Parabolic pulse propagation in mean-zero, dispersion-managed transmission systems and mode-locked laser cavities

Self-similarity is a ubiquitous concept in the physical sciences used to explain a wide range of spatial- or temporalstructures observed in a broad range of applications and natural phenomena. Indeed, they have been predicted or observed in the context of Raman scattering, spatial soliton fractals, propagation in the normal dispersion regime with strong nonlinearity, optical amplifiers, and mode-locked lasers. These self-similar structures are typically long-time transients formed by the interplay, often nonlinear, of the underlying dominant physical effects in the system. A theoretical model shows that in the context of the universal Ginzburg-Landau equation with rapidly-varying, mean-zero dispersion, stable and attracting self-similar pulses are formed with parabolic profiles: the zero-dispersion similariton. The zero-dispersion similariton is the final solution state of the system, not a long-time, intermediate asymptotic behavior. An averaging analysis shows the self-similarity to be governed by a nonlinear diffusion equation with a rapidly-varying, mean-zero diffusion coefficient. Indeed, the leadingorder behavior is shown to be governed by the porous media (nonlinear diffusion) equation whose solution is the well-known Barenblatt similarity solution which has a parabolic, self-similar profile. The alternating sign of the diffusion coefficient, which is driven by the dispersion fluctuations, is critical to supporting the zero-dispersion similariton which is, to leading-order, of the Barenblatt form. This is the first analytic model proposing a mechanism for generating physically realizable temporal parabolic pulses in the Ginzburg-Landau model. Although the results are of restricted analytic validity, the findings are suggestive of the underlying physical mechanism responsible for parabolic (self-similar) pulse formation in lightwave transmission and observed in mode-locked laser cavities

Analytic theory of self-similar mode-locking with rapidly varying, mean-zero dispersion

Self-similarity is a ubiquitous concept in the physical sciences used to explain a wide range of spatial- or temporalstructures observed in a broad range of applications and natural phenomena. Indeed, they have been predicted or observed in the context of Raman scattering, spatial soliton fractals, propagation in the normal dispersion regime with strong nonlinearity, optical amplifiers, and mode-locked lasers. These self-similar structures are typically long-time transients formed by the interplay, often nonlinear, of the underlying dominant physical effects in the system. A theoretical model shows that in the context of the universal Ginzburg-Landau equation with rapidly-varying, mean-zero dispersion, stable and attracting self-similar pulses are formed with parabolic profiles: the zero-dispersion similariton. The zero-dispersion similariton is the final solution state of the system, not a long-time, intermediate asymptotic behavior. An averaging analysis shows the self-similarity to be governed by a nonlinear diffusion equation with a rapidly-varying, mean-zero diffusion coefficient. Indeed, the leadingorder behavior is shown to be governed by the porous media (nonlinear diffusion) equation whose solution is the well-known Barenblatt similarity solution which has a parabolic, self-similar profile. The alternating sign of the diffusion coefficient, which is driven by the dispersion fluctuations, is critical to supporting the zero-dispersion similariton which is, to leading-order, of the Barenblatt form. This is the first analytic model proposing a mechanism for generating physically realizable temporal parabolic pulses in the Ginzburg-Landau model. Although the results are of restricted analytic validity, the findings are suggestive of the underlying physical mechanism responsible for parabolic (self-similar) pulse formation in lightwave transmission and observed in mode-locked laser cavities

The critical role of intracavity dynamics in high-power mode-locked fiber lasers

We present a theoretical description of the generation of ultra-short, high-energy pulses in two laser cavities driven by periodic spectral filtering or dispersion management. Critical in driving the intra-cavity dynamics is the nontrivial phase profiles generated and their periodic modification from either spectral filtering or dispersion management. For laser cavities with a spectral filter, the theory gives a simple geometrical description of the intra-cavity dynamics and provides a simple and efficient method for optimizing the laser cavity performance. In the dispersion managed cavity, analysis shows the generated self-similar behavior to be governed by the porous media equation with a rapidly-varying, mean-zero diffusion coefficient whose solution is the well-known Barenblatt similarity solution with parabolic profile

