Low Group Velocity Dispersion Research Articles

Kerr nonlinearity and group velocity dispersion of InGaAs/InP and GaAsSb/InP waveguides in the mid-infrared

We report measurements of Kerr nonlinearity and group velocity dispersion in In0.53Ga0.47As/InP and GaAs0.51Sb0.49/InP ridge waveguides in the mid-infrared using four-wave mixing at λ ≈ 5 µm. Measured values of Kerr nonlinearity are significantly higher compared to those reported for any other materials systems suitable for building dielectric waveguides with low losses and low group velocity dispersion in the mid-infrared (λ ≈ 3–15 μm). Our measurements establish both In0.53Ga0.47As/InP and GaAs0.51Sb0.49/InP materials as promising platforms for the development of on-chip mid-infrared frequency comb generation and supercontinuum light sources.

Bifurcation Analysis and Bounded Optical Soliton Solutions of the Biswas-Arshed Model

We investigate the bounded travelling wave solutions of the Biswas-Arshed model (BAM) including the low group velocity dispersion and excluding the self-phase modulation. We integrate the nonlinear structure of the model to obtain bounded optical solitons which pass through the optical fibers in the non-Kerr media. The bifurcation technique of the dynamical system is used to achieve the parameter bifurcation sets and split the parameter space into various areas which correspond to different phase portraits. All bounded optical solitons and bounded periodic wave solutions are identified and derived conforming to each region of these phase portraits. We also apply the extended sinh-Gordon equation expansion and the generalized Kudryashov integral schemes to obtain additional bounded optical soliton solutions of the BAM nonlinearity. We present more bounded optical shock waves, the bright-dark solitary wave, and optical rogue waves for the structure model via these schemes in different aspects.

Design and simulation of high modulation efficiency, low group velocity dispersion lithium niobate slow-wave electro-optic modulator based on a fishbone-like grating

Thin-film lithium niobate (LN) has emerged as an excellent platform for electro-optic modulators (EOMs) owing to its strong electro-optic (Pockels) effect. However, it remains an open challenge to achieve high modulation efficiency in chip-scale EOMs, primarily due to the limitation of light-matter interaction. Here, we propose an on-chip slow-wave LN EOM with a length of 3.4 mm with high modulation efficiency by using a fishbone-like grating. By assembling the fishbone-like grating, the Pockels effect is significantly enhanced as a result of the compression of the local density of states. Benefiting from this effect, the modulation efficiency of the modulator can be improved to 4.6 times of the original. In addition, a 3 mm matched micro-structure electrode is designed to realize the low group velocity of the microwave modulation signal. The simulation results show that the modulation efficiency of this slow-wave EOM is 1.42 V·cm. The slow-light effect is realized theoretically with a flat optical operating bandwidth of about 21 nm, group velocity dispersion < 2 ps2/mm, and low loss < 0.33 dB. Additionally, a 3 dB modulation bandwidth of 80 GHz is verified by simulation by virtue of the proposed micro-structure electrode.

Broadband resonance-enhanced frequency generation by four-wave mixing in a silicon Floquet topological photonic insulator

Floquet topological photonic insulators, whose light transport properties are dictated by the periodic drive sequence of the lattice, provide more flexibility for controlling and trapping light than undriven topological insulators. This can enable novel nonlinear optics applications in topological photonics. Here, we employ a novel resonance effect called Floquet Defect Mode Resonance (FDMR) in a 2D silicon Floquet microring lattice to demonstrate resonance-enhanced frequency generation by four-wave mixing of Floquet bulk modes in the presence of Kerr nonlinearity. The compact, cavity-less resonance mode, induced through a periodic perturbation of the lattice drive sequence, has the largest reported Q-factor for a 2D topological resonator of ∼105 with low group velocity dispersion, which enables efficient broadband frequency generation over several Floquet–Brillouin zones of the Floquet topological insulator. We achieved wavelength conversion over a 10.1 nm spectral range with an average enhancement of 12.5 dB in the conversion efficiency due to the FDMR. Our work could lead to robust light sources generated directly on a topologically protected photonic platform.

