## LESSON 29. Theory of Optical Fiber- Index Fiber

Ray Model

Modes; it can be observed as possible number of allowed paths of light in an optical fiber. Exact, an axial directed path, all other paths are “Zigzag”

These zigzag rays get repeatedly reflected at the interface of core-cladding of fiber and phase shift occurs. As a result, constructive interference occurred. Hence, light ray paths along which the waves are in phase inside the fiber is called modes.

Number of modes propagating in the fiber is depending upon fractional refractive index (Δ). Hence, RI of core increases, mode of propagating are increase.

Mode of propagation (Number of mode) depends on the ratio ${d \over \lambda }$  ;

d - Diameter of core.

$\lambda$  - Wavelength of the light is being transmitted.

A mode is a path taken by a ray of light through an optical fiber.

It is mathematically expression to understand the concept of propagation of light waves in an optical fiber.

The number of mode of propagation within the fiber depends on;

The diameter of the core- narrower the fiber core lesser is the number of mode of propagation.

The number of modes supported for propagation in the fiber is determined by a parameter called V-number. It is given by

V =  ${{2\pi d} \over \lambda }\sqrt {n_1^2 - n_2^2}$

Or

V =  ${{2\pi d} \over \lambda }\left( {NA} \right)$

V – V number; depends upon characteristics of fiber and the wavelength of light propagation through it.

d: Diameter of the core

$\lambda$: Wavelength of light

For step index fiber; the maximum of modes (Nm) = ${{{V^2}} \over 2}$  ,

Single Mode Step Index Fiber V < 2.405

Multimode Mode Step Index Fiber V > 2.405

For Gradded Index fiber; the maximum of modes (Nm) = ${{{V^2}} \over 4}$

The classification of the fiber on the basis of

• Material

• Refractive Index(RI)

• Path(Mode) of propagation of light through light

Before discussion of the mode of the fiber, we must to resolve the concept of refractive index based fiber structure.

Refractive Index Profile is “a graphical representation between Refractive Index and Distance from center of the core”.

The graphical representation shows Refractive Index on one axis; Refractive Index Axis

Distance from the center of the core on other axis; Core Axis

(1) Step Index Fiber(SI) Fig20(1)

• Refractive Index of the core is constant along radial direction.

• RI falls to a lower value at the cladding and core boundary.

• There is an abrupt change in the refractive index at the core-cladding interface and hence the refractive index profile takes place the shape of step. • At the core-cladding interface the RI of the core matches with the RI of cladding i.e n3 $\cong$ n2 (RI of cladding)