Abstract
In the absence of random mode mixing (RMM), linearization of the cross-mode modulation (XMM) under pump-probe configuration is in general complicated because the evolution of the pump light depends on the local mode decomposition of itself. In this work, general derivation of the Hamiltonian of the XMM system without RMM is carried out and discussed under two interesting scenarios where the pump evolution can be effectively linearized, leading to spatial dependent Hamiltonian of the probe light. Representative evolutions of pump and probe light over transmission are investigated with the assistance of Poincare sphere based on the Hamiltonian approach. Our results are benchmarked against the results given by precession equations examined by Lin and Agrawal and numerical simulations using nonlinear coupled mode equations (CMEs). By highlighting the eigenstates as well as eigenvalues of the system, our approach provides an intuitive yet powerful approach to understand the XMM nonlinear problems and to dynamically manipulate the spatial profiles of the probe light.
Highlights
Cross-Mode modulation (XMM) describes the rotation of the mode profile of a weak probe light induced by a strong co-propagating pump light in multimode nonlinear optical waveguides [1]–[3]
The XMM in multimode optical waveguides induced by third order non-linearity has received broad interests recently due to the rapid progresses in spatial division multiplexing technologies developed for optical fiber communications [6]
In an initial attempt of Hamiltonian approach in analyzing the XMM in degenerate mode group with random mode mixing (RMM), which greatly simplifies the coupling equations [1], we reveal the prediction as well as manipulation of the probe mode distribution with a clear picture of nonlinear birefringence [9], where the energy operator, i.e., the Hamiltonian of the system, indicates the allowed nonlinear propagation constants of probe light, derived by calculating the corresponding eigenvectors and eigenvalues
Summary
Cross-Mode modulation (XMM) describes the rotation of the mode profile of a weak probe light induced by a strong co-propagating pump light in multimode nonlinear optical waveguides [1]–[3]. When propagating along multimode fibers, mode couplings can occur randomly due to stress, bending, or technological irregularities of the fibers Such random mode mixing (RMM) may happen between modes with degenerate propagation constants. In an initial attempt of Hamiltonian approach in analyzing the XMM in degenerate mode group with random mode mixing (RMM), which greatly simplifies the coupling equations [1], we reveal the prediction as well as manipulation of the probe mode distribution with a clear picture of nonlinear birefringence [9], where the energy operator, i.e., the Hamiltonian of the system, indicates the allowed nonlinear propagation constants of probe light, derived by calculating the corresponding eigenvectors and eigenvalues. It is shown that the Hamiltonian of the probe light turns out to be spatially dependent, leading to fundamentally different properties from our previous analysis where the Hamiltonian is independent of propagation coordinates [9]
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