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

Abstract

Analog modulation of wireless microwave/radio waves as well as optical waves through multiplexing is well established in practice due to technological breakthroughs. Such modulation techniques are well established in practice due to technological breakthroughs. The basic methods of modulation of a carrier wave are amplitude modulation (Amplitude Shift Keying (ASK)), frequency modulation (Frequency Shift Keying (FSK)), and phase modulation (Phase Shift Keying (PSK)). Quadrature Amplitude Modulation (QAM) is a combination of amplitude and phase modulation. Among these methods, simple amplitude modulation is particularly suitable and practical in fiber-optic communication, as extraneous errors are prevented by the protective jacket of the fiber cable—a scenario that is not applicable in wireless communication. The waveguide action in a cylindrical optical fiber enables the development of a theoretical model of light propagation undergoing amplitude modulation. This theory is presented in this paper for a step-index fiber consisting of a homogeneous core with a cladding of slightly lower refractive index. The input signal is assumed to be a sequence of N bits, which is multiplexed onto the carrier light wave, and a general formula is developed for the field intensity determined from the axial component of the Hertz vector of the associated electromagnetic wave at a receiving point. The expression of that field is represented in the form of a Fourier integral, which is evaluated using the Fast Fourier Transform (FFT) for simple numerical cases. The theory covers both single-mode fibers, which support only the fundamental propagation mode, as well as multimode fibers of larger diameters. The theory provides the characteristics of the wave at a distant receiving station when the input is in bit form, for which demodulation techniques are available. In addition, the theory provides a method of serial transmission of multiple bits in a sequence, provided that suitable demodulation techniques are available at the receiver end. A simple measure based on maximum field strength is suggested in the paper.