Optical Fibres and Dispersion Concepts

Topics Covered

• Planar waveguides: Mirror and dielectric waveguides, number of modes, field distribution, phase and group velocity
• Fibre optics (circular waveguides): Fibre types, number of modes, acceptance angle, numerical aperture
• Dispersion: Material and modal
• Loss mechanisms: Absorption, scattering, bending

Definition of Dispersion

• Dispersion is the broadening of a light pulse as it propagates down an optical fibre.
• Two types of dispersion exist in optical fibres: Modal and material.
• Modal dispersion limits bandwidth due to different mode velocities in multimode fibres. 
• Material dispersion limits bandwidth due to different frequencies travelling at different velocities.
• Minimizing dispersion is vital for fast data transfer links.

Modal Dispersion

• Modal dispersion occurs in multimode fibres.
• Each mode travels at a different velocity.
• Rays that take longer paths (zigzag more) arrive later, causing the pulse to broaden.
• Single pulse input becomes multiple pulses due to different modes.
• Delay between fastest and slowest mode (σ) in a fibre length L is calculated by a specified formula.
• Single-mode fibres eliminate modal dispersion.
• Graded-index fibres (GRIN) mitigate modal dispersion in multimode fibres.
• Modes close to the cladding travel faster (due to decreasing refractive index).
• Axial modes travel slower.

Modal Dispersion - 2

• Fibre of length L, the difference in arrival times between fastest and slowest modes (σ) is given by a specific formula.
• Single-mode fibres do not experience modal dispersion.
• Graded-index (GRIN) fibres mitigate modal dispersion in multimode fibres.

Modal Dispersion - 3

• Modes close to the cladding travel faster due to the decreasing refractive index.
• Axial modes travel slower.
• This equalization of the different speeds helps reduce modal dispersion.

Material Dispersion

• Refractive index varies with wavelength.
• A pulse of light has different frequencies, and those frequencies travel at different speeds.
• This variation in speed causes pulse spreading.
• Fused silica's refractive index has greater variability at lower visible spectrum wavelengths, but variation is smaller at communication bands (e.g., 1300nm and 1550nm).

Summary

• Three types of dispersion in fibre optic cables: Modal, material
• Modal: varying propagation path lengths of different modes
• Material: variation of the fibre's refractive index with wavelength

### Introduction to Attenuation

• Attenuation reduces optical power at the destination.
• Repeaters/amplifiers boost signal strength periodically.
• Fundamental loss mechanisms: Absorption, scattering, bending.
• Losses are inherent and cannot be totally eliminated.

Absorption

• Absorption is a fundamental property of the fibre's material.
• Photons traveling in the fibre can lose energy by transferring energy to atoms or molecules.
• This energy loss translates to heat.
• If the excited atom/molecule returns to initial state without re-emission, the photon is lost.
• This loss is quantified using the attenuation coefficient, which expresses power loss over a fibre length.

Attenuation Coefficient

• Light intensity decreases exponentially with distance along the fibre.
• Attenuation coefficient (α) quantifies how quickly power is lost into the material; it's measured in m⁻¹.
• The attenuation coefficient is derived from the Beer-Lambert Law, which relates input and output power.
• Fibre loss can also be measured in dB.

Attenuation Coefficient - Decay Profile

• The graph shows a decay profile of 1W of input power into a material with varying attenuation coefficients (α).
• Increasing α indicates faster power decay with distance.

Absorption - 2

• Fused silica has strong absorption bands in mid-infrared and UV regions.
• Mid-infrared photons stimulate vibrational transitions.
• Ultraviolet photons cause electronic and molecular transitions.
• A low-absorption window exists in the near-infrared, crucial for communications.
• This window is centered around the 1300nm and 1550nm wavelengths.

Absorption - 2 (Attenuation Coefficient)

• Attenuation coefficient graph of silica versus wavelength.
• Local minimum at 1300nm (α ≈ 0.28dB/km).
• Absolute minimum at 1550nm (α ≈ 0.15dB/km).

Scattering

• Fused silica's imperfections, created from glass's random molecular motion during cooling, cause stationary fluctuations in refractive index.
• Photons encountering these variations are scattered in different directions.
• If the total internal reflection condition is no longer met then the incident photons exits the fibre.
• Scattered photons do not lose energy or change wavelength.
• This type of scattering is called Rayleigh scattering.

Rayleigh Scattering

• Rayleigh scattering occurs when the scattering particle is much smaller than the wavelength of light.
• Attenuation caused by Rayleigh scattering is proportional to the inverse of the fourth power of the wavelength.
• Short wavelengths are scattered more strongly than long wavelengths.
• Less attenuation is observed in the infrared region compared to the ultraviolet region of the spectrum.
• The near-infrared region (1300nm and 1550nm) are therefore, preferred for communications.
• The theoretical lower limit for Rayleigh attenuation in silica glass is 0.15dB/km.

Bending Losses

• Light can escape a bent fibre if the bending angle exceeds a critical value.
• This is due to the change in the fibre's geometry, which can perturb conditions for total internal reflection.
• The rays will be refracted towards the cladding, and light is lost.
• Loss caused by bending is called bending loss.
• The bend radius at which an axial ray would exit the fibre is given by a specific formula.

Summary (Attenuation)

• Optical power in a fibre optic cable is attenuated by three types of loss mechanisms.
• Absorption: Photons with sufficient energy excite electrons/molecules, losing energy as heat.
• Scattering: Material imperfections scatter photons from core without energy loss.
• Bending: Light escapes the core if bending exceeds critical value, causing loss.

This quiz covers essential concepts related to modal dispersion and various types of dispersion in optical fibres. Explore how these phenomena affect pulse energy and bandwidth, as well as the loss mechanisms involved. Test your understanding of graded-index fibres and the effects of scattering in fibre optics.