Lasers

LASERS LASER is an abbreviation for Light Amplification by Stimulated Emission of Radiation. A light emitted from a conventional source like Ne lamp is said to be incoherent because the light emitted from atomic transitions do not have same phase. When a light beam from a strong source is incident on a convex lens, then it can be focused in linear region where the linear dimension is (λf/a) where ‘f’ is the focal length of the lens, ‘a’ is the beam size and ‘λ’ is the wavelength of light used. If ‘f=a’ then the light beam can be focused to an area equal to ‘λ’ i.e. the light beam has a high intensity. Such a high intensity light beam is capable of drilling a hole in metallic target. Such a highly coherent light is called LASER.

CHARECTERISTICS OF LASER:i)

DIRECTIONALITY:-

A conventional light is non directional because it emits light in all directions. The laser light is highly directional. The directionality is a measure of divergence given by Δθ = (r1-r2)/(D1-D2) Where ‘r1‘ &’ r2‘ are the radii of the laser beam spots and D1- D2 is the distance between the source and the screen. For a laser beam Δθ=0.01 mille radians i.e. the laser beam spread is 0.01mm for a distance of 1metre. In comparison with a conventional light (search light), laser can travel a distance of several hundred kilometers with a little spread. ii)

MONO CHOROMATICITY:-

The non monochromatic factor is given by (dλ/λ) or (dν/ν). If this ratio is small then the light is highly monochromatic. For an ordinary monochromatic source such as a Ne source, (characteristic ‘d1’ and ‘d2’ lines with λ1=5890˚A and λ2=5896˚A and λavg=5893˚A) d λ=6˚A and λ=5893˚A Therefore the non-mono chromaticity factor is d λ/ λ = (50/5x104)≈ of the order of 10-3

For an ideal laser dν=50Hz and ν=5x1014Hz Therefore (dν/ν) = 10-13 Therefore LASER is highly monochromatic as compared to an ordinary light. iii)

CHORENCY:-

Two light waves are said to be coherent if their phase difference is correlating. The coherence is a measure of the degree of ordering. Due to this high coherency a laser can produce an optical power of 1012watts through a beam size of diameter 1μm there are two types of coherence. a) Spatial Coherence:If the two waves have a correlating phase difference at the same point along the direction of propagation, then the waves are spatially coherent or transverence coherence b) Temporal Coherence:The two light waves are said to be in temporal coherence if they have correlating phase difference over a period to time during their propagation. The distance up to which the coherency (spatial or temporal) Is maintained is called coherence length. The coherence length is inversely proportional to the non monochromaticity factor i.e. (dν/ν) α (1/μ) or the greater is the monochromaticity greater is the coherence length.

iv)

HIGH INTENSITY:-

In a Laser a lot of energy is concentrated in a small region. The power ranges from 10-3W for a gas laser to 109W for a solid state laser with a beam size of 1mm. The number of photons emitted by a laser per second per unit area is

N=(P/hν*∏r2) or

N(hν)=(P/area)

Where P=10-3W to 109W; hν=10-19J For an ordinary source N=1016 relatively for a laser it is 1034. Hence LASER is highly intense in nature.

SPONTANEOUS AND STIMULATED EMISSIONS:i)

STIMULATED ABSORPTION:-

A particle in a ground state (E1) when provided with an energy (E2-E1) it gets excited to the next higher energy level (E2). This process of transfer of particles from ground state to the excited state (with an emission of photon) by absorbing the incident energy is called stimulated absorption

the lower line denotes E1 and the upper line denotes E2 ii)

SPONTANEOUS EMISSION:-

The particle once exicted to the next higher energy state remains in the next energy state for a short period of time. This is called lifetime and is of the order of 10-8sec. b) METASTABLE STATES:These are the excited states for which the life time is more i.e. the particle stays there for a sufficiently long interval of time around 10-3sec. The particle after remaining for a life time in the exited state comes down to ground state with an emission of photon of a definite frequency in various directions. This process is called as spontaneous emission and is random in character. It is incoherent in nature and has a broad spectrum.

iii)

STIMULATED EMISSION:-

In this process, an electromagnetic radiation forces an atom (particle) in the excited state to reach a ground state with an emission of a photon which has the same frequency, same phase and which propagates in the same direction as the incident radiation. This leads to a highly coherent radiation. EINSTEINS COFFICENTS:In a collection of atoms all the three transition process, viz stimulated absorption, spontaneous emission and stimulated emission occur simultaneously. Consider a quantized atomic system in which the energy levels are denoted by 1,2,3… with energies E1, E2, E3……… the number of the atoms present at the each energy level is called the population at the respective energy levels. i)

