Anomalous Dispersion Regime Research Articles

Stable dispersion-managed soliton molecules in Yb-doped polarization-maintaining fiber laser with chirped fiber Bragg grating

We present stable dispersion-managed soliton (DMS) molecules in a passively mode-locked Yb-doped polarization-maintaining fiber laser based on chirped fiber Bragg grating in the anomalous dispersion regime. The generation of DMSs are characterized by their sech2-like spectral profile with no steep spectral edges, which is distinct from those of dissipative solitons generated in Yb-doped fiber lasers with a large net positive cavity group velocity dispersion regime. The pulse width is 4.8 ps if the sech2 profile is assumed. The corresponding pulses width could be compressed to 278 fs with grating pair compressor. Furthermore, DMS molecules exhibit multiple discrete equilibrium distances and a regular spectral modulation pattern. All these DMS molecules are stable in the sense that after being obtained they can remain several days. The proposed laser proves its great potential to future practical use in high-resolution optics for coding and optical communication.

Modulation instability in two-dimensional waveguide arrays with alternating signs of refractive index

We consider the propagation of coupled forward and backward waves in two-dimensional arrays of alternating waveguides with positive and negative refractive indices. The array has a cross section in the form of a face-centered square lattice. The unit cell consists of three different waveguides with different optical properties. We obtain the condensate solutions for electromagnetic pulse propagation in such an array of waveguides. The base equations describing this model have solutions that correspond to the static and homogeneous intensity distribution on the waveguides. The stability of these solutions in both normal and anomalous dispersion regimes is also investigated using modulation instability analysis.

Soliton mode-locked thulium-doped fiber laser with cobalt oxide saturable absorber

Abstract In this work, we propose and demonstrate a mode-locked thulium doped fiber laser (TDFL) with an integrated cobalt oxide (Co3O4) saturable absorber (SA). The SA is fabricated by suspending Co3O4 nanosheets in a polymer film before being secured between two fiber ferules. The laser operates in the anomalous dispersion regime, confirmed by the Kelly sidebands observed in the obtained optical spectrum. Mode-locking operation is obtained at a low threshold pump power of 77.32 mW, with further optimizations made using a polarization controller The laser generates pulses with a repetition rate of 11.36 MHz and a pulse width of 1.39 ps. The generated pulses are highly stable, with a high signal-to-noise ratio of 46.00 dB and minimum power fluctuations indicating a long-term stability. This work demonstrates a simple and a low-cost laser that would have potential applications for operation near the 2.0-µm region, especially for medical applications.

XPM-induced modulation instability in silicon-on-insulator nano-waveguides and the impact of nonlinear losses

We have carried out an extensive theoretical study of cross-phase modulation induced modulation instability (MI) in a silicon-on-insulator nano-waveguide for two co-propagating waves. The analysis has been performed for two sets (with zero and varying non-zero walk-off parameter) of three different cases: when the two waves are in (i) normal dispersion regime, (ii) anomalous dispersion regime, and (iii) different dispersion regimes. In particularly, we have discussed the nonlinear losses due to two-photon absorption and free-carrier absorption. Further, we have investigated the impact of the walk-off parameter on the MI gain spectrum in the above three cases.

Dispersion engineered high quality lithium niobate microring resonators.

Lithium niobate (LN) exhibits outstanding material properties with great potential for many applications. Recent advance in LN integrated photonics on chip-scale platforms has shown significant advantages in device engineering and functionality innovation. Precise engineering of group-velocity dispersion (GVD) is crucial for many important nonlinear photonic applications. In this paper, we demonstrate high-Q LN microring resonators, with optical Q above 1 million, whose GVD can be flexibly controlled in both normal and anomalous dispersion regimes, with a value between -0.128 ps2/m and 0.043 ps2/m in the telecom band, by controlling the device cross section and by utilizing the birefringence. We are able to achieve a small anomalous GVD of -0.015 ps2/m that is even smaller than that of a silica optical fiber. The flexible engineering of GVD paves a critical step towards broad nonlinear photonic applications in high-Q LN microring resonators.

Dissipative solitons with extreme spikes in the normal and anomalous dispersion regimes.

Prigogine's ideas of systems far from equilibrium and self-organization (Prigogine & Lefever. 1968 J.Chem. Phys.48, 1695-1700 (doi:10.1063/1.1668896); Glansdorff & Prigogine. 1971 Thermodynamic theory of structures, stability and fluctuations New York, NY/London, UK: Wiley) deeply influenced physics, and soliton science in particular. These ideas allowed the notion of solitons to be extended from purely integrable cases to the concept of dissipative solitons. The latter are qualitatively different from the solitons in integrable and Hamiltonian systems. The variety in their forms is huge. In this paper, one recent example is considered-dissipative solitons with extreme spikes (DSESs). It was found that DSESs exist in large regions of the parameter space of the complex cubic-quintic Ginzburg-Landau equation. A continuous variation in any of its parameters results in a rich structure of bifurcations.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)'.

