UNIT -1 LASER

LASER is an acronym for ‘light amplification by stimulated emission of radiation’. It is a source of light like incandescent lamp or discharge tube.

Albert Einstein in 1917, showed the process of stimulated emission must exist but it was in 1960 that T.H. mariman first achieved laser action of optical frequency in ruby.

Following are the properties of lasers which differ with other sources.

Most of the sources have monochromatic light beam but of low intensity It is difficult here to concentrate whole o/p of a light source.

Properties :-1) LASER is highly monochromatic beam

2) It has high intensity

3) It can produce long wave trains

4) It is innumerable for best focusing

5) It can be narrow as beam of 2-3 microns cross section.

6) The parallelism of emitted beam of light is of high degree.

Emission and absorption of radiation :

When an electron in an atom undergoes transition between two energy states or levels , it either emits or absorbs a photon, which can be discussed in terms of a wave of frequency (ѵ)= ∆E/h, ∆E bring the energy difference between the two levels concerned

Consider the electron transition occurring b/w the two level of the hypothetical atomic s/m . if the electron is in the lower level E1 than in the presence of photon of energy (E2-E1) it may be excited to the upper level E2 by absorbing a photon.

Alternatively, if the electron is in the level E2 it may return to the ground state with the emission of a photon . The emission process occurs in two distinct ways :

a) Spontaneous emission process in which the electron drops to the lower level in an entirely random way.

b) Stimulated emission process in which the electron is triggered to undergo the transition by the presence of photon of energy (E2-E1). The transition is simply stimulated by the presence of the stimulating photon.

Under normal circumstances we do not observe the stimulated process because the probability of the spontaneous process occurring is much higher.

The average time the electron exist in the excited state before making a spontaneous transition is called lifetime T21 of the excited state.

The ‘21’ level indicates the energy level involved. The probability that a particular atom will undergo spontaneous emission within a time interval dt is given by A21dt=dt/ T 21, where A21 is the spontaneous transition rate.

Because the spontaneous radiation from any atom is emitted at random, the radiation emitted by a large number of atoms will clearly be in coherent..

In contrast, the stimulated emission process results in coherent radiation since the waves associated with the stimulating or stimulated photon have identical frequencies, are in phase, have the same state of polarization & travel in the same direction.

It means that with the stimulated emission the amplitude of an incident wave can grow as it passes through a collection of excited atoms is clearly a amplification process.

As the absorption transition, is common with stimulated emission, can only occur in the presence of photons of appropriate energy, it is often referred as stimulated absorption. But both these process are inverse of one another.

Einstein relation :

Einstein showed that the parameters describing the above 3 processes are related through the requirement that, for a system in thermal equilibrium the rate of upward transition (from E1 TO E2) must equal the rate of the downward transition processes(from E2 to E1)

If there are N1 atom per unit volume in the collection with energy E2, then the upward transition or absorption rate will proportional to both N1 & to the no. of photons available at the correct frequency.

If ρv is the energy density at frequency ѵ, then (ρv=Ŋhѵ where Ŋ→ no. of phtons per unit volume having frequency ѵ )

Therefore, we can unite upward transition rate as N1 ρvB12 ―‹a›

B12= constant

Similarly if there are N2 atoms per unit volume in the collection with energy E2 then the induced transition rate from level 2 to level1 is N2 ρvB21

B21= constant

The spontaneous transition rate from level2 to level1 is N2A21

The total downward transition rate is the sum of the individual and spontaneous contribution

i.e N2 ρvB21+ N2A21 ―‹b›

A21,B21, & B22 are Einstein coefficients

The relationship between them can be established as follows:

For a s/m to be in equilibrium, the upward & downward transition rates must be equal.

i.e N1 ρvB12 = N2 ρvB21+ N2A21 ―‹1›

then ρv= N2A21 / (N1B12-N2B21)

OR ρv =A21B21/((B12 N1/B21*N2)-1) ―‹2›

Population of the various energy levels of a s/m in thermal equilibrium are given by Boltzmann statistics

Nj= (gjN0 exp (-Ej/kT))/∑gi exp (-Ei/kT) ―‹3›

Hence N1/N2 =g1/g2* exp ((E2-E1)/kT)

= g1/g2* exp(hѵ/kT) ―‹4›

Put (4) in (2) , we get

ρv =A21/B21/[(g1 * B12/g2*B21 )* exp(hѵ/kT)] -1 ―‹5›

Since the collection of atoms in the system are considered in thermal equilibrium it must give noise to radiation which is identical with black body radiates .

