Beam propagation in an active nonlinear graded-index fiber

A theoretical model is developed by exploiting the variational technique to investigate the evolution of an optical beam inside an optically pumped graded-index fiber amplifier. The variational analysis is a semi-analytical method that provides us with a set of coupled ordinary differential equations for the beam's four parameters. Numerical solution of these equations is much faster compared to the underlying multidimensional nonlinear wave equation. We compare the results of the variational and full numerical simulations for the two pumping schemes used commonly for high-power fiber amplifiers. In the clad-pumping scheme, the use of a relatively wide pump beam results in a nearly uniform gain all along the fiber. In the case of edge pumping, a narrower pump beam provides gain that varies both radially and axially along the fiber's length. In both cases, the variational results are found to be in good agreement with time-consuming full numerical simulations. We also derive a single equation for the beam's width that can predict amplification-induced narrowing of the signal beam in most cases of practical interest.Comment: 6 pages, 5 figure

Computational Modeling of Semiconductor Dynamics at Femtosecond Time Scales

The Interchange No. NCC2-5149 deals with the emerging technology of photonic (or optoelectronic) integrated circuits (PICs or OEICs). In PICs, optical and electronic components are grown together on the same chip. To build such devices and subsystems, one needs to model the entire chip. PICs are useful for building components for integrated optical transmitters, integrated optical receivers, optical data storage systems, optical interconnects, and optical computers. For example, the current commercial rate for optical data transmission is 2.5 gigabits per second, whereas the use of shorter pulses to improve optical transmission rates would yield an increase of 400 to 1000 times. The improved optical data transmitters would be used in telecommunications networks and computer local-area networks. Also, these components can be applied to activities in space, such as satellite to satellite communications, when the data transmissions are made at optical frequencies. The research project consisted of developing accurate computer modeling of electromagnetic wave propagation in semiconductors. Such modeling is necessary for the successful development of PICs. More specifically, these computer codes would enable the modeling of such devices, including their subsystems, such as semiconductor lasers and semiconductor amplifiers in which there is femtosecond pulse propagation. Presently, there are no computer codes that could provide this modeling. Current codes do not solve the full vector, nonlinear, Maxwell's equations, which are required for these short pulses and also current codes do not solve the semiconductor Bloch equations, which are required to accurately describe the material's interaction with femtosecond pulses. The research performed under NCC2-5149 solves the combined Maxwell's and Bloch's equations

Nonlinear Propagation in Multimode and Multicore Fibers: Generalization of the Manakov Equations

This paper starts by an investigation of nonlinear transmission in space-division multiplexed (SDM) systems using multimode fibers exhibiting a rapidly varying birefringence. A primary objective is to generalize the Manakov equations, well known in the case of single-mode fibers. We first investigate a reference case where linear coupling among the spatial modes of the fiber is weak and after averaging over birefringence fluctuations, we obtain new Manakov equations for multimode fibers. Such an averaging reduces the number of intermodal nonlinear terms drastically since all four-wave-mixing terms average out. Cross-phase modulation terms still affect multimode transmission but their effectiveness is reduced. We then verify the accuracy of our new Manakov equations by transmitting multiple PDM-QPSK signals over different modes of a multimode fiber and comparing the numerical results with those obtained by solving the full stochastic equation. The agreement is excellent in all cases studied. A great benefit of the new equations is to reduce the computation time by a factor of 10 or more. Another important feature observed is that birefringence fluctuations improve system performance by reducing the impact of fiber nonlinearities. Finally multimode fibers with strong random coupling among all spatial modes are considered. Linear coupling is modeled using the random matrix theory approach. We derive new Manakov equations for multimode fibers in that regime and show that such fibers can perform better than single-modes fiber for large number of propagating spatial modes.Comment: Submitted to journal of lightwave technology on the 17-Jul-2012. Ref number: JLT-14391-201

Spatial beam dynamics in graded-index multimode fibers under Raman amplification:a variational approach

We investigate the spatial beam dynamics inside a multimode graded-index fiber under Raman amplification by adopting a semi-analytical variational approach. The variational analysis provides us with four coupled ordinary differential equations that govern the beam's dynamics under Raman gain and are much faster to solve numerically compared to the full nonlinear wave equation. Their solution also provides considerable physical insight and allows us to study the impact of important nonlinear phenomena such as self-focusing and cross-phase modulation. We first show that the variational results corroborate well with full numerical simulations and then use them to investigate the signal's dynamics under different initial conditions such as the initial widths of the pump and signal beams. This allows us to quantify the conditions under which the quality of a signal beam can improve, without collapse of the beam owing to self-focusing. While time-consuming full simulations may be needed when gain saturation and pump depletion must be included, the variational method is useful for gaining valuable physical insight and for studying dependence of the amplified beam's width and amplitude on various physical parameters in a faster fashion.Comment: 7 pages, 6 figure

Nonlinear optical phenomena in silicon waveguides: modeling and applications

Several kinds of nonlinear optical effects have been observed in recent years using silicon waveguides, and their device applications are attracting considerable attention. In this review, we provide a unified theoretical platform that not only can be used for understanding the underlying physics but should also provide guidance toward new and useful applications. We begin with a description of the third-order nonlinearity of silicon and consider the tensorial nature of both the electronic and Raman contributions. The generation of free carriers through two-photon absorption and their impact on various nonlinear phenomena is included fully within the theory presented here. We derive a general propagation equation in the frequency domain and show how it leads to a generalized nonlinear Schrodinger equation when it is converted to the time domain. We use this equation to study propagation of ultrashort optical pulses in the presence of self-phase modulation and show the possibility of soliton formation and supercontinuum generation. The nonlinear phenomena of cross-phase modulation and stimulated Raman scattering are discussed next with emphasis on the impact of free carriers on Raman amplification and lasing. We also consider the four-wave mixing process for both continuous-wave and pulsed pumping and discuss the conditions under which parametric amplification and wavelength conversion can be realized with net gain in the telecommunication band

Maximization of Gain in Slow-Light Silicon Raman Amplifiers

We theoretically study the problem of Raman gain maximization in uniform silicon photonic-crystal waveguides supporting slow optical modes. For the first time, an exact solution to this problem is obtained within the framework of the undepleted-pump approximation. Specifically, we derive analytical expressions for the maximum signal gain, optimal input pump power, and optimal length of a silicon Raman amplifier and demonstrate that the ultimate gain is achieved when the pump beam propagates at its maximum speed. If the signal’s group velocity can be reduced by a factor of 10 compared to its value in a bulk silicon, it may result in ultrahigh gains exceeding 100 dB. We also optimize the device parameters of a silicon Raman amplifier in the regime of strong pump depletion and come up with general design guidelines that can be used in practice