Fiber Optic Cables

. The fiber optic cables are to be used under variety of situation such as underground, outdoor poles or submerged under water. The structure of cable depends on the situation where it is to be used, but the basic cable design principle remains same.

. Mechanical property of cable is one of the important factor for using any specific cable. Maximum allowable axial load on cable decides the length of the cable can be reliability installed.

. Also the fiber cables must be able to absorb energy from impact loads. The outer sheath must be designed to protect glass fibers from impact loads and from corrosive environmental elements.

1. Fiber Arrangements

. Several arrangements of fiber cables are done to use it for different applications. The most basic form is two fiber cable design. Fig. 1 shows basic two fiber cable design. It is also known as basic building block of fiber cable.

. For providing strength to the core several coatings of different materials  are applied as shown in Fig. 1.

. Multiple fiber cables can be combined together using similar techniques Fig. 2 shows commonly used six fiber cable.

. The basic fiber building blocks are used to form large cable. These units are bound on a buffer material which acts as strength element along with insulated copper conductor. The fiber building blocks are surrounded by paper tape, PVC jacket, yarn and outer sheath.

2. Fiber Optic Cable Ducts

. Number of cores are bundled in plastic ducts. To ease identification, individual fibers are colour coded Table 1 shows an example of the colour coding  used by manufactures.

.  If there are more than 12 fibers in a tube they are usually bundled together in quantities of 12 and held together with a coloured binding yarn.

3. Cable Jacket 

The cable jacket, the final outer layer of the cable, may use a number of materials depending on the required mechanical properties, attenuation, environmental stress and flammability. Table 2 lists the properties of common cable jacket materials.

4. Plastic Fiber Optic Cables

. Fibers can also be manufactured from transparent plastic which offers advantages of large diameter (1 mm), increased flexibility, can be cut using a hot razor blade, ease of termination. But because of high intrinsic loss use of plastic fibers is normally restricted to only few metres.

. Plastic optic fiber (POF) offers noise immunity and low cable weight and volume and is competitive with shielded copper wire making it suitable for industrial applications.

. Silica (glass) optical fiber has better transmission characteristics (Low loss) than POF. Also, silica fiber can tolerate higher temperature than plastic fiber. On the other hand, POF is more flexible, less prove to breakage, easier to fabricate and cost is low than glass fibers.

. Another advantages of glass/glass is that very clean fracture surface can be obtained which ensures that fiber cladding inside the connector retains its optical characteristics right upto the end face of fiber. Whereas in plastic glass/plastic fiber some additional losses exists due to fracture zone of plastic which even after grinding and polishing still have microscopic end face absorption areas. These advantages and disadvantages are summarized in table 3.

Mechanical Properties of Fibers

. The mechanical properties of fibers are equally important as that of transmission properties. The fibers must be able to sustains exerted during the cabling process.

Two basic mechanical properties of glass fibers are identified.
1. Strength
2. Static Fatigue
1. Strength

. The strength of the fiber is limited due to stress at surfaces or micro cracks. A hypothetical model of micro crack is shown in Fig. 1. This is popularly known as Griffith micro crack. The micro crack is elliptical shaped.

. The strength of fiber crack is expressed as, 

. A fiber contains many randomly distributed micro cracks of different sizes. Therefore fiber strength should be expressed statistically. The commutative probability of failure of a fiber is given as,

       where,

              L      = Fiber length

              σ      = Stress level

              N(σ) = Total cracks per unit length

. The expression for N(σ) is given by Weibull

       Where L₀, σ₀ and m are constant relating to initial inert strength distribution. The Weibull expression is given by

 2. Static Fatigue

. The static fatigue is the process of slowly growing micro cracks (flaws) due to humid conditions and tensile stress. There is possibility of fiber failure due to growing micro cracks. Also because of chemical erosion at the flaw tip due to water molecules, the flaw increases. To protect fiber from environmental erosion, coating are applied immediately after the manufacturing of fiber.

