Introduction:

You may have view advertisement displays (that is, made up of glass or plastic rods) and illuminated fountains. While looking at such, you might as well have observed that light seems to travel all along the curved path. In the above-illustrated cases, most of the incoming light is contained in the boundaries of the medium (that is, glass or plastic or water) due to the phenomenon of the total internal reflection.  And as the medium itself consists of a curved shape, the light travelling via it appears to travel all along a curved path. Optical fibre that is made up of transparent glass or plastic, as well transmit light in a similar fashion. Such fibres are thread like structure and a bundle of it can be employed to transmit light around corners and over long distances. As optical fibre can transmit light around corners, it is being employed for getting images of inaccessible areas example: the interior parts of human body. The real potential of the optical fibres was, though, revealed just after the invention of lasers.

Optical Fibres:

Define: The Fiber optics employs light to send information (or data). More generally, fiber optics is the branch of optical technology concerned by the transmission of radiant power (that is, light energy) via fibers.

Fiber optics is the technology in which signals are transformed from electrical into optical signals, transmitted via a thin glass fiber, and re-transformed into electrical signals. The fundamental optical fiber comprises of two concentric layers differing in optical properties and a protective outer coating.

• Core: It is the inner light-carrying member.
• Cladding: It is the middle layer that serves up to confine the light to the core.       
• Buffer: It is the outer layer that serves up as a shock absorber to protect the core and cladding from the damage.

The optical fibre comprises of a cylindrical glass core surrounded via a transparent cladding of lower refractive index. The assembly is further covered through a plastic coating to protect it against the chemical attack, mechanical impact and other handling damages. The figure shown below represents the geometry of a typical optical fibre. The core diameter is in the range of 5 µm to 125 µm by the cladding diameter generally in the range of 100 µ m to l50 µ m. The plastic coating diameter is approximately 250 µm.

The concentric layers of an optical fiber comprise the light-carrying core, the cladding and the protective buffer.

Light injected to the core and striking the core-to-cladding interface at an angle more than the critical angle will be reflected back into the core. As angles of incidence and reflection are equivalent, the light ray continues to zigzag down the length of the fiber. The light is trapped in the core. The light striking the interface at less than the critical angle passes to the cladding and is lost.

Once light starts to reflect down a fiber it will carry on to do so.

The rays of light don't travel arbitrarily. They are channeled into modes that are possible paths for a light ray traveling down the fiber. The fiber can support as few as one mode and as many as tens of thousands of modes. The number of modes in a fiber is important as it assists to find out the bandwidth of fibre. More modes usually denote lower bandwidth. This is because of the reason of dispersion.

As the pulse of light travels via the fiber, it spreads out in time. As there are some reasons for such dispersion, two are of main concern. The first is modal dispersion that is caused by various path lengths followed through light rays as they bounce down the fiber. Several rays follow a more direct route than others. The second kind of dispersion is material dispersion: different wavelengths of light travel at different speeds. With limiting the number of wavelengths of light, we limit the material dispersion.

The Dispersion limits the bandwidth of the fiber. At high data rates, dispersion will let pulses to overlap in such a way that the receiver can no longer differentiate where one pulse starts and the other ends.

Basic principles of light propagation:

Simple Ray model:

For the propagation of light within the core there are two possibilities.

1) A light ray is begun in a plane having the axis of the fibre. We can then view that the light ray after total internal reflection travels in the similar plane that is, the ray is confined to the plane in which it was launched and never leave the plane. In this condition the rays will for all time cross the axis of the fibre. These are termed as the Meridional rays.

2) The other prospect is that the ray is not launched in a plane having the axis of the fiber.

For illustration whenever the ray is launched at certain angle such that it doesn't intersect the axis of the fibre, then after total internal reflection it will go to some other plane. We can view that in this condition the ray will never intersect the axis of the fiber. The ray in essence will spiral around the axis of fiber. Such rays are termed as the Skew rays. 

