Introduction
Waveguides are fundamental to the design of fiber optic communications, laser systems, fiber lasers, photonic integrated circuits, and other systems where light is confined and directed by optical media. The confinement of light in waveguides may first be described by geometric optics using ray tracing, and later more accurately described by wave optics based upon Maxwell’s Equations. The combined points of view yield valuable insight into the development of engineering systems in which light is confined, and can be useful even in naturally occurring situations such as light propagation through living tissue.
Simple waveguides may be made by cladding a material with a high index of refraction with a material having a low index of refraction, providing total internal reflection when rays are incident upon the boundary at angles to the interface sufficiently shallow to experience total internal reflection. However, a situation of greater generality is one in which the index of refraction is continuously varying. One example is when the square of the index of refraction varies quadratically with the coordinate transverse to the optical axis. Materials with this index of refraction profile are called lenslike media. An analytical formulation of the ray path in lenslike media is constructed from a Lagrangian formulism, and the result is sinusoidal ray trajectories.
Figure 1. Index of refraction profile, and meridional ray path in parabolic index medium. (Ghatak, Eur. J. Phys.)
One example of practical devices modeled by such a profile is gradient-index optics (GRIN). GRIN optics are discrete optical components like lenses that have, similar to quadratic-index waveguides, a varying index of refraction in the radial d...
... middle of paper ...
...y equations yield a linear second-order differential equation analogous to a version of Hill’s equation called Ince’s equation. When the modulation strength is equal to zero, Ince’s equation is comparable to the harmonic oscillator, and linearized ray equations are found. The stability of rays passing straight down the optical axis to small perturbations is analyzed. Parameter regions are found for unstable ray trajectories in the perturbed system, and rays evolve exponentially fast away from the optical axis. Interestingly, the existence of such parameter regions is comparable to the existence of band gaps in solids and arises mathematically in the same way as a consequence of the theory of behavior of differential equations with periodic coefficients. This is called Floquet Theory whose counterpart in the realm of solid state physics is known as Bloch’s Theorem.
1. D. Halliday, R. Resnik & K. Krane, Physics, vol. 2, 4th ed. John Wiley & Sons Inc., 1992.
Serway, Jewett. Physics for Scientists and Engineers 6th Edition. Pomona: California State Polytechnic University. 2004.
...hich describes the angle at which a beam of X-rays of a particular wavelength diffracts from a crystalline surface. Bragg’s Law is as follows:
In September 1959 DiVita asked 2nd Lt. Richard Sturzebecher if he knew of a way to produce a strong glass fiber that would be capable of carrying a light signal. Sturzebecher had melted 3 triaxil glass systems together for his senior exam at Alfred University. In his exam, Sturzebecher had used SiO2, a glass powder produced by Corning. Whenever he had tried to look at the substance through a microscope he would end up with headache. Sturzebecher realized that these headaches came from the high amounts of white light produced from the microscopes light that was reflected through the eyepiece via the SiO2. SiO2 would be an ideal substance for transmitting strong light signals if it could be developed into a strong fibre.
Some Simple Optics Refraction Refraction occurs when light travels from one medium, crosses a boundary, and enters another medium of different properties. For example, light travels from air to water. The amount of refraction (or bending) can be calculated using Snell's Law. Refractor How Refractor Telescopes Work? The principle behind the refractive telescopes is the use of two glass lenses (objective lens and eyepiece lens) to gather and bend parallel light rays in a certain way so that the image fits the size of the eye's pupil.
1 David Halliday, Robert Resnick, and Jearl Walker, Fundamentals of Physics, Extended, 5th ed. (NewYork:Wiley, 1997) 361
Serway, Raymond A, and Robert J Beichner. Physics: For Scientists and Engineers. United States of
However optical signals have shorter wavelengths because the cables decrease the propagation speed (speed of light).
The concept of fiber optics is simple, yet it provides so many potentialities in the world of technology. Presently the world relies on fiber optical technology for its data and communications systems. The consumer can converse on the telephone and hear voices with clarity, as well as send and receive information on the Internet with ease. However, there still lay a sea of possibilities in this area of technology that has not yet been discovered.
Refraction of Light Aim: To find a relationship between the angles of incidence and the angles of refraction by obtaining a set of readings for the angles of incidence and refraction as a light ray passes from air into perspex. Introduction: Refraction is the bending of a wave when it enters a medium where it's speed is different. The refraction of light when it passes from a fast medium to a slow medium bends the light ray toward the normal to the boundary between the two media. The amount of bending depends on the indices of refraction of the two media and is described quantitatively by Snell's Law. (Refer to diagram below)
Tillery, B. (2012). Wave Motions and Sound. Physical science (9th ed., pp. 115-134). New York,
Refraction is a process that occurs when light travels between media of different optical density. Light travels at a speed of roughly 3.0 × 108ms-1 in a vacuum. A vacuum has a refractive index n=1.00. The speed at which the light is travelling will decrease as it moves into differently optically
Providing the basis of nineteenth century physics, Young's Double Slit Experiment proved that light was made up of waves. During Thomas Young’s time, it was very difficult to describe the behavior of light. The predominant theory was that light was made up of particles. However, in his experiment, Young was able to observe the interaction of light waves when passed through two slits, showing the wave-like nature of light. This report will cover the reasons for Young’s experiment, the experiment itself, and its implications.
Fiber optics is a new technology that uses rays of light instead of electricity to transmit information over optical fibers at very high speeds. The optical fibers are usually thin strands of glass that are combined into cables and used to send information and computer data in the form of pulses of light. The optical fibers provide much clearer transmission than conventional copper cable and satellite links. The world market for optical fiber continues to grow rapidly, with shipments increasing 14 percent from an estimated 7.0 million kilometers of fiber in 1990 to approximately 8.0 million in 1991. The demand for multimode fiber is predicted to continue to expand through the mid-1990s, with some market analysts indicating that 15 to 20 percent annual growth over the next three years is reasonable. Strong demand is expected for singlemode and multimode fiber to be used in cables for local area networks, telecommunications, cable television (CATV), and transoceanic fiber-optic systems.