Laser - Lecture notes 1 PDF

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PH1C01/PH2C01

Engineering Physics

Module IV - LASER LASER stands for Light Amplification by Stimulated Emission of Radiation. Laser is highly intense, monochromatic, directional and coherent. Consider an atomic system with various energy levels in which an atom can exist. When the atom is in the lowest energy level, it is said to be in the ground state. And an atom highest energy level, is said to be in an excited state. The lifetime of an atom in the excited state is very short (order of 10−8 sec). In between these two states is the metastable state, with lifetime of order of 10−3 sec. There is a definite amount of energy difference between the various energy levels. The atom can go to a higher energy state in many ways. E.g., by gaining energy by collision or absorbing energy when radiation is incident on the atom. Hence it will quickly return to the lower energy state. During the transition the energy released by the atoms is the difference between two energy levels. When the absorption and emission of energy is in the form of radiation(photons) the process is called as radiative transition. If the release of energy is in other forms(i.e., heat) it is called non-radiative transition.

Basic concepts To understand the construction and working of laser, it is necessary to know the basic process involved in the atomic system. 1. Induced absorption If an atom makes a transition to an excited state by absorbing a definite amount of energy, ∆E = E2 − E1 , then such a process is called induced absorption. If the energy absorbed is in the form of photon then, hν = E2 − E1 , where h is the Planck’s constant, ν is the frequency of radiation, E2 and E1 are the energies of higher and lower levels respectively. N2

E2

N2

E2

N1

E1

N1

E1

hn

INDUCED ABSORPTION

2. Spontaneous emission When the atom in the higher energy state makes a transition to a lower energy state by emitting a photon, without any external influence, the process is called spontaneous emission. In this case the direction and phase of the emitted photon is random. N2 N1

E2

N2

E2

E1

N1

E1

hn

SPONTANEOUS EMISSION

3. Stimulated emission If a photon of right frequency is incident on an atom in the higher energy state (such that hν = E2 −E1 ), then it can induce the atom to make a transition to the lower energy state. The atom gives out the excess energy as a photon, which is emitted along with the inducing photon. These two photons have the same frequency, direction, phase and sense of polarization, i.e., they are perfectly coherent. This process is called stimulated emission of radiation. Compiled by NS

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hn N2

E2

N2

N1

E1

N1

E2

hn hn

E1

Population inversion For laser action to take place higher level should contain more atoms. This condition when number of atoms in the higher level exceeds the number of atoms in the lower level (N2 > N1 ) is called population inversion or negative temperature state.

Requisites of Laser 1. Pumping The process of supplying energy to the atoms in lower energy state to raise them to higher energy levels. If visible radiation is used for this purpose it is called optical pumping.There are different types of pumping, namely optical pumping, chemical pumping, heat pumping and electric discharge pumping 2. Active medium A material or system having suitable set of energy levels in which population inversion can be created by pumping and lasing action can be obtained. eg., Solid (ruby rod, ND:YAG), Liquid (Organic liquid dye), Gas (He-Ne, CO2 ). 3. Resonant cavity The cavity is the space between mirrors. The active medium is placed in between two mirrors or reflecting surfaces, where photons travel to and fro causing more and more stimulated emissions until an intense beam of photons is generated. The cavity resonates when the λ distance between the mirror is an integer multiple of , where λ is the wavelength of the 2 radiation and n is an integer. nλ L= 2 The common resonant cavity in use are

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Energy density in terms of Einstein’s coefficients E2(N 2) r(n)

E (N1 )

Let E1 and E2 be two energy levels of an atomic system. Let N1 and N2 be the number of atoms/unit volume occupying these levels. Radiation of density ρ(ν) is incident on the system. Then, the number of induced absorption taking place per second is ∝ N1 ρ(ν) = B12 N1 ρ(ν) The number of spontaneous emissions taking place per second is ∝ N2 = A21 N2 The number of stimulated emissions taking place per second is ∝ N2 ρ(ν) = B21 N2 ρ(ν) The proportionality constants in the above equations A21 , B12 and B21 are known as Einstein’s coefficients. At equilibrium, number of transitions from E1 to E2 is equal to total number of transitions from E2 to E1 . Therefore B12 N1 ρ(ν) = A21 N2 + B21 N2 ρ(ν) ρ(ν) =