The large-mode-area multicore fiber with low and flat normal dispersion profile at 1.5–2.3 μm

For the purpose of realizing the large-mode-area (LMA) fibers with low and flat normal group velocity dispersion (GVD) profiles, the approach based on the multicore fiber (MCF) consisting of identical cores is proposed. The contribution of the coupling between two adjacent cores to tailoring the GVD of the MCF can be analyzed by using the dispersive equation, which is evaluated by the coupled mode theory (CMT) and can describe the GVD relation between the MCF and single-core waveguide. Furthermore, the designed 19- and 37-core MCFs with the step-index waveguides exhibit extremely flat normal GVD profiles with values of close to 0 ps/nm·km in the wavelength range of 1500 – 2300 nm, while the effective mode area of the 37-core MCF can reach 440 μm2 at 1900 nm. For the case of the MCF based on the photonic crystal fiber (PCF) structure, the 7-core MCFs can offer the concave-shaped normal GVD profiles in the 1900-nm wavelength region, where the minimum GVD values are around −46 ps/nm·km, and the wavelengths of the dip center can shift from 1880 to 2110 nm by tuning the core spacing. The effective mode areas are increased beyond 170 μm2 at 1900 nm. The proposed LMA normal-dispersion MCFs have potential applications in high-power ultrashort-pulse fiber lasers and amplifiers.

Phase-locked picosecond optical parametric oscillator.

We report a degenerate self-phase-locked picosecond optical parametric oscillator (OPO) synchronously pumped by a mode-locked Yb-fiber laser at 1064 nm, delivering broadband output near 2 µm with 2.8 W of average power at ∼80MHz repetition rate. By exploiting a 50-mm-long MgO:PPLN crystal providing high gain and low group velocity dispersion under type-0 (e→ee) phase matching, the OPO generates a phase-locked degenerate output spectrum with a bandwidth of ∼202nm centered at 2128 nm in pulses of ∼21ps duration with excellent passive long-term power and spectral stability in high spatial beam quality. Phase-locked operation results in spectral and power stabilization at exact degeneracy and is further validated by f-2f interferometry and radio frequency measurements of OPO output. To the best of our knowledge, this is the first degenerate self-phase-locked OPO in picosecond time scale, and the highest average power reported for a phase-locked ultrafast OPO to date.

Broadband Single‐Mode Hybrid Photonic Crystal Waveguides for Terahertz Integration on a Chip

AbstractBroadband, low‐loss, low‐dispersion propagation of terahertz pulses in compact waveguide chips is indispensable for terahertz integration. Conventional 2D photonic crystals (PCs) based terahertz waveguides are either all‐metallic or all‐dielectric, having either high propagation losses due to the Ohmic loss of metal, or a narrow transmission bandwidth restricted by the range of single‐mode operation in a frequency range defined by the PC bandgap, respectively. To address this problem, a hybrid (metal/dielectric) terahertz waveguide chip is developed, where the guided mode is completely confined by parallel gold plates and silicon PCs in vertical and lateral directions, respectively. A unique multiwafer silicon‐based fabrication process, including gold–silicon eutectic bonding, micropatterning, and Bosch silicon etching, is employed to achieve the self‐supporting hybrid structure. Theoretical and experimental investigations demonstrate that the hybrid waveguide supports a single‐mode transmission covering 0.367–0.411 THz (bandwidth of 44 GHz, over twice wider than that of all‐silicon PC waveguides) with low loss (below 0.05 dB mm−1) and low group velocity dispersion (from −8.4 to −0.8 ps THz−1 mm−1). This work enables more compact, wideband terahertz waveguides and auxiliary functional components that are integratable in chips toward ultra‐high‐density integrated terahertz devices in particular in the field of wireless communications.

Slow light with high normalized delay-bandwidth product in organic photonic crystal coupled-cavity waveguide.

In this theoretical study, a photonic crystal coupled-cavity waveguide created on polymer substrate was demonstrated to provide high-performance slow light with low group-velocity dispersion and large normalized delay-bandwidth product. Combined with structural-parameter optimization, the normalized delay-bandwidth product was enhanced to a large value of 0.809, and the group-velocity dispersion was on the order of 104(ps2/km). Furthermore, the optimized coupled-cavity waveguide had tunability capabilities by changing the external pump laser power. Importantly, while adjusting the slow light, the normalized delay-bandwidth product values remained above 0.8, which was necessary to maintain the performance of optical buffering devices.

Wideband Slow Light in a Line-defect Annular Photonic-crystal Waveguide

In this theoretical study, a line-defect photonic-crystal waveguide hosted in an annular photonic crystal was demonstrated to provide high-performance slow light with a wide band, low group-velocity dispersion, and a large normalized delay-bandwidth product. Combined with structural-parameter optimization and selective optofluid injection, the normalized delay-bandwidth product could be enhanced to a large value of 0.502 with a wide bandwidth of 58.4 nm in the optical-communication window, for a silicon-on-insulator structure. In addition, the group-velocity dispersion is on the order of 105 (ps2/km) in the slow-light region, which could be neglected while keeping the signal transmission unchanged.

