lecture one of laser and photonics course on optics
- 1. PHN-315 L1 CWS + Attendance = 25+5 = 30 Marks MTE = 20 Marks ETE = 50 Marks
- 2. • For today’s ( 19 July 2024) lecture content, you can go through the slides here. • You may refer to book “Photonics – Optical electronics in Modern Communications” , 6th Ed. By Yariv and Yeh, page numbers 211 to 213. • Some of the content may be further elaborated in the next class.
- 3. 3 Radiative Process & Atomic Transitions • If an atomic system is in ground state(E1) and is subjected to the radiation of an incident photon then the incident photon will get absorbed by the atomic system, provided ℏ⍵ = 𝐸2 − 𝐸1 …(1) where E2 = upper state or elevated state of atomic system ℏ = h 2π and ⍵ = 2πf • Let 𝑘1 & 𝑘2 are wave vectors corresponding to upper and lower state of atomic system then : ∆𝑘 = 𝑘1 − 𝑘2 = 𝑘𝑝 Where 𝑘𝑝 is wave vector of photon. • The atomic system undergoes transition when electron absorbs photon, thus 𝑘1 & 𝑘2 are wave vector corresponding to electrons in lower energy state (E1) and upper energy state (E2) respectively.
- 4. 4 Radiative Process & Atomic Transitions ∆𝑘 = 𝑘1 − 𝑘2 = 𝑘𝑝 𝑘1 = 𝑘2 + 𝑘𝑝 Generally, 𝑘2 ≫ 𝑘𝑝 𝒌𝟏 = 𝒌𝟐 • Such transitions are called direct or vertical transitions.
- 5. 5 Radiative Process & Atomic Transitions • If an electron is already in state 2 at t=0, there is a finite probability per unit time that it will undergo a transition to state 1 and will emit a photon of energy : 𝐸 = 𝐸2 − 𝐸1 = ℏ⍵ • Above process is happening without any incident radiation and it is known as spontaneous emission.
- 6. 6 Radiative Process & Atomic Transitions • If an atomic system is already in state 2 at t=0 and at the same time a photon is incident on it then atomic system may go to state 1, emitting a photon of energy equal to energy of incident photon (in addition to spontaneous emission). • Such a process is called stimulated emission.
- 7. 7 Summary of three basic optical processes
- 8. 8 Atomic Polarizability & Dielectric Constant • Consider transmission of a light beam through a transparent isotropic medium. • The elementary charged particles inside each atom of the medium are displaced from their equilibrium positions under the influence of electric field of light beam. • In most dielectrics, the charge separation is directly proportional to the strength of electric field of optical beam. • The induced dipole moment 𝒑 can be written as : Ԧ 𝑝 = 𝛼𝐸 Where 𝛼 = atomic polarizability or molecular polarizability. • The direction of charge separation is in the direction of electric field. • For atomic system with spherical symmetry, the polarizability reduces to a scalar and can be derived using a simple classical electron model.
- 9. 9 Atomic Polarizability & Dielectric Constant • The dielectric constant of any medium is decided by the manner in which the atoms are assembled in that medium. • Assuming the case of a gas medium and taking ‘N’ as the number of atoms per unit volume, then polarization: 𝑃 = 𝑁 Ԧ 𝑝 𝑃 = 𝑁𝛼𝐸 Also 𝑃 = ɛ0χ𝐸 = 𝑁𝛼𝐸 …(1) where χ = electric susceptibility of medium ɛ0 = permittivity of vacuum Electric displacement vector 𝐷 is often written as 𝐷 = ɛ0𝐸 + 𝑃 …(2)
- 10. 10 Atomic Polarizability & Dielectric Constant • From (1) & (2) 𝐷 = ɛ0𝐸 + ɛ0χ𝐸 𝐷 = ɛ0(1 + χ)𝐸 ɛ𝐸 = ɛ0(1 + χ)𝐸 ɛ = ɛ0(1 + χ) • From equ.(1), 𝑃 = ɛ0χ𝐸 = 𝑁𝛼𝐸 χ = 𝑁𝛼 ɛ0 Therefore; ɛ = ɛ0 1 + χ = ɛ0 1 + 𝑁𝛼 ɛ0 …(3)