UNIT -I LASERS AND WAVE OPTICS Department Of Applied Physics, ACET BE-Second Semester – Advanced Physics Page 1 LASERS Introduction: Laser is one of the outstanding inventions of the 20th century. LASER stands for Light Amplification by Stimulated Emission of Radiation. It is artificial light sources that differ vastly form the traditional light source. Laser have widespread applications in our everyday life and in technological devices ranging from CD players, DVD players, barcode readers in supermarket, laser printers, eye surgery equipments, dental drills, optical communication system etc. It is device which produces a highly directional, coherent, monochromatic, polarized and intense beam of light that depends upon the phenomenon of stimulated emission. Interaction of light radiation with matter / Three quantum processes: To understand the working principal of LASER it is required to understand the three quantum processes that takes place in material when it is exposed to radiation. A material is composed of identical atoms each of which has characterized by discrete allowed energy levels. Atoms are characterized by many energy levels but for the sake of simplicity, consider only two energy levels E1 and E2, E1 is lower energy state (ground state) and E2 is higher energy state (exited state). As the atoms of the material are identical, energy level E1 and E2 are common to all atoms within material. The incident radiation may be viewed as a stream of photons, each photon carrying an energy hv. If hv = E2 - E1, then interaction of radiation with atom leads to the following three transition. They are absorption, spontaneous emission and stimulated emission. Transition or Quantum jump is the process of transfer of atom from one energy state to another energy state. 1. Absorption / Induced Absorption / Stimulated Absorption : An atom residing in the lower energy level E1 may absorb the incident photon of energy E2 – E1= hv and jump to the excited state E2 . This transition is known as stimulated absorption or induced absorption or simply as absorption. Corresponding to each transition made by an atom one photon is disappears from the incident beam. It may be represented as A + hv A* Where A is an atom in the lower state and A* is atom in excited state. Department Of Applied Physics, ACET BE-Second Semester – Advanced Physics Page 2 Fig. Absorption Process The no of absorption transition take place is depended on N1 no of atom in lower energy level E1 and photon density Q. The number of absorption transitions occurring in the material at any instant will be proportional to the number of atoms at the energy level E1 and the photon density in incident beam. The number of atoms Nab excited during time Δt is therefore given by Nab = B12 N1Q Δt Where B12 is the constant of proportionality, known as the Einstein coefficient for induced absorption 2. Spontaneous Emission: Excited energy state with higher energy is inherently unstable. To achieve minimum potential energy condition, atoms are always tends to remain in the lower energy level. The excited atom in the state E2 may return to lower state E1 on its own out of natural tendency to attain minimum potential energy condition by releasing excess energy in the form of photon . This type of process in which photon emission occurs without any external impetus is called spontaneous emission. We may write the process as Where hv is energy of incident photon, A is an atom in the lower state and A* is an excited atom. Fig. Spontaneous Emission process Department Of Applied Physics, ACET BE-Second Semester – Advanced Physics Page 3 The no of spontaneous transition occurring during the time ∆t is depended on N2 number of atom in excited energy level E2 . Thus the no of spontaneous transition in time ∆t is given by Nsp = A21 N2∆t Where A21 is the constant of proportionality which is known as Einstein coefficient for Spontaneous Emission. The important features of this process are: (1) It cannot be controlled from outside. (2) The light emitted due to this process is incoherent i.e. the photons have different phases, planes of polarization and direction of propagations. (3) The light spreads in all direction around the source. The light intensity goes on decreasing rapidly with distance from the source 3. Stimulated Emission / Induced Emission : A photon of energy hv=E2-E1 can induce / trigger the excited atom to make a downward transition releasing the excess energy in the form of photon. The phenomenon of forced emission of photon by an excited atom due to the action of an external agency is called stimulated emission. It is also known as induced emission. It is represented as The existence of this mechanism was predicted by Einstein in 1916. Fig. Stimulated Emission process The no of Stimulated transition occurring in the material in time ∆t is depended on N2 no of atom in excited energy level E2 and photon density Q. Thus the no of Stimulated transition in time ∆t is given by Nst = B21 N2 Q ∆t Department Of Applied Physics, ACET BE-Second Semester – Advanced Physics Page 4 Where B21 is the constant of proportionality which is known as Einstein coefficient for Stimulated Emission. The phenomenon of stimulated emission is to be maximized for laser operation because it produces coherent photons and also multiplies it. Characteristics of stimulated emission: 1) The photon induced in this process propagates in the same direction as that of incident photon. 