Effective Group Index Research Articles

Exploring the influence of nanocavity alignment on slow light generation via multiple EIT and Fano resonances in square lattice plasmonic silver nanostructures

In this paper, we present a comprehensive investigation of multiple electromagnetic induced transparency (EIT) and Fano resonances in a square lattice plasmonic nanostructure, which is composed of four silver slabs arranged in a square configuration, with each slab featuring a cylindrical nanocavity at its center. Initially, symmetric structures were analyzed to explore the potential for achieving EIT effects. Subsequently, we introduce deliberate symmetry breaking by precisely aligning the nanocavity in a controlled manner, first within a single slab, then in combinations of two, three, and all four slabs simultaneously. This controlled alignment strategy enabled the relaxation of dipole coupling selection rules, leading to the mixing of dipole and higher-order modes. The interaction between these modes resulted in the generation of multiple EITs and Fano resonances in the optical spectrum. Furthermore, the effective group index was evaluated for the optimal results obtained in the single, double, triple, and four symmetry reduced structures. High group index values were observed in the vicinity of the EIT and Fano resonances, with a remarkable maximum group index value of 6900 achieved within the EIT window. These findings highlight the significant potential of these structures in the design of slow light devices and sensitive sensors.

Modal analysis of silicon-on-insulator based rib waveguide using fully vectorial finite-difference mode solver

In order to interface optical integrated devices with external sources, an understanding of the modal characteristics of the optical waveguide is essential. The finite difference approach is utilized in this work to analyse a rib waveguide based on a silicon-on-insulator platform. A silicon device layer with thickness of 220 nm and a buried oxide with thickness of 2000 nm are considered. It is important to study the modal field distribution and parameters of the waveguide. The simulation results on the behaviour of modal parameters show that both effective refractive index and group index decrease with wavelength. The effective refractive index of the guided mode increases with rib width and slab thickness. It is also observed that energy is more confined in a deeply etched waveguide than in a shallow etched waveguide. Additionally, it is noted that the effective mode area and full-width half maximum increase with rib width and slab thickness.

Highly sensitive based on a Mach-Zehnder interferometer with double-slot hybrid plasmonic waveguide

A refractive index sensor based on the Mach-Zehnder interferometer (MZI) with double-slot hybrid plasmonic waveguide is proposed. Numerical simulation shows that the dispersion turning point (DTP) will appear when the group effective refractive index equals zero and ultra-high refractive index sensitivities can be achieved around the DTP. By changing the surrounding refractive index (SRI), the sensitivity can reach 120,000 nm/RIU with the SRI ranging from 1.0000 to1.0004 and 40,000 nm/RIU with the SRI ranges from 1.3330 to 1.3334. More importantly, the unique dual interference dips around the DTP double the sensitivity. Finally, by taking advantages of the exceptional refractive index sensitivity, we demonstrate a pressure sensor with sensitivity of 800 nm/MPa.

Study on the temperature characteristic of tapered twin-core fiber working at dispersion turning point

We present a study on the spectral characteristics and ultrahigh sensitivity near the dispersion turning point (DTP) of tapered twin-core fiber (TCF). The tapered TCF with the DTP can be fabricated by the one-step taper method by the flame taper machine. Numerical simulations reveal that DTP exists when the group effective refractive index difference between the HE11 mode and the HE21 mode equals zero, where ultrahigh sensitivities can be achieved. The position of the DTP is dependent on the diameter of the taper waist and the refractive index of the external environment. We experimentally demonstrate the temperature characteristic of tapered TCF with DTP in the air, and its maximum sensitivity is − 994 pm/ºC. Finally, by coating polydimethylsiloxane (PDMS) material with the high refractive index and the high thermal-optical coefficient on the tapered TCF, not only the DTP can be achieved in large diameter, but also ultra-high temperature sensitivity can be obtained. The measured temperature sensitivity of the tapered TCF coated with PDMS is as high as 36.71 nm/ºC.

Distributed measurement of mode group effective refractive index difference in a few mode optical fibers.

The possibility to perform distributed measurements of the effective refractive index difference between distinct modes in few mode optical fibers is demonstrated using phase sensitive optical time domain reflectometry. Effective refractive index differences between LP02, LP21a and LP21b modes are measured with for a spatial resolution of 24m.

Ultrasensitive interferometers based on zigzag-shaped tapered optical microfibers operating at the dispersion turning point.

