Lasers-Compiled by Gaurang.docx

7/27/2019 Lasers-Compiled by Gaurang.docx

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LASERS

Well these are the notes I have compiled fromsomewhere on the internet.

These contain a very in-depth expalanation onevery aspect of LASERS which you may notrequire at times. So skip that.

What I would suggest is before startinganything from these set of notes first have alook at the entire material by scrolling leisurelyand then decide wht topics you have and whatarent of concern.

This document has stuff which you guys donthave at all!! So do not get dejected just bylooking at the huge chunk of pages.

Wish you all the best for your Quiz.Take care.

HISTORY OF LASERS

LASER is the acronym for Light Amplification by Stimulated Emission of Radiation.

Albert Einstein first explained the theory of stimulated emission in 1917, which became the basis ofLaser. He postulated that, when the population inversion exists between upper and lower levelsamong atomic systems, it is possible to realize amplified stimulated emission and the stimulatedemission has the same frequency and phase as the incident radiation. However, it was in late 1940sand fifties that scientists and engineers did extensive work to realize a practical device based onthe principle of stimulated emission. Notable scientists who pioneered the work include CharlesTownes, Joseph Weber, Alexander Prokhorov and Nikolai G Basov.


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Initially, the scientists and engineers were working towards the realization of a MASER (MicrowaveAmplification by the Stimulated Emission of Radiation), a device that amplified microwaves for itsimmediate application in microwave communication systems. Townes and the other engineersbelieved it to be possible create an optical maser, a device for creating powerful beams of lightusing higher frequency energy to stimulate what was to become termed the lasing medium. Despitethe pioneering work of Townes and Prokhorov it was left to Theodore Maiman in 1960 to invent the

first Laser using ruby as a lasing medium that was stimulated using high energy flashes of intenselight.

The development of Lasers has been a turning point in the history of science and engineering. It hasproduced a completely new type of systems with potentials for applications in a wide variety offields. During sixties, lot of work had been carried out on the basic development of almost all themajor lasers including high power gas dynamic and chemical lasers. Almost all the practicalapplications of these lasers in defense as well as in industry were also identified during this period.The motivation of using the high power lasers in strategic scenario was a great driving force for therapid development of these high power lasers. In early seventies, megawatt class carbon dioxidegas dynamic laser was successfully developed and tested against typical military targets. Thedevelopment of chemical lasers, free electron and X-ray lasers took slightly longer time because ofinvolvement of multidisciplinary approach.

The major steps of advances or breakthroughs in Laser research are given below:

Dates, Contributors and events

1917: Einstein, A. - Concept and theory of stimulated light emission

1948: Gabor, D. - Invention of holography

1951: Charles H Townes, Alexander Prokhorov, Nikolai G Basov, Joseph Weber - The inventionof the MASER (Microwave Amplification of Stimulated Emission of Radiation) at Columbia University,Lebedev Laboratories, Moscow and University of Maryland.

1956: Bloembergen, N. - Solid-state maser- [Proposal for a new type of solid state maser] atHarvard University.

1958: Schawlow, A.L. and Townes, C.H. - Proposed the realization of masers for light and infraredat Columbia University .

1960: Maiman, T.H. - Realization of first working LASER based on Ruby at Hughes ResearchLaboratories.

1961: Javan, A., Bennet, W.R. and Herriot, D.R. - First gas laser : Helium- Neon (He-Ne laser) atBell Laboratories.

1961: Fox, A.G., Li, T. - Theory of optical resonators at Bell Laboratories.

1962: Hall,R. -First Semiconductor laser (Gallium-Arsenide laser) at General Electric Labs.

1962: McClung,F.J and Hellwarth, R.W. - Giant pulse generation / Q-Switching.

1962: Johnson, L.F., Boyd, G.D., Nassau, K and Sodden, R.R. - Continuous wave solid-state laser.

1964: Geusic, J.E., Markos, H.M., Van Uiteit, L.G. - Development of first working Nd:YAG LASERat Bell Labs.


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1964: Patel, C.K.N. - Development of CO2 LASER at Bell Labs.

1964: Bridges, W. - Development of Argon Ion LASER a Hughes Labs.

1965: Pimentel, G. and Kasper, J. V. V. - First chemical LASER at University of California, Berkley.

1965: Bloembergen, N. - Wave propagation in nonlinear media.

1966: Silfvast, W., Fowles, G. and Hopkins - First metal vapor LASER - Zn/Cd - at University ofUtah.

1966: Walter, W.T., Solomon, N., Piltch, M and Gould, G. - Metal vapor laser.

1966: Sorokin, P. and Lankard, J. - Demonstration of first Dye Laser action at IBM Labs.

1966: AVCO Research Laboratory, USA. - First Gas Dynamic Laser based on CO2

1970: Nikolai Basov's Group - First Excimer LASER at Lebedev Labs, Moscow based on Xenon (Xe)only.

1974: Ewing, J.J. and Brau, C. - First rare gas halide excimer at Avco Everet Labs.

1977: John M J Madey's Group - First free electron laser at Stanford University.

1977: McDermott, W.E., Pehelkin, N.R,. Benard, D.J and Bousek, R.R. - Chemical Oxygen IodineLaser (COIL).

1980: Geoffrey Pert's Group - First report of X-ray lasing action, Hull University, UK.

1984: Dennis Matthew's Group - First reported demonstration of a "laboratory" X-ray laser fromLawrence Livermore Labs.

1999: Herbelin,J.M., Henshaw, T.L., Rafferty, B.D., Anderson, B.T., Tate, R.F., Madden, T.J.,Mankey II, G.C and Hager, G.D. - All Gas-Phase Chemical Iodine Laser (AGIL).

2001: Lawrence Livermore National Laboratory - Solid State Heat Capacity Laser(SSHCL).

PROPERTIES OF LASERS

LASERS: BASIC CHARACTERISTICS

Laser has certain unique properties, namely, high monochromaticity, coherence and directionality,compared to ordinary sources of light, though both are electromagnetic radiations. Theseproperties are briefly discussed in the following sections.

Monochromaticity

The energy of a photon determines its wavelength through the relationship E = hc/, where c is the

speed of light, h is Planck's constant, and is wavelength. In an ideal case, the laser emits allphotons with the same energy, and thus the same wavelength, it is said to be monochromatic. The


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light from a laser typically comes from one atomic transition with a single precise wavelength. Sothe laser light has a single spectral color and is almost the purest monochromatic light available.

However, in all practical cases, the laser light is not truly monochromatic. A truly monochromaticwave requires a wave train of infinite duration. The spectral emission line from which itoriginates does have a finite width, because of the Doppler effect of the moving atoms or

molecules from which it comes. Compared to the ordinary sources of light, the range of frequency(line width) of the laser is extremely small. This range is called line width or bandwidth.

Why the laser light is monochromatic? Following are the factors responsible for making thelaser beam monochromatic:

Laser light consists of essentially one wavelength, having its origin instimulated emission from one set of atomic energy levels. This ispossible because laser transition, in principle, involves well-definedenergy levels.

EM wave of frequency = (E2 - E1) only can be amplified, has a

certain range which is called line width. This line width is decided byvarious broadening factors such as Doppler effect of moving atomsand molecules.

The generation of laser is such that the laser cavity forms a resonantsystem and laser oscillation is sustained only at the resonantfrequencies of the cavity. This leads to the further narrowing of thelaser line width. So laser light is usually very pure in wavelength, wesay it has the property of monochromatic.

The lasers, in general, generate light in a very narrow band around a single, central wavelength.The degree of monochromoticity can be quantitatively described in terms of wavelength bandwidth

or frequency bandwidth. The narrower is the line width, higher degree of the monochromocity ofthe laser has. However this depends on the type of laser, and special techniques can be used toimprove monochromaticity. Typically, the frequency bandwidth of a commercial He-Ne laser isabout 1500MHz (full width at half-maximum, FWHM). In terms of wavelength, it means that at awavelength of 632.8nm this means a wavelength bandwidth of about 0.01nm. On the other hand,the bandwidth of a typically diode laser with a wavelength of 900nm is about 1nm as compared toLED, which has a bandwidth of approximately 30 - 60 nm.

Monochromatic output, or high frequency stability, is of great importance for lasers being used ininterferometric measurements since the wavelength is the measure of length and distance andmust be known with extreme precision, at least one part in a million, and it must remain constantwith time. The same holds true for lasers used in chemical and many other scientific analyticalapplications. Both these techniques are important in quality control and inspection. For these

applications, frequency stabilized 632.8 nm HeNe laser (a frequency of approximately 473 THz)with a 1 MHz bandwidth are commercially available.

Another important laser: the Nd:YAG laser used in most laser designators, generates an outputbeam at 1.064 microns, with a typical bandwidth of 0.00045 microns, an amazingly narrow linewidth of 0.04 percent of the central wavelength. This spectrally pure output is critical for amultitude of applications, including remote sensing for specific chemical constituents and highsignal-to-noise ratio (SNR) communications.