2) The induced photon has features identical to that of the incident photon. It has the same frequency, phase and plane of polarization as that of the incident photon. 3) The outstanding feature of this process is the multiplication of photons. For one photon interacting with an excited atom, there are two photons emerging. The two photons traveling in the same direction interact with two more excited atoms and generate two more photons and produce a total of four photons. These four photons in turn stimulate four excited atoms and generate eight photons, and so on. The number of photons builds up in an avalanche like manner, as shown in Fig. below. Fig: Multiplication of stimulated photons into an avalanche. Distinction between Spontaneous and Stimulated Emission: Sr. Spontaneous emission Stimulated emission No 1. Spontaneous emission is a random and Not a random process. probabilistic process. 2. Not controllable from outside. Controllable from outside. 3. Photons are emitted uniformly in all The photons emitted in the process travel in the directions from an assembly of atoms. As same direction as that of incident photon, so light a result, the light is non-directional. produced by the process is essentially directional. 4. Photons of slightly different frequencies The frequency of emitted photon is nearly equal are generated. As a result, the light is not to that of incident photon. As a result the light is Department Of Applied Physics, ACET BE-Second Semester – Advanced Physics Page 5 monochromatic. nearly monochromatic. 5. The photons emitted by this process have The photons emitted by this process are all in not any correlation in their phases. phase and therefore, the light is coherent. Therefore, the light produced by this process is incoherent. 6. In this process multiplication of photons In this process multiplication of photons take does not take place. Hence light place. Hence light amplification occurs. (One amplification does not occur. stimulating photon causes emission of two more photons. These two produce four photons, which in turn generate eight photons and so on. Thus, if there are N excited atoms, 2N photons will be produce.) 7. The net intensity of the generated light is As all the photons are in phase, they given by constructively interfere and produce an intensity 2 IT.=N I IT =N I Where N is the number of atoms emitting photons and I is the intensity of each photon. 8. The planes of polarization of the photons The planes of polarization are identical for all are oriented randomly. Hence, light from photons. Consequently, light is polarized. the source is unpolarized. Active Medium A medium in which light gets amplified is called active medium. The medium may be solid, liquid or gas. Active Centers Out of the different atoms in the medium only small fraction of the atoms are responsible for stimulated emission and consequent light amplification. They are called active centers. The remaining bulk of the medium supports the active centers. Department Of Applied Physics, ACET BE-Second Semester – Advanced Physics Page 6 Population and thermal equilibrium The number of active atoms occupying an energy state is called as population of that state. Let N1 and N2 be the population of lower energy level E1 and upper energy level E2 . In thermal equilibrium the population of energy level E1 and E2 is given by Boltzmann factor N 2 (E2 E1 ) exp N1 kT The negative exponent in this equation indicates that N2 N1 at equilibrium. It means more atoms are in lower energy levels E1. This state is called as “Normal State” or “Thermal Equilibrium state”. Conditions for Light Amplification: Light amplification requires that stimulated emission occur almost exclusively. In practice, absorption and spontaneous emission always occur together with stimulated emission. The laser operation is achieved when stimulated emission exceeds than absorption and spontaneous emission. 1) Condition for Stimulated emission to dominate spontaneous emission process Stimulated transition B21N 2 Q B21 Q --------------- (1) spontaneous transition A21 N 2 A21 Eq. (1) shows that in order to increase stimulated transition the photon density Q is must be larger. 2) Condition for Stimulated emission to dominate Absorption transitions process Stimulated Transition B21N 2 Q N 2 ---------------(2) Absorption Transition B12 N1 Q N1 Where B21 = B12 as the probability of Stimulated Emission must be equal to probability of absorption transition.