Modulational instability for normal dispersion

Evolution from Periodic Intensity Modulations to Dissipative Vector Solitons in A Single-Mode Fiber Laser

We investigated—both experimentally and numerically—the operation of a weakly birefringent cavity fiber laser under different net cavity dispersion values. Experimentally, we found that under coherent cross-polarization coupling, either in-phase or anti-phase low frequency intensity modulations between the two orthogonal polarization components of the laser emission could be obtained. The evolution of the periodic intensity modulations in the fiber laser under different operation conditions was studied. In this paper, we show that under suitable conditions, they can be shaped into a train of bright-bright, dark-dark, or dark-bright vector solitons.

Noise-related polarization dynamics for femto and picosecond pulses in normal dispersion fibers

We report how the complex intra-pulse polarization dynamics of coherent optical wavebreaking and incoherent Raman amplification processes in all-normal dispersion (ANDi) fibers vary for femto and picosecond pump pulses. Using high temporal resolution vector supercontinuum simulations, we identify deterministic polarization dynamics caused by wavebreaking and self-phase modulation for femtosecond pulses and quasi-chaotic polarization evolution driven by Raman amplification of quantum noise for picosecond pulses. In contrast to cross-phase modulation instability, the Raman-based polarization noise has no power threshold and is reduced by aligning the higher energy polarization component with the lower index axis of the fiber. The degree of polarization stability is quantified using new time domain parameters that build on the spectrally averaged degree of coherence used in supercontinuum research to quantify the output spectral stability. We show that the spectral coherence is intrinsically linked to polarization noise, and that the noise will occur in both polarization maintaining (PM) and non-PM fibers, spanning a broad range of pulse energies, durations, and fiber birefringence values. This analysis provides an in-depth understanding of the nonlinear polarization dynamics associated with coherent and incoherent propagation in ANDi fibers.

Chalcogenide Taper and Its Nonlinear Effects and Sensing Applications

The nonlinear coefficient of chalcogenide glass is 200-1000 times larger than that of silica glass, and it is transparent in the 1-15 μm wavelength windows, which makes the nonlinear effects happen at much low power with a short length in near- and mid-infrared wavelength window. With tapered chalcogenide fibers, the power density in the core and the waveguide nonlinearity can be enhanced to make nonlinear signal processing unit at a compact size. The threshold of Raman scattering and supercontinuum generation is reduced due to the enhanced Kerr effect and enhanced optical power intensity. Phase-matching condition required in four-wave mixing (FWM) can be realized by tailoring fiber structures to engineer the chromatic dispersion, which enables new wavelengths creation over a large range at mW power and sub-meter length. The guided acoustic waves and longitudinal acoustic waves can be generated and detected in mW power with chalcogenide tapers. The high power density in the microwires and the high photosensitivity of chalcogenide glass in the 1550 nm band enable the inscription of FBGs in the fiber directly. The chalcogenide microwires are fragile and the core diameter cannot be tapered down to sub-microns, which can be mitigated by polymer coating that can provide mechanical strength. Polymers not only provide high mechanical strength as the coating and cladding materials but also bring over 10 times larger thermal expansion than chalcogenide cores, which enhances the sensor prospect of the chalcogenide fibers for temperature, strain, and acoustic sensing. This work reviews the present and emerging trends in investigation of chalcogenide tapers, mainly focusing on the fabrication procedure of chalcogenide microwires, the nonlinear effects, and sensing applications.

Integrability and Linear Stability of Nonlinear Waves

It is well known that the linear stability of solutions of 1 + 1 partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the linearized equation which makes use only of the associated Lax pair with no reference to spectral data and boundary conditions. This local construction is given in the general N × N matrix scheme so as to be applicable to a large class of integrable equations, including the multicomponent nonlinear Schrödinger system and the multiwave resonant interaction system. The analytical and numerical computations involved in this general approach are detailed as an example for N = 3 for the particular system of two coupled nonlinear Schrödinger equations in the defocusing, focusing and mixed regimes. The instabilities of the continuous wave solutions are fully discussed in the entire parameter space of their amplitudes and wave numbers. By defining and computing the spectrum in the complex plane of the spectral variable, the eigenfrequencies are explicitly expressed. According to their topological properties, the complete classification of these spectra in the parameter space is presented and graphically displayed. The continuous wave solutions are linearly unstable for a generic choice of the coupling constants.

