Fibre Optics

Optical Fibre #

Has 3 coaxial regions

1. Innermost region: light guiding region: core
2. Middle region: cladding
   1. Surrounds the core
   2. Its refractive index is lower than the core
   3. Reduces scattering losses.
3. Outermost region: Sheath/protective buffer/outer jacket
   1. Adds mechanical strength

They are constructed as either as a single fibre or a bundled up cable.

Snell’s Law #

$$ n_1 \sin i = n_2 \sin r $$

Total Internal Reflection #

The angle of incidence is such that the refracted angle goes to 90° and then turns into total internal reflection if it’s greater than the ‘critical angle’

$$ \sin i_c = \frac{n_2}{n_1}<1 $$

Light in a fibre optic travels by utilizing this property of reflection/refraction

Types of Optical Fibres #

There are 2 types:

1. Single Mode Fibre (SMF): Has a smaller core diameter and can support only one mode of propagation.
2. Multimode Fibre (MMF): Has a larger core diameter and supports a number of modes. Further distinguished based on index-profile
   1. Step index type
   2. Graded index (GRIN) type

Single Mode Step Index Fibre #

• Refractive index changes abruptly at the core-cladding boundary: “step index”
• Core diameter: 4 μm
• Path: Single and almost straight
• NA: 0.05-0.4

Multimode Step Index Fibre #

• Referactive index changes abruptly at the core-cladding boundary: “step index”
• Core diameter: 100 μm
• Path: Many zigzag paths
• NA: order of 3

Multimode Graded Index Fibre #

• Refractive index of the core varies with distance from the fibre axis. Has high value at the center and falls off with increasing radial distance from the axis.
• Acceptance angle and Numerical aperture decreases with radial distance from axis.

Parameters of Fibres #

Numerical Aperature #

There are three rays that are involved

1. Incident ray going into the tube →
2. Refracted ray bouncing the wall of the core →
3. Totally internally reflected ray

i: Angle of the initial incident ray with respect to the axis of the tube

i_max: acceptance angle of incidence for which the total internal refraction can occur.

$$\sin i_{max}=\sqrt{n_1^2-n_2^2}=NA\approx n_1\sqrt{2\Delta}$$

$\Delta=\frac{n_1-n_2}{n_1}$

i_max: acceptance angle of incidence for which the total internal refraction can occur.

V-Number #

Called normalized frequency of the fibre.

a: radius of the core $$ V=\frac{2\pi a}{\lambda}NA $$

Maximum possible modes #

N_m: maximum number of modes supported

• by a Step Index fibre: $\frac{V^2}{2}$ (if V<2.405: N_m=1, else N_m>1)
• by a GRIN fibre: $\frac{V^2}{4}$

Losses in optical fibre #

For a fibre of length L and Power input P_i and output P_o,

loss = $\frac{10}{L} \log \frac{P_i}{P_o}$

Advantages (over coaxial cables) #

• No loss
• Speed/Bandwidth
• Cost effective
• Light weight
• Strong and flexible
• Non Hazardous
• Low Interference. No cross talk.
• Low/no electromagnetic and radio frequency interference

Applications #

1. Medical applications
   1. A bundle of fibres (MMF) is used to illuminate areas of body
   2. A 2nd bundle is used to collect the reflected light
   3. A laser beam is also used as a guide in many cases.
2. Military applications
   1. Maintains true communication silence to the enemy.
   2. Use of Fibre-guided missiles that send video and receive commands for operations
3. Entertainment Applications
   1. For optical projection systems
4. Optical Fibre Sensors: To measure
   1. Temperature changes
   2. Smoke/pollution detector
   3. Level of liquid in a container.
5. Communications Applications