Modulation Instability In Optical Fibers Research Articles

Enhancing optical modulator and link performance through modulation instability: design, simulation and implementation

In future optical communication applications, broadband tools and technologies are essential for increasing transfer and processing speeds. Conventional microwave tools are too slow and inflexible to meet these demands. Photonic microwave technology offers that most current solution to this issue, utilizing modulation tools to convert microwave signals to the optical domain. However, these modulation tools face significant challenges, including low bandwidth and high voltage requirements. Although various methods have been proposed in recent decades to address these issues, most increase structural complexity and cost without significantly improving modulator performance and bandwidth. In this article, by using a modulation instability in optical fibers, without manipulating and complicating the structure of the modulator and only by using common modulators, their bandwidth was multiplied and the required voltage was significantly reduced. Finally, a special fiber channel was designed, which showed a much better performance.

Analysis of interaction dynamics and rogue wave localization in modulation instability using data-driven dominant balance

We analyze the dynamics of modulation instability in optical fiber (or any other nonlinear Schrödinger equation system) using the machine-learning technique of data-driven dominant balance. We aim to automate the identification of which particular physical processes drive propagation in different regimes, a task usually performed using intuition and comparison with asymptotic limits. We first apply the method to interpret known analytic results describing Akhmediev breather, Kuznetsov-Ma, and Peregrine soliton (rogue wave) structures, and show how we can automatically distinguish regions of dominant nonlinear propagation from regions where nonlinearity and dispersion combine to drive the observed spatio-temporal localization. Using numerical simulations, we then apply the technique to the more complex case of noise-driven spontaneous modulation instability, and show that we can readily isolate different regimes of dominant physical interactions, even within the dynamics of chaotic propagation.

Modulational instability in optical fibers with randomly kicked normal dispersion

We study modulational instability (MI) in optical fibers with random group velocity dispersion (GVD) generated by sharply localized perturbations of a normal GVD fiber that are either randomly or periodically placed along the fiber and that have random strength. This perturbation leads to the appearance of low frequency MI side lobes that grow with the strength of the perturbations, whereas they are faded by randomness in their position. If the random perturbations exhibit a finite average value, they can be compared with periodically perturbed fibers, where Arnold tongues appear. In that case, increased randomness in the strengths of the variations tends to affect the Arnold tongues less than increased randomness in their positions.

Single-shot observation of breathers from noise-induced modulation instability using heterodyne temporal imaging.

We report phase and amplitude measurements of large coherent structures originating from the noise-induced modulation instability in optical fibers. By using a specifically designed time-lens system (SEAHORSE) in which aberrations are compensated, the complex field is recorded in single-shot over long durations of 200 ps with sub-picosecond resolution. Signatures of Akhmediev breather-like patterns are identified in the ultrafast temporal dynamics in very good agreement with numerical predictions based on the nonlinear Schrödinger equation.

Auto-modulation versus breathers in the nonlinear stage of modulational instability.

The nonlinear stage of modulational instability in optical fibers induced by a wide and easily accessible class of localized perturbations is studied using the nonlinear Schrödinger equation. It is shown that the development of associated spatio-temporal patterns is strongly affected by the shape and the parameters of the perturbation. Different scenarios are presented that involve an auto-modulation developing in a characteristic wedge, possibly coexisting with breathers which lie inside or outside the wedge.

PT symmetry and antisymmetry by anti-Hermitian wave coupling and nonlinear optical interactions.

Light propagation in systems with anti-Hermitian coupling, described by a spinor-like wave equation, provides a general route for the observation of antiparity-time (PT) symmetry in optics. Remarkably, under a different definition of parity operator, a PT symmetry can be found as well in such systems. Such symmetries are ubiquitous in nonlinear optical interactions and are exemplified by considering modulation instability in optical fibers and optical parametric amplification.

A Geometrical View of Scalar Modulation Instability in Optical Fibers

Full models of scalar modulation instability (MI) in optical fibers available in the literature usually involve complex formulations. In this paper, we present a novel approach to the analysis of MI in optical fibers by means of a simple geometrical description in the power versus frequency plane. This formulation allows us to relate the shape of the MI gain to any arbitrary dispersion profile of the medium, thus providing a simple insight. As a result, we derive a straightforward explanation of the nontrivial dependence of the cutoff power on high-order dispersion and explicitly derive the power that maximizes the gain. Our approach puts forth a tool to synthesize a desired MI gain with the potential application to a number of parametric-amplification and supercontinuum-generation devices whose initial-stage dynamics rely upon MI.