The radiation density of which can be described by

―‹6›

Comparing (5) & (6) we get for we get

=g2B21 ―‹7›

& ―‹8›

(7) & (8) are called Einstien relations

(8)Enables to evaluate the ratio of the rate of spontaneous emission to the rate of stimulated emission for a given pair of energy levels.

Ratio is given by R= & ―‹9›

The above discussion indicates that the process of stimulated emission compete with the process of spontaneous emission & absorption.

If we want to amplify a beam of light by stimulated emission then we must increase the rate of this process in relation to the other two processes.

(1) Indicates that to achieve this for a given pair of energy levels we must increase both the radiation density and the population density N2 of the upper level in relation to the population density N1 of the lower level.

In fact to produce a laser action we must create a condition in which N2

Even though E2>E1 i.e we must create a so called population inversion.

Population inversion:- it is a condition required for light amplification in a non equilibrium distribution of atoms among the various energy levels of the atomic system.

The Boltzmann distribution which applies to s/m in thermal equilibrium is given by (3) & is illustrated in fig (a) below.

Nj is the population density of the Jth energy level and clearly as Ej increases Nj decreases for a constant temperature.

(If the energy difference between E1 & E2 is nearly equal to ICT (≈.025eV at room temp ) then the population of the upper level would be 1/e or 0.37 of that of the lower level)

For an energy difference large enough to give visible radiation (≈2.0eV), however, the population of the upper level is almost negligible.

“if we want to create a population inversion, fig(b) we must supply a large amount of energy to excite atoms into the upper level E2.”

This excitation process is called pumping & much of the technology of laser is concerned with low the pumping energy can be supplied to a given laser s/m

Pumping produces a non thermal equilibrium situation.

Attainment of a population inversion :

One of the methods used for pumping is stimulated absorption the energy levels which one hopes to use for laser action are pumped by intense irradiation of the s/m.

Consider a 3 level s/m (eg ruby laser)

Initially the distribution 0beys the Boltzmann level of the collection of atoms is initially illuminated the electron can be exited (pumped) into the level. E2 from the ground state Eo.

From E2 the elation delay by non radiation pronouses to the level E1 and a population inversion may be created between E1&E0. Ideally the transition from level E2 to E1 should be very rapid , these by ensuring that there are always vacant state at E2, while that from E1 to E2 should be very slow i.e E1 should be a metastable state

This allows a large build up in the no of atom in level E1 as the probability of spontaneous inversion is relatively small .Eventually N1 may become greater than N0 and then population emission will have been achieved .

level E2 should preferably consist of a large no of closely spaced levels so that pumping uses as wide a part of the spectral range of the pumping radiation as possible there by increasing the pumping radiation as possible thereby increasing the pumping efficiency.

Normally there require very high pump powers become the terminal level of the less transition is the ground state more than half of GND state atom have to be pumped to the upper state to achieve population inversion.

From level s/m:

4 layer s/m has much lower pumping requirements . if (E1-E0) is rather large compared to Kt (Thermal energy ) then the population of the levels E1,E2,& E3 are all very small in conditions of thermal equilibrium. Thus if atoms are pumped from the ground state to the level E3 from which they delay very rapidly to the metastable state E2, a population inversion is quickly created b/w levels E2 & E1.

Again upper level E2 should preferably consist of a large no. of levels for greatest pumping efficiency.

If the lifetimes of the transitions E3→E2 & E1→E0 are short, the population inversion between E2 & E1 can be maintained with moderate pumping or continous laser action be obtained.

The energy level schemes of the media used in lasers are often complex but they can usually be approximated by other 3 or 4 level schemes.

Methods of excitation : 1) optical pumping

2) electric discharge

Optical pumping : Here xenon or incandescent lamps are used as pump sources. High pressure discharged tubes for optical pumping.

For a 3 level ruby crystal is used & for a 4 level CaF2 (calcium flouride) is used .