A21 N2 B12 N1 − B21 N2

(1)

Dividing the numerator and denominator of RHS of equation (1) by B21 N2 , we get ρ(ν) =

A21 /B21 B12 N1 −1 B21 N2

(2)

According to Maxwell-Boltzmann statistics, the number of atoms Ni in the ith energy level having energy Ei is given by Ni ∝ e−Ei /kT , where k is the Boltzmann constant and T is the absolute temperature. Thus we can write N1 ∝ e−E1 /kT N2 ∝ e−E2 /kT Therefore,

N1 = e−(E1 −E2 )/kT N2 Compiled by NS

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N1 = e−(−hν)/kT N2 N1 = e(hν)/kT N2 Substituting equation (3) in equation (2), we get ρ(ν) =

A21 /B21 B12 hν/kT e −1 B21

This is the expression for energy density in terms of Einstein’s coefficients. From Planck’s law of radiation ρ(ν) =

8πhν 3 /c 3 ehν/kT − 1

Comparing equation (4) with equation (5), we get B12 =1 B21 B12 = B21 This means that probability of induced absorptions is equal to probability of stimulated emissions . Further, 8πhν 3 A21 = B21 c3 Assuming ν = 1015 Hz, the ratio value is small. Thus, probability of spontaneous emission is much less than probability of stimulated emissions.

Population of the energy states From equation(3) above, N2 = e−hν/kT N1 Assuming ν = 1015 Hz and T = 300K and substituting the values of the constants (h = 6.63 × 10−34 , k = 1.38 × 10−23 ) in the above equation we find that N2 /N1 is very very small. Thus the higher level is much less populated than the lower level.

Ruby laser It was invented by Maiman in 1960. It is a three level laser.

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Construction The schematic representation of a ruby laser is shown in the figure Ruby is a crystalline form of silica or aluminium oxide Al2 O3 doped with chromium ions. The triply ionized C r ions replace some of the Al3+ ions giving transparent crystal a pink or red colour depending upon its concentration. The doping concentration is 0.05%, which is equal to 1.6 × 1025 ions/m3 . Ruby crystal taken in the form of cylindrical road act as the active medium. The diameter of the rod is 0.25 − 0.5 cm and 10− 20 cm in length. The ends of the rod are made optically flat and accurately parallel, which acts a resonant cavity. One end of the rod is partially polished and the other is fully polished for nearly 100% reflection. The rod is surrounded by a hollow glass tube through which water is circulated to extract the heat. The glass tube is surrounded by helical xenon flash lamp, which acts as pumping source. The ends of the flash tube is connected to DC power supply. XENON FLASH LAMP PARTIALLY POLISHED

RUBY ROD FULLY POLISHED

GLASS TUBE

LASER BEAM

WATER OUTLET

COLD WATER INLET

POWER SUPPLY



Working 4

BLUE

F1

E2 GREEN

4

F2

RADIATIONLESS TRANSITION

E3

E4 0

4000 A

5500 A

0

(OPTICAL PUMPING)

LASER 0

6943 A

E1

G

The energy level diagram for Cr+3 ion in the Al2 O3 lattices is as shown in the fig. When the key is closed, the xenon lamp flashes and the chromium ions absorb energy in the wavelength region ˚ , making transition from ground level to higher energy level E2 (4 F1 ) and E3 (4 F2 ). 4000 to 5500 A The excited ions are unstable in the state E2 and E3 , whose life time is about 0.1 µs. They quickly undergo non-radiative transition from excited state E2 and E3 to metastable state E4 . The lifetime of the metastable state is about 3 ms. The energy difference between E2 and E3 to E4 appears

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as heat in the system. The transition from E4 to E1 is radiative and under normal population condition it produces spontaneous incoherent light red in colour. For pumping rate beyond threshold value, population inversion occurs in E4 with respect to E2 and E3 . Under this condition one of the spontaneously emitted photon travelling parallel to the axis of the ruby rod initiates stimulated emission. The ends of the rod act as reflecting mirrors. Hence,photons that are moving away from the axis escape from the side. Photons moving along or parallel to the axis are reflected back and forth, they stimulate the emission of similar photons and the system lases. The laser beam emerges from partially polished end of the rod in the form pulse, red in colour corresponding to a wavelength of 6943 ˚ A. As it travels parallel to the rod, hence highly monochromatic and coherent. Once the excited levels are depleted, the laser will stop. The pumping takes place again with another flash of the lamp. Thus ruby laser is a pulsed laser.