. Proof testing is the method for high assurance of fiber reliability. In proof testing the fiber is subjected to a tensile load greater than the load at the time of manufacturing and installation. The fibers are rejected if it is does not pass the test. The failure probability F_s for a fiber after it has been proof tested is given as,

Single Mode Fibers

. Propagation in single mode fiber is advantageous because signal dispersion due to delay differences amongst various modes in multimode is avoided. Multimode step index fibers cannot be used for single mode propagation due to difficulties in maintaining single mode operation. Therefore for the transmission of single mode the fiber is designed to allow propagation in one mode only, while all other modes are attenuated by leakage or absorption.

. For single mode operation, only fundamental LP₀₁ mode may exist. The single mode propagation of LP₀₁ mode in step index fiber is possible over the range.

. The normalized frequency for the fiber can be adjusted within the range by reducing core radius and refractive index difference ˂ 1 %. In order to obtain single mode operation with maximum V number (2.4), the single mode fiber must have smaller core diameter than the equivalent multimode step index fiber. But smaller core diameter has problem of launching light into the fiber, jointing fibers and reduced relative refractive index difference.

. Graded index fibers can also be used for single mode operation with some special fiber design. The cut-off value of normalized frequency V_c in single mode operation for a graded index fiber is given by,

1. Cut-off Wavelength

. One important transmission parameter for single mode fiber is cut-off wavelength for the first higher order mode as it distinguishes the single mode and multimode regions.

. The effective cut-off wavelength λ_C is defined as the largest wavelength at which higher order (LP₁₁) mode power relative to the fundamental mode (LP₁₁) power is reduced to 0.1 dB. The range of cut-off wavelength recommended to avoid modal noise and dispersion problems is : 1100 to 1280 nm (1.1 to 1.2 µm) for single mode fiber at 1.3 µm.

. The cut-off wavelength λ_C can be computed from expression of normalized frequency.

Where,

V_C is cut-off normalized frequency.

. λ_C is the wavelength above which a particular fiber becomes single moded.

For same fiber dividing λ_C by λ we get the relation as :

But for step index fiber V_C = 2.405 then

2. Mode Field Diameter and Spot Size

. The mode field diameter is fundamental parameter of a single mode fiber. This parameter is determined from mode field distribution of fundamental LP₀₁ mode.

. In step index and graded single mode fibers, the field amplitude distribution is approximated by Gaussian distribution. The mode field diameter (MFD) is distance between opposite 1/e = 0.37 times the near field strength (amplitude) and power 1/e² = 0.135 times.

. In single mode fiber for fundamental mode, on field amplitude distribution the mode field diameter is shown in Fig. 1.

. The spot size is given as –

       The parameter takes into account the wavelength dependent field penetration into the cladding. Fig. 2 shows mode field diameters variation with λ.

3. Fiber Materials

3.1 Requirements of Fiber Optic Material

1. The material must be transparent for efficient transmission of light.

2. It must be possible to draw long thin fibers from the material.

3. Fiber material must be compatible with the cladding material.

Glass and plastic fulfills these requirements.

. Most fiber consists if Silica (SiO₂) or silicate. Various types of high loss and low loss glass fibers are available to suite the requirements. Plastic fibers are not popular because of high attenuation they have better mechanical strength.

3.2 Glass Fibers

. Glass is made by fusing mixture of metal oxides having refractive index of 1.458 at 850 nm. For changing the refractive index different oxides such as B₂O₃, GeO₂ and P₂O₅ are added as dopants. Fig. 3 shows variations of refractive index with doping concentration.

. Fig. 3 shows addition of dopants GeO₂ and P₂O₅ increases refractive index, while dopants Fluorine (F) and B₂O₃ decreases refractive index. One important criteria is that the refractive index of core is greater than that of the cladding, hence some important compositions are used such as 

. The principal raw material for silica is sand and glass. The fiber composed of pure silica is called as silica glass. The desirable properties of silica glass are :-

- Resistance to deformation even at high temperature.

- Resistance to breakage from thermal shocks (low thermal expansion).

