Mode Effective Index Research Articles

Vector Magnetic Field Sensing at Tiny Angles Through a Nanofluid Functionalized Ultrathin Taper Interferometer

Aiming at the requirement of high precision and long life in tasks of mechanical and navigation industries, a highly sensitive and compact, magnetorheological fluid film-suspended nonadiabatic biconical tapered optical fiber interferometer-based vector magnetometer has been proposed and demonstrated in the manuscript. The reported magnetometer keeps the ability to detect the strength of the magnetic field and its direction in the 3D plane concurrently. Magnetically regulated effective index amendment is used to stimulate the higher order modes propagating in the cladding region of the ultrathin biconical fiber interferometer. Hence, the detection principle of the sensor depends on the changes in the effective indices of higher-order excited modes with respect to the applied magnetic field. The proposed magnetometer detects slight angular variations of -2° to +2° in the magnetic field over a broad range from 0 mT to 567 mT by using the azimuth-dependent anisotropic distribution of nanoparticles in the vicinity of the fiber-optic sensor arm. The reported sensor offers to its angular sensitivities of ~ ∓14.68 pm/mT, and ~ ∓11.79 pm/mT at minor inclinations of ∓1° and ∓2° whereas having its maximum sensitivity of ~ 16.48 pm/mT at 0°.

Differential group delay behavior in homogeneous weakly coupled multicore fiber under bending and twisting condition

The impacts of core count/layout on the mode effective refractive index (\({n}_{\mathrm{eff}}\)), bend- and twist-induced differential group delay (DGD) of different cores, worst-case DGD, and intercore DGD (\({\mathrm{DGD}}_{\mathrm{IC}}\)), in weakly coupled homogeneous multicore fibers (WC-HMCFs), have been analyzed to select the proper core layout with low DGD value for a particular core count. The core counts such as 3-core, 4-core, 6-core, and 12-core and the core layouts namely linear, triangular, square, rectangular, circular one ring structure (ORS), circular dual ring structure (DRS), hexagonal ORS, and square lattice structure (SLS) have been considered in the investigation. Moreover, in order to calculate the \({\mathrm{DGD}}_{\mathrm{IC}}\) values, the generalized expressions of core pitch (Λ) for the different core layouts have been derived. Further, the impacts of core radius (\(a\)), relative refractive index difference (\(\Delta\)), and Λ on the \({n}_{\mathrm{eff}}\) and DGD levels for the 3-core WC-HMCFs, with linear and triangular core layouts, have been analyzed numerically by using the finite element method-based FemSIM simulation platform, and MATLAB. It is observed that for a certain core count value, the core layout and Λ have significant impacts on the DGD levels, while the variations in the values of \(a\) and \(\Delta\) have no significant impact on the DGD levels. Further, increase in core count normally increases the DGD levels in all core layouts. On the other hand, for the fixed values of core count, cladding diameter (D), and outer cladding thickness (OCT), the core layout which has the lowest core pitch leads to the lowest value of \({\mathrm{DGD}}_{\mathrm{IC}}\), as compared to the other core layouts. The investigations carried out in this work may provide the guidelines in different MCF applications, such as MCF-based multi-parameter sensing and signal processing in microwave photonics.

Propagation Properties of Vortex Beams in a Helically Twisted Photonic Bandgap Fiber

We propose a helically twisted hollow-core photonic bandgap fiber (PBGF) for orbital angular momentum (OAM) generation. Results demonstrate that this fiber can effectively separate and transmit higher-order OAM modes while reducing crosstalk. The mode effective refractive index curves as a function of wavelength and the transmission characteristics of OAM are investigated in this letter. We show that this fiber has the potential to be used in OAM generators, light-controlling devices, and all-fiber optical communication applications.

Analysis of BCB and SU 8 photonic waveguide in MZI architecture for point-of-care devices

The proposed refractive index-based biosensor made of cost-effective polymer material in Mach-Zehnder configuration with novel horizontal slot waveguide structure offers high sensitivity. Due to the recent demand for low-cost point-of-care biosensor, silicon wafer-based polymer material has the potential for developing new hybrid waveguides for sensors. Hence we designed BenzoCycloButene (BCB), SU8 material as the core, and polymethyl methacrylate (PMMA) clad on a silicon wafer. The novelty of proposed BCB and SU8 horizontal slot waveguide structure of 2.5 μ m wide and 1.8μ m thick with a slot height of 400 ​nm, which handles the analyte effectively without any external sample holder. In Mach-Zehnder Interferometer architecture, reference arm 1 ​cm and sensing arm at a length of 1.1 ​cm with analyte refractive index of cancer cell (RI ​= ​1.401) and Influenza A type virus (RI ​= ​1.48) are used. Effective mode index of BCB core and SU8 are investigated through Finite-difference time domain (FDTD) analysis, and sensitivity results are calculated. Detection of disease are plotted in the transmission spectrum with reference to normal human serum (RI ​= ​1.35). This horizontal slot waveguide of BCB core achieves a sensitivity of 19280 nm/RIU and SU8 horizontal slot core waveguide provides a sensitivity of 16500 nm/RIU, which is higher in this polymer based refractive index biosensing.

