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G Ni Re En Ig N E Fo Eg Ell O C .S. E. P S CI S Y H P F O T N E M T R a P PHYSICS, Un ti – IV : La es rs and Optical Fi sreb , PES EC .P E.S. oC ll ege fo Engi reen ing, Mandya – 571 04 1, Karna at ka (An A ut ono mous Instituti no af ilif ated to VTU, Belaga iv ) DEP RA TMENT OF PHYSICS Unit - IV Las re s and Op it ac l rebiF s Notes Laser Dr. T. S. Shashikumar, Department of Physics, PESCE, Mandya LASERS INTRODUCTION: LASER is an optical device that amplifies light. LASER is the acronym of Light Amplification by Stimulated Emission of Radiation. Laser device is a source of highly intense and highly parallel coherent beam of light produced by stimulated emission. Laser action is achieved by creating population inversion between a pair of energy levels. Production of laser light is a particular consequence of interaction of radiation with matter. Basic Principle and Production of LASERS: The working principle of laser is based on the phenomenon of interaction of radiation with matter. A material medium is composed of identical atoms or molecules each of which is characterized by a set of discrete allowed energy states E1 and E2 as shown in figure (1). An atom can move from one energy state to another when it receives or releases an amount of ∆Ε E − E energyγ = ⇒ γ = 2 1 ⇒ γh = E − E equal to the energy to the energy difference h h 2 1 between those two states (∆E = E2 − E1 ). There are three possible ways through which interaction of radiation with matter can take place. They are, (1) Induced Absorption, (2) Spontaneous Emission, and (3) Stimulated Emission. (1) Induced Absorption: “Induced absorption is the absorption of an incident photon by an atom as a result of which the atom makes a transition from a ground state to an excited state, wherein the difference in energy of the two states is equal to energy of the photon”. Let E1 and E2 be two energy levels, in which E1 corresponds to lower energy (figure (a)). Let a photon having an energy ∆E equal to (E2-E1) be incident on the atom, then the atom will make a transition to the higher energy state E2 (figure (b)) by the absorption of the photon. As a result, its energy becomes E1+∆E = E2. In such a condition, atom is said to have made transition to the excited state and is indicated as atom*. This is called Induced absorption and could be represented as atom + photon → atom* (2) Spontaneous Emission: “Spontaneous emission is the emission of a photon, when an atom in an excited state makes a transition to a lower energy state without the aid of any external agency”. Consider an atom in the excited state. Excited states with higher energy are inherently unstable because of a natural tendency of atoms to attain the lowest energy configuration. Normally the excited atoms exist in the -8 excited state E2 for about 10 seconds (figure (c)) and tend to return to the lower state E1 by giving up the excess 1 Laser Dr. T. S. Shashikumar, Department of Physics, PESCE, Mandya energy (γh = E2 − E1 ) in the form of spontaneous emission. The energy of the atom is then given by E1 = E2 - ∆E as shown in figure (d). Due to spontaneous emission, the photons are emitted in all possible directions. Two such photons which are spontaneously emitted by two atoms under identical conditions may not have any phase similarities, and even they may not come in same direction. Hence they are incoherent in nature and the process is denoted as atom* → atom + photon (3) Stimulated Emission: “Stimulated emission of a photon by an atom under the influence of a passing photon (stimulating photon) of just the right energy, due to which the atom make a transition from a higher energy state to a lower energy state. The photon thus emitted is called the stimulated photon and it will have the same energy, same phase and direction of movement as that of the passing photon called the stimulating photon”. Consider an atom in the excited state. Let a photon having an energy ∆E precisely equal to (E2 – E1) interact with the atom by passing in its vicinity as shown in figure (e). Under such stimulation, the atom emits a photon and transits to the lower energy state. The two photons travel in exactly the same direction, and with exactly the same energy. The electromagnetic waves associated with the two photons will have identical phase and thus they are coherent as shown in figure (f). The process can be represented as atom* + photon → atom + ( photon + photon) This kind of emission is responsible for laser action. Einstein Co-efficient: Consider two energy states E1 and E2 of a system of atoms. Let N1 and N2 be