Optical Fiber Communications Lecture 2 Light Propagation Light Propagation

2 Wave Nature of Light Newton believed in the particle theory of light. He explained the straight-line casting of sharp shadows of objects placed in a light beam. but he could not explain the textures of shadows Wave theory: Explains the interference where the light intensity can be enhanced in some places and diminished in other places behind a screen with a slit or several slits. The wave theory is also able to account for the fact that the edges of a shadow are not quite sharp. This theory describes: Propagation, reflection, refraction and attenuation G Ekspong, Stockholm University, Sweden, 1999.

3 Wave Nature of Light - contd James Clerk Maxwell His mathematical theory of electromagnetism led to the view that light is of electromagnetic nature, propagating as a wave from the source to the receiver. 1880s Heinrich Hertz Discovered experimentally the existence of electromagnetic waves at radio-frequencies Max Planck, Neils Bohr and Albert Einstein Invoked the idea of light being emitted in tiny pulses of energy Wave theory does not describe the absorption of light by a photosensitive materials

4 Particle Nature of Light Light behavior can be explained in terms of the amount of energy imparted in an interaction with some other medium. In this case, a beam of light is composed of a stream of small lumps or QUANTA of energy, known as PHOTONS. Each photon carries with it a precisely defined amount of energy defined as: W p = h*fJoules (J) where;h = Plank's constant = x J.s, f = Frequency Hz The convenient unit of energy is electron volt (eV), which is the kinetic energy acquired by an electron when accelerated to 1 eV = 1.6 x J. Even although a photon can be thought of as a particle of energy it still has a fundamental wavelength, which is equivalent to that of the propagating wave as described by the wave model. This model of light is useful when the light source contains only a few photons.

5 Electromagnetic Spectrum

6 Electromagnetic Radiation Carries energy through space (includes visible light, dental x-rays, radio waves, heat radiation from a fireplace) The wave is composed of a combination of mutually perpendicular electric and magnetic fields the direction of propagation of the wave is at right angles to both field directions, this is known as an ELECTROMAGNETIC WAVE EM wave move through a vacuum at 3.0 x 10 8 m/s ("speed of light") Speed of light in a vacuum

Light as an Electromagnetic Wave An electromagnetic wave consists of two fields. An electric field and a magnetic field. Both of these fields have a direction and a strength (or amplitude). An electromagnetic wave consists of two fields. An electric field and a magnetic field. Both of these fields have a direction and a strength (or amplitude). Within the electromagnetic wave the two fields (electric and magnetic) are oriented at precisely 90° to one another. The fields move (by definition at the speed of light) in a direction at 90° to both of them! In three dimensions you could consider the electric field to be oriented on the y-axis, and the magnetic field on the x- axis. Direction of travel would then be along the z-direction. Within the electromagnetic wave the two fields (electric and magnetic) are oriented at precisely 90° to one another. The fields move (by definition at the speed of light) in a direction at 90° to both of them! In three dimensions you could consider the electric field to be oriented on the y-axis, and the magnetic field on the x- axis. Direction of travel would then be along the z-direction.

Continued The key here is that we have two fields and they oscillate in phase. That is the electric and magnetic fields reach their peaks and their nulls at exactly the same time (and place). The rate of oscillation is the frequency of the wave. The key here is that we have two fields and they oscillate in phase. That is the electric and magnetic fields reach their peaks and their nulls at exactly the same time (and place). The rate of oscillation is the frequency of the wave. The distance traveled during one period of oscillation is the wavelength. The distance traveled during one period of oscillation is the wavelength.

10 One Dimensional EM Wave For most purposes, a travelling light wave can be presented as a one-dimensional, scalar wave provided it has a direction of propagation. Such a wave is usually described in terms of the electric field E. A plane wave propagating in the direction of z is: The propagation constant (or wave number) Wavelength EoEo Phase z n = Propagation medium refractive index Phase velocity

Wave optics

Waves of different frequencies interfere to form a localized pulse if they are coherent

Polarization If we have an electromagnetic field with the electric field in the vertical position (in relation to some arbitrary axis) then we could have another electromagnetic field with the electric field in the horizontal orientation (in relation to the same axes). If we have an electromagnetic field with the electric field in the vertical position (in relation to some arbitrary axis) then we could have another electromagnetic field with the electric field in the horizontal orientation (in relation to the same axes). When this happens the two electromagnetic waves are orthogonal to one another! That is, they are independent and do not interfere with each other. When this happens the two electromagnetic waves are orthogonal to one another! That is, they are independent and do not interfere with each other. It is also clear that any electromagnetic wave that is oriented between what we have called “vertical” and “horizontal” can be resolved as two components (one in each of the orthogonal directions). It is also clear that any electromagnetic wave that is oriented between what we have called “vertical” and “horizontal” can be resolved as two components (one in each of the orthogonal directions).