Delineation of profoundly birefringent nonlinear photonic crystal fiber in terahertz frequency regime

Abstract The photonic aspects of semiconducting hexagon-shaped photonic crystal fiber including effective mode area, effective mode index, dispersion, and confinement loss, have already been investigated. The finite element method has been used to compute the maximum distribution of the studied photonic crystal fiber by COMSOL software. The linear modifications from both the effective mode index and an effective mode area have been investigated. Dispersion and confinement loss are examined in terms of air hole ring number and wavelength. For every wavelength, the effective-index model implies that the studied fiber can indeed be single mode. Even though its practical single-mode range inside the opacity aperture of silica appears large, it is eventually confined by a bend-loss edge at both brief & medium wavelengths. Moreover, the reported fiber offers minimal confinement loss of almost 10−8 dB/cm, birefringence 0.0012, and dispersion around 10−11 ps/km nm.

Analytical analysis of inhomogeneous and anisotropic metamaterial cylindrical waveguides using transformation matrix method

Several applications of a cylindrical waveguide filled with inhomogeneous materials have been demonstrated. Analytical solutions for modes, an inhomogeneous cylindrical waveguide, are available only for a few material parameters and those are also mostly approximations. We have obtained exact analytical solutions for cylindrical waveguides filled with different inhomogeneous and anisotropic material parameters. Different sets of material parameters are obtained using the geometric transformation method. The analytical and numerical modal field distributions, the value of cutoff frequencies and effective mode indices for different propagating modes are well matched to each other. The inhomogeneity can be used to miniaturize the radial dimensions of the waveguide. This is highly desirable for many applications like sensing, near-field coupling and magnetic resonance imaging (MRI).

Realization of efficient 3D tapered waveguide-to-fiber couplers on a nanophotonic circuit.

We report the realization of efficiently coupled 3D tapered waveguide-to-fiber couplers (TWCs) based on standard lithography techniques. The 3D TWC design is capable of achieving highly efficient flat-cleaved fiber to silicon nitride photonic waveguide coupling, with T ≈ 95% polarization-insensitive coupling efficiency, wide bandwidth, and good misalignment tolerance. Our fabricated 3D TWCs on a functional nanophotonic circuit achieve T ≈ 85% coupling efficiency. Beyond applications in high-efficiency photon coupling, the demonstrated 3D lithography technique provides a complementary approach for mode field shaping and effective refractive index engineering, potentially useful for general applications in integrated photonic circuits.

Few-mode fiber design for multiple-input-multiple-output-less mode division multiplexing by machine learning

Neural networks (NNs), random forests (RF), and extreme gradient boosting (XGBoost) are applied separately to inversely design the ring-core few-mode fiber (FMF) with a desired weakly coupled performance. We demonstrate the procedure of inverse designing of FMF via machine learning (ML) algorithms and evaluate the prediction accuracy of the above ML algorithms. Compared with RF and XGBoost, the NN performs the highest prediction accuracy. For the NN, RF, and XGBoost, the correlation coefficients of the mode effective index difference are 0.99993, 0.99857, and 0.99937, respectively. Subsequently, by utilizing the method of permuting feature importance ranking, we obtain the high-correlation fiber structural features with the mode effective index difference. Moreover, we analyze the effect of the minimum index difference between two adjacent modes ( Δ n e f f , m i n ) on the structural parameters and get consistent feature attribution via permuting feature importance ranking above. Finally, we design a weakly coupled ring-core fiber that supports four modes ( H E 11 , T E 01 , H E 21 , T M 01 ) based on the NN algorithm, which could be successfully applied in vector mode division multiplexing.

