On the Theory of Digital Modulation of Light Transmitted Through a Step-Index Optical Fiber

Abstract

Analog modulation of wireless micro/radio waves as well as optical light waves by multiplexing. An input signal is well established in practice due to technological breakthroughs. The basic methods of modulation of a carrier wave are amplitude modulation Amplitude Shifted Keying (ASK), frequency modulation Frequency Shifted Keying (FSK), and phase modulation Phase Shifted Keying (PSK). Quadrature Amplitude Modulation (QAM) is a combination of amplitude and phase modulation. Among these methods, the simple amplitude modulation is suitable and of practical use in fiber-optic communication as extraneous errors are prevented are prevented by the jacket of the cable containing the fiber-a scenario not applicable in wireless communication. The wave-guide action in a cylindrical optical fiber enables the development of a theoretical model of light propagation which has undergone amplitude modulation. This theory is presented in this paper for a step-index fiber consisting of a homogeneous core with a cladding of slightly less refractive index. The input signal is assumed to be a batch of N bits, which is multiplexed to the carrier light wave, and a general formula is developed for the field intensity measured by the axial component of the Hertz vector of the associated electromagnetic wave at a receiving point. The expression of that field is found in the form of a Fourier integral, which is computed by Fast Fourier Transform (FFT) for simple numerical cases. The theory covers both single mode fibers which can transmit only the fundamental mode of propagation, as well as multimode fibers of greater diameters. The theory provides the character of the wave at a distant receiving station, when the input is in bits for which demodulation techniques are available. In addition the theory provides a method of serial transmission of a number of bits in a batch, provided suitable demodulation technique is available at the receiver end. A simple maximum field strength measure is suggested in the paper.