| It is well-known that it is complex to describe optical polarization. Now polarized light is usually described by Stokes vector and Jones vector, and Mueller matrix is used to describe polarization properties of optical devices. However the mentioned methods all have limitations. The Stokes vector is the result of statistical average either in time domain or frequency domain. In frequency domain, it is only valid when Mueller matrix remains unchanged within the considered frequency band. When the frequency band is wider, it is necessary to consider its higher order components. In addition, Mueller matrix is a 4x4 matrix with 16 elements dependent on each other, but parameters being of pivotal role are not reflected intuitively in Mueller matrix. Quaternion is a mathematical concept proposed by William Rowan Hamilton, the famous Irish Mathematician, in 1843. Quaternion has its unique advantages to describe vectors. Therefore using Quaternion method to solve optical polarization has significant academic value.Polarization includes both phenomena of linear and nonlinear polarization. There have been many researches about the linear polarization, and less reports about the nonlinear polarization due to its complexity. In recent years, with the rapid development of high-speed optical communication technology, transmission rate of single wavelength can be over 100Gb/s. Polarization Multiplexing (PM) can double the bit rate with a single fiber, so it is one of the important methods to increase transmission capacity. While doubling the bit rate, PM also doubles the optical power in the fiber, and consequently the nonlinear polarization effect emerges. When using fiber as Raman amplifier or other amplifiers, the high power pump light will affect the signal light because of the nonlinear polarization evolution.To investigate various features of the optical fiber amplifiers, experimental system should be set up first. With the resource of C band, S band and L band using up, it is tendency to use U band (>1625nm). For now, techniques of U band semiconductor laser and detector have matured. Meanwhile fiber can have low loss in wide band 1200nm-1700nm because of the development of fiber manufacturing technology. Therefore U band optical amplifier becomes the key point to develope U band.First, we researched the fiber polarization properties using the quaternion method, and analyzed and measured the quaternion polarization properties of fiber. We also analyzed three-level cascaded each state ergodic polarization state generator, and deduced quaternion formula of three-level polarization controller and SOA. We studied polarization state jitter in polarization multiplexing system caused by nonlinear polarization effect, did numerical simulations of a 100 Gb/s polarization multiplexing system using NRZ and QPSK, and studied crosstalk of constellation. At last, we proposed and set up fiber Raman amplifier system using commercial single mode fiber to amplify signal light at 1.66μm in U band, and studied nonlinear polarization phenomenon of this kind of amplifier. Finally, we obtained some theories and simulation results.The innovative works are as the following in this paper:1. With the method of decomposing 2×2 matrix using Pauli matrix, a pare transformation between 2x2 matrix and quaternion is proposed, we obtained Jones quaternion and Stokes quaternion, and got the relationship between Jones quaternion and Stokes quaternion, while the latter can be described as 2 times of the product of the former and its Hermitian transpose. We got the quaternion with exponential expressions of the birefringence device and polarization dependent loss device. The complex scalar part of the exponential quaternion is a parameter independent on the polarization effect, whose real part is gain or loss and imaginary part is phase shift. The complex vector part of exponential quaternion is dependent of polarization, the direction of the vector is the rotation axis and the real part of the amplitude is polarization dependent phase shift and the imaginary part is the polarization dependent loss. Based on the above works, we obtained the quaternion expression when polarized light passed through the polarization devices, and derived quaternion Baker-Campbell-Hausdorff formula in condition of paraxial, which can be used in the polarization devices cascaded system where there is tiny difference between both rotation axes. Above-mentioned work indicates that the quaternion can precisely express various effects of polarization, and parameter of every effect has its corresponding item in the quaternion.2. We analyzed the quaternion polarization property using the quaternion theory, measured the fiber polarization quaternion. For the first time, proposed a three-point quaternion method, and measured the direction and magnitude of the vector part of the birefringence quaternion. By using quaternion Baker-Campbell-Hausdorff formula in paraxial condition, we proposed an five-point quaternion method to estimate the error in the detection of P-OTDR, and analyzed the error of actual measurement data. The results show that this method is obviously superior to MM method for the measurement of fiber polarization property. We also analyzed three-level cascaded all state ergodic polarization state generator, derived quaternion formula of three-level polarization controller. Experiments showed us the quaternion formula when SMF is pressed and when voltage changes. At last, we did theoretical research of quaternion method of polarization controller based on SOA, got quaternion formula of SOA, and obtained quaternion formula when polarized light passing through SOA after theoretical analysis.3. We studied the nonlinear polarization effects caused by the nonlinear polarization coupling in polarization multiplexing (PM) system, discovered that polarization multiplexing system based on NRZ has serious polarization jitter and noise, and found that there exist crosstalk between both multiplexing channels in the PM-QPSK system. Using quaternion method, we transformed the coupling nonlinear Schrodinger equation into quaternions coupling equation, then we transformed the nonlinear Schrodinger equation into a partial differential equation of a single function by using the property that the circular polarization quaternion is the product of a constant quaternion and a time and space dependent coefficient. We derived the general formula and time domain waveform of composite signal in polarization multiplexing system and the general formula of polarization jitter. With some simulations of a 100 Gb/s PM-NRZ system, we got the noise and the Stokes parameters of the output signal with its evolution on Poincare sphere. A prioritization scheme is proposed to suppress the noise. We also simulated the fiber nonlinear polarization in a 100 Gb/s PM-QPSK system, and discovered that there exist crosstalk between both multiplexing channels, which is like a revolving constellation with the rotation angle proportional to the intensity of input light signal.4. We proposed and set up a Fiber Raman Amplifier at 1.66um in U band using SMF. Its pumping source is a two-step pump structure:a 6.5W 980nm LD with multimode output serves as a primary pump, it pumps a high-power Yb3+-Er3+ codoped double-cladding fiber amplifier to output over 1W at 1550nm as the main pump of Fiber Raman Amplifier, to amplify the signal light at 1.66μm in U band. We did theoretical analysis of nonlinear polarization effect of Fiber Raman Amplifier, and derived gain formula of ideal fiber without natural birefringence. The results showed that the nonlinear polarization rotation will easily appear because of the very great pump power. |
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