Electric discharge : it is used for gas medium the gas laser depend on electrical discharge by means of radio frequency dc (or) a pulsed pointer supply response for population inversion.

Optical feed back : laser despite its name, it is more analogous to an oscillator then an amplifier. In an electric oscillator, an amplifier tuned to a particular frequency is provided with +ve f/b & when switched on , any electrical noise signal of the appropriate frequency appearing at the i/p will be amplified.

The amplified o/p is fed back to i/p & again amplified & so on & a stable o/p is quickly reached.

(In laser, +ve f/b is obtained by placing the gain medium between a pair of mirrors, which from a optical cavity )

The initial stimulus is provided by any spontaneous transition between appropriate energy levels in which the emitted photon travels along the axis of the system.

The signal is amplified as it passes through the medium & fed back by the mirrors. Saturation is reached. When the gain provided by the medium exactly matches the losses incurred during a complete round trip.

Some commonly used laser cavity mirror configurations are :

Q-switching : it is one of the technique for obtaining short, intense bursts of oscillation from lasers. it increases the peak power obtainable from lasers.

The laser o/p would be in the form of a giant pulse since the gain is far above the steady state condition for gain in the cavity and would therefore be quickly reduced by stimulated emission such a process can be implemented by technique of Q-switching.

Since the cavity is quickly changed from a low Q to high Q state where `Q’ denotes the ratio of energy stored to the energy dissipated within the cavity .

Single high power pulses can be obtained by introducing time or irradiance dependent losses into the cavity. Initially a very high loss in the laser cavity, the gain due to population inversion can reach a very high value without laser oscillation occurring. The high loss prevents laser action while energy is being pumped into the excited state of medium . when a large population inversion has been

achieved the cavity loss is immediately reduced i.e the cavity `Q’ is switched to a high value, laser oscillation will suddenly commence. On Q-switching the threshold hold gain remain high because of the large population inversion.

This makes large difference between the actual & threshold gain, laser oscillation with cavity build very quickly & all the available energy is emitted in a single large pulse. This rapidly depopulates the upper level to such an extent that the gain is reduced below threshold & the lasing action stops.

Eg :- ND:YAG consists of many random `spikes’ of about 1µs; the length of the train of spike depends principally on the duration of the exciting flash tube source, which may be about 1ms. Peak power within the `spikes’ are typically of the order of kilowatts.

When the laser is `Q’ switched, however, the result is a single `spike’ OF great power, typically in the mega watt range, with a duration of 10-100 ns.

Hence although there is a vast increase in the peak power of a `Q-switched’ laser, the total energy emitted is less than in non-Q switched operation resulting to losses associated with the Q-switching mechanism.

“ Q-switching is carried out by placing a closed shelter (i.e the Q-Switch) within the cavity, thereby effectively isolating the cavity from the laser medium.

After the laser has been pumped, the shelter is opened so restoring the Q of the cavity

Requirement for effective Q switching.

1) The rate of pumping must be faster than the spontaneous delay rate, otherwise upper level will empty more quickly than it can be filled so large population inversion cannot be achieved.

2) Q switch must switch rapidly in comparision to the build up of laser oscillation, otherwise the rather will build up gradually & a larger pulse will be obtained so reducing the peak power.

In practice Q switching is operated in time less than 1ns.

Methods of Q switching :

1. Rotating mirror method 2. Electro –optic Q switching3. Passive

1) Rotating mirror : it was first to be developed , involves rotating one of the mirrors at a very high angular velocity such that the optical losses are large except for the brief interval in each rotation cycle . when the mirrors are very nearly parallel. When the mirror become parallel Q switching other allowing the Q switched pulse to develop . if the laser is fixed every revolution, the repetition rate would be ≈1000 times per second.

The repetition rate of laser firing is determined by control of the flash temp & not by the speed of rotation of the mirror, which may as high as 60,000 rev min^-1

Advantages : cheap, reliable & rugged

Disadvantages : slow hence results in an insufficient production of Q-switched pulses with lower peak power.

