Surface Engineering of Metals - Principles, Equipment and Technologies Part 5 pot

3.4.4 Surface phenomena The occurrence of surplus free energy of particles making up the surface, i.e., ofsurface energy, their greater activity and changed orientation, as well as struc

pressure) equals zero because in such conditions the difference between phasesfades, hence an atrophy of the surface follows [8].

Surface energy should not be understood as the energy of the atoms andmolecules forming that surface Such understanding is erroneous becausethe energy of molecules forming the surface rises with the rise of the tempera-ture while surface energy drops and at critical temperature assumes zerovalue [8]

In the case where the elements that go to make up the body have thepossibility of free movement, as in liquids, such a body will tend to mini-mize its surface, i.e minimize its energy-rich zone This is caused by theinteraction of the molecules of the body situated inside the body on thosemolecules which are situated in the surface layer, and directed into thecore of the body from the surface The tension thus created at the surface

of the liquid is called surface tension Hence, the measure of surface

ten-sion - from the mathematical standpoint - could be the force per unitlength or the surface energy of a unit area Similarly to surface energy,surface tension in solids changes with a change in temperature and in thecritical state equals zero [3]

The term “surface tension” suggests that there exists a real state of tensionbetween surface molecules and even - as assumed in models - that in the surfacezone there exists something in the form of a flexible membrane [3]

3.4.4 Surface phenomena

The occurrence of surplus free energy of particles making up the surface, i.e., ofsurface energy, their greater activity and changed orientation, as well as struc-tural and chemical differences between the surface, the underlying matrix andthe surrounding medium, cause that the physical surface is the site of severalcharacteristic phenomena Generally, these are connected with the spontane-ous tendency to reduce the surface energy, proportional to the surface area onwhich they occur

Of special significance are surface phenomena occurring in highly persed (colloidal) systems These are the generation of colloidal systems bycondensation or dispersion, joining of droplets or tiny blisters in emulsions,mists and foams (coalescence), the coagulation of the dispersed phase and itsgeneration due to the presence of three-dimensional structures (chains andnets) These phenomena also affect the thermodynamic equilibrium of phases

dis-in well developed surfaces [6]

The solid is a material object, rigid and reacting with resistance tostresses It can be said that under the influence of applied forces, the solidundergoes some elastic deformation and that its shape is determined more

by its “past history”, i.e., by the method of its preparation, than by the forces

of surface tension The surface of crystalline bodies differs from that of liquid

in that the components of its structure have only limited freedom of ment It is assumed that at ambient temperature, surface molecules are sim-ply imprisoned in the crystal lattice and have no freedom of movement Thegrowth of their mobility is caused by extraneous factors, e.g., rise of tempera-

move-ture When heating up a solid to melting point, the mobility of surface atomsdramatically rises, followed by enhanced diffusion of these atoms in the di-rection of the inside; finally, there is some movement toward the surface,caused by evaporation [6] At temperatures where some atom mobility oc-curs, there is a tendency to equalize energy in those zones in which it achieveshigh values, i.e, in places with enhanced curvature, crystal corners,microcrevices, etc By way of example, if a silver or copper sphere is placed

on a flat surface, made of the same material, at a temperature close to meltingpoint, the gap between the sphere and the flat surface will become filled.Thus, in practice, the surfaces of solids are sufficiently “plastic” to be able to

“flow”, albeit very slowly, in certain conditions The mobility of surface oms at temperatures close to the melting point is utilized in such technologi-cal processes as sintering or diffusion welding [9]

at-In the liquid - gas system, such as water and water vapour, at room perature, for each 1 cm2 of water surface, 3·1021 new molecules reach thesurface during each 1 s but the same number departs from it Thus, it is avery turbulent state The time of dwell of one molecule at the surface is of theorder of a microsecond In the said system there also occurs an exchange ofmolecules between the surface zone and the adjoining layers of the liquid Thediffusion coefficient of the majority of liquids is of the order of 10-5 cm2/s Amolecule reaches the depth of 10 nm in a time of approximately 10-6 s [6]

tem-It follows that the exchange of molecules between the surface and theadjoining zone of volume phase is very rapid Thus the apparently “still”water, and, more generally, liquid, is in a state of turbulent movement atthe molecular level [3]