- Good chemical durability.

. Other types of glass fibers are :

- Halide glass fibers

- Active glass fibers

- Chalgenide glass fibers

- Plastic optical fibers

4. Fiber Fabrication Methods

. The vapour-phase oxidation process is popularly used for fabrication optical fibers. In this process vapours of metal halides such as SiCI₄ and GeCI₄ reactive with oxygen and forms powder of SiO₂ particles. The SiO₂ particles are collected on surface of bulk glass and then sintered to from a glass rod called perform. The performs are typically 10-25 mm diameter and 60-120 cm long from which fibers are drawn. A simple schematic of fiber drawing equipment is shown in Fig. 4. 

. The perform is feed to drawing furnace by precision feed mechanism. The perform is heated up in drawing furnace so that it becomes soft and fiber can be drawn easily.

. The fiber thickness monitoring decides the speed of take up spool. The fiber is then coated with elastic material to protect it from dust and water vapour.

4.1 Outside Vapour-Phase Oxidation (OVPO)

. The OVPO process is a lateral deposition process. In OVPO process a layer of SiO₂ (Soot) is deposited from a burner on a rotating mandrel so as to make a perform. Fig. 5  shows this process.

. During the SiO₂ deposition O₂ and metal halide vapours can be controlled so the desired core-cladding diameters can be incorporated . the mandrel is removed when deposition process is completed. This perform is used for drawing thin filament of fibers drawing equipment.

4.2 Vapour-Phase Axial Deposition (AVD)

. In VAD process, the SiO₂ particles are deposited axially. The rod is continuously rotated and moved upward to maintain symmetry of particle deposition.

. The advantages of VAD process are

- Both step and graded index fibers are possible to fabricate in multimode and single mode.

- The performs does not have the central hole.

- The performs can be fabricated in continuous length.

- Clean environment can be maintained.

4.3 Modified Chemical Vapour Deposition (MCVD)

. The MCVD process involves depositing ultra fine, vapourized raw materials into a pre-made silica tube. A hollow silica tube is heated to about 1500 °C and a mixture of oxygen and metal halide gases is passed through it. A chemical reaction occurs within the gas and glass '500t' is formed and deposited on the inner side of the tube. The soot that develops from this deposition is consolidated by heating. The tube is rotated while the heater is moved to and along the tube and the soot forms a thin layer of silica glass.

       The rotation and heater movement ensures that the layer is of constant thickness. The first layer that is deposited forms the cladding and by changing the constituents of the incoming gas the refractive index can be modified to produce the core. Graded index fiber is produced by careful continuous control of the constituents.

. The temperature is now increased to about 1800 °C and the tube is collapsed to form a solid rod called a perform. The perform is about 25 mm in diameter and 1 metre in length. This will produce 25 km of fiber. 

. The perform is placed at a height called a pulling tower and its temperature is increased to about 2100 °C. to prevent contamination, the atmosphere is kept dry and clean. The fiber is then pulled as a fine strand from the bottom, the core and cladding flowing towards the pulling point. Laser gauges continually monitor the thickness of the fiber and automatically adjust the pulling rate to maintain required thickness. After sufficient cooling, the primary buffer is applied and the fiber is drummed.

. Fig. 6 shows the overall MCVD process.

Fig. 6 MCVD process

4.4 Plasma-Activated Chemical Vapour Deposition (PCVD)

. PCVD process is similar to MCVD process where the deposition occurs on silica tube at 1200 °C. it reduces mechanical stress on glass films. There is no soot formation and hence sintering is not required. Non-isothermal microwave plasma at low pressure initiates the chemical reaction.

4.5 Double-Crucible Method

. Double-crucible method is a direct melt process. In double-crucible method twp different glass rods for core and cladding are used as feedstock for two concentric crucibles.the inner crucible is for core and outer crucible is for cladding. The fibers can be drawn from the orifices in the crucible. Fig. 7 shows double crucible method of fiber drawing.

       Major advantages of double crucible method is that it is a continuous production process.

