Light Propagation in Waveguides (Loughborough University) PDF

Module structure  Fundamentals of light  Propagation of light in waveguides  Light interaction with matter  Laser  Photobiology basics  Biophotonics applications  Bioimaging  Tissue engineering From Fundamentals of Photonics ...

Module structure  Fundamentals of light  Propagation of light in waveguides  Light interaction with matter  Laser  Photobiology basics  Biophotonics applications  Bioimaging  Tissue engineering From Fundamentals of Photonics  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  The origin of the ‘light pipe’  In 1854, John Tyndall was the first to publically demonstrate light guided by total internal reflection inside a curved dielectric cylinder  His dielectric cylinder was a free-flowing stream of water falling from the side of a water tank. Total internal reflection occurred at the water-air interface. From Wikipedia  In his demonstration, light focused on the exit hole was successfully guided by the water column and illuminated the water collecting bowl.  The modern equivalent of the light pipe is the flexible glass fibre optic cable. This has revolutionized modern communications and has many applications in Biophotonics.  Endoscopes for delivering light inside the body,  Delivering light to and collecting light from Biosensors  Laser surgery  Wave propagation in a planar waveguide  Fibre optic cables well known but complex.  Two parallel mirrors simpler and easier  Dielectrics closer to fibre optics  EM Wave propagating between two perfect mirrors From Fundamentals of Photonics  Ray-optics is not sufficient to describe how light propagates between the two mirrors.  Use wave-optics :- A monochromatic TEM plane wave propagates in the yz plane down the waveguide. The E-field is x polarized  The plane wave makes an angle θ with the surface as it zigzags between the top and bottom mirrors  EM Wave propagating between two perfect mirrors From Fundamentals of Photonics  We impose a self-consistency condition such that the wave reproduces itself after reflecting off the top and bottom mirrors. i.e. there should be only two distinct plane waves  Waves that can fulfil this From Fundamentals of Photonics condition are called modes of the waveguide  “Modes are fields that maintain the same transverse distribution and polarization at all locations along the waveguide” From Fundamentals of Photonics From Fundamentals of Photonics  EM Wave propagating between two perfect mirrors - 2 From Fundamentals of Photonics  To fulfil this self-consistency, the phase shift encountered by the wave travelling from A to B must be equal to or differ exactly by an integer multiple of , from that experienced by the wave travelling from A to C.  The self-consistency condition is only fulfilled at certain bounce angles.  Known as waveguide modes  Number of modes  Since only certain angles create modes between the two mirrors, there has to be a limited number of achievable modes  To find the maximum number of modes, set sinθm less than 1: Why is it n2  Total internal reflection ensures the light is guided along the middle block.  Rays at angles less than the critical angle refract (and reflect), loosing some of their power at each interface and finally vanish  EM Wave propagating in a dielectric slab  We use TEM waves in a similar fashion to that of the two mirror waveguide.  As before a self-consistency condition is required for the waves to regenerate.  New factors to consider are the refractive index of the materials, the phase shift that occurs at the interface between and , and the critical angle which ensures total internal reflection 𝜆0 𝑐 𝜆= 𝑣= 𝑛1 𝑛1  Number of modes  The number of TE modes is given by  NOTE the resulting value for mmax has to be increased to the nearest integer. i.e. mmax has to be a whole integer. For example, if the calculation yielded 0.98, 1 and 1.95, the results should be rounded up to 1, 2, and 2 respectively  When , only one mode is allowed  No matter how thin the dielectric is, there will be a m=0 mode supported in the waveguide. This is a single-mode waveguide.  Field distribution From Fundamentals of Photonics  Unlike in the two mirror waveguide, the fields at the dielectric boundaries are not zero.  Instead, the waves decay exponentially as they travel into n2.  These waves are called evanescent waves  The profiles of the fields inside n1 are similar to those in the two mirror waveguide. For each mode, there are m zero points and m+1 maxima  Summary  Light travels in modes in waveguides. Light wave fronts entering the waveguide at specific angles will reinforce themselves and will continue to propagate  In a two parallel mirror waveguide:  Max. number of modes by:  The forward velocity of a particular mode is given by:  In a waveguide, the max. number of modes by:  Energy in cladding: evanescent wave