Negative Fourth-order Dispersion Research Articles

Analysis and optimization of optical frequency comb spectra of magnesium fluoride microbottle resonator

<sec>Optical frequency comb has shown great potential applications in many areas including molecular spectroscopy, RF photonics, millimeter wave generation, frequency metrology, atomic clock, and dense/ultra-dense wavelength division multiplexed high speed optical communications. Optical frequency comb in the microresonator supporting whispering-gallery mode has attracted widespread interest because of its advantages such as flexible repetition rate, wide bandwidth, and compact size. The exceptionally long photon lifetime and small modal volume enhance light-matter interaction, which enables us to realize intracavity nonlinear frequency conversions with low pump threshold. With the advantages of small size, low power consumption, wide spectral coverage and adjustable dispersion, the magnesium fluoride microresonator optical frequency comb has potential applications in optical communication and mid-infrared spectroscopy.</sec><sec>In this work, the spectral characteristics of the optical frequency comb generated by a magnesium fluoride whispering-gallery mode microbottle resonator platform are investigated. In order to optimize the spectral distribution of the optical frequency comb of the magnesium fluoride microbottle resonator, the second-order dispersion and higher-order dispersion of the bottle resonator structure under different curvatures and axial modes are solved iteratively by the finite element method, and the spectral evolutions of the optical frequency comb under different axial mode excitations are simulated by solving the nonlinear Schrödinger equation through the split-step Fourier method. The results show that near-zero anomalous dispersion tuning can be achieved in a wide bandwidth range by exciting low-order axial mode at an optimal radius of curvature, while the high-order axial mode will lead the microbottle resonator to present the weak normal dispersion. The weaker anomalous dispersion in the lower-order axial mode broadens the bandwidth of the optical comb, demonstrating that the third-order dispersion and the negative fourth-order dispersion can broaden the Kerr soliton optical comb; the weak normal dispersion in the higher-order axial mode suppresses the generation of the Kerr optical comb, and the Raman optical comb dominates. The selective excitation of Kerr soliton combs and Raman combs can be achieved by modulating the axial mode of the microbottle resonator under suitable pumping conditions. The present work provides guidance for designing the dispersion in magnesium fluoride microresonator and the experimental tuning of broadband Kerr soliton optical combs and Raman optical combs.</sec>

Pure-quartic Bragg solitons in chip-scale nonlinear integrated circuits

Pure-quartic solitons have gained significant attention recently due to their ability to achieve higher energy than classical solitons for short pulse durations, leveraging the interaction between self-phase modulation and anomalous fourth-order dispersion. However, challenges in generating the required dispersion profile and the scarcity of sufficiently low-loss devices with high nonlinearity and negligible nonlinear loss have restricted experimental progress. In this paper, we report a class of pure-quartic Bragg solitons that balances self-phase modulation and the ultra-strong Bragg-grating-induced negative fourth-order dispersion in combination with negligible group velocity dispersion and negligible third-order dispersion. We demonstrate pure-quartic Bragg soliton-effect compression of 2.4× in a compact millimeter-scale integrated low-loss and highly nonlinear waveguide circuit. Our findings show the potential of exploiting the exceptional dispersion profile of nonlinear Bragg gratings for advanced soliton generation and pulse shaping, particularly the advantageous energy scaling and associated compression of pure-quartic solitons.

Pure-quartic solitons in presence of weak nonlocality

In this paper, we study the characteristics of pure-quartic optical solitons in a nonlinear medium having a weakly nonlocal response. We propose an nonlinear Schrödinger equation incorporating pure fourth-order diffraction, Kerr nonlinearity and weak nonlocality to describe the transmission of solitons in the system. We obtain analytic pure-quartic soliton solutions to this model in a variety of shapes and forms, unlike the case of the model without taking into account the weak nonlocal contribution. Besides, we find that the obtained localized structures have both bright and dark type waveforms in the transmission system. Interestingly, the functional forms of these solitons are expressed in terms of sech and tanh functions which do not possess oscillating tails, markedly different from the conventional pure-quartic solitons in the absence of weak nonlocality. These structures exist for both positive and negative quartic diffraction coefficient whereas pure-quartic solitons in the absence of nonlocality occur only for negative fourth-order dispersion. The numerical examples are presented for illustrating the soliton evolution dynamics in the optical waveguide.

Dissipative pure-quartic soliton fiber laser.

The evolution of ultrafast laser technology hinges partially on the understanding of the soliton nonlinear dynamics. Recently, the concept of pure-quartic soliton (PQS) that arises from the balance of pure negative fourth-order dispersion (FOD) and nonlinearity was proposed to generate high peak power pulse. Herein, we investigate the generation of dissipative pure-quartic soliton (DPQS) in a fiber laser, which is balanced among the positive FOD, nonlinearity, gain and loss. The DPQS features the shape-preserving propagation despite the asymmetrical temporal profile at higher pulse energy. It is found that the asymmetrical temporal profile of DPQS is resulted from the mismatching of the phase shift profiles caused by self-phase modulation and FOD. Moreover, it is demonstrated that the DPQS possesses a higher energy-scaling ability compared to conventional dissipative soliton, owing to the nonlinear relationship between the pulse energy and pulse duration. These findings demonstrated that the employment of positive FOD could be a promising way for manipulation of optical pulse as well as the improvement of laser performance.

