Normal Dispersion Regime Research Articles

Coherent supercontinuum generation in all-normal dispersion Si3N4 waveguides.

Spectral broadening of optical frequency combs with high repetition rate is of significant interest in optical communications, radio-frequency photonics and spectroscopy. Silicon nitride waveguides (Si3N4) in the anomalous dispersion region have shown efficient supercontinuum generation spanning an octave-bandwidth. However, the broadening mechanism in this regime is usually attained with femtosecond pulses in order to maintain the coherence. Supercontinuum generation in the normal dispersion regime is more prone to longer (ps) pulses, but the implementation in normal dispersion silicon nitride waveguides is challenging as it possesses strong requirements in propagation length and losses. Here, we experimentally demonstrate the use of a Si3N4 waveguide to perform coherent spectral broadening using pulses in the picosecond regime with high repetition rate. Moreover, our work explores the formation of optical wave breaking using a higher energy pulse which enables the generation of a coherent octave spanning spectrum. These results offer a new prospect for coherent broadening using long duration pulses and replacing bulky optical components.

Mode crossing induced soliton frequency comb generation in high-Q yttria-stabilized zirconia crystalline optical microresonators

We demonstrate for the first time, to the best of our knowledge, the fabrication of high- Q crystalline optical microresonators from cubic yttria-stabilized zirconia (YSZ). Intrinsic Q factors up to 80 million are obtained, indicating an upper bound absorption coefficient of 0.001 cm − 1 for YSZ crystals at the telecom wavelength. Through laser-scanned spectroscopy on a few-mode YSZ microresonator with a radius of 300 μm, we find that the mode crossing effect in the case of weak coupling can induce a repelling disruption of free spectral range values between transverse mode families. Generation of soliton and soliton crystals in such a YSZ microcomb platform operated in the normal dispersion regime is observed. A breathing comb behavior is also reported. Our finding has enriched comb generation platforms with potential multidisciplinary capabilities linked to properties of YSZ crystals in superconducting films and sensors.

Multiple coherent dispersive waves generation in silicon nitride slot waveguide

A method to generate multiple dispersive waves (DWs) with pumping in a normal dispersion regime is proposed. We show flexibility of producing four DWs in a silicon nitride (Si3N4) slot waveguide and explain the underlying dynamics of a four DWs generation process in detail, i.e., DWs emission via the optical wave-breaking phenomenon in an anomalous dispersion regime. Compression of the first anomalous DW results in the subsequent cascade DW generation. Combined with the soliton induced blue-shifted dispersive wave and red-shifted dispersive wave, the spectrum spans from visible to mid-IR with high coherence. The four DWs generation process has agreement with prediction of the phase-matching condition. Overall, this multiple DWs generation method in a Si3N4 waveguide provides the possibility for having an efficient, compact, and coherent mid-IR light source.

Impact of higher order dispersions and nonlinearities on instability criterion of oppositely directed coupler in the presence of negative index material channel

This paper intends to investigate the modulational instability (MI) criterion of two core positive-negative index coupler channel setup from the obtained analytical dispersion relation for MI gain profile. The governing equation, the modified nonlinear Schrodinger equation (MNLSE) is studied for the role of higher order dispersion (HOD) and higher order nonlinearity (HON) on instability spectra of two core positive indexed coupler (PIM) and negative indexed coupler (NIM) arrangement. The HOD comprises of the second, third, fourth and fifth order linear dispersion terms and HON is inclusive of cubic, quintic, septic, cubic-quintic-septic-self-steepening (SS), and cubic-quintic-septic-intrapulse Raman scattering (IRS). Our study reveals that it is the 6th order linear dispersion term which brings in the considerable changes of MI gain spectrum in both normal and anomalous dispersion regimes. In particular, the combined effect of septic SS and IRS in two core directional coupler with NIM channel proves to be very crucial in the generation of instability gain spectra. This study has higher prospects in generation of solitary wave in two core directional system for optical fiber communication.

