Normal Group-velocity Dispersion Regime Research Articles

Experimental observation of stimulated Raman scattering enabled localized structure in a normal dispersion FP resonator

Dissipative Kerr nonlinear cavities attract intense interest due to their rich dynamics and capability to generate broadband, low-noise, mode-locked optical frequency combs for applications in optical communications, dual-comb spectroscopy, photonic lidar, etc. Different from the Kerr effect, which is an electronic response, stimulated Raman scattering (SRS) is a delayed response to molecular vibrations in materials. In microcavities, when driven in an anomalous group velocity dispersion (GVD) regime, SRS typically leads to a self-frequency shift of solitons and generation of breather solitons, which have been verified both theoretically and experimentally. However, when driven in a normal GVD regime, recent theoretical work predicts that SRS can cause the locking of switching waves (SWs) and thus support bright moving localized structure (LS), which we term as SRS enabled localized structure (SRS-LS). Limited by the design of suitable experimental parameters, experimental observation of this SRS-LS is not achieved yet. Here, we provide numerical investigation and, to our knowledge, the first experimental observation of the SRS-LS in a fiber Fabry–Perot (FP) resonator with ultra-low normal GVD. Such SRS-LS exhibits localized temporal features with strong oscillations at ∼13THz local frequency on the top of a flat-top pulse. The corresponding spectrum is a low-noise and broadband Kerr comb with a typical platicon-like spectrum in the center and two Raman Stokes and anti-Stokes peaks located near ±13THz away from the center. With such an SRS enabled broadband Kerr comb, we have achieved an SRS-LS spectrum with a repetition rate of ∼3.68GHz and a −30dB spectral width of 255 nm. The corresponding comb tooth count is >8500, covering the S + C + L telecommunication bands. Moreover, the formation process of such SRS-LS is also revealed, and it is found that the GVD plays a key role in its generation. Our work will help to advance the study of the dynamics of optical frequency combs under the influence of SRS, as well as provide a broadband coherent mode-locked optical source for wide applications.

Coherent Combining for High‐Power Kerr Combs

AbstractKerr frequency combs enable the miniaturization of comb sources for applications such as data communications and spectroscopy. However, due to the high field confinement and effective nonlinearity, Kerr combs typically operate with low output comb powers. While nonsolitonic Kerr combs operating in the normal group velocity dispersion (GVD) regime can access high pump‐to‐comb conversion efficiencies and relatively flat spectral profiles, many frequency comb applications require even higher comb‐line powers that are otherwise fundamentally unattainable without the use of optical amplifiers. A high efficient coherent beam combining of Kerr combs is demonstrated via on‐chip synchronization to greatly enhanced comb‐line powers. Two normal GVD Kerr combs are coherently combined for a 2.9 dB increase in comb power compared to a single comb while maintaining a high total pump‐to‐comb conversion efficiency of 26%. Lastly, it is shown that via spectral engineering of two normal GVD combs, it should be possible to significantly increase the spectral flatness of a combined comb. This platform enables fully integrated systems with powers that can readily exceed that of an individual comb system by more than an order of magnitude.

Quartic Kerr cavity combs: bright and dark solitons.

We theoretically investigate the dynamics, bifurcation structure, and stability of localized states in Kerr cavities driven at the pure fourth-order dispersion point. Both the normal and anomalous group velocity dispersion regimes are analyzed, highlighting the main differences from the standard second-order dispersion case. In the anomalous regime, single and multi-peak localized states exist and are stable over a much wider region of the parameter space. In the normal dispersion regime, stable narrow bright solitons exist. Some of our findings can be understood using a new, to the best of our knowledge, scenario reported here for the spatial eigenvalues, which imposes oscillatory tails to all localized states.

Supercontinuum generation in single-crystal YAG fibers pumped around the zero-dispersion wavelength.

Yttrium aluminum garnet (YAG) is a common host material for both bulk and single-crystal fiber lasers. With increasing interest in developing optical technologies in the short-wave infrared and mid-infrared wavelength range, YAG may be a potential supercontinuum medium for these applications. Here, we characterize femtosecond laser pumped supercontinuum generation with 1200-2000 nm pump wavelengths (λp) for undoped, single-crystal YAG fibers, which are representative of the normal, zero, and anomalous-dispersion regimes. Supercontinuum was observed over the spectral region of about 0.2 to 1.6λp. Z-scan measurements were also performed of bulk YAG, which revealed little dispersion of the nonlinear index of refraction (n2) in the region of interest. The measured values of n2 (∼1×10-6cm2/GW) indicate a regime in which the nonlinear length, LNL, is less than the dispersion length, LD, (LNL≪LD). We report intensity clamping of the generated filament in the normal group velocity dispersion (GVD) regime and an isolated anti-Stokes peak in the anomalous GVD regime, suggesting further consideration is needed to optimize supercontinuum generation in this fiber medium.

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.

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.

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.

