Normal Group Velocity Dispersion Research Articles

Few-cycle optical pulses in negative index materials with dispersive permittivity and permeability

Propagation of few-cycle optical pulses in nonlinear optical Kerr (cubic) and non-Kerr (quintic) type metamaterials, exhibiting frequency-dependent dielectric susceptibility and magnetic permeability, is considered. Considering the theory of electromagnetic waves from Maxwell’s equations, a new nonlinear evolution equation describing the combined influences of higher-order nonlinearities and higher-order linear and nonlinear dispersions, appropriate for electromagnetic ultrashort pulse propagation in negative index materials, is derived beyond the slowly varying envelope approximation. A fully numerical simulation of the newly derived model equation, based on the lossy Drude model, shows the propagation of soliton-like stable few-cycle optical pulses under some parameter values. The change in types of self-steepening parameters induces structural changes of the initial input pulse, characterized by a soliton molecule made of either asymmetric or symmetric optical pulses. Also, the mutual balancing between Kerr and non-Kerr nonlinearities and higher-order dispersions is found to support the formation of soliton-molecules in both the normal and anomalous group velocity dispersion regimes.

Two-color flat-top solitons in microresonator-based optical parametric oscillators

We studied numerically the generation of the two-color flat-top solitonic pulses, platicons, in the microresonator based doubly resonant optical parametric oscillator. We revealed that if the signs of the group velocity dispersion (GVD) coefficients at interacting harmonics are opposite, platicon excitation is possible via pump amplitude modulation or controllable mode interaction approach. Upon pump frequency scan generation of platicons was observed at positive pump frequency detunings for the normal GVD at pump frequency and at negative detunings in the opposite case. Interestingly, we found the effect of the transformation of the flat-top platicon profile at half-frequency into the bell-shaped bright soliton profile upon frequency scan. For platicon excitation one needs simultaneous accurate matching of the microresonator free spectral ranges at interacting harmonics and resonant eigenfrequencies. Excitation conditions and platicon generation domains were found for the different generation methods, and properties of the generated platicons were studied for various combinations of the medium parameters.

Femtosecond filament self-reconstruction after an air gap in fused silica

The results of investigation of light filament self-reconstruction after penetration through the air gap in fused silica at anomalous and normal group velocity dispersion are presented. It is revealed that at anomalous dispersion the light bullet formed before the gap was recovered after passing some distance behind the gap up to 1 mm length. This distance increased with the gap length and the bullet pathway before the gap. At normal dispersion filament reconstruction does not occur for a gap larger than 0.1 mm due to dispersive pulse splitting into two subpulses.

Coupler-induced phase matching of resonant hyperparametric scattering.

We show that an evanescent field coupler can break the symmetry of a high quality factor monolithic ring microcavity, enabling generation of strongly nondegenerate frequency harmonics involving a few mode families that are orthogonal in an unperturbed microcavity. Using this property, we explain observed experimental generation of frequency combs in magnesium fluoride whispering gallery mode resonators characterized with strong normal group velocity dispersion.

Dispersion tailoring in wedge microcavities for Kerr comb generation.

The shaping of group velocity dispersion in microresonators is an important component in the generation of wideband optical frequency combs. Small resonators-with tight bending radii-offer the large free-spectral range desirable for wide comb formation. However, the tighter bending usually limits comb formation as it enhances normal group velocity dispersion. We experimentally demonstrate that engineering the sidewall angle of a small-radius (∼100µm), 3-µm-thick silica wedge microdisk enables dispersion tuning in both normal and anomalous regimes, without significantly affecting the free spectral range. A microdisk with a wedge angle of 55° (anomalous dispersion) is used to demonstrate a 300 nm bandwidth Kerr optical frequency comb.

Dynamics of localized dissipative structures in a generalized Lugiato-Lefever model with negative quartic group-velocity dispersion.

We study localized dissipative structures in a generalized Lugiato-Lefever equation, exhibiting normal group-velocity dispersion and anomalous quartic group-velocity dispersion. In the conservative system, this parameter-regime has proven to enable generalized dispersion Kerr solitons. Here, we demonstrate via numerical simulations that our dissipative system also exhibits equivalent localized states, including special molecule-like two-color bound states recently reported. We investigate their generation, characterize the observed steady-state solution, and analyze their propagation dynamics under perturbations.

Numerical Investigation of the Impact of the Saturable Absorber Recovery Time on the Mode-Locking Performance of Fiber Lasers

We investigated the impact of the recovery time of a saturable absorber (SA) on the mode-locking performance of a fiber laser. This study was conducted for two types of fiber cavities with different net cavity group velocity dispersion (GVD) at a wavelength of 1.55 μm: normal and anomalous. The impact of modulation depth variation was also analyzed. It was found that the recovery time of the SA has little influence on the output pulse characteristics in the case of the anomalous net cavity GVD due to an interplay between saturable absorption-induced pulse shaping and modulation instability-induced soliton evolution, irrespective of the SA operating in the fast or slow saturable absorption regime. However, the recovery time was found to have a significant impact on the output pulse characteristics for the case of a normal net cavity GVD. An SA operating in the fast saturable absorption regime produces mode-locked pulses with symmetric temporal shapes for the normal GVD cavity, whereas asymmetric pulses are generated in the slow saturable absorption regime. From the simulation results, the optimum recovery time range for fiber laser mode-locking is discussed.