Helium Neon Laser It is a four level, low power, continuous wave gas laser.

Construction It consists of a discharge tube filled with a mixture of helium and neon in the ratio 10:1 under a reduced pressure of 1 mm of mercury or 1 torr. Electrodes are provided inside the tube for the application of high voltage of 2 to 4 kV across the tube and maintained at a current of 10 − 20 mA. Two mirrors are tightly sealed at the ends of the tube with multilayer coating, which has wavelength dependent reflectance and it is oriented at Brewster’s angle, in order to get plane polarised light. Discharge tube

Brewster's window

LASER

(He + Ne)

Fully polished mirror

Partially polished mirror HT Electrodes

Working The combined energy level diagram of helium and neon is shown in the diagram.

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Transfer of energy from He to Ne by collision

Laser transition 632.8 nm Excitation of the He atoms by collisions with electrons Sponataneous transition

Decay to the ground by collisons with walls of the discharge tube

He

Ne

When high voltage is applied ionisation takes place. The electrons generated start moving towards the positive electrode. Their velocity increases and their kinetic energy increases. These electrodes collide with ground state helium atoms and transfer their energy during collisions. Thus the helium atoms get energy and make transitions to the higher energy states 21 S and 23 S. These excited helium atoms in turn collide with ground state neon atoms. During collisions energy is transferred from helium to neon and neon atoms are raised to the corresponding higher levels 3S and 2S. Since the lower levels are practically empty, population inversion is achieved easily between the higher and lower levels of neon. At this instant one photon of suitable energy starts a series of stimulated emissions and laser is obtained. Since there are many energy levels many different transitions take place. Out of these only the 3S to 2P transition (λ = 632.8 nm) is selectively amplified by adjusting the distance between the mirrors or with multilayer coating, which has wavelength dependent reflectance . From 2P , the neon atoms return to the ground state quickly by spontaneous transition and collisions with the walls of discharge tube. Thus this laser works continuously.

Applications of LASER 1. Communication : Laser beam is used as carrier wave to transmit a large number of voice signals in long distance telephone lines using optical fibers. 2. Computers : Lasers used in CD writers and laser printers. 3. Medicine : They are used in endoscopes to examine the internal organs of the human body. Also they are used to carry out bloodless surgeries like fusing the detached retina of the eye and destroying cancer and tumor cells. They are also used to rebore the blocked arteries. 4. Defence : Lasers are used in laser guided missiles and to transmit coded signals in warfields. 5. Scientific research : Laser is the source of extremely powerful, coherent and monochromatic source of light for scientific research. 6. Display : Used in the spectacular laser shows. Compiled by NS

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7. Engineering : Used in engineering fields like bridge construction, tunneling and pipe laying etc for alignment purpose. 8. Photography : They are used in three dimensional photography called holography. 9. Industry : Lasers are used for cutting metal sheets, welding metals, drilling etc. 10. Pollution control : Lasers are used for identifying pollutants in atmosphere.

Holography It is in principle an interference based technique of obtaining a three dimensional image of an object. A light of high degree of coherence is required for its realization. In the case of ordinary or conventional photography the variation of intensity of light reflected by an object is recorded. In holography variations in both intensity and phase are recorded so that the complete detail of the object gets recorded. Holography consists of two parts (i) Recording of the image (ii) Reconstruction of the image.

Recording of the image MIRROR

BEAM SPLITTER

LASER

BEAM EXPANDER OBJECT OBJECT BEAM

MIRROR

PHOTOGRAPHIC PLATE REFERENCE BEAM

A beam of laser is expanded with the help of beam expander and split into two parts using a beam splitter. One is the reference beam and the other is the object beam. The reference beam is reflected towards a photographic plate by a mirror. The object beam falls on the object and after reflection from the object arrives at the photographic plate. The two beams interfere on the plane of the photographic plate. The resultant interference pattern is recorded on the photographic plate. The pattern is very fine, the spacing between the fringes being as small as 0.001 mm. The developed photographic plate containing the interference pattern is called the hologram. The fine structure of the interference fringes requires photographic emulsion with a high spatial resolution.

