Practical high-dimensional quantum key distribution protocol over deployed multicore fiber.

Quantum key distribution (QKD) is a secure communication scheme for sharing symmetric cryptographic keys based on the laws of quantum physics, and is considered a key player in the realm of cyber-security. A critical challenge for QKD systems comes from the fact that the ever-increasing rates at which digital data are transmitted require more and more performing sources of quantum keys, primarily in terms of secret key generation rate. High-dimensional QKD based on path encoding has been proposed as a candidate approach to address this challenge. However, while proof-of-principle demonstrations based on lab experiments have been reported in the literature, demonstrations in realistic environments are still missing. Here we report the generation of secret keys in a 4-dimensional hybrid time-path-encoded QKD system over a 52-km deployed multicore fiber link forming by looping back two cores of a 26-km 4-core optical fiber. Our results indicate that robust high-dimensional QKD can be implemented in a realistic environment by combining standard telecom equipment with emerging multicore fiber technology.

Plasmon-enhanced circular dichroism spectroscopy of chiral drug solutions.

We investigate the potential of surface plasmon polaritons at noble metal interfaces for surface-enhanced chiroptical sensing of dilute chiral drug solutions with nl volume. The high quality factor of surface plasmon resonances in both Otto and Kretschmann configurations enables the enhancement of circular dichroism differenatial absorption thanks to the large near-field intensity of such plasmonic excitations. Furthermore, the subwavelength confinement of surface plasmon polaritons is key to attain chiroptical sensitivity to small amounts of drug volumes placed around ≃100 nm by the metal surface. Our calculations focus on reparixin, a pharmaceutical molecule currently used in clinical studies for patients with community-acquired pneumonia, including COVID-19 and acute respiratory distress syndrome. Considering realistic dilute solutions of reparixin dissolved in water with concentration ≤5 mg/ml and nl volume, we find a circular-dichroism differential absorption enhancement factor of the order ≃20 and chirality-induced polarization distortion upon surface plasmon polariton excitation. Our results are relevant for the development of innovative chiroptical sensors capable of measuring the enantiomeric imbalance of chiral drug solutions with nl volume.

Dependence of nonlinear interference on mode dispersion and modulation format in strongly-coupled SDM transmissions.

We study the role of the modulation format in the interaction between mode dispersion and the fiber nonlinear interference (NLI) in space-division multiplexed (SDM) systems with strongly-coupled spatial modes. We show that the interplay between mode dispersion and the modulation format has a significant impact on the magnitude of cross-phase modulation (XPM). We propose a simple formula that accounts for the modulation-format dependence of the XPM variance in the presence of arbitrary levels of mode dispersion, thus extending the ergodic Gaussian noise model.

Optical polarization-based seismic and water wave sensing on transoceanic cables.

Seafloor geophysical instrumentation is challenging to deploy and maintain but critical for studying submarine earthquakes and Earth's interior. Emerging fiber-optic sensing technologies that can leverage submarine telecommunication cables present an opportunity to fill the data gap. We successfully sensed seismic and water waves over a 10,000-kilometer-long submarine cable connecting Los Angeles, California, and Valparaiso, Chile, by monitoring the polarization of regular optical telecommunication channels. We detected multiple moderate-to-large earthquakes along the cable in the 10-millihertz to 5-hertz band. We also recorded pressure signals from ocean swells in the primary microseism band, implying the potential for tsunami sensing. Our method, because it does not require specialized equipment, laser sources, or dedicated fibers, is highly scalable for converting global submarine cables into continuous real-time earthquake and tsunami observatories.

Enhancing the Kramers-Kronig receiver via dispersion-based spatial diversity.

We report a scheme for reconstructing the complex envelope of an optical signal from two decorrelated measurements of its intensity. The decorrelation is achieved by splitting the received optical signal into two copies, and by dispersing one of the copies prior to photo detection. The reconstructed complex-valued signal is obtained by means of an iterative algorithm that requires only a few tens of iterations. The starting point of the search procedure is produced by Kramers-Kronig (KK) reconstruction. With this procedure, the continuous-wave tone that accompanies the received signal is reduced by 5 dB to 6 dB compared to the requirement of a KK receiver alone.