This property of monochromoticity has excellent applications in high-resolution spectroscopy toobserve specific transitions in a molecule. A practical application is the separation of isotopes inthe nuclear industry where the fissionable isotope of Uranium, 235U, is separated from the non-fissionable one 238U by exploiting the minute difference in their energy levels.

Coherence


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When an excited atom, depending on its lifetime at the higher energy level, comes down to lowerenergy level, a photon is emitted, corresponding to the equation,

h = E2 - E1,where h is the Planks constant, is the frequency of the emitted photon and E2 and E1 correspondto higher and lower energy levels respectively. This type of natural emission occurs in differentdirections and is called spontaneous emissions. It is characterized by the lifetime of the upperexcited state after which it spontaneously returns to lower state and radiates away the energy byemission. Interestingly, apart from spontaneous emission, an excited atom can be induced to emit aphoton by another photon of same frequency - i.e. a passing photon can stimulate a transition froma higher level to the lower level, thus resulting in the emission of two photons, which is gain. Thetwo emitted photons are said to be in phase, which means that the crest or the trough of the waveassociated with one photon will occur at the same time as on the wave associated with the otherphoton. An avalanche of similar photons is created and these photons have a fixed phaserelationship with each other. This fixed phase relationship between the photons from various atomsin the active medium results in the laser beam generated having the property of coherence. Since

the radiation emitted is by the stimulation process, it is referred to as the stimulated emission andthe generation of laser is by stimulated emission.

In the case of spontaneous emission, the emission is natural where as in the case of stimulatedemission, it is induced or stimulated. Further there is no amplification in the case of spontaneousemission as well as no phase relationship between emitted photons, as it happens in the case ofstimulated emission. But one has to remember that under normal conditions, there is far moreatoms in the lower level than in the upper level and as such absorption dominates stimulatedemission. In order to reverse this trend, there must be much more atoms in the upper level than inthe lower level. This specific condition is called population inversion and is essential for stimulatedemission to be in a predominant position for generation of laser. In the case of laser, thestimulated emission process is responsible for the emission of photons and amplification. Since theemitted photons have a definite phase relationship with each other, coherent output is produced.

i.e. the atoms emit photons in phase with the incoming stimulating photons and emitted wavesadds to the incoming waves, generating brighter output. Addition is due to the relative phaserelationship. Photons of ordinary light also come from atoms without any phase relationship witheach other and are not coherent. Therefore, laser is called a coherent light source where as anordinary light is called an incoherent light source.

To sum up, the two conditions necessary for laser action are population inversion and stimulatedemission. Inside a laser, the stimulated emission occurs in a resonant cavity with mirrors at bothends. Thus by repeating this process of interaction of photon with excited atoms many times, onecan produce a highly coherent beam of light. Since a common stimulus triggers the emission events,which provide the amplified light, the emitted photons are "in step" and have a definite phaserelation to each other. These emitted photons having a definite phase relation to each other,generates coherent output, i.e. the atoms emit photons in phase with the incoming stimulating

photons and emitted waves add to the incoming waves, generating brighter output. Addition is dueto the relative phase relationship. Photons of ordinary light also come from atoms, but independentof each other and without any phase relationship with each other and are not coherent. Therefore,laser is called a coherent light source where as an ordinary light is called an incoherent source oflight. The concept of coherence can be well understood from the following figure.

(a) (b)


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Figure (a) depicts a typical beam of light waves from an ordinary source traveling through space.One can see that these waves do not have any fixed relationship with each other. This light is saidto be "incoherent", meaning that the light beam has no internal order. Figure (b), on the otherhand, illustrates the light waves within a highly collimated laser beam. All of these individual wavesare in step, or "in phase", with one another at every point. "Coherence" is the term used to describesuch a property of laser light.

There are two types of coherence - spatial and temporal

Correlation between the waves at one place at different times, or along the path of a beam at asingle instant, are effectively the same thing, and are called " temporal coherence". Correlationbetween different places (but not along the path) is called "spatial coherence".

To understand coherence, let us take two points on a wave front, at time equal to zero. There willbe a certain phase difference between these two points and if it remains same even after lapse of aperiod of time, then the electromagnetic wave (em) has perfect coherence between the twopoints. In case, the phase difference remains same for any two points anywhere on the wave front,then we say that the electromagnetic wave has perfect spatial coherence, where as if this is trueonly for a specific area, then the electromagnetic wave is said to have only partial spatial

coherence. Spatial coherence is related to directionality and uniphase wave fronts.

Now let us consider a single point on the wave front. There will be a phase difference betweentime, t = 0 and t = t of the electromagnetic wave. If this phase difference remains same for anyvalue of t, then we say that the em wave has perfect temporal coherence. But if this is only for aspecific value of t, then the em wave has partial temporal coherence.

It may be understood that these two types of coherence are independent of each other. i.e. anem wave with partial temporal coherence can have perfect spatial coherence.

Some important points:

Coherence is a property of waves that indicates the ability of thewaves to interfere with each other. Two waves that are coherent canbe combined to produce an unmoving distribution of constructive anddestructive interference (a visible interference pattern) depending onthe relative phase of the waves at their meeting point. Waves thatareincoherent, when combined, produce rapidly moving areas ofconstructive and destructive interference and therefore do notproduce a visible interference pattern.

Another way of saying the same thing is that coherence is a measureof the ability of a light source to produce high contrast interferencefringes when the light is interfered with itself in an interferometer.High coherence means high fringe visibility with excellent contrast,(i.e., good black and white fringes, or black and whatever color thelight is); low coherence means washed-out fringes, and zerocoherence means no fringes.

One of the ways of understanding coherence is to predictit. Suppose one can take a snapshot of the waves, and then takeanother snapshot at a later time. If the two snapshots look almostidentical, even with a long time interval, then we have a high degreeof coherence.

A wave can also be coherent with itself, a property knownas temporal coherence. If a wave is combined with a delayed copy of

itself, the duration of the delay over which it produces visibleinterference is known as the coherence time of the wave, tc. From


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this, acorresponding coherence length lc, can be estimated as :

lc= tc

where c is the speed of the light wave.

Coherence time (tc) relates to the finite bandwidth of the source andin general, it is proportional to the bandwidth

tc1/where is the frequency bandwidth. The temporal coherencecomes from the monochromaticity of the laser beam. The narrowerthe line width or of the light source, the better is its temporalcoherence.

If the laser supports the oscillation of multiple longitudinal modes butno higher-order transverse modes, it means that the laser output hasfinite temporal coherence but perfect spatial coherence. Thelongitudinal modes in a laser are equally spaced in frequency by c/2Lwhere c is the velocity of light and L is the effective length of thelaser resonator. The number of longitudinal modes determines thecoherence length of the laser. The relation between the coherencelength lc, the longitudinal mode spacing c/2L and the number ofmodes N (N>!) is

N = [c/2 lc ] / c/2 L = L/ lc

Small coherence lengths are obtained with lasers, which supportoscillation over a very wide spectral bandwidth.

There are certain gas lasers which have very long coherence length oftens of meters, while other lasers, especially Diode lasers have

coherence length of the order of millimeters.

Typically for a commercially available He-Ne laser with 632.8 nmwave-length and 0.01 nm spectral bandwidth, the coherence length isabout 4cm or at the most of the order of the length of its resonatorbecause of the presence of many longitudinal modes.

A frequency stabilized 632.8 nm HeNe laser (a frequency ofapproximately 473 THz) with a 1 MHz bandwidth would have acoherence length of about 300 meters. In this case, the coherencelength is much longer than the length of the cavity because only asingle longitudinal is forced to be active in it at any given time.

An 800 nm laser diode with a 1 nm spectral width would have acoherence length of about 0.64 mm.

A 600 nm LED with a spectral width of 60 nm would have a coherencelength of around 6 um.

He-Ne lasers are also much more spatially coherent than LEDs. LEDsgenerally have a very short spatial coherence length, typically only acouple of wavelengths.

In holography, the temporal coherence length determines the

maximum depth of the object in a reflection hologram, and thespatial coherence length determines the lateral size. Holography,


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which is based on interference between light beams, long coherencelength enables taking holograms of large bodies, which requiregreater depth of field. Both the light reflected from the near part ofthe body, and the light reflected from the far part of the body, willstill be coherent with the reference beam.

Spatial coherence refers to how spherical the wave front is. Doesevery portion of the wave front appear to have exactly the samecenter of curvature?

The requirement for high temporal coherence is in coherent, orheterodyne detection. In these systems, energy reflected off thetarget is mixed with energy from the original laser to create a fringepattern. The photons are supposed to maintain the fixed phaserelationship for the time needed to hit the target and return in orderto have proper contrast in the fringe pattern.

