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EE 230: Optical Fiber Communication Lecture 2

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Fibers from the view of Geometrical

Optics

From the movie

Warriors of the Net

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

- 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

- Fabrication of fiber preform: macroscopic version with correct index profile
- Drawing of preform down into thin fiber
- Jacketing and cabling

- 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

Fiber Optics Communication Technology-Mynbaev & Scheiner

Meridional Rays

Skew Rays

Fiber Optics Communication Technology-Mynbaev & Scheiner

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

n0

θ2

θ1

φ2

φ1

nCO

nCL

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

nco=1.4504, nCL=1.4447 at 1550 nm

NA = 0.13

Acceptance angle = 7.35 degrees

- 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

- 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

Fiber Optics Communication Technology-Mynbaev & Scheiner

No intermodal time shift for single

Mode Fiber

Fiber Optics Communication Technology-Mynbaev & Scheiner

Fiber Optic Communication Systems-Agarwal

Fiber Optic Communications-Palais

Graded Index Slab Uniform in X and Z

Fundamentals of Photonics - Saleh and Teich

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