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Optical Fiber Communications

Week 2

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Skew Rays

• Another category of ray exists which is transmitted without passing through the fiber axis.

• These rays, which greatly outnumber the meridional rays, follow a helical path through the fiber and are called skew rays.

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Conti…

• Helical path traced through the fiber gives a change in direction of 2γ at each reflection, where γ is the angle between the projection of the ray in two dimensions and the radius of the fiber core at the point of reflection.

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Conti...

Fiber axis

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34

5

Skew ray1

3

2

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5

Fiber axis

1

2

3Meridional ray

1, 3

2

(a) A meridionalray alwayscrosses the fiberaxis.

(b) A skew raydoes not haveto cross thefiber axis. Itzigzags aroundthe fiber axis.

Illustration of the difference between a meridional ray and a skew ray.Numbers represent reflections of the ray.

Along the fiber

Ray path projectedon to a plane normalto fiber axis

Ray path along the fiber

© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

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Acceptance Angle Calculation for Skew Rays

• In order to calculate the acceptance angle for a skew ray it is necessary to define the direction of the ray in two perpendicular planes.

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Conti….

On White board

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Example

• An optical fiber in air has an NA of 0.4. Compare the acceptance angle for meridional rays with that for skew rays which change direction by 100° at each reflection.

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Number of Modes and Cut-off Parameters

• A finite number of modes are available in optical fibers.

• For propagation of the light rays the diameter of the fiber core must be greater than the wave length(λ) of the incident light (But this is Theoretical Limit)

• In practice cut off actually occurs before this: Sin θc= n2/n1

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Conti…

• So, as we increase the number of modes (n) the angle of incident also increases and reaches its critical value ( θi= 90 – θc).

• If we go on increasing n , then θi will exceed its acceptance condition and propagation will be stopped.

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How can Increase the number of modes

1. Making large difference between refractive indices of the core and cladding material.

2. Increase the ratio d/λ large (but this is not practical).

3. Fabricate the fiber with larger core diameter.

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Cut-off Parameter

• The number of modes supported by the fiber is determined by an important parameter called cut-off parameter.

• Its various aliases are “normalized frequency of cut-off” and denoted by V

V=ᴫ (d/λ)(n1^2-n2^2)^1/2• The approximate number of modes which the

fiber supports are: Number of modes=(1/2)V^2

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Conti…

• Smallest multimode fiber have V=2.405 value, while for single mode fiber this value is greater than zero but less than 2.405.

• V number can be reduced either by reducing the diameter or by reducing the NA.

• The greatest disadvantage of the Multimode fiber is that it has intermodal dispersion phenomenon, which can be reduced by using Graded Index Fiber.

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Classification of the Fiber

• Optical fiber is a piece of very thin and absolutely pure glass, outside is made of a cladding of glass/plastic, which is different from inner core material in chemical composition.

• Manufacturers classify fibers into three main categories:

1. Stepped Index Multimode Fiber2. Graded Index Multimode fiber3. Single mode fibers

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Stepped Index Fiber

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Conti….

• The basic structure of the stepped index fiber consists of the two portions, Inner one is called core made of normally pure glass material, and outer portion may be air ( In the case of the air core diameter should be 200 micro meters to work on) or glass/ plastic.

• The refractive index of the core is constant throughout the fiber axis and stepped increases at the cladding and then will remain same.

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Modes in Stepped index fiber

• In stepped index fiber two types of modes are possible:1. Multimode Step index Fiber2. Single mode step index Fiber• In multimode step index fiber the core diameter can be

large enough to propagate thousands of modes in practical.

• Here we can use low cost light transmitting source (LED) but in return we may encounter with Modal dispersion problem.

• If number of modes are greater than 50 then modes can be calculate as:

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Single mode Stepped Index fiber

• The time transit dispersion problems can be solved by making the core very thin, so that the diameter of the core is of the same order as the wave length of the light to be propagated. It has following characteristics:

1. Very small core diameter2. Low numerical aperture3. Low attenuation4. Very high bandwidth

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Conti…

• In order to get a single mode, with all other modes cut off, the diameter of the core must satisfy:

d< 0.766λ/NA• In spite of its so many good qualities, the use

of the thin cores creates mechanical difficulties in manufacture, handling and splicing of the fiber.

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Graded Index Multimode Fiber

• Graded index fiber have intermediate bandwidth and capacity, and it is less expensive way to over come time transit dispersion.

• This fiber has a property of gradually changing refractive index ( increasing from the outside of the fiber core to the center of it).

• Here light rays with larger angle of incidence travel more path lengths those with smaller path lengths.

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Conti…..

• But we know that decrease of the refractive index allows a higher velocity of light energy propagation, thus all waves will reach virtually at the same time.

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Conti…

• The variation is of the refractive index of the core of the graded index fiber with radius measured from the center of core is as follows:

• Number of modes in graded index fiber can be computed as:

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Conti…

High Purity Silica Fiber: This type of the fiber is suitable for

transmission of light in the range of the 180nm to 800nm, and its fiber type is step index multimode.

• Its cladding material is doped silica, and numerical aperture is around 0.24.

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Mechanism of Refractive index Variation

• As we know that there is a refractive index difference between the core material and cladding material.

• Dopants such as flourine (f) and boron oxide decreases the refractive index of the silica, where as dopants such as Phosphorous oxide and germanium oxide increases the refractive index of silica.

• The lowest loss single mode fiber has been attained with pure silica core and a flourine doped cladding.

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ATTENUATION, SCATTERING, POLARIZATION

Transmission Characteristics of Optical fibers

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Introduction

• Transmission characteristics of Optical fiber of most interest are those of attenuation (or loss) and bandwidth.

• Careful investigation of the attenuation showed that it was largely due to absorption in the glass, caused by impurities such as iron, copper, manganese and other transition metals which occur in the third row of the periodic table.

• Hence, research was stimulated towards a new generation of ‘pure’ glasses for use in optical fiber communications.

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Attenuation

• The attenuation or transmission loss of optical fibers has proved to be one of the most important factors in bringing about their wide acceptance in telecommunications, Channel attenuation largely determined the maximum transmission distance.

• Signal attenuation within optical fibers, as with metallic conductors, is usually expressed in the logarithmic unit of the decibel.

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Conti…

• Input and output power ratio can also be calculated as:

• In optical fiber communications the attenuation is usually expressed in decibels per unit length (i.e. dB km−1) following:

• where αdB is the signal attenuation per unit length in decibels which is also referred to as the fiber loss parameter and L is the fiber length

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Example

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Attenuation mechanism

• A number of mechanisms are responsible for the signal attenuation within optical fibers.

• They may be categorized within several major areas which include:

1. Material absorption2. Material scattering (linear and nonlinear scattering), 3. Micro-bending losses,4. Mode coupling radiation losses losses due to leaky

modes.