RAY THEORY AND OPTICAL WAVEGUIDE BY DR. NEENA GUPTA Assistant Professor E&EC Deptt. Punjab Engineering College,Deemed University,CHANDIGARH

Overview  Introduction  Total internal reflection  Acceptance Angle  Numerical Aperture  Skew Rays

Introduction  The transmission of light via dielectric waveguide structure was first proposed and investigated at the beginning of twentieth century.  Initially a waveguide consist of transparent dielectric rod typically of silica glass with a refractive index of around 1.5,surrounded by air was proposed.  Due to excessive losses at any discontinuities of the glass air interface,clad dielectric was proposed.  In this structure losses were 1000 db/km  These losses were reduced to 4.2 db/km by purification of materials used.

 After that fiber with wavelength 1.55 with losses as low as 0.2 db/km have been investigated.  At present the best developed fiber with losses around 0.01 db/km at wavelength 2.55 is based on fluoride glass.

Core cladding cross section

Total Internal Reflection  The refractive index of medium is defined as the ratio of the velocity of light in a vacuum to the velocity of light in the medium.  More the medium is dense, lesser will be the velocity of light.  When a ray is incident on the interface between two dielectric of different refractive index, refraction occurs as shown below.  Snell’s law of refraction

Critical Angle  The incidence angle at which angle of refraction becomes equal to 90 degree i.e. parallel to interface ; is called as critical angle.  As the angle of incidence becomes greater than critical angle, total internal reflection takes place.

Refraction & total Internal Reflection

Acceptance Angle  The cone of acceptance of light into the core is defined by the acceptance angle of the fibre, whose maximum value can be calculated directly by:

 The ray entering with angle with core axis makes critical angle at core-cladding interface.  The ray entering with angle greater than with core axis makes angle less than critical angle at core-cladding interface. Thus will not be totally internally reflected.  The angle is called acceptance angle.

Numerical Aperture  The numerical aperture measures the light gathering capacity of a fibre and is the sine of the maximum acceptance angle. Derivation:

From Snell’s law Consider the angle which is greater than critical angle. refractive index of air refractive index of core refractive index of cladding

Since Another important parameter is the NORMALIZED REFRACTIVE INDEX DIFFERENCE whose relation with the numerical aperture is:numerical aperture

 If NA is very large multi path dispersion,intermodal dispersion occurs.  As different ray travels along path of different length & they disperse at the output end. (They may travel at same speed). An impulse may broaden due to different path lengths.  Shortest path for=0, equal to fiber length L Then longest path has length if v=c/n 1 The time delay & should be less than the allocated bit slot

It tells the property and capacity of various fibers Inter modal dispersion reduced by graded index fiber because ray velocity changes due to change in Refractive Index.

SKEW RAYS  Skew rays transmit through the fiber without touching the fiber axis.  These rays follow the helical path through the fiber.  Skew rays scatter out of the core at bends and irregularities and do not contribute significantly.

 The ray 1 takes shortest path but travels most slowly & 3 takes longest path but travels most fast & arrive at o/p at same time.  Acceptance angle condition for skew rays are:

And in case of the fiber in air (n0 =1