Numerical Simulation of Three-Core Photonic Crystal Fiber With Large Group-Velocity Dispersion

The three-core photonic crystal fiber (TC-PCF) is proposed to obtain large group-velocity dispersion (GVD) because of the coupling effects between the fundamental modes (FMs) of the central core and higher-order modes (HOMs) of the two side cores. The supermodes of the TC-PCF can provide concave anomalous- and normal-GVD profiles with large peak values at the maximum dispersion wavelengths (MDWs), which can be shifted in three wavelength windows of 1030 nm, 1550 nm and 1900 nm by properly tuning the refractive indexes of the cores or the air-hole diameters. Furthermore, the numerical results show that two segments of the TC-PCFs with large anomalous GVDs and opposite values of the third-order dispersion (TOD) can provide much higher efficiency of pulse compression than one segment of the TC-PCF. Additionally, the TC-PCFs with large normal GVDs can be used to stretch pulses due to their low nonlinearities and short fiber lengths.

Coherence of bulk-generated supercontinuum

We have developed a numerical framework that allows estimation of coherence in spatiotemporal and spatiospectral domains. Correlation properties of supercontinuum (SC) pulses generated in a bulk medium are investigated by means of second-order coherence theory of non-stationary fields. The analysis is based on simulations of individual space–time and space–frequency realizations of pulses emerging from a 5 mm thick sapphire plate, in the regimes of normal, zero, and anomalous group velocity dispersion. The temporal and spectral coherence properties are analyzed in the near field (as a function of spatial position at the exit plane of the nonlinear medium) and as a function of propagation direction (spatial frequency) in the far field. Unlike in fiber-generated SC, the bulk case features spectacularly high degrees of temporal and spectral coherence in both the spatial and spatial-frequency domains, with increasing degrees of coherence at higher pump energies. When operating near the SC generation threshold, the overall degrees of temporal and spectral coherence exhibit an axial dip in the spatial domain, whereas in the far field, the degree of coherence is highest around the optical axis.

Regimes of two-color light bullet formation in a gradient waveguide

In this paper we concentrate on the remarkable role of a gradient waveguide in two-color light bullet formation. We study generation of the second harmonic in such an inhomogeneous nonlinear medium, taking into account diffraction and relatively weak temporal dispersion. Using the averaged Lagrangian method we consider all possible combinations of the range of group velocities (normal or anomalous dispersion) and waveguide geometry (focusing or defocusing waveguide). Stability conditions for a propagating two-color light bullet are derived analytically. We demonstrate the formation of a stable two-component light bullet in a parabolic planar quadratically nonlinear waveguide either at anomalous or at normal group velocity dispersion. We discuss also the results of numerical simulation confirming our analytical findings. Besides that, simulation allows us to expand the scope of the study and to show light bullet propagation at a certain phase mismatching and the formation of a stable coupled localized structure from a signal at the fundamental frequency as well.

Turn-key, high-efficiency Kerr comb source.

We demonstrate an approach for automated Kerr comb generation in the normal group-velocity dispersion (GVD) regime. Using a coupled-ring geometry in silicon nitride, we precisely control the wavelength location and splitting strength of avoided mode crossings to generate low-noise frequency combs with pump-to-comb conversion efficiencies of up to 41%, which is the highest reported to date for normal-GVD Kerr combs. Our technique enables on-demand generation of a high-power comb source for applications such as wavelength-division multiplexing in optical communications.

Frequency combs in a microring optical parametric oscillator.

We report the soliton frequency comb generation in microring optical parametric oscillators operating in the downconversion regime and with the simultaneous presence of the χ(2) and Kerr nonlinearities. The combs are studied considering a typical geometry of a bulk LiNbO3 toroidal resonator with the normal group velocity dispersion spanning an interval between the pump and the downconverted signal. We have identified critical power signaling a transition between the relatively low pump power predominantly χ(2) combs and the high pump power ones shaped by the competition between the χ(2) and Kerr nonlinearities.

Trapping of two-component light bullets in a gradient waveguide with normal group dispersion.

In this paper we consider the process of the second harmonic generation in a gradient waveguide, taking into account diffraction and relatively weak temporal dispersion. Using the slowly varying envelope approximation and neglecting the dispersion of the nonlinear part of the response of the medium we obtain the system of parabolic equations for the envelopes of both harmonics. We also derive integrals of motion of this system. To solve it numerically we construct a nonlinear finite-difference scheme based on the Crank-Nicolson method preserving the integrals. Primarily, we focus our investigations on the processes of a two-component light bullets generation. We demonstrate that the generation of a coupled pair is possible in a planar waveguide even at normal group velocity dispersion.

