Lc, is related to the coherence time by the equationLc =ctc where c is the speed of light.

Thus the coherence length is the average length of light beam along which the phase of the wave remains unchanged. For the He-Ne laser described in table 1 the coherence time is of the order of milliseconds (compared with about 10-11s for light from a sodium discharge lamp), and the coherence length for the same laser is thousands of kilometers (compared with fractions of a centimeter for the sodium lamp).

Improve temporal coherence Improve spatial coherence

Figure 4. A tungsten lamp requires a pinhole and filter to produce coherent light. The light from a laser is naturally coherent. (a) Tungsten lamp. The Tungsten lamp is an extended source that emits many wavelength. The emission lacks both temporal and spatial coherence. The wave front are irregular and change shape in a haphazard manner. (b) Tungsten lamp with pinhole. An ideal pinhole limits the extent of the tungsten source and improve the spatial coherence of the light. However the light still lacks temporal coherence since all wavelengths are present. Power in the beam has been decreased.

(c) Tungsten lamp pinhole and filter. Adding a good narrow band filter further reduces the power but improves the temporal coherence. Now the light is "coherent" but the available power that initially radiated by the lamp. (d) Laser. Light coming from the laser has a high degree of spatial and temporal coherence. In addition, the output power can be very high.

Directionality. When one sees thin, pencil-like beam of a He-Ne laser for the first time, one is struck immediately by the high degree of beam directionality. No other light source, with or without the help of lenses or mirrors, generates, a beam of such precise definition and minimum angular spread. The astonishing degree of directionality of a laser beam is due to the geometrical design of the laser cavity and to the monochromatic and coherent nature of light generate in the cavity. Figure (5) shows a specific cavity design and an external laser beam with an angular spread signified by the angel .

The cavity mirrors shown are shaped with surfaces concave toward the cavity, thereby focusing the reflecting light back into the cavity and forming a beam waist at one position in the cavity. Figure 5. external and internal laser beam for a given cavity. Diffraction or beam spread, measured by the beam divergence angle f, appears to be caused by an effective aperture of diameter D, located at the beam waist.

The nature of the beam inside the laser cavity and its characteristics outside the cavity are determined by solving the rather complicated problem of eectromagnetic waves in an open cavity. Although the details of this analysis beyond the scope of this discussion, several results are worth examining. It turns out that the beam- spread angel f is giving by the relationship (1) Where is the wavelength of the laser beam and D is the diameter of the laser beam at its beam waist. One cannot help but observe that Eq. (1) is quite similar to that obtained when calculating the angular spread in light generated by the diffraction of plane waves passing thought a circular aperture .

The pattern consists of a central, bright circular spot, the Airy disk, surrounded by a series of bright rings. The essence of this phenomenon is shown in figure (6). The diffraction angle , tracking the Airy disk, is given by (2)

Figure (6). Fraunhofer diffraction of plane waves through a circular aperture. Beam divergence angle is set by the edges of the Airy disk.

where is the wavelength of the collimated. Monochromatic light and D is the diameter of the circular aperture. Both Eqs. (1) and (2) depend on the ratio of a wavelength to a diameter. They differ only by a constant coefficient. It is tempting, then, to think of the angular spread inherent in laser beams and given in Eq. (1) in terms of diffraction. If we treat the beam waist as an effectives circular aperture located inside the laser cavity, then by controlling the size of the beam waist we control the diffraction or beam spread of the laser. The beam waist, in practice, is determined by the design of the laser cavity and depends on the radii of curvature of the two mirrors and the distance between the mirror.

Therefore, one ought to be able to build lasers with a given beam waist and, consequently, a given beam divergence or beam spread in the far field, that is, at sufficiently great distance L from the diffracting aperture that L >> area aperture/. Such is indeed the case. With the help of Eq. (1), one can now develop a feel for the low beam spread, or high degree of directionality, of laser beams. He-Ne lasers (632.8 nm) have an internal beam waist of diameter near 0.5 mm. Equation (1) then yields

This is a typical laser-beam divergence, indicating that the beam width will increase about 1.6 cm every 1000cm. Since we can control the beam waist D by laser cavity design and select the wavelength by choosing different laser media, what lower limit might we expect for the beam divergence? How directional can lasers be? If we design a laser with a beam waist of 0.5 cm diameter and a wavelength of 200 nm, the beam divergence angle becomes about radian,. This beam would spread about 1.6cm every 320m.