Fast light in the generation configuration of stimulated Brillouin scattering based on high-Q micro-cavities.

In this article, we reported self-pumped stimulated Brillouin scattering (SBS)-induced fast light in a micro-resonator. The optically induced thermal effect in the micro-resonator will lead to a shift of the dispersion spectrum and make the SBS gain occurred in the anomalous dispersion regime. The group delay could be experimentally optimized from -91.0 microsecond to 2.6 microsecond by changing the modulation frequency in a microsphere with its diameter of 175 μm. The experimental results will benefit applications utilizing anomalous dispersion such as gyroscope.

Highly stable mode-locked fiber laser with graphene oxide-coated side-polished D-shaped fiber saturable absorber

A highly stable mode-lock fiber laser with a thin film coating of graphene oxide (GO) nanoparticles on a D-shaped fiber is proposed and demonstrated. The GO-coated D-shaped fiber, which serves as the cavity's saturable absorber (SA), is fabricated by drop-casting GO nanoparticles on the smooth and consistently polished area of the D-shaped fiber made using a disk-polishing machine. Mode-locking is induced through the interaction of the evanescent field from the D-shaped fiber and GO nanoparticle layer. The cavity has a length of 12.5 m with a fundamental frequency of 16.5 MHz and operates in the anomalous dispersion regime. Stable soliton modelocking is obtained above a pump power of 76.6 mW, with a central lasing wavelength of 1555.7 nm and welldefined Kelly's sidebands. The generated pulses have a repetition rate of 16.5 MHz and pulse duration of 1.18 ps over a pump power range of 76.6 to 280.5 mW, with only minor fluctuations observed. A signal-to-noise ratio of 58.3 dB is computed, indicating a highly stable output. The proposed SA fabrication technique provides a simple, cost-effective, and consistent method of generating mode-locked pulses in fiber lasers. © 2018 Society of Photo-Optical Instrumentation Engineers (SPIE).

Generation of bound states of pulses in a SESAM mode-locked Cr:ZnSe laser

We report on the generation of bound states of pulses in a SESAM mode-locked Cr:ZnSe laser around 2415 nm. A thulium-doped double-clad fiber laser at 1908 nm was used as the pump source. Bound states with various pulse separations at different dispersion regimes were obtained. Especially, in the anomalous dispersion regime, vibrating bound state of solitons exhibiting an evolving phase was obtained.

Effects of Nanomaterial Saturable Absorption on Passively Mode-Locked Fiber Lasers in an Anomalous Dispersion Regime: Simulations and Experiments

In recent years, several kinds of nanomaterials have been successfully used for passive mode-locking, but it is not fully understand how the mode-locking performance is influenced by the different characteristics of these saturable absorbers (SAs). In this paper, we numerically and experimentally investigate the effects of nanomaterial saturable absorption (e.g., modulation depth and saturation intensity) on a passively mode-locked fiber laser in an anomalous dispersion regime. First, by numerically solving the Ginzburg–Landau equation, we analyze the evolution of the output performances (spectral bandwidth, pulse duration, and peak power) of passively mode-locked Er $^{3+}$ -doped fiber laser as the SA's modulation depth or saturation intensity. Then, we fabricate four nanomaterial-based SAs, which have the different modulation depth from 1.8% to 19.1%, the different saturation intensity from 11 to 180 MW/cm $^{2}$ , and the similar insertion loss of $\sim$ 3 dB. Finally, we perform the experimental comparison of passively mode-locked Er $^{3+}$ -doped fiber laser using the four nanomaterial-based SAs, respectively. Our results reveal that: 1) as the modulation depth increases, the mode-locked spectral bandwidth becomes wide and the pulse duration becomes short; and 2) the SA's saturation intensity has little influence on the output performance. The experimental results are in good agreement with the numerical simulations. This work could provide a useful guideline for choosing proper nanomaterial-based SA for different practical applications.

Route to Larger Pulse Energy in Ultrafast Fiber Lasers

Principles of pulse shaping aiming larger pulse energy in fiber lasers are reviewed. From conventional solitons generated in the anomalous dispersion regime, stretched pulses in dispersion-managed fiber lasers, similaritons in normal dispersion regime, dissipative solitons in large normal dispersion regime, and amplifier similaritons in fiber lasers with narrow bandwidth filtering to dissipative-soliton-resonance (DSR) pulses in fiber lasers, scaling of pulse energy from picojoule level to microjoule is successfully achieved. DSR is a possible way to achieve endless pulse energy, which is limited by the available pump power and material damage threshold. Properties of DSR pulses are reviewed. Specifically, we experimentally and numerically demonstrate tilt-top DSR pulses in a normal dispersion mode-locked fiber laser. Two fronts of the tilt-top pulses exhibit different intensity, and the intensity disparity maintains while the pulses extend with increasing gain. The tilt-top DSR pulses have rectangular spectral pedestal and a peak. The spectral peak deviates from the center of the rectangle spectral pedestal. Further results show that the asymmetry of two fronts is closely related to the wavelength deviation of spectral peak. Numerical simulations reveal the importance of the saddle-type spectral filtering on asymmetric DSR pulse generation.