Generation of two-temporal-mode photon states by vector four-wave mixing

Photon pair states and multiple-photon squeezed states have many applications in quantum information science. In this paper, Green functions are derived for spontaneous four-wave mixing in the low- and high-gain regimes. Nondegenerate four-wave mixing in a strongly-birefringent medium generates signal and idler photons that are associated with only one pair of temporal (Schmidt) modes, for a wide range of pump powers and arbitrary pump shapes. The Schmidt coefficients (expected photon numbers) depend sensitively on the pump powers, and the Schmidt functions (shapes of the photon wavepackets) depend sensitively on the pump powers and shapes, which can be controlled.

Self-inscribed antisymmetric long-period grating in a dual-core As2Se3-PMMA fiber

We report for the first time that transmission of optical pulses centered at a wavelength of 1550 nm through a tapered dual-core As₂Se₃-PMMA fiber inscribes an antisymmetric long-period grating. The pulse power is equally divided between even and odd modes that superpose along the dual-core fiber to form an antisymmetric intensity distribution. A permanent refractive-index change that matches the antisymmetric intensity distribution is inscribed due to photosensitivity at the pulse central wavelength. The evolution of the transmission spectrum of the dual-core fiber is experimentally measured as the accumulated time that the fiber is exposed to the pulse is increased. A theoretical model of an antisymmetric long-period grating in a dual-core fiber computationally reproduces the experimentally observed evolution of the transmission spectrum. Experimental results indicate that antisymmetric long-period gratings induce effective group-velocity matching between the even and odd modes of the dual-core fiber, and reveal for the first time that long-period gratings can lead to slow light propagation velocities.

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.

High-quality ultraviolet beam generation in multimode photonic crystal fiber through nondegenerate four-wave mixing at 532 nm

All-fiber ultraviolet (UV) light sources are of great practical interest for a multitude of applications spanned across different sectors, from industrial processes such as nonthermal, high-resolution materials processing, to biomedical applications such as eye surgery, to name a few. However, production of UV light sources with high beam quality has been a problem to this day as the fiber designs required to reach UV wavelengths by four-wave mixing with widely available pumps (i.e., 532 nm) are challenging because of their small size and increased risk of material damage. In this Letter, a specific pumping scheme is presented that allows the conversion of two pump photons in different modes to UV light in the fundamental mode and the corresponding idler in a higher order mode. The process has also been shown to work experimentally, and UV light at 390.5 nm in the fundamental mode was successfully generated.

Vector rogue waves and baseband modulation instability in the defocusing regime

We report and discuss analytical solutions of the vector nonlinear Schrödinger equation that describe rogue waves in the defocusing regime. This family of solutions includes bright-dark and dark-dark rogue waves. The link between modulational instability (MI) and rogue waves is displayed by showing that only a peculiar kind of MI, namely baseband MI, can sustain rogue-wave formation. The existence of vector rogue waves in the defocusing regime is expected to be a crucial progress in explaining extreme waves in a variety of physical scenarios described by multicomponent systems, from oceanography to optics and plasma physics.

Cross-phase modulational instability induced by Raman scattering in highly birefringent fiber

We report experimental and theoretical studies of Raman-induced cross-phase modulational instabilities (XPMI) in a high-birefringence, normally dispersive optical fiber. Experimental results reveal that the Raman-Stokes wave, generated by a quasi-CW pump beam, interacts with the latter to create a novel type of XPMI sidebands. These sidebands are characterized by a narrow gain bandwidth. The sideband frequencies are well reproduced by a linear stability analysis as well as by full numerical solutions of the coupled generalized nonlinear Schrödinger equations.

Simultaneous scalar and cross-phase modulation instabilities in highly birefringent photonic crystal fiber

We report the experimental observation of scalar and cross-phase modulation instabilities by pumping a highly birefringent photonic crystal fiber in the normal dispersion regime at 45° to its principal polarization axes. Five sideband pairs (two scalar and three vector ones) are observed simultaneously in the spontaneous regime, four of which have a large frequency shift from the pump, in the range 79-93 THz. These results are in excellent agreement with phase-matching arguments and numerical simulations.

Observation of modulationally unstable multi-wave mixing

We demonstrate experimentally that multiple four-wave mixing (FWM) pumped by a dual-frequency input in a single-mode fiber is modulationally unstable. This collective type of instability leads, in the anomalous dispersion regime, to sideband growth around all orders of FWM. This is in contrast with the normal dispersion regime where our measurements show that FWM exhibits no instability. Our conclusions are based on the first systematic mapping of the phenomenon as a function of the dual-pump input frequency separation.

