Laser Physics - Properties, Interaction, Components PDF

Properties of Laser Light : Highly Directional (Collimated) Beam Laser light can travel very large distance without divergence and without loss of energy. It’s angular spreading will be less. Hence it possesses “high degree of directionality”.  Properties of Laser Light : Highly Intense beam...

Properties of Laser Light : Highly Directional (Collimated) Beam Laser light can travel very large distance without divergence and without loss of energy. It’s angular spreading will be less. Hence it possesses “high degree of directionality”.  Properties of Laser Light : Highly Intense beam Since ordinary light spreads in all directions, the intensity reaching the target is very less. In laser, due to high directionality, the intensity reaching the target is of high intensity. Example: 1 mW power of He-Ne laser appears to be brighter than the sunlight.  Coherence Length Coherence length is a measure of how far electromagnetic waves, can maintain a consistent phase relationship. In optics, it describes the distance over which the wave front of a light wave remains relatively stable. Interaction of Electromagnetic Radiation with Matter  Interaction of Electromagnetic Radiation with Matter Einstein explained the interaction of e-m radiation with matter with the help of three processes. 1.Stimulated Absorption 2.Spontaneous Emission 3.Stimulated Emission Interaction of e-m Radiation with Matter : Einstein’s Theory ΔE Condition ℎν = 𝐸2 − 𝐸1 = ∆𝐸 Einstein’s theory of matter-radiation interaction E2 E1 hν = E2 - E1 ………. (i) Interaction of matter with radiation: Stimulated Absorption  Consider an atom is initially in lower energy state (E1).  A photon of energy hν (= E2 - E1) when incident on the atom in (E1), it is absorbed by the atom.  On absorbing the energy, the atom transits to its higher energy state (E2).  This phenomenon in which the atom transits to the higher energy state with the help of external agent (radiation energy) is called STIMULATED Absorption. Interaction of matter with radiation: Stimulated Absorption ρ(ν) Interaction of matter with radiation: Spontaneous Emission  Lifetime of upper energy state is very short.  Consider an atom is initially in excited state (E2).  It can come down to the ground state E1 by emitting a photon of energy hν (= E2 - E1) on its own after 10-8 s (without any external agent).  This process is called SPONTANEOUS Emission. Interaction of matter with radiation: Spontaneous Emission The probability of occurrence of this spontaneous emission transition from state 2 to state 1 depends only on the properties of states 2 and 1 and is given by P’21 = A21 …………(iii) Where A21 is known as the Einstein’s coefficient of spontaneous emission of radiation. Interaction of matter with radiation: Stimulated Emission ρ ρ(ν) ρ(ν) ………. (iv) Interaction of matter with radiation: Stimulated Emission  Relation between Einstein’s Coefficients Let us consider an assembly of independent atoms which can exists only in 2 levels, 1 and 2 with energies E1 and E2. Let N1 and N2 be the number of atoms per unit volume in the states 1 and 2 respectively. These numbers are called Population of respective levels. At thermal equilibrium, the no of atoms present in a particular energy is determined by Maxwell’s- Boltzmann Statistics, i.e. N𝟐 = N1 exp {- (E2 - E1)/KT} Here, Where, B12= Einstein Coefficient Stimulated Absorption K= Boltzmann’s constant = 1.38 x 10-23 J/K B21=Einstein Coefficient of Stimulated Emission T= Absolute Temperature in Kelvin A21=Einstein Coefficient of Spontaneous Emission We have these following equations: The Rate of Stimulated Absorption (R1) transition is given by: R1(St. Absorption) = B12 ρ(n) N1 ----- (1) The Rate of Spontaneous Emission (R2) is given by: R2 (Sp. Emission) = A21 N2 -------- (2) The Rate of Stimulated Emission (R3) is given by: R3 (St. Emission) = B21 ρ(n) N2 ------ (3)  Relation between Einstein’s Co-efficients Under thermal equilibrium, The number of atoms absorbing photons per second/unit volume = The number of atoms emitting photons per second /unit volume Thereby, we can write, (R1) = (R2) + (R3) i.e. B12 ρ(n) N1 = A21 N2 + B21 ρ(n) N2 𝐀𝟐𝟏 𝐍𝟐 Or, 𝝆 𝝂 = 𝐁𝟏𝟐 𝐍𝟏 −𝐁𝟐𝟏 𝐍𝟐 Dividing the above equation by B21.N2, we get, B N B N 𝝆 𝝂 = (A21 / B21) / [ 12 1 - 21 2] B21 N2 B21 N2 𝐀𝟐𝟏 𝟏 Thereby, 𝝆 𝝂 = ……. (4) 𝐁𝟐𝟏 𝐁𝟏𝟐 𝐍𝟏 −𝟏 𝐁 𝟐𝟏𝐍 𝟐  Relation between Einstein’s Co-efficients Now, we know that −𝐄𝟏ൗ 𝐍𝟏 𝐞 𝐤𝐓 𝐄𝟐 −𝐄𝟏 ൗ 𝐡𝛎ൗ = −𝐄𝟐ൗ =𝐞 𝐤𝐓 = 𝐞 𝐤𝐓 𝐍𝟐 𝐞 𝐤𝐓 Where (h = Planck’s constant: k = Boltzmann’s constant) Putting the values in equation (4), the values of N1/N2, we have, 𝐀𝟐𝟏 𝟏 𝛒 𝛎 = 𝐁 𝒉𝝂 …. (5) 𝐁𝟐𝟏 𝟏𝟐 𝒆 𝒌𝑻 −𝟏 ൗ 𝐁𝟐𝟏 Now, for an ideal 2 level system, as we have considered, must result in a radiation similar to a black body radiation, hence ρ(ν) is given by Planck’s Radiation law, 𝟖𝛑𝐡𝛎𝟑 𝟏 i. e. 𝛒 𝛎 = 𝟑 𝐡𝛎 …….. (6) 𝐜 ൗ 𝐞 𝐤𝐓 −𝟏  Relation between Einstein’s Co-efficients Comparing, equations (5) & (6), we get, 𝐀𝟐𝟏 𝟖𝛑𝐡𝛎𝟑 = 𝟑 and B12 = B21 ----- (7) 𝐁𝟐𝟏 𝐜 Where c = speed of light These relations are known as Einstein’s Relations. We can observe that : R = Rate of spontaneous Emission / Rate of Stimulated Emission Or, R = A21 N2 / [ B21 N2 ρ(ν)] = exp (hν /KT) – 1 If R>>1, probability of stimulated emission is negligible compared to spontaneous emission. If R N2. But to achieve higher rate of stimulated emission we should have N2 >> N1.  Conditions for achieving Light amplification In practice, absorption and spontaneous emission always occurs together with stimulated emission. The laser operation is achieved when simulated emission exceeds in a large way than the other two processes. A light amplification only occurs when these 3 conditions are fulfilled, they are as follows: 1. Population at the excited level should be large than that of lower energy level (𝑁2 >>𝑁1 ). Artificial situation known as Population Inversion is to be created in the medium. 2. The ratio of B21/A21 should be very large and this can be achieved by choosing a metastable state at the higher level.. 3. The energy density of radiation ρ ν should be very large. Large number of photons in the active medium are required. It is made larger by enclosing the emitted radiation in the optical resonant cavity formed by 2 parallel mirrors. The radiation is reflected many times till the photon density reaches to a very high value and stimulated emissions are triggered on a large scale.  Multiplication of Photons in LASER When a photon strikes an excited atom, the single photon transforms into two identical photons. Those two photons can then strike other excited atoms, resulting in 4 photons and then 8 and so on. This is how amplification of light happens and we get a coherent monochromatic highly intense laser beam. Image Source: Engineering Physics by H K Malik and A K Singh  Population Inversion Definition : Population Inversion is an artificial non-equilibrium process/condition of the material that is established by generation of large numbers of atoms in the higher energy state than ground state (N2>>N1).This is achieved by pumping. [At ordinary conditions N1 > N2, i.e., the population in the ground or lower state is always greater than the population in the excited or higher states.]  Metastable States Metastable states are excited states which have relatively longer lifetime due to slow radiative or non-radiative decay. Population inversion can be established if the lifetime of the excited states (metastable) is 10-6 to 10-3 s which is considerably more than the lifetime of the ordinary excited state levels. Metastable state can be obtained in a crystal system containing impurities. These levels lie in the forbidden band gap of the host crystal.  