High-performance Mach–Zehnder modulator using tailored plasma dispersion effects in an ITO/graphene-based waveguide

A high-performance electro-optic Mach–Zehnder modulator (MZM) with outstanding characteristics is proposed. The MZM is in a push-pull configuration that is constructed using an ITO/graphene-based silicon waveguide. A novel idea for engineering of the plasma dispersion effect in an ITO/graphene-based waveguide is proposed so that the modulation characteristics of the MZM are highly improved. Plasma dispersion effects of ITO and graphene layers are tailored in such a way that a large difference between real parts of guided mode effective index of the two arms is achieved while their corresponding imaginary parts are equal. As a result, a very low {{mathrm {V}}}_{pi }L_{pi } of 10 , hbox {V} upmu hbox {m} is achieved. To the best of our knowledge, this is one of the lowest {{mathrm {V}}}_{pi }L_{pi } reported for an electro-optic modulator. In addition, the proposed modulator exhibits a very high extinction ratio of more than 30 dB, low insertion loss of 2.8 dB and energy consumption of as low as 10 fJ/bit, which are all promising for optical communication and processing systems.

3D Dirac semimetals-dielectric elliptical fiber supported tunable terahertz hybrid waveguide.

Based on the proposed elliptical dielectric fiber-polyethylene gap-3D Dirac semimetal (DSM) hybrid plasmonic waveguide structure, the tunable propagation characteristics have been systematically investigated in the terahertz region, taking into account the influences of the structural parameters, the modified dielectric fiber, and the 3D DSM Fermi levels. The results show that as the ratio of the elliptical semi-axis along the y-direction ay and the x-direction ax (ay/ax) increases, the hybrid mode confinement increases. The real part of the effective mode index and propagation length increase with increasing the refractive index of the elliptical fiber. The propagation length and figure of merit of the hybrid modes reach 1.56×104µm and 300, respectively. In addition, by changing the Fermi level of the 3D DSM layer, the propagation properties of the hybrid modes can also be modulated in a wide range, e.g., the modulation depth of the propagation length reaches about 71.53% if the Fermi level varies in the range of 0.03-0.15 eV. The propagation properties of the hybrid modes are enhanced significantly by utilizing the modified three elliptical fiber structures, the real part of the effective mode index, and the propagation length of the modified structure are enhanced simultaneously. The results are very helpful for understanding the tunable mechanism of the 3D DSM devices and aids the design of novel plasmonic devices, e.g., lasers, modulators, and resonators.

Ultimate Limit for Optical Losses in Gold, Revealed by Quantitative Near-Field Microscopy.

We report thorough measurements of surface plasmon polaritons (SPPs) running along nearly perfect air-gold interfaces formed by atomically flat surfaces of chemically synthesized gold monocrystals. By means of amplitude- and phase-resolved near-field microscopy, we obtain their propagation length and effective mode index at visible wavelengths (532, 594, 632.8, 729, and 800 nm). The measured values are compared with the values obtained from the dielectric functions of gold that are reported in literature. Importantly, a reported dielectric function of monocrystalline gold implies ∼1.5 times shorter propagation lengths than those observed in our experiments, whereas a dielectric function reported for properly fabricated polycrystalline gold leads to SPP propagation lengths matching our results. We argue that the SPP propagation lengths measured in our experiments signify the ultimate limit of optical losses in gold, encouraging further comprehensive characterization of optical material properties of pure gold as well as other plasmonic materials.

Multi-Ring-Air-Core Fiber Supporting Numerous Radially Fundamental OAM Modes

Orbital angular momentum (OAM) multiplexing technology is expected as one of the prospective candidates for sustaining the further increment of data-transmission capacity in the optical communication systems. Advanced multiplexing technology of combining OAM-based mode division multiplexing (MDM) in the multicore fiber (MCF) with wavelength division multiplexing (WDM) can further improve the transmission rate and spectrum efficiency in the communication systems. In this paper, a multi-ring-air-core fiber (MRACF) supporting thousands of OAM modes is designed and analyzed. The tradeoffs between ring number/density and their corresponding system performance parameters in this fiber are systematically investigated. Based on the analytical results, MRACF with 37 rings can support a record high 4440 radially fundamental OAM modes at 1550 nm, featuring <−53 dB inter-ring crosstalk and >5.67 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−4</sup> intra-ring modal effective refractive index difference. Furthermore, a record-high 4144 radially fundamental OAM modes with <−40 dB inter-ring crosstalk can be supported across C and L bands from 1530 nm to 1625 nm, which is one order of magnitude larger than the number of linearly polarized (LP) modes or supermodes ever reported within one single fiber.