Modeling nonlinear high-pressure sensors based on degenerate four-wave mixing in photonic crystal fibers.

We propose a high-pressure sensing mechanism in solid-core silica photonic crystal fibers (PCF) that is based on the nonlinear optical process of degenerate four-wave mixing. A quite simple configuration for the pressure sensor is given and is theoretically investigated by obtaining signal gain spectra. We focus on the Stokes and anti-Stokes sidebands that are generated during propagation of the field along the PCF due to the interplay of dispersion and nonlinear optical effects. We have considered wave propagation in the normal dispersion regime with the inclusion of negative fourth-order dispersion. We have also considered a pumping field with wavelength of 1076 nm and peak power of 3000 W that propagates along a PCF with 40 cm of length. We have optimized sensitivity, varying lattice pitch and air-hole diameter, and we have obtained high sensitivities of the Stokes and anti-Stokes lines of 3.672 and -0.146nm/MPa, respectively. The proposed sensors have potential applicability in high-pressure environments.

Stability and non-linear dynamic analysis of Kerr optical frequencycombs in dual-coupled microcavities with high-order dispersion

We investigate the stability and nonlinear dynamics of the Kerr optical frequency comb inside a dual coupled microcavity with high-order dispersion effect based on the theoretical model of coupled nonlinear Schrödinger equation. The effects of different high-order dispersion parameters on the evolution and spectral characteristics of the optical field in the cavity are also explored. Theoretical results indicate that the addition of the third-order dispersion enlarges the stability domain of the parametric space and transforms the periodically varying soliton breathers and chaos into stable bright soliton. In order to obtain an accurate Kerr optical frequency comb spectral envelope, higher-order dispersion should be considered. Moreover, high-order dispersion terms have a significant effect on the spectral characteristics of the optical frequency comb, such as the spectral envelope frequency shift and the dispersive wave spectral position. Specifically, the third-order dispersion and positive fourth-order dispersion can broaden the spectrum and enhance the dispersive waves; while the negative fourth-order dispersion can suppress the dispersive wave generation and obtain a symmetric soliton frequency comb; the fifth-order dispersion can regulate the drift direction and speed of the optical solitons. The theoretical results are of great value for dispersion regulation and design and also for stability studies in double-coupled microcavity experiments.

Soliton shedding from Airy pulses in a highly dispersive and nonlinear medium

We present a numerical investigation of the propagation dynamics of a truncated Airy pulse in a highly dispersive and nonlinear medium by employing the split-step Fourier transform method and look, in particular, into the effects of fourth-order dispersion (FOD) and cubic-quintic-septic nonlinearity on pulse evolution. Presence of FOD cancels the Airy pulse’s self-acceleration along with eclipsing the oscillatory tail during propagation in the linear regime. Further, we observe soliton shedding at low input pulse power in the presence of cubic and quintic nonlinearity and negative FOD. The emergent soliton exhibits temporal shift, and the direction and the extent of the shift depend upon the strengths of cubic and quintic nonlinearities. In the presence of anomalous group-velocity dispersion (GVD) with negative FOD, soliton shedding is observed at relatively high input pulse power. The strengths of GVD and nonlinearity play a vital role in the temporal shifting of the emergent soliton. Furthermore, we have explored the effects of septic nonlinearity on soliton shedding in different scenarios of nonlinearity and dispersion.

Modulation instabilities in nonlinear two-core optical fibers with fourth order dispersion

We study in detail the modulation instabilities (MIs) in nonlinear two-core optical fibers (TCFs) in the presence of fourth-order dispersion (FOD) by considering the symmetric and antisymmetric CW states. The analytical instability gain spectra with the FOD are shown explicitly. For the symmetric CW state, in the normal (anomalous) dispersion regime, the positive (negative) FOD reduces the original MI band, and the negative (positive) FOD can generate a completely new dominate MI band in the very high frequency range even with quite small amplitude of FOD for typical TCF parameters. For the antisymmetric CW state, in the normal dispersion regime, there is no MI without FOD. With the negative FOD, MI is generated at any given total powers. In the anomalous dispersion regime, being similar with the behaviors for symmetric CW state, the positive (negative) FOD effect is to reduce the original MI band, and the negative (positive) FOD can generate a completely new dominate MI band in the very high frequency range. We also verify our MI analysis by solving the coupled-mode equations numerically.

Pure-quartic solitons.

Temporal optical solitons have been the subject of intense research due to their intriguing physics and applications in ultrafast optics and supercontinuum generation. Conventional bright optical solitons result from the interaction of anomalous group-velocity dispersion and self-phase modulation. Here we experimentally demonstrate a class of bright soliton arising purely from the interaction of negative fourth-order dispersion and self-phase modulation, which can occur even for normal group-velocity dispersion. We provide experimental and numerical evidence of shape-preserving propagation and flat temporal phase for the fundamental pure-quartic soliton and periodically modulated propagation for the higher-order pure-quartic solitons. We derive the approximate shape of the fundamental pure-quartic soliton and discover that is surprisingly Gaussian, exhibiting excellent agreement with our experimental observations. Our discovery, enabled by precise dispersion engineering, could find applications in communications, frequency combs and ultrafast lasers.