Switchable slow light rainbow trapping and releasing in strongly coupling topological photonic systems

We design and present a switchable slow light rainbow trapping (SLRT) state in a strongly coupling topological photonic system made from a magneto-optical photonic crystal waveguide channel. The waveguide channel supports slow light states with extremely small group velocity (vg=2.1×10−6c), low group-velocity dispersion, and a broadband operation bandwidth (3.60–4.48 GHz, near 22% of bandwidth). These slow light states originate from the strong coupling between two counter propagating topological photonic states. Under a gradient magnetic field, different frequency components of a wave packet are separated and stored at different positions for a long temporal duration with high spatial precision (without crosstalk and overlap between the electric fields of different frequencies) to form SLRT. Besides, these SLRT states can be easily switched among the forbidden state, trapped state, and releasing state by tuning the external magnetic field. The results suggest that the topological photonic state can offer a precise route of spatial-temporal-spectral control upon a light signal and find applications for optical buffers, broadband slow light systems, optical filters, wavelength-division multiplexing, and other optical communication devices.

Optical solitons with Biswas–Arshed model using mapping method

In this work, the Biswas–Arshed model with Kerr law nonlinearity in the absence of self-phase modulation (SPM) and where group velocity dispersion (GVD) is insignificantly small, is studied for optical solitons using the sustained effort of several forms of mapping methods. Both spatio-temporal dispersion of third and second order are comprised to balance this model for low group velocity dispersion. When the modulus m of the Jacobi elliptic functions approaches 0 and 1, the solutions are derived in terms of trigonometric functions and hyperbolic functions respectively. From this scheme singular, dark and bright soliton solutions appear.

Slow light with high normalized delay-bandwidth product in low-dispersion photonic-crystal coupled-cavity waveguide

Slow-light performance based on photonic-crystal coupled-cavity waveguide (PC-CCW) is investigated with low-dispersion pulse transmission. A chain of periodically arranged specific defect cavities of air holes are created along the axis of the waveguide and each of the cavities looks like an irregular hexagon with arrow-like left and right sides to form the PC-CCW. By changing the radius and position of certain defects, slow light modes are achieved. Through optimization, we obtained a highest compromise value for an operating bandwidth of 12.9 nm with an average group index of 70.75 and a normalized delay-bandwidth product (NDBP) of 0.5873. This value of NDBP with low group velocity dispersion is higher than that in other structures based on waveguides or coupled cavities reported previously. The arrow-like shape of the cavity sides is shown to be perfect for reducing the transmission loss of the waveguide. The proposed structure with high NDBP is beneficial for buffering applications and slow light devices.

W-shaped, bright and dark solitons of Biswas–Arshed equation

We investigate the new model proposed by Biswas and Arshed which applies for soliton transmission through optical fibers where self-phase modulation is totally absent. For the low group velocity dispersion to be compensated, both spatio-temporal dispersions of second- and third-order are included in the model. A class of solitary wave solutions of the W-shaped, bright and dark type are obtained by adopting a complex amplitude ansatz solution. The conditions on the fiber parameters for the existence of these structures are also reported. Our results may raise the possibility of some experiments and potential applications related to optical fiber systems in the in presence of higher-order dispersions and absence of cubic nonlinearity.

Optical solitons in presence of higher order dispersions and absence of self-phase modulation

This paper proposes a new model for soliton transmission through optical fibers where self-phase modulation is negligibly small and hence removed. The model however includes spatio-temporal dispersions, of second and third order, to compensate for low group velocity dispersion. The balance for sustaining solitons is provided by nonlinear dispersion terms that are considered in this model.

Ultra-wideband slow light transmission with high normalized delay bandwidth product in W3 photonic crystal waveguide

By separating two photonic crystals with a distance of 23a, where a is the lattice constant, shifting the positions of some discriminatory air holes in the upper and lower edges, and inserting a defect central row, a specific waveguide is set up, W3 photonic crystal waveguide (W3 PCW). An equivalent transmission line model is given, giving the theoretical basis of for the proposed waveguide to have a wider transmission bandwidth and thus higher normalized delay bandwidth product (NDBP). Slow-light properties and performance are studied by using plane-wave expansion and finite-difference time-domain methods. We obtained ultra-wideband of 65.70 nm with low group-velocity dispersion and at the same time a high NDBP of 0.496 through optimization which is a worthy indicator for slow light device performance. Wider bandwidth can allow shorter duration of pulse waves, causing higher field intensity and stronger nonlinear effect.

