Optical Fiber Communications

1. Optical Fiber Communications Lecture 10

2. Topics • Single Mode Fiber • Mode Field Diameter • Propagation Modes in Single Mode Fiber • Graded Index Fiber

3. Single Mode Fiber • Single Mode fiber are constructed by • letting dimensions of core diameter be a few wavelengths and • by having small index difference between core and cladding • In practice core cladding index difference varies between 0.1 and 1.0 percent • Typical single mode fiber may have a core radius of 3 micron and NA =0.1 at wavelength = 0.8 micron

4. Mode Field Diameter • Geometric distribution of light in propagation mode is important when predicting performance characteristics. • Mode Field Diameter (MFD) is analogues to core diameter in multimode fibers except not all light that propagates is carried in the core • Many models for characterizing MFD with main consideration of how to approximate electric field distribution

6. MFD • Assume electric field distribution to be Gaussian • Where r is radius, Eo is field at zero radius, and Wo is the width of the electric field distribution • Take width 2Wo of MFD to be 2e-1radius of optical electric field (e-2 of optical power)

7. MFD • The MFD width 2Wo can be defined for LP01 mode as

8. Propagation Modes in Single Mode Fiber • In single mode fiber there are two independent degenerate propagation modes • These modes are similar but their polarization planes are orthogonal • Electric field of light propagating along the fiber is linear superposition of these two polarization mode

9. Fig. 2-24: Polarizations of fundamental mode

10. contd • Choose one of the modes to have its transverse electric field along x direction and the other in y direction • In ideal fiber, two modes are degenerate with equal propagation constants and will maintain polarization state injected into the fiber • In actual fiber there are imperfections, such as asymmetrical lateral stress, noncircular cores and variations in refractive index profiles • These imperfections break circular symmetry

11. contd • The modes propagate with different phase velocities and the difference between their effective refractive indices is called birefringence • Or • If light is injected into the fiber so that both modes are excited, then one will be delayed in phase

12. contd • When this phase difference is an integral m*pi, the two mode will beat at this point and input polarization state will be reproduced. • The length over which this beating occurs is the fiber beat length

13. Example • A single mode optical fiber has a beat length of 8 cm at 1300nm, the modal birefringence • Or

14. Graded Index Fiber Structure • In graded index fiber, core refractive index decreases continuously with increasing radial distance r from center of fiber and constant in cladding • Alpha defines the shape of the index profile • As Alpha goes to infinity, above reduces to step index • The index difference is

15. contd • NA is more complex that step index fiber since it is function of position across the core • Geometrical optics considerations show that light incident on fiber core at position r will propagate only if it within NA(r) • Local numerical aperture is defined as • And

16. contd • Number of bound modes

17. Examples If a = 9.5 micron, find n2 in order to design a single mode fiber, if n1=1.465. Solution, The longer the wavelength, the larger refractive index difference is needed to maintain single mode condition, for a given fiber

18. Examples • Compute the number of modes for a fiber whose core diameter is 50 micron. Assume that n1=1.48 and n2=1.46. Wavelength = 0.8 micron. • Solution For large V, the total number of modes supported can be estimated as

19. Example • What is the maximum core radius allowed for a glass fiber having n1=1.465 and n2=1.46 if the fiber is to support only one mode at wavelength of 1250nm. • Solution

20. HW • Due 2/11/08 • 2-2 • 2-8 • 2-11 • 2-18 • 2-19 • 2-21 • 2-24 • 2-25 • 2-27 • 2-28