Photonic-Crystal-Reflector Nanoresonators for Kerr-Frequency Combs

We demonstrate Kerr-frequency-comb generation with nanofabricated Fabry–Perot resonators, which are formed with photonic-crystal-reflector (PCR) mirrors. The PCR group-velocity dispersion (GVD) is engineered to counteract the strong normal GVD of a rectangular waveguide, fabricated on a thin, 450 nm silicon nitride device layer. The reflectors enable resonators with both high optical quality factor and anomalous GVD, which are required for Kerr-comb generation. We report design, fabrication, and characterization of devices in the 1550 nm wavelength bands. Kerr-comb generation is achieved by exciting the devices with a continuous-wave laser. The versatility of PCRs enables a general design principle and a material-independent device infrastructure for Kerr-nonlinear-resonator processes, opening new possibilities for manipulation of light. Visible and multispectral-band resonators appear to be natural extensions of the PCR approach.

Generation and dynamics of solitonic pulses due to pump amplitude modulation at normal group-velocity dispersion

We studied generation and dynamics of solitonic pulses, platicons, at normal group velocity dispersion due to the pump amplitude modulation. We proposed, that if the required frequency of amplitude modulation is too large for available modulators, it is possible to use subharmonic phase modulation for platicon generation. It was also demonstrated that it is possible to control the repetition rate of platicons by tuning modulation frequency. Tuning range for platicons was found to be much wider than for bright solitons. We also studied the influence of the high-order dispersion on platicon properties. It was shown that both third-order dispersion and pump modulation govern platicon dynamics making it quite different from dynamics of dissipative Kerr solitons. Third-order dispersion was also shown to affect significantly the optimal conditions for the platicon generation and repetition rate tuning range.

Self-phase modulation-induced modulation instability in silicon-on-insulator nano-waveguides

We present an investigation of the impact of two-photon absorption and free-carrier effects on modulation instability (MI) in silicon-on-insulator (SOI) nano-waveguide. We have analyzed nano-waveguide with both the anomalous and the normal group velocity dispersion (GVD) parameters at telecommunication wavelength. The power dependence of MI gain spectra in these waveguides has been explored. Also, we have studied the nonlinear losses and carrier density in the two dispersion regimes. Further, the impact of carrier lifetime on the MI gain spectrum is discussed in detail.

Modulation instability of discrete angular momentum in coupled fiber rings

We present an analysis of temporal modulation instability in a ring array of coupled optical fibers. Continuous-wave signals are shown to be unstable to perturbations carrying discrete angular momenta, both for normal and anomalous group velocity dispersion. We find the frequency spectrum of modulation instability is different for each perturbation angular momentum and depends strongly on the coupling strength between fibers in the ring. Twisting the ring array also allows the frequency spectra to be tuned through the induced tunnelling Peierls phase.

Cross-phase modulation instability under delayed response and walk-off effects in the anomalous regime of dispersion

The dynamics of the modulation instability induced by cross phase modulation is studied by considering the influence of the walk-off and noninstantaneous response effects for two copropagating optical fields travelling in the anomalous regime of dispersion. To do so, we make use of extensions of the nonlinear Schrdinger equation jointly with the Debye model for polarization, which is shown to be effective and simplified when compared to the implementation of other methods for the noninstantaneous nonlinear response. In analyzing the sideband formation, two bands are observed with different behaviors with respect to the way the maximum gain and the respective frequency vary with increasing phase mismatch. Further, we also show the manner in which the maximum gain as well as its corresponding frequency scale with the delay parameter τ is substantially different from the cases of both fields experiencing the normal group-velocity dispersion regime and the case of mixed regimes. These facts may give rise to many new possibilities for the evolution of the modulated wave when compared to the nonanomalous cases studied in the literature.

Cross-phase modulation instability in an elliptical birefringent positive-negative index coupler with self-steepening and intrapulse Raman Scattering effects

In this paper, we investigate the modulational instability (MI) in an elliptical birefringent positive-negative index coupler. Also, we derive the general expression for instability gain by taking into account cross-phase modulation (XPM), self-steepening (SS) and intrapulse Raman scattering. The instability gain is attained. Using standard linear stability analysis, particularly, we study different configurations of the birefringence with self-steepening or intrapulse Raman scattering effects on MI for both normal and anomalous group velocity dispersion regimes. We observe that the instability gain exhibits significant changes due to the effects of the cross-phase modulation. Finally, we show that efficient control of the MI can be realized by adjusting the self-steepening and intrapulse Raman scattering term, even in the presence of different configurations of the birefringence.

Influence of dispersion distribution on the propagation and compression of self-similar optical beam

The influence of different dispersion-distribution in dispersion-decreasing optical fiber with normal group-velocity dispersion (ND-DDF) on the generation and compression of self-similar optical beam is investigated in this paper. The split-step Fourier numerical method is adopted and the amplitude of the pulses’ envelope under different distributed dispersion is determined numerically. The generation and compression of the self-similar optical beam are simulated and analyzed based on the perspective of chirp feature. The result shows that chirp nonlinear region and chirp linearity level in different dispersion distribution fiber affect the generation and compression of the self-similar optical beam significantly. The quality of obtained self-similar and compressed optical beam in different tapered fiber increases in order of: cosinoidally tapered DDF, linearly tapered DDF, exponentially tapered DDF and hyperbolically tapered DDF, from the lowest to the highest.