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Optical Fiber CommunicationsPowerPoint Presentation

Optical Fiber Communications

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### Optical Fiber Communications

Lecture 10

Topics

- Single Mode Fiber
- Mode Field Diameter
- Propagation Modes in Single Mode Fiber

- Graded Index Fiber

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

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

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)

MFD

- The MFD width 2Wo can be defined for LP01 mode as

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

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

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

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

Example

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

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

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

contd

- Number of bound modes

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

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

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

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

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