Analytical model and experimental verification of the critical power for modulation instability in optical fibers.

Modulation instability is thoroughly investigated and a simple analytical model for its power critically modifying the wave properties in terms of system parameters is derived and experimentally validated. The differences on the modulation instability gain spectrum in lossless and lossy optical fibers are analyzed based on theoretical models and numerical simulations. In particular the impact of background noise on the behavior of modulation instability is studied analytically and verified by measurements and simulations. The proposed analytical model is experimentally validated by monitoring the wave propagation along an optical fiber using a Brillouin optical time-domain analyzer. This way, the evolution of the optical signal traveling through optical fibers, especially, the pump depletion and the recurrence phenomenon are investigated.

Modulational instability in dispersion-kicked optical fibers

We study, both theoretically and experimentally, modulational instability in optical fibers that have a longitudinal evolution of their dispersion in the form of a Dirac delta comb. By means of Floquet theory, we obtain an exact expression for the position of the gain bands, and we provide simple analytical estimates of the gain and of the bandwidths of those sidebands. An experimental validation of those results has been carried out in several microstructured fibers specifically manufactured for that purpose. The dispersion landscape of those fibers is a comb of Gaussian pulses having widths much shorter than the period, which therefore approximate the ideal Dirac comb. Experimental spontaneous modulational instability spectra recorded under quasicontinuous wave excitation are in good agreement with the theory and with numerical simulations based on the generalized nonlinear Schr\"odinger equation.

Incoherent resonant seeding of modulation instability in optical fiber

We report control of the spectral and noise properties of spontaneous modulation instability (MI) in optical fiber using an incoherent seed with power at the 10(-6) level relative to the pump. We sweep the seed wavelength across the MI gain band, and observe significant enhancement of MI bandwidth and improvement in the signal-to-noise ratio as the seed coincides with the MI gain peak. We also vary the seed bandwidth and find a reduced effect on the MI spectrum as the seed coherence decreases. Stochastic nonlinear Schrödinger equation simulations of spectral and noise properties are in excellent agreement with experiment.

Modulation instability of copropagating light beams in nonlinear metamaterials

Linear stability analysis predicts that transverse modulation instability (MI) can occur for two optical beams copropagating in a Kerr nonlinear metamaterial (MM) interacting with each other through cross-phase modulation. A detailed discussion on the role of cross-phase modulation-induced coupling between beams on MI is presented, and it is found that MMs will enrich the propagating characteristics of beams. MI that occurs when beams are in different refractive-index regions is particularly interesting since it is a precursor to the formation of bright and dark spatial solitons. Furthermore, transverse MI can develop for different combinations of the signs of refractive index decided by the two beams, respectively, which makes the temporal MI in optical fibers find its transverse MI counterpart in MMs. Based on the Drude model, numerical simulations are performed to confirm theoretical predictions.

Modulational instability in optical fibers with arbitrary higher-order dispersion and delayed Raman response

We analyse modulational instability (MI) of electromagnetic waves in a large variety of optical fibers having different refractive-index profiles. For the normal-, anomalous-, and zero-dispersion regimes of the wave propagation, we show that whenever the second-order dispersion competes with higher-order dispersion (HOD), propagation of plane waves leads to a rich variety of dynamical behaviors. Most of the richness comes from the existence of critical behaviors, which include situations in which the HOD suppresses MI in the anomalous dispersion regime, and other situations in which the HOD acts in the opposite way by inducing non-conventional MI processes in the normal- and anomalous-dispersion regimes. We show that non-conventional MI sidebands are more prone to Raman-induced degradations than ordinary MI sidebands can be.

Experimental study of the reversible behavior of modulational instability in optical fibers

We report what is to our knowledge the first clear-cut experimental evidence of the reversibility of modulational instability in dispersive Kerr media. It was possible to perform this experiment with standard telecommunication fiber because we used a specially designed 550-ps square-pulse laser source based on the two-wavelength configuration of a nonlinear optical loop mirror. Our observations demonstrate that reversibility is due to well-balanced and synchronous energy transfer among a significant number of spectral wave components. These results provide what we believe is the first evidence, in the field of nonlinear optics, of the universal Fermi–Pasta–Ulam recurrence phenomenon that has been predicted for a large number of conservative nonlinear systems, including those described by a nonlinear Schrödinger equation that is relevant to the context of the present study.