One of the important applications includes Doppler velocity

measurements of the target through the measurements of thefrequency shift because of the moving targets. The frequency shiftfrom the target-reflected energy is a function of the target velocity.However, if the frequency of the laser itself is shifting (because ofpoor coherence) during the time of flight, this creates a broadening oran error in the frequency of the returned beam that limits howaccurately one can measure the Doppler velocity.

Spatial coherence is high for sphere waves and plane waves, and isrelated to the size of the light source. A point source emits spatiallycoherent light, while the light from a finite source has lowercoherence. Spatial coherence can be increased with a spatial filter; a

very small pinhole preceded by a condenser lens. The spatialcoherence of light will increase as it travels away from the source andbecomes more like a sphere or plane wave. Light from distant stars,though far from monochromatic, has extremely high spatialcoherence.

Coherence length is defined as the length over which energy in twoseparate waves remains constant. With respect to the laser, it is thegreatest distance between two arms of an interferometric system forwhich sufficient interferometric effects can be observed.

Using Michelson Interferometer, one can estimate the coherencelength by measuring the maximum path difference between the twobeams, which still show the interference pattern.

Since the temporal coherence is a measure of the ability of theradiation to perform interference, as a result of differences in pathlengths between the two beams, it is thus important in interferometryand holography.

Ordinary light is not coherent because it comes from independentatoms, which emit on time scales of about 10-8 seconds. There is adegree of coherence in sources like the mercury green line and someother useful spectral sources, but their coherence does not approachthat of a laser.

Beam diameter


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It is very interesting to note that, the intensity of laser light isnot same throughout the cross section of the beam. This isbecause of the fact that the cavity also controls the trans-versemodes, or intensity cross sections. The ideal beam has asymmetric cross section: The intensity is greater in the middleand tails off at the edges. This is called the Transverse

Electromagnetic Mode (TEM 00) output as shown in the figure. Thesubscripts n and m (0 and 0 in this case) in the TEM nm arecorrelated to the number of nodes in the x and y directions. Atheoretical TEM 00 beam has a perfect Gaussian profile. Detaileddiscussion on modes is given in the next section. Lasers can produce many other TEM modes, whichwould be discussed in later sections. In general, one can say that laser beams have a symmetricintensity profile. i.e. if we run across the beam, the intensity is minimum at the edge and as wemove towards the center it increases and is maximum at the center and then it falls in a similarfashion as on the other side, where from we started. In fact, we can start at any point on the rim ofthe laser beam and the result will be same, as discussed earlier. Beam diameter is defined as thediameter of a circular beam at a certain point where the intensity drops to a certain fraction of itsmaximum value. The common definitions are half the intensity i.e. full width at half maximum(FWHM), 1/e (0.368) and 1/e2 (0.135) of the maximum value. In other words, beam diameter is the

diameter of the laser beam cross section between points near the outer edge of the beam where itsintensity is only 50 % (FWHM), 63% (1- 1/e) and about 86% (1-1/e2) of the intensity at the beamcenter.

Directionality and beam divergence

One of the important properties of laser is its high directionality. The mirrors placed at oppositeends of a laser cavity enables the beam to travel back and forth in order to gain intensity by thestimulated emission of more photons at the same wavelength, which results in increasedamplification due to the longer path length through the medium. The multiple reflections alsoproduce a well-collimated beam, because only photons traveling parallel to the cavity walls will bereflected from both mirrors. If the light is the slightest bit off axis, it will be lost from the beam.

The resonant cavity, thus, makes certain that only electromagnetic waves traveling along the opticaxis can be sustained, consequent building of the gain.

The high degree of collimation arises from the fact that the cavity of the laser has very nearlyparallel front and back mirrors, which constrain the final laser beam to a path, which isperpendicular to those mirrors. Collimation refers to the degree to which the beam remainsparallel with distance. A perfectly collimated beam would have parallel sides and would neverexpand at all. Its divergence angle would be exactly zero. Diffraction plays an important role indetermining the size of laser spot that can be projected at a given distance. The oscillation of thebeam in the resonator cavity produces a narrow beam that subsequently diverges at some angledepending on the resonator design, the size of the output aperture, and resulting diffractioneffects on the beam. These diffraction effects usually referred as a beam-spreading effect are aresult of the light waves passing through a small opening. These diffraction phenomena impose a

limit on the minimum diameter of a light point after passing through an optical system. For a laser,the beam emerging from the output mirror can be thought of as the opening or aperture, and thediffraction effects on the beam by the mirror will limit the minimum divergence and spot size ofthe beam. For beams in TEM 00 mode, diffraction is usually the limiting factor in beam divergence.

In fact one can say that, divergence angle describes the directionality of the laser. For a perfectspatially coherent laser beam, the diffraction limited divergence angle is given by,

K X / D,

where and D are the wavelength and diameter of the laser beam respectively. K is a constantfactor that is usually unity but depends on the wavelength. The relationship clearly demonstratesthat beam divergence increases with wavelength, and decreases as beam (or output lens) diameterincreases. In other words, a smaller diameter beam will suffer more divergence and greater spread


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with distance than a larger beam. For a perfect gaussian beam, the divergence o (half angle), isrelated to beam waist radius wo as

o= (1 / [ / wo])

Using the above equations, and assuming K or 2 x (1 / ) as unity, let us calculate the minimumdivergence (full angle) that can be theoretically achievable for the most well known lasers, i.e.Nd:YAG ( = 1.06 mm with 3mm diameter) and He-Ne laser ( = 0.6328 mm with 1mm beamdiameter). The divergence angles are 0.353 milli-rad or 0.02014 and 0.6328 mrad or0.03607 respectively. Compare this with the divergence of the light from a torchlight (20 ormore) and the high directionality of laser beams becomes quite obvious. As the spatial coherencebecomes partial or the degree of coherence reduces, the divergence increases accordingly and forcalculating the divergence, the diameter of the beam D is to be replaced with the coherence areain the above-mentioned equation.

Consider the size (diameter) of a collimated beam as it propagates as shown in the figure. It can beseen that the diameter increases. This increase of the beam size is due to the beam divergence andthe same is measured in milliradians (mrad). It is

either measured as full angle (measure of increasein diameter) or as half angle (measure of increasein radius). For example, the diameter of a beamof 1mrad full angle divergence, after propagationof 1Km, will be 1m (Physical optics). For small angle, the divergence can be approximated as theratio of the beam diameter to the distance from the laser aperture.

Brightness

While summing up the discussion on monochromaticity (narrow line width) and directionality (lowdivergence) of laser, radiance of laser cannot be missed out. It is defined as the power emitted perunit surface area per unit solid angle. The units are

watts per square meter per steradian. A steradian isthe unit of solid angle, which is three-dimensionalanalogue of conventional two-dimensional (planar)angle expressed in radians. For small angles therelation between a planar angle and the solid angle ofa cone with that planar angle is to a goodapproximation is:

= ( / 4) 2

where is the planar angle and is the solid angle as shown in the figure. The radiance of a 1mmHe-Ne laser with 1 mm out put diameter and a divergence of 1 milli-radian is 1.6 x 109 Watts/m2-steradian, which can be estimated in the following manner.

The solid angle corresponding to one millirad is:

= ( / 4) (1 mrad)2 = 0.8 x 10-6 sterad and the radiance is power divided by the area of thebeam and the solid angle. Thus radiance B is

B = 10-3W/(0.785 x 10-6)(0.8 x 10-6) = 1.6 x 109 Watts/m2-steradian

The radiance of a milliwatt helium neon laser is far greater than 106 Watts/m2-steradian, that ofthe sun which emits more than 1026 W.

This is a unique advantage for many of the laser applications in various areas.

Laser Modes


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As we know that part of the laser light in the laser cavity emerges through the output mirror. Theoptical waves within an optical resonant cavity are characterized by their resonant modes, whichare discrete resonant conditions governed by the dimensions of the cavity. The laser beam radiatedfrom the laser cavity is thus not arbitrary. Only the waves oscillating at modes that match theoscillation modes of the laser cavity can be produced. The laser modes governed by the axialdimensions of the resonant cavity are called the longitudinal modes, and the modes determined by

the cross-sectional dimensions of the laser cavity are called transverse modes.

Longitudinal Mode

Generally speaking light modes means possible standing EM waves in a system. The number ofmodes in this meaning is huge. Laser mode means the possible standing waves in laser cavity. Wesee that stimulated lights are transmitted back and forth between the mirrors and interfere witheach other, as a result only light of those frequencies, which create nodes at both mirrors areallowed. In other words, if the round trip distance is integer multiples of the wavelength ?, onlythen it can result in a standing wave. Thus, the cavity length must be an integer multiplication ofhalf their wavelengths. The result is the condition of resonance: light waves are amplified strongly,if and only if, they satisfy the equation:

2nL=Nwhere L is the cavity length, n is the refractive index of the laser medium, nL is theopticalpath, Nis an integer and denotes the wavelength.

