Mode Effective Refractive Index Research Articles

Machine learning aided inverse design for vector modes-based weak-coupling few-mode fiber

The vector modes (VMs) are the eigenstate modes of the optical fiber, which can be degenerated into linearly polarized (LP) modes. VMs-based weak-coupling few-mode fiber (FMF) has more advantages in communication systems and the design of these fibers is also more difficult. In this work, we present an inverse design method for VMs-based weak-coupling FMF with machine learning (ML) algorithms. The artificial neural network (ANN) and random forest (RF) are applied separately in the process of inverse designing. The lowest prediction accuracy of the two algorithms is 0.99360 and 0.99200, respectively, which shows the excellent performance of these two ML algorithms and the ANN has higher prediction accuracy than RF. Meanwhile, the inversely designed few-mode fiber can realize the degenerative separation of vector modes in the second-order and third-order mode groups, and meet the performance requirements of weak-coupling FMFs. And we obtain the effect of fiber structural parameters on mode effective refractive index (Δneff) by using feature importance ranking. In addition, the performance of the above two algorithms and the traditional optimization algorithms (Particle swarm optimization algorithm and Genetic Algorithm) in the design of weak-coupling FMFs is compared and analyzed. The proposed ML-based method provides an efficient and accurate prediction of weak-coupling FMFs, which could be greatly applied in the field of the generation of vector beam and mode division multiplexing.

Suppressing the mechanochromism of flexible photonic crystals.

Photonic crystal slabs (PCS) are a promising platform for optical biosensing. Yet, flexible applications based on PCS for biosensing have been limited, as the mechanical properties influence the optical ones. Here, we show the suppression of the mechanochromism effect for flexible PCS. We obtained flexible photonic crystal slabs by sputtering of a dielectric 100 nm Nb2O5 high refractive index layer onto a flexible nanostructured polydimethylsiloxane (PDMS) substrate with 370 nm grating period. The PCS exhibit a guided mode resonance at around 650 nm. We demonstrate that these flexible photonic crystal slabs show less than 0.5 nm resonance shift for 4% strain and call them stabilized PCS (sPCS). We compare this to a resonance shift of ∼21 nm for ∼4% strain of a flexible photonic crystal with a flexible nanoparticle high index layer (mechanochromatic PCS, mPCS). This high resonance shift is expected from the Bragg equations, where 4% grating period change correspond to approximately 4% change of the resonance wavelength (i.e., ∼26 nm at a resonance wavelength of 650 nm), if changes in the mode effective refractive index are neglected. In a stretch series we obtain color-to-strain dependencies of 4.79 nm/% strain for mPCS and 0.11 nm/% strain for our stabilized sPCS. We analyze the suppression of the mechanochromism with detailed microscopy results. We observe that fissures and fractures form in the rigid waveguiding layer of the sPCS upon mechanical stress. An algorithm based on Holistically-Nested Edge Detection (HED) is used for automated counting of cracks. Rigid photonic crystal cells with sizes on the order of 10 µm to 100 µm are formed that explain the stable optical properties. Even more stable optical properties with less than 0.03 nm wavelength shift per 1% strain are demonstrated for sPCS with an additional dielectric 100 nm SiO2 low index layer beneath the Nb2O5 waveguide layer decoupling the waveguide further from the flexible PDMS substrate.

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.

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.

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.

An Integrated-Plasmonic Chip of Bragg Reflection and Mach-Zehnder Interference Based on Metal-Insulator-Metal Waveguide

In this paper, a Bragg reflector is proposed by placing periodic metallic gratings in the center of a metal-insulator-metal (MIM) waveguide. According to the effective refractive index modulation caused by different waveguide widths in a period, a reflection channel with a large bandwidth is firstly achieved. Besides, the Mach-Zehnder interference (MZI) effect arises by shifting the gratings away from the waveguide center. Owing to different optical paths with unequal indices on both sides of the grating, a narrow MZI band gap will be obtained. It is interesting to find out that the Bragg reflector and Mach-Zehnder interferometer are immune to each other, and their wavelengths can be manipulated by the period and the grating length, respectively. Additionally, we can obtain three MZI channels and one Bragg reflection channel by integrating three different gratings into a large period. The performances are investigated by finite-difference time-domain (FDTD) simulations. In the index range of 1.33–1.36, the maximum sensitivity for the structure is as high as 1 500 nm/RIU, and it is believed that this proposed structure can find widely applications in the chip-scale optical communication and sensing areas.

