# Communication Systems/Fiber Optic Systems

Long-haul trunks were the first application of optical fiber to gain
universal acceptance. Three alternate methods are coax (copper),
terrestrial microwave and satellite. While microwave towers can be used
to bridge relatively small bodies of water, cables or satellites are
needed to span oceans.

Telegraph cables were first deployed in the mid-1800s and the first
successful trans-Atlantic cable was laid in 1858. For 100 years copper
submarine cables were the principal means of communication between North
America and Europe. In the 1960s satellites gained ascendancy but today
fiber cable dominates.

Fiber cable has some significant advantages over satellite technology:

:   • Fiber systems can be repaired, geo-stationary satellites cannot
:   • Fiber systems have a slightly longer life expectancy
:   • Fiber systems can be upgraded while in service
:   • Fiber deployment has a lower risk than launching a satellite
:   • Fiber propagation delay is significantly lower than satellites

## Fiber Deployment (ground based)

**Telecom Canada**

The current Trans-Canada fiber system stretches some 4100 miles and
includes under water links to PEI and Newfoundland. The cable is buried
at a minimum depth of 5 feet in most places. The cable is buried 2 feet
in rocky areas, but over major rivers such as the Thompson, it is 6 feet
below the riverbed.

Eight fibers are reserved for Trans-Canada traffic, with additional
fibers are used for toll traffic from the participating operating
companies.

The cable has a Kevlar strength member surrounded by a star shaped
polyethylene core, which can support up to 5 fiber tubes. Each fiber
tube can contain up to 6 fibers. The cable has multiple layers of
protection, but in avalanche prone areas, it was also encased in an 8
inch steel conduit.

## Submarine Fiber

## Optical Phenominon

### Wave-Particle Duality

In 1678 Huygens showed that reflection and refraction could be explained
by wave theory. While not rejecting the wave theory entirely, Einstein
in 1905 suggested that light could be thought of as a small energy
packet called a photon. This idea although not actually original, seemed
to explain the Compton effect later discovered in 1921.

Today light is generally thought of as an electromagnetic wave when it
is propagating. However, when it interacts with matter by means of
emission or absorption, it is preferable to think in terms of photons.
Photons have energy, but no rest mass. If a photon stops, it ceases to
exist as a particle, and is transformed into some other form of energy,
such as heat.

A rather hybrid way of thinking of light, is as a wave packet. Perhaps
someday, a better model will be developed.

:   

    :   ![](Wave_packet.gif "fig:Wave_packet.gif")

Light in the everyday world is incoherent. That is to say that the wave
packets arrive in a chaotic, random fashion. On the other hand, coherent
light as generated from a laser has the wave packets synchronized or in
phase.

The perceived color of light is a function of its wavelength. The
characteristic wavelength in the packet is related to its velocity and
frequency:

$$v=\lambda f$$

:   where:

$$v=$$ velocity

$$\lambda =$$ wavelength

$$f=$$ frequency

It has been experimentally determined that the velocity of light in a
vacuum, is about 299,793,000 meters per second. Fiber optic systems
operate at a frequency of approximately 3 x 10^8^ GHz, with the most
common transmission bands at wavelengths of 0.8 - 0.9 μm and 1.2 - 1.4
μm. The amount of energy in light can be determined by quantum theory
and is proportional to frequency and given by:

$$E=hf=\frac{hc}{\lambda }$$

:   where:

$$E=$$ Energy in Joules

$$h=6.625\times 10^{-34}\frac{J}{\sec }=$$ Planck\'s constant

$$f=$$ frequency

$$c=3\times 10^{8}\frac{m}{\sec }=$$ velocity of light

$$\lambda =$$ wavelength

The radiated spectral energy in watts per unit area is given by:

If we examine light at the macroscopic level, we observe that waves
radiate spherically from their source. This is readily observable with
incoherent sources and less pronounced with coherent sources. At a large
distance, the wavefront flattens out into a plane wave. A ray path shows
the direction that the wave or photon is traveling. In the case of a
point source, this might resemble:

:   

    :   ![](Ray_path.gif "fig:Ray_path.gif")

When light strikes an object, it can be reflected, refracted, or
absorbed. A ray of light striking the boundary between two dissimilar
transparent materials is usually split into reflected and refracted rays
with generally very little absorption.