Role of polarization-mode coupling in the crosstalk between cores of weakly-coupled multi-core fibers.

We develop a theory of crosstalk in weakly-coupled multi-core fibers that accounts for the effect of intra-core polarization-mode coupling. We show that random polarization-mode coupling plays a critical role, just like other polarization-independent effects such as fiber bending and twist, in explaining the observed incoherent crosstalk in weakly-coupled multi-core fibers.

Nonlinear Optics: feature issue introduction.

This joint issue of Optics Express and Optical Materials Express features 18 state-of-the art articles that witness actual developments in nonlinear optics, including those by authors who participated in the international conference Nonlinear Optics held in Waikoloa, Hawaii from July 15 to 19, 2019. As an introduction, the editors provide a summary of these articles that cover all aspects of nonlinear optics, from basic nonlinear effects and novel frequency windows to innovative nonlinear materials and devices, thereby paving the way for new nonlinear optical concepts and forthcoming applications.

Coherent detection with an incoherent local oscillator.

We demonstrate the feasibility of fully coherent reconstruction of the complex envelope of arbitrary optical fields while using an incoherent source as a local oscillator (LO). The reconstruction relies on a signal processing procedure that we describe, and the only requirement from the system is that the receiver's electrical bandwidth and sampling rate are at least twice as high as the bandwidth of the received signal and of the LO. The proposed scheme is particularly attractive in spectral regions where no high-quality lasers are available.

Nonlinear interference noise in space-division multiplexed transmission through optical fibers.

We study the nonlinear interference noise (NLIN) generated in SDM systems, and generalize the NLIN model introduced in the context of single-mode fibers to the multi-mode case. The generalized model accounts for the modulation-format dependence of the NLIN, and gives the scaling of the NLIN power with the number of transmitted modes. It also provides the tools for extending the results of the NLIN Wizard to SDM. Unlike in the case of single-mode systems, the effect of MD cannot in general be ignored in the SDM case. We show that inclusion of MD erases the contribution of FWM effects, and significantly suppresses the effect of XPM.

Feature issue introduction: Nonlinearity mitigation for coherent transmission systems.

The authors introduce the feature issue on nonlinearity mitigation for coherent transmission systems.

The delay spread in fibers for SDM transmission: dependence on fiber parameters and perturbations.

Contrary to single mode fibers, where random imperfections are responsible for polarization-mode dispersion, modal dispersion (MD) in multi-mode fiber structures for space-division multiplexed (SDM) transmission, originates chiefly from the intrinsic non-degeneracy of the propagating modes, also known as modal birefringence. The presence of random imperfections in such fibers has a positive aspect, as it reduces the intrinsic MD, and in the limit of strong coupling it causes the signal delay spread to increase with the square root of the propagation distance, rather than linearly, as would be the case in an ideal fiber. In this paper we derive a formula that relates the signal delay spread to the fiber geometry and to the statistical properties of the structural fiber perturbations. The derived formula provides insight into the MD phenomenon and facilitates the design of low-MD multi-mode fiber structures.

Modeling and performance metrics of MIMO-SDM systems with different amplification schemes in the presence of mode-dependent loss.

Mode-dependent loss (MDL) is a major factor limiting the achievable information rate in multiple-input multiple-output space-division multiplexed systems. In this paper we show that its impact on system performance, which we quantify in terms of the capacity reduction relative to a reference MDL-free system, may depend strongly on the operation of the inline optical amplifiers. This dependency is particularly strong in low mode-count systems. In addition, we discuss ways in which the signal-to-noise ratio of the MDL-free reference system can be defined and quantify the differences in the predicted capacity loss. Finally, we stress the importance of correctly accounting for the effect of MDL on the accumulation of amplification noise.

Intensity impulse response of SDM links.

We study the response of space-division multiplexed fiber links to an excitation by a short impulse of the optical intensity. We show that, in the presence of full mixing, the intensity impulse response is Gaussian, confirming recently reported experimental observations, and relate its variance to the mean square of the mode dispersion vector of the link τ(->). The good agreement between our theory and the previously published experiments provides solid foundations to the random coupling model of SDM fiber links, and provides a tool for efficient design of MIMO-DSP receivers.