Temporal walk-off induced dissipative quadratic solitons

A plethora of applications have recently motivated extensive efforts on the generation of low noise Kerr solitons and coherent frequency combs in various platforms ranging from fiber to whispering gallery and integrated microscale resonators. However, the Kerr (cubic) nonlinearity is inherently weak, and in contrast, strong quadratic nonlinearity in optical resonators is expected to provide an alternative means for soliton formation with promising potential. Here, we demonstrate the formation of a dissipative quadratic soliton via non-stationary optical parametric amplification in the presence of significant temporal walk-off between pump and signal leading to half-harmonic generation accompanied by a substantial pulse compression (exceeding a factor of 40) at low pump pulse energies ($\sim$ 4 picojoules). The bright quadratic soliton forms in a low-finesse cavity in both normal and anomalous dispersion regimes, which is in stark contrast with bright Kerr solitons. We present a route to significantly improve the performance of the demonstrated quadratic soliton when extended to an integrated nonlinear platform to realize highly-efficient extreme pulse compression leading to the formation of few-cycle soliton pulses starting from ultra-low energy picosecond scale pump pulses that are widely tunable from ultra-violet to mid-infrared spectral regimes.

Modulation instability of Kerr optical frequency combs in dual-coupled optical cavities

Kerr optical frequency combs generated in a coherently driven Kerr nonlinear resonator have the potential for a wide range of applications. However, in a single cavity which is a widely adopted configuration for Kerr optical frequency-comb generation, modulation instability is suppressed in the normal dispersion regime, and the pump-to-comb conversion efficiency is extremely low for a single dissipative Kerr soliton (DKS) in the anomalous dispersion regime. Dual-coupled cavities have been proposed to generate Kerr optical frequency combs in the normal dispersion regime, and have the potential to remarkably increase conversion efficiency for Kerr optical frequency combs. Here, we investigate modulation instability and Kerr optical frequency-comb formation in dual-coupled cavities. Based on solutions of the continuous-wave steady state, we obtain a quadric algebraic equation describing the modulation instability gain, and we find that it is intensely influenced by the scaled free spectral range mismatch between the two cavities. Our numerical simulations demonstrate that platicons can be generated via a pump scanning scheme for the case that both the two cavities possess normal dispersion, and a single DKS can be generated in the cavity with anomalous dispersion while the dispersion of the other cavity is normal. The conversion efficiency of a single DKS is determined by the pump power and detunings as well as intrinsic quality factors of two cavities. Our analysis of modulation instability provides a powerful tool for Kerr optical frequency-comb generation via pump modulation and cavity detuning tuning scheme in dual-coupled cavities.

Dark-Bright Soliton Bound States in a Microresonator.

Dissipative Kerr solitons in microresonators have facilitated the development of fully coherent, chip-scale frequency combs. In addition, dark soliton pulses have been observed in microresonators in the normal dispersion regime. Here, we report bound states of mutually trapped dark-bright soliton pairs in a microresonator. The soliton pairs are generated seeding two modes with opposite dispersion but with similar group velocities. One laser operating in the anomalous dispersion regime generates a bright soliton microcomb, while the other laser in the normal dispersion regime creates a dark soliton via Kerr-induced cross-phase modulation with the bright soliton. Numerical simulations agree well with experimental results and reveal a novel mechanism to generate dark soliton pulses. The trapping of dark and bright solitons can lead to light states with the intriguing property of constant output power while spectrally resembling a frequency comb. These results can be of interest for telecommunication systems, frequency comb applications, and ultrafast optics.

All-fiber high-power spatiotemporal mode-locked laser based on multimode interference filtering.

Multimode interference (MMI) has been considered to be critical and investigated extensively in mode-locked laser based on single transverse mode systems, whereas there are few researches related to three-dimensional nonlinear dynamics within lasers. In this paper, we demonstrate all-fiber high-power spatiotemporal mode-locked (STML) laser by optimizing MMI filtering, where we find that the MMI filtering plays an important role in counteracting the coupling of high-order modes and improving output power of STML laser. The results under weak coupling condition when the length of graded-index multimode fiber (GIMF) is integral multiple of beat length show that the oscillator generates dissipative soliton pulses at 1036.86 nm with pulse width of 5.65 ps, and the slope efficiency of pump-signal is up to 10.3% with average power/energy of 215 mW/6 nJ, which is the highest among all-fiber STML lasers in normal dispersion regime. Besides, the multiple-soliton of STML, including multiple pulses and harmonic mode-locking can be observed in the experiment. Our work significantly broadens the dimensions of design for all-fiber high-power STML and makes them much more accessible for being put into applications.