On the other hand, in the case of a metal of low volatility, such astungsten (with a high melting point: 2400…C), whose vapour pressure at am-bient temperature is estimated at approximately 10-43 hPa, the number ofatoms colliding with the surface is approximately 10-20 per cm2·s, while theaverage dwell time of an atom at the surface is approximately 1037 s Even formetals with higher volatility (with relatively low boiling points) these times atroom temperature are very long Thus, in reality the molecules of a solid at itssurface are quite immobile when considering changes at the surface duringevaporation and condensation [3]

At temperatures above 0.75 of the melting point (temperatures at whichsintering and diffusion welding processes are carried out) dwell times of at-oms at the surface may be very short For example, copper at 725…C has avapour pressure of the order of 10-6 Pa It follows that the dwell time of atoms

at the surface is of the order of 1 s The general picture of the phenomenon issimilar when diffusion rate is considered In the case of copper at 725…C thecoefficient of self-diffusion in the volume phase is approximately 10-11 cm2/s.The time needed to move an atom to a depth of 10 nm is 0.1 s At room tempera-ture this time would be 1027 s

From the examples quoted here it stems unequivocally that the movement

of atoms at the surface of the solid depends on temperature and that forsolids at room temperature the picture of the surface zone is quite differentfrom that of the surface of a liquid where a very turbul+ent movement ofmolecules crossing the interface takes place And it is because of the fact that

surface molecules of solids are practically immobile in normal conditions, thesurface energy and other physical properties of the surface depend to a largeextent on the “history” of the given substance For instance, a fresh fracturesurface (a cleaved surface of the crystal) of a brittle substance will have a differ-ent surface energy than a surface prepared by grinding, polishing or by thermo-chemical treatment [6].

At the solid surface, besides the already mentioned surface mobility ofatoms, there also occur effects of cohesion, adhesion, wetting, activated andchemical adsorption and propagation of the formed surface layer across theabsorbing surface These are accompanied by two-dimensional migration ofatoms and particles, i.e., two-dimensional diffusion, friction, corrosion, nucle-ation of new phases, condensation, and crystallization, capillary and electro-capillary effects, electro-kinetic, temperature and thermoelectronic emissionand many others [6]

Among the group of surface phenomena are those which occur withinthe multi-phase solid at interfaces (phase boundaries), formed as the re-sult of defects of the crystalline lattice, during deformation (slip planes)and chipping of solids, causing the exposure of new surfaces, nucleation

of new phases, etc The dimensions and properties of interfaces, selves dependent on the type of particles and their surface structure, affectthermal and mass exchange processes, i.e., the transport of substance fromone phase to another by diffusion Other such processes include: dissolu-tion, evaporation, condensation, crystallization, multi-phase chemical pro-cesses, such as intercrystaline and stress corrosion, multi-phase catalysisand others [6]

them-The knowledge of surface phenomena and purposeful exertion of fluence on them enables the shaping of properties of surface layers

in-References

1 Szulc, L.: Structure and physico-chemical properties of treated metal surfaces (in Polish) Special

edition by Warsaw University of Technology, Warsaw, September 1965.

2 Kolman, R.: Mechanical strain-hardening of machine part surfaces (in Polish) WNT, Warsaw

1965.

3 Burakowski, T., Roli nski, E., and Wierzchon, T.: Metal surface engineering (in Polish)

War-saw University of Technology Publications, WarWar-saw 1992.

4 Kaczmarek, J.: Fundamentals of machining, abrasive and erosion treatment (in Polish) WNT,

8 Hebda, M., and Wachal, A.: Tribology (in Polish) WNT, Warsaw 1980.

9 Izycki, B., Maliszewski, J., Piwowar, S., and Wierzchon, T.: Diffusion welding by pressure (in

Polish) WNT, Warsaw 1974.

chapter three

Laser technology

3.1 Development of laser technology

The history of laser technology is over 40 years old; lasers have been knownfor over 30 years and used in practical applications for more than 25 years.The scientific basis of laser technology lies in the realm of atomic physics,more strictly speaking, foundations were laid by the Danish physicist NielsBohr (1913 - theory of the structure of the hydrogen atom) and the GermanAlbert Einstein (1916 - introduction of the concept of stimulated emission)[1, 2]