Design of weakly coupled 20-eigenmode bow-tie rectangular dual-step fiber for short-haul communication in O band

We present a weakly coupled bow-tie rectangular dual-step few-mode fiber supporting 20 eigenmodes for short-haul communication systems across the O band. The rectangular dual-step core and bow-tie stress-applying area are introduced to effectively split adjacent eigenmodes. We evaluate the impact of parameters on modal mode effective refractive index difference (MERID) Δneff, min Δneff, min Aeff, Bm, and bending loss at a wavelength of 1310 nm. Broadband performance of the entire O band, including neff, MERID Δneff, differential mode delay, and dispersion, is also analyzed. Results indicate that the 20 eigenmodes supported by the designed fiber are completely separated with MERID Δneff between adjacent modes larger than 2.319 × 10 − 4 over the whole O band. The designed fiber can be used for short-haul multiple-input multiple-output-free eigenmode-division multiplexing systems to improve transmission capacity and expand bandwidth.

Magneto-refractive properties and measurement of an erbium-doped fiber.

The magneto-refractive properties of an erbium-doped fiber (EDF) are investigated by theoretically analyzing the change in mode characteristics with a magnetic field and experimentally measuring it based on a fiber-optic Mach-Zehnder interferometer (MZI). The numerical results indicate that the mode effective refractive index (RI) increases as the magnetic field increases, and the mode field intensity distribution tends to be more concentrated in the core region with an increasing magnetic field. The variation in the mode effective RI of the fundamental mode with the magnetic field is greater than that of the higher-order modes. A magneto-refractive measurement system based on a fiber-optic MZI is set up to analyze the magneto-refractive effect of the EDF. The changes in the mode effective RI measured with a direct-current (DC) magnetic field and with a 100 Hz alternating-current (AC) magnetic field are 4.838×10-6 and 4.245×10-6 RIU/mT, respectively. The experimental results are in reasonable agreement with the theoretical analysis. Furthermore, the error between the experimental and numerical results is discussed. The magneto-refractive properties of the EDF exhibit potential in all-fiber magnetic field or current sensing area.

A novel microstructured polymer tube for THz vortex beams guidance

A novel microstructured polymer tube (MPT) incorporating a central hollow, ring core, porous outer cladding is proposed for terahertz (THz) orbital angular momentum (OAM) guidance, focusing on the enhancement of the quantity of modes and bandwidth. The proposed MPT can support 70 modes (66 THz OAM ones) with large mode effective refractive index separation (>2.197×10−3) over 0.6∼1.25 THz while maintaining single-mode condition radially, and the number of guiding modes can be further increased by properly equiproportional enhancing the size of the tube. Besides, the designed MPT has strong confinement property, high purity (>97.06%), and flat dispersion over the whole operating bandwidth. The result of this work reveals that this kind of MPT is promising to accelerate the development of the compact, light-weight THz communication system, and can be applied in OAM-based mode-division multiplexing combined with wavelength-division multiplexing technique without multiple-input multiple-output digital signal processing.

Analysis of supermode properties in three-core homogeneous strongly coupled multicore fiber

We have investigated the supermode properties, namely, mode effective refractive index (RI) (neff), effective area (Aeff), and chromatic dispersion (CD), in three-core homogeneous strongly coupled multicore fibers (SC-MCFs) for different core RI profiles (step index and RI dip) and in different possible core arrangements (triangular and linear). Further, the impacts of fiber parameters, namely, core radius (a), relative RI difference between core and cladding (Δ), and core pitch (Λ), on the differential group delay (DGD) between different supermodes have also been analyzed for all the considered configurations of SC-MCFs. The analysis presented has been done numerically using the FemSIM simulation platform. It has been observed that core arrangement has significant impact on the levels of neff, Aeff, CD, and DGD, and it also affects the degeneracy of the supermodes in a three-core homogeneous SC-MCF. Further, there exist certain core pitches in which the Aeff values of fundamental supermodes in different core layouts are equal. Furthermore, there exists a certain relative RI difference between the core and cladding (Δ) values in which DGD values in all the considered SC-MCF configurations are equal. On the other hand, over a range of Δ values, DGD in a linear layout is flattened compared to a triangular layout. Incorporating the RI dip structure in the cores of SC-MCFs affects the CD levels significantly. Therefore, by careful control of the fiber parameters and core arrangement, large mode effective area and low and flattened dispersion SC-MCF can be designed that may be suitable in dense wavelength division multiplexing application.