Modulation instability induced by high-order dispersion to a coupled nonlinear Schrödinger equation in a single-mode optical fiber with Kerr nonlinearity

We investigate the modulation instability of two incoherently copropagating optical waves in a nonlinear fiber taking into account the relaxing Kerr nonlinearity, walk-off effects, delay response time and cross-phase modulation. We intend to provide a detailed analysis of the interplay between the instantaneous and noninstantaneous Kerr response for the beams experiencing a normal group velocity dispersion (GVD) regime and for the other beams undergoing an anomalous GVD regime. We unveil the influence of the parameters on the generation of the modulational instability gain with particular attention to the delay response time as well as the high-order dispersion. We show that the high-order dispersion particularly influences the magnitude as well as the sidebands of the gain spectrum.

Observation of photon-pair generation in the normal group-velocity-dispersion regime with slight detuning from the pump wavelength

A fiber-based photon-pair source in the telecom C-band is suitable for quantum information science including quantum communications. Spontaneous four-wave mixing effects are known to create photon pairs that are slightly detuned from the pump wavelength only in the anomalous group-velocity-dispersion (GVD) regime. Here, we achieve high-quality photon-pair generation slightly detuned from the pump wavelength in the normal GVD regime through a dispersion shifted fiber, for the first time. The photon pairs in C-band exhibit strong temporal correlation with each other and excellent heralded anti-bunching property. This photon-pair generation scheme can be exploited as telecom-band quantum light sources for quantum information applications.

Coherent, directional supercontinuum generation.

We demonstrate a novel approach to producing coherent, directional supercontinuum and cascaded dispersive waves using dispersion engineering in waveguides. By pumping in the normal group-velocity dispersion (GVD) regime, with two zero-GVD points to one side of the pump, pulse compression of the first dispersive wave generated in the anomalous GVD region results in the generation of a second dispersive wave beyond the second zero-GVD point in the normal GVD regime. As a result, we achieve an octave-spanning supercontinuum generated primarily to one side of the pump spectrum. We theoretically investigate the dynamics and show that the generated spectrum is highly coherent. We experimentally confirm this dynamical behavior and the coherence properties in silicon nitride waveguides by performing direct detection of the carrier-envelope-offset frequency of our femtosecond pump source using an f-2f interferometer. Our technique offers a path towards a stabilized, high-power, integrated supercontinuum source with low noise and high coherence, with applications including direct comb spectroscopy.

Midinfrared wavelength conversion in hydrogenated amorphous silicon waveguides

Midinfrared (MIR) wavelength conversion based on degenerate four-wave mixing is theoretically investigated in hydrogenated amorphous silicon (a-Si:H) waveguides. The broadband phase mismatch is achieved in the normal group-velocity dispersion regime. The conversion bandwidth is extended to 900 nm, and conversion efficiency of up to −14 dB with a pump power of 70 mW in a 2-mm long a-Si:H rib waveguides is obtained. This low-power on-chip wavelength converter will have potential for application in a wide range of MIR nonlinear optic devices.

Effects of higher-order nonlinear dispersions on modulational instability in a three-core coupler with negative index material channel and saturable nonlinearity

A theoretical investigation on the impact of high-order nonlinear dispersions of the modulation instability (MI) spectra in the three core triangular oppositely directed coupler with negative index material channel is carried out. A keen attention was paid to find out the influence of self-steepening (SS), intrapulse Raman scattering (TR), second-order nonlinear dispersion (SOND) as well as saturable nonlinearity (SNL) on the MI spectra. Gain spectra has been investigated for both anomalous group velocity dispersion (GVD) and normal GVD regime. Particularly, our results show that in the normal GVD regime, the instability gain exists even if the perturbation frequency (Ω) is zero; and the instability gain at Ω=0 is nil when the dispersion is anomalous. We also find that the magnitude and sign of SOND exert strong influences on MI sideband. Furthermore, by adjusting various parameters such as SS, intrapulse Raman scattering, and SOND, we observe the occurrence of new instability regions. The MI sidelobes, as well as its bandwidth, have also been affected by the SNL. Finally, the SNL may influence considerably the number of wave trains induced by MI. These results can help to understand the generation of soliton-like excitation in nonlinear three-core oppositely directed couplers with a particular attention on a negative-index material channel.

Dynamics of mode-coupling-induced microresonator frequency combs in normal dispersion

We experimentally and theoretically investigate the dynamics of microresonator-based frequency comb generation assisted by mode coupling in the normal group-velocity dispersion (GVD) regime. We show that mode coupling can initiate intracavity modulation instability (MI) by directly perturbing the pump-resonance mode. We also observe the formation of a low-noise comb as the pump frequency is tuned further into resonance from the MI point. We determine the phase-matching conditions that accurately predict all the essential features of the MI and comb spectra, and extend the existing analogy between mode coupling and high-order dispersion to the normal GVD regime. We discuss the applicability of our analysis to the possibility of broadband comb generation in the normal GVD regime.

Quantum random number generator using a microresonator-based Kerr oscillator.

We demonstrate an all-optical quantum random number generator using a dual-pumped degenerate optical parametric oscillator in a silicon nitride microresonator. The frequency-degenerate bi-phase state output is realized using parametric four-wave mixing in the normal group-velocity dispersion regime with two nondegenerate pumps. We achieve a random number generation rate of 2MHz and verify the randomness of our output using the National Institute of Standards and Technology Statistical Test Suite. The scheme offers potential for a chip-scale random number generator with gigahertz generation rates and no postprocessing.