Soliton Booting Dynamics in an Ultrafast Anomalous Dispersion Fiber Laser

We reported on the soliton booting dynamics of an ultrafast fiber laser operating in an anomalous dispersion regime. Based on the advanced experimental methodologies of spatio-temporal reconstruction and dispersive Fourier transform (DFT), the soliton booting dynamics are analyzed in the time and spectral domains. The spectral interference pattern with strong intensity oscillation behavior was observed near the mode-locking transition. It was found that the spectral pattern distributions are induced by the transient structured soliton formation during the pulse shaping from the noise background. The experimental results were further verified by the theoretical simulations. The obtained results would provide a general guideline for understanding the soliton booting dynamics in the ultrafast fiber lasers, and will prove to be fruitful to the various communities interested in solitons and fiber lasers.

Critical Power in Three-Core Photonic Crystal Fibers

When a photonic crystal fiber has more than one core, the switching capacity loss among the cores as of a given power, called critical power, becomes a relevant effect for switching applications. In this paper, we study the critical power obtained when ultrashort pulses are propagated in a nonlinear directional coupler. Here, we consider the specific example of a three-core photonic crystal fiber in two possible arrangements: one-dimensional and triangular array. In each core, the pulses propagate in the anomalous dispersion regime, in which an input pulse in the form of a hyperbolic secant is injected into one of the cores, considering different input peak powers. By relating the group velocity dispersion and the coupling coefficient with the temporal width of the input pulse, we can observe some relations between the fiber parameters and the critical power. In addition, we show that when self-phase modulation is combined with other effects, the critical power can be increased or decreased depending on the combination of these effects.

Stability and interaction of few-cycle pulses in a Kerr medium.

The different aspects of few-cycle pulse dynamics governed by the regularized short pulse equation (RSPE) are reported. It is shown that the RSPE provides an accurate description of the dynamics of the few-cycle pulse whose duration is larger than a single optical period when the few-cycle pulse's spectrum is in the medium's anomalous dispersion regime. The approximate solutions of the RSPE are constructed from the soliton solutions of the nonlinear Schrödinger (NLS) equation. We demonstrate numerically that the stability of these few-cycle pulses strongly depends on their pulse duration. Furthermore, the interactions of the two and three few-cycle pulses are studied. When pulse parameters are suitably chosen, we show the elastic collision, inelastic collision and repulsive interaction between these multi few-cycle pulses. It is revealed that the interactions of the multi few-cycle pulses rely heavily on their pulse duration.

Influences of multiphoton absorption and free-carrier effects on frequency-comb generation in normal dispersion silicon microresonators

We investigate frequency-comb generation in normal dispersion silicon microresonators from the near-infrared to mid-infrared wavelength range in the presence of multiphoton absorption and free-carrier effects. It is found that parametric oscillation is inhibited in the telecom wavelength range resulting from strong two-photon absorption. On the contrary, beyond the wavelength of 2200 nm, where three- and four-photon absorption are less detrimental, a comb can be generated with moderate pump power, or free-carriers are swept out by a positive-intrinsic-negative structure. In the temporal domain, the generated combs correspond to flat-top pulses, and the pulse duration can be easily controlled by varying the laser detuning. The reported comb generation process shows a high conversion efficiency compared with anomalous dispersion regime, which can guide and promote comb formation in materials with normal dispersion. As the comb spectra cover the mid-infrared wavelength range, they can find applications in comb-based radiofrequency photonic filters and mid-infrared spectroscopy.

The cubic–quintic–septic complex Ginzburg–Landau equation formulation of optical pulse propagation in 3D doped Kerr media with higher-order dispersions

We investigate the propagation characteristics and stabilization of generalized-Gaussian pulse in highly nonlinear homogeneous media with higher-order dispersion terms. The optical pulse propagation has been modeled by the higher-order (3+1)-dimensional cubic–quintic–septic complex Ginzburg–Landau [(3+1)D CQS-CGL] equation. We have used the variational method to find a set of differential equations characterizing the variation of the pulse parameters in fiber optic-links. The variational equations we obtained have been integrated numerically by the means of the fourth-order Runge–Kutta (RK4) method, which also allows us to investigate the evolution of the generalized-Gaussian beam and the pulse evolution along an optical doped fiber. Then, we have solved the original nonlinear (3+1)D CQS-CGL equation with the split-step Fourier method (SSFM), and compare the results with those obtained, using the variational approach. A good agreement between analytical and numerical methods is observed. The evolution of the generalized-Gaussian beam has shown oscillatory propagation, and bell-shaped dissipative optical bullets have been obtained under certain parameter values in both anomalous and normal chromatic dispersion regimes. Using the natural control parameter of the solution as it evolves, named the total energy Q, our numerical simulations reveal the existence of 3D stable vortex dissipative light bullets, 3D stable spatiotemporal optical soliton, stationary and pulsating optical bullets, depending on the used initial input condition (symmetric or elliptic).