Design and amplification performance analysis of Er3+-doped photonic crystal fiber carrying orbital angular momentum

In order to reduce the loss of communication system based on orbital angular momentum (OAM), an Er3+-doped photonic crystal fiber (PCF) amplifier which can support amplification for 30 OAM modes is proposed. The structure of the PCF is optimized to obtain larger effective mode field area and effective refractive index difference. Then, the optimal PCF with a nonlinear coefficient lower than 0.002 m−1·W−1 is proposed, and it is used to setup an orbital angular momentum erbium-doped fiber amplifier (OAM-EDFA). Finally, an OAM-EDFA with a flat-high gain of about 28 dB, a DMG lower than 0.18 dB, and a NF no more than 4.4 dB is obtained. Compared with the existing OAM-EDFA, the gain of the proposed OAM-EDFA is increased by 6 dB. The OAM-EDFA based on the novel PCF designed in this work is of great interest to the OAM-based long-distance communication system.

Design, Analysis, and Optimization of a Plasmonic Slot Waveguide for Mid-Infrared Gas Sensing.

In this work, we investigated the optimization of a plasmonic slot waveguide (PSWG) in the mid-IR region particularly for a representative wavelength of 4.26 µm, which is the absorption line of CO2 and thus particularly relevant for applications. We analysed the mode features associated with metal-dielectric-metal (MDM), dielectric-metal-dielectric (DMD), and truncated metal film (TMF) structures with respect to the considered PSWG. Subsequently, the mode features of the PSWG were considered based on what we outlined for MDM, DMD, and TMF structures. Furthermore, as confinement factor and propagation length are two crucial parameters for absorption sensing applications, we optimized the PSWG based on a figure of merit (FOM) defined as the product of the aforementioned quantities. To characterize the propagation length, the imaginary part of the effective mode index of a guided mode was considered, leading to a dimensionless FOM. Finally, we investigated the PSWG also for other wavelengths and identified particularly attractive wavelengths and geometries maximizing the FOM.

Heterogeneous integrated phase modulator based on two-dimensional layered materials

Silicon nitride, with ultralow propagation loss and a wide transparency window, offers an exciting platform to explore integrated photonic devices for various emerging applications. It is appealing to combine the intrinsic optical properties of two-dimensional layered materials with high-quality optical waveguides and resonators to achieve functional devices in a single chip. Here we demonstrate a micro-ring resonator-based phase modulator integrated with few-layer MoS 2 . The ionic liquid is employed directly on the surface of MoS 2 to form a capacitor configuration. The effective index of the composite MoS 2 – SiN waveguide can be modulated via adjusting bias voltages to achieve different charged doping induced electro-refractive responses in MoS 2 film. The maximum effective index modulation of the composite MoS 2 – SiN waveguide can be achieved to 0.45 × 10 − 3 . The phase tuning efficiency is measured to be 29.42 pm/V, corresponding to a V π L of 0.69 V·cm. Since the micro-ring resonator is designed near the critical coupling regime, the coupling condition between the bus waveguide and micro-ring resonator can also be engineered from under-coupling to over-coupling regime during the charged doping process. That can be involved as a degree of freedom for the coupling tailoring. The ability to modulate the effective index with two-dimensional materials and the robust nature of the heterostructure integrated phase modulator could be useful for engineering reliable ultra-compact and low-power-consumption integrated photonic devices.

High extinction ratio and broadband polarization beam splitter based on bricked subwavelength gratings on SOI platform

A compact asymmetrical directional coupler (ADC) based on coupling between a conventional subwavelength grating (SWG) and a bricked subwavelength grating (BSWG) is proposed to realize broadband polarization beam splitter (PBS) with high extinction ratio (ER) on silicon-on-insulator (SOI) platform. Apart from conventional SWG structural parameters (duty cycle and period), the BSWG is utilized to provide a new design space to control TE and TM modal effective index for accurate phase match. Accordingly, as to the TM mode, it is possible to satisfy phase-matching condition and then can be coupled more efficiently with higher ER by introducing the BSWG. Meanwhile, there is a significant phase mismatch for the TE mode. In this way, the proposed PBS that separates TE and TM mode to the through and cross ports can be realized. Simulation results show that the proposed PBS with a compact coupling length of 8.4 μm can achieve a high ER of 35.06 dB and an insertion loss of 0.25 dB for the TM mode at 1.55 μm, while the ER is 18.92 dB and insertion loss is 0.01 dB for the TE mode. Moreover, the operating bandwidth is up to 300 nm (1400∼1700 nm) for the TE mode and 155 nm (1487∼1642 nm) for the TM mode when the ER is >15 dB.