Different wavelengths of light travel at the same velocity in a vacuum,
but this is not true in other mediums. This change in velocity leads to
refraction and color separation. If the speed is slowed in a medium, the
ray is redirected towards the normal. As light leaves a slower medium
and enters a faster one, it accelerates and is redirected away from the
normal.

:   

    :   ![](Reflection_refraction.gif "fig:Reflection_refraction.gif")

By convention, the angles involved in reflection and refraction are
measured with respect to the normal at the point of contact. All three
components are in the same plane \[there are some exceptions\]. In the
above illustration, the plane of incidence is the paper.

**Displacement and Polarization**

Energy displacement in waves can be either longitudinal or transverse
with respect to the direction of travel. Longitudinal waves such as
sound and seismic waves, are displaced in the direction of travel.
Transverse waves such as radio and water waves are displaced at right
angles to the direction of propagation.

Light travels as a TEM wave, having electric and magnetic fields
perpendicular to the direction of travel. If there is no particular
reason for the electrical fields of light to favor any particular
orientation, the field of the waves are directed (polarized) at any
angle perpendicular to the direction of propagation. This is the case
with sunlight.

The combined effect of many simultaneous waves is the vector sum of all
of their components. This is known as the superposition principle. This
principle holds true with all forms of waves, including light. This
raises an interesting question: Since the polarization and phase of
natural light is totally random, why don't the electric field components
of all the waves simply average out to zero and the light cancel itself
out? The reason is simple: they do average out, but, since this
averaging is not exact, but is a random one, the laws of statistics
hold. So, when we sum N random fields which oscillate, say, from minus
to plus one, we expect that the sum is of the order of the square root
of N, which can be enormously less than N, but is not zero. And, since
the energy (the intensity) of light is proportional to the square of the
electric field, we have that the mean energy of the sum is just N times
the individual energies, which is precisely what we expect.

A cancellation or enhancement effect do occur, but to observe it the
light must be coherent. Traditionally coherent light was created by
passing light from some distant source through a small hole. This
effectively selects light coming from only a very small part of the
originating source thus causing it to be more uniform. Today, it is
easier to use a laser, which is not only very coher ent, but also
essentially monochromatic. Interference patterns of light and dark areas
can be observed when coherent waves intersect.

Unpolarized light can be polarized by absorption, scattering and
reflection.

### Reflection

There are two types of reflection: diffuse and specular.

**Diffuse Reflection**

This is the most common form of reflection. If the illuminated object is
not microscopically homogeneous in its structure, the light is scattered
in all directions by multiple reflections or diffusions by its
inhomogeneities (both internal and on the surface). Most materials are
inhomogeneous: minerals are generally polycrystalline, organic matter is
generally made by cells or fibers, so the light sent to our eyes by most
objects is diffusely reflected. Because of this phenomenon, we can see
other objects.

:   

    :   ![](Diffuse_reflection.gif "fig:Diffuse_reflection.gif")

Sunlight contains all of the perceived colors in such a way that their
combined values look colorless. When it strikes an object, some
wavelengths are absorbed, while others are reflected. The perceived
color is the vector sum of all the reflected waves.

**Specular Reflection**

Light striking a smooth surface is reflected at the same angle with
which it strikes, but suffers some loss. Instead of seeing the
reflecting surface, one sees an image of where the light originates.

The reflected light can have the appearance of coming from either in
front of or behind the reflecting surface. If the image appears to be
behind the surface, as in the case of a mirror, it is referred to as a
virtual image.

:   

    :   ![](Virtual_image.gif "fig:Virtual_image.gif")

If the image is seen on a screen placed in front of the reflecting
surface, it is called a real image. This principle is used in reflecting
telescopes. Real images are most often generated by refraction and are
used in cameras and projectors.

:   

    :   ![](Real_image.gif "fig:Real_image.gif")

**Variable Reflective Coatings**

About 4% of light striking a smooth air-glass boundary is reflected.
This can be reduced by applying non-reflecting coatings. Photographers
and fiber optics designers are interested in non-glare coatings, since
reflection reduces the amount of light entering and exiting the glass.