Collective modulation instability of multiple four-wave mixing

We investigate the modulation instability of multiple four-wave mixing arising from a dual-frequency pump in a single-mode fiber or waveguide. By applying the Floquet theory on account of the periodic nature of four-wave mixing, we reveal a collective type of instability occurring in the anomalous dispersion regime. Our interpretation of the linear stability analysis is validated by the numerical solution of the nonlinear Schrödinger equation.

Impact of the third-order dispersion on the modulation instability gain of pulsed signals

We demonstrate that modulation instability gain of time-localized signals (i.e., pulsed signals) depends strongly on the third-order dispersion, contrary to the well-known case of time-extended signals (cw signals). This surprising contribution of an odd dispersion term on this four-photon-mixing process is established analytically and confirmed by numerical simulations.

Polarization-independent amplification and frequency conversion in strongly-birefringent fibers

The inverse modulation interaction is a degenerate four-wave mixing process in which two strong pumps drive a weak signal, whose frequency is the average of the pump frequencies. Theoretical analyses and numerical simulations of this process are made for wave frequencies that are near the zero-dispersion frequency of a fiber, in which case dispersion is unimportant, and wave frequencies that are far from the zero-dispersion frequency, in which case dispersion is important. The results show that the inverse modulation interaction in a strongly-birefringent fiber amplifies a linearly-polarized signal by an amount that depends on its phase angle, but not its polarization angle. Phase conjugation and Bragg scattering are nondegenerate four-wave mixing processes in which two strong pumps drive a weak signal and a weak idler. Studies show that phase conjugation and Bragg scattering in strongly-birefringent fibers produce polarization-independent phase-insensitive amplification and frequency conversion, respectively.

Control and removal of modulational instabilities in low-dispersion photonic crystal fiber cavities

Taking up to fourth-order dispersion effects into account, we show that fiber resonators become stable for a large intensity regime. The range of pump intensities leading to modulational instability becomes finite and controllable. Moreover, by computing analytically the thresholds and frequencies of these instabilities, we demonstrate the existence of a new unstable frequency at the primary threshold. This frequency exists for an arbitrary small but nonzero fourth-order dispersion coefficient. Numerical simulations for a low and flattened dispersion photonic crystal fiber resonator confirm analytical predictions and open the way to experimental implementation.

Modulation instability in silicon photonic nanowires

We demonstrate that strong modulation instability (MI) of copropagating optical waves can be observed in Si photonic nanowires with a length of only a few millimeters. We consider two distinct cases, namely one in which one wave propagates in the normal group-velocity dispersion (GVD) region and the other one experiences anomalous GVD, and a second case in which both waves propagate in the anomalous GVD region. In both cases we show that, for comparable optical powers, the peak value of the MI gain spectrum is 2 to 3 orders of magnitude larger than that achieved in optical fibers.

Polarization modulation instability in photonic crystal fibers

Polarization modulation instability (PMI) in birefringent photonic crystal fibers has been observed in the normal dispersion regime with a frequency shift of 64 THz between the generated frequencies and the pump frequency. The generated sidebands are orthogonally polarized to the pump. From the observed PMI frequency shift and the measured dispersion, we determined the phase birefringence to be 5.3 x 10(-5) at a pump wavelength of 647.1 nm. This birefringence was used to estimate the PMI gain as a function of pump wavelength. Four-wave mixing experiments in both the normal and the anomalous dispersion regimes generated PMI frequency shifts that show good agreement with the predicted values over a 70 THz range. These results could lead to amplifiers and oscillators based on PMI.

Cross-phase modulation instability in photonic crystal fibers

We report on the observation of cross-phase modulation instability in a highly nonlinear photonic crystal fiber. In such fibers the presence of higher orders of dispersion results in a complex phase-matching curve. We are able to observe this behavior experimentally and obtain excellent agreement between the measured and predicted shifts.

Cross-phase-modulation-induced instability in photonic-crystal fibers

Cross-phase-modulation-induced instability is identified as a significant mechanism for efficient parametric four-wave-mixing frequency conversion in photonic-crystal fibers. Fundamental-wavelength femtosecond pulses of a Cr, forsterite laser are used in our experiments to transform the spectrum of copropagating second-harmonic pulses of the same laser in a photonic-crystal fiber. Efficient generation of sidebands shifted by more than 80 THz with respect to the central frequency of the second harmonic is observed in the output spectrum of the probe field.