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Reconstruction of the image Virtual image

Real image

Hologram

Reference beam from laser and beam expander

Reconstructed object wavefronts

Observer

For reconstruction of the image a laser beam similar to the reference beam is used and relative positions of reference beam and hologram is maintained. Due to diffraction of reference beam by the hologram a real image of the object is obtained. A virtual image can also be seen by keeping the eye closed to the hologram and looking through it as if it is a window. The virtual image is seen at the same place where the object was situated during recording. Both the images are exactly identical to the object and posses three dimensional characteristics.

Laser welding High power lasers like CO2 laser and Nd:YAG lasers are used for welding applications. Spot welding as well as seam welding is done using lasers. Laser welding has many advantages over conventional welding. 1. As direct contact is not required, infusion of impurities to the welded area is avoided. 2. Welding is done in atmosphere unlike electron beam welding which requires vacuum. 3. Normally inaccessible areas can be welded as shown in the diagram provided light can reach the area. 4. Fast and accurate welding is possible. 5. Since heating is fast and precisely localised, this method is very useful in welding heat sensitive materials. One example is welding of microelectronic components. 6. Metals and non-metallic substances like glass can be welded with same ease. 7. Weldment is as strong as the material.

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Laser cutting Laser

Lens

Line of contact

plates

An arrangement of gas-laser cutter is shown in the diagram. This is especially useful in cutting metals. A stream of oxygen is used to blow away the molten metal by oxidation so that less laser power is sufficient and quality of cut edges, depth and velocity of cutting increases. Laser cutting offers the following advantages: 1. A wide variety of materials can be cut e.g., metal sheets, clothes, glass, wood, cardboard, ceramics etc. 2. Automation and hence high production rates are possible. 3. Two dimensional and even three dimensional cutting is possible according to profile. 4. Precise and fine cuts. 5. Minimum mechanical distortion of the material being cut.

Problems 1. Find the ratio of population of two energy levels in a laser if the transition between them produces light of wavelength 694.3nm. Assume the ambient temperature to be 27◦ C. Solution: h = 6.63 × 10−34 J − s, c = 3 × 108 m/s, λ = 694.3 × 10−9 m, k = 1.38 × 10−23 J/k, T = 27◦ C = 300K hc hν N2 = e−( kT ) = e−( λkT ) N1 N2 − =e N1

h

i 6.63×10−34 ×3×108 694.3×10−9 ×1.38×10−23 ×300

N2 = 8.874 × 10−31 N1 2. The ratio of population of two energy levels is 1.059 × 10−30 . Find the wavelength of light emitted at 300K . N2 = 1.059 × 10−30 , T = 300K , λ =? Solution: N1 hc N2 hν = e−( kT ) = e−( λkT ) N1

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  6.626 × 10−34 × 3 × 108 hc =− λ=−   N2 ln(1.059 × 10−30 ) × 300 ln kT N1 λ = 6948.56 ˚ A 3. A medium in thermal equilibrium at temperature 300 K has two energy levels, emits a radiation of wavelength of 1 µm. Find the ratio of population densities of the upper and lower levels. N2 Solution: T = 300 K, λ = 1 µm, k = 1.38 × 10−23 J/K, h = 6.626 × 10−34 Js, =? N1 hc N2 − = e−(λkT ) = e N1



6.626×10−34 ×3×108 1×10−6 ×1.38×10−23 ×300



N2 = 1.484 × 10−21 N1 4. A semiconductor laser has a peak emission radiation of wavelength of 1.24 µm. What is its band gap value in eV. Solution: λ = 1.24 µm, Eg =? Eg = hν =

Eg =

Eg =

hc λ

6.626 × 10−34×3×10 1.24 × 10−6

8

1.609 × 10−19 = 1 eV 1.609 × 10−19

5. A pulsed laser emits a photons of wavelength 780 nm with 20 mW average power/pulse. Calculate the number of photons contained in each pulse, if the pulse duration is 10 ns. Solution: λ = 780 nm, power of each pulse, p = 20 mW, Duration of each pulse, t = 10 ns, number of photons in each pulse, N =?. Energy of each photon, hc 6.626 × 10−34 × 3 × 108 ∆E = = λ 780 × 109 ∆...