Mode theory for Cylindrical Waveguide

. To analyze the optical fiber propagation mechanism within a fiber, Maxwell equations are to solve subject to the cylindrical boundary conditions at core-cladding interface. The core-cladding boundary conditions lead to coupling of electric and magnetic field components resulting in hybrid modes. Hence the analysis of optical waveguide is more complex than metallic hollow waveguide analysis.

. Depending on the larger E-field or H-field, the hybrid modes are HE or EH modes. The two lowest order modes are HE and TE.

1. Overview of Modes

. The order states the number of field zeros across the guide. The electric fields are not completely confined within the core i.e. they do not go to zero at core-cladding interface and extends into the cladding. The low order mode confines the electric field near the axis of the fiber core and there is led penetration into the cladding. While the high order mode distribute the field towards the edge of the core fiber and penetrations into the cladding. Therefore cladding modes also appear resulting in power loss.

. In leaky modes the fields are confined partially in the fiber core attenuated as they propagate along the fiber length due to radiation and tunnel effect.

. Therefore in order to mode remain guided, the propagation factor must satisfy the condition.

Where,

n₁ = Refractive index fiber core

n₂ = Refractive index of cladding

K=Propagation constant = 2π/λ

. The cladding is used to prevent scattering loss that results from core material discontinuities. Cladding also improves the mechanical strength of fiber core and reduces surface contamination. Plastic cladding is commonly used. Materials used for fabrication of optical fibers are silicon dioxide (SiO₂), boric oxide-silica.

2. Summary of Key Modal Concepts

 . Normalized frequency variable, V is defined as

       Where,                 a = Core radius

                                     λ= Free space wavelength.

       The total number of modes in a multimode fiber is given by 

3. Wave Propagation

3.1Maxwell's Equations

       Maxwell's equation for non-conducting medium :

       Where,

              E and H are electric and magnetic field vectors.

              D and B are corresponding flux densities.

. The relation between flux densities and field vectors :

       Where,

              ε₀    is vacuum permittivity

              µ₀   is vacuum permeability.

              P     is induced electric polarization.

              M    is induced magnetic polarization (M = 0, for non-magnetic silica glass).

              P and E are related by:

       Where,

       x is linear susceptibility.

       Wave equation :

       Fourier transformer of E (r, t)

       Where,

       n is refractive index.

       α is absorption coefficient.

. Both n and α are frequency dependent. The frequency dependent of n is called as chromatic dispersion or material dispersion..For step index fiber, 

. For step index fiber,

4. Fiber Modes

Optical mode : an optical mode is a specific solution of the wave equation that satisfy boundary conditions. There are three types of fiber modes.

a) Guided modes

b) Leaky modes

c) Radiation modes

. For fiber optic communication system guided mode is used for signal transmission. Considering a step index fiber with core radius 'a'.

The cylindrical co-ordinates ρ, Φ and can be used to represent boundary conditions.

. The refractive index 'n' has values

. The general solution for boundary condition of optical field under guided mode is infinite at ρ = 0 and decay to zero at ρ = ∞. using Maxwell's equation in the core region.

       The cut-off condition is defined as –

       It is also called as normalized frequency.

5. Graded Index Fiber Structure

. The refractive index of graded index fiber decreases continuously towards its radius from the fiber axis and that for cladding is constant.

.The refractive index variation in the core is usually designed by using power law relationship.

       Where,

              r     = Radial distance from fiber axis

              a     = Core radius

              n₁   = Refractive index core

              n₂   = Refractive index of cladding and

              α     = The shape of the index profile

. For graded index fiber, the index difference Δ is given by, 

. In graded index fiber the incident light will propagate when local numerical aperture at distance r from axis, NA(r) is axial numerical aperture NA(0).The local numerical aperture is given as,

. The axial numerical aperture NA(0) is given as,

       Hence NA for graded index decreases to zero as it moves from fiber axis to core-cladding boundary.

       The variation of NA for different values of α is shown in Fig. 1.

. The number of modes for graded index fiber is given as,