The effect of coherent coupling nonlinearity on modulation instability and rogue wave excitation

We study modulation instability (MI) in both anomalous and normal dispersion regimes of a coherently coupled system. It is found that there exist three types of MI spectra with distinct characteristics termed baseband, passband, and zero-baseband based on the instability analysis of the in-phase and out-of-phase CW solutions. The coherent coupling nonlinearity is the source of the passband and zero-baseband variants. Guided by analytical predictions, we investigate numerically the excitation of rogue waves on weakly perturbed in-phase and out-of-phase continuous wave solutions in the parameter space where different kinds of MI exist. Simulations provide supporting evidence that rogue waves can only emerge in regimes where baseband or zero-baseband MI occurs. Moreover, the peak intensity of rogue waves in the case of baseband MI is greater than in the zero-baseband case. Finally, a combination of analysis and numerics uncovers the parameter conditions necessary for the generation of rogue waves.

Birefringence-Managed Normal-Dispersion Fiber Laser Delivering Energy-Tunable Chirp-Free Solitons

Chirp-free solitons have been mainly achieved with anomalous-dispersion fiber lasers by the balance of dispersive and nonlinear effects, and the single-pulse energy is constrained within a relatively small range. Here, we report a class of chirp-free pulse in normal-dispersion erbium-doped fiber lasers, termed birefringence-managed soliton, in which the birefringence-related phase-matching effect dominates the soliton evolution. Controllable harmonic mode locking from 5 order to 85 order is obtained at the same pump level of ~10 mW with soliton energy fully tunable beyond ten times, which indicates a new birefringence-related soliton energy law, which fundamentally differs from the conventional soliton energy theorem. The unique transformation behavior between birefringence-managed solitons and dissipative solitons is directly visualized via the single-shot spectroscopy. The results demonstrate a novel approach of engineering fiber birefringence to create energy-tunable chirp-free solitons in normal-dispersion regime and open new research directions in fields of optical solitons, ultrafast lasers, and their applications.

Observations of existence and instability dynamics of near-zero-dispersion temporal Kerr cavity solitons

Dissipative Kerr cavity solitons (CSs) are persisting pulses of light that manifest themselves in driven optical resonators and that have attracted significant attention over the last decade. Whilst the vast majority of studies have revolved around conditions where the resonator exhibits strong anomalous dispersion, recent studies have shown that solitons with unique characteristics and dynamics can arise under conditions of near-zero-dispersion driving. Here, we report on experimental studies of the existence and stability dynamics of Kerr CSs under such conditions. In particular, we experimentally probe the solitons' range of existence and examine how their breathing instabilities are modified when group-velocity dispersion is close to zero, such that higher-order dispersion terms play a significant role. On the one hand, our experiments directly confirm earlier theoretical works that predict (i) breathing near-zero-dispersion solitons to emit polychromatic dispersive radiation, and (ii) that higher-order dispersion can extend the range over which the solitons are stable. On the other hand, our experiments also reveal a novel cross-over scenario, whereby the influence of higher-order dispersion changes from stabilising to destabilising. Our comprehensive experiments sample soliton dynamics both in the normal and anomalous dispersion regimes, and our results are in good agreement with numerical simulations and theoretical predictions.

Coexistence of dark vector soliton Kerr combs in normal dispersion resonators

We investigate the formation of dark vector dissipative solitons in the presence of nonlinear polarization mode coupling in optical resonators subject to a coherent optical injection in the normal dispersion regime. This simple device is described by coupled Lugiato-Lefever equations. The stabilization of dark dissipative solitons is attributed to a front locking mechanism in the bistable regime as shown in a recent communication [B. Kostet et al., OSA Continuum 4, 1564 (2021)]. Here, we focus on a tristable homogeneous steady state regime. We show that two branches of dark dissipative solitons can coexist for a fixed value of the system parameters. These coexisting solutions possess different polarization states and different peak powers in the microresonator. We characterize their formation by drawing their bifurcation diagrams in regimes far from any modulational instability. It is shown that both branches of localized structures exhibit a heteroclinic collapsed snaking type of behavior. The coexistence of two vectorial branches of dark localized states is not possible without taking into account polarization degrees of freedom.

