LASER.pdf

LASER Dr. Sharad B. Patil Assistant Professor Department of Applied Physics, School of Engineering and Management, D Y Patil Education Society (Deemed to be University) Kasaba Bawada, Kolhapur Contents 1. Concept of laser...

LASER Dr. Sharad B. Patil Assistant Professor Department of Applied Physics, School of Engineering and Management, D Y Patil Education Society (Deemed to be University) Kasaba Bawada, Kolhapur Contents 1. Concept of laser 2. Principles and working of laser a) Absorption of radiation b) Spontaneous emission of radiation c) Stimulated or forced emission of radiation. d) Population inversion 3. Einstein's coefficient 4. Properties of laser beam 5. Types of laser: Ruby laser and He-Ne laser 6. Applications of laser: Industrial and Medical Concept of LASER In order to realize the applications of interference and diffraction in an efficient way there was a need to use coherent and monochromatic sources as the phase of an incoherent source (light) varies randomly with time and position. This need for monochromatic and coherent sources contributed to the birth of a special type of device that amplifies light and produces a highly intense and highly directional beam that mostly has a very pure wavelength. This device is called LASER. LASER is an acronym for light amplification by stimulated emission of radiation. In laser, the intensity of light is amplified by a process called stimulated emission. The laser is perhaps the most important optical device to be developed in the past few decades. Since it arrived in the 1960s, it has provided the stimulus to make optics one of the most rapidly growing fields in science and technology today. Principle and working of Laser Let us consider a material medium composed of identical atoms. Let us assume that the atoms of the material medium under consideration be characterized by only two energy levels, namely energy level E1 and energy level E2. E1 is the ground state while E2 is the excited state. The number of atoms per unit volume at an energy level is called the population density. Let the populations at the two energy levels E1 and E2 be N1 and N2 respectively. Under normal conditions higher the energy, lesser is its population. Hence, N1 > N2. The formation of a laser involves three fundamental processes of interaction between light (radiation) and matter (atoms, molecules, ions or active centers), namely 1) Induced absorption of radiation 2) Spontaneous emission of radiation 3) Stimulated or forced emission of radiation.  1. Induced absorption of radiation Consider two energy levels 1 and 2 of lower energy E1 and higher E2 energy E2 respectively of an atom (or molecule, ion etc.). Suppose, the atom is in the energy state E1. When a photon of energy, hυ = E2-E1 strikes it, it absorbs this energy and makes a h12 transition to higher energy, a state of energy E2, this process is called induced absorption of radiation, wherein the incident photon is lost by absorption and atom goes to higher energy state. E1 E2 = E1 + h E2 − E1 = E= h (1) The probability of occurrence of this transition from state 1 to state 2 is proportional to the energy density () of the radiation (P12  (), where P is the probability) P12 = B12 () (2) where the proportionality constant B12 is known as the Einstein’s coefficient of induced absorption of radiation. 2. Spontaneous emission of radiation When an atom is in an excited state of higher energy E2, it E2 emits a photon spontaneously and drops to the lower energy state E1. It cannot stay in the excited state for a relatively longer time. In a time of about 10–8 s, the atom reverts to the lower energy state by releasing a photon of energy hυ. The h12 energy of the photon is E2 – E1 = hυ. The emission process is called spontaneous because it takes place without any external stimulus. This spontaneous process is random, hence, when a large number of excited atoms emits spontaneously, E1 the photons are emitted in all possible directions and in random phases and hence, the emitted light is incoherent. The probability of spontaneous transition depends only on the properties of energy states E2 and E1 and is independent of the photon energy density (). Thus, (P21)Spont. = A21 (3) where A21 is a constant and known as the Einstein coefficient for spontaneous emission. A21 is a constant characteristic of the atom. 1/A21 is a measure of the lifetime of the upper state against spontaneous transition to the lower state. The number of spontaneous transitions, Nsp, taking place during the time t depends only on the number of atoms N2 staying at the excited state E2. Thus, Nsp = A21 N2 t (4) It is the process of spontaneous emission that dominates in conventional light sources. The light from the conventional sources originates in spontaneous emission process and is incoherent. It contains a superposition of many waves of random phases. The net intensity of such incoherent waves is proportional to the number of radiating atoms. 