1. EE 230: Optical Fiber Communication Lecture 2 From the movie Warriors of the Net Fibers from the view of Geometrical Optics

2. Total Internal Reflection

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

4. Principal Types of Optical Fiber Understanding Fiber Optics-Hecht 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

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 0.3-1.0%) 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 Optics-Hecht & Zajac 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

11. φ1φ1 φ2φ2 θ1θ1 θ2θ2 n CO n CL n0n0

12. From Snell’s Law, For total internal reflection, θ 2 =90º What value of φ 1 corresponds to θ c ? That is the maximum acceptance angle for the fiber. φ 2 = 90º-θ c sinφ 2 = cos θ c, so Again from Snell’s Law, (= NA), so Numerical Aperture

13. For Corning SMF-28 optical fiber n co =1.4504, n CL =1.4447 at 1550 nm NA = 0.13 Acceptance angle = 7.35 degrees

14. Geometrical View of Modes Fiber Optics Communication Technology-Mynbaev & Scheiner 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”

15. Rays and Their E-field Distribution

16. Origin of Modal Dispersion Straight path along fiber axis has distance L and velocity c/n CO for transit time of Ln CO /c Path at maximum acceptance angle φ c has distance L/cosφ 2 where φ 2 =90º-θ c 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 1.4cn CO /L(NA) 2

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

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

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

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

21. Ray spreading comparison

22. Comparison, continued If NA=0.13 and n CO =1.45, ∆t SI /L=19 ps/m ∆t GI /L=0.039 ps/m Graded-index fiber has substantially less modal dispersion