Normalized Delay Bandwidth Product Research Articles

Slow light effect with high group index and wideband by saddle-like mode in PC-CROW

Slow light with high group index and wideband is achieved in photonic crystal coupled-resonator optical waveguides (PC-CROWs). According to the eye-shaped scatterers and various microcavities, saddle-like curves between the normalized frequency f and wave number k can be obtained by adjusting the parameters of the scatterers, parameters of the coupling microcavities, and positions of the scatterers. Slow light with decent flat band and group index can then be achieved by optimizing the parameters. Simulations prove that the maximal value of the group index is > 104, and the normalized delay bandwidth product within a new varying range of n g > 102 or n g > 103 can be a new and effective criterion of evaluation for the slow light in PC-CROWs.

Slow light engineering in a photonic crystal slab waveguide through optofluidic infiltration and geometric modulation

In this paper, a new type of flat-band slow light structure with high group index (n g) and large normalized delay-bandwidth product (NDBP) in a silicon on insulator (SOI) based photonic crystal (PC) slab waveguide with a triangular lattice of circular holes is demonstrated. The dispersion engineering is performed by infiltrating optical fluids with different refractive indices n f in the first row and shifting the second row of air holes adjacent to the PC waveguide (PCW) in the longitudinal direction. In the optimized case, a high NDBP of 0.32 with a group index of 54.55 and a bandwidth of 9.13 nm could be obtained. Furthermore, an ultra-low group velocity dispersion (GVD) in the range of 10–20 s2/m is achieved in all of the structures. These results are obtained by numerical simulations based on three-dimensional (3D) plane wave expansion (PWE) method.

Slow light photonic crystal waveguides with large delay-bandwidth product

We present a slow light photonic crystal waveguide. In our structure design, we displace some air holes perpendicular to the line defect. By tuning the group index, ng, from 11.8 to 40, we attain a wide bandwidth varying from 15.9 to 46.9 nm. The group velocity dispersion is kept below 10−20 m−1 s2, and the normalized delay—bandwidth product of 0.448—is attained at ng=14.8 by this structure. This study uses plane wave expansion and finite-difference time domain methods.

Experimental GVD engineering in slow light slot photonic crystal waveguides.

The use in silicon photonics of the new optical materials developed in soft matter science (e.g. polymers, liquids) is delicate because their low refractive index weakens the confinement of light and prevents an efficient control of the dispersion properties through the geometry. We experimentally demonstrate that such materials can be incorporated in 700 μm long slot photonic crystal waveguides, and hence can benefit from both slow-light field enhancement effect and slot-induced ultra-small effective areas. Additionally, we show that their dispersion can be engineered from anomalous to normal regions, along with the presence of multiple zero group velocity dispersion (ZGVD) points exhibiting Normalized Delay Bandwidth Product as high as 0.156. The reported results provide experimental evidence for an accurate control of the dispersion properties of fillable periodical slotted structures in silicon photonics, which is of direct interest for on-chip all-optical data treatment using nonlinear optical effects in hybrid-on-silicon technologies.

Slow light in dual-periodic photonic crystals based slotted-waveguide coupled cavity

Considering the capacity of the nanoscale width area with the low-refractive index can confine light waves, the dual-periodic slotted photonic crystals, which is constructed by coupling low-refractive index's slotted-waveguide with high-refractive index's cavity is proposed in this paper. The best slow light properties and the optimal slotted-waveguide coupled cavity are achieved by adjusting the slotted-width and the period of cavity respectively. In this structure, the slow-light properties are simulated by Plane Wave Expansion (PWE), the result reveals that the group velocities are all three orders of magnitude smaller than the speed of light in vacuum, the slowest value is 7.96×10−4c when the slotted-width is 0.54a and the period of cavity is 0.95a. Moreover, the corresponding Normalized Delay-Bandwidth Product (NDBP) values are larger than 0.24. Besides, the slotted-waveguide coupled cavity can be reconfigured, which accordingly changes the corresponding slow-light property. At last, the numerical results provide a new thought and method for decreasing group velocity and potential application for optical buffer in photonic crystals field.