Accumulation of nonlinear interference noise in fiber-optic systems.

Through a series of extensive system simulations we show that all of the previously not understood discrepancies between the Gaussian noise (GN) model and simulations can be attributed to the omission of an important, recently reported, fourth-order noise (FON) term, that accounts for the statistical dependencies within the spectrum of the interfering channel. We examine the importance of the FON term as well as the dependence of NLIN on modulation format with respect to link-length and number of spans. A computationally efficient method for evaluating the FON contribution, as well as the overall NLIN power is provided.

Properties of nonlinear noise in long, dispersion-uncompensated fiber links.

We study the properties of nonlinear interference noise (NLIN) in fiber-optic communications systems with large accumulated dispersion. Our focus is on settling the discrepancy between the results of the Gaussian noise (GN) model (according to which NLIN is additive Gaussian) and a recently published time-domain analysis, which attributes drastically different properties to the NLIN. Upon reviewing the two approaches we identify several unjustified assumptions that are key in the derivation of the GN model, and that are responsible for the discrepancy. We derive the true NLIN power and verify that the NLIN is not additive Gaussian, but rather it depends strongly on the data transmitted in the channel of interest. In addition we validate the time-domain model numerically and demonstrate the strong dependence of the NLIN on the interfering channels' modulation format.

Random coupling between groups of degenerate fiber modes in mode multiplexed transmission.

We study random coupling induced crosstalk between groups of degenerate modes in spatially multiplexed optical transmission. Our analysis shows that the average crosstalk is primarily determined by the wavenumber mismatch, by the correlation length of the random perturbations, and by the coherence length of the degenerate modes, whereas the effect of a deterministic group velocity difference is negligible. The standard deviation of the crosstalk is shown to be comparable to its average value, implying that crosstalk measurements are inherently noisy.

Raman amplification in multimode fibers with random mode coupling.

We present the theory of Raman amplification in long multimode optical fibers, where strong random mode coupling within groups of quasi-degenerate modes is unavoidable. In such fibers, the signal components in modes that belong to the same strongly coupled group experience the same Raman amplification, where the differential gain is linearly dependent on the aggregate powers of the pump in each of the mode groups. The equations that we derive significantly facilitate the numerical and analytical study of Raman amplification in long multimode fibers.

Coupled Manakov equations in multimode fibers with strongly coupled groups of modes.

We derive the fundamental equations describing nonlinear propagation in multi-mode fibers in the presence of random mode coupling within quasi-degenerate groups of modes. Our result generalizes the Manakov equation describing mode coupling between polarizations in single-mode fibers. Nonlinear compensation of the modal dispersion is predicted and tested via computer simulations.

Nonlinear propagation in multi-mode fibers in the strong coupling regime.

We show that light propagation in a group of degenerate modes of a multi-mode optical fiber in the presence of random mode coupling is described by a multi-component Manakov equation, thereby making multi-mode fibers the first reported physical system that admits true multi-component soliton solutions. The nonlinearity coefficient appearing in the equation is expressed rigorously in terms of the multi-mode fiber parameters.

Stokes-space analysis of modal dispersion in fibers with multiple mode transmission.

Modal dispersion (MD) in a multimode fiber may be considered as a generalized form of polarization mode dispersion (PMD) in single mode fibers. Using this analogy, we extend the formalism developed for PMD to characterize MD in fibers with multiple spatial modes. We introduce a MD vector defined in a D-dimensional extended Stokes space whose square length is the sum of the square group delays of the generalized principal states. For strong mode coupling, the MD vector undertakes a D-dimensional isotropic random walk, so that the distribution of its length is a chi distribution with D degrees of freedom. We also characterize the largest differential group delay, that is the difference between the delays of the fastest and the slowest principal states, and show that it too is very well approximated by a chi distribution, although in general with a smaller number of degrees of freedom. Finally, we study the spectral properties of MD in terms of the frequency autocorrelation functions of the MD vector, of the square modulus of the MD vector, and of the largest differential group delay. The analytical results are supported by extensive numerical simulations.