Mode Effective Index Research Articles

Solution of dispersion relations of multilayer optical fibers: a comprehensive study.

The exact solution of the modal dispersion relation of multilayer optical fibers is very critical and complicated, especially in the case of complex refractive indices of some layers added to the fiber. In this paper, a different methodology is proposed to solve the complex dispersion relations for cladding modes, based on the well-defined proper expressions of electromagnetic fields in the different layers of optical fibers. An optical fiber, coated by a dielectric nonlinear layer, is analyzed using the exact four-layer model, and the results obtained are compared with those analyzed in the literature based on the approximate three-layer model, where the effect of the coating layer is neglected when solving the dispersion relation. The results obtained show a remarkable difference between the exact and the approximate values of the effective refractive indices of the cladding modes. Inappropriate values of the effective refractive indices strongly affect phase matching and coupling between modes, which are required in different applications such as second-harmonic generation. The proposed approach for solving general dispersion relations is also employed to obtain complex values of the effective refractive indices of the cladding modes for a five-layer optical fiber with a metallic thin film inserted between the nonlinear layer and the fiber cladding. Using the appropriate expressions that describe the electric field in the different dielectric and metallic layers of optical fibers, field distributions are displayed for some cladding modes.

High-sensitive optical force sensor based on enhanced effective index modulation

A high-sensitive force sensor with large measurement range has been realized by inserting a microbend at the edge of a long period fiber grating (LPFG) written on single-mode fiber. The force sensitivity is improved mainly dependent on the enhanced effective index modulation. Experiment results present that the resonance dip wavelength of the proposed grating varies with applied axial force in an approximate exponential functional manner, and the grating with lower bending radius microbend has higher force sensitivity. A maximum arithmetic mean value of force response ∼−41.24 nm/N is achieved by a microbend edge-inserted grating with a bending radius 1.14 mm, which is almost two order enhanced than that of the original LPFG. In addition, the power-referenced sensitivity is almost a hundred times larger than that of the original LPFG in a certain measurement range. The sensor enables double demodulation of wavelength and energy and is a candidate for force sensors.

Highly efficient integrated mode de/multiplexing based on modified asymmetric Y-junctions

Asymmetric Y-junctions at which a wide waveguide is divided into several waveguides with different widths are commonly employed as mode de/multiplexers. These structures are inherently wide-band and simple in design and fabrication. However, the cross talk between modes increases rapidly as the number of modes increases, limiting the application of these structures to four modes and below. The design methodology of low cross talk-integrated mode de/multiplexers based on asymmetric Y-junctions is presented. It is shown that the difference between mode-effective indices plays a crucial role in determining the cross talk. A modified asymmetric Y-junction structure is presented to minimize the cross talk and based on this structure, six- and eight-mode de/multiplexers are designed utilizing a silicon-on-insulator platform. Finite-difference time-domain (FDTD) simulations are performed for the presented structures, and it is shown that the maximum cross talk is as low as −8 and −7 dB for six- and eight-mode de/multiplexers, respectively. The design of a low cross talk 10-mode de/multiplexer based on the proposed method is also discussed.

Optical Planar Waveguides Fabricated by Using Carbon Ion Implantation in Terbium Gallium Garnet

Optical planar waveguides in terbium-gallium-garnet (TGG) crystals are promising photonic devices, particularly for optical isolators and rotators. In this work, to the best of our knowledge, we report on the fabrication and the characterization of TGG waveguides for the first time. The fabrication procedure involved carbon ion implantation at an energy of 6.0 MeV and a fluence of 5.0×1014 ions/cm2. The effective refractive indices of the propagation modes in the carbonimplanted waveguide were measured by using the prism-coupling technique. The profile of the refractive index and the distribution of the near-field intensity were calculated by using the reflectivity calculation method and the finite-difference beam propagation method, respectively. The carbon-implanted TGG waveguide is considered to be a candidate for a magneto-optical photonic device.

Weakly-coupled 4-mode step-index FMF and demonstration of IM/DD MDM transmission.

