The Mathematics inside the optical fibre
By Shawn Shen (Yr 13)
Introduction of Optical Fibres Developing a highly efficient communication system has always been one of the principal interests of human beings since ancient time. In ancient China, the army used smoke which was to light the wolves’ dung on the smoke tower along the great walls to send the message in order to defence or defend, furthermore, fireworks were used to send messages and pigeon were used to send letters. However, these kinds of communication systems was either time consuming or limited by short distance. Two hundred years ago, Samuel F.B Morse devised the first commercial telegraph service using wire cables which ushered in a new era in communication – electrical communication. The electrical communication is commonly used throughout the world and an increasing portion of the electromagnetic spectrum was utilized for conveying information from one place to another in the following years. However, entering the century which is called the century of explosion of information. The copper wire is no longer capable of transmitting such tremendous amount of information. Therefore, a great interest in optical communication was created in 1960 since optical frequencies are on the order of 5 × 10 14 Hz, which means the information capacity of lasers exceeds that of microwave systems by approximately 10 million TV channels. (Keiser, 1991) Charles Kuen Gao, who is known as the father fibre optic communication, discovered some certain physical properties of glass which laid the groundwork for high-speed data communication in the information age. Since then, more than 10 billion kilometre optical fibres were installed to make internet connection faster. Optical fibre, nowadays, has become the most widely used system to transfer information. To attain a more detailed understanding of the optical power propagation mechanism in the fibre, there are two methods. The first method is to use the geometrical optics such as concepts of light refraction and reflection to provide a clear picture of the propagation mechanisms. The second method, which involves solving Maxwell’s equations subject to the cylindrical boundary conditions of the fibre, treats light as an electromagnetic wave which propagates along the optical fibre waveguide. However, the geometrical approach is only valid when the ratio of the fibre radius to the wavelength is large. So when it comes to the analysis of single- mode fibres or problems involving interference or coherence phenomena, they must be dealt with by using electromagnetic theory.
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