Slow light in reconfigurable two-dimensional nested ferrite magnetic fluid photonic crystal coupled-cavity waveguides

Photonic crystal waveguide (PCW), due to its large bandwidth, small size, and diversified design of the waveguide structures, represents a breakthrough in the field of optical buffer. Here, a nested structure is designed to improve delay-bandwidth product with ferrite magnetic fluid infiltrated photonic crystal coupled-cavity waveguides. Specifically, three types of coupled cavities, i.e., horizontal-, vertical-, and cross-defect cavity are studied with different concentrations of magnetic fluid. Overall, this aspect of the work is interesting from the perspective of coupled defect waveguides design, which is different from previous line-defect waveguides. Plane wave expansion simulations on the slow light property of the three PCWs reveal that the group velocities are all three orders of magnitude smaller than the speed of light in vacuum and that the corresponding normalized delay-bandwidth product (NDBP) values are all >0.35, with 0.41 being the highest value achieved in vertical-defect coupled cavity. Interestingly, the quality factor (Q), normalized bandwidth (Δω), and NDBP can be readily tuned by varying the concentrations of magnetic fluid. Moreover, all the three coupled-cavity waveguides can be reconfigured, which accordingly changes the corresponding slow light property. Compared to previous works, the results of this work have further improved the slow light property in slow light devices and realized the tunable slow light.

Achievement of Large Normalized Delay Bandwidth Product by Exciting Electromagnetic-Induced Transparency in Plasmonic Waveguide

In this paper, we have generated an effect of electromagnetic-induced transparency (EIT)-like transmission in a pair of resonators coupled to a metal–insulator–metal waveguide. Resonators are separated by the metallic nanoslit. By controlling single parameter (i.e., the width of the metallic slit), the device is made to exhibit EIT-like transmission. EIT is the result of destructive interference between two resonating modes, which leads to an asymmetrical-shaped resonance called Fano resonance. EIT is generally accompanied with sharp dispersion that reduces the velocity of light near the resonance. The slow-light characteristics of the device are also investigated. An ultra large value of group index ( ${n}_{g}=117.06$ ) and a large value of normalized delay bandwidth product (NDBP = 0.88) is obtained over an ultra large bandwidth ( $\Delta f=1.39$ THz). Furthermore, it is theoretically predicted that asymmetry parameter ( $q$ ) of Fano resonance experiences a sign reversal when resonances are swept each other in the tuning process. This reversible Fano resonance and slow-light nature of proposed device open up the avenues for designing on-chip optical buffers, switches, modulators, and so on.

Slow light in tunable low dispersion wide bandwidth photonic crystal waveguides infiltrated with magnetic fluids

We analyze the properties of a photonic crystal waveguide as a device capable of producing slow light along a wide bandwidth. The proposed structure consists of a square lattice of hollow silicon cylinders rotated 45° immersed on a colloidal suspension of magnetic nanoparticles; this arrangement produces “U-type” group index–frequency curves. The cylinder inner radius is carefully chosen to maximize the normalized delay bandwidth product (NDBP) and the concentration of the magnetic fluid is changed in order to make the device tunable in frequency.

Slow light enabled time and wavelength division demultiplexer in slotted photonic crystal waveguide

We have proposed a design for slow light with ultraflat dispersion in a slotted photonic crystal waveguide consisting of a hexagonal arrangement of elliptical air holes on a silicon-on-insulator substrate. The proposed structure has low group velocity and low group velocity dispersion with a wide normalized bandwidth range of 0.0089. The proposed structure can be used as an optical buffer for the storage of a large amount of data due to the large value of the normalized delay bandwidth product equal to 0.634. An optimized structure for a slotted photonic crystal has been analyzed for its applications as both a time and wavelength division demultiplexer. Furthermore, the time delay between two adjacent wavelengths (1550 and 1555 nm) is more than that reported earlier.

Tunable Slow Light with Large Bandwidth and Low-dispersion in Photonic Crystal Waveguide Infiltrated with Magnetic Fluids

Two kinds of magnetic fluids with different volume fractions are symmetrically filled into the W0.9 photonic crystal waveguide structure. The 2D plane-wave expansion method is used to investigate the slow light properties numerically. The constant group index criterion is employed to evaluate the slow light performance. The wavelength bandwidth <TEX>${\Delta}{\lambda}$</TEX> centering at <TEX>${\lambda}_0=1550nm$</TEX> varies from 32.4 to 44.2 nm when the magnetic field factor <TEX>${\alpha}_{\parallel}$</TEX> changes from 0 to 1. And the corresponding normalized delay bandwidth product can be tuned from 0.221 to 0.258. For comparison and optimization, two infiltration cases are investigated and the more advantageous infiltration scheme is found.

Wideband slab photonic crystal waveguides for slow light using differential optofluidic infiltration.