In 1950, A Kastler from France proposed optical pumping (creation ofchanges in the distribution of filling of different atomic energy levels as aresult of excitation by light radiation) which earned him the Nobel Prize

In 1954, Townes, together with co-workers J Gorgon and H Zeiger,applied the concept in practice, utilizing ammonia as the active mediumand building the world’s first wave amplifier in the microwave range (emit-

ting radiation of wavelength 12.7 mm) which they called maser This term is

derived from the acronym of Microwave Amplification by Stimulated Emission of

Radiation [1].

In 1958, Ch H Townes and A L Schavlov predicted the possibility ofbuilding a maser for light radiation but the first attempt at its construc-tion in 1959 was unsuccessful [5] In 1981, A L Schavlov received theNobel Prize in physics for his overall contribution to the development oflasers [2]

It was only in May of 1960 that a young American physicist, T H Maiman,working in the laboratory of Hughes Research Aircraft Co., built the world’s

first maser, operating in the range of light radiation, initially called optical

maser The name was changed later to laser (Light Amplification by Stimulated

Emission of Radiation) This was a pulse ruby laser, generating visible radiation

of red color (of wavelength l = 0.694 µm) [1-10].

The construction of a laser based on the ruby crystal initiated the called solid crystal laser series In 1961 F Snitzer constructed the first laser

so-on neodymium glass and three years later, a young physicist,I.E Guesic, together with his co-workers at the Korad Department Labo-ratory in the US, implemented the first laser based on an Nd-YAG crystal,

emitting short-wave infrared radiation (l = 2.0641 µm) [8].

The first gas laser operating continuously, in which a mixture of heliumand neon replaced ruby as the active medium, was built in the Bell Tele-phone Laboratories in the United States in 1961 by A Javan, W.R Bennet Jr.and D.R Herriote, according to a suggestion published two years earlier by

A Javan This is today the most popular type of laser [5, 8]

In 1962, F.J McClung and R.W Hellwarth from Hughes Aircraft ratory (US) implemented the operation of the first laser with an activebandwidth modulation which later made possible the obtaining of high

Labo-power and very short duration laser pulses, so-called gigantic pulses [5].

In 1964, the American physicist C.K.N Patel, working at the Bell phone Laboratories built the world’s first gas laser based on carbon diox-

Tele-ide, emitting continuous infrared radiation of wavelength l = 10.59 µm,

which later found greatest application in industry [5]

The first excimer laser of the ultra-violet range (xenon, with a

wave-length l = 0.183 µm) was made in 1972 (H.A Köhler et al.); nine years

earlier, in 1963, the first nitrogen-based gas laser emitting UV radiation wasbuilt by H.G Hard [5]

From the moment of invention of the first laser, a tumultuous ment of laser technology has taken place, recognized, not without reason,

develop-as one of the foremost achievements of our times in the field of science andtechnology As a result, today there are several hundred different designs

of lasers, i.e., quantum optical generators of almost coherent electromagneticradiation for a spectrum range from UV to far IR [11]

Lasers have found application in many domains of everyday life andtechnology, where they have proven themselves to be of priceless service.They are successfully utilized in medicine, surveying and cartography, inrocket and space technology, in military and civilian applications To thisday, unfortunately, what triggers their further development are militaryrequirements In such applications as the so-called star-wars, lasers are to

be the basic weapon destroying the enemy’s weaponry (satellites, cosmicvehicles and rocket heads) Laser designs of very high pulse power orenergy are known [11]

Somewhat overshadowed by these applications, although with equalintensity, we observe the development of design and application of lasers

for industrial purposes, so-called technological lasers These are mainly

lasers operating with carbon dioxide as the active medium [11]

Technological lasers allow continuous operation or by repeated or singlepulses of extremely short duration, i.e., within 10-3 to 10-12 s They enable highprecision delivery to selected sites of treated materials of great power densi-ties (up to 1020 W/m2), power of the order of terawatts, energy of hundreds ofkilojoules and heating rates up to 1015 K/s [6]

It is estimated that in 1985, the industries of different countries of theworld employed over 2000 technological lasers, of which approximatelyone third found application in the metal industry [11].