Meridional rays: The rays which for all time pass through the axis of fiber giving high optical intensity at the center of the core of the fiber.

Skew Rays: The rays that never intersect the axis of the fiber, providing low optical intensity at the center and high intensity towards the rim of fiber.

Propagation of Meridional Rays:

1) Let us assume the figure shown above. A ray is launched from outside (air) at an angle θ_o, from the axis of the fiber.

2) Assume that the ray forms an angle θ₁ with the axis of the fiber within the core, and let the ray make an angle Φ₁ by core-cladding interface.  Assume that Φ₂ be the angle of refraction in the cladding.

When Φ₁ < critical angle, the ray is refracted in cladding.  The ray that goes to cladding is lost and is not helpful for communication. The ray that is confined to the core is helpful for the optical communication.

3) Now as we raise the launching angle θ_o, the angle θ₁ as well rises.

As,

θ₁ + Φ₁ = π/2

Φ₁ reduces and at certain point becomes less than the critical angle. If Φ₁ equivalents the critical angle, Φ₂ equivalents π/2. The maximum launching angle then corresponds to Φ₂ = π/2

4) Let us apply Snell's law at the launching point and at the core-cladding interface for the maximum launching angle θ_omax. For this case assume that θ₁ = θ₁ and Φ₁ = Φ₁ we then have:

n₁ sin Φ₁' = n₂ (since Φ₂' = π/₂)

=> sin Φ₁' = n₂/n₁

Now,

sin θ_omax = n₁ cos Φ₁' = n₁√(1 - sin² Φ₁')

sin θ_omax = n₁√[1 - (n₂²/n₁²)] = √(n₁² - n₂²)

Therefore the sine of the maximum angle at which the ray will be directed within the fiber is given by the square root of the difference of squares of the refractive indices of the core and cladding. The quantity sin θ_omax is termed as the Numerical Aperture of an optical fiber. The NA is the measure of power launching proficiently of an optical fiber.

Numerical Aperture: This parameter state us that whenever we take an optical fiber and put it in front of the optical source then how much light is gathered by the fiber from the source. Smaller the value of Numerical aperture, smaller the value of θ_omax (that is, maximum launching angle) and smaller is the power accepted through the fiber.  In another word, whenever the light is available from different directions from the source, only a part of light is accepted via an optical fiber and the remaining portion of the light is discarded by it.

Dispersion:

1) The amount of light accepted through an optical fiber is merely one of the parameters in the optical communication. An additional significant parameter is the data rate that the fibre can handle as the main purpose here is to send information from one point to the other. 

2)

a)  As we observe from the above figure, all the rays contained in the cone 2θ_omax are accepted through the optical fiber.                                                               

b) Let us take two extreme rays; one at the lowest possible angle (that is, all along the axis of the fibre) and one at the highest possible angle (θ_omax). Take a length 'L' all along the fibre axis traveled through the rays.

c)  Now transmit a narrow pulse of light. The light pulse points out binary information. When there is a pulse then a bit is present, or else the bit is absent. If the light is switched on, all the rays are switched on at similar time. The pulse energy is thus splitted between different rays that travel through various paths within the fibre.

d) The pulse all along the axis of the optical fiber acquires less time to travel the distance 'L', than the pulse that travels at the extreme angle θ_omax.

e) As illustrated in the figure above, the distance traveled through the extreme ray is L/cosθ₁

The time difference between the axial ray and the extreme ray is then represented by:       

Δt = (L/cosθ_1') (n₁/c) - (L/c)n₁

Δt = (Ln₁/c) [(1/cosθ₁') - 1]

Δt = (Ln₁/c) [(n₁/n₂) - 1]

Δt = (Ln₁/cn₂) (n₁ - n₂)

Here 'c' is the velocity of light. As the core material is glass, n1 ≈ 1.5, and since n₂ ≤ n₁ it can lie among 1 and 1.5.  The ratio (n₁/n₂) then lies between 1 and 1.5 only.  The time difference Δt per unit length thus is more or less proportional to (n₁ - n₂)

Δt per km ∝ (n₁ - n₂)

The time difference Δt necessarily is the measure of pulse widening on the optical fibre.