A new type of wideband slow light with a large delay bandwidth product in a slab photonic crystal waveguide with a triangular lattice of circular air holes in a silicon-on-insulator substrate based on optofluidic infiltration is demonstrated. It is shown that dispersion engineering through infiltrating optical fluids-with different refractive indices n(1f) and n(2f)--in the first two rows of the air holes innermost to the waveguide results in an improved normalized delay bandwidth product ranging from 0.187 to 0.377 with large bandwidth (12 nm<Δλ<32 nm) and group index (14.20< n(g)< 24.62) around 1550 nm. The nearly zero group velocity dispersion on the order of 10-(20) s(2)/m is achieved in all of the structures. These results are obtained by numerical simulation based on a three-dimensional-plane-wave expansion method.

Issues when designing hypoellipse photonic crystal waveguides

This work designs a type of line-defect photonic crystal waveguide (PCW) called hypoellipse PCW (HPCW) that considers two conflicting issues: group index and bandwidth. To do so, the recent multi objective framework called MoMIR is employed. A wide range of designs obtained demonstrates the advantage of considering group index and bandwidth simultaneously when designing HPCWs. Comparison of the proposed HPCW with the current best PCWs shows a nearly 7% improvement over the latter in terms of normalized delay-bandwidth product (NDBP). Analysis of the results reveals some of the physical rules about the structure of the HPCW. Finally, optical pulse propagation in obtained HPCWs and the process of designing an optical buffer by using an obtained design are explained.

Slow light performance enhancement of Bragg slot photonic crystal waveguide with particle swarm optimization algorithm

Recently, majority of current research in the field of designing Phonic Crystal Waveguides (PCW) focus in extracting the relations between output slow light properties of PCW and structural parameters through a huge number of tedious non-systematic simulations in order to introduce better designs. This paper proposes a novel systematic approach which can be considered as a shortcut to alleviate the difficulties and human involvements in designing PCWs. In the proposed method, the problem of PCW design is first formulated as an optimization problem. Then, an optimizer is employed in order to automatically find the optimum design for the formulated PCWs. Meanwhile, different constraints are also considered during optimization with the purpose of applying physical limitations to the final optimum structure. As a case study, the structure of a Bragg-like Corrugation Slotted PCWs (BCSPCW) is optimized by using the proposed method. One of the most computationally powerful techniques in Computational Intelligence (CI) called Particle Swarm Optimization (PSO) is employed as an optimizer to automatically find the optimum structure for BCSPCW. The optimization process is done by considering five constraints to guarantee the feasibility of the final optimized structures and avoid band mixing. Numerical results demonstrate that the proposed method is able to find an optimum structure for BCSPCW with 172% and 100% substantial improvements in the bandwidth and Normalized Delay-Bandwidth Product (NDBP) respectively compared to the best current structure in the literature. Moreover, there is a time domain analysis at the end of the paper which verifies the performance of the optimized structure and proves that this structure has low distortion and attenuation simultaneously.

Wideband Slow Surface Plasmons in Double Resonator Plasmonic Grating Waveguide

We propose a theoretical and numerical investigation of surface plasmon polaritons supported by a metal–insulator–metal (MIM) waveguide, periodically coupled to a series of adjacent resonators. The slow light characteristics of the MIM-coupled resonator is analyzed by controlling separation or displacement between resonators. By tailoring this displacement factor, group velocity of slow wave structures is reduced to a great extent with a large value of the normalized delay bandwidth product (NDBP = 0.667) that measures the capacity of the device. A low value of group velocity ( ${v}_{g} = c/7$ ) is reported over an ultralarge bandwidth ( $\Delta f = 21$ THz). An unusual U-shaped group index—frequency curves with a constant group index ${n}_{g}$ is obtained, which leads to a nearly-zero value of group velocity dispersion followed by positive and negative peaks. The structure is also analyzed for changing the depth of the resonators. The structure can be further modified to suit different applications in optical switching device, dispersion compensating units, and nonlinear optics devices.

Slow Light with High Normalized Delay Bandwidth Product in Photonic Crystal Line Defect Waveguide

In this paper, to generate slow light with large group index, wideband, and low dispersion in suggested line defect photonic crystal waveguide, a systematic optimization procedure is performed. Two structural parameters in the adjacent rows of the waveguide are carefully adjusted. Dispersion engineering in the proposed structure is done by using plane wave expansion method. By tuning the structural parameters, normalized delay-bandwidth product (NDBP) with nearly constant group index is significantly improved. In the optimum case, a high NDBP of 0.373 with a group index of 38.6 and a bandwidth of 14.97 nm is obtained, while restricting the group-index variation within a 10% range. Also,a negligible group velocity dispersion over a broad wavelength range is obtained that can cause a small expansion of the pulse through the waveguide.