3. Stimulated emission of radiation Suppose that an atom is in the excited state of E2 higher energy level E2 and a photon of frequency υ strikes the excited atom. [The energy of a photon is, h12 E2-E1=hυ] This photon forces or stimulates the atom to drop to the lower energy state E1. In this h12 h12 transition, a photon of frequency υ is emitted. The passing photon is not affected while the excited atom emits a photon. This process of emission of the photon is stimulated by the incident photon, E1 whose frequency is also υ, hence is called stimulated emission. The emitted Photon is identical to the colliding or incident photon, in respect of phase, the state of polarization, and the direction of travel. Thus the number of identical photons is increased or amplified. If these photons could be made to collide with two more atoms in excited state 2, then there will be four identical photos; if these process is allowed to continue soon there will be 8, then 16 and so on identical photons. Such a process of increasing the number of photons is practically possible and is called amplification of light by stimulated emission of radiation. It should, however, be noted that the amplification of light by stimulated emission of radiation is possible only if, (i) There is a large number of atoms in the higher energy state E2 (or excited state E2) and, (ii) photons are not absorbed by an appreciable number of the atoms in the lower energy state E1. Stimulated emission of radiation thus forms the basis of laser formation. The most important fact about the stimulated emission is that the photon of the radiation thus produced is totally coherent with the incident stimulating photon, that is, it agrees in phase, direction of travel, and polarization with the incident photon. The probability of stimulated emission by transition from the upper level 2 to the lower level 1 is proportional to the energy density () of the radiation and is expressed as (P21)Stimul. = B21 () (5) where B21 is the Einstein’s coefficient of stimulated emission of radiation. It is a constant characteristic of the atom and represents the properties of the energy states E1 & E2. The total probability of transition from the upper level 2 to the lower level 1 is given by P21 = (P21)Spont. + (P21)Stimul. P21 = A21 + B21 () (6) The number of stimulated transitions occurring in the material at any instant will be equal to the product of the number of atoms at the energy level E2 and the probability P21 for the stimulated transition. Thus, the number of stimulated transitions, Nst, that occurs during the time t is Nst = B21 N2 () t (7) Einstein’s Coefficients The coefficients indicated by B are related to the induced transitions, i.e., transitions induced by external photons. Thus, B12 represents the transition induced by a photon from lower energy level E1 to the higher energy level E2. The coefficient B21 denotes the transition induced by a photon from higher energy level E2 to the lower energy level E1. It turns out that B12 and B21 are equal under the special condition that the quantum states E1 and E2 are single energy levels. The coefficient A is related to the spontaneous transition, i.e., transition occurred on its own without the assistance of external agent. Since a spontaneous transition cannot take place from lower energy state E1 to the higher energy state E2, we do not have the coefficient A12. In other words, A12 = 0. Let N1 and N2 be the number of atoms at any instant in the state 1 and 2, respectively. The probability of absorption transition for number of atoms from state 1 to 2 per unit time is given by N1 P12 = N1 B12 () (1) The total probability of transition for number of atoms from state 2 to 1, either by spontaneously or by stimulated emission per unit time is given by N2 P21 = N2 [A21 + B21 ()] (2) In thermal equilibrium at temperature T, the absorption and emission probabilities are equal and thus, we can write N1 P12 = N2 P21 Using equations (1) & (2), we can write N1 B12 () = N2 [A21 + B21 ()] N1 B12 () – N2 B21 () = N2 A21 𝑁2 𝐴21   = 𝑁1 𝐵12 −𝑁2 𝐵21  𝐴21 1   = (3) 𝐵21 (𝑁1 /𝑁2 )(𝐵12 /𝐵21 )−1 But we know that B12 = B21 , Thus equation (3) becomes 𝐴21 1   = (4) 𝐵21 (𝑁1 /𝑁2 )−1 According to Boltzmann’s law, the distribution of atoms among the energy states E1 and E2 at the thermal equilibrium at temperature T is given by 𝑁1 𝑒 −𝐸1 /𝑘𝑇 = = 𝑒 (𝐸2 −𝐸1 )/𝑘𝑇 (5) 𝑁2 𝑒 −𝐸2 /𝑘𝑇 = 𝑒 ℎ/𝑘𝑇 𝑁1 Or (6) 𝑁2 Here k is the Boltzmann constant. Using equation (6), we can write equation (4) as 𝐴21 1   = (7) 𝐵21 𝑒 ℎ/𝑘𝑇 −1 To maintain thermal equilibrium, the system must release energy in the form of electromagnetic radiation. It is required that the radiation be identical with black body radiation and be consistent with Planck’s radiation law for any value of T. According to Planck’s radiation law 8ℎ3 3 1   =( ) (8) 