Efficient interrogation method of forward Brillouin scattering in optical fibers using a narrow bandwidth long-period grating

A new technique, to the best of our knowledge, for the characterization of the effective refractive index modulation in optical fibers due to transverse acoustic mode resonances excited by electrostriction is reported. The resonances excited by an optical pulse are probed by a narrow bandwidth long-period grating (LPG) inscribed in the fiber, which is interrogated by a continuous wave (CW) beam. The LPG used in this experiment has a narrow bandwidth and high sensitivity to small mode index perturbations, allowing the measurement of index variations from below 10-9 to 10-6. Radial and torsional-radial acoustic modes were characterized up to 1.1 GHz. The linewidth of resonances was found to be much shorter than in previous reports in which long fiber lengths are typically required, obtaining Q factors as high as 5000.

Comparative crosstalk performance analysis of different configurations of heterogeneous multicore fiber

Abstract In order to select the heterogeneous multicore fiber (MCF) configuration with ultra-low crosstalk and low peak bending radius, comparative crosstalk analysis have been done for the three possible core configurations, namely, Configuration 1 - different refractive index (R.I.) and different radius, Configuration 2 - different R.I., and Configuration 3 - different radius. Using the coupled mode equation and the simplified expressions of mode coupling coefficient (MCC) for different configurations of heterogeneous cores, the crosstalk performance of all the heterogeneous MCF configurations along with the homogeneous MCF have been investigated analytically with respect to core pitch (D) and fiber bending radius ( R b ${R}_{b}$ ). Further, these expressions of MCC have been extended to obtain the simplified expressions of MCC for the estimation of crosstalk levels in respective trench-assisted (TA) heterogeneous MCF configurations. It is observed from the analysis that in Configuration 1, crosstalk level is lowest and the rate of decrease in the crosstalk with respect to the core pitch is highest compared to the other configurations of heterogeneous MCF. The values of crosstalk obtained analytically have been validated by comparing it with the values obtained from finite element method (FEM) based numerical simulation results. Further, we have investigated the impact of a fixed percent change (5%) in the core parameters (radius and/or R.I.) of one of the core of a homogeneous MCF, to realize the different heterogeneous MCF configurations, on the variations in crosstalk levels, difference in the mode effective refractive index of the core 1 and core 2 ( Δ n e f f = n e f f 1 − n e f f 2 $\Delta {n}_{eff}={n}_{eff1}-{n}_{eff2}$ ), and the peak bending radius ( R p k ${R}_{pk}$ ). For the same percent variations (5%) in the core parameters (radius and/or R.I.) of different configurations of cores (Config. 1-Config. 3), Config. 1 MCF has highest variation in Δ n e f f $\Delta {n}_{eff}$ value compared to other configurations of MCF. Further, this highest variation in Δ n e f f $\Delta {n}_{eff}$ value of Config. 1 MCF results in smallest peak bending radius. The smaller value of peak bending radius allows MCF to bend into smaller radius. Therefore, Configuration 1 is the potential choice for the design of MCF with smaller peak bending radius and ultra-low crosstalk level compared to the other configurations of SI-heterogeneous MCF.