Clearly, if beam waist size is at our command and lasers can be built with wavelength below the ultraviolet, there is no limit to how parallel and directional the laser beam can be made. The high degree of directionality of the laser, or any other light source, depends on the monochromaticity and coherence of the light generated. Ordinary sources are neither monochromatic nor coherent. Lasers, on the other hand, are superior on both counts, and as a consequence generate highly directional, quasi-collimated light beams.

Laser Source Intensity. It has been that a 1-mW He-Ne laser is hundreds of times brighter than the sun. As difficult as this may be to imagine, calculations for luminance or visual brightness of a typical laser, compared to the sun, substantiate these claims. To develop an appreciation for the enormous difference between the radiance of lasers and thermal sources we consider a comparison of their photon output rates (photons per second).

Small gas lasers typically have power outputs P of 1mW. Neodymium-glass lasers, such as those under development for the production of laser-induced fusion, boast of power outputs near 1014 W!. Using these two extremes and an average energy of 10-19 J per visible photon (E=h), the photon output of laser (P/h) varies from 1016 photons/s to 1033 photons/s. For comparison, consider a broadband thermal source with a radiating surface equal to that of the beam waist of a 1-mW He-Ne laser with diameter of 0.5 mm, an area of A=2X103 cm2.

Let the surface emit radiation at a wavelength of 633 nm with a linewidth of =100nm (or=7x1013HZ) and temperature T=1000K. The photon output rat for the broadband source can be calculated from the equation(3) Substituting the values given above into Eq. (3), we find that the thermal photon output rat is only about 109 photons/s! This value is 7 orders of magnitude smaller than the photon output rat of low-power 1-mW He-Ne laser and 24 orders of magnitude smaller than a powerful neodymium-glass laser. The comparison is summarized in figure 7.

Figure (7). Comparison of photon output rates between a low-power He-Ne gas laser and a hot thermal source of the same radiating surface area. (a) 1-mW He-Ne laser (=633nm), A=2x10-3cm2, o=633nm =100nm. Note that the laser emits all of the photons in a small solid angle (2x10-6 sr) compared with the 2 solid of the thermal source.

We see also from figure 7 that the He-Ne laser emits 1016 photons/s into a very small solid angle of about 2X10-6sr. whereas the thermal emitter, acting as a Lambertian source, radiates 109 photons/s into a forward, hemispherical solid angel of 2 sr. If we were to ask how many thermal photons/second are emitted by the thermal source into a solid angel equal to that of the laser, we would find the answer to be 320 photons/s: The comparison between 1016 photons/s for the laser source and 320 photons/s for the thermal source is now even more dramatic.

Types of lasersGas Lasers Gas lasers are the workhorses of the laser industry. They range from the powerful industrial carbon dioxide units to the ubiquitous helium-neon lasers of modest powers. They can be operated continuously or on a pulsed basis: their output frequencies range from the ultraviolet to the infrared. Depending on the nature of the active medium, three types of gas lasers can be distinguished: atomic, ionic, and molecular.

Although several different excitation mechanisms have been employed for pumping them, most gas lasers are excited by means of an electric discharge. Electrons in the discharge are accelerated by the electric filed between a pair of electrodes. As the electrons collide with the atoms, ions, or molecules of the active medium, they induce transition to higher energy states. With sufficient pumping, a population inversion is created.

Atomic Lasers The principal example of a laser that utilizes a transition between energy levels of non ionized atoms is the helium-neon laser. The lasing medium is a mixture of ten parts helium to one part neon. Only the energy levels of the neon atom are directly involved in the laser transition: the helium gas is present to provide an efficient excitation mechanism for the neon atoms. Most helium-neon lasers are excited by a direct-current (de) discharge, created by placing a high voltage across a gas-filled space (see figure 1). The helium atoms are easily excited by electron impact to any one of several low-lying metastable energy states.

Figure(1): Simple components of He-Ne gas laser. Micrometer adjusting screws for making the mirror planes highly parallel are not shown.

The neon atom, having six more electrons than the helium atom, has an extremely complicated distribution of excited states. Tow of its higher energy states have almost exactly the same energy as two of the metastable helium states. With the energy much so close, a collision between a helium atom and a neon atom can result in the efficient transfer of energy from the metastable helium atom to the unexcited neon atom. The helium atom returns to its ground state upon-excitation of the neon atom into its excited state. A collision that results in this type of energy transfer is called a resonant collision. A diagram of the energy states for helium and neon is shown in fig. 2.

The helium excited states are identified by combinations of latter and numbers. 21S and 23S, which specify the total angular momentum and spin of the tow electrons in the excited atom. The neon excited states are identified by the quantum numbers of the single excited state electron. (The other nine electrons in the neon atom retain their ground-state quantum numbers. ) As noted earlier.

