Laser - Engineering Physics

Chapter Laser 11 OBJECTIVES • To understand the principle, theory, operations and applications of laser • To discuss the fundamental terms such as absorption, spontaneous and stimulated emission • To derive Einstein expressions for stimulated emission and to study its importance • To explore the different methods of population inversion • To derive Schawlow and Townes condition for achieving laser action • To study the different types of lasers and their applications • To discuss the laser applications such as holography, and the use of lasers in the fields of computers, industry, medicine, etc 11.1 i n t r o d u c t i o n Laser is an acronym for Light Amplification by Stimulated Emission of Radiation. The theoretical explanation for laser oscillation was given by A L Schawlow and C H Townes in the year 1958. The first laser, namely, ruby laser was demonstrated by T H Maiman, in the year 1960. The discovery of laser made an enormous impact in the scientific world and showed that the function of optics was very much alive. The laser beam has the properties given below which distinguish it from an ordinary beam of light. (i) Directionality The light beam can travel as a parallel beam up to a distance of d2/l, where d is the diameter of the aperture through which the light is passing and l the wavelength of the light used. After travelling the distance d2/l, the light beam spreads radially. In an ordinary light beam, the angular spread is given by Dq = l . For a typical laser beam, the angular d spread is 1 mm per 1 m, but for an ordinary source of light, the angular spread is 1 m per 1 m. This shows the directionality of the laser beam. For example, the laser beam can be focused to moon from the earth with an angular spread of a few kilometres. 11.2 Engineering Physics (ii) Intensity The intensity of the laser beam is very high. If a person is allowed to observe an ordinary light, emitted by a 100 W bulb at a distance. One foot from the source, he can perceive only one thousand watt of light. While, if the person is allowed to observe the laser beam from the same distance, the entire laser beam penetrates through his eye. It will damage the eye of the observer. This shows the high intensity of the laser beam. (iii) Monochromaticity The laser beam is strictly monochromatic (single frequency) than any other conventional monochromatic source. The bandwidth (Dn = 0) of the laser beam is narrow, while ordinary light spreads over wide range of frequencies. Obtaining absolute monochromaticity is difficult; however, one can get high degree of monochromaticity in laser beam with very small bandwidth, of about one kilocycle per second. For example, the line width Dl emitted by ruby laser is 5 ¥ 10-4 Å. (iv) Coherence The degree of coherence of laser beam is very high than the other sources. The coherence of laser emission results in extremely high power (5 ¥ 1012 W cm-2 ). The light from a laser source consists of wave trains that are identical in phase and directions of propagation. Further, it can be focused to a very small area of 0.7 mm thickness. It is, indeed, these properties, that differentiate the laser beam from other conventional light beams. Let us discuss the principle, generation and application of the laser in this chapter in detail. 11.2 PrinciPle of laser From the theory of interaction of radiation with matter, we can get an idea regarding the working of laser. Consider an atom that has only two energy levels, E1 and E2. When it is exposed to radiation having a stream of photons, each with energy hn, three distinct processes can take place. (i) Absorption (ii) Spontaneous emission, and (iii) Stimulated emission (i) Absorption An atom or molecule in the ground state E1 can absorbs a photon of energy hv and go to the higher energy state E2. This process is known as absorption and is illustrated in Fig. 11.1 E2 E2 hn Photon E1 E1 Before absorption After absorption Fig. 11.1 Absorption The rate of upward transition R12 from ground state E1 to excited state E2 is proportional to the population of the lower energy level N1 (number of atoms per unit volume) and to the energy density of radiation rn, 11.3 Laser i.e. R12 a rn a N1 Thus (11.1) R12 = B12 rn N1 where B12 is the probability of absorption per unit time. Normally, the higher energy state is an unstable state and hence, the atoms will make a transition back to the lower energy state with the emission of a photon. Such an emission can take place by one of the two methods given below. (ii) Spontaneous Emission In spontaneous emission, the atoms or molecules in the higher energy state E2 eventually return to the ground state by emitting their excess energy spontaneously. This process is independent of external radiation. The rate of the spontaneous emission is directly proportional to the population of the energy level E2, i.e. R21 (SP) a N2 R21 (SP) = A21 N2 (11.2) where A21 is the probability per unit time that the atoms will spontaneously fall to the ground state and N2 the number of atoms per unit volume in the state E2. This process is illustrated in Fig. 11.2 E2 hn E1 Fig. 11.2 Spontaneous emission (iii) Stimulated Emission In stimulated emission, a photon having energy E, equal to the difference in energy between the two levels E2 and E1, stimulate an atom in the higher state to make a transition to the lower state with the creation of a second photon as shown in Fig. 11.3. E2 hn hn hn E1 Fig. 11.3 Stimulated emission 11.4 Engineering Physics The rate of stimulated emission R21 (ST) is given as, R21 (ST) = B21rnN2 (11.3) where B21 is the probability per unit time that the atoms undergo transition from higher energy state to lower state by stimulated emission. Under conditions of thermal equilibrium, the population of energy levels obey Boltzmann’s distribution function. 11.3 einstein’s theory of stimulated emission In 1917, Einstein proposed a mathematical expression for the existence of stimulated emission of light. This expression is known as Einstein’s expression. Consider a two-level energy system (E1 and E2). Let N1 and N2 be the number of atoms in the ground state and excited state, respectively. Let us assume that only the spontaneous emission is present and there is no stimulated emission of light. At thermal equilibrium condition, the rate of absorption = the rate of emission of light From Eqs (11.1) and (11.2), we can write, rn ¥ B12N1 = A21N2 rn = A21 N 2 B12 N1 (11.4) According to Boltzmann’s distribution function, the population of atoms in the upper and lower energy levels are related by, N 2 e - E2 / kT = N1 e - E1 / kT Substituting N2/N1 in Eq. (11.4), we get, A - ( E - E )/ kT rn = 21 e 2 1 B21 rn = (11.5) (11.6) A21 1 B21 e hn / kT According to black-body radiation, the energy density 8p hn 3 1 rn = c 3 e hn / kT - 1 (11.7) where h is the Planck’s constant and c the velocity of light. Comparing the above two equations [Eqs (11.6) and (11.7)], one can observe that they are not in agreement. To rectify this discrepancy, Einstein proposed another kind of emission known as stimulated emission of radiation. Therefore, the total emission is the sum of the spontaneous and stimulated emissions of radiation. At thermal equilibrium condition, the rate of absorption = the rate of emission From Eqs (11.1), (11.2) and (11.3), B12 N1 rn = A21N2 + B21N2rn