The integer Ncannot be an arbitrary number. It is limited by the fluorescence curve and only themodes for which the gain of laser of the laser medium G () > 1 would be supported.

The above equation can be rewritten as:

N = 2L/ = 2 L/(c/f)

And f = c / 2L

Where c and f are the velocity and frequency of light.

Assuming a cavity of length 50 cm, it gives us the possible number of modes as 159 x 104 andthe separation between two modes as 300 MHz. However, if the laser bandwidth is of the orderof 2.5 GHz, it can support only 6 longitudinal modes.

Some important points related to longitudinal modes:

Modes governed by the axial dimensions of the resonant cavity arecalled longitudinal modes. The longitudinal modes are formed whenthe two waves with the same frequency and amplitude are movingagainsteach other.

The to and fro movement of the electromagnetic radiation iscontrolled by the laser cavity end mirrors and only the waves withnodes at both ends are sustained or allowed, which means thatthe cavity lengthshould be an integral multiple of the halfwavelengths. Thus the cavity length and the refractive index of thelaser medium determine the frequencies that are allowed inside thecavity.

The other important aspect is that the frequencies are spaced atequal intervals.

In applications where power is more important as in most high powerapplications for material processing or medical surgery, multimodelasers can be used. As such the laser is being used as a mean for


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transferring the energy on to the target. Thus there is not muchimportance for the longitudinal laser modes. However, forapplications involving interference such as holography orinterferrometric measurements, and in applications related tospectroscopic and photochemical, where single well-definedwavelength is required, single mode lasers are very critical.

Increase in the cavity length increases the number of possible lasermodes under the fluorescence curve. However, it reduces thefrequency gap between the adjacent modes. This leads to that asingle mode laser can be made by reducing the length of the cavity,such that only one longitudinal mode will remain under thefluorescence curve with GL>1.

The multiple longitudinal mode structure gives rise to a powerfluctuation phenomenon termed mode sweeping. All unstabilizedhelium neon lasers exhibit this effect, which is due to thermalinstability causing variation in the cavity length. As the cavity length

changes, there is a small change in mode spacing which is typically 10kHz or less under normal conditions.

Transverse Mode


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The configuration of the optical cavity determines thetransverse modes of the laser output, whichcharacterizes the intensity distribution of laser beam

in the transverse plane that is perpendicular to thedirection of propagation. If we intersect the outputlaser beam and study the transverse beam cross

section, we find the light intensity can be ofdifferentdistributions(patterns). These are called TransverseElectromagnetic Modes (TEM). Twoindices are used to indicate the TEMmodes - TEMpq, p and q are integer

numbers indicating the number of pointsof zero illumination (between illuminatedregions) along x axis and y - axisrespectively.

As explained earlier that the amplitude ofa light beam is increased in a laser bymultiple passes of coherent light wavesthrough the active medium. The process is accomplished by an active medium placed between apair of mirrors that act as a feedback mechanism. During each round trip between the mirrors, thelight waves are amplified by the active medium and reduced by internal losses and laser output. Anumber of different combinations of mirrors, such as plane and curved, have been utilized in

practical laser. Some of them are shown in the figure.

Most common form of structure is a stable resonator, which concentrate light along the laser axis,extracting energy efficiently from that region, but not from the outer regions far from the axis.This cavity will then have a set of nearly loss less resonant modes, which will have the form of verynearly perfect Hermite-gaussian or Laguerre-gaussian mathematical functions. The lowest-ordermode will have an essentially ideal gaussian profile with a certain spot size, which depends only onthe spacing and radii of the mirrors and the wavelength of the light and not on the mirror diameter,which is assumed to be very large typically four to five times of the beam size. This spot size,called the "gaussian spot size" and can be estimated by a simple formula in terms of the cavitylength L, the end mirror radii r1 and r2, and the wavelength. The beam thus it produces has anintensity peak in the center, and a Gaussian drop in intensity with increasing distance from theaxis. The fundamental TEM00 mode is only one of many transverse modes that satisfy the round-trippropagation criteria.

For most applications for example like holography, the TEM00 mode is considered most desirable,but multi-mode beams can often deliver more power, though with a poorer beam quality, and maybe acceptable in applications where power is the main criterion.

The laser can be forced to lase in a single TEM00 mode by simply putting a pinhole with properdiameter between the two mirrors. The pinhole diameter should be equal to the diameter of thelower mode as this would allow only this mode to pass through the pinhole, and all higher modeswill be attenuated. Since radiation inside the optical cavity undergoes multiple passes, only thebasic mode will be amplified, and appear in the output.

Beam quality


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Discussion on properties of laser will not be complete without making an assessment of beamquality. Laser beam quality is important since the closer a real laser beam is to diffraction-limited,the more tightly it can be focused, the greater depth of field, and the smaller the diameter ofbeam-handling optics need to transmit the beam. For applications such as directed energyapplications, a better beam quality translates into better delivery of optical power to the target inthe far field. For material processing, the more tightly focused the laser beam results in the higher

intensities. The design of optical delivery systems for laser systems is highly dependent on thelaser's beam quality.

It was thus felt that to recognize, quantify and determine the beam propagation characteristics, afigure of merit would be very necessary and useful. Therefore, the concept of a dimensionlessbeam propagation parameter, M2 was developed in 1970 for all types of lasers. M2 is a quantitativemeasure of the quality of the laser beam and according to ISO standard 11146, it is defined asthe beam parameter product (BPP) divided by / . The beam divergence, as discussed earlier, is

= M2X / w0R

where w0Ris the beam radius at the beam waist and the wave length.

(Beam parameter product (BPP) is the product of a laser beam's divergence angle and the diameterof the beam at its narrowest point (the "beam waist"). Its units are mm mrad.

M2 can also be defined in the following manner:

The ratio of the BPP of an actual beam to that of an ideal Gaussianbeam at the same wavelength . This parameter is a wavelength-independent measure of beam quality.

It is the ratio of the divergence of the real beam to that of atheoretical diffraction-limited beam of the same waist size with aGaussian beam profile.

ISO standard 11146 has laid down procedures for the measurement of M2 also. This was necessitatedby the use of large number of high power lasers for industrial applications like cutting, drilling andwelding, with high cost of investment. Here it is necessary to focus the laser beams 'tightly' toproduce highest possible radiance with minimum collateral damage. Technically, only high qualityand reliable laser beams can ensure this aspect as well as profitable return to the investment.M2 beam quality factor limits the degree to which a laser beam can be focused for a given beamdivergence, which in turn is limited by the numerical aperture of the focusing lens. A word ofcaution that is necessary since M2 factor would be different for two orthogonal directions to thebeam axis for non-circular beams. For example, for diode bars, M2 is low for the fast axis and highfor the slow axis.

For any laser beam, the product of the beam radius (w 0R) and the far-field divergence () is aconstant, and the ratio,

M2 = w0Real. Real / w0R. ,

where w0Real and qReal are the beam waist and far field divergence of the real beam respectively.M2 is an accurate indication of the propagation characteristics of the beam.

There are some other important points related to M2:

The value of M2 is always greater than or equal to 1 and ranges from 1 for a diffraction-limitedTEM00 laser beam, to several hundred for a distorted, poor quality beam.

M = 1 only occurs for single-mode TEM00 Gaussian beams.

Helium neon lasers typically have an M2 factor that is less than 1.1. For ion lasers, the M2 factoris typically between 1.1 and 1.3. Collimated TEM00 diode laser beams usually have an M

2 ranging


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from 1.1 to 1.7. For high-energy multimode lasers, the M factor can be as high as 3 or 4. In allcases, the M2 factor, which varies significantly, affects the characteristics of a laser beam andcannot be neglected in optical designs.

Though carefully/optimally designed lasers can achieve the M2 ~ 1, high power lasers have verymuch higher M2 value of 100 or even more. Thermal distortions in the active gain media, use of

poor optical quality of components, diffraction effects at apertures etc. are the main reasonsfor the reduction of beam quality. Beam quality also gets affected adversely when the laserswork at higher cavity modes. A pump source with uniform intensity distribution, an optimizedcavity design with least sensitivity to thermal lensing, high optical quality components and again medium least prone to thermal disturbance are a pre-requisite to a laser system for thegeneration of high beam quality output.


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PRINCIPLES OF LASER ACTION

We have already discussed the properties of Lasers in the previous section. In this section weintend to describe the basic principles involved in the generation of laser. In order tounderstand the basic laser operation, we must consider the important terms like absorptionand losses, stimulated emission, spontaneous emission, feedback etc.