Figure (2): Energy level diagram of helium-neon laser system

These numbers determine the probability of a given transition. For example, a quantum mechanical calculation shoes that the transitions between the neon s states (e.g.,5s 4s) are forbidden . The helium atoms are excited to metastable levels 21S and 23S by direct electron impact. The helium atoms then collide with the unexcited neon atoms and the neon atoms are raised to the 5s and 4s states. These states have longer lifetimes than the lower-energy 4p and 3p states. Thus the 5s and 4s states are pumped by the metastable helium atoms, while the 4p and 3p states are depleted because of their short lifetimes.

An inversion of the population between the s and p states results, and amplification by stimulated emission occurs. The population inversion is increased substantially if the excited neon atoms are allowed to collide with the walls of the chamber confining the discharge. The collisions allow non-radiative transitions* to take place between the 3s and ground states of the neon, atom : these transitions prevent *A transition in which deexcitation is not accompanied by an emission of radiation is said to be nonradiative. The stored energy is given up by the atom to its surroundings as thermal motion: or in the case of a molecule, the energy may be converted to molecular vibrations.

a buildup of neon atoms in the lower excited states and a subsequent reduction in the population inversion. It is because of this particular depopu lation mechanism that one cannot increase the output power of a He-Ne laser by increasing the tube cross section. The reason is that any increase in the radius of the bore, the cylindrical region to which the discharge is confined, beyond a certain value reduces the population inversion and thus the overall gain of the laser.

There are many more laser transitions in the He-Ne laser than we have shown in Fig. 2. Each of the energy states of neon shown as bars in the diagram) is split into several sublevels. Each sublevel can serve as the initial or terminal level for several different laser transitions, producing the 130-plus stimulated emission lines that have been observed in neon. All of the lasing lines can be produced in a discharge of pure neon. However, the output of many lines is greatly increased by the resonant collision pumping described.

Both the 633nm and the 3.39 m transitions start with the same upper energy state (5s). The 3.39 m (infrared) transition has a much higher gain than the 633nm (visible red) transition and can deplete the 5s level, reducing or eliminating completely the visible output of the laser. Several techniques can be employed to discriminate against the 3.39 m transition and to encourage the 633nm transition:

1- In the method most commonly employed, the laser mirrors are designed to be highly reflective at 633nm but highly transmissive at 3.39 m. The round-trip gain at the visible wave transition can then be satisfactorily high, while at the same time the gain for the infrared transition never reaches threshold. 2- Another technique consists of placing small magnets along the length of the laser tube, thereby creating an inhomogeneous magnetic field. The magnetic field produces a splitting (Zeeman splitting) of certain spectral lines in several components. It is possible to show that the gain per unit length at the lasing transition is inversely proportional to the linewidth. The zeeman splitting broadens the infrared 3.39 m laser line more than the visible line, decreasing its gain, so that the visible transition is favored.

Molecular lasers From the standpoint of potential industrial applications, the carbon dioxide laser unquestionably ranks first. The CO2 laser offers both high power and high efficiency at an infrared wavelength. Carbon dioxide lasers have been used to weld metals, cut ceramics, and perform many other materials-processing tasks. The CO2 laser is the most important example of the class of lasers referred to as molecular lasers. Thus far in our discussion, the energy levels of interest for laser transitions have been electronic energy levels of an atom or an ion. Molecules have a more complicated structure and have energy levels that correspond to rotating-or vibrating motions of the entire molecular structure.

The carbon dioxide molecule, composed of two oxygen atoms and a carbon atom between them, undergoes three different types of vibrational oscillation, as shown in fig. 3 These three fundamental vibrational configurations are called vibrational modes (not to be confused with the modes of the laser cavity). According to quantum theory, the energy of oscillation of a molecule in any one mode can have only discrete values, just as the energy of an electron in an atom is quantized. The discrete values are all integer multiples of some fundamental value. At any one time, a carbon dioxide molecule can be vibrating in a linear combination of the three fundamental modes.

The energy state of the molecule can then be represented by three numbers (ijk). These numbers represent the amount of energy, or number of energy quanta, associated with each mode. For example, the number ( 002) next to the highest energy level shown in fig. 4 means that a molecule in this energy state is in the pure asymmetric stretch mode with two units of energy (i.e. no units of energy associated with the symmetric stretch or bending mode). In addition to vibrational states, rotational states, associated with rotation of the molecule about the center of mass, are also possible.

