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.

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.


 * [[Image:Wave_packet.gif|left|thumb]]

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 108 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:


 * [[Image:Ray_path.gif|left|thumb]]

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.


 * [[Image:Reflection_refraction.gif|left|thumb]]

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.


 * [[Image:Diffuse_reflection.gif|left|thumb]]

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.


 * [[Image:Virtual_image.gif|left|thumb]]

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.


 * [[Image:Real_image.gif|left|thumb]]

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.


 * [[Image:Brewsters_angle.gif|left|thumb]]

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.


 * [[Image:White_light_refraction.gif|left|thumb]]

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.


 * [[Image:Refraction_in_glass.gif|left|thumb]]

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


 * [[Image:Prism_refraction.gif|left|thumb]]

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:


 * [[Image:Borosilicate_Glass.gif|left|thumb]]

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).