Absorption, spontaneous emission and stimulated emission:

As we all know that atoms and molecules can exist only in certain energy states. The state oflowest energy is called the ground state; all other states have more energy than the ground

state and are called excited states. Each excited state, of which there are many, has a fixedamount of energy over and above that of the ground state. Under ordinary conditions, almostall atoms and molecules are in their ground states. Three types of processes are possible for atwo-level atomic system. In the first, an incoming photon excites the atomic system from alower energy state into a higher energy state. This is called absorption orsometimes stimulated absorption. It is called stimulated absorptions because of the fact thatthe atoms absorb the incident energy at certain frequencies only. Stimulated absorption occurswhen a photon strikes an atom with just exactly the proper energy to induce an electronictransition between two energy states. In case a broadband light is incident on a given two levelatomic system, we can observe that the complete spectrum is not absorbed but only certaindiscrete lines are absorbed depending on the difference in their energy levels. This processreduces the lower level population and in the process increases the upper level population. Thepopulation or the number of atoms in states E1 and E2 at any time would be N1 and

N2 respectively. When radiation passes through a material, it is absorbed according to:

Ix = I0e-x

(1)

Where Ix is the radiance after traveling distance x through the material with absorptioncoefficient as a and I0 is the initial intensity of light. The absorption depends on thepopulation difference between N1 and N2 and the refractive index of the medium.

Rate of stimulated absorption, R12 (abs), from level 1 to 2 is given as:

R12 (abs) = B12 N1 (2)

Where B12 is the Einstein's coefficient for stimulated absorption and has the units as cm3/s2J,

N1is the population in the ground state and is the energy density per unit frequency of theincoming photons.

Once the atom or molecule has been produced in its excited state, there is a probability that itwill emit radiation again and return to a lower energy state. This lower energy state may beeither the ground state or still one of the excited states but having lower energy level. In theprocess, a photon is emitted. In this emission process, where the atoms spontaneously goes to alower energy state through the emission of a photon is called spontaneous emission orfluorescence. This emission process is a random one and the emitted light goes off in alldirections, and the wave properties of the light are randomly out of step with each other andthus are incoherent.


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The rate of spontaneous emission, R21 (spon), from level 2 to 1 is given as:

R21 (spon) = A21 N2 (3)

Where A21 is the coefficient of spontaneous emission and has the unit of s-1, N2 is the number of

atoms in level 2.One can observe that this spontaneous decay of the upper level takes place in the absence ofan electromagnetic field and the rate is proportional to the population of that level and thusdoes not depend on the intensity of the excitation source. It is purely a statistical phenomenonrelated with time and space and is dependent on the lifetime of the excited state. If thetransition lifetime is very large, it is considered as a forbidden transition.

Excited atoms can loose their energy not only by spontaneous emission, but also by induced orstimulated emission and therefore the emission output of the system consists of spontaneousand stimulated emissions. The probability of stimulated emission is proportional to theintensity of the energy density of external radiation and the induced emission has a firm phaserelationship with it, unlike spontaneous emission. Since the spontaneous photons have no phase

relations with each other, the output is incoherent. But stimulated emission has the samephase, direction, spectral and polarization properties as the stimulating field and both areindistinguishable in all aspects. Consequently, the laser output is coherent. In fact it is thisstimulated emission, under certain conditions as explained in the earlier section that comes outof the laser device as laser.

Rate of stimulated emission, R21 (stim), from level 2 to 1 is given as:

R21 (stim) = B21 N2 (4)

Where B21 is the Einstein's coefficient for stimulated emission and has the dimensions as m3/s2J,

N2 is the population in the excited state and is the energy density per unit frequency of the

triggering photons.Considering an ideal material with only two non-degenerate energy levels, where absorption,spontaneous emission and stimulated emission takes place, one can arrive at the followingconclusion.

Absorption = spontaneous emission + stimulated emission

i.e. B12N1 r(n) = A21N2 + B21N2 r (5)

This situation is shown in the figure 1.


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At any given instance, under normal circumstances, both stimulated and spontaneous emissionsmay occur, but the probability of stimulated emission is pretty low. One can find out this ratioof spontaneous to stimulated emission using one of the following equations:

(6)

(7)

where is the radiation energy density and is equal to Nh, N being the number of photons offrequency per unit volume and k is Boltzmann's constant. Considering a case of ordinary bulbhaving a filament temperature of about 5000K and emitting radiation in the wavelength rangeof 0.6 micron corresponding to frequency of 5 x 10 14 Hz, the probability of stimulatedemission is approximately one hundredth of that of the spontaneous emission. At lowertemperatures, it would even be orders less than this.

The ratio of the probability of spontaneous to stimulated light emission depends directly onthe frequency of emission or inversely to the wavelength. Thus in the microwave region,stimulated emission is more probable than spontaneous, hence the early production of themaser. In the optical region, spontaneous emission is more likely than stimulated emission andthis gets worse as we go into the UV and X-ray regions of the spectrum.

Under thermal equilibrium, the population N2 and N1 of levels E2 and E1 respectivelygoverned by the fact that the rate of upward transitions should be equal to rate of

downward transitions.


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The population density of atoms N1 and N2 in ground level E1 and excited state E2 can beestimated using Boltzmann's relationship as follows:

(8)

Since, (E2 - E1) / kT is always positive, irrespective of the value of temperature T, N2 must beless than N1 if the system is remain at thermal equilibrium. At the most the excited statepopulation N2 (t) reaches a steady state at t, and the highest proportion of atoms that canexist in the excited state N2/Ntotal N1. This non-equilibrium condition is known as called population inversion.

Before we discuss about the techniques of population inversion and laser action, these aresome additional important points related to Absorption, spontaneous emission and stimulatedemission:

In case of spontaneous emission of a photon, the probability of itsemission is inversely related to the average length of time that an atomcan reside in the upper level of the transition before it relaxes. Thistime is known as the SPONTANEOUS LIFETIME. Typically, thespontaneous lifetime is of the order of 10 -8 - 10-9 sec. The shorter thespontaneous lifetime, the greater is the probability that spontaneousemission will occur.

In certain materials, there are energy levels, which has the spontaneouslifetime of the order of microseconds to a few milliseconds. Theselevels are known as METASTABLE levels. The probability of transitionsinvolving metastable levels is relatively low.

As the likelihood of spontaneous emission decreases the conditions thatfavor stimulated emission are enhanced. If an atom is excited into ametastable state it can stay there long enough for a photon of thecorrect frequency to arrive. Such a situation promotes stimulatedemission at the expense of spontaneous emission.

In case of stimulated emission, atoms in an upper energy level can betriggered or stimulated in phase by an incoming photon of a specificenergy. The incident photon must have an energy corresponding to theenergy difference between the upper and lower states. The emittedphotons have the same energy as incident photon. These photons are inphase with the triggering photon and also travel in its direction.

Stimulated processes like stimulated absorption, or stimulated emission


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require incoming photons of the right frequency, whereas spontaneousemission can take place in the absence of incoming photon also.

Spontaneous emission is completely isotropic. Stimulated processes, onthe other hand, have a built-in preference for emission in the directionof the incident flux of photons.

Population Inversion and Laser Operation

As discussed above, whenever light is incident on the material, there is competition betweenabsorption, spontaneous emission and stimulated emission processes. Under normal equilibriumconditions, the population of various levels is given by Boltzmann's relationship and thus N2 willalways be less than N1. Further, stimulated photon emission is much less than the spontaneousphoton emission and the absorption. For a system to work as a laser one requires thatstimulated emission should exceed photon absorption; it leads us to the following two

conditions:

N2 > N1: i.e. Population Inversion

As per equation (6) or (7), the value of (the radiation energy densitywhich is equal to Nh) should be as large as possible.

First condition cannot be achieved under thermal equilibrium conditions. This implies that inorder to create population inversion, one must look for non-thermal equilibrium system andthus the need for special laser materials.

The second condition that requires higher value of r necessitates the use of an additionalsupply of large amount of energy of correct wavelength to excite the desired transition. Theprocess is known as pumping. Various techniques include optical, electrical, chemical, gasdynamic etc.

Population inversion though is the primary condition, but in itself is not sufficient for producinga laser. As there are certain losses of the emitted photons within the material itself in additionto spontaneous emission, one has to think about the geometry that can overcome these lossesand there is overall gain. This requires an optical cavity or resonator.

The principle behind the laser is like this. Suppose we can produce a large number of atoms allin excited states. If one of the atoms emitted spontaneously, then the emitted photon would

stimulate other atoms to emit. These emitted photons would, in turn, stimulate furtheremission. The result would be an intense burst of coherent radiation.


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These issues havebeen discussedbelow:

A representativelaser system isshown in Figure (2).It consists of threebasic parts.

An active medium with a suitable set of energy levels to support laseraction.

A source of pumping energy in order to establish a population inversion.

An optical cavity or resonator to introduce optical feedback and somaintain the gain of the system overcoming all losses.

Brief description of each of the above components and their basic function are givenbelow.

