1. Optical Fiber Communication
Fibers from the view of Geometrical
Optics

2. Total Internal Reflection

3. Reflection as a function of angle
The reflectivities of waves polarized
parallel and perpendicular to the plane of
incidence as given by the Fresnel equations
This additional Phase Shift is not accounted for in geometrical wave approach
Fiber Optics Communication Technology-Mynbaev & Scheiner

4. Principal Types of Optical Fiber
Types of Fibers
Single mode/Multi-mode
Step Index/Graded Index
Dispersion Shifted/Non-dispersion shifted
Silica/fluoride/Other materials
Major Performance Concerns for Fibers
Wavelength range
Maximum Propagation Distance
Maximum bitrate
Crosstalk
Understanding Fiber Optics-Hecht

5. Fabrication of Optical Fiber
Fabrication of fiber preform: macroscopic version with correct index profile
Drawing of preform down into thin fiber
Jacketing and cabling

6. Step-Index Fiber Cladding typically pure silica
Core doped with germanium to increase index
Index difference referred to as “delta” in units of percent (typically %)
Tradeoff between coupling and bending losses
Index discontinuity at core-clad boundary

7. Basic Step index Fiber Structure
Fiber Optics Communication Technology-Mynbaev & Scheiner

8. Ray Trajectories in Step Index fiber
Meridional Rays
Skew Rays

9. Coupling Light into an Optical Fiber
Fiber Optics Communication Technology-Mynbaev & Scheiner

10. Acceptance Angle
The acceptance angle (i) is the largest incident angle ray that can be coupled into a guided ray within the fiber
The Numerical Aperature (NA) is the sin(i) this is defined analagously to that for a lens
Optics-Hecht & Zajac

11. θ2 θ1 φ2 φ1
nCO
nCL

12. For Corning SMF-28 optical fiber
nco=1.4504, nCL= at 1550 nm
NA = 0.13
Acceptance angle = 7.35 degrees

13. Geometrical View of Modes
Ray approximation valid in the limit that  goes to zero
Geometrical Optics does not predict the existance of discrete modes
Maxwells Equations and dielectric boundary conditions give rise to the requirement that the fields and phase reproduce themselves each “cycle”
Fiber Optics Communication Technology-Mynbaev & Scheiner

14. Rays and Their E-field Distribution

15. Origin of Modal Dispersion
Straight path along fiber axis has distance L and velocity c/nCO for transit time of LnCO/c
Path at maximum acceptance angle φc has distance L/cosφ2 where φ2=90º-θc and thus a longer transit time.
Transit time difference equal to
Dispersion limits rate of signals that fiber can handle
If spread can be up to 70% of bit period, then maximum bit rate is 1.4cnCO/(NA)2

16. Intermodal Dispersion
Fiber Optics Communication Technology-Mynbaev & Scheiner

17. Bandwidth for Various Fiber Types
No intermodal time shift for single
Mode Fiber
Fiber Optics Communication Technology-Mynbaev & Scheiner

18. Graded Index Fiber Fiber Optic Communication Systems-Agarwal
Fiber Optic Communications-Palais

19. Ray Propagation in Graded-Index Fiber
Graded Index Slab Uniform in X and Z
Fundamentals of Photonics - Saleh and Teich

20. Ray spreading comparison

21. Comparison, continued If NA=0.13 and nCO=1.45, ∆tSI/L=19 ps/m
∆tGI/L=0.039 ps/m
Graded-index fiber has substantially less modal dispersion