Modulation instability of femtosecond pulses in dispersion-decreasing fibers

Modulation instability (MI) to generate femtosecond pulse in dispersion-decreasing fibers (DDF) is investigated. Higher-order dispersion effect and higher-order nonlinear effects are taken into account when continuous wave or quasi-continuous wave evolves into sub-picosecond or femtosecond pulses by MI in optical fibers. Our research results show that the gain spectrum of the DDF is much wider than that in conventional fibers. The third-order dispersion effect has no contribution to gain spectrum, self-steepening effect reduces the maximum value and gain bandwidth of gain spectrum, and Raman self-scattering effect widens the extent where MI occurs.

Role of polarization mode dispersion on modulational instability in optical fibers.

We introduce the theory of modulational instability (MI) of electromagnetic waves in fibers with random polarization mode dispersion. Applying a linear stability analysis and stochastic calculus, we show that the MI gain spectrum reads as the maximal eigenvalue of a constant effective matrix. In the limiting cases of small or large fluctuations, we give explicit expressions for the MI gain spectra. In the general configurations, we give the explicit form of the effective matrix and numerically compute the maximal eigenvalue. In the anomalous dispersion regime, polarization dispersion widens the unstable bandwidth. Depending on the type of variations of the birefringence parameters, polarization dispersion reduces or enhances the MI gain peak. In the normal dispersion regime, random effects may extend the instability domain to the whole spectrum of modulations. The linear stability analysis is confirmed by numerical simulation of the full stochastic coupled nonlinear Schrödinger equations.

Nonlinear dynamics of polarization modulation instability in optical fiber

The nonlinear dynamics of polarization modulation instability in the strong conversion regime is investigated both theoretically and experimentally. We observe oscillations in the polarization modulation instability sidebands’ power as a function of input-pump power. These oscillations correspond to the changing direction of the flow of energy between the sidebands and the pump. With the inclusion of Raman gain between the three waves, good agreement is found between theory and experiment.

Quasi-phase matching in an optical fiber with periodic birefringence

The propagation of light in a polarization-preserving optical fiber with a periodically induced birefringence is analyzed theoretically and investigated experimentally. Regions of quasi-phase-matched four-wave mixing are predicted on the basis of an analysis of the light-amplitude fluctuations and full numerical simulations. The experimental results are in good agreement with the theoretical analysis, including the effect of external variation in the birefringence. The process, generated in an optical fiber having an induced periodic birefringence, is similar to that used for second-harmonic generation in a χ(2) waveguide and for modulational instability in optical fibers with periodically varying group-velocity dispersion.

Modulational instability in optical fibers with variable dispersion

We study modulational instability in optical fibres whose dispersion varies with the propagation distance. We distinguish between two cases, viz. periodic and random dispersion variation. In the former case it is found that due to the parametric resonance between the dispersion modulation and the modes of the linearized system new domains of modulational instability arise for anomalous as well as normal average dispersion. In the latter case stochastic parametric resonances again lead to the occurrence of modulational instability for normal dispersion. If the dispersion is anomalous the region of modulational instability increases and the respective gain decreases in comparison with a fibre with constant dispersion.

Modulational instability in lossy optical fibers

The modulational instability in an optical fiber, with loss taken into account, is analytically investigated. It is demonstrated how the linearized equation for perturbation can be solved exactly in terms of Bessel functions, and qualitative differences from previous analytic approaches are pointed out. Finally, the limits imposed by this instability on optical communication systems are discussed. The use of this theory in system design is examined.

Modulational instability in optical fibers near the zero dispersion point

Modulational instability (MI) of electromagnetic waves in an optical fiber near the zero dispersion point is investigated both analytical and numerical. The effect of fourth order dispersion is taken into account and a new region with MI is found. The possibility of MI is shown for the case of positive second and fourth order group dispersion. For both positive and negative fourth order dispersion a recurrence phenomenon is observed analogous to the Fermi-Pasta-Ulam problem.