Weakly coupled-mode division multiplexing (MDM) over few-mode fibers (FMF) for short-reach transmission has attracted great interest, which can avoid multiple-input-multiple-output digital signal processing (MIMO-DSP) by greatly suppressing modal crosstalk. In this paper, step-index FMF supporting 4 linearity polarization (LP) modes for MIMO-free transmission is designed and fabricated for the first time, to our knowledge. Modal crosstalk of the fiber is suppressed by increasing the mode effective refractive index differences. The same fabrication method as standard single-mode fiber is adopted so that it is practical and cost-effective. The mode multiplexer/demultiplexer (MUX/DEMUX) consists of cascaded mode-selective couplers (MSCs), which are designed and fabricated by tapering the proposed FMF with single-mode fiber (SMF). The mode MUX and DEMUX achieve very low modal crosstalk not only for the multiplexing/demultiplexing but also for the coupling to/from the FMF. Based on the fabricated FMF and mode MUX/DEMUX, we successfully demonstrate the first simultaneous 4-modes (LP01, LP11, LP21 & LP31) 10-km FMF transmission with 10-Gb/s intensity modulation and MIMO-free direct detection (IM/DD). The modal crosstalk of the whole transmission link is successfully suppressed to less than -16.5 dB. The experimental results indicate that FMF with simple step-index structure supporting 4 weakly-coupled modes is feasible.

Design of cladding rods-assisted depressed-core few-mode fibers with improved modal spacing

Abstract This paper investigates the design details of cladding rods-assisted (CRA) depressed-core (DC) few-mode fibers (FMFs) that feature more equally spaced linearly polarized (LP) modal effective indices, suitable for high-spatial-density weakly-coupled mode-division multiplexing systems. The influences of the index profile of cladding rods on LP mode-resolved effective index, bending sensitivity, and effective area Aeff, are numerically described. Based on the design considerations of LP modal Aeff-dependent spatial efficiency and LP modal bending loss-dependent robustness, the small LP21-LP02 and LP22-LP03 modal spacing limitations, encountered in state-of-the-art weakly-coupled step-index FMFs, have been substantially improved by at least 25%. In addition, the proposed CRA DC FMFs also show sufficiently large effective areas (in excess of 110 μm2) for all guided LP modes, which are expected to exhibit good nonlinear performance.

Waveguide Engineering of Graphene Optoelectronics—Modulators and Polarizers

The concept of incorporating graphene into nanophotonic waveguides has pullulated into massive broadband optoelectronic applications with compact footprint. We theoretically demonstrate that by solely altering the dimension design of graphene-laminated silicon waveguides, the phase, amplitude, and polarization of the fundamental propagating modes can all be effectively tailored under different bias voltages. Different device functionalities, including optical amplitude/phase modulators and polarizers, are ascribed into the devising of the effective mode index. A comprehensive analysis and unified design scenarios upon waveguide geometries are summarized, with fabrication robustness and moderate process complexity. Moreover, design examples are manifested. We report a TM-mode-based phase modulator, achieving a π phase shift within an active length of 49.2 μm with dual graphene layers. A feasible polarization-independent amplitude modulator is also demonstrated, where the discrepancy of the imaginary parts of the effective mode index between the two fundamental modes is kept at an order of 10−5 over a broad wavelength range from 1.35 to 1.65 μm.

Analysis of scattering loss due to sidewall roughness in slot waveguides by variation of mode effective index

Sidewall-roughness scattering loss is generally severe in slot waveguides manufactured by lithography process. A suitable model is absent for evaluating this scattering loss in slot waveguides. In this paper, basing on the mechanism of sidewall-roughness scattering, we analyze the relative extent of the scattering loss in slot waveguides by the variation of mode effective refractive index induced by the sidewall roughness, i.e. the derivative of the effective refractive index with respect to the width of the waveguide’s high-index strips. Effects of waveguide structure on this derivative are obtained and their rationality is discussed. The characteristics of the sidewall-roughness scattering loss in slot waveguides are extrapolated. We demonstrate that this model is feasible for estimating the relative extent of the scattering loss in slot waveguides and the influence of waveguide parameters on it. In addition, referring to the same model for solid-core strip waveguides, the proportionality factor relating attenuation coefficient and the effective index derivative is provided. Comparison between calculation results and measured loss further verifies the applicability of this model to slot waveguides.