1.Active lasermedium or gainmedium: Lasermedium is theheart of the lasersystem and isresponsible forproducing gain andsubsequentgeneration oflaser. It can be acrystal, solid,

liquid,semiconductor or


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gas medium and can bepumped to a higherenergy state. Thematerial should be ofcontrolled purity, sizeand shape and should

have the suitable energylevels to supportpopulation inversion. Inother words, it musthave a metastable stateto support stimulatedemission. Most lasers arebased on 3 or 4 levelenergy level systems, which depends on the lasing medium. These systems are shown in figs3a and 3b. In case of a three-level laser, the material is pumped from level 1 to level 3,which decays rapidly to level 2 through spontaneous emission. Level 2 is a metastable leveland promotes stimulated emission from level 2 to level 1.

On the other hand in a four level laser, the material is pumped to level 4, which is a fastdecaying level, and the atoms decay rapidly to level 3, which is a metastable level. Thestimulated emission takes place from level 3 to level 2 from where the atoms decay back tolevel 1. Four level lasers is an improvement on a system based on three level systems. Inthis case, the laser transition takes place between the third and second excited states.Since lower laser level 2 is a fast decaying level which ensures that it rapidly gets emptyand as such always supports the population inversion condition.

2.Excitation or pumping mechanism: Absorption of the energy by the atoms, electrons, ionsor molecules as the case may be, of the active medium is a primary requisite in thegeneration of laser. In order to excite these elements to higher energy levels, an excitationor pumping mechanism is necessary. It is well known that under the equilibrium state, as

per Boltzman?s conditions, higher energy levels are much less populated than the lowerenergy levels. One of the requirements of laser action is population inversion in the levelsconcerned. i.e. to have larger population in the upper levels than in the lower ones.Otherwise absorption will dominate at the cost of stimulated emission. There are varioustypes of excitation or pumping mechanisms available, the most commonly used ones areoptical, electrical, thermal or chemical techniques, which depends on the type of the lasergain medium employed. For example, Solid state lasers usually employ optical pumpingfrom high energy xenon flash lamps (e.g., ruby, Nd:YAG) or from a second pump laser orlaser diode array (e.g., DPSS frequency doubled green lasers). Gas lasers use an AC or DCelectrical discharge through the gas medium, or external RF excitation, electron beambombardment, or a chemical reaction. The DC electrical discharge is most common for'small' gas lasers (e.g., helium-neon, argon ion, etc.). DC most often pumps semiconductorlasers current. Liquid (dye) lasers are usually pumped optically.

3.Optical resonator: Optical resonator plays a very important role in the generation of thelaser output, in providing high directionality to the laser beam as well as producing gain inthe active medium to overcome the losses due to, straying away of photons from the lasermedium, diffraction losses due to definite sizes of the mirrors, radiation losses inside theactive medium due to absorption and scattering etc. In order to sustain laser action, onehas to confine the laser medium and the pumping mechanism in a special way that shouldpromote stimulated emission rather than spontaneous emission. In practice, photons needto be confined in the system to allow the number of photons created by stimulatedemission to exceed all other mechanisms. This is achieved by bounding the laser mediumbetween two mirrors as shown in figure 2. On one end of the active medium is the highreflectance mirror (100% reflecting) or the rear mirror and on the other end is the partially

reflecting or transmissive mirror or the output coupler. The laser emanates from the outputcoupler, as it is partially transmissive. Stimulated photons can bounce back and forward


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along the cavity, creating more stimulated emission as they go. In the process, anyphotons which are either not of the correct frequency or do not travel along the opticalaxis are lost.

Laser action: Interaction of electromagnetic radiation with matter produces absorption andspontaneous emission. Absorption and spontaneous emission are natural processes. For thegeneration of laser, stimulated emission is essential. Stimulated emission has to be induced orstimulated and is generated under special conditions as stated by Einstein in his famous paperof 1917. i.e. ?when the population inversion exists between upper and lower levels amongatomic systems, it is possible to realize amplified stimulated emission and the stimulatedemission has the same frequency and phase as the incident radiation?. Einstein combinedPlank? law with Boltzmann?s statistics in formulating the concept of stimulated emission. Inelectronic, atomic, molecular or ionic systems the upper energy levels are less populated thanthe lower energy levels under equilibrium conditions. Pumping mechanism excites say, atomsto a higher energy level by absorption (Figs.3a and 3b).

The atom stays at the higher level for a certain duration and decays to the lower stable ground

level spontaneously, emitting a photon, with a wavelength decided by the difference betweenthe upper and the lower energy levels. This is referred to as natural or spontaneous emissionand the photon is called spontaneous photon. The spontaneous emission or fluorescence has nopreferred direction and the photons emitted have no phase relations with each other, thusgenerating an incoherent light output (Fig.4). But it is not necessary that the atom is alwaysde-excited to ground state. It can go to an intermediate state, called metastable state with aradiation less transition, where it stays for a much longer period than the upper level andcomes down to lower level or to the ground state. Since period of stay of atoms in themetastable state is large, it is possible to have a much larger number of atoms in metastablelevel in comparison to the lower level so that the population of metastable state and the loweror ground state is reversed. i.e. there are more atoms in the upper metastable level than thelower level. This condition is referred to as population inversion. Once this is achieved, laseraction is initiated in the following fashion. The atom in the metastable state comes down to

the ground state emitting a photon. This photon can stimulate an atom in the metastable stateto release its photon in phase with it. The photon thus released is called stimulated photon. Itmoves in the same direction as the initiating photon, has the same wavelength and polarizationand is in phase with it, thus producing amplification. Since there are a large number ofinitiating photons, it forms an initiating electromagnetic radiation field. An avalanche ofstimulated photons is generated, as the photons traveling along the length of the activemedium stimulates a number of excited atoms in the metastable state to release their photons.This is referred to as the stimulated emission. These photons are fully reflected by the rearreflector (100% reflective) and the number and consequently the intensity of stimulatedphotons increases as they traverse through the active medium, thus increasing the intensity ofradiation field of stimulated emission. At the output coupler, a part of these photons arereflected and the rest is transmitted as the laser output. This action is repeated and thereflected photons after striking the rear mirror, reach the output coupler in the return path.

The intensity of the laser output increases as the pumping continues. When the input pumpingenergy reduces, the available initiating and subsequently the stimulated photons decreaseconsiderably and the gain of the system is not able to overcome the losses, thus laser outputceases. Since the stimulation process was started by the initiating photons, the emittedphotons can combine coherently, as all of them are in phase with each other, unlike in the caseof spontaneous emission and coherent laser light is emitted (Fig.5). Though the laser action willcontinue as long as the energy is given to the active medium, it may be stated that pulsed laseris obtained if the population inversion is available in a transient fashion and continuous wave(CW) laser is possible if the population inversion is maintained in a steady-state basis. If theinput energy is given by say a flash lamp, the output will be a pulsed output and the laser iscalled a pulsed laser. If equilibrium can be achieved between the number of photons emittedand the number of atoms in the metastable level by pumping with a continuous arc lampinstead of a flash lamp, then it is possible to achieve a continuous laser output, which is calledcontinuous wave laser.


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We may conclude that, laser action is preceded by three processes, namely, absorption,spontaneous emission and stimulated emission - absorption of energy to populate upper levels,spontaneous emission to produce the initial photons for stimulation and finally, stimulatedemission for generation of coherent output or laser.

LASER GENERATION

n this section, we will discuss pumping mechanisms to excite active ions to higher levels for

population inversion, laser resonators for control of amplification and creation of special beamprofiles, Q-switching techniques to increase the power of the laser output to very high levels,thermal and birefringence effects produced by the heating of the laser medium affecting the beamquality etc. related to laser generation in solid state, gas, semiconductor, dye, free electron and X-Ray lasers. Although these technologies vary very much for each of the above-mentioned lasers,there are lots of common factors as can be seen from the following paragraphs.

Pumping or excitation mechanisms:

First requirement in the generation of laser is the creation of population inversion. Input energy invarious forms have to be supplied to the gain media for excitation and transition of ground levelatoms, molecules, ions or electrons as the case may be, to higher levels to create populationinversion and consequent generation of laser. Commonly used excitation techniques are opticalpumping (solid state lasers), electrical discharge / radio frequency excitation (gas lasers), electron


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beam / injection current (semiconductor lasers), chemical (chemical lasers), thermal (Gas DynamicLasers), high-energy electrons from accelerator (free electron lasers) etc. Lasers, with output inthe spectral region matching the absorption band of the active media, are also employed forexcitation. The type of excitation techniques used is decided by the nature of the active lasermedia. The different types of excitation mechanisms are optical, electrical, chemical, thermal,laser etc.