Experimental studies of two sets of four-wave mixing processes in a single-zero-dispersion microstructured fiber by the same pump

A highly nonlinear microstructured fiber with single-zero-dispersion wavelength is designed and drawn by reducing the core area in order to observe two groups of four-wave mixing processes by a single pump. The foundational material of the fiber is silica and its cladding is comprised of seven-layer air holes. The air holes are arranged in a hexagonal lattice and the lattice pitch is =2.5 m. The radius of each of the air holes is r=1.03 m. There is just one zero-dispersion wavelength in our considerable wavelength range for the microstructured fiber and the corresponding wavelength D is nearly 0.85 m（D=0.85 m). The basic properties of the fiber including effective refractive index, dispersion coefficient, and nonlinear coefficient are calculated by the finite element method. The effective mode area is 4.4 m2 and the nonlinear coefficient is 0.057 m-1W-1 for the foundation mode near the wavelength of 0.8 m, and the nonlinear coefficient reaches 0.053 m-1W-1 near the zero dispersion wavelength of 0.85 m. In short, the optical fiber has a stable and high nonlinear coefficient in the whole experimental band（0.80-0.83 m), which provides an important guarantee for the occurrence of four-wave mixing double parameter gain process. In addition, the phase mismatch curve is simulated by using the four-wave mixing phase mismatch formulation. Numerical simulation shows that two sets of four-wave mixing processes can occur in the designed fiber. At the normal dispersion wavelengths of 0.800, 0.810 and 0.820 m with different powers, the experimental result shows a significant feature of four gain wavebands located at both sides of the pump wavelength. By comparing experimental data with the phase mismatch curve, we find that the band generation meets four-wave mixing phase matching condition, thus, the simultaneous occurrence of two groups of four-wave mixing processes observed in the experiment is explained in theory. The experimental results are consistent well with the theoretical predictions. This also proves the theoretical predictions that two sets of parametric gain processes and two pairs of signal and idle frequency waves can be generated in PCF. The four-wave mixing effect occurring in the normal dispersion region can be attributed to the contribution of negative fourth-order dispersion to the phase matching process. The present work can provide valuable reference to designing the microstructure fibers and developing the multi-wavelength conversion technology based on four-wave mixing effect. At the same time, this work can also supply guidance for developing the uncommon waveband lasers and broadband light sources.

Far-detuned mid-infrared frequency conversion via normal dispersion modulation instability in chalcogenide microwires

We report the observation of modulation instability (MI) in the mid-infrared (mid-IR) spectral region by pumping a hybrid polymer-chalcogenide optical microwire with a femtosecond optical parametric oscillator operating at 2.6 μm. It is further shown that this MI occurs in the normal dispersion regime through negative fourth-order dispersion and leads to far-detuned parametric frequency conversion at 2 and 3.5 μm, despite the presence of a strong absorption band around 2.8 μm. Stochastic nonlinear Schrödinger equation simulations of mid-IR MI are in excellent agreement with experiments.

Optical light bullets in a pure Kerr medium.

We show that small negative fourth-order dispersion can arrest spatiotemporal collapse of ultrashort pulses with anomalous dispersion in a planar waveguide with pure Kerr nonlinearity, resulting in (2 + 1)D optical bullets. Similarly to solitons, these bullets undergo elastic collisions. Since these bullets can self-trap from noisy Gaussian input beams and propagate without any power losses, this result may be used to realize experimentally stable, nondissipative optical bullets.

Critical exponents and collapse of nonlinear Schrödinger equations with anisotropic fourth-order dispersion

We calculate the critical exponent of nonlinear Schrödinger (NLS) equations with anisotropic negative fourth-order dispersion using an anisotropic Gagliardo–Nirenberg inequality. We also prove global existence, and in some cases uniqueness, for subcritical solutions and for critical solutions with small L2 norm, without making use of Strichartz-type estimates for the linear operator. At exponents equal to or above critical, the blowup profile is anisotropic. Our results imply, in particular, that negative fourth-order temporal dispersion arrests spatio-temporal collapse in Kerr media with anomalous time-dispersion in one transverse dimension but not in two transverse dimensions. We also show that a small negative anisotropic fourth-order dispersion stabilizes the (otherwise unstable) waveguide solutions of the two-dimensional critical NLS.

Femtosecond solitary waves in optical fibers—beyond the slowly varying envelope approximation

We present a theoretical calculation which demonstrates that optical solitary waves can propagate in an optical fiber well into the femtosecond regime. Dispersive effects up to fourth order have been considered and more importantly, the ‘‘slowly varying envelope’’ approximation is not invoked. The optical fiber which can support such a wave must exhibit negative fourth-order dispersion ( βIV0e <0) and must be used close to appropriate ‘‘operating’’ points. Use of such waves in optical fiber communication systems may finally result in the full exploitation of the bandwidth of light.