Vector modulation instability induced by vacuum fluctuations in highly birefringent fibers in the anomalous-dispersion regime

We report a detailed experimental study of vector modulation instability in highly birefringent optical fibers in the anomalous-dispersion regime. We prove that the observed instability is mainly induced by vacuum fluctuations. The detuning of the spectral peaks agrees with linear perturbation analysis. The exact shape of the spectrum is well reproduced by numerical integration of stochastic nonlinear Schrödinger equations describing quantum propagation.

Modulational instability and parametric amplification induced by loss dispersion in optical fibers

We show that modulational instability may arise even in the normal group-velocity dispersion regime of an optical fiber when the fiber loss (gain) varies depending on the wavelength. A simple analytical expression for the instability gain is obtained, which reveals that the odd-order terms of the loss dispersion are responsible for this phenomenon. The instability gain is measured experimentally in an optical-parametric-amplification configuration. Large parametric gain is induced in a non-phase-matched regime as we apply narrow band loss at the idler wavelength.

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.

Modulational instability of bright solitary waves in incoherently coupled nonlinear Schrödinger equations

We present a detailed analysis of the modulational instability (MI) of ground-state bright solitary solutions of two incoherently coupled nonlinear Schrödinger equations. Varying the relative strength of cross-phase and self-phase effects we show the existence and origin of four branches of MI of the two-wave solitary solutions. We give a physical interpretation of our results in terms of the group-velocity-dispersion- (GVD-) induced polarization dynamics of spatial solitary waves. In particular, we show that in media with normal GVD spatial symmetry breaking changes to polarization symmetry breaking when the relative strength of the cross-phase modulation exceeds a certain threshold value. The analytical and numerical stability analyses are fully supported by an extensive series of numerical simulations of the full model.

Observation of modulational instability induced by velocity-matched cross-phase modulation in a normally dispersive bimodal fiber

We demonstrate experimentally the existence of cross-phase-modulation-induced modulational instability in the absence of group-velocity mismatch between the interacting nonlinear dispersive waves. The experiment is performed by means of a normally dispersive isotropic bimodal fiber. The group-velocity mismatch between the fundamental and the first-order modes that constitute the two interacting waves is controlled by wavelength tuning. A strong power dependence of the modulational instability spectra is observed near the condition of group-velocity matching.

Quasi-phase-matched modulation instability in birefringent fibers

The phase-sensitive nature of polarization modulation instability has been demonstrated in optical fibers whose birefringence has been manipulated to generate phase mismatches. Quasi-phase-matched modulation instability has been demonstrated, and the gain of the quasi-phase-matched sidebands has been investigated. The results are in good agreement with experiment.

Demonstration of a nonlinear gap in the modulational instability spectra of wave propagation in highly birefringent fibers

We investigate modulational instability in normally dispersive highly birefringent fibers. By means of a technique based on a two-frequency pump field we are able to provide evidence for strong nonlinear dependence of the modulational instability spectra. This dependence manifests itself by the appearance of a nonlinear spectral gap in which modulational instability vanishes.

Effect of modulation instability on phase modulation-amplitude modulation conversion in optical fibers

Phase modulation-amplitude modulation conversion in dispersive fibers is affected by nonlinear phase modulation and modulation instability. A differential equation is derived under adiabatic approximations and is solved analytically. The results agree well with experimental values. A simple measurement of the nonlinear coeff icient is thus feasible.

Polarization modulation instability in weakly birefringent fibers

Modulation instability generated by the coherent interaction of two polarization modes in a weakly birefringent optical fiber has been observed in the normal dispersion regime. In contrast to previous observations of crossphase-modulation instability in the visible, the two generated sidebands have the same polarization, which is orthogonal to that of the pump, and their frequency shift is readily controlled by variation of the birefringence of the fiber. The frequency of the modulation and its qualitative features agree with those theoretically predicted.

Induced modulational instability in high-birefringence fibers: the strong conversion regime

We show that modulational instability pumped by a mixed mode beam propagating in a high-birefringence fiber is driven in the regime of strong conversion by a four-wave-mixing interaction. This allows one to predict new period-doubling instabilities as well as the optimum conditions for frequency conversion.

Observation of the buildup of modulational instability from wave breaking

Orthogonally polarized pulses copropagating in birefringent fiber are observed to develop coherent terahertz intensity oscillations owing to modulational instability. Rather than forming spontaneously from noise with random phase, the modulational instability is coherently initiated from wave-breaking oscillations. This results in stable terahertz oscillations that have little timing jitter from pulse to pulse. Experimentally this is evidenced by the terahertz modulation observed in cross correlations that are obtained by averaged sampling over many pulses. Numerical integrations of coupled nonlinear Schrödinger equations verify this description.