the number of atoms per unit per volume in the states of energies E1 and E2 respectively. N1 and N2 are called the number density of atoms in the states 1 and 2. Let radiation with a continuous spectrum of frequencies is incident on the atomic system. Let Uγ be the energy density/unit volume of frequency γ and Uγdγ be the energy density/unit volume of the system for the radiations of frequencies lie in the range γ and γ+dγ. Let us consider the absorption and the two emission process case by case. 2 Laser Dr. T. S. Shashikumar, Department of Physics, PESCE, Mandya (i) Case of Induced Absorption: In the case of induced absorption, an atom in level E1 can go to the level E2, when it absorbs a E − E radiation of suitable frequency γ = 2 1 (figure.5). h The number of such induced absorptions/unit time/unit volume is called rate of induced absorption. The rate of induced absorption depends upon, (a) the number density of lower energy state. i.e., N1 and (b) the energy density i.e., Uγ ∴Rate of absorption α N1 Uγ ∴Rate of absorption α B12 N1 Uγ → (1) Where, B12 is the constant of proportionality called Einstein Co-efficient of Induced absorption. (ii) Case of Spontaneous Emission: In the case of spontaneous emission, an atom in higher energy level E2 under goes transition to the lower energy level E1 voluntarily by emitting a photon (figure.5). Since it is voluntary transition, it is independent of the energy density of any frequency in the incident radiation. The number of such spontaneous emissions/unit time/unit volume is called rate of spontaneous emission. Which is proportional to only the number density in the higher energy state i.e., N2 ∴Rate of spontaneous emission α N2 ∴Rate of spontaneous emission α A21 N2 → (2) Where, A21 is the constant of proportionality called Einstein Co-efficient of Spontaneous Emission. (iii) Case of Stimulated Emission: In the case of stimulated emission, the system requires an external photon of appropriate E − E frequency γ = 2 1 , to stimulate the atom for the corresponding downward transition, and thereby cause emission of h stimulated photons (figure.5). The number of such stimulated emissions/unit time/unit volume is called rate of stimulated emission. The rate of stimulated emission depends upon, (a) the number density of higher energy state. i.e., N2 and (b) the energy density i.e., Uγ ∴Rate of stimulated emission α N2 Uγ ∴Rate of stimulated emission α B21 N2 Uγ → (3) Where, B21 is the constant of proportionality called Einstein Co-efficient of Stimulated Emission. Relationship between the Einstein Co-efficient: Let the System be in thermal equilibrium, which means that the total energy of the system remains unchanged in spite of the interaction that is taking place between itself and the incident radiation. ∴At thermal equilibrium, Rate of Absorption = Rate of Spontaneous emission + Rate Stimulated emission 3 Laser Dr. T. S. Shashikumar, Department of Physics, PESCE, Mandya ∴From equations (1), (2) & (3), we have ⇒ ⇒ A21N2 B12 N1U γ = A21 N 2 + B21 N 2U γ (B12 N1 − B21N2 )Uγ = A21N2 Uγ = (B12 N1 − B21N2 ) By rearranging the above equation, we get, A21 1 → (4) Uγ = B B12 N1 21 −1 B21N2 But, by Boltzmann-law, we have E −E hγ hγ − 2 1 − KT KT N1 KT N2 = N1e ⇒ N2 = N1e ⇒ = e → (5) N2 Now, by substituting equation (5) in equation (4), we have A21 1 → (6) Uγ = B B hγ 21 12 e KT −1 B21 According to Planck’s law, the equation for energy density Uγ is given by 8πhγ 3 1 U = → (7) γ c3 hγ e KT −1 Now, comparing equation (6) and equation (7), term by term on the basis of positional identity, we have A 8πhγ 3 21 B12 = 3 & = 1 or B12 = B21 B21 c B21 This implies that the probability of induced absorption is equal to the probability of stimulated emission. Because of the above identity, the subscripts could be dropped, and A21 and B21 can be represented simply as A and B equation (6) can be rewritten. At thermal equilibrium the equation for energy density is A 1 U = γ B hγ e KT −1 Requisites of Lasing systems: The requisites of Laser system are: (1) Laser cavity, (2) Active medium and (3) An excitation source for pumping action (i) Laser Cavity: A laser cavity consists of two opposing plane-parallel mirrors M1 and M2 with the active material placed in between them as shown in figure (8). These mirrors are generally coated with multilayer dielectric material to reduce the absorption loss in the mirrors. A sequence 4 Laser Dr. T. S. Shashikumar, Department of Physics, PESCE, Mandya λ of quantum-wave ( 4) layers of alternate high and low refractive index materials are coated on these mirrors.
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