Optical: In solid-state lasers (SSLs), the laser media are in the form of optically transparent solidmaterials with active ions having strong absorption bands in the visible or near infrared region. Apump source, giving maximum emission at wavelengths to excite fluorescence in the laser material,is most suited for SSLs. Noble gas filled flash lamps, metal vapour discharge lamps, tungsten-halogen filament lamps, semiconductor lasers, etc. are all used in this connection. Xenon flashlamps for pulsed operation and CW arc lamps for CW operation of lasers are the most commonlyemployed optical pumps. An optical reflector cavity is required to couple the high intensity lightoutput efficiently from the flash lamp to the laser rod. Various reflecting geometries have beenemployed for this purpose. Elliptical reflector, with the laser rod at one focus and the flash lamp atthe other, cylindrical reflector with the lamp and the rod in close proximity or the rod surroundedby the helical flash lamp, have all been used for efficient coupling of light on to the rod. Endpumping as well as side pumping geometries have been employed for diode laser pumping of solid-

state lasers. Examples of optically pumped SSLs are Nd:YAG, Nd: Glass and Alexandrite, to sight afew.

Electrical: In gas lasers (helium-neon, argon ion and carbon dioxide lasers), electrical discharge isemployed to excite neon atoms, argon ions and CO2 molecules respectively to higher levels tocreate population inversion. The most common type of excitation is either a direct currentelectrical discharge or a radio frequency discharge. For high power CO2 lasers, instead of having thedischarge along the length of the laser tube, a transverse excitation, with a series of electrodesspaced along the gas tube, is employed.

Chemical: In chemical lasers, the chemical reaction generates a large amount of excited moleculesand then another gas is introduced in to the system. Now depending on the system, one of the twofollowing things can happen. Either it takes energy from the excited molecule, as in the case of

COIL (iodine molecules from singlet oxygen) or it reacts with those particles, producing an excitedmolecule, as in the case of DF / HF laser (deuterium or hydrogen respectively with fluorineradicals) These excited molecules produce population inversion. COIL, DF and HF lasers are some ofthe examples of chemical lasers.

Thermal: In gas dynamic laser, adiabatic expansion cooling of hot gases is utilized to producepopulation inversion. The technique is to expand hot gases through specially shaped nozzles from ahigh pressure, high temperature chamber into a low-pressure chamber, thus creating a highly non-equilibrium state in the resonator. Due to adiabatic expansion, the upper level population is frozenand the lower level population is depleted, resulting in strong population inversion. Carbon dioxidegas dynamic laser (CDGDL) is an example of a thermally excited laser.

Laser: Ti: Sapphire laser is a good example of a laser pumped laser. As the peak of the absorptionband of Ti: Sapphire is around 500 nm, frequency doubled Nd: YAG laser (532 nm) for pulsedoperation and Argon ion laser (514 nm) for CW mode of operation are used for excitation to createpopulation inversion and subsequent laser emission. Diode laser pumping of Nd: YAG laser isanother example of a laser being employed for excitation.

These pumping techniques have been discussed in greater details in the next chapter, whichdeals with specific type of lasers.

Resonators:

The two mirrors, between which the gain medium is situated is referred to as the laser resonator.

Resonator plays a very important role in controlling small signal gain as well as total gain of thelaser system and developing transverse and longitudinal modes. It is responsible for generating


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special types of laser beam profiles and also gives the laser its unique property of directionality andcoherence. The spectral characteristics of the laser, like beam diameter, divergence and energydistribution are controlled primarily by transverse modes. Line width and coherence length arebasically determined by longitudinal modes. Various types of resonators were discussed in theearlier section and the same will not be repeated. Further, the intention of this site is only to givean insight into the subject and to provide references for a serious study.

Different resonator types are distinguished by the focal lengths of the two mirrors and thedistance between them. The most common types of optical cavities consist of two flat orspherical mirrors. The simplest of these is the plane-parallel or Fabry - Perot cavity,consisting of two flat mirrors separated by some distance L. These arrangements of flat mirrors areusually not preferred because of the difficulty of their alignment with required accuracy, which istypically few seconds of arc. Fabry - Perot cavities suffer from another type of problem, whichfurther results in increased losses. The plane waves that exist in F-P cavities generate largediffraction losses at the edges of the mirrors. Losses, in general, are very carefully monitored inlaser cavities because they can wipe out the gain of the active medium. The resonator geometrymust be chosen so that the beam remains stable. By stability, we mean that the size of the beamdoes not continually grow with multiple reflections. However, this problem is much reduced forvery short cavities with a small mirror separation distance (L < 1 cm). Plane-parallel resonators are

therefore commonly used in microchip and semiconductor lasers. In these cases, rather than usingseparate mirrors, the laser medium itself is suitably coated at both the ends to serve as fullyreflecting and partially reflected mirror.

The plane-parallel cavity (shown in the above figure) is an important component in pulsed solidlasers and some other pulsed lasers as well because its high mode volume makes efficient use ofthe active medium. Though, the cavity has the highest diffraction loss of any configuration, but thisloss is overcome easily in pulsed lasers by the additional gain achieved by the larger mode volume.It has the additional advantage of not focusing the laser beam inside the active medium. Suchinternal focusing can damage solid laser rods. As mentioned earlier, the plane parallel cavity is,however, the most difficult to align,

Optical cavities are designed to have a large Q factor, so that the beam can reflect large number of

times without any significant attenuation. As such, the frequency and thus the line width of thebeam are very small as compared to the frequency of the laser.

For the type of lasers we are discussing, flat mirror geometries are not feasible. Only certain rangesof values for R1, R2, and L produce stable resonators in which periodic refocusing of the intra-cavitybeam is produced. If the cavity is unstable, the beam size will grow without limit, eventuallygrowing larger than the size of the cavity mirrors and being lost. The stability criterion in terms ofR1, R2 and L is given as:

OR

WHERE


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The stability criterion can be shown graphicallyby plotting g1 against g2 as shown. Areas boundedby the line g1 g2 = 1 and the g1 g2 axes are stable.Cavities at points exactly on the line aremarginally stable. Even a little variation in cavitylength can cause the resonator to become

unstable. The plane-parallel cavity correspondsto point (1,1) in the stability diagram.

For a resonator with two mirrors with radii of

curvature R1 and R2, there are a number ofcommon cavity configurations. Some of theseconfigurations are discussed below:

If the two curvatures are equal to half the cavitylength (R1 = R2 = L / 2), a concentric or sphericalresonator results. This type of cavity produces adiffraction limited beam waist in the centre ofthe cavity, with large beam diameters at themirrors, filling the whole mirror aperture. This

type of configuration corresponds to point (-1,-1)in the stability diagram.

The spherical cavity is shown in the adjoining figure and is basically functionally opposite to theplane- parallel cavity. It is easiest to align, has the lowest diffraction loss, and has the smallestmode volume. CW dye lasers usually employ this type of cavity because a focused beam isnecessary to cause efficient stimulated emission of these lasers. The spherical cavity is notcommonly used with any other type of laser.

The confocal cavity is a compromise between the plane-parallel and the spherical cavities. Theconfocal cavity combines the ease of alignment and low diffraction loss of the spherical cavity withthe increased mode volume as in case of flat and parallel mirror configuration. This configurationcorresponds to a point (0,0) in the stability diagram. Confocal cavities can be utilized with almost

any CW laser for moderate power levels. A common and important design is the confocal resonator,with equal curvature mirrors equal to the cavity length (R1 = R2 = L). This design produces thesmallest possible beam diameter at the cavity mirrors for a given cavity length, and is often used inlasers where the purity of the transverse mode pattern is important. In case of confocal resonatorthe foci F1 and F2 of mirrors are coincident. In this case, the center of curvature of one mirror lieson the surface of another mirror as L=R.

Resonators formed by two spherical mirrors of the same radius of curvature R and separated by adistance L such that R


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The hemispherical cavity, which is actually ahalf of the spherical cavity, has characteristicssimilar to that of spherical. This configurationcorresponds to point (0,1) in the stabilitydiagram. The advantage of this type of cavity

over the spherical cavity is the cost of themirrors. The hemispherical cavity is used withmost low-power HeNe lasers because of lowdiffraction loss, ease of alignment, and reducedcost.

Cavities can be identified as stable or unstableaccording to whether a particular configuration allows the cavity oscillations to remainwithin the cavity or the laser beam spreads out of the cavity. The output mirror of the laserresonator is precisely coated to achieve the required reflection into the cavity. In case thebeam is too intense, the mirror may suffer damage, which may result in the cessation of laseraction. Generally, for low powers typically less than a kilowatt, lasers mainly use stable cavityconfigurations. The laser output is from the center of optical axis. Stable cavity design allows the

beam to oscillate many times inside the cavity to get high gain, and also the focal property anddirectionality are also improved. However, for high power lasers, unstable cavity configurations areusually preferred as shown in the adjoining figure. The laser output comes from the edge of theoutput mirror, which is often a totally reflecting metal mirror. This concave-convex cavitynormally is used only with high power lasers. In practice, the diameter of the convex mirror issmaller than that of the beam. The output beam is formed by the part of the beam that passesaround the mirror and, consequently, has a "doughnut" configuration. The beam must pass aroundthe mirror because mirrors that will transmit the intense beams of these high-power lasers cannotbe fabricated. The ring shaped beam reduces the intensity of the beam, thus reduces the risk ofdamaging the mirror. In this cavity configuration, the ring shaped beam is however, poor forfocusing. Unstable cavities are suitable for high gain per round trip laser systems, which don'trequire large numbers of oscillation between the mirrors.