The energies associated with the rotational states are generally small compared to those of the vibrational states, and are observed as splittings of the vibrational levels into a number of much finer sublevels. The separations between vibrational - rotational states are usually much smaller on the energy scale than separations between electronic states.Figure (3): Vibrational modes of CO2 molecule

Figure (4): Energy-level diagram for the CO2 laser.Pumping occurs to the higher energy levels (not draw to scale). Bands shown contain numerous discrete rotational levels.

The radiation associated with the energy difference between electronic transitions is usually visible or ultraviolet, whereas the vibrational-rotational transitions are in the near and far infrared. For this reason, most molecular lasers have infrared outputs. The various low-lying energy levels of the CO2 molecule that are responsible for the laser transitions are shown in Fig. 4. Each group of lines represents a different vibrational energy levels: each individual line represents a different rotational energy level.

In the CO2 laser, molecules are pumped from the ground state to higher energy states (out of the diagram) from which they trickle back by radiative and nonradiative processes to state (001), which is metastable. With sufficient pumping, a population inversion is produced between the (001) state and the (100) and (020) states. If the losses in the laser cavity are sufficiently low, laser oscillations begin. The strongest line of the CO2 laser is at a wavelength of 10.6 m, in the infrared. A weaker line at 9.6m competes with the 10.6 m line for the available excited molecules.

For improved laser output, nitrogen and helium are generally added to the gas mixture (approximately 10 percent CO2, 40 percent N2, and 50 percent He). The nitrogen in the CO2 discharge takes the role that helium plays in the helium-neon and metal vapor lasers: excited nitrogen molecules transfer energy to the CO2 molecules by resonant collisions. The helium serves to increase the laser efficiency by speeding up the transition from the (100) energy level, the receiving end of the 10.6 m laser transition, to the ground level, thereby maintaining a large population inversion.

Carbon dioxide lasers are capable of producing tremendous amounts of output power. Primarily because of the high efficiency of the 10.6 m transition. A well- constructed system can achieve an efficiency of about 30 percent, as compared to less than 0.02 percent for helium- neon laser. Gigawatts of peak power have been obtained in short nanosecond- duration pulses. The principal difference between the CO2 laser and other gas lasers we have discussed is that the optics must be coated or made of special materials so that they are reflective or transmissive in the infrared.

If the cavity has external mirrors, the plasma tube usually has Brewster-angle windows fabricated from germanium, cadmium sulfide, or, in the case of high power systems, from sodium chloride or potassium bromide. These materials are transparent at 10.6 m, a region where most other materials, including glass, are opaque. The optical resonator itself is provided with a pair of long radius-of-curvature mirrors, with multilayer dielectric reflective coating. The output mirror can be made of germanium or gallium arsenide, both of which if cooled have low loss at 10.6 m.

The power supply for CO2 laser must provide a sufficiently high voltage to maintain a discharge with cavity pressure of 10 mm of mercury or more. This voltage, which is about 8 KV per meter of discharge, constitutes a major hazard if not carefully shielded. The power output of a CO2 laser is approximately proportional to the active length of the laser. In attempts to obtain greater output power, researchers have built CO2 lasers tens of meters long with CW output powers ranging to the tens of kilowatts.

Figure (5): Carbon dioxide laser with water cooling jacket, Brewster's window, and rotating mirror for pulsing the output laser beam.

Chemical Lasers

The lasers studied in this chapter are classified primarily on the basis of the state of the active medium (gas, solid, liquid, semiconductor). The term chemical laser refers not to the state of the lasing medium, but to the method of creating a population inversion. In the chemical laser, the excitation is produced by at chemical reaction. Although the chemicals can be in the solid, liquid, or gaseous state, most chemical lasers use gases as the active medium, with an arrangement similar to the gas dynamic CO2 laser just discussed.

Chemical lasers are attractive from several viewpoints: 1- A purely chemical laser, relying on the direct mixing of hemicals to produce coherent light, does not require electronic components or electrical power. 2- Chemical lasers have the potential for higher output power per unit volume and per unit weight than appears possible with electrical excitation. 3- Because the chemical reactions employed excite primarily vibrational states rather than electronic states, most chemical lasers have output power in the near infrared, with wavelengths between the neodymium laser at and the carbon dioxide laser at.

4 - Chemical lasers have produced some of the most powerful laser pulses ever observed. Pulses as large as 4200 joules with a peak power of 200 billion (2 1011) watts have been achieved by a hydrogen fluoride chemical laser. Most of the chemical reactions used in chemical lasers are of the form A+BC AB +C +energy(1) The energy released by the reaction servers to excite the molecule AB, which servers as the active medium. One reaction that has been investigated extensively is the reaction of a halogen with hydrogen or deuterium. e.g.