3.2 Physical fundamentals of lasers

3.2.1 Spontaneous and stimulated emission

All atom systems which go to make up the bodies surrounding us, aswell as ourselves, exist in certain quantum states, characterized by givenvalues of energy, in other words, by given energy levels Each change of

this state can only take place in the form of a non-continuous jump

tran-sition of an electron from the basic state to the excited state or reverse,

which is accompanied by absorption or emission of a strictly defined tion of energy The smallest such portion by which a system may change

por-its energy is called quantum (from the Latin quantum, meaning: how much).

Lasers utilize electron transitions between energy levels of particles - oms, ions or particles which form solids, liquids and gases Transitions ofelectrons are accompanied by changes of the energy level of the atomsystem

at-Fig 3.1 Diagrams showing emission and absorption of energy: a) in an atom; b) in a

set of atoms (Fig a – from Oczoœ, K [2] With permission.)

The simplest quantum system is the two-level one, i.e., such a microsystem

in which processes of emission and absorption of radiation take place

be-tween two discrete energy levels: basic (level 1 with energy E 1) and excited

(level 2 with energy E 2) (Fig 3.1) For simplification it can be assumed thatenergy levels are infinitely narrow, although in real systems they have adefined width

The transition of such an isolated quantum system from one energy

level to another may be of a radiant nature, in which case the energy

absorbed or emitted by the quantum system takes the form of electromagneticradiation.

The transition of such a quantum system but one that is part of a set of

other quantum systems, from one level to another, may also be of a

non-radiant nature, in which case the absorbed or emitted energy is passed

over to a different atom system Such non-radiant transitions of ation are those occurring with the exchange of energy between particles

relax-of gases, liquids or solids and they are accompanied by a change in perature

tem-In accordance with the basic quantum correlation, established in 1913

by N Bohr, radiant transitions obey the rule:

(3.1)

where: h ν - value of a quantum of radiation (infra-red, visible, ultraviolet,

X-ray, gamma); E 2 - E 1 - difference in energy levels, between which quantumtransition occurred; h - Planck’s constant (h = 6.62517·10-34 Js);

ν - frequency of emitted or absorbed radiation, Hz; λ - radiation

wave-length, µm; c - rate of propagation of light in vacuum (speed of light) c =

2.998·108 m/s

The transition of a system from a lower energy level E 1 to a higher one

E 2 occurs after delivery, from an external source, to the system of a

quan-tum of radiation (photon, from Greek phos - light) of h ν value The system

absorbs the delivered energy and absorption transitions take place.

When the system undergoes a transition from a higher energy level E 2

to a lower one E 1, it gives off (emits) its surplus energy in the form of a

quantum of radiation, the value of which is h ν In such conditions,

emis-sion transitions take place.

If the level of energy in the quantum system considered is the lowestpossible, as shown in Fig 3.1, it is termed basic level (or state) Any other

level, e.g., E 2 is an excitation level (or state).

When an excited electron finds itself at an energy level which is higherthan basic, there always occurs the natural tendency to spontaneous tran-sition to the basic level which is the stable state of the system Naturally,such spontaneous transition is accompanied exclusively by the emission

of a quantum of radiation This effect is termed spontaneous emission.

In the case of a set of different atomic systems, with different numbers

of electrons orbiting atomic nuclei at different levels, atrophy of tion of atoms or particles is of a random character Photons are emitted byparticles independently and, besides, different particles emit radiation of dif-ferent frequency, corresponding to different wavelength This is chaotic ra-

excita-diation, non-coherent with relation to either itself, time or space For a

given body it depends only on the degree of excitation, which itself pends mainly on body temperature The spectrum of such radiation bears

de-a continuous chde-arde-acter de-and is described by the Stefde-an-Boltzmde-ann de-and Plde-ancklaws This is the manner in which radiation is emitted spontaneously by allbodies, including light sources.