Fine tuning of the center frequency of the slow light regime in an infiltrated W09 photonic crystal waveguide

We report the tuning process of center frequency in a dispersion engineered slow light regime in W09 photonic crystal slab waveguide (W09-PhCSW). The W09-PhCSW consists of hexagonal lattice of air holes of radii r = 0.3ɑ in a Si substrate with a reduced waveguide width. This end is achieved by means of simultaneous infiltration of magneto and opto-fluidics in first and second rows adjacent to the waveguide. In particular, change in infiltration of opto-fluidics (1.5 ≤ nf ≤ 2.1) is used for selecting the optimized group index with low group velocity dispersion. Concurrently, the center frequency in the constant group index regime (Δng = ±5%) get tuned with an external magnetic field. This course of external controllability originated from the field dependent refractive index of magneto-fluidic. After all, this design leads to a considerable low group velocity dispersion of |β2| ≤ 2000 (ɑ/2πc2), the group index values in the range of 23 ≤ ng ≤ 103 and reasonable group index-bandwidth product values (0.114 ≤ ng × Δω/ωc ≤ 0.26).

Geometrically tunable slow light based on a modified photonic crystal waveguide

In this paper, we have proposed a design for slow light in a modified photonic crystal waveguide by inserting reduced air holes along the middle of the waveguide with a half period of the lattice and by shifting the second rows of holes toward the center of the modified waveguide. A wideband slow light with a high group index and low group velocity dispersion has been achieved. A nearly constant group index of 21, 20, 35.5 and 65 over 20.3 nm, 15.6 nm, 9.5 nm, 5.3 nm bandwidth in the environment of 1550 nm, respectively, are also obtained.

Supercontinuum generation in low dispersion and highly nonlinear hexagonal photonic crystal fibers

We design a solid hexagonal photonic crystal fiber (PCF) with air holes of different diameters in the cladding region using the finite element method. We achieve a low group velocity dispersion of −5.483 ps2/km and a high nonlinearity of 111.4 W−1 km−1 at 450 nm with d1/Λ being 0.345, which could ensure single-mode propagation. The low dispersion and high nonlinearity form the crucial requirements to generate the supercontinuum (SC) pulse. The designed PCF exhibits a broad SC spectrum of bandwidth 600 nm at an operating wavelength of 450 nm which might find a great relevance in optical sensing applications.

Flat-Band Slow Light in a Photonic Crystal Slab Waveguide by Vertical Geometry Adjustment and Selective Infiltration of Optofluidics

In this paper, a photonic crystal slab waveguide (PhCSW) for slow light applications is presented. To obtain widest possible flat-bands of slow light regions—regions with large group index (n g), and very low group velocity dispersion (GVD)—two core parameters of PhCSW structure are investigated. The design procedure is based on vertical shifting of the first row of the air holes adjacent to the waveguide center and concurrent selective optofluidic infiltration of the second row. The criteria of $${{\langle n_g \rangle}}$$ ± 10% variations is used for ease of definition and comparison of flat-band regions. By applying various geometry optimizations for the first row, our results suggest that a waveguide core of W 1.09 would provide a reasonable wide flat-band. Furthermore, infiltration of optofluidics in the second row alongside with geometry adjustments of the first row result in flexible control of 10 < n g < 32 and provide flat-band regions with large bandwidth (10 nm < Δλ < 21.5 nm). Also, negligible GVD as low as β 2 = 10−24 (s2/m) is achieved. Numerical simulations are calculated by means of the three-dimensional plane wave expansion method.

A Novel Terahertz Semiconductor Metamaterial for Slow Light Device and Dual-Band Modulator Applications

In this paper, we propose a novel planar semiconductor metamaterial which consists of two H-shape structures which are nested together and composed of InSb deposited on a thin quartz substrate. The two H-shape structures serve as the bright modes and are exited strongly by the incident wave and interact with each other. This coupling leads to a powerful plasmonically induced transparency (PIT) effect at terahertz frequencies. This scheme provides a way to achieve slow light, and the corresponding group index can reach a value of 1300. We calculated group velocity dispersion (GVD) and saw this structure was a low group velocity dispersion (LGVD) system. Therefore, the proposed structure will be useful in designing slow-light devices, optical buffers, delay lines, and ultra-sensitive sensors. We also showed that the proposed design is tunable, namely changes in geometric parameters and type of semiconductor can largely change the group index. In addition, we considered another application for our design that is a thermal dual-band terahertz metamaterial modulator and numerically obtained frequency and amplitude modulation depth, tunability bandwidth, and loss for this device. We obtained an amplitude modulator depth of 99.7 % and a frequency modulator depth of 47 % that verified this structure can be used in wireless communication and encode information systems in the THz regime.