SoMIR framework for designing high-NDBP photonic crystal waveguides.

This work proposes a modularized framework for designing the structure of photonic crystal waveguides (PCWs) and reducing human involvement during the design process. The proposed framework consists of three main modules: parameters module, constraints module, and optimizer module. The first module is responsible for defining the structural parameters of a given PCW. The second module defines various limitations in order to achieve desirable optimum designs. The third module is the optimizer, in which a numerical optimization method is employed to perform optimization. As case studies, two new structures called Ellipse PCW (EPCW) and Hypoellipse PCW (HPCW) with different shape of holes in each row are proposed and optimized by the framework. The calculation results show that the proposed framework is able to successfully optimize the structures of the new EPCW and HPCW. In addition, the results demonstrate the applicability of the proposed framework for optimizing different PCWs. The results of the comparative study show that the optimized EPCW and HPCW provide 18% and 9% significant improvements in normalized delay-bandwidth product (NDBP), respectively, compared to the ring-shape-hole PCW, which has the highest NDBP in the literature. Finally, the simulations of pulse propagation confirm the manufacturing feasibility of both optimized structures.

Slow light in ellipse-hole photonic crystal line-defect waveguide with high normalized delay bandwidth product

In this paper, a novel flatband slow light device with low group velocity dispersion (GVD) is presented in an ellipse-hole photonic crystal (PC) line-defect waveguide. Utilizing dispersion engineering in the proposed structure, normalized delay-bandwidth product (NDBP) under a constant group index criterion is significantly improved. A step-by-step optimization process is done on the adjacent rows to the waveguide, which are filled by silica. For optimum case a high NDBP of 0.461 with a group index of 41.86 and a bandwidth of 17.06 nm is obtained by three-dimensional plane-wave expansion method. To the best of our knowledge, this NDBP is one of the highest values in PC waveguides reported to date, in which the group index value is relatively high. The numerical results show that GVD is negligible over a broad wavelength range. Also, optical pulse propagation through the waveguide is performed based on the finite-difference time-domain method. The results indicate that the shape of output pulse experiences a broadening of 2.1% compared with the incoming pulse after traveling a distance of 30a.

PM245 Effect of Obstructive Sleep Apnea Hypopnea Syndrome on Blood Pressure And C-Reactive Protein In Male Hypertension Patients

In this paper, the slow light properties of the polyatomic Photonic Crystal (PhC) which has multiple different air holes in each primitive cell are investigated. A slow light waveguide with “U-type” group index–frequency curve, which results in nearly constant group index over large bandwidth, is achieved using this new photonic crystal geometry based on the square lattice. Also, the radius and position of the innermost rows of small air holes have been modified to investigate the feasibility of controlling the dispersion relation by subtle structural modification. Numerical results demonstrate that decreasing the group velocity effectively and meanwhile maintaining a large Normalized Delay-Bandwidth Product (NDBP) can be achieved by only modifying the radius of the innermost rows of small air holes. Shifting the innermost rows of small air holes toward the waveguide core is highly beneficial to enlarge the slow light bandwidth, but it contributes nothing to the promotion of NDBP. Our results provide important theoretical basis for the potential application offered by the polyatomic photonic crystal in future optical networks.

Nonlinear performance in silicon nitride slow light photonic crystal waveguides with elliptical holes

We propose a slow-light photonic crystal waveguide, which uses a combination of circular and elliptical air holes arranged in a hexagonal lattice with the background material of silicon nitride (refractive index n=2.06). Large value of normalized delay bandwidth product (NDBP=0.3708) is obtained. We have analyzed nonlinear performance of the structure. With our proposed geometry strong SPM is observed at moderate peak power levels. Proposed photonic crystal waveguide has slow light applications such as reduction in length and power consumption of all-optical and electro-optic switches at optical frequency.

Unit Cell Topology Optimization of Line Defect Photonic Crystal Waveguide

In this paper we utilize a systematic method to optimize the topology of a line defect Photonic Crystal Wave guide (PCW), a very popular and effective optical device for realizing optical buffer in room temperate operation. In order to do this, we divide the unit cell PCW to 25 squares and utilize a Binary Particle Swarm Optimization (BPSO) algorithm to find the optimum topology. During the optimization process, we apply some constraints to avoid band mixing as well. Calculation results show that Normalized Delay-Bandwidth Product (NDBP) for the structure optimized is 0.27. This structure optimized possesses a high bandwidth (20.9 nm) with group index of 21.7 as well.