H+CL2HCL+CL +energy(2) and F+D2DF+D +energy(3)

In general, chemical reactions can be employed successfully in laser systems using several approaches: 1- Chemical reactions can directly produce the radiant energy from the reacting species. with the addition of no external energy.2- Chemical reactions can result in light emission from the reacting species, but external energy may be necessary to initiate or sustain the reaction.3- External energy can be provided to initiate or sustain a chemical reacting that results in the transfer or energy from the reaction species to another species that radiates.

The chemical reaction can provide all the energy, as in type(1),but energy is transferred from one reacting species to another species that emits radiation. Lasers using the latter two approaches, in which the reaction species do not actually participate in the lasing action, are called chemical transfer lasers. The reactions represented by Eqs.(2) are examples of approach (2). Although the chemical reactions produce HCl or DF (the active lasing medium) in the excited state, the dissociation of the hydrogen or fluorine atoms form their initial molecular states (H2 or F2) must be accomplished with an additional energy source, a flash-lamp in the case of reaction (2) or a thermal source in the case of reaction (3).

Another example of approach (2) is the carbon monoxide chemical laser, which emits relatively high power in the infrared. A mixture of helium, air and cyanogen (C2N2) has used to obtain several watts of power in the wavelength range between 5 and 6 mm. In this laser, the gas is flowed through an electric discharge. The helium does not participate in the lasing, but provides resonant transfer of energy, as in the helium-neon laser. The discharge dissociate the (C2N2) molecules and the O2 molecules to form vibrationally excited CO via the reaction (4(

The Ruby Laser The first successful laser, developed by Maiman in 1960, used a single crystal of synthetic pink ruby as its resonating cavity. The ruby is primarily a transparent crystal of corundum (AL2O3) doped with approximately 0.05 percent of trivalent chromium ions in the form of Cr2O3, the latter providing its pink color. The aluminum and oxygen atoms of the corundum are inert; the chromium ions are the active ingredients. As grown in the laboratory, a ruby crystal is cylindrical in shape (see Fig 5). It is cut some 10 cm or so long and the ends polished flat and parallel. In a typical ruby laser one end is highly reflective (about 96 percent), and the other end is close to half-silvered (about 50 percent).

When white light enters a crystal, strong absorption by the chromium ions Cr2O3 in the blue-green part of the spectrum occurs (see Fig. 6). light from an intense source surrounding the crystal will therefore raise many electrons to a wide band of levels as shown by the up arrow at the left. These electrons quickly drop back, many returning to the ground level. However, some of the electrons drop down to the intermediate levels, not by the emission of photons, but by the conversion of the vibrational energy of the atoms forming the crystal lattice. Once in the intermediate levels the electrons remain there for several milliseconds (about 10,000 times longer than in most excited states), and randomly jump back to the ground level, emitting visible red light. This fluorescent radiation enhances the pink or red color of the ruby and gives it its brilliance.

Figure (5): Ruby laser using a helical flash lamp for optical pumpingFig 6. Energy level diagram for a ruby crystal

Fig. 7 Elliptical r for Concentrating light from a source S on a laser L.

Axial Modes of a Laser The optical cavity of a laser is a resonator with extremely high Q (see box) and low losses. If these losses are smaller than the gain in the amplifying medium, threshold is achieved and lasing occurs. But the high-Q condition does not hold for all frequencies within the laser emission line width: only certain frequencies fulfill the resonance conditions, similar to the transmission conditions of the Fabry-Perot interferometer. Thus the laser output spectrum does not resemble the spontaneous emission lineshape, but rather consists of a series of a narrower lines corresponding to the high-Q frequencies of the laser cavity.

To determine the conditions for high Q in a laser, we start with a plane wave of light propagating along a line normal to and between two parallel mirrors. The round-trip distance for a wave undergoing reflection at the mirror is 2L, twice the distance between mirrors. The total phase change, Df, undergone by the wave in traveling a full round trip is equal to 2 times the distance traveled divided by the wavelength

If the reflected wave is 180 out of phase with the original wave and of equal magnitude, then within the cavity there is no net field and therefore no net energy density to stimulate the atoms to emit, even if a suitable population inversion exists. The most useful way of viewing such a situation is to note that the wave has not replicated itself upon reflection. Only at such a frequency that the wave and its reflections are in phase (D f =2q, q an integer) does the wave replicate itself. With replication, the electric fields add in phase. The resultant energy density is sufficient to induce substantial stimulated emission at that frequency.