Mode evolution and nanofocusing of grating-coupled surface plasmon polaritons on metallic tip

We present a detailed analysis on mode evolution of grating-coupled surface plasmonic polaritons (SPPs) on a conical metal tip based on the guided-wave theory. The eigenvalue equations for SPPs modes are discussed, revealing that cylindrical metal waveguides only support TM01 and HEm1 surface modes. During propagation on the metal tip, the grating-coupled SPPs are converted to HE31, HE21, HE11 and TM01 successively, and these modes are sequentially cut off except TM01. The TM01 mode further propagates with drastically increasing effective mode index and is converted to localized surface plasmons (LSPs) at the tip apex, which is responsible for plasmonic nanofocusing. The gap-mode plasmons can be excited with the focusing TM01 mode by approaching a metal substrate to the tip apex, resulting in further enhanced electric field and reduced size of the plasmonic focus.

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.

TE modes of UV-laser generated waveguides in a planar polymer chip of parabolic refractive index profile

The UV-laser lithographic method is used for the preparation of Polymeric integrated-optical waveguides in a planar polymer chip. The waveguide samples are irradiated by an excimer laser of wavelength 248 nm with different doses and with the same fluencies. The refractive index depth profile for the waveguides, in the first zone is found to have a parabolic shape and Gaussian shape in the second one that can be determined by Mach–Zehnder interferometer. Both the mode field distribution and the effective mode indices for the first zone only are determined by making use of the theoretical mode and the experimental data. It is found that the model field distribution is strongly dependent on the refractive indices for each zone.

Efficient strategy to increase higher order inter-modal stability of a step index multimode fiber.

We demonstrate a novel approach to enhance the mode stability through increased effective index difference (Δneff) between the higher-order modes (LP18, LP09 and LP19) of a multimode fiber. Fibers with large diameters have bigger effective mode areas (Aeff) and can be useful for high power lasers and amplifiers. However, a large mode area (LMA) results in an increased number of modes that can be more susceptible to mode coupling. The modal effective index difference (Δneff) strongly correlates with mode stability and this increases as the modal order (m) increases. We report here that the mode spacing between the higher order modes can be further enhanced by introducing doped concentric rings in the core. In our work, we have shown a more than 35% increase in the mode spacing between the higher order modes by optimizing the doping profile of a LMA fiber. The proposed design technique is also scalable and can be applied to improve the mode spacing between different higher order modes and their neighboring antisymmetric modes, as necessary.

Ultracompact graphene-assisted ring resonator optical router

Optical routers with compact footprint and low energy consumption are of high demand for optoelectronic integrations. We demonstrate a graphene-assisted optical router based upon silicon ring resonator configurations. The electrical tunability and the influence that graphene has upon the effective mode index are investigated, from monolayer to multiple graphene layers. The corresponding waveguide structure design is further discussed and optimized via numerical simulations. Meanwhile, the design recipes are also discussed and our proposal possesses broad free spectrum range reaching 3.64 THz, lenis crosstalk below −15 dB, low loss and low power consumption that is propitious to versatile wavelength division multiplexing systems and on-chip silicon optical interconnects.

Phonon polaritons in cylindrically curved h-BN.

Hexagonal boron nitride supports phonon polaritons in its two Reststrahlen bands. In this paper, we investigate phonon polaritons in cylindrically curved hexagonal boron nitride thin films. The phonon polariton modes in such structure carry orbital angular momentums depending on its azimuthal index. For extremely small-size structures, high order polariton modes show cutoff behaviors; while, for large-size ones, modes with low azimuthal indexes are nearly degenerate, showing similar mode effective indexes. In dimer structures, phonon polariton modes in the neighboring structures are coupled, creating hybrid modes; gap phonon polaritons arise due to such coupling. For large-size dimers, multiple gap phonon polariton modes have been found. Then, cylindrically curved hexagonal boron nitride thin film is placed on a substrate, which also leads to the emergence of multiple gap phonon polariton modes near the touching point. In the end, we vary the geometric parameters of the structures and give some discussions about the phonon polariton modes. Based on these investigations, we may say that the curvature can strongly affect the phonon polariton modes in h-BN thin films.

High-order mode conversion based on adiabatical mode evolution for mode division multiplexing applications.

