Research On Gain And Loss In Optical Fiber Amplifiers With Huygens Principle

Optical fiber amplifiers are widely used in optical fiber communications and sensing.It is of great theoretical and practical value to study the interaction of light and micro-particles in fiber amplifiers.For the first time,the Huygens principle is applied to the research of the gain and loss in the erbium-doped fiber amplifier(EDFA)in this dissertation.Firstly,the Huygens wavelet and the wavelet envelope are analyzed mathematically.According to that the Huygens wavelet is the spherical wave solution of the wave equation,we obtain that the mathematical essence of the Huygens wavelet envelope is the transformation between different solutions of the wave equation.Based on this new understanding of the Huygens' principle,the expression of the Huygens wavelet is derived in a more concise manner,and the Huygens principle is proved by mathematical analysis.In this dissertation,the directionality,the amplitude and phase of the wavelet are obtained by the self-consistent method.Using the Poynting vector of electromagnetic waves and vector analysis,the tilt factor of Huygens wavelet is obtained.From the viewpoint that the phase of the stimulated emission is ahead of that of the incident light by ?/2,the gain of the stimulated emission of erbium ions is studied.In the process of optical gain,the phase of the stimulated emission of particle ensemble is the same as that of the incident light,which explains the gain in the optical fiber well,and the forward amplification characteristics of the fiber amplifier.Considering that the optical loss is equivalent to a negative gain,an expression of the absorption loss of the particles in the gain fiber is obtained.Using the Huygens wavelet as the primitive function,and representing the non-uniform refractive index regions in free space by microspheres,the losses of the Rayleigh scattering and the transmitted light are obtained.Subsequently,we extend the method above to the optical fiber,and use the microspheres whose refractive indexes vary abruptly and gradually,respectively,to represent the local non-uniform refractive index regions in the fiber.The losses of the Rayleigh scattering and the transmitted light are obtained in the two cases,respectively.