Física

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Analytical study of coherence in seeded modulation instability
(2016-09) Bonetti, Juan I.; Hernández, Santiago M.; Fierens, Pablo Ignacio; Grosz, Diego
"We derive analytical expressions for the coherence in the onset of modulation instability, in excellent agreement with thorough numerical simulations. As usual, we start by a linear perturbation analysis, where broadband noise is added to a cw pump; then, we investigate the effect of adding a deterministic seed to the cw pump, a case of singular interest as it is commonly encountered in parametric amplification schemes. Results for the dependence of coherence on parameters such as fiber type, pump power, propagated distance, and seed signal-to-noise ratio are presented. Finally, we show the importance of including higher-order linear and nonlinear dispersion when looking at longer-wavelength regions"
Anti-stokes Raman gain enabled by modulation instability in mid-IR waveguides
(2018-11) Sánchez, Alfredo D.; Fierens, Pablo Ignacio; Hernández, Santiago M.; Bonetti, Juan I.; Brambilla, Gilberto; Grosz, Diego
"The inclusion of self-steepening in the linear stability analysis of modulation instability (MI) leads to a power cutoff above which the MI gain vanishes. Under these conditions, MI in mid-IR waveguides is shown to give rise to the usual double-sideband spectrum but with Raman-shaped sidelobes. This results from the energy transfer of a CW laser simultaneously to both stokes and anti-stokes bands in pseudo-parametric fashion. As such, the anti-stokes gain matches completely the stokes profile over the entire gain bandwidth. This remarkable behavior, not expected from an unexcited medium, is shown not to follow from a conventional four-wave mixing interaction between the pump and the Stokes band. We believe this observation to be of relevance in the area of Raman-based sensors, which, in several instances, rely on monitoring small power variations of the anti-stokes spectral component."
Dispersive waves in optical fibers with a zero-nonlinearity wavelength
(2021-08) Sparapani, Alexis; Linale, N.; Grosz, Diego; Bonetti, Juan I.; Fierens, Pablo Ignacio; Hernández, Santiago M.
"We present results on dispersive waves radiated by solitons in the context of fibers with arbitrary frequency-dependent nonlinearities. In particular, we focus on the effect of a zero-nonlinearity wavelength within the spectral region of interest."
Enhanced anti-stokes Raman gain in nonlinear waveguides
(2019) Sánchez, Alfredo D.; Hernández, Santiago M.; Bonetti, Juan I.; Grosz, Diego; Fierens, Pablo Ignacio
"We show that, under certain conditions, modulation instability in nonlinear waveguides gives rise to the usual double-sideband spectral structure, but with a Raman gain profile. This process is enabled by the energy transfer from a strong laser pump to both Stokes and antiStokes sidebands in a pseudo-parametric fashion. We believe this striking behavior to be of particular value in the area of Raman-based sensors which rely on sensitive measurements of the anti-Stokes component".
A geometrical view of scalar modulation instability in optical fibers
(2017) Hernández, Santiago M.; Fierens, Pablo Ignacio; Sánchez, Alfredo D.; Grosz, Diego; Bonetti, Juan I.
"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 initialstage dynamics rely upon MI."
A higher-order perturbation analysis of the nonlinear Schrödinger equation
(2019-06) Bonetti, Juan I.; Hernández, Santiago M.; Fierens, Pablo Ignacio; Grosz, Diego
"A well-known and thoroughly studied phenomenon in nonlinear wave propagation is that of modulation instability (MI). MI is usually approached as a perturbation to a pump, and its analysis is based on preserving only terms which are linear on the perturbation, discarding those of higher order. In this sense, the linear MI analysis is relevant to the understanding of the onset of many other nonlinear phenomena, such as supercontinuum generation, but it has limitations as it can only be applied to the propagation of the perturbation over short distances. In this work, we propose approximations to the propagation of a perturbation, consisting of additive white noise, that go beyond the linear modulation instability analysis, and show them to be in excellent agreement with numerical simulations and experimental measurements."