Modulation instability in noninstantaneous Kerr media with walk-off and cross-phase modulation for mixed group-velocity-dispersion regimes

Taking into account relaxing Kerr nonlinearity and walk-off effects, the conditions and gain spectra of cross-phase modulation-induced modulational instability (XPM-MI) of two incoherently copropagating optical waves of different frequencies and same polarization are investigated. We devote particular attention to the mixed case in which one pulse propagates under the normal group-velocity dispersion (GVD) regime, while the second one is under an anomalous GVD regime. We unveil that in the limit of an instantaneuous nonlinear response, the typical frequency with maximum gain converges to a finite value in the mixed GDV regime, while it continuously grows with the group-velocity mismatch in the normal GVD regime. As a result, the maximum gain typically decreases with the group-velocity mismatch in the mixed regime, contrasting with the opposite trend in the normal GVD regime. Further, we show that besides the mode having maximum gain at a frequency decaying with $1/{\ensuremath{\tau}}^{1/3}$ in the slow response limit, there is a second mode having maximum gain with a distinct scaling behavior ${\mathrm{\ensuremath{\Omega}}}_{\text{max}}\ensuremath{\propto}1/\ensuremath{\tau}$ in the absence of group-velocity mismatch. The associated maximum gains scale, respectively, as $1/{\ensuremath{\tau}}^{2/3}$ and $1/\ensuremath{\tau}$, thus signaling the corresponding quadratic and linear dispersion relation of these modes in the low-frequency limit. A detailed analysis of the influence of the nonlinear response time and group-velocity dispersion on the MI gain spectrum is also provided.

Experimental demonstration of nonlinear pulse propagation in a fiber Bragg grating written in a fiber amplifier.

We study experimentally nonlinear propagation of sub-nanosecond optical pulses in a fiber Bragg grating written in a Ytterbium-doped fiber amplifier (YD-FBG). The magnitude and the sign of group velocity dispersion (GVD) in YD-FBG can be controlled by adjusting the fiber tension. In the case of anomalous GVD, pulse breakup was observed due to modulation instability. However, for the same input pulse power in the normal GVD regime, the output pulse duration was increased, and pulse breakup was not observed. The deterioration of pulse spectrum due to Raman and four-wave mixing effect was also reduced in the normal GVD regime. Since GVD in YD-FBG is six orders of magnitude higher than in standard fibers, the advantages of normal GVD in fiber amplifiers that were demonstrated in previous works for femtosecond and picosecond pulses can be exploited for amplifying sub-nanosecond pulses. The experimental results are in good agreement with numerical simulations. We have also demonstrated a gain coefficient enhancement by a factor of 1.7 due to slow-light propagation in the YD-FBG.

Dual-pumped degenerate Kerr oscillator in a silicon nitride microresonator.

We demonstrate a degenerate parametric oscillator in a silicon nitride microresonator. We use two frequency-detuned pump waves to perform parametric four-wave mixing and operate in the normal group-velocity dispersion regime to produce signal and idler fields that are frequency degenerate. Our theoretical modeling shows that this regime enables generation of bimodal phase states, analogous to the χ(2)-based degenerate OPO. Our system offers potential for realization of CMOS-chip-based coherent optical computing and an all-optical quantum random number generator.

Three-octave-spanning supercontinuum generation and sub-two-cycle self-compression of mid-infrared filaments in dielectrics.

We experimentally and numerically investigate the spectral and temporal structure of mid-infrared (mid-IR) filaments in bulk dielectrics with normal and anomalous group velocity dispersion (GVD) pumped by a 2.1μm optical parametric chirped-pulse amplifier (OPCPA). The formation of stable and robust filaments with several microjoules of pulse energy is observed. We demonstrate a supercontinuum that spans more than three octaves from ZnS in the normal GVD regime and self-compression of the mid-IR pulse to sub-two-cycle duration in CaF2 in the anomalous GVD regime. The experimental observations quantitatively agree well with the numerical simulations based on a three-dimensional nonlinear wave equation that reveals the detailed spatio-temporal dynamics of mid-IR filaments in dielectrics.

Effect of group velocity dispersion on supercontinuum generation and filamentation in transparent solids

We experimentally investigate the spectral extent and spectral profile of the supercontinuum (SC) generated in transparent solids: barium fluoride, calcium fluoride, and fused silica upon irradiation by intense femtosecond-long pulses of 800, 1,380, and 2,200 nm light. These wavelengths correspond to the normal and anomalous group velocity dispersion (GVD) regimes in fused silica calcium fluoride and barium fluoride. We observe an isolated (anti-Stokes) wing on the blue side most prominently in fused silica but also in CaF2. The SC conversion efficiency is measured for the long wavelengths used in our experiments. We also present results on filamentation in BaF2 in the anomalous GVD regime, including visualization of focusing–refocusing events within the crystal; the size of a single filament is also determined. The 15-photon absorption cross section in BaF2 is deduced to be 6.5 × 10−190 cm30 W−15 s−1.