𝑐3 𝑒 ℎ/𝑘𝑇 −1 Where  is the refractive index of the medium and c is the velocity of light in free space.. Comparing equation (7) and (8), we get 𝐴21 8ℎ3 3 = (9) 𝐵21 𝑐3 𝐵21 We know that =1 or B12= B21 (10) 𝐵12 Thus we get 𝐶3 𝐵12 = 𝐵21 = 𝐴 (11) 8ℎ3 3 21 Equations (9) and (10) are known as the Einstein’s relations. (i) The equation (10) shows that the coefficients for both absorption and stimulated emission are numerically equal. The equality implies that when an atom with two energy levels is placed in the radiation field, the probability for an upward (absorption) transition is equal to the probability for a downward (radiative) transition. (i) The equation (9) shows that the ratio of coefficients of spontaneous versus stimulated emission is proportional to the third power of frequency of the radiation. This is why it is difficult to achieve laser action in higher frequency ranges such as X-rays. Population Inversion When the material is in thermal equilibrium condition, the population ratio is governed by the Boltzmann factor according to the following equation: 𝑁2 = 𝑒 −(𝐸2 −𝐸1 )/𝑘𝑇 (1) 𝑁1 It means that the population N2 at the excited level E2 will be far smaller than the population N1 at the level E1. For example, if we take typical values for E1 and E2, the population N1 would be 1030 times of N2. The condition in which there are more atoms in the lower energy level and relatively lesser number of atoms in the higher energy level is called normal state or equilibrium state as shown in figure. Thus, under thermal equilibrium condition, N1 >> N2. Population inversion is the condition of the material in which population of the upper energy level N2 far exceeds the population of the lower energy level, N1 as shown in Figure. That is N2 >> N1 In this condition the population distribution between the levels E1 and E2 is inverted and hence it is known as the inverted state. This is a non-equilibrium state and exists only for a short time. Population inversion is obtained by employing pumping techniques, which transfer large number of atoms from lower energy level to higher energy level. Normally, excited atoms have short lifetimes and release their Pumping level (10-9 s) energy in a matter of nanoseconds (10–9 s) through spontaneous emission. Population inversion cannot be established under such circumstances. Rapid decay Metastable state In order to establish the condition of population inversion, the (10-6 to 10-3 s) excited atoms are required to ‘wait’ at the upper energy level till a large number of atoms accumulate at that level. Such an opportunity would be provided by metastable states. Atoms excited to a metastable state remain excited for an appreciable time, which is of the order of 10–6 to 10–3 s. This is 103 to 106 times the lifetimes of the ordinary excited energy levels. The metastable state population can exceed the population at a lower level and establish the condition of population inversion in the lasing medium. Metastable state can be readily obtained in a crystal system containing impurity atoms. These levels lie in the forbidden band gap of the host crystal. For example, phosphorescent materials are made up of atoms with metastable states. There could be no population inversion and hence no laser action, if metastable states do not exist. Lasing action Figure shows the active medium enclosed in optical resonator and being excited by a pumping agent. The resulting laser action consists of the following steps: Step-1: Pumping The atoms (active centers) in the medium are in the ground state initially, as shown in Fig. (a). By supplying energy from an external source, the atoms are excited from the ground level to an excited state. Step-2: Population inversion The lifetime of atoms at the excited state is extremely small. Therefore, the atoms drop spontaneously from the excited state to the metastable state. As the lifetime of atoms at the metastable state is comparatively longer (10–3 s), the atoms go on accumulating at the metastable state. As soon as the number of atoms at the metastable state exceeds that of the ground state, the medium goes into the state of population inversion, Fig. (b). Lasing action Step-3: Spontaneous emissions Some of the excited atoms at the metastable state may emit photons spontaneously in various directions (Fig. (c)). Each spontaneous photon can trigger many stimulated transitions along the direction of its propagation. As the initial spontaneous photons are moving in different directions, the photons stimulated by them also travel in different directions. Many of such photons leave the medium without reinforcing their strength. The photons emitted in a direction other than the axial direction will pass through the sides of the medium and are lost forever. Step-4: Amplification A majority of photons traveling along the axis cause stimulated emission and are reflected back on reaching the