The Thermo-refractive Noise In Runtime Of Gauss Pulse Streams In Fiber

When light signals traveling along the fiber, they will lose energy continually and heat the fiber. The fluctuation of lost energy induces the fluctuations of both temperature and volume of the fiber , which excites the fluctuation of fiber refractive index and induces thermo-refractive noise.Soliton is one kind of light pulses, which keeps the same shape, amplitude and velocity in its transmission. An optical soliton storage ring is a close fiber loop, which has some kinds of optical apparatuses that insure the soliton runs steadily. The optical soliton storage ring is generator of optical solitons, it can be used to measure the long distance run of the optical solitons. Recently, the optical soliton storage ring is used to detect weak signals too.Recently, an optical soliton storage ring was designed to be a ground detector measuring gravitational red-shift. In detection, the gravitational red-shift is recorded by the difference of soliton runtime, that is the difference of group delays of solitons in storage rings. The optical soliton storage ring is used to detect gravitational waves too. Both gravitational red-shift and gravitational waves are very weak signals and the detection of them are disturbed more easily. So, one has to analyze various perturbations including feeble noises in the detection more detailedly, thermo-refractive noise is such a feeble noise. When a light Gauss pulse stream runs along an infinitely straight fiber with an equi-span, the pulse power will lose part of its energy. And it will increase the temperature of the fiber and induce the fluctuations of the refractive index, as a result it induces thermo-refractive noise. It influences the transmission of light signals by an additive phase delay or group delay.Thermo-refractive noise will influence the runtime of optical solitons in precise measure with optical solitons. We will study this influence by Gauss pulse.The pulse power decides the thermal conduction in the transmission of light pulse, and the shape of the pulse is irrespective to the thermal conduction. So, when we study the upper limit of thermo-refractive noise induced by pulse streams, we can use Gauss pulse streams to substitute optical soliton strings. Though the Gauss pulse will be wider in the transmission as the result of dispersion, but we will ignore the influence of dispersion in order to model the transmission of optical solitons in our paper.This article is divided into four parts mainly.In chapter one, we introduce the detecting of weak signals by optical soliton storage rings.In chapter two, we introduce the thermo-refractive noise.In chapter three, we introduce a 1-Dimension(1-D) thermal conduction equation of the fiber and its solution. In the last chapter, we introduce a 3-Dimension(3-D) thermal conduction equation of the fiber and its solution.When a Gauss pulse stream runs in an infinitely straight fiber, we give the 1-Dimension(1-D) and 3-Dimension(3-D) thermal conduction equation of the fiber with a random source. Through strict theoretical analyse and detailed calculations , we obtain the upper limit of the mean square fluctuation of the fiber temperature, and the relation between the upper limit of the total runtime and the bit rate of the pulse stream is determined too. The result is adapted to other light pulse. Through this relation one can choose right bite rate according to the change of the runtime and the sensitivity of the measurement. It avails to design a measurement by using pulse streams involving optical solitons in storage rings .