Thermal problems:

Efficiency of most of the laser systems is very poor (less than 5%) and as such the unutilized inputenergy goes as heat. To understand effect of thermal problems on the resonator, let us consider asolid-state laser. Since most of the input energy goes up in heating the laser rod, fluid cooling isemployed to get the rod with in the thermal limit of working. During the cooling cycle, radialtemperature gradient arises between the center of the rod and its surface i.e. center of the rod isat higher temperature than the periphery, as the surface gets cooled faster than the central region.Consequently, refractive index variation in the material takes place, resulting in thermal lensing.We can say that the input power of the optical pump controls the beam radius with in the laser rodin the resonator. Thus, thermally induced birefringence occurs and depolarization effects become a

hindrance for power scaling or increasing the repetition rate of the laser. It becomes imperative toknow the compensation of depolarization in order to design a resonator for high power lasers.Further, the finite size of the resonator mirrors and inherent in-homogeneity of the laser crystalalso produce aberration of the output beam. Resonator dielectric mirrors in the lasers are passivestructures and they cannot correct the aberration introduced. The use of self-correcting adaptiveresonators and phase conjugate mirrors has reduced these aberrations to a great extent.

Q-switching techniques:

The losses associated with the modes generated in the resonator are radiation losses produced byscattering and absorption due to impurities in the laser material, diffraction losses associated withthe finite dimensions of the laser material, mirrors, other optical components etc and reflection

losses produced by the imperfect mirrors. It is necessary to overcome these losses by way ofbuilding up gain with the feed back between the mirrors, while the population inversion and


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stimulated emission exist. The Q or quality factor of an optical cavity describes the ability of thecavity to store light energy in the form of standing waves. The Q factor is the ratio of energycontained in the cavity divided by the energy lost during each round trip in the cavity:

This means that a cavity with high losses dissipates a lot of energy per cycle hence it has a low Qvalue; a high Q cavity means the energy loss per cycle is small in the given cavity. Hence higher thequality factor, lower is the losses.

This implies that by controlling Q, one can control the output of the laser. Q-switching or Q-spoilingis a technique to generate high power laser output by controlling the quality factor in a laser cavityi.e. controlling the losses. Q-switch, located in the cavity can change temporal and power

characteristics of the laser beam.

Q switching technique can be defined as a method to create high power / energy laser pulses.It modulates the Q of laser cavity to build population inversion first, and then release theaccumulated energy suddenly, in this way high-energy pulses can be created.

If a closed shutter is kept inside the laser cavity during pumping, the optical feedback betweenmirrors will be prevented. Consequently, the population inversion caused by energy stored in thematerial, as well as the gain increases to a high value. But the losses are also high (low Q) and dueto the absence of feedback, the increase in gain to overcome the losses are not available andconsequently the laser action is inhibited. When the shutter is suddenly opened, high Q (low loss) isrestored and the excess energy stored is discharged in a very short time, resulting in a high powerlaser pulse, which is several orders of magnitude higher than the normal pulse. The basic idea isthat for only a brief time is the beam allowed to pass back and forth between the mirrors toachieve the laser action, but the pumping action is continuous so that a large population inversionis already build up when the lasing condition is satisfied. Since the power of the pulse is very high itis called a giant pulse. Q-switched lasers normally emit only one giant pulse in an operational cycle.The pulse typically has time duration of nanoseconds and the peak intensity is of 106 - 109 watts.The extremely short, high-energy output pulses make the Q-switched lasers an ideal transmittersource for rangefinders and surveillance radar applications.

A good Q-switch should reduce the loop gain to zero when closed and should introduce no loss inthe cavity when opened. It should switch from one condition to the other as fast as possible, andthe switching should be synchronized to external events.

There are a number of techniques employed for the generation of high power laser pulses, whichare discussed briefly below:

Mechanical:

In the mechanical Q-switching technique, rotational, oscillatory or translational motion ofoptical components are used to create a situation, where laser action is inhibited duringpump cycle either by putting a shutter between mirrors or by misaligning mirror itself i.e.to introduce high loss during pumping for storing the excess energy in the material. Pulse widths ofthe order of few tens of nano-seconds have been obtained with this technique.

The simplest type of Q-switch uses a rotating mirror or prism to form one end of the optical cavity.

A sensor triggers the pump source i.e. flash lamp just before the mirror or other optical elementrotates into position such that the resonator mirrors are parallel to each other. Usually the


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maximum-reflectivity mirror is rotated so that the mirror is tilted out of alignment. The system isQ-switched when the mirror rotates back into alignment. This alignment happens once in eachrevolution. Rotating mirror Q-switches offer 100% dynamic loss and 0% insertion loss. This is fairlyeasy to do with ruby as the lasing medium with its long (3 ms) fluorescence lifetime. However, the

corresponding value for Nd: YAG is only 230 s.Thus, only 100 to 200 s is available oncethe flash lamp fires and sensing the position of a rotating optical element to this precision

would be somewhat more difficult. For example, at 6,000 rpm or 100 rps, one revolution iscompleted in 10-4 sec. Thus 100 microseconds correspond to 1/100th of a full rotation. However, ifrotating mirror can be made multifaceted or the Q-switch speed can be made fast enough byrotating the mirror at high speed typically 20,000 to 60,000 rpm, even lasers like Nd: YAG can be Q-switched and switching time typically of a few nanoseconds can be achieved. However, rotatingmirror Q-switches are prone to alignment difficulties because each face of the mirror must bealigned to within a fraction of milliradian. Thus, roof prisms are often used as rotating elements. Aslong as the roof of the prism is perpendicular to the axis of rotation, reflection is guaranteed atsome angle of rotation. Simple set ups are shown in the adjoining figures.

Mechanical Q-switches are simplest and least expensive of the Q-switches. They have the additionaladvantages of polarization and wavelength insensitivity. However, the high rotational speeds meanthat the devices are noisy and possess relatively short lifetimes. Furthermore, mechanicalcomponents are not robust in harsh environments.

Electro-optical:

Probably the most reliable and commonly used Q-switches employ electro-optical (E-O) effect incrystals (Pockels effect) and liquids (Kerr effect). An E-O element like the properly oriented lithiumniobate crystal, under the influence of electric field, becomes birefringent, producing 'fast' and'slow' axes orthogonal to each other, with different refractive indices. A plane polarized optical

beam at 45 to these axes and incident normal to their plane, will split in to two orthogonalcomponents, traveling along the same path, but with different velocities, causing a phasedifference between the them. Depending on the voltage applied to the E-O element (eg. Lithium

niobate crystal), the combination of the two beams will produce a linearly, circularly or anelliptically polarised beam. E-O Q-switch is formed by the combination of a polariser and an E-Oelement in the resonator cavity. These are called Pockels cell Q-switches also, since the working isbased on Pockels effect.

This common arrangement for an electro-optic Q-Switch in which the Q-Switch is placedbetween a linear polarizer and the rear mirror is shown in the figure. The applied voltage

across the Q-Switch is chosen so as to cause a /4 difference in the phases of the emergingcomponents. If linearly polarized light enters the crystal, then circularly polarized light willemerge. In other words, when voltage is applied to the Q-Switch, it acts like a quarter-wave plate.Initially, the beam passes through the linear polarizes. It enters the electro-optic crystal andemerges as right circularly polarized light. After it reflects from the mirror, it converts into leftcircularly polarized light. When the beam passes through the electro-optic crystal, it emerges aslinear polarized light but perpendicular to the direction of the original light polarization. In other

words, the /4 Q-switch plus the mirror reflection plus the /4 Q-switch again, acts like a /2 orhalf-wave plate that will convert linear polarization in one direction to linear polarization in theorthogonal direction. This orthogonal polarized beam is then ejected from the cavity by thepolarizer. When the voltage is removed from the Q-Switch, the crystal is no longer birefringent.Thus, the emerging beam from the crystal is unchanged and is not affected by thepolarizer. Therefore, this Q-Switch only produces a pulse when the voltage is off.

Another method is to place the E-O element between two crossed linear polarisers. Initially,the beam passes through the linear polarizer. It enters the electro-optic crystal andemerges as linear polarized light rotated by 90 degrees (orthogonal to the original

polarization). It then can pass through the second polarizer. When the voltage is removed from the

Q-Switch, the crystal is no longer birefringent and emerging be

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