Mode conversion based on adiabatical mode evolution in a two-core configuration is investigated. The configuration can convert all the launching modes to higher-order modes from one port and convert all the launching modes to lower-order modes from another port. Mode conversion between the two degenerated high-order modes is also demonstrated numerically. The mode conversion feature is only dependent on the relationship between the effective mode indices of the two cores in the configuration, which shows the characteristics of high flexibility and large fabrication tolerance.

Characteristics of solid-core square-lattice microstructured optical fibers using an analytical field model

The excellent propagation properties of square-lattice microstructured optical fibers (MOFs) have been widely recognized. We generalized our recently developed analytical field model (Sharma and Sharma, 2016), for index-guiding MOFs with square-lattice of circular air-holes in the photonic crystal cladding. Using the field model, we have studied the propagation properties of the fundamental mode of index-guiding square-lattice MOFs with different hole-to-hole spacing and the air-hole diameter. Results for the modal effective index, near and the far-field patterns and the group-velocity dispersion have been included. The evolution of the mode shape has been investigated in transition from the near to the far-field domain. We have also studied the splice losses between two identical square-lattice MOFs and also between an MOF and a traditional step-index single-mode fiber. Comparisons with available numerical simulation results, e.g., those based on the full-vector finite element method have also been included.

Hybrid plasmonic waveguides formed by metal coating of dielectric ridges.

Bound hybrid plasmon-polariton modes supported by waveguides, which are formed by gold coating of ridges etched into a silica substrate, are analyzed using numerical simulations and investigated experimentally using near-field microscopy at telecom wavelengths (1425-1625 nm). Drastic modifications of the fundamental mode profile along with changes in the mode confinement and propagation loss are found when varying the ridge height. The main mode characteristics (effective mode index, propagation length, and mode profile) are determined from the experimental amplitude- and phase-resolved near-field images and compared with the simulations. The possibility of strongly influencing the mode properties along with subwavelength confinement found simultaneously with relatively long propagation can further be exploited in mode shaping and sensing applications.

The Brillouin gain of vector modes in a few-mode fiber

In this work, we demonstrate the measurement of the Brillouin gain spectra of vector modes in a few-mode fiber for the first time using a simple heterodyne detection technique. A tunable long period fiber grating is used to selectively excite the vector modes supported by the few-mode fiber. Further, we demonstrate the non-destructive measurement of the absolute effective refractive indices (neff) of vector modes with ~10−4 accuracy based on the acquired Brillouin frequency shifts of the modes. The proposed technique represents a new tool for probing and controlling vector modes as well as modes carrying orbital angular momentum in optical fibers with potential applications in advanced optical communications and multi-parameter fiber-optic sensing.

Are optical fibers really uniform? Measurement of refractive index on a centimeter scale.

Many applications of optical fiber, such as specialized fiber Bragg gratings (FBGs), require high uniformity of a fiber's refractive index (RI) along its length. We show here that the mode effective index of most fibers is not constant, even on a short length scale. To help improve fiber manufacturing and selection, we demonstrate a technique for characterizing a meter length single-mode optical fiber's effective RI over a centimeter scale with a precision of 3×10-6 RI units (RIUs) and an absolute accuracy of 2×10-4 RIU. By writing several weak probe FBGs as frequency references and then measuring the frequency deviation of these probe FBGs along the length of the fiber with an optical frequency domain reflectometer, the RI distribution of the effective mode index may be found. We validate our measurements on reference and fibers under test with theoretical simulations.

3-D near-field imaging of guided modes in nanophotonic waveguides

Abstract Highly evanescent waveguides with a subwavelength core thickness present a promising lab-on-chip solution for generating nanovolume trapping sites using overlapping evanescent fields. In this work, we experimentally studied Si3N4 waveguides whose sub-wavelength cross-sections and high aspect ratios support fundamental and higher order modes at a single excitation wavelength. Due to differing modal effective indices, these co-propagating modes interfere and generate beating patterns with significant evanescent field intensity. Using near-field scanning optical microscopy (NSOM), we map the structure of these beating modes in three dimensions. Our results demonstrate the potential of NSOM to optimize waveguide design for complex field trapping devices. By reducing the in-plane width, the population of competing modes decreases, resulting in a simplified spectrum of beating modes, such that waveguides with a width of 650 nm support three modes with two observed beats. Our results demonstrate the potential of NSOM to optimize waveguide design for complex field trapping devices.