Generation of bright-dark soliton trains with a central wide dip in optical fibers

The nonlinear propagation dynamics of the dark soliton pulse with hyperbolic tangent profile in the anomalous dispersion regime of an optical fiber is investigated numerically. The corresponding temporal evolutions are provided for different integral or non-integral soliton order and loss perturbations. The results show that, irrespective of the integral or non-integral soliton order, with increase of distance, the width of the dark soliton broadens and more and more bright and dark pulses appear symmetrically on the two sides of the central black soliton. Correspondingly, bright-dark soliton trains with a central wide black soliton can gradually form. The higher the soliton order, the more the bright-dark pulses at the same distance. With increase of distance, the peak values of the bright pulses exhibit oscillation behavior. The loss perturbation only influences the evolutions slightly, which means that the generated soliton trains can resist loss perturbations to some extent. Moreover, this work provides us an alternative approach to generate bright-dark soliton trains by using the dark soliton pulse propagating in the anomalous dispersion regime of the passive optical fiber besides directly using the fiber laser.

Effects of intermode nonlinearity and intramode nonlinearity on modulation instability in randomly birefringent two-mode optical fibers

We analyze in detail the effects of the intermode nonlinearity (IEMN) and intramode nonlinearity (IRMN) on modulation instability (MI) in randomly birefringent two-mode optical fibers (RB-TMFs). In the anomalous dispersion regime, the MI gain enhances significantly as the IEMN and IRMN coefficients increases. In the normal dispersion regime, MI can be generated without the differential mode group delay (DMGD) effect, as long as the IEMN coefficient between two distinct modes is above a critical value, or the IRMN coefficient inside a mode is below a critical value. This critical IEMN (IRMN) coefficient depends strongly on the given IRMN (IEMN) coefficient and DMGD for a given nonlinear RB-TMF structure, and is independent on the input total power, the power ratio distribution and the group velocity dispersion (GVD) ratio between the two modes. On the other hand, in contrast to the MI band arising from the pure effect of DMGD in the normal dispersion regime, where MI vanishes after a critical total power, the generated MI band under the combined effects of IEMN and IRMN without DMGD exists for any total power and enhances with the total power. The MI analysis is verified numerically by launching perturbed continuous waves (CWs) with wave propagation method.

Cross-phase-modulation-induced temporal reflection and waveguiding of optical pulses

Cross-phase modulation (XPM) is commonly viewed as a nonlinear process that chirps a probe pulse and modifies its spectrum when an intense pump pulse overlaps with it. Here we present an alternative view of XPM in which the pump pulse creates a moving refractive-index boundary that splits the probe pulse into two parts with distinct optical spectra through temporal reflection and refraction inside a dispersive nonlinear medium. The probe even undergoes a temporal version of total internal reflection for sufficiently intense pump pulses, a phenomenon that can be exploited for making temporal waveguides. We investigate the practical conditions under which XPM can be exploited for temporal reflection and waveguiding. The width and shape of the pump pulses as well as the nature of the medium dispersion at the pump and probe wavelengths (normal versus anomalous) play important roles. The super-Gaussian shape of a pump pulse is particularly helpful because of the relatively sharp edges of the super-Gaussian shape. When the pump wavelength lies in the anomalous-dispersion regime, the pump pulse can form a soliton, whose unique properties can be exploited to our advantage. We also discuss a potential application of XPM-induced temporal waveguides for compensating for timing jitter.

Decomposition of group-velocity-locked-vector-dissipative solitons and formation of the high-order soliton structure by the product of their recombination.

By using a polarization manipulation and projection system, we numerically decomposed the group-velocity-locked-vector-dissipative solitons (GVLVDSs) from a normal dispersion fiber laser and studied the combination of the projections of the phase-modulated components of the GVLVDS through a polarization beam splitter. Pulses with a structure similar to a high-order vector soliton could be obtained, which could be considered as a pseudo-high-order GVLVDS. It is found that, although GVLVDSs are intrinsically different from group-velocity-locked-vector solitons generated in fiber lasers operated in the anomalous dispersion regime, similar characteristics for the generation of pseudo-high-order GVLVDS are obtained. However, pulse chirp plays a significant role on the generation of pseudo-high-order GVLVDS.