The sensing characteristics of microstructure-core photonic crystal fiber filled with liquid based on Sagnac interferometer

A highly-sensitive temperature sensor based on the Sagnac interferometer embedded with a microstructure-core photonic crystal fiber (PCF) has been demonstrated and studied. The PCF structure with the micro holes distributed on its core is designed and the unique core is called microstructure core. All the air holes of the PCF are assumed to be filled with a temperature-sensitive liquid whose thermo-optic coefficient is much higher than that of the background material. The mode field distribution and effective refractive index are calculated based on finite element method (FEM). The influences of the structural parameter d3 of the micro holes on the sensing characteristics are analyzed. The sensitivity of the designed PCF sensor increases as the diameter d3 increases and the average sensitivity is up to 21.05 nm/ °C as the temperature varies from 28.35 °C to 46.35 °C. The sensing characteristics are also discussed by just filling the air holes on the fiber cladding with the temperature-sensitive liquid and removing the air holes on the microstructure core.

Fe2O3 nanotube coating micro-fiber interferometer for ammonia detection

This paper presents a convenient and effective method for the determination of ammonia concentration. The structure is manufactured of Fe2O3 coated tapered microfiber interferometer (MFI). The Fe2O3 nanotube coated on the MFI acts as sensing layer, which enhance the gas selectivity, adsorptivity for ammonia molecule and also enhances the evanescent field strength distribution of the sensor and changes the mode effective refractive index of guided mode in MFI. When the quantity of ammonia molecule adsorbed on the sensing layer changes, the transmission spectrum of the sensor will shift. By determining the wavelength shift of the dips of the transmission spectrum, the concentration of ammonia will be detected. The experimental results show that the tapered microfiber interferometer (MFI) sensor coated with Fe2O3 nanotube has better time response repeatability and high sensitivity in detecting ammonia gas at room temperature. The sensor has a sensitivity of 1.30 pm/ppm and can be used for the detection of harmful gas ammonia in the environment.

Nano-optical filter based on multicavity coupled photonic crystal ring resonator

In this present work, a narrow wavelength tunable filter is proposed for ultra-low crosstalk optical networking and sensing applications. The proposed optical device is realized by the novel structure of multicavity coupled photonic crystal ring resonator. The presented nanostructure contains ring resonator, waveguides and reflectors in a square lattice platform with ferroelectric materials arranged in the air medium. The wavelength tuning mechanism of the proposed device is based on effective refractive index modulation of barium titanate and it is employed to extremely shift the spectral position over a wide range of wavelength. For the computation of quality factor, output efficiency and sensitivity, Finite-Difference-Time-Domain (FDTD) simulations are performed. The designed tunable filter provides a high output efficiency of 100% and very narrow bandwidth of 0.6 nm with an ultra-footprint is 174.24 μm2; hence, it extraordinarily suitable for wavelength division based optical communication systems and nanosensing applications.

Diffusion kinetics investigations of Nano Ag-doped holographic polymer dispersed liquid crystal gratings

ABSTRACTIn this paper, we use multicomponent mutual diffusion method to derive a one-dimensional non-local diffusion dynamic model to describe the diffusion kinetics of a dynamic holographic polymer dispersed liquid crystal grating (H-PDLC) doped with nano-silver. The physical mechanism of diffusion between monomer and liquid crystal, monomer and nano-silver particles is analysed using this model. Using coupled-wave theory, the H-PDLC’s diffraction efficiency curve with the expose time are simulated due to the vivid changing of effective refractive index modulation caused by the movement of concentration of each component with the expose time. Correspondingly, in the experiment, the diffraction efficiency of the grating is measured in real time, which shows the improvement for the holographic properties because of nano-silver doped H-PDLC. The simulation results have a good agreement with experimental data by fitting the corresponding parameters of the model. In addition, through comparing with simulation and experimental results with doping different concentrations of nano-silver particles, the recipe and diffraction characteristics of H-PDLC grating can be improved. Thus, the diffusion Kinetics model can be used to optimise the phase separation of the PDLC grating, and finally to improve the opto-electrical properties of H-PDLC gratings.