Ultra-low loss polymer-based photonic crystal fiber supporting 242 OAM modes with high bending tolerance for multimode THz communication

A novel polymer-based ring-core circular photonic crystal fiber (C-PCF) is proposed and investigated. The solid core C-PCF structure is composed of Topas as background material, a high refractive index (RI) Kapton polymer as a ring material and four layers of air hole patterns. Numerical simulation is used to optimize the PCF geometry to support maximum stable modes with minimum losses. The proposed C-PCF supports 242 stable OAM modes near 1.9 THz with mode purity >0.9. The fiber exhibit low confinement loss (CL) ∼10-9 dB/cm, large effective mode area ∼ 10-2 mm2, low dispersion <1 ps/THz/cm and high effective mode index difference (Δneff) >10-3 in the range 1.5 THz to 3.5 THz. Attenuation, mode stability, material dispersion and fiber bending tolerance of PCF are analyzed to increase the transmission capacity. The detailed experimental feasibility and design sensitivity are theoretically addressed. The proposed PCF supports stable modes and works at a wider spectrum then the previously reported studies. The fiber has the potential to be employed for next-generation THz multimode communication systems.

Mechanisms driving self-organization phenomena in random plasmonic metasurfaces under multipulse femtosecond laser exposure: a multitime scale study

Abstract Laser-induced transformations of plasmonic metasurfaces pave the way for controlling their anisotropic optical response with a micrometric resolution over large surfaces. Understanding the transient state of matter is crucial to optimize laser processing and reach specific optical properties. This article proposes an experimental and numerical study to follow and explain the diverse irreversible transformations encountered by a random plasmonic metasurface submitted to multiple femtosecond laser pulses at a high repetition rate. A pump-probe spectroscopic imaging setup records pulse after pulse, and with a nanosecond time resolution, the polarized transmission spectra of the plasmonic metasurface, submitted to 50,000 ultrashort laser pulses at 75 kHz. The measurements reveal different regimes, occurring in different ranges of accumulated pulse numbers, where successive self-organized embedded periodic nanostructures with very different periods are observed by post-mortem electron microscopy characterizations. Analyses are carried out; thanks to laser-induced temperature rise simulations and calculations of the mode effective indices that can be guided in the structure. The overall study provides a detailed insight into successive mechanisms leading to shape transformation and self-organization in the system, their respective predominance as a function of the laser-induced temperature relative to the melting temperature of metallic nanoparticles and their kinetics. The article also demonstrates the dependence of the self-organized period on the guided-mode effective index, which approaches a resonance due to system transformation. Such anisotropic plasmonic metasurfaces have a great potential for security printing or data storage, and better understanding their formation opens the way to smart optimization of their properties.

High-sensitivity integrated SiN rib-waveguide long period grating refractometer

In this research, we demonstrate a high-sensitivity integrated silicon nitride long period grating (LPG) refractometer based on a rib waveguide with sinusoidally modulated width. While integrated LPG architectures typically achieve ultrahigh sensitivity only over a narrow optical bandwidth using a phase-matching turning-point optimization technique, our sensor exhibits a very high refractometric sensitivity that was designed to remain constant over a broad operational optical spectral bandwidth. The proposed design method relies on multi-modal dispersion tailoring that consists of homogenizing the spectral behaviors of both group and effective indices of the coupling modes. Experimental results are in agreement with numerical simulations, demonstrating not only a sensitivity reaching 11,500 nm/RIU but, more significantly, also that this sensitivity remains almost constant over a broad spectral range of at least 100 nm around 1550 nm. Additional advantages of the proposed sensor architecture encompass a low temperature sensitivity, down to −0.15 nm/K, and simplicity of the fabrication process. These results demonstrate the feasibility of chip-scale photonic integration to achieve both high sensitivity and large dynamic range of the proposed refractometer.

Numerical analysis of an infrared gas sensor utilizing an indium-tin-oxide-based plasmonic slot waveguide

Abstract. Plasmonic waveguides have attracted much attention owing to the associated high field intensity at the metal–dielectric interface and their ability to confine the modes at the nanometer scale. At the same time, they suffer from relatively high propagation loss, which is due to the presence of metal. Several alternative materials have been introduced to replace noble metals, such as transparent conductive oxides (TCOs). A particularly popular TCO is indium tin oxide (ITO), which is compatible with standard microelectromechanical systems (MEMS) technology. In this work, the feasibility of ITO as an alternative plasmonic material is investigated for infrared absorption sensing applications: we numerically design and optimize an ITO-based plasmonic slot waveguide for a wavelength of 4.26 µm, which is the absorption line of CO2. Our optimization is based on a figure of merit (FOM), which is defined as the confinement factor divided by the imaginary part of the effective mode index (i.e., the intrinsic damping of the mode). The obtained optimal FOM is 3.2, which corresponds to 9 µm and 49 % for the propagation length (characterizing the intrinsic damping) and the confinement factor, respectively.