Ee 230 optical fiber communication lecture 2
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EE 230: Optical Fiber Communication Lecture 2. Fibers from the view of Geometrical Optics. From the movie Warriors of the Net. Total Internal Reflection. Reflection as a function of angle. The reflectivities of waves polarized parallel and perpendicular to the plane of

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EE 230: Optical Fiber Communication Lecture 2

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Ee 230 optical fiber communication lecture 2

EE 230: Optical Fiber Communication Lecture 2

Fibers from the view of Geometrical

Optics

From the movie

Warriors of the Net


Total internal reflection

Total Internal Reflection


Reflection as a function of angle

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


Principal types of optical fiber

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


Fabrication of optical fiber

Fabrication of Optical Fiber

  • Fabrication of fiber preform: macroscopic version with correct index profile

  • Drawing of preform down into thin fiber

  • Jacketing and cabling


Step index fiber

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


Basic step index fiber structure

Basic Step index Fiber Structure

Fiber Optics Communication Technology-Mynbaev & Scheiner


Ray trajectories in step index fiber

Ray Trajectories in Step Index fiber

Meridional Rays

Skew Rays


Coupling light into an optical fiber

Coupling Light into an Optical Fiber

Fiber Optics Communication Technology-Mynbaev & Scheiner


Acceptance angle

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


Ee 230 optical fiber communication lecture 2

n0

θ2

θ1

φ2

φ1

nCO

nCL


Numerical aperture

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


For corning smf 28 optical fiber

For Corning SMF-28 optical fiber

nco=1.4504, nCL=1.4447 at 1550 nm

NA = 0.13

Acceptance angle = 7.35 degrees


Geometrical view of modes

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


Rays and their e field distribution

Rays and Their E-field Distribution


Origin of modal dispersion

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


Intermodal dispersion

Intermodal Dispersion

Fiber Optics Communication Technology-Mynbaev & Scheiner


Bandwidth for various fiber types

Bandwidth for Various Fiber Types

No intermodal time shift for single

Mode Fiber

Fiber Optics Communication Technology-Mynbaev & Scheiner


Graded index fiber

Graded Index Fiber

Fiber Optic Communication Systems-Agarwal

Fiber Optic Communications-Palais


Ray propagation in graded index fiber

Ray Propagation in Graded-Index Fiber

Graded Index Slab Uniform in X and Z

Fundamentals of Photonics - Saleh and Teich


Ray spreading comparison

Ray spreading comparison


Comparison continued

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


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