For stimulated absorption, the stimulated absorption rate depends on the number of particles at the ground state and energy density i.e. stimulated emission per second α N1 α e(ν) consisting stimulated absorption rate= N1 B12 e(ν) where B12 is a proportionality constant called the einstein’s coefficient of stimulated absorption. Energy density is defined as the total energy per unit volume.

ii)

iii)

For spontaneous emission:The spontaneous emission rate is proportional to the number of particles in the excited state. Therefore spontaneous emission rate α N2 A21--------------------------2 Where A21 is the einsteins cofficent for spontaneous emission. For stimulated emission:-

The transition takes place from excited state to the ground state with the emission of a photon in the presence of an induced photon of frequency ν=(E2-E1)/h thus the stimulated emission rate is proportional to the number of excited atoms in the excited state and which is proportional to the energy density. Therefore stimulated emission rate α N2 B21 e(ν)------------------3

Where B21 is the Einstein coefficient for stimulated emission Under equilibrium conditions, The net absorption rate = net emission rate i.e.

N2 B12 e(ν) = N2 A21 + N2 B21 e(ν)

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e(ν) = (N2 A21/ N1 B12 - N2 B21) = [N2 (A21 / B21)]/ [N1 (B12/B21) – N2] e(ν) = (A21 / B21)/{[ (N1/ N2)(B12/B21)]-1}-----------------5 The population in the various energy levels is given by the boltmann distribution law given by Ni = N0e-Ei/kT Where ‘k’ is the Boltzmann constant N1 / N2 = e(E2-E1)/kT = ehν/kT----------------------------------------------6 Using eq.6 in eq.5 we get e(ν) = (A21 / B21)/ {[(B12/B21)x ehν/kT]-1}-------------------7 From plank’s radiation law, we get e(ν) = (8*∏*h*ν3)/( (c3*( ehν/kT-1))-------------------------8 from eq.7 and eq.8, we get (A21 / B21) = (8*∏*h*ν3) / c3

and

(B12 / B21) = 1 The above two equations are known as the Einstein relations. Spontaneous emission dominates over stimulated emission. Similarly stimulated emission rate / stimulated absorption rate = N2 B21 e(ν)/ N1 B12e(ν) = N2 / N1 At thermal equlibrum N2 <<< N1 the number of particles in the excited state is always less than in the ground state i.e. stimulated absorption dominates stimulated emission.

POPULATION INVERSION:The heat of a laser system is a certain medium which is either a solid, liquid or a gas generally called as the active medium that contains atoms,

ions or molecules decaying from their higher energy state. These are called as the active centres. The number of the active centers ranges from 1015 to 1020 depending on the medium. Consider a two level system in which the ground state is E1 and the excited state is E2. Let N1 and N2 be the number of active centers per unit volume in the respective energy levels. A photons of energy ν=(E2-E1)/h has an identical probability to induce either a transition from E1 to E2 or E2 to E1.This if these two transistions will result will depend on the energy level in which the active centers lies . If the lower level of the mechanism is more populated than the upper level then the absorption process dominates and if the upper level is more populated than the lower level then the stimulated emission is favored. Under thermo dynamic equilibrium the N2 N1. This process of increasing the population of excited level greater than the lower level is called ‘population inversion’, An active system is one in which the population inversion is achieved. The underlying principle for laser action is population inversion. This process of raising the particles from lower energy state to the higher energy state is called pumping. The principal mechanism of population inversion will depend on the process through which population inversion is created. The commonly used processes are

i) ii) iii) iv)

Optical pumping Electric discharge Chemical reaction Injection current

In optical pumping process the population inversion is achieved by different discharge flash tubes. Example Xenon flash lamp. This is a very fast mechanism. Recently flash lamps are being replaced by the light diodes to make the laser systems more efficient and more reliable. The electrical discharge phenomena is used in gas energy is more populated by using high intense electrical discharge which converts the gas into plasma and causes predominant population of the upper pumping level. In the chemical

pumping process, the active centers raises into the higher level by a suitable chemical reaction. In semi conducting lasers the pumping device by the injection currents through the junction which creates population inversion among the charge carriers.

THREE LEVEL SCHEME:-

If the collection of atoms is intensely pumped with a xenon flash lamp, a large number of atoms are excited through the stimulated absorption to the excited state E2. If this level has a very short lifetime, they undergo fast decay to level E1, which is a meta stable state and which has a relatively longer life period. Therefore the atoms accumulate at E1. Hence the population at E1 is greater than at E0. The laser transition takes place from E1 to E0. In this situation more than half of the atoms in the ground state will be pumped into E1. Therefore the three level scheme requires a high degree of pumping. This system works only in a pulse mode Eg. Ruby Laser.