Attitude of the Modulation Instability gain in Oppositely Directed Coupler with the effects of the Intrapulse Raman Scattering and Saturable Function

To establish the effects of the Higher-Order Dispersion (HOD) and Raman Scattering (RS) on Modulation Instability (MI) in the presence of the Saturable Function (SF), it is used the Coupled Nonlinear Schrödinger Equation (CNLSE) which describes pulses propagating in a higher optical beam in oppositely guided coupler. It has been shown through the MI gain spectra the power of the SF in the presence of HOD and Raman effects (RE). By utilizing the HOD with the saturable nonlinearity (SN), it is formed three sides lobes and some new MI bands emerged. On the same way, it is observed that the RE have more potency in the presence of saturable parameter (SP) in the normal and anomalous dispersion regime. It is important to mention that by varying the SF, third-order dispersion (TOD) and Group Velocity Dispersion (GVD) in the absence of Raman parameter (RP) it is obtained three sides lobes which is an supplementary results compare to Alves et al. (2020), Guérin et al. (1995) and Mohamadou et al. (2010). These results could be important to stress the dynamics of the MI in optical fibers such as optical amplification of poor signal, supercontinuum generation, data transmission and signal processing system and very fast transmission signal and so on.

W-shaped profile and multiple optical soliton structure of the coupled nonlinear Schrödinger equation with the four-wave mixing term and modulation instability spectrum

We investigate diverse optical solitons and other solution for the Coupled Nonlinear Schrödinger Equation (CNLSE) having Four-Wave Mixing (FWM) and Kerr nonlinearity term. We stress the effects of different parameters of the model on the obtained optical soliton by employing the New Generalized Extended Direct Algebraic Method (NGEDAM). The solutions contain W-shaped profile of the bright optical soliton, dark optical soliton and diverse other solutions including the combined complex optical soliton. Interestingly, W-shaped optical soliton and dark optical soliton own a good argument for long communication and big data transmission originating from the self-steepening, Kerr nonlinearity effects and FWM. We also, emphasize the Modulation Instability (MI) gain spectra to narrow the impact of the FWM in birefringence. Thereafter, we involve the ellipticity angle effects in normal and anomalous dispersion regime on the MI gain spectra. Parametric conditions for the existence of the obtained optical soliton solutions and MI gain are given.

Tunable Terahertz Wavelength Conversion Based on Optofluidic Infiltrated Rib Silicon Waveguides

Terahertz (THz) sources have attracted special attention for various applications. Compared to the standard silica-based optical fibers, silicon waveguides have more advantages such as higher refractive index and lower absorption loss over the THz region. In this paper, for the first time, a rib silicon waveguide based on the photonic crystal (PC) idea is designed and by using the scalar modulation instability (SMI) phenomenon, tunable wavelength conversion for THz wave generation is simulated. By changing the structural parameters such as the air-hole diameter of the PC and infiltration of optical fluids into the air holes, linear and nonlinear characteristics of the waveguide are controlled and hence the generated THz radiation is considered as a tunable source. Simulation presents that the maximum converted wavelength, 326.17 μm, is obtained when the air-hole diameter is set at d = 0.86 μm and the pump wavelength is in the normal dispersion regime. Also, we have infiltrated optical fluids into PC air holes in order to change the dispersion properties of the waveguide while keeping the geometrical parameters unchanged. This led to converted wavelengths of 70.5, 76.8 and 107.5 μm, all located in the THz region. The loss of this waveguide is less than 0.8\( \raisebox{1ex}{$ dB$}\!\left/ \!\raisebox{-1ex}{$ cm$}\right. \), which is less than that of previously reported in similar silicon waveguides.

Chirped-pulsed Kerr solitons in the Lugiato-Lefever equation with spectral filtering.