Modulation of orbital angular momentum in long periodchirally-coupled-cores fiber

A type of fiber-based orbital angular momentum (OAM) modulator is designed according to transformation relation between OAM beam and optical fiber vector mode, together with mode-coupling theory, which is based on the combination of multimode fiber structure and chirally-coupled-cores structure. Instead of applying external force or grating etching to the fiber in the system, chirally-coupled-cores fiber can realize the modulation of any optical OAM by using single fiber at 1550 nm. Therefore, the test system is relatively simple. From the equation <inline-formula><tex-math id="M1000">\begin{document}${\rm{OAM}}_{ \pm l,n}^{ \pm \sigma } = {\rm{HE}}_{l + 1,n}^{{\rm{even}}} \pm {\rm{i}} \times {\rm{HE}}_{l + 1,n}^{{\rm{odd}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182036_M1000.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182036_M1000.png"/></alternatives></inline-formula>, it can be seen that the OAM mode generated by long period chirally-coupled-cores fiber depends on the higher-order modes supported by the central fiber core. Therefore, the generation and modulation of any order OAM beam can be realized by changing the diameter of the central fiber core in theory. Through theoretical analysis and numerical simulation, the effects of different structure parameters on OAM modes are analyzed, including mode purity, mode transmission loss and effective refractive index. By keeping the propagation constants of the center core and side cores unchanged, the number of side cores has no effect on mode purity nor effective refractive index, but which is not for mode transmission loss. The loss of mode transmission increases with the increase of the number of side cores. However, it does not mean that the less number of side cores is a better case, in that the fiber symmetry and processing technology should also be considered. And the pitch calculated by the formula of phase matching condition can change in value within a certain numerical range without strongly affecting the mode purity and mode transmission loss. Pitch has a great influence on the effective refractive index of modes, therefore the pitch can be under control to change the difference in effective refractive index between OAM modes and reduce crosstalk between disparate modes. The distance between the center core and side cores of fiber has little effect on mode purity, great effect on mode transmission loss, but no effect on effective refractive index. Theoretically, the mode purity and mode transmission loss perform better with the distance between two kinds of cores increasing. But it will be limited by the fiber integration level.

Nano-electric field sensor based on Two Dimensional Photonic Crystal resonator

In this paper, hybrid Silicon-Barium Titanate (Si-BTO) based Two Dimensional Photonic Crystal (2DPC) platform is proposed for electric field sensing based on the effective refractive index modulation of electro-optic material. The nano-sensing platform is composed of the PC based resonator and inline quasi-waveguides in a 2D triangular lattice with circular rods that are arranged in the air medium. The BTO based nano-cavity resonator is playing a very important role in sensing the different electric field over a wide wavelength range. The operating wavelength range of the proposed sensor is investigated via Photonic Band Gap (PBG) which is obtained by the Plane Wave Expansion (PWE) method. The transmission efficiency, quality factor, electric field sensitivity and change in refractive index are analyzed by using Finite Difference Time Domain method (FDTD). The simulation results reveal that the resonant wavelength of the electric field sensor is linearly shifted to the higher wavelength region while increasing the electric field from 0 kV/mm to 25 kV/mm. The proposed sensing platform provides high transmission efficiency and very high refractive index sensitivity with an ultra-compact size. Hence, it is highly suitable for nano-chip based sensing applications.

Nano-Pressure and Temperature Sensor Based on Hexagonal Photonic Crystal Ring Resonator

In the present work, two-dimensional (2D) hexagonal photonic crystal ring resonator (PCRR) structure is designed for both pressure and temperature sensing based on effective refractive index modulation of silicon. The nanosensor is designed to monitor the pressure from 0.04 to 6 GPa and temperature from 5 to 540 °C. The proposed nanosensing platform is composed of hexagonal PCRR and two inline quasi-waveguides in a 2D hexagonal lattice with circular rods arranged in air host. The hexagonal PCRR is playing a very important role in sensing the different pressure and temperature levels over a wide dynamic range. The plane wave expansion method (PWE) is implemented to calculate photonic band gap (PBG), which is used to identify the operating wavelength range of the sensor. The functional parameters of the sensor are evaluated by finite-difference time-domain method (FDTD). The functional parameters are the dynamic range, resonant wavelength, sensitivity, transmission efficiency, and quality factor. The FDTD results show that the resonant wavelength of the PCRR is red shifted with increasing the pressure and temperature. The designed sensor offers high sensitivity, high transmission efficiency and good quality factor with ultra-compact size; hence, it is extremely suitable for nanotechnology-based sensing applications.