University:
Santa Fe College
Course:
ETS 2527C | Electromechanical Components and Mechanisms
Academic year:

2024
Views:

56

Pages:

5
Author:

Jabin F.

Polarization in E.M. Waves Polarization in longitudinal waves: E // k Equations: E₁ = ε₀e^(i(kz-ωt)) E₂ = αε₀e^(i(kz-ωt)) E = 2ε₀e^(i(kz-ωt)) Direction of polarization is the direction of the E-field. Types of polarizations: (i) Plane polarized (linearly polarized) EM waves (ii) Circularly polarized (iii) Elliptically polarized P.P (plane polarized) or L.P (linearly polarized) along n-direction: B = (k × E) / ω Magnetic field is perpendicular to both E and k Superposition of two plane polarized waves: If their directions are parallel: Plane polarized (P.P) Δφ = 0°, 180° E = 2ε₀e^(i(kz-ωt)) Outcome is P.P If their directions are perpendicular to each other: Δφ ≠ 0°, 90°, 180° E₀₁ ≠ E₀₂ Outcome is elliptically polarized (E.P) Circularly Polarized: E₁ = E₀ŷe^(i(kz-ωt)) E₂ = (i)E₀ẑe^(i(kz-ωt)) Phase difference of π/2 If waves are parallel polarized: Intensity I = I₁ + I₂ + 2√(I₁I₂)cos(Δφ) Δφ = phase difference In optics: I₁ = (1/2)ε₀c(E₀₁)² I₂ = (1/2)ε₀c(E₀₂)² If waves are perpendicularly polarized: No role of Δφ in intensity Intensity I = I₁ + I₂ Ques. 8: E = E₀sin(ωt - kz)ŷ + 2E₀sin(ωt - kz + π/3)ẑ Perpendicular Δφ = π/2 → Circularly polarized. E₀₁ ≠ E₀₂ → Elliptically polarized. (option-d) Intensity of the wave: I₁ = (c / 2)ε₀E₀² I₂ = (1/2)ε₀c(2E₀)² = 2ε₀E₀² I = I₁ + I₂ = (5/2)ε₀E₀² In optics: I₁ = E₀² I₂ = 4E₀² I = 5E₀² Can superposition of these two waves produce interference pattern? No. Condition: Coherent waves. Same state of polarization.