Abstract
The comprehension of pulsed light propagation is of paramount importance in fiber optics. Here, we present a general method to describe the propagation of pulses in any kind of optical fiber, regardless of its fabrication process or constituent materials. As a result, we obtain a rich toolbox for the analysis and synthesis of optical fibers, which allows us to circumvent the resolution of Maxwell's equations by using heavy-computational numerical methods. To illustrate this, we analyze the pulse propagation problem in non-paraxial anisotropic single-core and multi-core fibers that cover a large variety of optical fibers including classical weakly guiding fibers, optical gain fibers, polarization-maintaining fibers, highly nonlinear fibers, and photonic crystal fibers. Moreover, it is shown that our method can be applied to any kind of guided and unguided medium undergoing spatial and temporal perturbations, provided that the distance and temporal width between different consecutive spatial and temporal medium perturbations are respectively higher than the spatial and temporal width of the optical pulses.
Highlights
Since the introduction of Maxwell’s equations in 1865 [1], engineers have been able to unveil a large gamut of electromagnetic technologies, among others, the optical fiber
The generalized pulse propagation method (GPPM) generalizes the formalism describing the propagation of pulses in any kind of single-core and multi-core optical fiber taking into account the spatial and temporal medium perturbations along with higher-order nonlinear effects and, leading to the emergence of a new fiber design toolbox
A large diversity of fiber-optic applications can be covered by the GPPM, spanning the next-generation optical communications based on spacedivision multiplexing transmissions [45], and biomedical [46], [47] and physical applications [3]
Summary
Since the introduction of Maxwell’s equations in 1865 [1], engineers have been able to unveil a large gamut of electromagnetic technologies, among others, the optical fiber. Optical fiber technology has uncovered new possibilities and applications in other fields of science, such as in experimental physics (e.g., to study exotic phenomena such as the Hawking radiation using analog gravity [3]) and in biomedicine (e.g., to develop crucial advances in lasers [4], sensors [5] and medical imaging [6]). In this vein, diverse types of optical fibers have been proposed and developed in the last decades: the standard single-mode fiber [7], photonic crystal fibers [8], fiber. A variety of numerical methods to solve Maxwell’s equations in an optical fiber have been reported in the literature [13]–[24]
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