Target-Normal Single Spin Asymmetries Measured with Positrons

Two-photon exchange and the larger class of hadronic box diagrams are difficult to calculate without a large degree of model-dependence. At the same time, these processes are significant radiative corrections in parity-violating electron scattering, in neutron decay, and may even be responsible for the proton's form factor ratio discrepancy. New kinds of experimental data are needed to help constrain models and guide future box-diagram calculations. The target-normal single spin asymmetry, $A_n$, formed with an unpolarized beam scattering from a target that is polarized normal to the scattering plane, is sensitive to the imaginary part of the two-photon exchange amplitude, and can provide a valuable constraint. A measurement with both electrons and positrons can reduce sources of experimental error, and distinguish between the effects of two-photon exchange and those of time-reversal symmetry violation. This article describes a proposed experiment in Hall A, using the new Super Big-Bite Spectrometer that can cover a momentum transfer range in the critical zone of uncertainty between where hadronic calculations and those based on partonic degrees of freedom are expected to be accurate.Comment: 7 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:2007.1508

Application of waveguide arrays and spectral filtering for a multi-frequency picosecond mode-locked pulse source

Current optical fiber-communication networks increasingly rely on wavelength-division multiplexing (WDM) technologies in conjunction with optical time-division multiplexing (OTDM) of individual WDM channels. The combination of high-repetition-rate data streams with a large number of WDM channels has pushed transmission rates to nearly 1 TB/s, creating a demand for all-optical transmission sources that can generate pico-second modelocked pulses at various wavelengths. Through nonlinear mode-coupling in a wave-guide array and a periodically applied multi-notch frequency filter, robust multi-frequency mode-locking can be achieved in a laser cavity in both the normal and anomalous dispersion regimes. We develop a theoretical description of this multiplewavelength mode-locking, and characterize the mode-locked solutions and their stability for an arbitrary number of frequency channels. The theoretical investigations demonstrate that the stability of the mode-locked pulse solutions of multiple frequency channels depends on the degree of inhomogenity in gain saturation. Specifically, only a small amount of inhomogeneous gain-broadening is needed for multi-frequency operation in the laser. In this presentation, the conditions on the system parameters necessary for generating stable mode-locking is explored for arbitrary number of frequency channels. The model suggests a promising source for multi-frequency photonic applications

Mode-locked laser pulse sources for wavelength division multiplexing

Recent theoretical investigations have demonstrated that the stability of mode-locked solution of multiple frequency channels depends on the degree of inhomogeneity in gain saturation. In this paper, these results are generalized to determine conditions on each of the system parameters necessary for both the stability and existence of mode-locked pulse solutions for an arbitrary number of frequency channels. In particular, we find that the parameters governing saturable intensity discrimination and gain inhomogeneity in the laser cavity also determine the position of bifurcations of solution types. These bifurcations are completely characterized in terms of these parameters. In addition to influencing the stability of mode-locked solutions, we determine a balance between cubic gain and quintic loss, which is necessary for existence of solutions as well. Furthermore, we determine the critical degree of inhomogeneous gain broadening required to support pulses in multiple frequency channels

Waveguide arrays and spectral filtering for multi-frequency mode-locked pulse sources

Current optical fiber-communication networks increasingly rely on wavelength-division multiplexing (WDM) technologies in conjunction with optical time-division multiplexing (OTDM) of individual WDM channels. The combination of high-repetition-rate data streams with a large number of WDM channels has pushed transmission rates to nearly 1 TB/s, creating a demand for all-optical transmission sources that can generate pico-second modelocked pulses at various wavelengths. Through nonlinear mode-coupling in a wave-guide array and a periodically applied multi-notch frequency filter, robust multi-frequency mode-locking can be achieved in a laser cavity in both the normal and anomalous dispersion regimes. We develop a theoretical description of this multiplewavelength mode-locking, and characterize the mode-locked solutions and their stability for an arbitrary number of frequency channels. The theoretical investigations demonstrate that the stability of the mode-locked pulse solutions of multiple frequency channels depends on the degree of inhomogenity in gain saturation. Specifically, only a small amount of inhomogeneous gain-broadening is needed for multi-frequency operation in the laser. In this presentation, the conditions on the system parameters necessary for generating stable mode-locking is explored for arbitrary number of frequency channels. The model suggests a promising source for multi-frequency photonic applications