From an alternative point of view, the mirrors from a resonant cavity in which light energy may be stored by multiple reflections between them. If the waves are replicated in the cavity, then the mirror cavity has a high Q. The condition for a self-repeating field (setting Df=2q in Eq. 1) is that the length of the cavity be equal to an integral number of half -

Q-the quality factorFundamental to discussion of any resonator is the concept of the Q-or quality factor, of the resonator, defined byThis definition of Q is a very general one applies to circuits, mechanical systems, microwave cavities, and laser cavities. A typical oscillating circuit, such as one containing a resistor, capacitor, and inductor, can have a Q of several hundred; a laser cavity can have a Q as high as 105 or 106.

A high-Q cavity stores energy well, whereas a low-Q cavity does not. In addition, we note that a high Q is associated with a small relative linewidth, and a low Q with a large relative linewidth. This relationship between Q and linewidth can be expressed rather simply as wavelengths, or L=q(/2), q an integer. Only at those wavelengths is the cavity resonant. The integer q is in most cases quit large. For example, if the central wavelength is 500 nm (5X10-5cm) and the mirror separation is 25 cm, q has a value of 106.

Since q can be any integer, there are many possible wavelengths within the laser transition lineshape for which the field is self-replicating. We refer to each such self-replicating field pattern as a longitudinal mode, or axial mode, of the cavity. It is easier to refer to these axial modes by their frequency than by their wavelength. Using the condition for the self-replicating field stated above. We have (2)Each mode frequency can be labeled with its corresponding integer, q, with the result

(3)It is at these frequencies that the laser cavity is resonant. By subtracting the frequency of one cavity mode from that of its nearest neighbor, we find that the separation between mode frequencies isor(4)

The separation between longitudinal mode frequencies is seen to be the same as the free spectral range of a Fabry-Perot interferometer with plate separation L . Note that the separation between neighboring modes is dependent only on the separation between mirrors and is independent of q. If we use values from our example above, the separation between neighboring resonance frequencies for a typical laser (25 cm long) is calculated to be(5)

Many laser transition lines much broader than 600 MHz, and thus there can be many axial modes (q-2, q-1, q, q+1, q+2) within the broadened linewidth. Since sustained laser action can occur only at those frequencies within the lasing transition for which the cavity is resonant, the output of a laser contains a number of discrete frequencies, separated by c/(2L), as shown in Fig. 1. These frequencies are called the axial mode frequencies of the laser.

Figure (1): The combination of the lasing transition lineshape with the resonant cavity modes gives the resulting output of a laser. Only when the Q of the cavity is high can lasing occur.

Examining the Mode Structure of a Laser The longitudinal mode structure of a laser output can be investigated with a Fabry-Perot interferometer. The experimental arrangement is shown in Fig. 2. You may know that there are many frequencies, spaced c/2d apart, transmitted by the interferometer when its plates are spaced a distance d apart. To block all extraneous light at frequencies other than in a narrow region about the laser line, we insert a narrowband filter between the laser and the interferometer. The spacing of the plates is then adjusted so that the free spectral range of the interferometer exceeds the linewidth of the laser.

The transmitted light is focused by a lens onto a screen, where a pattern of concentric circles can be seen. A pinhole in the screen is positioned at the center of the pattern: light of one frequency passes the screen whereas other frequencies are blocked. As the spacing of the mirrors is changed, the frequency illuminating the pinhole changes. If d is changed in a continuous manner, the frequency passed by the pinhole is swept through the range of frequencies, which includes those of the laser line. A photomultiplier detector measures the amount of light transmitted at the different frequencies.

An increase in signal occurs whenever the Fabry-Perot resonance scans through a frequency component of the laser output. The output of the detector is plotted as a function of time, the observed result is a series of lines within the broadened transition lineshape, as sketched in Fig. 1. Each of these lines corresponds to a different axial mode, or q-value, of the laser. Knowing the interferometer scanning rate, one can verify that the frequency separation Dn between these modes is c/2L, where L is the distance between laser mirrors, in agreement with the analysis above.

Fig. 2 Experimental arrangement for observing the longitudinal (or axial) mode characteristics of a laser. Light from the laser is filtered to remove all but the laser light. The separation between the Fabry-Perot interferometer mirrors is changed by applying a sawtooth voltage to a piezoelectric transducer (PET) attached to one of the mirrors. The change in separation d changes the transmission frequency of the interferometer. The transmitted light is focused onto a pinhole in a screen and detected by a photomultiplier tube (PMT). The output of the PMT is displayed on an oscilloscope. The oscilloscope trace displays the frequency spectrum of the laser.

