Libro De Comunicaciones Opticas

   

• • • • •

Hardcover: 400 pages Publisher: McGraw-Hill Professional; 1 edition (June 18, 2009) Language: English ISBN-10: 0071499199 ISBN-13: 978-0071499194 

Source: Planning Fiber Optic Networks

CHAPTER

1

Signal Propagation
1.1 Introduction
It is important to understand the basics of optical fiber signal propagation to be able to better apply fiber design principles. Thischapter introduces the theory behind signal propagation in a single-mode fiber. Multimode fiber is not discussed in this book.

1.2

Carrier Wave Propagation
A single-mode fiber signal can be separated into two basic waveforms: the optical carrier and the information signal. The optical carrier is generated by a laser or LED in the transceiver and ideally has constant power (intensity),wavelength, and phase. The information signal is a waveform that contains serially encoded information that is transmitted in the fiber. Let’s first consider the case of an optical carrier propagating in free space. It can be considered as a plane transverse electromagnetic (TEM) wave with the electric and magnetic field components represented by Eqs. (1.1) and (1.2),1 see Fig. 1.1. The electric fieldexists in the x-z plane and the magnetic field exists in the y-z plane both propagating along the fiber’s z axis. Both electric and magnetic fields are perpendicular to the direction of propagation of the z axis and hence transverse. The components of these fields can be written as Eqs. (1.3), (1.4), and (1.5). Assume for now that the optical wave is monochromatic, consisting of just onewavelength. In reality this is not possible but is used here to help simplify the theory. E = e xEx (t , z) H = e y H y (t , z)

(1.1) (1.2)

1
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Signal Propagation

2Chapter One
Ex = Ex 0 cos k(vt + z) H y = H y 0 cos k(vt + z) k= where 2π λ

(1.3) (1.4) (1.5)

E = electric field vector polarized in x-z plane, V/m H = magnetic field vector polarized in y-z plane, A/m Ex = electric field amplitude, V/m Ex0 = peak electric field amplitude, V/m Hy = magnetic field amplitude, A/m Hy0 = peak magnetic field amplitude, A/m k = wave number, 1/m v = phase velocity ofthe propagating wave, m/s λ = wavelength, m t = time, s z = z axis, m

To determine how this carrier wave propagates in a dielectric waveguide such as a fiber, we must consult Maxwell’s equations. In 1873, James Clerk Maxwell developed a theory that explained how electromagnetic waves behave in any medium. Maxwell’s theory is

X

↑

E

0

↑
H Y

Z
FIGURE 1.1 Optical TEM wave.Downloaded from Digital Engineering Library @ McGraw-Hill (www.accessengineeringlibrary.com) Copyright © 2009 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.

Signal Propagation

Signal Propagation
based on the four equations shown in Eqs. (1.6) to (1.9) in differential form (point form). ∇ i D = ρv ∇iB = 0 ∇×E = − ∂B ∂t ∂D ∂t

3(1.6) (1.7) (1.8)

∇×H = J+

(1.9)

where D = electric-flux density vector, C/m2. In any medium D = ε 0E + P where P is the electric polarization vector. B = magnetic-flux density vector H/m. In any medium B = μ 0 (H + M). M is the magnetic polarization of the medium. Silica is nonmagnetic, therefore M = 0. E = electric-field amplitude vector, V/m H = magnetic-field amplitude vector, A/mJ = current density vector, A/m2. For fiber J = σ E, where σ is the conductivity of the medium. For silica it is very low, therefore σ ≈ 0 and assume J = 0, therefore no current flow in a fiber. ρv = charge density and we can assume there are no free charges in the medium so that ρv = 0. ∇ i = divergence of the vector field ∇ × = curl of the vector field Simplification of the above results in...