end mirror. They travel towards the opposite mirror and on their way stimulate more and more atoms and build up the photon strength, as shown in Fig. (d). The photons that strike the opposite mirror are reflected once more into the medium, as shown in Fig. (e). As the photons are reflected back and forth between the mirrors, stimulated emission sharply increases and the amplification of light takes place. The mirrors thus provide positive feed back of light into the medium so that stimulated emission acts are sustained and the medium operates as an oscillator. Lasing action Partially reflecting Front-end mirror Step-5: Oscillations At each reflection at the front-end mirror, light is partially transmitted through it. The transmitted component constitutes a loss of energy from the resonator. When the losses at the mirrors and within the medium balance the gain, a steady and strong laser beam will emerge from the front-end mirror, as shown in Fig. (f). Properties of Laser The important properties of a laser beam are discussed bellow. i Directionality: The conventional light sources emit light uniformly in all directions. When we need a narrow beam in a specific direction, we obtain it by placing a slit in front of the source of light. In case of laser, the active material is in a cylindrical resonant cavity. Any light that is travelling in a direction other than parallel to the cavity axis is eliminated and only the light that is travelling parallel to the axis is selected and reinforced. Light propagating along the axial direction emerges from the cavity and becomes the laser beam. Thus, a laser emits light only in one direction. ii. Divergence: Light from conventional sources spreads out in the form of spherical wave fronts and hence it is highly divergent. On the other hand, light from a laser propagates in the form of plane waves. The light beam remains essentially as a bundle of parallel rays. The small divergence that exists is due to the diffraction of the beam at the exit mirror. A typical value of divergence of a He-Ne laser is 10–3 radians. It means that the diameter of the laser beam increases by about 1 mm for every meter it travels. Properties of Laser Determination of divergence of laser beam The extent of divergence of a laser beam can be estimated in a simple way as follows: If the diameters of spot produced by the laser on a screen which is held at two different distances from the laser are measured, then the angle of divergence is given by 𝑑2 −𝑑1 = (in radians) 𝑙2 −𝑙1 Where d1 is the spot diameter at the distance l1 and d2 is the spot diameter at the distance l2. Properties of Laser iii Intensity: The intensity of light from a conventional source decreases rapidly with distance as it spreads out in space. Laser emits light in the form of a narrow beam with its energy concentrated in a small region of space. Therefore, the beam intensity is tremendously large and stays constant with distance. The intensity of a laser beam is approximately given by 10 2 𝐼= 𝑃  where P is the power radiated by the laser. To obtain light of same intensity from a tungsten bulb, it would have to be raised to a temperature of 4.6 × 106 K. iv Monochromaticity: If light is coming from a source that has only one frequency (single wavelength) of oscillation, the light is said to be monochromatic and the source a monochromatic source. Light from traditional monochromatic sources spreads over a wavelength range of 100 Å to 1000 Å. On the other hand, the light from lasers is highly monochromatic and contains a very narrow range of a few angstroms (< 10 Å). Properties of Laser v Coherence: In simple words, the meaning of coherent is highly ordered. The word coherent comes from another word “Cohero” which has the meaning “to stick together”. In fact, different parts of the laser beam have a definite relationship to each other. This coherence is described in terms of temporal coherence (coherence in time) and spatial coherence (coherence in space) as shown in figure, which are required to produce high quality interference. Ordinary light is not coherent because it comes from independent atoms which emit on the time scale of 10–8 s. A train of incoherent photons is shown in Figure from which it is clear that these photons are not in order, i.e., they do not have a definite relationship with each other. Incoherent light Types of Laser Lasers are divided into different types based on the material used. Some of the important types of lasers are i. Solid-state lasers: Examples: Ruby laser, Nd:YAG laser etc ii. Gas lasers: Examples: Helium-Neon laser, CO2 laser etc iii. Semiconductor diode lasers: Examples: GaAs laser, InP laser etc Most lasers emit light in the Red or InfraRed regions. Lasers work in continuous mode or in a pulsed mode. Ruby laser Construction Ruby laser is made up of a crystal of ruby in the form of cylindrical rod having size 2 to 30 cm in