2) Electro optic Q-switching : some times electro- optic magneto-optic & acousto – optic modulators can be used for fast Q switching. Hence if a laser o/p is not naturally polarized, than be placed in the cavity along with the Quanti wave plate which converts the linearly polarized light incident on it onto circularly polarized light. The laser mirror reflects this light and in so doing reverses its direction of rotation so that on re-passing through the electro-optic cell it emerges as plane polarized light ; but at 90⁰ to its original direction of polarization.This light is therefore not transmitted by the polarizer and the cavity is `switched off’ . when the vj is reduced to zero, then in no rotation of the plane of polarization & Q-switching occurs .

Electro optic crystal used as a q switch with the voltage v on, the electro optic crystal acts as a quanta wave plate & converts the vertically polarized light at b into circularly polarized light at c. The reflected light is connected to horizontally polarized light and eliminated by the polarizer so that cavity Q is low. With voff, the crystal is ineffective & the cavity Q is high.Passive Q SWITCHING :- this is accomplished by placing a saturable absorber (bleachable dye) in the cavity.At the beginning of the excitation flash the dye is opaque, thereby preventing laser action and allowing a larger population in waves to be achieved than would otherwise be there.

As the light irradiance within the cavity increases, the dye can no longer absorb i.e it bleaches and Q Switching occurs.Advantage :- simple to implement as it requires only a dye in a suitable solvent held in a transparent cell.Suitable dyes include crypto cyamine for ruby lasers & sulphurhexa fluoride for c02 lasers.Mode locking : it is a technique for producing periodic, high power, short duration laser pulses. The broadened laser cavity may support oscillation in many modes simultaneously The o/p of such a laser as a function of time depends on the relative phases, frequencies & amplitudes of the modes.i.e here the phase relationships of the modes are kept constant & the o/p consists of a several of narrow intense pulses of time spacing 2L/C or cluster

types : 1) active mode locking : mode locking is achieved by forcing the longitudinal modes to maintain fixed relationship.

2. passive mode locking : certain dyes whose absorption decreases with increasing irradiance are used

Classification of laser : 4 types

1.doped insulator (solid) 2. Semiconductor

3. gas laser 4. Dye laser (liquid)

Requirements of a laser operation

1. There must be an active medium which units radiation in the required region of the electromagnetic spectrum.

2. A poplation inversion must be created within the medium which requires the existence of suitable energy levels associated with the lasing transition for pumping.

3. There must be an optical f/b at the ends of the medium to form a resonant cavity

Doped insulator laser : it is used to describe a laser whose active medium consists of an array of atoms usually in crystalline form, with impurity atoms intentionally introduced (doped) into the array during growth.

These are rugged, easy to maintain & capable of generating high peak powers

Eg :- ruby & Nd-Yag

ND:YAG laser :- the active medium for this laser is yttrium aluminium garnet (Y3al5O12) with the rate earth metal ion neodymium nd+3 present as an impurity. The nd+3 ions, which are randomly distributed as substitutional impurities on lattice sites normally occupied by the yttrium ions,

provide the energy levels for both the lasing transition and pumping .

From the fig nd:yag laser is essentially a 4 level s/m i.e the terminal laser level 4I is sufficiently far removed from the ground state 4I that its room temp population is very small, thereby a number of laser transitions may occur between . some of the pairs of levels shown to the right of the figure, the most intense line at 1.064µm arises from the superposition of the two transition sown.

Pumping is normally achieved by using an intense flash of white light from a xenon flash tube. This excites the nd_3 ions from the governed state tot the various energy states above the 4f state.

To ensure that as much radiation as possible from the flash tube is absorbed in the laser medium , close optical coupling is required.

The arrangement is shown in the fig :

Typical construction of a doped insulator laser showing the ellipsoidal reflector used to maximize optical coupling b/w the flash tube & laser rod.

A linear flash tube and the lasing medium in the form of a rod are placed inside a highly reflecting elliptical cavity. If the flash tube is along one focal axis and the laser rod along the other, then the properties of the ellipse ensure that most of the radiation from the flash tube passes through the laser. The flash tube is find by discharging a capacitor bank through the tube; the discharge is often initiated by using a secondary high ng(app. 20kV) trigger pulse.

As the pumping flash lasts for only a short time the laser o/p is in the form of a pulse, which starts about after the pumping flash starts. This represents the time for the population inversion to build up.

Once started , stimulated emission builds up rapidly and the depopulates the upper lasing level2 much faster in fast than the pumping can replace the excited atom so that laser action momentarily stops until population inversion achieved again.