Modifying the Laser Output Selection of laser emission lines: interacavity elements Many lasers can lase in several emission lines simultaneously. Here we are speaking not of the multiple-mode structure beneath a single broadened emission line, but of several of these lines spaced across the spectrum. While this multiple-line emission may provide high-power output, there are cases where a higher degree of monochromaticity is desired. In these cases, a wavelength-dependent element, which disperses or absorbs the light according to its colors, is introduced into the cavity. This element can be a prism, a grating, or a filter.

The action of these elements can be demonstrated by the example of an intra-cavity prism. The arrangement is shown in fig.3. We assume that three wavelength 1,2 and 3, are undergoing amplification by stimulated emission, with 1< 2< 3 . The shorter wavelengths suffer greater refraction by the prism than the longer wavelengths. One beam, at 2 , is directed normally to the end mirror and then retraces its path back into the laser tube. Rays at other wavelengths do not retrace their paths exactly and, consequently, experience additional loss. Only for light in a small wavelength rang about 2 are the losses smaller than the available gain. By using a properly cut prism, the angles of incidence can be set at the Brewster angles, reducing the losses due to reflection at the prism surface.

Figure (3): Intra-cavity prism for wavelength selection. The prism disperses the light so that only one ray, at l2, is reflected back into the active medium, and lasing occurs only at the selected wavelength.

SINGLE-MODE OPERATION The linewidth of a single laser mode is far smaller than the broadened transition linewidth: in some cases smaller than the linewidth due to the natural lifetime of the excited state. Since an inhomogeneously broadened laser can support many longitudinal-transverse modes simultaneously. Single-mode output can be achieved only by assuring that one mode has a gain higher than all the others. There are several methods for obtaining single-mode output, two of which we discuss here:

1) Let us ensure that the cavity supports only a single transverse mode, the TEM00 mode, by placing apertures in the laser cavity as we discussed earlier. Once this single transverse mode has been obtained, the problem is to eliminate all but one of the axial modes. One way to achieve single axial-mode operation is to design the cavity so that only one axial mode is possible within the laser transition line-width. If the mode corresponding to q0 is within the transition linewidth and those corresponding to q0+1 and q0-1 are outside it, as shown in fig.4. then only the TEM00q0 mode will lase.

For this to occur, the distance between cavity modes,c/2L. must be somewhat greater than the broadened linewidth. Since we cannot control the width of the lasing line., we must construct the cavity in figure (4): The "short cavity" method of single-moding a laser. If the length of the laser cavity is reduced to a length that yielding a cavity mode separation somewhat greater than the line width, only one cavity mode can lase.

such a manner that c/2L is larger than the laser linewidth.If we make the distance between mirrors sufficiently small so that only one mode is supported, we produce a single mode laser. The drawback of this method is that the active length of the laser is also small, severally limiting the power output.

2) Another method for obtaining increased single axial-mode output from a TEM00 laser is to introduce large losses for all but one of the modes. This can be done by introducing a small fixed-spacing Fabry-Perot cavity within the laser cavity, as illustrated in fig. 5. The additional cavity consist of a special piece of glass, called an etalon, that has two faces ground and polished to a high degree of parallelism. The etalons cavity differs from the laser cavity in two important respects.

First, the etalon surfaces are either uncoated or lightly coated, and their reflectivity is thus quite low. Because of this low reflectivity, the etalon cavity resonances are broader than the laser cavity resonances. Second, the etalon cavity is much shorter than the laser cavity, and the separations between etalon resonant frequencies are therefore much larger than those between the laser resonant frequencies.

The etalon, in effect, makes slats in the picket fence unequal: Some cavity resonances have a higher loss than others. The laser tends to lase in that single mode with the smallest loss. This single-mode selection is illustrated in fig. 6. As much as 75 percent of the power distributed over all the axial modes present before the etalon is inserted can appear in this single mode in a typical laser. If the etalon is tilted with respect to the optic axis, the frequency of the etalon resonance shifts within the lasing transition linewidth. A different laser cavity mode becomes the high-Q mode, and lasing occurs at the corresponding new frequency. It is thus possible to tune the frequency of the laser over a narrow frequency band by merely tilting the etalon.

Figure (5): The "etalon" method of single modeing a laser. Introduction of a piece of glass with parallel face (the etalon) into the cavity renders the Q of the cavity modes unequal. Only the highest Q mode lasers

There are more complicated methods of obtaining single-mode output for inhomogeneously broadened laser transitions. Those we have discussed give some idea, however, of how a single laser mode is obtained and emphasize the importance of understanding the concept of laser modes.

