Basic Physics Behind Laser (Principle) PDF

Basic Physics Behind LASER (Principle) Before that we have to know 3 TYPES OF TRANSITIONS i.e. Quantum process that takes place between the energy (Photon)& matter (atom) Dr JB: BPHY101L School of Physics,VIT Vellore ...

Basic Physics Behind LASER (Principle) Before that we have to know 3 TYPES OF TRANSITIONS i.e. Quantum process that takes place between the energy (Photon)& matter (atom) Dr JB: BPHY101L School of Physics,VIT Vellore  Absorption Upper level E2 Upper level A* E2 photon atom A + hν → A* Induced/stimulated Absorption E1 A E1 Lower level atom Lower level Before After Absorption: When a photon incident on atoms then atoms absorb the energy from the photon and jump from a lower energy state (E1) to a higher energy state (E2). This transition is known as absorption. For absorption to occur, the photon must have energy E2−E1 = hν Dr JB: BPHY101L School of Physics,VIT Vellore  Spontaneous Emission Upper level A* Upper level E2 E2 atom photon A* → A + hν Spontaneous emission Random direction In-coherent E1 E1 A Lower level Lower level atom Before After Spontaneous emission: The atoms in the excited energy state (E2) undergo a transition to the lower energy level (E1) on its own and gives up the excess energy in the form of a photon. This process is called spontaneous emission. The emitted photon will have energy hν = E2−E1 Dr JB: BPHY101L School of Physics,VIT Vellore  Stimulated Emission Upper level A* Upper level E2 E2 atom two photon A* + hν → A + 2hν photon Stimulated emission Same direction A Coherent E1 E1 In-phase Lower level Lower level atom Two photon Before After Stimulated emission: If a photon with energy E2−E1=hν interacts with an atom in the excited energy state( E2), it can trigger the atom to undergo a transition to the lower level ( E1 ) resulting in the emission of another photon. This process is known as stimulated emission. In this process, one photon strikes the photon and one other photon is emitted! A total of two photons comes out at the end. Can we amplify radiation using stimulated emission? Dr JB: BPHY101L School of Physics,VIT Vellore  Stimulated Emission leads to Amplification 21 22 23 24.......... 2N Dr JB: BPHY101L School of Physics,VIT Vellore  Population Inversion N1>N2 N1 E1, we have N1> N2. Thus, at any finite and positive temperature, the number of atoms in the higher energy level is always less than that in lower energy level. This is equilibrium condition. However, for stimulated emission to dominate over stimulated absorption, we require N2 > N1. This is called as population inversion. Dr JB: BPHY101L School of Physics,VIT Vellore  Einsteins Coefficient: Absorption ρ(ν) Photon Density So the probability of the transition from E1 to E2 is: P12 ∝ρ(ν) B12 is the Einstein P12 = B12 ρ(ν) coefficient for absorption So the no. of atoms absorption from E1 to E2 in a time duration Δt is : = N1 P12 Δt = N1 B12 ρ(ν) Δt Dr JB: BPHY101L School of Physics,VIT Vellore Einsteins Coefficient: Spontaneous Emission ρ(ν) Photon Density So the probability of the transition from E2 to E1 is: A21 is the Einstein P21 = A21 coefficient for Spontaneous Emission So the no. of atoms transition from E2 to E1 in a time duration Δt is : = N2 P21 Δt = N2 A21 Δt Dr JB: BPHY101L School of Physics,VIT Vellore  Einsteins Coefficient: Stimulated Emission ρ(ν) Photon Density So the probability of the transition from E1 to E2 is: P′21 ∝ρ(ν) B21 is the Einstein P′21 = B21 ρ(ν) coefficient for Stimulated Emission A: spontaneous process So the no. of atoms absorption from E1 to E2 in a time duration Δt is : B: stimulated process = N2 P′21 Δt = N2 B21 ρ(ν) Δt Dr JB: BPHY101L School of Physics,VIT Vellore  Einsteins Coefficient: Derivation N1 B12 ρ(ν) Δt N2 A21 Δt N2 B21 ρ(ν) Δt In thermal equilibrium: No of transition from E1 to E2 = No of transition from E2 to E1: N1 P12 = N2 P21 + N2 P′21 N1 B12 ρ(ν) = N2 A21 + N2 B21 ρ(ν) [N1 B12 −N2 B21]ρ(ν) = N2 A21 N2 A21 ρ(ν) = [N1 B12 −N2 B21] Dr JB: BPHY101L School of Physics,VIT Vellore  Einsteins Coefficient: Derivation N2 A21 At, thermal equilibrium, it will also radiate the ρ(ν) = [N1 B12 −N2 B21] EM wave according to the Planck’s radiation: 8πhν 3 1 divide both n/d by B12N2 ρ(ν) = [ hν ] c 3 e kβT −1 A21 /B12 ρ(ν) = N1 B21 on comparison of the both the photon density: −B B21 N2 12 A21 8πhν 3 = 1 = At, thermal equilibrium, Boltzmann’s statistics B12 c3 B12 N1 (E2 −E1) = e kβT N2 A21 8πhν 3 A21 /B12 B21 = B12 = 1 & = ρ(ν) = B21 c3 (E2 −E1) B e kβT −B21 12 A21 /B12 ρ(ν) = hν Einsteins Coefficient relations B21 “Stimulated emission rate = absorption rate” e −B kβT 12 Stimulated emission at higher frequency is difficult to achieve Dr JB: BPHY101L School of Physics,VIT Vellore  Einsteins Coefficient: Significance “Stimulated emission rate = absorption rate” Stimulated emission at higher frequency is difficult to achieve Population inversion not possible in two level systems B21 = B12 = 1 Einstein proved that the rate of stimulated emission is equal to the rate of absorption. Therefore, at best, number of atoms in energy levels in E1 and E2 are equal (E2 −E1) Also, under thermodynamics equilibrium N1 = N0 e kβ T N2 Dr JB: BPHY101L School of Physics,VIT Vellore