Measuring self-steepening with the photon-conserving nonlinear Schrödinger equation
(2020-08-15) Linale, N.; Fierens, Pablo Ignacio; Bonetti, Juan I.; Sánchez, Alfredo D.; Hernández, Santiago M.; Grosz, Diego
"We propose an original, simple, and direct method to measure self-steepening (SS) in nonlinear waveguides. Our proposal is based on results derived from the recently introduced photon-conserving nonlinear Schrödinger equation (NLSE) and relies on the time shift experienced by soliton-like pulses due to SS upon propagation. In particular, a direct measurement of this time shift allows for a precise estimation of the SS parameter. Furthermore, we show that such an approach cannot be tackled by resorting to the NLSE. The proposed method is validated through numerical simulations, in excellent agreement with the analytical model, and results are presented for relevant spectral regions in the near infrared, the telecommunication band, and the mid infrared, and for realistic parameters of available laser sources and waveguides. Finally, we demonstrate the robustness of the proposed scheme against deviations expected in real-life experimental conditions, such as pulse shape, pulse peak power, pulsewidth, and/or higher-order linear and nonlinear dispersion."
Modified nonlinear Schrödinger equation for frequency-dependent nonlinear profiles of arbitrary sign
(2019) Bonetti, Juan I.; Linale, N.; Sánchez, Alfredo D.; Hernández, Santiago M.; Fierens, Pablo Ignacio; Grosz, Diego
In recent times, materials exhibiting frequency-dependent optical nonlinearities, such as nanoparticle-doped glasses and other metamaterials, have gathered significant interest. The simulation of the propagation of intense light pulses in such media, by means of the nonlinear Schrödinger equation (NLSE), poses the problem in that straightforward inclusion of a frequency-dependent nonlinearity may lead to unphysical results, namely, neither the energy nor the photon number is conserved in general. Inspired by a simple quantum-mechanical argument, we derive an energy- and photon-conserving NLSE (pcNLSE). Unlike others, our approach relies only on the knowledge of the frequency-dependent nonlinearity profile and a generalization of Miller’s rule for nonlinear susceptibility, enabling the simulation of nonlinear profiles of arbitrary frequency dependence and sign. Moreover, the proposed pcNLSE can be efficiently solved by the same numerical techniques commonly used to deal with the NLSE. Relevant simulation results supporting our theoretical approach are presented.
Narrowband and ultra-wideband modulation instability in nonlinear metamaterial waveguides
(2020-11-01) Linale, N.; Fierens, Pablo Ignacio; Hernández, Santiago M.; Bonetti, Juan I.; Grosz, Diego
"Waveguides based on metamaterials may exhibit strongly frequency-dependent nonlinearities. In this work, we focus on the phenomenon of modulation instability in this type of waveguide, departing from a new modeling equation that ensures strict conservation of both the energy and photon number of the parametric process. In particular, we analyse the case of a waveguide with a linearly frequency-dependent nonlinear coefficient, revealing unique features such as narrowband and ultra-wideband gain spectra and the suppression of the power cutoff giving rise to an ever-growing MI gain. These markedly distinct regimes are enabled by self-steepening (SS) and manifest themselves depending upon the magnitude and sign of the SS parameter.We believe these findings to be most relevant in the context of mid-IR supercontinuum sources."
On the spectral dynamics of noise-seeded modulation instability in optical fibers
(2017) Fierens, Pablo Ignacio; Hernández, Santiago M.; Bonetti, Juan I.; Grosz, Diego
"We revisit modulation instability in optical fibers, including all relevant effects, such as higher-order dispersion terms, self-steepening, and the Raman response. Our analysis allows us to calculate the spectral evolution of a small perturbation to a continuous pump, and thus obtain an analytical expression for the small-signal spectral dynamics, showing excellent agreement with numerical simulations. We apply the expression for the spectral evolution to the case of white Gaussian noise and calculate some relevant metrics of the resulting signal, such as its coherence and signal-to-noise ratio. These calculations might shed some light on the nonlinear phenomena of supercontinuum generation."
