Theory of four-wave mixing of cylindrical vector beams in optical fibers

Abstract

Cylindrical vector (CV) beams are a set of transverse spatial modes that exhibit a cylindrically symmetric intensity profile and a variable polarization about the beam axis. They are composed of a non-separable superposition of orbital and spin angular momentum. Critically, CV beams are also the eigenmodes of optical fiber and, as such, are of wide-spread practical importance in photonics and have the potential to increase communications bandwidth through spatial multiplexing. Here, we derive the coupled amplitude equations that describe the four-wave mixing (FWM) of CV beams in optical fibers. These equations allow us to determine the selection rules that govern the interconversion of CV modes in FWM processes. With these selection rules, we show that FWM conserves the total angular momentum, the sum of orbital and spin angular momentum, in the conversion of two input photons to two output photons. When applied to spontaneous four-wave mixing, the selection rules show that photon pairs can be generated in CV modes directly and can be entangled in those modes. Such quantum states of light in CV modes could benefit technologies such as quantum key distribution with satellites.

Vectorial light-matter interaction -- exploring spatially structured complex light fields

“…Experimental studies have demonstrated birefringence, dispersion and intermodal nonlinear interactions, such as Raman scattering and four-wave mixing, of cylindrically polarized modes in fibers. [117][118][119] These features can be used for nonlinear quantum squeezing, permitting the creation of continuousvariable hybrid-entangled states. 120 The highly nonlinear interaction provided by gas-filled hollow-core fiber is particulary suitable to achieve ultra-short pulses in the few, single or even sub optical cycle regime.…”

Spatio-Temporal Dynamics of Pulses in Multimode Fibers

“…When short pulses propagate in multimode fibers, a new world of nonlinear phenomena is added to the field of nonlinear single-mode interactions thanks to the additional spatial dimension [1]. As the pulse travels in the multimode fiber, the different modes in the pulse are coupled by nonlinear interactions, and the energy is transferred between the modes [2][3][4]. These nonlinear multimode interactions, as well as the spatial separability of the output pulse, are important for different applications, such as improving the brightness of nonlinear imaging [5,6], detecting the temporal shapes of ultrashort pulses by deep learning [7,8], and increasing the output power from ultrashort fiber lasers [9][10][11].…”

High-performance surface plasmon resonance fiber sensor based on cylindrical vector modes

“…Although higher-order modes in conventional fibers are usually formed as linearly polarized (LP) modes, new designs of optical fibers such as circular photonic crystal fibers (C-PCF) 2 – 4 , have been able to generate the orbital angular momentum (OAM) and cylindrical vector modes that can be propagated orthogonally along the fiber 5 . In the C-PCFs, OAM modes are generated from the linear combination of even and odd modes in the same order while TE 01 and TM 01 are the only pair modes that are independently propagated without combination and hence are the so-called cylindrical vector modes 6 . The use of TE 01 in the sensing performance of C-PCF-based sensors can be introduced as a new idea because TE 01 has significant optical properties such as high intensity, symmetric propagation, low confinement loss and azimuthal polarization.…”