The optical cavity is formed by grinding the ends of the nd-yag rod flat and parallel and then slurring than more usually, however, external mirrors are used as shown in the fig.

One mirror is made totally reflecting while the other is about 10% transmitting to give an o/p

A large amount of heat is dissipated by the flash tube and consequently the laser rod quickly becomes very hot.

To avoid damage resulting from this, and to allow a reasonable pulse repetition rate, cooling has to be provided by forcing air over the crystal using the reflector as a container.

Ruby laser : the basic principle of operation of the ruby laser is the same as that of the nd:yag laser.

The active medium is a synthetically grown crystal of ruby i.e aluminium oxide, with about 0.005 % by weight of chromium as an impurity.

Chromium ions, cr+3 , replace aluminium ions in the lattice and the crystal filled partially removes the degeneracy of the isolated ions to provide levels for pumping and for the laser transitions.

3level ruby laser s/m

Pumping is due to the cr+3 ions absorbing blue (excitation of 4t levels) and given light (excitation to 4T2 levels)

The wavelengths of the R1 & R2 laser lines are temperature development; typical values as given.

The energy level diagram shows it is a 3 level s/m more than half of the total no. of ions have to be pumped to level 1 via level 3 to create a population inversion.

Then the laser has a very low efficiency compared to a 4 level s/m such as nd:yag

Pumping is achieved through the absorption of the green and blue spectral regions of a white light discharge; this absorption, of course, accounts for the color of ruby

Gas laser : these are the most widely used type of laser; they range from the low power helium neon laser commonly found in teaching laboratories to very high power co2 laser, which have many individual application

These are excited by electron collision in a gas discharge.

He-ne laser : the active medium is a mixture of about ten part of helium to one part of neon. The neon provides the energy levels for the laser transition, while the helium atoms , though not directly involved in the laser transition, have an important role in providing an efficient excitation mechanism for the neon atom.

Excitation usually takes place in a d.c discharge created by applying a high voltage () the gas contained in a narrow diametric glass tube at a pressure of about 10 torr. As shown in fig.

As the discharge tube exhibits a negative dynamic resistance when a discharge has been initiated , it is necessary to include a load resistor to limit a t it and protect the power supply.

The pumping process can be described as follows.

The first step in the electron impart excitation of helium atom to one of two meta states designated .this is representated by

e1 + He = He + e2

e1 & e2 → electron energies before and after the collision

He → one of their excited states

Fig 2 shows that there is a group of 4 neon levels at almost the same energies as each of the two excited helium states, and resonant transfer this occurs quite readily.

The energy transfer is represented by He*+Ne = Ne * + He

A population inversion is then created between the 3s and (3p,2p) groups of levels and also between the 2s & 2p levels

Transition between the 3s & 2s levels and between the 3p & 2p levels are forbidden by quantum mechanical solution rules.

The he-ne laser is another example of a 4 level s/m , and as such we require that the population of the lasing transition terminal level be kept as low as possible.

This implies that electron in the terminal level should decay as rapidly as possible back to the ground state.

In neon this is a two step process:

The first , is a rapid transition, but the second, to the ground state is not so rapid

The latter transition rate is, however , enhanced by collision with the walls of the discharge tube, and indeed the gain of the laser is found to be inversely proportional to the tube radius, for this reason , the discharge tube diameter should be kept as normal as possible.

Each of the 4 main laser transition (at 3.39µm,1.15µm,632.8nm and 543.5 nm) shares with one of the others either a common starting or terminating level.

Fig1 shows the essential elements of he-ne laser. The discharge is usually inititated by a high vg trigger pulse and then maintained at a urrent of 10 to 20 ma

The mirror forming the resonant cavity are sometimes cemented to the ends of the discharge tube, thereby forming a gas-tight seal.

Alternatively, the mirrors can be external to the tube which is then sealed with glass windows oriented at the Brewster angle to the axis of the tube.

This allows 100% transmission for the radius with its electron vector vibrating parallel to the plane of incidence, therby ensuring the maximum possible gain in each round trip.

The power o/p from he-ne laser is rather small () however, the radiation is extremely useful in a wide range of application because it is highly collimated, coherent and has an extremely narrow line width.