FOUR LEVEL SCHEME:-

In this scheme, the atoms are excited from the ground state to the highest of the four levels. Due to the fast decay the atoms reach the metastable state E2 and get accumulated due to a longer lifetime. The population inversion is achieved with a moderate pumping the laser transition takes place from E2 to E1. Since, the ground state is not involves in laser action, it is easy to maintain population inversion between E2 and E1 for continuous wave move, the decay between E3 and E2+ must be very fast. Ex. He-Ne Laser.

TYPES OF LASERS:1) Ruby laser:This laser was constructed in the year 1960 by Haiman. This comes under the category of the three level solid state Laser in the pulse mode. The active medium is a solid material in the form of a cylindrical rod (ruby rod) whose ewes are optically polished to a high degree. The ruby rod is made of synthetic sapphire (Al2O3) doped with 0.025% of Cr2O3. The presence of Cr3+ ions gives pink color to the rod. THE RESENANT CAVITY:T obtain the coherent radiation, the spread of the photons should be narrowed (spontaneous emission). This is done by restricting the number of

possible photon states. Therefore a certain photon states are selected to establish favorable conditions to develop stimulated emission. The selection of the same photon states and separation of other states is done by OPTICAL RESOMETER. The optical resonating cavity consists of a pair of mirrors arranged in the optical axis which defines the direction of the laser beam. The active medium is placed in between these two mirrors the solid active medium will be in the form of a cylinder whose length is ten times greater than its diameter is aligned parallel to the axis of the resonometer in the two mirrors present in the cavity one of the meter should be made semi transperarent so to reflect the light from the resonator. The arrangement of the mirrors in the simple cavity is shown in the figure

The active medium is present in between the mirrors M1 & M2. The photons produced spontaneously in the OOI will travel within the active material a relatively long waywhich is elongated by multiple reflections from the resonator mirrors. These photons interact with the excited active centers to start the laser action. The photons emitted in the other directions will travel a relatively short part in the material and die out soon. Therefore the optical resonator cavity provides the DEBYE’S selectivity of photon states by primarily configuring the possible direction of the photon propagation and results in the laser radiation. The losing action occurs only along this direction. → Flash light has a wave length of 5600˚A The ruby (Al2O3 + Cr2O3) is a crystal of aluminum oxide (Al2O3 doped with 0.05% of Cr2O3, such that same of the Al3+ ions are replaced by Cr3+ ions. The

active medium in the ruby rod is Cr3+ ions. The ruby rod is 4cm in length and 5mm in diameter with highly polished ends. Both the ends are silvered such that the end is fully reflecting and the other end is partially reflecting. The optical pumping is provided by a helical flash lamp tube surrounding the rod to raise the Cr3+ ions to higher energy levels. Under the intense flash which lasts for only a few seconds. The energy levels of Cr3+ broaden up and convert into bands. The Cr3+ ions absorbs strongly in the blue and green region of the visible light. Only a part of the light energy is used in pumping the Cr3+ ions and the remaining goes as heat to the apparatus which should be cooled. The energy level diagram is shown in figure The Cr3+ ions are excited from the ground state to the 4T1 or 4T2, the absorption of energy corresponding to these two absorption bands causes Cr3+ ions to be excited to these levels. Cr stay in these levels for a very short interval of time 10-8 sec and drop to level E2 which is a meta stable state. The level E3is a band which helps in pumping more effectively.

The transition from E3 to E2 is a non radiative which is accompanied by heat therefore the rod must be cooled using water circulated around the ruby rod during the losing action. The life time of level E2 is 105 times greater than E3,

therefore the particles goes on increasing in this state (E2). Thus achieving population inversion between the level (E2) and the ground state. The laser transition takes place between E2 and E1. When excited particles passes from meta stable state E2 to the ground state E1. It emits a photon of wavelength 6943˚A corresponding to laser radiation. Since this is a three level laser system ground state is involved in laser transition, the efficiency is less and also requires intense pumping. The emitted photon travels through the ruby rod and it travels parallel to the axis, it is reflected back and forth by the silvered ends until it stimulates an excited ion in the level E2 and emits a fresh photon in phase with the induced photon. This stimulation causes a laser transition. This process is repeated and the photons are multiplied, when the photon beam gets sufficiently intense, it comes out of the semi silvered end of the rod. The meta stable state has two energy levels close to each other. The transition R1 has a wavelength of 6943˚A (low probability and can be filtered using a normal optical filter). The rapid pumping flash lasts only for atoms, during this time the population inversion exceeds a threshold value and stimulated emission increases rapidly which results in depopulation of upper laser level. Hencr, the losing action momentarily stops and before the output falls to zero the population increases and the laser action is initiated. This process repeats until the pumping flash ends. The opposite consists of a large number spikes

with a duration of 1μsec. The real power has a value of 1kW.