Optical Kerr resonators support a variety of stable nonlinear phenomena in a simple and compact design. The generation of ultrashort pulses and frequency combs has been shown to benefit several applications, including spectroscopy and telecommunications. The most common anomalous dispersion Kerr resonators can be accurately described by a well-studied mean-field Lugiato-Lefever equation (LLE). Recently observed highly chirped pulses in normal dispersion resonators with a spectral filter, however, cannot. Here we examine the LLE in the normal dispersion regime modified with a Gaussian spectral filter (LLE-F). In addition to solutions associated with the LLE, we find stable highly chirped pulses. Solutions are strongly dependent on the filter bandwidth. Because of the large changes per round trip, the validity of the LLE-F fails over a large range of experimentally relevant parameters. While the mean-field approach leads to accurate predictions with respect to the nonlinearity coefficient and the dispersion, the dependence of drive power on loss deviates significantly from an experimentally accurate model, which leads to opportunities for Kerr resonators including frequency comb generation from low-Q-factor cavities.

Numerical observation of SPM rogue waves in normal dispersion cascaded supercontinuum generation

Numerical modeling of cascaded mid-infrared (IR) supercontinuum generation (SCG) is used to study how an ensemble of spectrally and temporally distributed solitons from the long-wavelength part of an SC evolves when coupled into the normal dispersion regime of a highly nonlinear chalcogenide fiber. This has revealed a novel phenomenon—the generation of a high-energy rogue wave in the normal dispersion regime in the form of a strong self-phase-modulation (SPM) chirped pulse. This SPM rogue wave is generated by swallowing the energy of many sufficiently closely spaced pulses through inter-pulse Raman amplification and is a key effect behind efficient cascaded mid-IR SCG.

Dispersive-wave self-frequency shift unveiled through length scales propagation.

Nonlinear propagation of light pulses can excite dispersive waves anchored at frequencies determined by the chromatic dispersion curve. In this work, conditions enabling dispersive-wave self-frequency shift over the propagation distance are analytically derived in the normal dispersion regime. Importantly, this novel, to the best of our knowledge, scenario is not found by solving the complex dynamics of the pulse, but by studying the evolution of the nonlinear and dispersive length scales. This approach allows a simpler, yet consistent and insightful, analysis that may also be very useful in other nonlinear regimes.

Omnipresent coexistence of rogue waves in a nonlinear two-wave interference system and its explanation by modulation instability

We investigate the coexisting rogue wave dynamics associated with two fundamental-frequency optical waves interacting in a quadratic nonlinear medium. Using the vector Chen--Lee--Liu nonlinear Schr\"odinger equation model, we obtain exact rogue wave solutions at first and higher orders on the more general periodic backgrounds. We unveil that the inherent self-steepening effect may allow an omnipresent rogue wave coexistence over a broad range of parameters in both the normal and anomalous dispersion regimes, in addition to allowing ultrastrong peak amplitudes. We also demonstrate that such universality of coexistence can be anticipated by the appearance of two peaks in the modulation instability spectrum. We numerically confirm the robustness of the coexisting Peregrine solitons against initial noise as well as their excitation from a turbulent wave field caused by modulation instability. We expect that these findings will shed light on the generation of extreme wave events resulting from the interference of multiple continuous-wave fields.

Noise-like pulses with 2.15 MHz repetition rate in an all-polarization-maintaining mode-locked fiber laser at the center wavelength of 1550 nm

We demonstrate a 2.15 MHz repetition-rate mode-locked figure-of-9 erbium-doped fiber laser at a center wavelength of 1550 nm by using an all-polarization-maintaining nonlinear amplifying loop mirror configuration. This laser can be self-started mode-locked and generate Gaussian-shape noise-like pulses (NLPs). The single pulse energy is approximately 11.68 nJ at a repetition rate of 2.15 MHz. Dispersion compensation fibers are added into the cavity to make the laser operate in a net normal dispersion regime and generate NLPs at the center wavelength of 1550 nm. These characteristics give it a great application potential, such as low spectral coherence interference, optical sensing and micromachining. In addition, we have investigated the evolution of these characteristics, contributing to further understanding the Gaussian-shape NLP.