Figure (6): The "etalon" method of single modeing a laser. The box on the right illustrates the Q versus frequency for the laser cavity and or the etalon cavity. Their combined Q versus frequency is shown in the middle curve. The combination of the lasing transition and single high-Q mode results in a single-mode laser output.

Applications of LaserI- Laser in IndustryI.1- LASER WELDING In the basic welding process two metals (which may be the same or dissimilar) are placed in contact and the region round the contact heated until the materials melt and fuse together. Enough heat must be supplied to cause melting of a sufficient volume of material but not enough to give rise to significant amounts of vaporization, otherwise weak porous welds are produced. With most metals the reflectance decreases dramatically as the temperature approaches the melting point (see Fig.1) so that care needs to be taken in controlling the amount of incident laser energy.

It is also evident that the problems associated with vaporization will increase if the two materials have widely differing melting points.

Laser welding has to compete with many well-established techniques such as soldering, arc welding, resistance welding and electron beam welding. Laser welding has, however, a number of advantages, for example:

(1) there is no physical contact with external components;

(2) the heating is very localized(3) dissimilar metals can be welded;(4) welding can be carried out in a controlled atmosphere with the workpiece sealed if necessary within optically transparent materials.

Fig. 1. Schematic variation of absorption with temperate for a typical metal surface for both YAG and CO2 laser wavelengths.

Welding is normally carried out using a shielding gas. This is an inert gas, usually argon or helium, which is applied to the welding area via a nozzle concentrically placed with respect to the laser beam (Fig. 2). The main purpose of the shielding gas is to cover the weld area and eliminate oxidation, which results in a poor weld. It also helps to remove any metal vapor that may be formed (and that may deposit on the focusing lens). If metal vapor is produced it may be hot enough for ionization to take place and thus form a plasma above the metal surface. This is often highly absorbent at the laser wavelength and can prevent some, or in extreme cases all, of the laser energy reaching

Fig.2 Schematic beam focusing head design for laser welding when using a shielding gas.the surface. For medium- to low-power lasers argon is often used as the shield gas, as it is less expensive than helium but can itself ionize in the presence of high-power pulsed beams. In such cases helium or a mixture of helium and argon may be used.

Both CW and pulsed lasers can be used in welding. For situations where only a small spot weld is required a single pulse from a pulsed laser may be sufficient. If a continuous weld is required, however, the beam is moved across the workpiece. The CW laser produces a continuous weld, while the pulsed laser produces a train of spot welds, which may overlap (and hence produce effectively a continuous weld) or be separated, depending on the scanning speed. Figure 3 shows how weld penetration depends on beam scanning speed at various power levels in 304-type stainless steel. The actual joint geometry itself can exert a strong influence on the thickness of material that can be welded. Close-fitting joints are desirable since there is usually little time for the molten metal to flow to any extent.

In any case only small amounts of liquid are present, mainly because the heating is usually very local. Figure 4 shows some typical joint designs suitable for laser welding.welding speed (mms-1)Fig. (3) Typical variation of weld penetration with welding speed observed in stainless steel for various CO2 laser powers.

Fig.(4) Two geometries suitable for laser welding (a) the butt join; (b) the lap join.

I.1.1 Deep penetrating welding When using a multikilowatt CW or pulsed-mode laser the welding process becomes somewhat more complicated than just the simple diffusion of heat away from the surface considered hitherto. When a high-power beam initially strikes the surface a significant amount of material may be vaporized, forming

Direction of travel (workpiece)Fig. (5) Formation of a keyhole during high-power laser welding.

a small hole known as a keyhole. Laser energy that subsequently enters the hole is trapped and carried deeper into the material than would otherwise be the case. Figure 5 illustrates this process when a CW laser is being used. Pulsed CO2 lasers can also make efficient use of this process by employing a pulse consisting of a very high-power initial spike of duration about 100ms followed by a much lower irradiance for the remainder of the pulse (Fig.6). Such a pulse shape can be obtained by controlling the discharge current in the laser. The peak power during the spike is sufficient to create the initial keyhole but during the rest of the pulse there is insufficient power to cause further vaporization.

The material round the keyhole melts, however, and fills in the hole. Since the absorption of energy within the keyhole is not very dependent on the condition and type of metal surface this type of action enables materials with high melting points to be welded. CO2 lasers are now available with CW powers of tens of hundreds of kilowatts and consequently it is possible to weld steel plates of up to several tens of millimeters thick at rates of some meters/minute. It has thus become possible to contemplate the use of laser welding in heavy industrial situations such as shipbuilding.

Fig(6). idealized laser pulse shape for efficient keyhole welding