length and 0.5 to 2 cm in diameter whose both ends are optically flat. One of the end is fully silvered and other is partially silvered, so that they can act as fully and partially reflecting surfaces, respectively, as shown in Figure. Ruby rod is a crystal of Al2O3 in which chromium oxide is mixed as impurity so that some of the Al3+ ions are replaced by Cr3+ ions. These ‘impurity’ chromium ions give rise to the laser action. Figure: Schematic of Ruby laser. The laser rod is surrounded by a helical photographic flash lamp filled with xenon. Whenever activated by the power supply, the lamp produces flashes of white light. Ruby laser Working A simplified energy level diagram of chromium ions in ruby crystal is shown in Figure. In the normal state, most of the chromium ions are in the ground state E1. When light from the flash tube of wavelength 5500 Å is made to fall upon the ruby rod, these incident photons are absorbed by the chromium ions that rise to the excited state E3. Then they give a part of their energy to the crystal structure and reach the metastable state, i.e., the E2 state by radiation-less transition. These ions in metastable state can remain for a longer duration 10–3 sec. Therefore, the number of ions in this state goes on increasing while at the same time number of ions in ground state goes on decreasing due to the optical pumping. Thus, the population inversion is established between the metastable state and the ground state. Ruby laser Working When an excited ion passes spontaneously from the metastable state to the ground state, it emits a photon of wavelength 6943 Å. This photon travels parallel to the axis of ruby rod and stimulates the surrounding ions present in the metastable state then by stimulated emission other photons are emitted, which are in the phase with the stimulating photons. By successive reflections of these photons at the ends of the rod, every time the stimulated emission is achieved, we obtain an intense, coherent and unidirectional laser beam from the partially silvered face. The laser emission occurs in the visible region at a wavelength of 6943 Å (694.3 nm). Once stimulated transitions commence, the metastable state gets depopulated very rapidly and the state of population inversion disappears and lasing action ceases. The laser becomes active once again when population inversion state is reestablished. Therefore, the output of the laser is not a continuous wave but occurs in the form of pulses of microsecond duration. Ruby laser Advantages and applications Advantages 1. It has large power output. 2. The pumping efficiencies can be increased by using cylindrical Mirrors. 3. It has a narrow line width. Applications 1. It is used as a high power source of pulse coherent radiation in interferometry and in pulsed holography. 2. It is used for drilling brittle material, soldering, welding, etc. Helium-Neon (He-Ne) Laser The output beam of the ruby laser is not High voltage power supply continuous. To overcome this drawback, the gas laser was developed by A. Javan, W. Bennett and D. Herriott in 1961. This laser operate with gases as the active Discharging electrodes media and are excited by an electric discharge. Construction The schematic of a He-Ne laser is shown in Figure. It consists of a discharge tube of 1 meter long and 1.5 cm in diameter filled with a mixture of helium and neon gases in Figure: Schematic of He-Ne laser. the ratio 10:1. The both ends of the tube are sealed by optically plane and parallel mirrors, one of them being partially silvered and the other one is fully silvered. A high potential difference is applied across the two electrodes of the discharge tube for creating population inversion. Electrons present in the discharge transfer energy to atoms in the laser gas by collisions. Helium-Neon (He-Ne) Laser Working The energy levels of helium and neon are shown in Figure. The Pumping Mechanism: The energetic electrons in the discharge excite helium atoms more readily, as they are lighter. The excited level of helium F2(2s) is at 20.61 eV above the ground level which is a metastable state and the excited helium atom cannot return to the ground level through spontaneous emission. However, the excited helium atom can return to the ground level by transferring its excess energy to a neon atom through collision. Such an energy transfer can take place when the two colliding atoms have identical energy levels. Such an energy transfer is known as resonant energy transfer. The Ne energy level E5(5s) is at 20.66eV, which is close to the excited energy level F2 of He atom. The kinetic energy of He atoms provides the additional 0.05 eV required for excitation of the Ne atoms. Helium-Neon (He-Ne) Laser Working Population Inversion: The upper state of neon atom E5 is a metastable state. Therefore, neon atoms accumulate in this upper state. The E3 (3p) level is lightly populated at ordinary