Unit 2: Lasers Lecture 2 (PHY109) September 2024 PDF

UNIT 2: LASER AND APPLICATIONS 1 LECTURE 2 September 6, 2024  https://www.mpoweruk.com/radio.htm 2 Cosmic rays are not electromagnetic waves and so are not described by wavelength. They are high speed protons (or other nucleons). Howev...

UNIT 2: LASER AND APPLICATIONS 1 LECTURE 2 September 6, 2024  https://www.mpoweruk.com/radio.htm 2 Cosmic rays are not electromagnetic waves and so are not described by wavelength. They are high speed protons (or other nucleons). However, when they hit the atmosphere, they release Cherencov radiation which is blue light September 6, 2024  Revision Lecture 1 3 When photons of energy (h) travel through a material three different processes occur 1. Absorption, 𝑹𝒂𝒃𝒔 = 𝑷𝟏𝟐 𝑵𝟏 = 𝑩𝟏𝟐 𝑵𝟏 𝒖 𝝂 2. Spontaneous emission 3. Stimulated emission 𝑹𝒔𝒕𝒊𝒎𝒖 = (𝑷𝟐𝟏 )𝒔𝒕𝒊𝒎𝒖 𝑵𝟐 = 𝑩𝟐𝟏 𝑵𝟐 𝒖 𝝂 Prof. Reji Thomas DRC-DRD September 6, 2024  2. SPONTANEOUS EMISSION 4 In other words, A21 is a measure of the lifetime of atoms at E2 state against the spontaneous emission and subsequent transition of atom to the E1. Note; spontaneous transition is not possible from E1 to E2 so Characteristics of the Spontaneous Emission 1. No way to control the process from outside 2. Direction of propagation, phase and plane of polarization of emitted photons are random - Incoherent 3. Light emitted are polychromatic not monochromatic 4. The intensity of the emitted radiation is proportional to the number radiating atoms(N).. i.e excited atoms at level E2 Itot=N I, where I is the intensity of light emitted by one atom. Spontaneous emission is what we see in conventional light sources. September 6, 2024  CHARACTERISTICS OF THE STIMULATED EMISSION 5 1) The process is controllable from outside- control it through the photon interaction 2) Induced and inducing photon propagate in the same direction 3) Identical to incident photon-coherent 4) Multiplication of the photon 5) Light amplification 6) Net intensity of light is proportional to the square of the number of atoms (N) radiating light.. Itot=N2 I, where I is the intensity of light emitted by one atom. September 6, 2024 Stimulated emission: Multiplication of the photons 6 September 6, 2024  Stimulated emission: Amplification of the photons 7 All the waves are coherent and hence constructively interfere and that results in an amplified light source September 6, 2024  The probability of a stimulated emission transition (P21) is proportional to (a) photon density () only (b) Number of particles in the energy levels only (c) Both number of particles in the energy levels and photon density (d) Neither on the number of particles nor on the photon density Lifetime of unstable state is 10 QUICK Quiz September 6, 2024 11 LASER is the acronym of a) Light amplification and stimulated emission of radiation b) Light amplification by stimulated emission of radiation c) Light absorption by stimulated emission of radiation d) Light absorption by spontaneous emission of radiation Ans: B September 6, 2024 12 Which of the following is used in atomic clocks? a) Laser b) Quartz c) Maser d) Helium Ans: C September 6, 2024 13 DVD uses laser. True or false? a) True b) False Ans: A September 6, 2024  POPULATION OF ENERGY LEVELS 14 Populations of energy levels is nothing but the total number of atoms occupying the particular Energy level (E). E3 N3 E2 N2 E1 N1 the Boltzmann distribution tells us that the ratio of populations varies exponentially with the energy difference, and the greater the level difference the smaller the population in the E2 level. September 6, 2024  EINSTEIN RELATIONS 15 Under steady state condition, Rate of absorption transitions and rate of emissions (induced as well as spontaneous) will balance each other 𝑩𝟏𝟐 𝒖 𝝂 𝑵𝟏 = 𝑨𝟐𝟏 𝑵𝟐 + 𝑩𝟐𝟏 𝑵𝟐 𝒖 𝝂 Where, B12, A21, B21 are Einstein’s coefficients for induced absorption, spontaneous emission and stimulated /induced emission respectively. N1 and N2 populations of atoms in the ground ( E1) are excited (E2) states, respectively. September 6, 2024  EINSTEIN RELATIONS 16 Just now we saw 𝑩𝟏𝟐 𝒖 𝝂 𝑵𝟏 = 𝑨𝟐𝟏 𝑵𝟐 +𝑩𝟐𝟏 𝒖 𝝂 𝑵𝟐 under thermal equilibrium Eq.1 Number of atoms absorbing Number of atoms emitting photons photons per second per volume = per second per volume Re-arranging equation 1 we get, So the photon density can be expressed as Eq. 2 September 6, 2024  EINSTEIN RELATIONS 17 Now divide numerator and denominator by B12N2, we get Eq. 3 But Boltzmann's law, the distribution of atoms among the energy levels E1 and E2 at thermal equilibrium at Temperature T is And k Boltzmann's constant, h Planck’s const and frequency of photon Eqn.3 becomes Eq. 4 September 6, 2024  Eq. 4 18 But according to Planck’s law, the energy density of radiation (), is given by the formula Eq. 5 Where µ is the refractive index of the medium and c is the velocity of light in free space. Photon energy density given by Eq.4 must be consistent with and Eq.5, then we get two relations for 3 Einstein’s coefficients Eq. 6 Eq7 September 6, 2024  EINSTEIN RELATIONS 19 Eq.6 and 7 are known as Einstein relation and B12,B21 and A21 are Einstein coefficients Eq. 8 Eq.8 Implied: ❑ Probability of induced absorption and induced/stimulated emissions are same.. Means? ❑ Laser actions at high frequencies are difficult to achieve (x-rays onwards).. Why? September 6, 2024  LASER 20 Light Amplification through (by) Stimulated Emission of Radiation So to realize LASER we need light amplification and for that stimulated emission is essential But Under normal conditions 1. Induced absorption dominate stimulated emission for given a photon density. N1>>N2 2. Spontaneous emission dominate stimulated emission for lower life time at the excited level.  < 10-7s How to get rid of these two issues to succeed in stimulated emission and hence light amplification? Stimulated emission/spontaneous emission (R1=Rst/Rsp)? 21 To get an idea about it let us find the typical value of Rst/Rsp From our last lecture we know, rate of stimulated transition (Rst) and rate of spontaneous transitions (Rsp)are Now take the ratio of Rst to Rsp Eq. 9 Substitute from Eq. 5 September 6, 2024 Stimulated emission/ spontaneous emission (R1=Rst/Rsp)? 22 Now Eq.9 changes to Eq. 10 But then Eq.10 becomes Eq. 11 In the optical region, say 5x1014 Hz (600 nm) and at room temperature T=300 K, the value of R1 can be found to be 10-58. Stimulated emission is negligible compared to spontaneous emission. September 6, 2024 How to increase R1=Rst/Rsp to realize LASER? 23 We have ; so when the photon density () and ratio of Einstein coefficient (B21/A21) are large, stimulated emission will dominate 1. But as the radiation density () increase absorption also increases, due to B21=B12. Hence large photon density of course help but not enough for more stimulated emissions…. Optical cavity? 2. If the excited state has more life time (1/A21 represents the lifetime of the excited state), R1 increases many fold and stimulated emission increases substantially…. Metastable state? So an increase in the photon density () and the lifetime of atoms in the excited state, along with the dominance over absorption transition may work out for increasing the stimulated transition. September 6, 2024 How to increase R2=Rst/Rabs to realize LASER? 24 R21=R12 Eq. 12 i.e. stimulated transition overcomes absorption transition if N2 >>N1. 3. Unfortunately, under normal condition population in the excited level (N2) is very much lower than that in the ground state(N1). We have to invert this situation…. Population inversion? So we need three different requirements for getting dominant stimulated transition and LASER action (i) Large photon density () –Optical resonant cavity (ii) Large lifetime of atoms in the excited state- Metastable state (iii) Large number of excited atoms - population inversion How to attain these three requirements? we will see next…. September 6, 2024  Meeting the requirements? 1. POPULATION INVERSION by Pumping 25 When the material is at thermal equilibrium, population ratio between E1 and E2 is given by the Boltzmann’s law Negative temperature to achieve (N2>> N1) population inversion? The lowest temperature one can achieve is T=0° K(-273°C) So one has to supply energy from outside to attain N2>> N1 and hence population inversion occurs…. There are different excitation mechanisms which we will see later September 6, 2024  Meeting the requirements? 1. POPULATION INVERSION by Pumping 26 In the inverted case, stimulated transition is triggered, and photon multiplication occurs and hence light amplification happens However, due to continued stimulated emission, population of E2 reduces and this action comes to an end. To sustain one has to continuously excite atoms from E1 to E2 and this process is called pumping or optical pumping– like you pump water to your tank for continuous usage of water☺ September 6, 2024 Meeting the requirements? 2. METASTABLE STATE to increase lifetime 27 After achieving population inversion, one has to suppress spontaneous emission that generally happens in nanoseconds time. To increase the population at the excited state, the lifetime at that state should be increased 10-6 to 10-3 s. This is achieved by allowing the excited atoms at the pumping level to lose fraction of the energy and jump to another level where they stay longer time.. This third state is called the Metastable state This is possible in the material by doping September 6, 2024  Meeting the requirements? 3. Large photon density () –Optical resonant cavity 28 To make stimulated emission to overtake spontaneous emission That can be achieved By placing laser medium (material) between two mirrors Photon density build-up due to repeated reflections Contained in the cavity to increase interaction- confinement September 6, 2024 Quick Quiz September 6, 2024 30 In normal conditions, absorption is more probable, and hence spontaneous emission dominate the stimulated emission.. Why? a) More atoms are in the ground state compared to excited state. b) Less atoms are in the excited state compared to ground state. c) All of the above. d) None of the above. September 6, 2024 31 Einstein coefficient B12 for the absorption transition is equal to B21 of the stimulated transition.. Means? a) When atoms are placed in a radiation field probability upward transition is more b) When atoms are placed in a radiation field probability downward transition is more c) Probability for downward and upward transition are equal d) None of the above September 6, 2024 32 Laser actions at high frequencies are difficult to achieve (x-rays onwards).. Why? a) Coefficient of stimulated emission B21 is inversely proportional to the cube of the frequency b) Coefficient of stimulated emission B21 is directly proportional to the cube of the frequency c) Coefficient of stimulated emission B21 is nothing to do anything with frequency d) None of the above September 6, 2024