EEE 529: Features of optical communications

Danson Njue

Basic Propagation Theory

m a x

Total Reflection

Cladding

Core

Refractive Index

n1

n2

n2

Basic Propagation Theory Refractive Index

The refractive index of a medium is defined as the ratio of the velocity of light

In a vacuum to the velocity of light in the medium.

(Example)

n = 1 for air

n = 1.3 for water

n1 = 1. 4495 for core

n2 = 1.4444 for cladding

n = ------ v c c = 3e+8 [m/s]

Reflection and Refraction

Higher Index(n1)

Lower Index(n2)

Reflection and Refraction

Higher Index(n1)

Lower Index(n2)

Example

n1=1, 1=30o

n2=1.3 Compute 2

1 x sin( x 30/180) = 1.3 x sin(2) sin(2) = 0.5/1.3 = 0.38 2 = asin(0.38) = 0.395 [rad] = 0.395 x 180 / = 22.6o

Critical Angle

Higher Index(n1)

Lower Index(n2)

Critical Angle

Acceptance Angle (a)

• Refers to the maximum angle to the axis of that light may enter the fibre in order to be propagated through total internal reflection.

cladding

n1

n2

core

n2

cladding

air

a

n2

n1

core

Numerical Aperture (NA)

• The Numerical Aperture (NA) is a measure of how much light can be collected by an optical system such as an optical fibre or a microscope lens.

• The NA is related to the acceptance angle a, which indicates the size of a cone of light that can be accepted by the fibre.

Critical Angle: n1 . sin2 = n2

Exercise

Express the numerical aperture of a fiber (NA) using n1 and n2.

Critical Angle: n1 x sin2 = n2

Snell's law:

n0 x sin0 = n1 x sin

1

Hint: 1 +

2 =

Solution

Fiber is in the air

Numerical Aperture (NA)

• The Numerical Aperture (NA) may also be given in terms of the relative refractive index difference between the core and the cladding.

• The relative refractive index difference is given by;

∆

Substituting in the expression for NA yields;

∆

Exercise A silica optical fibre has a core refractive index of 1.5 and a cladding

refractive index of 1.47.

Determine the following:

• Critical angle at the core-cladding interface

• Numerical Aperture of the fibre

• Acceptance angle for the fibre in the air

Features of optical fiber communications

Figure: Digital optical communication system

Classification of optical fibres

Optical Fibres

Graded-Index Fibres

Step-Index Fibres

Single-mode step-Index Fibres

Multi-mode step-Index Fibres

Multi-mode step-Index Fibres

Step-Index fibres

• Characterised by core of constant refractive index n1 and a cladding of slightly lower refractive index n2.

• As such, the refractive index profile makes a step change at the core-cladding as shown in the figure below;

Multi-mode step index fibre

Single-mode step index fibre

Step-Index fibres • The refractive index profile of a step-index fibre is given by;

Single-mode vs Multi-mode step-index fibres • Single-mode allows only one transverse electromagnetic mode and has a slightly

lower core diameter. The propagation of a single mode corresponds to a single ray-path only through the fibre

• Multi-mode fibres allows the propagation of a finite number of guided modes along the channel

• The number of guided modes depends on the physical parameters of the fibre (relative refractive index difference and core radius) and the wavelength of the transmitted light. The two are included in the normalized frequency, V of the fibre.

• The total number of guided modes in a multi-mode step-index fibre is approximated as follows;

𝑀𝑔 ≃V²

2

Single mode vs multi-mode

Advantages of single-mode

• Low inter-modal dispersion (broadening of transmitted light pulses) since only one mode is transmitted

• Can attain high bandwidth capacities as opposed to multi-mode fibres

Advantages of multi-mode

• Ability to use spatially incoherent optical sources that cannot be efficiently be coupled to single mode fibres

• Have larger NA and core diameters making coupling easier

• Have lower tolerance requirements on fibre connectors

These advantages applies for lower bandwidth applications

Graded-Index fibres

• Characterised by non-constant core refractive index n1 . The core refractive index n(r) decreases with the radial distance from a maximum of n1 at the axis to a constant value of n2 beyond the core radius a in the cladding.

Where Δ is the relative refractive index difference and α is the profile parameter that gives the characteristic refractive index profile of the fibre core. The fibre may different profiles depending on the value of α:

Value of α Profile

1 Triangular

2 Parabolic

Step-index

Graded-Index fibres

Parabolic profile, α=2