1. Optical Fiber Communications
Lecture 10

2. Topics Single Mode Fiber Graded Index 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= 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