In lasers, however, the emission which is utilized is not spontaneousbut stimulated, although in all quantum effects spontaneous emission plays

a significant role This is manifest in the so-called background noise Itinitiates the processes of amplification and excitation of vibrations and -together with non-radiant relaxation transitions - it participates in theformation and sustaining of a thermally unstable state of generation [6].Stimulated emission always accompanies absorption and spontaneousemission because if it did not, it would be impossible to reach the state ofthermodynamic equilibrium of many particles emitting and absorbing ra-diant energy [8]

In a set of atomic systems subjected to electromagnetic radiation of afrequency determined by eq (3.1), two mechanisms of interaction of thephoton (quantum of energy) with the particle may take place:

– if the particle is at a lower energy level - the particle passes to ahigher level as the result of absorption of radiation [2];

– if the particle is already at a higher (excited) energy level - under theinfluence of an external stimulus (collision with a photon), the excitedparticle returns to its basic state: the electron drops to the basic energylevel (to an orbit closer to the nucleus), emitting a photon of same energy

hv as the falling photon (Fig 3.2); this is the so-called resonance tion.

stimula-Fig 3.2 Diagram showing forced emission of quanta of radiation - photons (From

Oczoœ, K [2] With permission.)

This process is named stimulated emission Instead of one photon

entering an excited atomic system, two photons of equal energy (equalfrequency of corresponding wavelength) exit the system A process of

amplified radiation thereby occurs The probability of such a process

taking place is proportional to the number of photons at the incomingend, i.e., to the power density of the stimulating radiation [13]

If in spontaneous emission both directions, as well as frequencies, phasesand polarization planes of radiation are not the same, in stimulated emis-sion these parameters for both forcing and forced radiation (i.e., externalelectromagnetic field and the field formed by stimulated transitions) arethe same Frequencies, phases, polarization planes and directions of propa-

gation are mutually indistinguishable The radiation of a set of only particlesand atoms exhibits properties of radiation by a single quantum system: itpropagates in the exact same direction, has the same frequency, it is in phase

agreement and polarized the same Such radiation is termed coherent and

this is the type of radiation emitted by lasers

– inversion of occupation of energy levels,

– creation of conditions favoring the occurrence of resonance stimulation

3.2.2.1 Inversion of occupation of energy levels

Inversion of occupation of energy levels consists of inversion of the ergy structure of the set of quantum systems, appropriate for thermody-namic equilibrium The set should contain a predominance of excited par-ticles because only in those conditions is it possible to achieve a surplus ofemitted photons over absorbed ones, i.e., achieve amplification of radiation It

en-is therefore necessary to effect an inversion of site occupations, i.e., to getically amplify the set of quantum systems which is called the active me-

ener-dium of the laser Presently, over a million laser transitions are known which

enable the achievement of site occupation inversion [7]

Inversion is achieved in many ways Very often it consists of subjectingthe active medium of the laser to electromagnetic (stimulating) radiation

Achieving inversion as the result of absorption of radiation is called

pump-ing When radiation in the light range is utilized, the process is called optical pumping Inversion of energy level occupation of the laser active

medium can also be achieved by electrical pumping: electrical discharge

in gases (glow, spark or arc), bombardment by a stream of electrons, byutilization of the conducting current in semiconductor materials by chemi-cal reactions, etc [1-13] The source of energy serving to attain the desired

energy levels is named pumping source.

The effectiveness of optical pumping is relatively low because it isusually difficult to fit the spectrum range of work of pumping valves tothe desired spectrum range of absorption of the active medium This leads

to high losses of light energy on heating the active medium Optical ing is most often used in solid and liquid lasers [7]

pump-The effectiveness of electrical pumping taking place during electricaldischarge in gases, attained as a result of collisions of active particlesbetween themselves and between them and free electrons, is substantiallyhigher It depends on gas pressure and on the intensity of the electric field[7] This type of pumping is used in gas lasers

In high power gas lasers gas-dynamic pumping is also employed,

utiliz-ing the difference in times of relaxation of the lower and higher energy level

of active medium particles, occurring during rapid decompression of a priorheated gas, characterized by thermodynamic equilibrium at the initial tem-perature This type of excitation enables direct exchange of thermal energy tothe radiant energy of a laser beam [7]

Fig 3.3 shows schematics of three- and four-level optical pumping

Fig 3.3 Schematic representation of pumping systems: a) three-level; b) four-level.