This work proposes and demonstrates a novel interferometric sensor based on a zigzag-shaped tapered optical microfiber (Z-OMF) working at the dispersion turning point (DTP). The Z-OMF can be fabricated in a controllable manner through a modified fiber tapering method. Our study shows that the bending taper can transfer a portion of the fundamental HE11 mode to higher-order modes, and when the bending angle of the Z-OMF reaches 1.61°, high contrast interference fringes can be formed between the HE11 and the HE21 modes. More importantly, we find that by optimizing the diameter of the OMF, the group effective refractive index (RI) difference between HE11 and HE21 mode equals zero, and the refractive index sensing performance can be dramatically improved. To validate our proposed sensing mechanism, we experimentally demonstrate an ultrahigh sensitivity of 1.46×105 ± 0.09×105 nm/RIU. The proposed Z-OMF interferometer has the advantage of high sensitivity and low cost and shows excellent potential in chemical and biological detection.

Mode analysis of orbital angular momentum modes carrying multi-mode ring-core fibers

We discuss the mode properties for orbital angular momentum (OAM) modes supporting multi-mode ring-core fiber (MM-RCF). For strongly-guiding MM-RCF, by introducing one more layer to the ring-core, a two-layer ring-core fiber (TL-RCF) is proposed. It is proven that this TL-RCF can increase the separation degree between the vector eigenmodes and meanwhile weaken the spin–orbit coupling. For mode-group supporting MM-RCF, the maximum mode number is limited by the thickness of ring-core and the cut-off of radial higher-order mode. We also present the tradeoff relationship between the mode group effective index difference and inter-eigenmode differential mode delay in one mode group. The discussion in this paper can give guidance for the design of MM-RCF.

Electromagnetic-Induced Transparency and Slow Light in Plasmonic Metasurfaces

We report numerically electromagnetic-induced transparency (EIT) and Fano resonances in simple plasmonic metasurfaces consisting of gold nanobars arranged in pi, H, and four-shaped fashion. The bright and dark elements in the metasurfaces are responsible for the emergence of EIT and Fano effects in the transmission spectrum. The concept of symmetry breaking is also introduced by incorporating multiple cavities in the metasurface, which relaxes the dipole coupling selection rules resulting in a mixture of dipole and higher order modes that interact and engenders EIT and Fano modes simultaneously in a nanostructure. Furthermore, the EIT and Fano resonances experience a significant red shift by increasing the refractive index of the background medium due to which high sensitivity of around 574 nmRIU−1, figure of merit of 32, and contrast ratio of 41% are realized. Moreover, the effective group index of the proposed metasurface is retrieved and is observed to be very high around the steep asymmetric Fano line shape and within the EIT window, signifying its potential use in slow light applications.

Modelling and Analysis of a Corrugated PN Junction Phase Shifter in Silicon MZM

The essential requirement for an efficient optical modulator is to have high modulation efficiency at a high data rate. The performance of the phase shifter determines the efficiency of the modulator. In this paper, a corrugated PN junction phase shifter on a silicon waveguide is designed and analysed. Doped horizontal slabs of corrugated structure are designed to produce multiple PN junctions to maximise the index change that influences the optical modulation. With the travelling wave electrode, the optical group and RF effective index are matched to obtain high-speed modulation. The optimised design is imported in a silicon Mach Zehnder modulator, and circuit-level simulation analysis is performed. At 70Gbps, a maximum extinction ratio of 10.57dB with a bit error rate of 1.94 × 10− 6 is obtained at Vπ L of 0.75V.cm for the phase shifter length of 1.5mm. The energy per bit transmission is calculated to be 3.3pJ/bit. Further analysis is performed to identify the maximum communication distance supported by this proposed phase shifter design in the silicon Mach Zehnder modulator for the data centre requirements.

What optical fiber modes reveal: group velocity and effective index for external perturbations

Precise control of fiber modes and their dispersion is essential, particularly for fields such as nonlinear frequency conversion or biosensing, both of which often require extensive and time-consuming simulations for design optimization. Here, we develop a first-order perturbation theory for predicting the effective index of bound and leaky fiber modes that is applicable for arbitrary global perturbations as long as the perturbations in the external surrounding are constantly homogeneous and isotropic deviations from the unperturbed fiber. This includes changes not only in permittivity and permeability, but also in wavelength. Thus, we are able to calculate the group velocity solely from the field distributions of the fiber modes at a single wavelength, which therefore allows for large-scale parameter sweeps for accurately managing dispersion. We demonstrate the capabilities of our theory for various trial systems such as step index fibers, photonic crystal fibers, and light cages.