temperatures. As the population at the higher energy level E5 is greater than the population at the lower level E3, a state of population inversion is established between E5 and E3 levels. Lasing action: Random photons of red colour of wavelength 6328 Å are emitted spontaneously by a few of the atoms at the energy level E5. The spontaneous photons traveling through the gas mixture prompt stimulated emission of photons of red colour of wavelength 6328 Å. The photons bounce back and forth between the end mirrors, causing more and more stimulated emission during each passage. The strength of the stimulated photons traveling along the axis of the optical cavity (discharge tube) builds up rapidly while the photons traveling at angles to the axis are lost. Thus, the transition E5 → E3 generates a laser beam of wavelength 6328 Å. Helium-Neon (He-Ne) Laser Working From the level E3 the neon atoms drop to E2 (3s) level spontaneously. E2 level is a metastable state. Consequently, neon atoms tend to accumulate at E2 level. Neon atoms return to the ground state E1 through frequent collisions with the walls of the dishcharge tube holding the helium-neon gas mixture. The neon atoms are once again available for excitation to higher state and participate in lasing action. The neon atoms are excited to the upper lasing level continuously through collisions. As the population inversion can be maintained in the face of continuous laser emission, the laser operates in continuous wave mode. Helium-Neon (He-Ne) Laser Advantages and applications Advantages 1. It is more directional and monochromatic than a solid-state laser. 2. It has high stability of frequency. 3. It can operate continuously without the need for cooling as in done in a ruby laser. 4. Low cost. 5. High stability. Applications 1. He-Ne laser is used in data processing. 2. He-Ne laser used in holography. 3. Studying interference and diffraction patterns. 4. Used in telecommunication. Applications of Laser Lasers find application in almost every field. They are used in mechanical working, industrial electronics, entertainment electronics, communications, information processing, and even in wars to guide missiles to the target. Lasers are used in CD players, laser printers, laser copiers, optical floppy discs, optical memory cards etc. Industrial applications 1. Laser cutting: A CNC laser cutter uses a coherent beam of light to cut materials, most often metal sheets, wood, diamond, glass, plastic, and silicon. Applications of Laser 2. Laser welding: The main advantage of the laser welding is that it is a contact-less process and hence there is no possibility of introduction of impurities into the joint. In the process, the work-pieces do not get distorted, as the total amount of input is very small compared to conventional welding processes. The heat-effected zone is relatively small because of rapid cooling. Laser welding can be done even at difficult to reach place. Applications of Laser 3. Surface hardening: Heat treatment is the process, which is done for sometime to harden metals and certain other materials. Heat-treating converts the surface layer to a crystalline state that is harder and more resistant to wear. In general CO2 lasers of about 1 kW output power operating in cw mode are used for heat treatment. As metals are more reflecting at IR frequencies, a heat absorbing coating such as graphite or zinc phosphate is applied on the surface of the work piece to help it absorb laser energy more efficiently. Laser heat treatment requires a low amount of energy input to the work piece. Laser processing is advantageous as it can provide selective treatment of the desirable areas. Heat treatment is used to strengthen cylinder blocks, gears, camshafts etc. in the automobile industry. As the method is a non-contact method, stress is not induced in the work-pieces. Applications of Laser Medical applications 1. Dermatology Some skin imperfections are being treated by laser irradiations. This technology have revolutionized its use in the treatment of many skin conditions. These applications cover a variety of conditions, including wrinkle removal, sun-damaged skin, age spots, and acne spots. 2. Dentistry Lasers have been used in dentistry since the 1990s to treat several conditions. The acceptance of laser technology has been growing, although it is still a subject of active research. Lasers have been demonstrated in the treatment of tooth decay, gum disease, biopsies, removal of lesions, activating a bleaching solution for whitening teeth, and curing dental compositions Applications of Laser 3. Surgery Lasers have been used in surgical applications include urology, cardiovascular, and veterinary surgery. Lasers offer an advantage because the high intensity can cure tissue and coagulate blood at the same time. Laser surgery results in the removal of much less tissue than the traditional process.