NAME: _____Chandler Swaim___ COURSE ____MEGR 3171L____________ SECTION ___L11___
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To:
Martin Hodgins, Jon Pope
From:
Chandler Swaim MEGR 3171L Section 11
Subject:
Optical Theory
Date:
December 8, 2020
Theory
Fiber Optics General Background
Fiber optics make use of light refraction to transmit signals quickly over large distances. Light
rays are used as theoretical models of how light interacts with the environment. These rays
always travel slower when travelling through mediums or materials that are not in a vacuum.
Index of refraction explains this phenomenon by comparing the speed of light in a vacuum to the
speed of light in the specific material to give a ratio. The equation for index of refraction is given
by Equation (1):
𝑛=
𝑐
𝑣𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙
(1)
where c equals the speed of light inside a vacuum and vmaterial equals the speed of light inside the
given material. Snell’s Law uses the index of refraction to compare refraction angles of
transmitted and reflected light rays between mediums. When light is sent through a certain
material and then encounters a different, second material, some of the light rays are transmitted
to the second material and some light rays are reflected to the original material. For the purpose
of fiber optic communication, total internal reflection is desired. For total internal reflection to be
achieved, the angles at which light rays enter the fiber must be calculated using Snell’s Law.
Equation (2) shows this relationship between index of refraction and entrance angle of the light
rays:
𝑛2 sin(∅2 ) = 𝑛1 sin(∅1 ) (2)
where ∅2 and ∅1 are the angles the light beam makes with the neutral axis of the fiber for each
respective material. Figure 1 below serves as a visual aid for Snell’s Law.
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Figure 1: Snell’s Law (OnlineMathLearning 2005)
As shown in Figure 1, the material index of refraction value as well as refraction angle effect the
resulting light wave path. To have total internal reflection of the light within the first material, a
critical angle must be found. Critical angles are the angles at which light does not transmit into
the second material. It should be noted that light does not begin reflecting unless the index of
refraction of the first material is greater than the index of refraction of the second material
(n1>n2). Total internal reflection allows the light beams to travel great distances with little to no
effect on beam intensity (Editors 2020).
Attenuation
Attenuation refers to the loss of the light beam intensity throughout the fiber path. The three
main causes are scattering, intrinsic absorption, and extrinsic absorption (UNC 2020). Rayleigh
scattering accounts for roughly 96 percent of attenuation in fiber optics. It occurs when light
interacts with the silica molecules of the fiber, slightly diminishing the intensity of the light
beam. The intensity of the scattering is the inverse of the wavelength to the fourth power of the
incoming light wave (UNC 2020). Intrinsic absorption occurs when a particle of light interact
with electrons present and excite the electrons to another energy level. This can be attributed to
the physical properties of the silica, causing energy transfer. Extrinsic absorption is caused by
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imperfections in the silica caused by manufacturing (UNC 2020). “Water in silica glass forms a
silicon-hydroxyl (Si-OH) bond. This bond has a fundamental absorption at 2.7 um and harmonic
absorption at 1.383 um, 1.250 um and 0.950 um” (UNC 2020). Transmission windows are used
to describe frequencies of light waves that are accompanied by the least amount of attenuation.
For Short Haul Fibers the wavelengths of transmission windows include 650 nm and 850 nm and
Long Haul Fibers have wavelengths of 1.31 um and 1.55 um (UNC 2020). Figure 2 below
illustrates scattering and absorption in silica fibers.
Loss dB/km
10.0
1.0
Rayleigh
Scattering
OH 1.383 mm
Impurity
Absorption
0.1
0.6
0.8
1.0
1.2
1.4
Wavelength mm
1.6
1.8
Figure 2: Scattering and Absorption in Silica Fibers
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Dispersion
Dispersion occurs when the light pulses of a signal become spread out over the course of
travelling throughout a fiber. “This phenomenon is due to the fact that speed of light depends on
its wavelength and propagation mode. In case of travelling long distances, slight differences in
speed accumulate” (Mai 2014). Dispersion does not decrease the intensity of the light beam, but
makes it difficult for the receiver to read the signals as the signals will be distorted. In
multimodal fiber, each mode has its own velocity for travelling along the fiber. When larger
distances are being communicated across, the signals of each mode become increasingly spread
out, causing dispersion (Mai 2014).
Couplers/Multiplexors
Couplers and multiplexors both have similar applications of changing the flow of the signal
inputs and outputs. Couplers are primarily used to combine input signals and combine them to an
output signal. Multiplexors takes a single input signal and sends this signal to multiple outputs.
EDFA
Erbium Doped Fiber Amplifier (EDFA) is an op-amp designed to amplify signals at 1550 nm
and allow high bit-rate transmission of signals over long distances. This is achieved by doping
the core of the op-amp with Erbium, a rare element found on Earth. The ions of Erbium are
easily excited, thus making it easy to achieve energy transfer at appropriate wavelengths (IVY
2017). EDFAs allowed for cheaper bandwidth solutions as the previous technology required
multiple signal repeaters at intermediate points along the fiber path. With EDFA, signals can be
transmitted further, faster, and without interruption.
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References
Editors of Encyclopaedia Britannica. 2020. “Fiber optics”. Accessed December 8, 2020.
https://www.britannica.com/science/fiber-optics
IVY HTFuture. 2019. “The Role of EDFA in Optical Fiber Communication”. Accessed
December 8, 2020. https://medium.com/@ivyhtfuture/the-role-of-edfa-in-optical-fibercommunication-3ad5995c0880
Mai Vinh Nguen. 2014. “Dispersion in Fiber Optics”. Last Modified December 16, 2020.
https://wiki.metropolia.fi/display/Physics/%28M%29+Dispersion+in+Fiber+Optics#:~:te
xt=Dispersion%20is%20defined%20as%20the,its%20wavelength%20and%20propagatio
n%20mode.&text=Like%20attenuation%2C%20dispersion%20shortens%20the,signal%2
0travels%20inside%20optic%20fibers.
OnlineMathLearning. 2005. “Refraction and Snell's Law”. Accessed December 8, 2020.
https://www.onlinemathlearning.com/snells-law.html
UNC CHARLOTTE WILLIAM STATES LEE COLLEGE OF ENGINEERING
DEPARTMENT OF MECHANICAL ENGINEERING AND ENGINEERING
SCIENCE. 2020. “Fall 2020 Fiber Optic (Trans & Sens)(On-Line)”.
https://uncc.instructure.com/courses/131610/files/9996899?module_item_id=2840021
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