Light Waves and Polarization

1. Light Waves and Polarization Xavier Fernando Ryerson Communications Lab http://www.ee.ryerson.ca/~fernando

2. The Nature of Light • There are three theories explain the nature of light: • Quantum Theory – Light consists of small particles (photons). This theory better explains light detection and generation processes. • Wave Theory – Light travels as a transverse electromagnetic wave. • Ray Theory – Light travels along a straight line and obeys laws of geometrical optics – usefultool when the objects are much larger than the wavelength of light

3. Quantum Theory of Light • Light consists of discrete units called photons. The energy in a photon h= 6.6256 X10(-34)J.sis the Planck’sconstant and νis the frequency. • Ex1: Find the energy of a photon travelling with 200 THz frequency • Ex2: Show

4. Wave Theory of Light • Electromagnetic light signal has electric and magnetic fields orthogonal to each other. • The frequency of this EM wave is in the order of THz. Therefore, it is convenient to measure it in terms of wavelength. • where, c - speed of light 3 X 108 m/s in air,ν - frequencyandλ- wavelength • Ex: Find the νwhenλ = 1550 nm. • Answer: 193.5 THz

5. Wavelength Ranges

6. Plane Waves • Most Light waves are plane waves • A plane wave is a constant-frequency wave whose wave fronts (surfaces of constant phase) are infinite parallel planes. • The electric field vector of a plane wave may be arbitrarily divided into two perpendicular components labeled x and y (with z indicating the direction of travel).

7. Field distributions in plane E&M waves Electric and magnetic fields are orthogonal to each other and to the direction of propagation Z

8. Basics about Plane Waves / propagation constant The combined wave s

9. vp Phase Velocity co: Speed of light in air n: Refractive index Phase velocity:

10. Phase Velocity • Light travels faster in air than water: apparent and true depth • Light in the fiber core travels slower than light in the fiber cladding ‘waveguide dispersion’

11. Changing Refractive Index • The refractive index n is not constant • It is a function of the wavelength of light, n = n(λ). • Therefore, different wavelengths will travel at different velocity in glass fiber • The wavelength dependency of n is given by an empirical formula, the Cauchy or Sellmeier equations

12. Group of Waves Most practical light sources emit group of waves, not just one 2Δω

13. Carrier and Envelope vp vg

14. Group Velocity m/s • Group of waves travel at group velocity, slightly different from phase velocity • The group refractive index ng is a function of n,ω and dn/d ω • If ω proportional to k, then the ng = n and vg = vp. • Usually it is not the case; This results in “Group Velocity Dispersion“. • The GVD is important single mode optical fibers.

15. Sellmeier Equation • Refractive Index n is a nonlinear function of wavelength • The slope of this graph is related to ng

16. Polarization • Polarization of a plane wave is the orientation of the oscillations of the E field; perpendicular to the direction of propagation • For a simple harmonic wave, the electric vector in orthogonal directions may have: • Different amplitude • Different phase • The resulting wave is • Linearly, elliptically or circularly polarized

17. Polarization states • If the resulting electric field is oscillating along a straight line, it is called a linearly polarized (LP) or plane polarized wave • If the Efield rotates in a circle (constant magnitude) it is called circularly polarized • If the E field rotates in an ellipse then, it is called elliptically polarized wave • Natural light has random polarization – The orientation of E filed keep changing randomly

18. Adding two linearly polarized waves with a phase shift will produce an elliptically polarized light

19. Elliptical Polarization

20. Adding two linearly polarized waves with zero phase shift will generate another linearly polarized wave

21. Linear Polarization

22. Adding two linearly polarized waves with equal amplitude and 90o phase shift results in circular polarized wave

23. Circular Polarization

24. X and Y Polarizations A Linear Polarized wave will always have two orthogonal components. These can be called x and y polarization components Each component can be individually handled if polarization sensitive components are used

25. Birefringence • Birefringence is the decomposition of a ray of light into two rays types of (anisotropic) material • In optical fibers, birefringence can be understood by assigning two different refractive indices nx and nyto the material for different polarizations. • In optical fiber, birefringence happens due to the asymmetry in the fiber core and due to external stresses • There are Hi-Bi, Low-Bi and polarization maintaining fibers.

26. Polarization Dependent Modulation

27. Polarization Mode Dispersion • Since optical fiber has a single axis of anisotropy, differently polarized light travels at slightly different velocity • This results in Polarization Mode Dispersion • PMD is usually small, compared to GVD or Modal dispersion • May become significant if all other dispersion mechanisms are small

28. Polarization Mode Dispersion (PMD) Each polarization state has a different velocity  PMD

29. Faraday Effect • When a magnetic field is applied to linearly polarized light, the plane of polarization rotates. • The rotation is proportional to the intensity of the applied magnetic field in the direction of the beam of light This effect is used in Optical Isolators

30. Optical Isolator output polarizer (allows light at 45o) • Vertically polarized light enters the isolator. • The Faraday rotator rotates it by 45o. • Output polarizer passes the light. • Backward traveling (reflected) light starts with 45o tilt. • It gets horizontal polarization at the rotator and will be extinguished. Faraday rotator Input Polarizer (allows only vertically polarized light) Polarization Controller (creates vertical polarization)