Spontaneous Emission Vs. Stimulated Emission NO: Spontaneous emission Stimulated emission 1. The spontaneous emission was The stimulated emission was postulated by postulated by Bohr Einstein 2. Additional photons are not required in Additional photons are required in spontaneous emission stimulated emission 3. One photon is emitted in spontaneous Two photons are emitted in stimulated emission emission 4. The emitted radiation is polychromatic The emitted radiation is monochromatic 5. The emitted radiation is incoherent The emitted radiation is coherent 6. The emitted radiation is less intense. The emitted radiation is highly intense 7. The emitted radiation have less The emitted radiation have high directionality Example: light from directionality Example: light from laser sodium or mercury lamp source.  Components of Laser Laser requires three Components: 1) Active Medium/Gain Medium 2) Pumping scheme 3) Optical Cavity/Resonator  Components of Laser: Active Medium 1) Active Medium: The fundamental component of laser is material medium which is known as an Active/Gain Medium. This active medium can be solid, liquid or gaseous in nature. After the invention of ruby laser (solid state laser), other active media such as glasses, plastics, liquids, gases and even plasma were used. In Active Medium, only a small fraction of the atoms are responsible for the light amplification known as ACTIVE CENTRES. The rest part of the medium behaves as a Host and supports the active centres in the bulk. An active medium should possess good mechanical, thermal and optical properties as well as transparency to stimulated radiation and laser output.  Components of Laser : Pumping techniques 2) Pumping techniques: To produce population inversion, the method of raising the atoms from lower energy state to higher energy state is called pumping. The most commonly used pumping methods are: I. Optical pumping II. Electrical discharge pumping III. Chemical pumping  Components of Laser : Pumping techniques I. Optical pumping: Majorly used in solid state laser. Xenon flash tubes are used for optical pumping. Examples of optically pumped lasers are ruby, Nd: YAG Laser  Components of Laser : Pumping techniques II. Electrical discharge pumping Electrical discharge pumping is used in gas lasers. Electrical discharge pumped lasers are He-Ne laser, CO2 laser, argon-ion laser, etc  Components of Laser: Optical Cavity/Resonator Optical resonator is a pair of plane parallel mirrors set on optic axis which defines the direction of laser output. One is perfectly reflecting mirror and the other surface is partially reflecting mirror. In this resonant cavity, the intensity of photons is raised tremendously through stimulated emission process (amplification of stimulated photons). M1 M2  Working of Laser: Lasing Action  The atoms excited with the light of suitable wavelength jumps from ground states E1 to excited state E2 by absorbing incident photons. They can’t remain in excited state for more than 10-8 s and drops back by spontaneous emission.  During this, many of the atoms get dropped in the metastable state where the atoms can stay for a longer time than that of its excited state as the lifetime of an atom in metastable state is greater than its excited state. So, due to their longer stay, a large number of atoms exist in the metastable state than that in ground state indicating population inversion (N2 >> N1).  When population inversion is achieved using pumping, then one or more atoms may be excited spontaneously by emitting a photon hv. This photon acts as a stimulant and is made to strike the atoms present in the metastable state.  The atoms thus gets excited and it is stimulated to emit a photon of same energy as that of the stimulating photon.