Fiber Optics Propagation Lecture Presentation PDF

Topics to be covered  Planar waveguides – mirror and dielectric waveguides, number of modes, field distribution  Fibre optics (circular waveguides) – fibre types, number of modes, acceptance angle, numerical aperture  Dispersion – material, modal, waveguide  Loss mechanisms – absorption,...

Topics to be covered  Planar waveguides – mirror and dielectric waveguides, number of modes, field distribution  Fibre optics (circular waveguides) – fibre types, number of modes, acceptance angle, numerical aperture  Dispersion – material, modal, waveguide  Loss mechanisms – absorption, scattering, bending  A brief history  Early fibre optics in medicine: endoscopes  Lasers in 1960s: possible applications in telecommunications  High losses  In 1970, Charles Kao: removing impurities  Glass losses down to 2dB/km by 1975  Today: 0.15dB/km are possible  Types of optical fibre From Fundamentals of Photonics  There are three basic types of fibre optic cables:  Step-index multimode fibre  Single-mode fibre  Graded-index fibre  Elements of a step-index fibre optic cable From Wikipedia  Core (n1) with a circular cross-section surrounded by a cladding (n2), also with a circular cross-section.  Buffer: rubber/plastic sheath for protection  Fused silica glass (SiO2).  Titanium, Germanium, Boron.  Typical core:cladding diameter ratios are 8m:125m, 50:125, 62.5:125, 85:125 and 100:140  Total internal reflection  For total internal reflection, n1 > n2 and ray must hit the core-cladding boundary at angle greater than θc (where θc = 90-θ)  Critical angle also governs the acceptance angle α.  Third medium n0 is usually treated as air  Guided and unguided rays From Photonics and Lasers: An Introduction  Rays that continue to propagate down the fibre are in guided or propagating modes  When the ray angle is less than θc, the ray is refracted into the cladding and some energy is lost. After a few more reflections at this angle, all the ray energy finally leaks out of the core.  These rays that do not continue to propagate down the fibre are called unguided or non-propagating modes  Acceptance angle From Photonics and Lasers: An Introduction  Acceptance angle αmax defines a cone through which light entering the core will successfully undergo total internal reflection at the core-cladding boundaries  Rays from angles outside this cone may still enter the core but will soon vanish due to refraction into the cladding layer Derive of αmax  Numerical aperture  The maximum acceptance angle (αmax) into the fibre can be derived as:  Normally, n0 is the refractive index of free-space (i.e. n0=1) and we define the Numerical Aperture (NA) as:  Therefore, the maximum acceptance angle can be given as:  The numerical aperture describes the light-gathering capacity of the fibre optic cable e.g. if NA = 0.1, acceptance angle is just 5.7 degrees.  Fibre optic modes  When the wavelength and fibre diameter become comparable, ray theory has to be replaced with wave theory  Define a dimensionless parameter called the V Parameter  The V Parameter is directly proportional to the radius to wavelength ratio and the numerical aperture NA  The number of modes in a fibre optic cable with V >> 1, can be approximated by: 2𝜋𝑎 𝑤h𝑒𝑟𝑒 𝑉 = 𝜆0 √ 1 2 𝑛 2 − 𝑛 2 𝑎= 𝑓𝑖𝑏𝑟𝑒 𝑐𝑜𝑟𝑒𝑟𝑎𝑑𝑖𝑢𝑠 𝜆 0= 𝑓𝑟𝑒𝑒 𝑠𝑝𝑎𝑐𝑒 𝑤𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡h  Single-mode fibres  A fibre optic cable can only support one mode when:  In this condition, the fibre is called a single-mode fibre  All modes except for the fundamental mode are cut off  The cut-off wavelength (λc) is when the fibre supports just one mode:  What three ways are there for realising a single mode fibre? 4 2𝜋𝑎 𝑚𝑚𝑎𝑥 ≈ 2 𝑉 𝜋 2 𝑤h𝑒𝑟𝑒 𝑉 = 𝜆0 √ 1 2 𝑛 2 − 𝑛 2  Single-mode fibres - 2  Single-mode fibres are realised by either  reducing the core diameter  Increasing the wavelength  Reducing the difference between n1 and n2  The operating wavelength is normally dictated by other factors such as absorption and scattering  Making the difference between n1 and n2 too small would make the fibre ultra sensitive to bending  Normal technique for achieving single-mode operation is to reduce the core diameter to between 5m and 10m. Cladding is maintained at 60m to 100m for mechanical strength and to reduce bending  Graded-index fibre  Refractive index of the core n1 decreases with increasing radius.  Oscillatory propagation rather than a zigzag  Speed increases further away from core centre  of n1 profile unique to length of cable.  Reduce intermodal dispersion compared to standard step-index multimode fibres  Summary  Fibre optic cables can be described as single-mode step-index, multimode step-index or graded-index multimode  Fibres have a circular core surrounded by a cladding layer with a lower refractive index than the core  Acceptance angle and Numerical Aperture are used to describe the maximum light entry angle into the fibre  The number of modes in a multimode fibre is given by: 4 2 2a 2 m max  2 V where V  n1  n 22  0  A fibre becomes a single-mode fibre supporting only one mode when V Parameter (V) < 2.405  The refractive index of the core of a Graded-index fibres decreases with increasing radius. These fibres are designed to reduce dispersion