Photon-conserving generalized nonlinear Schrödinger equation for frequency-dependent nonlinearities
(2020) Bonetti, Juan I.; Linale, N.; Sánchez, Alfredo D.; Hernández, Santiago M.; Fierens, Pablo Ignacio; Grosz, Diego
"Pulse propagation in nonlinear waveguides is most frequently modeled by resorting to the generalized nonlinear Schrödinger equation (GNLSE). In recent times, exciting new materials with peculiar nonlinear properties, such as negative nonlinear coefficients and a zero-nonlinearity wavelength, have been demonstrated. Unfortunately, the GNLSE may lead to unphysical results in these cases since, in general, it does not preserve the number of photons and, in the presence of a negative nonlinearity, predicts a blue shift due to Raman scattering. In this paper, we put forth a modified GNLSE that can be used to model the propagation in media with an arbitrary, even negative, nonlinear coefficient. This novel photon-conserving GNLSE (pcGNLSE) ensures preservation of the photon number and can be solved by the same tried and trusted numerical algorithms used for the standard GNLSE. Finally, we compare results for soliton dynamics in fibers with different nonlinear coefficients obtained with the pcGNLSE and the GNLSE."
Quasi-analytical perturbation analysis of the generalized nonlinear Schrödinger equation
(2019) Bonetti, Juan I.; Hernández, Santiago M.; Fierens, Pablo Ignacio; Temprana, Eduardo G.; Grosz, Diego
"The Generalized Nonlinear Schrödinger Equation (GNLSE) finds several applications, especially in describing pulse propagation in nonlinear fiber optics. A well-known and thoroughly studied phenomenon in nonlinear wave propagation is that of modulation instability (MI). MI is approached as a weak perturbation to a pump and the analysis is based on preserving those terms linear on the perturbation and disregarding higher-order terms. In this sense, the linear MI analysis is relevant to the understanding of the onset of many other nonlinear phenomena, but its application is limited to the evolution of the perturbation over short distances. In this work, we propose quasi-analytical approximations to the propagation of a perturbation consisting of additive white noise that go beyond the linear modulation instability analysis. Moreover, we show these approximations to be in excellent agreement with numerical simulations and experimental measurements. "
Simple method for estimating the fractional Raman contribution
(2019-02) Sánchez, Alfredo D.; Linale, N.; Bonetti, Juan I.; Hernández, Santiago M.; Fierens, Pablo Ignacio; Brambilla, Gilberto; Grosz, Diego
"We propose a novel and simple method for estimating the fractional Raman contribution, fR, based on an analysis of a full model of modulation instability (MI) in waveguides. An analytical expression relating fR to the MI peak gain beyond the cutoff power is explicitly derived, allowing for an accurate estimation of fR from a single measurement of the Raman gain spectrum."
Soliton solutions and self-steepening in the photon-conserving nonlinear Schrödinger equation
(2020-12-09) Hernández, Santiago M.; Bonetti, Juan I.; Linale, N.; Grosz, Diego; Fierens, Pablo Ignacio
"We have recently introduced a new modeling equation for the propagation of pulses in optical waveguides, the photon-conserving Nonlinear Schrödinger Equation (pcNLSE) which, unlike the canonical NLSE, guarantees strict conservation of both the energy and the number of photons for any arbitrary frequency-dependent nonlinearity. In this paper, we analyze some properties of this new equation in the familiar case where the nonlinear coefficient of the waveguide does not change sign. We show that the pcNLSE effectively adds a correction term to the NLSE proportional to the deviation of the self-steepening (SS) parameter from the photon-conserving condition in the NLSE. Furthermore, we describe the role of the self-steepening parameter in the context of the conservation of the number of photons and derive an analytical expression for the relation of the SS parameter with the time delay experienced by pulses upon propagation. Finally, we put forth soliton-like solutions of the pcNLSE that, unlike NLSE solitons, conserve the number of photons for any arbitrary SS parameter. "
Tunable Raman gain in mid-IR waveguides
(2018) Sánchez, Alfredo D.; Hernández, Santiago M.; Bonetti, Juan I.; Fierens, Pablo Ignacio; Grosz, Diego
"By means of theoretical analysis and numerical simulations, we show a tunable Raman gain which may find applications in a variety of fields, ranging from mid-IR fiber Raman lasers and supercontinuum generation to ultra-wideband slow-light Raman-based devices. In particular, by analyzing the interplay among Raman gain, dispersion, and self-steeping (SE) in a full model of modulation instability (MI) in waveguides, we show that there exists a range of pump powers where the gain spectrum is not only dominated by the Raman contribution, but also, most strikingly, it can be fine-tuned at will. We present analytical and numerical results, in excellent agreement, confirming this observation. "

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