(From Oczoœ, K [2] With permission.)

In the three-level system it consists of transporting particles from the

basic level 1 to the level of excitation 3, also called the pumping band.

From this level they rapidly pass without radiation to a metastable mediate level Transition to the intermediate level is accompanied by aloss of a portion of the energy by the particles, this loss being used up byraising the temperature of the system, e.g., causing vibrations of the crys-talline lattice of trivalent chromium ions in the ruby laser which must becooled In a three-level active medium, inversion may be achieved on con-dition that at least one half of the active centers is excited Generation ofradiation in such a medium requires intensive excitation by high powerradiation [7]

inter-The four-level system is free of these faults Examples of this are mium ions in crystals or glass, as well as particles of CO2 and CO In such

neody-a system, the pneody-articles neody-are trneody-ansported from the bneody-asic level to the excitneody-ation

level 4, while laser action takes place during transition from level 3 to level 2 When level 2 is far from the basic level 1, occupation of level 2 will be very small In this case inversion of occupation relative to the final level 2 (Fig.3.3b) requires less pumping energy than inversion of occupation in the three-

level system, relative to level 1 (Fig 3.3a).

In the intermediate stage, at the metastable level, particles may remainrelatively long, compared to times of occurrence of atomic effects, e.g forthe ruby laser, up to 3 ms In this time it is possible to bring many particles

of the active medium to a state of excitation in which, by way of neous emission, they may give off their energy in a very short period oftime As the result of pumping, the particular particles of the active me-dium do not reach the intermediate state simultaneously but they attainthe potential possibility of simultaneous giving off of surplus energy Thispotential possibility is made real by designing the laser in such a way as tocreate conditions for almost simultaneous giving off of surplus energy, in

sponta-a time of the order of seversponta-al nsponta-anoseconds [7] Such sponta-a possibility is tained in optical resonators

ob-3.2.2.2 Optical resonator

The optical resonator, also known as the laser resonator or the resonancechamber, serves to contain the active medium (sometimes the active me-dium itself constitutes the resonator) and to amplify stimulated radiation

by causing multiple transition of that radiation through the active dium The basic element of the optical resonator is a set usually compris-ing two mirrors, placed perpendicularly to the axis of the resonator Mul-tiple reflections of radiation from these mirrors may not only react along

me-a long pme-ath with excited pme-articles of the medium, but me-also increme-ase its sity The power of the stimulated radiation must be greater than its lossesdue to diffraction, dispersion or undesired reflection The resonator allows,therefore, the accomplishment of positive optical feedback

den-Laser action in the form of an avalanche of photon emission causesonly radiation along the optical axis of the resonator or one insignifi-cantly deviated from it Radiation propagating in other directions doesnot have the possibility of appropriate amplification with the help of stimu-lated emission and thus exits the active medium

The properties of optical resonators depend mainly on the type of rors, their geometry and distance between them Depending on the method

mir-of exiting the resonator by laser radiation, stable and unstable resonatorsare distinguished

In stable resonators, laser radiation is conducted out of the resonator

through one of the mirrors which for this purpose is made as partiallypermeable Usually, its permeability to infrared radiation of 10.6 µm wave-length is 30 to 35% Most often resonators are designed as flat and parallel,with flat and strictly parallel circular mirrors (Fig 3.4) Precision of set-ting of mirror parallelism should not be inferior to 5 to 10 µrad [15] Such a

Fig 3.5 Schematics showing the generation of a laser beam in an optical ruby laser resonator: a) optical pumping systems used in ruby lasers;

b) pumping of active medium; c) laser action in a ruby rod; d) growth of axial laser beam; 1 - ruby rod, doped by C2O3 which is the active

medium; 2 nonpermeating mirror (totally reflecting); 3 semipermeable mirror; 4 cooling jacket; 5 xenon pumping flash lamp; 6 photons of flash lamp penetrating into the ruby rod; 7- photons parallel to optical axis of rod; 8 - photons exiting rod with active medium; 9

laser beam pulses; 10 reflector surface of flash lamp (Fig a from Gozdecki, T., et al [7], Fig b and c from Oczoœ, K [2] With permission.)

