EE 230: Optical Fiber Communication Lecture 2

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

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

11. n0 θ2 θ1 φ2 φ1 nCO nCL

12. Numerical Aperture From Snell’s Law, For total internal reflection, θ2=90º What value of φ1 corresponds to θc? That is the maximum acceptance angle for the fiber. φ2 = 90º-θc sinφ2 = cos θc , so Again from Snell’s Law, (= NA), so

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

14. Geometrical View of Modes • Ray approximation valid in the limit that l 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

15. Rays and Their E-field Distribution

16. 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/L(NA)2

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

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

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 nCO=1.45, ∆tSI/L=19 ps/m ∆tGI/L=0.039 ps/m Graded-index fiber has substantially less modal dispersion