Ultrasensitive Broadband Refractometer Based on Single Stress-Applying Fiber at Dispersion Turning Point

Optical microfiber-based refractometer, which relies on modal interference operating near the dispersion turning point (DTP), has attracted a high level of research interest. The ultrahigh sensitivity can be achieved by mitigating the group effective refractive index difference between the modes in the coupling. Through modifying the microfiber diameter, the group effective refractive index difference can be modified to zero which is defined as DTP. However, all the DTP-based sensors report low fabrication tolerance and narrow operation bandwidth of probing wavelength for the high-sensitivity region where the refractive index (RI) sensitivities higher than 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> nm/RIU can be achieved, which extremely limits the practical applications. To address the challenge, we manipulate and optimize the mode dispersion by using a tapered specially-designed single stress-applying fiber (SSAF). By introducing the stress-applying part (SAP) into the cladding, the wavelength sensitivity of the group effective RI difference can be significantly reduced through the flexibly engineerable control over the material index. In this way, the operation bandwidth is dramatically broadened for 500 nm in comparison with that of conventional microfiber with the same diameter based on DTP, indicating a broad range of optional probing wavelength and high fabrication tolerance. We experimentally verify the ultrahigh sensitivity and broadband operation around the DTP using an SSAF-based microfiber with a waist diameter of about 2.3 μm. The maximum RI sensitivity of 30563 nm/RIU is obtained.

Dual-Path Mach—Zehnder Interferometers With Unequal Geometrical Path Length for Ultrasensitive Refractive Index Sensing

High-sensitivity fiber-optic interferometric refractive index sensors (FIRSs) have been of interest to researchers due to their potential to fabricate specific physical, chemical, and biological sensors. Fabricating interferometers working near the dispersion turning point (DTP) is an effective approach to improve the sensitivity of FIRSs. However, the group effective refractive index (RI) difference approaching 0 and the ratio of the variation of the effective RI difference to the external RI change being −1 cannot be simultaneously realized in low RI sensing, which restricts the further improvement of sensing sensitivity. Here, dual-path Mach-Zehnder interferometers (MZIs) with unequal geometrical path length are proposed for ultrasensitive RI sensing. The dual-path MZIs contain fiber path and sample path of different geometrical lengths to form the optical path difference. The dual-path MZIs can not only show a turning point where the sensing sensitivity tends to be infinite, which is similar to the previously reported DTP, but also get the constant value −1 for the RI response factor, leading to the result that the dips within an over-500-nm band width around the turning point can achieve high sensitivity reaching 105 nm/RIU level or higher. Ultrahigh sensitivity of −1.26 × 106 nm/RIU has been experimentally demonstrated at the RI around 1.35022. The dual-path MZIs proposed here may enlighten new ideas for developing high-sensitivity FIRSs.

Inverse photonic-crystal-fiber design through geometrical and material scalings

Geometrical and material — i.e., external and internal — scaling symmetries are exploited to obtain approximated analytical expressions for the mode effective index, group index, and chromatic dispersion of a scaled fiber. Our results include material refractive index scaling that changes the numerical aperture. First, the analytical expressions are successfully tested with a conventional step index fiber in a broadband range of wavelengths, from 1 to 2 μm. Then, we establish a procedure to adapt the analytical expressions to photonic crystal fibers (PCFs) and illustrate its application in a triangular PCF with circular holes. These adapted analytical expressions show good agreement with a rigorous numerical solution of the fundamental fiber mode. Finally, we demonstrate how powerful these expressions are for the design of PCFs. In particular, we illustrate our approach designing, in four iterations or less, PCFs with flattened dispersion profile over 300 nm or high dispersion slope over 40 nm, with different chromatic dispersion values.

Enhanced tuneable rotatory power in a rotating plasma.

The gyrotropic properties of a rotating magnetized plasma are derived analytically. Mechanical rotation leads to a new cutoff for wave propagation along the magnetic field, and polarization rotation above this cutoff is the sum of the classical magneto-optical Faraday effect and the mechanico-optical polarization drag. Exploiting the very large effective group index near the cutoff, we expose here that polarization drag can be 10^{4} larger than Faraday rotation at GHz frequency. The rotation leads to weak absorption while allowing direct frequency control, demonstrating the unique potential of rotating plasmas for nonreciprocal elements. The very large rotation frequency of a dense non-neutral plasma could enable unprecedented gyrotropy in the THz regime.

A new method to improve the sensitivity of nitrate concentration measurement in seawater based on dispersion turning point

The nitrate concentration is extremely low in seawater, which needs highly sensitive sensors to measure. In this paper, a new method to improve the sensitivity of nitrate concentration measurement in seawater based on dispersion turning point (DTP) theory is demonstrated using a microfiber mode interferometric sensor. The high sensitivity is achieved by the interference of HE11 mode and HE12 mode. Different parameters that influence DTP have been calculated theoretically, including positions of dips and diameters for obtaining DTP, the relationship between DTP and group effective refractive index difference, and the effects of refractive indexes of solutions on the DTP. Calculated results show that the sensitivity of dip will be ultra-high near the DTP and the ultra-high sensitivity region is very narrow in a certain band or a certain diameter. In the experiment, six sensors with different diameters are fabricated to realize the concentration of sodium nitrate sensing in seawater. By optimizing the parameters of sensor, the maximum sensitivity and detection limit of sodium nitrate in seawater can reach to be 5.98 pm/ppm (refractive index sensitivity is 50396.09 nm/RIU) and 0.17 ppm, respectively. The sensor demonstrated here shows advantages of easy to construct, low cost, high precision and high sensitivity, which provides a new optical detection method for in-situ detection of marine environment or low concentration substances sensing in other liquids.