Polarization The orientation of the electromagnetic field is referred to as “polarization”. The orientation of the electromagnetic field is referred to as “polarization”. The established convention when discussing polarization of electromagnetic fields is to refer to the direction of the electric field with respect to some plane or boundary towards which the wave is headed. The established convention when discussing polarization of electromagnetic fields is to refer to the direction of the electric field with respect to some plane or boundary towards which the wave is headed. At any instant in time the fields are oriented in a particular direction (vertical or horizontal or somewhere in between). At any instant in time the fields are oriented in a particular direction (vertical or horizontal or somewhere in between). The field orientations can also change over time and we get what are called “circular” and “elliptical” polarizations. The field orientations can also change over time and we get what are called “circular” and “elliptical” polarizations.

These polarizations occur when the moving fields rotate during their travel. These polarizations occur when the moving fields rotate during their travel. Circular polarization results when the direction of the electric field rotates through 360° during one wavelength. Of course the associated magnetic field rotates with it. This is illustrated in Figure 5. Elliptical polarization results when the period of rotation of the fields is not the same as the wavelength. Circular polarization results when the direction of the electric field rotates through 360° during one wavelength. Of course the associated magnetic field rotates with it. This is illustrated in Figure 5. Elliptical polarization results when the period of rotation of the fields is not the same as the wavelength. Actually, circular and elliptical polarizations result when the propagation speed of the two orthogonal polarizations are slightly different (usually caused by the material having a slightly different refractive index in each polarization). Actually, circular and elliptical polarizations result when the propagation speed of the two orthogonal polarizations are slightly different (usually caused by the material having a slightly different refractive index in each polarization).

Classification of Optical Fiber Three common type of fiber in terms of the material used: Glass core with glass cladding-all glass or silica fiber Glass core with plastic cladding -plastic cladded /coated silica (PCS) Plastic core with plastic cladding -all plastic or polymer fiber

All glass fiber The refractive index range of glass is limited which causes the refractive index difference n 1 -n 2 to be small. This small value then reduces the light coupling efficiency of the fiber, i.e. large loss of light during coupling. The attenuation is the lowest compared to the other two fibers making it suitable for long and high capacity. Typical size: 10/125 µm, 62.5/125 µm, 50/125 µm and 100/140µm.

Plastic Clad Silica (PCS) ÙThis fiber have higher loss than the all glass fiber and is suitable for shorter links. ÙNormally, the range of refractive index achievable with plastic fibers are large. ÙA larger range for the value of refractive index difference. Light coupling efficiency is better than all-glass. Typical size: 62.5/125 µm, 50/125 µm, 100/140µm and 200µm.

All-plastic fiber  This type has the highest transmission loss.  Normally used for very short links.  Large core size,therefore light coupling efficiency is high  The core size can be as large as 1mm.

Basic Optical Laws and Definitions Refractive Index The ratio of the speed of light in a vacuum to that in matter is known as the refractive index or index of refraction n of the material and is given by Typical values of n are 1.00 for air, 1.33 for water, 1.45 for silica glass 2.42 for diamond. C: Speed of light in vacuum v : speed of light in matter

Reflection of light Some part of the light reflected when strikes on a surface Some part of the light reflected when strikes on a surface Laws of reflection of light Laws of reflection of light Angle of incident is equal to angle of reflectionAngle of incident is equal to angle of reflection The incident ray, the normal and the reflected ray all lies in same directionThe incident ray, the normal and the reflected ray all lies in same direction Refraction and reflection

Refraction of light When light enters from one medium to other medium When light enters from one medium to other medium Direction and velocity are changedDirection and velocity are changed It is called refraction of lightIt is called refraction of light When light passes from rare to dense medium, it bends towards the normalWhen light passes from rare to dense medium, it bends towards the normal When light passes from dense to rare medium, it bends away from the normalWhen light passes from dense to rare medium, it bends away from the normal Refraction and reflection

Example Find the fraction of incident light reflected at normal incidence from the interface between air and fused silica (1.45). Find the fraction of incident light reflected at normal incidence from the interface between air and fused silica (1.45). Let R indicate the reflected power Let R indicate the reflected power R=[(1.45-1) /(1.45+1)] 2 R=[(1.45-1) /(1.45+1)] 2 R= or 3.37% R= or 3.37% 96.63% transmitted 96.63% transmitted Fresnel reflection law Determines the fraction of light reflected as a function of the incident ray as well as the amount of light refracted or transmitted into the medium