Unstable resonators are characterized by greater diffraction losses but low the utilization of active media with a high degree of amplification andfilling of the entire volume of the active medium with radiation [2, 7] Theyfind application in lasers generating radiation of high power density.The course of laser action, as exemplified by the now classical rubylaser, is the following: the active medium in the ruby crystal (crystalline

al-Al2O3 corundum) is a 0.05% coloring additive of Cr2O3 Chromium ions,which number 5000 times less than the remaining atoms, are excited In

a ruby rod of 10 mm diameter and 100 mm length, the number of mium atoms is approximately 1019 The excitation of chromium ions con-sists of irradiation of the ruby rod usually by blue light of a xenon photoflash lamp in the form of a pipe wrapped around the rod or in the form

chro-of pipes situated parallel to the ruby rod The radiation from the lamp isaimed directly onto the rod and by way of reflectors (Fig 3.5a) Afterinitializing stimulated emission of the active medium (Fig 3.5b, c), ra-diation in the form of wave beams propagates in the ruby rod in diversedirections (Fig 3.5d) A portion of the radiation exits through the sidesurface During the first phase of the process the portion of radiationwhich does not exit the rod is that which propagates parallel or almostparallel to the rod’s axis because its end surfaces are silver-plated andform two mirrors, one of which is partially permeable The rod withmirrors forms a flat-parallel resonator The power of radiation exitingthrough the side surface decreases gradually On the other hand, thepower of radiation propagating parallel to the resonator axis increasesbecause photons moving parallel to the rod’s axis sputter other photonsfrom excited chromium ions which leads to avalanche amplification ofradiation A radiant beam falling on the impermeable mirror is reflectedand on its path to the partially permeable mirror its power increases asthe result of liberating successive photons Upon reaching the partiallypermeable mirror, a portion of the radiation exits the laser, while theremaining portion is reflected, travels along the rod, is again reflected bythe impermeable mirror and again travels back Thus the process is re-peated while the power of the exiting beam increases After some succes-sive pass, this power begins to decrease because the number of excitedatoms is steadily reduced The entire process is then repeated: a newflash of the lamp excites the chromium atoms, etc As a result, the laseremits pulses of coherent, monochromatic and non-divergent radiation of0.694 mm wavelength, which is equal to the wavelength of the excitingradiation The energy emitted in the form of one pulse reaches severalhundred Joules, while the energy supplied by the flash lamp in the form

of non-coherent radiation must be at least 100 times greater The ciency of a ruby laser is very low - 0.1 to 1% Because the ruby rodbecomes hot and must be cooled, the frequency of pulse repetition, de-spite the cooling, may not exceed 1 to 3 s [7]

effi-3.2.3 Single-mode and multi-mode laser beams

In optical resonators there occur standing waves, as the result of

interfer-ence of plane waves of light radiation of same amplitudes and periods,propagating along the resonator axis but in opposite directions, due toreflection from mirrors (Fig 3.6) A condition for proper functioning of

Fig 3.6 Formation of standing wave in a plane-parallel optical resonator (From

Oczoœ, K [2] With permission.)

the resonator is precise maintenance of such a distance L between mirrors which equals an integral number n of half wavelengths λ [2, 3, 6, 8].

Meeting this condition allows the formation of wave nodes on mirrorsurfaces of the resonator

Usually the value of L is very big relative to λ For this reason, in the

optical resonator it is possible to obtain several types of resonance

vibra-tions or longitudinal modes, fulfilling the condition:

(3.3)

where: k = 1, , n; q k - number of half-waves

The range of wavelengths or corresponding frequencies forms a trum (frequency spectrum) of resonance waves of the active medium, in

spec-other words the laser radiation spectrum The spectrum composition of

this radiation depends on longitudinal modes

Diffraction occurs at mirror edges, giving rise to changes of amplitudeand phase of the waves at mirror surfaces The result of this is the occur-

rence of transverse vibrations (modes) or changes in the distribution of

radiation intensity at the mirror surfaces and, consequently, in the section of the laser beam after it exits the resonator, i.e., in the plane parallel

cross-to the mirrors

The spatial distributions of laser radiation intensity depend on verse modes which are denoted by symbols TEMmn (Transverse Electro-