This phenomenon is termed as dispersion of the optical fiber. The dispersion (that is, pulse broadening) has to be small as the data rate is inversely proportional to the pulse broadening. For high speed communication (that is, high speed doesn't refer to the time taken by the data to reach the destination however it refers to the number of bits per sec) the pulse broadening and therefore the dispersion must be minimal.

f) For low dispersion (n₁ - n₂) must be as small as possible. Therefore for an optical fiber the refractive index of core has to be made as close to the refractive index of the cladding as possible. 

Different types of fibers:

The Optical fiber falls into three fundamental categorizations: Step-index multimode, graded-index multimode and single mode.

Step index fibres:

The Step index fibres are the most utilized fibres in the fields other than telecommunications. They are relatively economical and they encompass the broadest range of core diameters: mostly from 50 μm up to 2 mm. The material might be plastic, liquid or glass.

Plastic fibres are not broadly employed nowadays; their optical transmission is poor and the core relatively big (that is, 0.5 to 2 mm). The most proficient fibres are made in acrylic and they are mostly employed for short length telecommunication networks. Despite of their limited performances, new progress in the plastic fibres might open applications in the field of high speed home networks (Gigabit/s). Latest polymers are being proposed by the attenuations approaching the silica fibres.

Most of the common step index fibres are made up of silica glass (that is, core and cladding) due to its high optical transmission in a very wide spectral range. Though, throughout the manufacturing of fibres several contaminants remain in the glass that modifies its transmission. The most complex part is to remove OH radicals. A huge amount of such radicals produce absorption bands in the near IR range (that is, mainly 726nm, 880nm, 950nm and 1136nm) however fortunately leave a high transmission in the near UV region which is close to the theoretical limit (that is, Rayleigh dispersion). High purity silica fibres having low amounts of OH contaminants greatly decrease such absorption peaks in the near IR. Though, crystalline structures come out while manufacturing prevents a good transmission in the UV range.

Gradient index:

Gradient fibres are broadly employed in the telecommunications; they are economical and simple to procure. Though, as far as we are familiar, never for the astronomical instrumentation. There is a general principle among instrumentalists which gradient fibres exhibit low transmission in the blue region. This argument is supported through the fact that these fibres require to be doped to form the axial gradient index; however we have never seen published a transmission curve in the broad spectral range. Most of the manufactures simply announce the attenuation for some wavelengths in the near IR.

Single mode fibres:

In a single mode fibre, the core diameter is decreased to few wavelengths of the incoming light. For illustration for a beam having λ = 0.55 μm, the core diameter must be of the order of 4.5 μm. Under such conditions, the core is so small that merely the primary mode can travel within the fibre. Given the wave propagation of the light within the cavity, there is no mode for the light to take longer optical paths which the wave travelling on the axis. This is the main reason why single mode fibres are employed in telecommunications to deliver high baud rates: the width of a short single square light pulse entering to the fibre will expand less in a single mode fibre that in the multimode one. In a multimode fibre the various modes travelling slower will spread the pulses.

Applications of Optical Fibres:

The main applications of optical fibres are as follows:

1) Communication: Telephone transmission process utilizes fibre-optic cables. The Optical fibres transmit energy in the form of light pulses. The technology is identical to that of the coaxial cable; apart from that the optical fibres can handle tens of thousands of conversations concurrently.

2) Medical uses: The optical fibres are well appropriate for the medical use. They can be made in very thin, flexible strands for insertion to the blood vessels, lungs and other hollow portions of the body. Optical fibres are mainly used in a number of instruments which allow doctors to view internal body parts devoid of having to carry out surgery.

3) Simple uses: The simplest application of optical fibres is the transmission of light to locations or else hard to reach. As well, bundles of some thousand extremely thin fibres assembled exactly side by side and optically polished at their ends, can be employed to transmit the images.

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