By depositing a thin high refractive index film over a thin low
refractive index film, the amount of reflection can be increased to
about 50%. This principle is used to make a beam splitter, a device of
great value in optical measuring equipment and color TV cameras.

**External Reflection**

A phase reversal occurs when light is reflected by a more optically
dense medium. This also happens when radio waves strike a metallic
surface. The electric field component is short-circuited. Since the
incident and reflected fields cancel at the point of incidence, the
reflected waves are equal in amplitude but opposite in phase to the
incident wave.

The relationship between angle of incidence and amount of reflection is
very complex. At normal incidence, a reflecting surface reflects all
components equally well. However, at other angles, objects prefer to
reflect light having the electric field component perpendicular to the
plane of incidence. At the extreme case, Brewster's angle, only
perpendicular components are reflected, and complete polarization
occurs. Brewster's angle is defined by:

$$\tan \left( \theta _{P} \right)=\frac{\eta _{1}}{\eta _{2}}$$

At Brewster's angle, the reflected and refracted rays are at right
angles to each other.

:   

    :   ![](Brewsters_angle.gif "fig:Brewsters_angle.gif")

When noncoherent light strikes glass, about 15% of the perpendicular
components are reflected, and none of the others. The refracted ray
consists of the remaining 85% of the perpendicular component as well as
all other orientations. The polarized reflection can be enhanced by
stacking many thin glass plates together.

**Internal Reflection**

If light strikes an optically less dense medium, the reflected wave is
not phase reversed. When the angle of incidence is greater than the
critical angle, total internal reflection occurs.

However, a refracted beam of sorts does exist. It is sometimes
designated as frustrated total reflection or more commonly evanescent
wave. This wave does not dissipate power, and extends only a few
wavelengths into the faster medium. It decays exponentially according to
the relationship:

$$e^{\alpha x}$$

:   where

$$\alpha =k_{0}\sqrt{\eta _{1}^{2}\sin ^{2}\Theta _{i}-\eta _{2}^{2}}$$

$$k_{0}=$$ free space propagation factor

$$\Theta _{i}=$$ angle of incidence

$$x=$$ distance into the faster medium

### Refraction

Refracted rays create diverse effects ranging from the rainbow to the
apparent bending of sticks protruding into water. From experimentation,
it was observed that the ratio of the sines of the incident and
refracted rays is constant:

$$\frac{\sin \left( \theta _{0} \right)}{\sin \left( \theta _{1} \right)}=\text{ constant}$$

This constant is actually a function of the optical wavelength.
Therefor, white light is separated into its various color components
when refracted.

If the originating medium is a vacuum, this ratio is known as the
refractive index. In practice, the refractive index for air is 1.000293
for yellow light. Therefor, for terrestrial measurements, air is
regarded as a vacuum, with a refractive index of 1.

:   

    :   ![](White_light_refraction.gif "fig:White_light_refraction.gif")

**Snell\'s Law**

The relationship between the incident and refracted angles is given by
Snell's Law:

$$\eta _0\sin \left( \theta _{0} \right)=\eta _{1}\sin \left( \theta _{1} \right)$$

When a light ray passes through a glass block, it is refracted twice. If
the block has parallel faces, the ray will resume it original angle of
attack but is slightly displaced.

The refractive index of a material is the ratio of the speed of light in
a vacuum to the speed of light in the specific material.

:   

    :   ![](Refraction_in_glass.gif "fig:Refraction_in_glass.gif")

If the faces are not parallel, such as in a prism, the white light is
separated into its various spectral components.

:   

    :   ![](Prism_refraction.gif "fig:Prism_refraction.gif")

In some cases these simple rules of reflection and refraction are not
valid. Reflection for example, assumes a smooth boundary, and Snell's
law of refraction assumes an isotopic material. The velocity of light
varies with direction in anisotopic materials.

Snell's Law predicts the following refraction response in glass:

:   

    :   ![](Borosilicate_Glass.gif "fig:Borosilicate_Glass.gif")

The reflected intensity depends on the angle of incidence and on the
polarization of incident light. At a high angle of incidence, for
example, the reflectance can be very high. At a certain angle
(Brewster\'s angle) reflected light is completely polarized. The
Fresnel equations give
quantitatively the intensity of reflected light as a function of the
angle of incidence and of its polarization (and, of course, of
refraction index).