Refraction of light Law of refraction isLaw of refraction is The incident ray, the normal, and the refracted ray at the point of incident all lies in the same plane. The incident ray, the normal, and the refracted ray at the point of incident all lies in the same plane. The ratio of the sine of angle incidence to the sine of angle of refraction is always constant The ratio of the sine of angle incidence to the sine of angle of refraction is always constant This ratio is called refractive indexThis ratio is called refractive index Refraction and reflection

Snell's Law Snell's Law Snell discovered the relationship between the refractive index of the materials and the sine of the angles as:Snell discovered the relationship between the refractive index of the materials and the sine of the angles as: Refraction and reflection Light rays incident on high to low refractive index interface (e.g. glass-air)

Critical Angle, Ө c If the angle of refraction is 90 then it is equal to 1 so

Example Light ray proceeds from air (n 1 =1) into glass (n 2 =1.5).find transmission angle when : Light ray proceeds from air (n 1 =1) into glass (n 2 =1.5).find transmission angle when : 1. Ө 1 = 0 o 2. Ө 1 =15 o Assume that this second boundary is parallel to first the first one find the direction of the transmitted ray.

Example Calculate the angles of refraction Calculate the angles of refraction The first material has a refractive index of 1.51 and the angle of incidence is 38°and the second material has a refractive index of The first material has a refractive index of 1.51 and the angle of incidence is 38°and the second material has a refractive index of Solution: Solution: Starting with Snell’s law:

Example A light ray is traveling in a transparent material of refractive index 1.51 and approaches a second material of refractive index Calculate the critical angle.

H.W A ray of light in a transparent material of refractive index 1.5 is approaching a material with a refractive index of At the boundary, the critical angle is: A ray of light in a transparent material of refractive index 1.5 is approaching a material with a refractive index of At the boundary, the critical angle is: (a) 90° (b) 9.4° (c) 75.2° (d) 80.6°

Total internal reflection Total internal reflection When light passes from denser medium to rarer medium it bends away from the normalWhen light passes from denser medium to rarer medium it bends away from the normal The incident angle for which angle of refraction is 90° is called critical angleThe incident angle for which angle of refraction is 90° is called critical angle If incident angle becomes more than critical angle all the light will reflect back to the same denser mediumIf incident angle becomes more than critical angle all the light will reflect back to the same denser medium Such a phenomenon is called total internal reflectionSuch a phenomenon is called total internal reflection Refraction and reflection

Optical fiber modes and configurations Fiber Structures Cross sections of a generic fiber structure showing a core, a cladding, and a buffer coating

Core 1.Light propagates along the core of the fiber. 2.Core material is highly pure silica SiO 2 and is surrounded by glass cladding. Cladding 1.Cladding reduces scattering loss that results from the dielectric discontinuities at the core surface. 2.It adds mechanical strength to the fiber 3.It protects the core from absorbing surface contaminants with which it could come in contact.

Acceptance angle Acceptance angle The entering rays which have the angle greater than θ c can be transmitted in optical fiber.The entering rays which have the angle greater than θ c can be transmitted in optical fiber. As the fiber is Circular, so angle is applicable in two dimensions and would look like a cone.As the fiber is Circular, so angle is applicable in two dimensions and would look like a cone. The range of incident angles which can be used for total Internal Reflection is called Cone of acceptance.The range of incident angles which can be used for total Internal Reflection is called Cone of acceptance. Ray Optics

Cone of acceptance Cone of acceptance The cone of acceptance is the angle within which the light is accepted into the core and is able to travel along the fiber. The cone of acceptance is the angle within which the light is accepted into the core and is able to travel along the fiber. Calculating the cone of acceptance was no easy job and it would be nice to find a more straightforward way of finding it. Luckily there is one and it involves a property of the fiber called the numerical aperture. Calculating the cone of acceptance was no easy job and it would be nice to find a more straightforward way of finding it. Luckily there is one and it involves a property of the fiber called the numerical aperture. Ray Optics

Numerical Aperture Numerical Aperture It is measure of fiber’s light gathering ability. This represent the coupling of light into the fiber core. It is measure of fiber’s light gathering ability. This represent the coupling of light into the fiber core. The formula for the numerical aperture is based on the refractive indices of the core and the cladding. The formula for the numerical aperture is based on the refractive indices of the core and the cladding. Ray Optics

A silica optical fiber with a core diameter large enough to consider by ray theory analysis, and it has a core refractive index of 1.5 and a cladding refractive index of A silica optical fiber with a core diameter large enough to consider by ray theory analysis, and it has a core refractive index of 1.5 and a cladding refractive index of Determine: (a) The critical angle at the core-cladding interface Determine: (a) The critical angle at the core-cladding interface (b) The NA for the fiber (b) The NA for the fiber (c) The acceptance angle in air for the fiber (c) The acceptance angle in air for the fiber Example