Molecular laser :

Co2 laser : the co2 molecule is basically an in line arrangement of the two oxygen atoms and the causion atom, which can undergo 3 fundamental modes of vibration as shown in fig. 1

At any one time, the molecule can be vibrating in any linear combination of there fundamental modes. The mode of vibration are denoted by a set of 3 quantum numbers (ѵ1,ѵ2,ѵ3) which represents the amount of energy or no. of energy quanta associated with each mode.

The set(100) , for eg means that a molecule in this state is vibrating in a pure symmetric mode with one quantum of vibrational energy, it has no energy associated with the asymmetric in bending modes.

Many co2 lasers contain a mixture of co2, nitrogen and helium in the ratio 1:4:5

Excited nitrogen molecules transfer energy to the co2 molecules in resonant collisions, exciting hem to the (001)levels,

The (100) co2 levels have a lower energy and cannot be populated in this way, so that populationinversion is created between the (001) and(100) levels giving stimulated emission at about 10.6µm

The helium has a dual role, firstly it increases the thermal conductivity to the walls of the tube, there by decreasing the temperature and doppler broadening , which inturn increases the gain.

Secondly it increases the laser efficiency by indirectly depleting the population of the (100) level, which is linked by resonant collisions to the (020) and (010) levels, the latter being depleted via collisions with the helium atoms.

The high voltage is applied to a set of electrode placed along the tube as shown in fig 2

With the arrangement , peak powers in the gigaurate range are obtained in very short pulse with about 20 pulses occurring per second .

Cool gas flowing through the lasing region further increases population inversion & hence o/p power.

In the fig 2 the discharge perpendicular to the axis of the laser cavity.

Liquid dye laser: these have useful advantages compared to solid & gas lasers.

Solids are very difficult to prepare with the requisite degree of optical homogeneity and they mayt suffer permanent damage if overheated.

Gases do not suffer from the difficulties but have a much smaller density of active atoms.

Several liquid lasers have been developed but most important is the dye laser. It has the advantage that it can be termed over a significant wavelength range.

Application : spectroscopy & study of chemical reaction

The active medium is an organic dye dissolved in a solvent. When the dye is excited by short wavelength light it emits radiation at a longer wavelength i.e fluorescene

The energy level diagram fig2 shows, the molecule has two groups of closely spaced electronic energy levels ; the singlet states (S0,S1 & S2) and the triplet states (T1 & T2)

The singlet states occur when the total spin of the excited electrons in each moleculeis zero (the value of 2S+1 is then unity)

The triplet states occur when the total spin is unity (2s+1=3)

Pumping results in the excitation of the molecule from the ground state o to the first excited state s1. This is followed by very rapid non radi0active decay processes to the lower of the energy levels in s1.

The laser transition is then from these levels to a level in s0. Since there are many such rotational/vibrational levels within s0 & s1, there are many transition resulting in an emission line which is very broad.

As the termination of the laser transition in so is at an energy much large than Kt ABOVE THE bottom of s0,

The dye laser is a 4 level s/m and threshold is reached with a very small population inversion.

Fig() energy level scheme for a dye molecule

This laser transition terminate above the lowest energy in the so singlet state, so the laser is a 4 leve ls/m . s1 transition lead to stray absorption at the laser wavelength, therby quenching laser action, s1 transitons may also quench laser action in some dyes.

Semiconductor laser : eg : ga as laser

There are some what similar to L.e.d ‘s hence a p-n junction provides the active medium thus to obtain laser action we need only must other necessary requirements of population inversion or optical f.b .

To obtain stimulated emission, there must be a region of the device where there are many excited electron and valent state (i.e holes) present together.

This is achieved by forward biasing a junction formed from very heavily doped n & p materials.

In such n+ type material, the Fermi level lies within the conduction band. Similarly for the p+ type material the Fermi level lies in the valence band.

The equilibrium and forward biased energy band diagram for a junction formed from such so called

degenerate materials as shown in fig

When the junction is forward biased with a voltage that is nearly equal to the energy gap voltage that is nearly equal to the energy gap voltage Eg/e, electrons and holes are injected across the junction in sufficient no’s to create a population inversion is a narrow zone called the active region