Improvement on refractive index sensing by exploiting the tapered two-mode fibers

The spectral characteristics and sensitivities of a tapered two-mode fiber sandwiched between two single-mode fibers are systematically investigated. Theoretical calculations reveal that a dispersion turning point (DTP) appears when the group effective refractive index (RI) difference between the fundamental mode and the higher-order mode equals zero; as a result, ultrahigh RI sensitivities can be achieved. Furthermore, the location of the DTP is strongly dependent on the tapering condition. Then, we experimentally demonstrate high sensitivities of the RI sensor with the waist diameter of ∼4 μm by means of immersing it in a flow cell filled with glycerol solution. In further tracking of the resonant wavelength shift around the DTP, it is found that the proposed RI sensor exhibits a sensitivity of 1.81 × 104 nm/RIU and a limit of detection down up to 3.29 × 10−5 RIU in a liquid glycerol solution.

Multispectral broadband PIT and Fano resonance in skewed dipolar metasurface

The dipolar charge distribution are most common phenomenon behind the electromagnetic radiating elements and antennas. Plasmonic nanostructures are used to induce nanoscale dipolar resonances when coupled to incident light. It is interesting to investigate the effect of skewness in the conventional dipolar resonances, which is introduced through geometrical effects in nanostructures. Here, S-shaped skewed dipolar nanostructure is used to add skewness to the dipole modes and therefore induce plasmon hybridization effects between bright and dark plasmon modes, leading to multispectral broadband plasmon induced transparency (PIT) and Fano resonances. Additionally, effective group index of the skewed dipole metasurface is retrieved and is found to be very high within the PIT window suggesting its potential use in slow light applications.

Spectral Characteristics and Ultrahigh Sensitivities Near the Dispersion Turning Point of Optical Microfiber Couplers

We present a systematic study on the spectral characteristics and ultrahigh sensitivity near the dispersion turning point (DTP) of optical microfiber couplers. Numerical simulations reveal that a DTP exists when the group effective refractive index (RI) difference between the even mode and the odd mode equals zero, where both ultrahigh positive RI sensitivities and negative RI sensitivities can be achieved. The position of the DTP is dependent on the coupler width, and it always exists over the surrounding RI (SRI) range of 1.333-1.41, which enables the ultrasensitive RI sensing in this wide RI range. Then, we studied the interference spectra characteristics around the DTP both theoretically and experimentally. We further experimentally demonstrate ultrahigh sensitivities of 59624 nm/refractive index unit (RIU) and -58470 nm/RIU around the SRI of 1.333 and 26999 nm/RIU and -29267 nm/RIU around the SRI of 1.35, respectively. High figure of merits of 4192 and 5280 are also achieved around the SRI of 1.333 and 1.35, respectively. Finally, utilizing the exceptional RI sensitivity, we demonstrate an ultrasensitive temperature sensor with a negative sensitivity of -15.23 nm/°C and a positive sensitivity of +16.78 nm/°C.

Refractive index sensing using silicon-on-insulator waveguide based modal interferometer

We propose a refractive index sensor based on modal interference between the first two TE modes in a silicon-on-insulator dual-mode waveguide. It is shown that by appropriately choosing the waveguide dimensions one can achieve a large variation of the modal effective index difference with the ambient refractive index (ARI) as well as a smaller group effective index difference between the two modes, resulting in an extremely high RI sensitivity in the wavelength interrogation scheme. The RI sensitivity of the proposed sensor is found to be ∼ 9100 nm/RIU for the ARI∼1.33, which is the highest reported RI sensitivity achieved in the integrated optic modal interferometers till date. The figure of merit is also found to be extremely high and is more than 2800.

Demonstration of a highly subluminal laser with suppression of cavity length sensitivity by nearly three orders of magnitude.

We have demonstrated a laser in which the frequency shift due to small cavity fluctuations is far less than what would be expected from a conventional laser. The factor of sensitivity suppression is inferred to be equal to the effective group index experienced by the laser, implying that this laser is subluminal. We have observed a suppression factor as high as 663. Such a laser is highly self-stabilized compared to a conventional laser, and is expected to have a far smaller Schawlow-Townes linewidth. As a result, this laser may have potentially significant applications in the fields of high-precision optical metrology and passive frequency stabilization.