Full-vectorial Finite-difference Method Research Articles

Highly coherent supercontinuum generation in a photonic crystal fiber based on GeSe2–As2Se3–PbSe chalcogenide in the mid-infrared region

We numerically demonstrated highly coherent mid-infrared (IR) super-continuum (SC) generation using all-normal dispersion (AND) GeSe2−As2Se3−PbSe chalcogenide photonic crystal fiber (PCF). The structural parameters of this PCF were optimized to obtain an ultra-flat-AND region and high nonlinearity characteristics using the full-vectorial finite difference method with the perfectly matched layer boundary conditions to calculate the linear properties of the fiber. We show that, pumping a light source at 9.8 µm pump wavelength with an input pulse energy of 3.5 nJ and pulse width of 200 fs, corresponding to the peak power of 17.5 kW, into a 10-cm-long fiber, an ultra-flat-coherent mid-IR SC extended from 2851.8 nm to 13538.8 nm (bandwidth of 10687 nm) is obtained. This ultra-wide and flattened spectrum has excellent stability and coherence properties that can be used for mid-IR applications such as biological imaging, optical coherence tomography, and frequency metrology.

Asymmetric dual-core liquid crystal channel-based tunable mode converter

In this work, a higher order-to-fundamental mode converter is reported and analyzed based on an asymmetric dual channel waveguide (ADC-WG) on silicon. In the reported structure, one of the two waveguides is infiltrated with nematic liquid crystal (NLC) material to add temperature tunability while the other one is a solid BK7 waveguide. The modal characteristics are obtained using the full vectorial finite difference method (FVFDM). In addition, the structural parameters and optical characteristics of the employed materials are investigated to achieve good wavelength selectivity with a short device length (LD). Thus, a compact mode converter that can work at different wavelengths including the telecommunication wavelength i.e., 1.55 μm with LD ~ 482.31 μm and a low crosstalk of − 19.86 dB is presented. To prove the thermal tunability of the suggested mode converter, its operation is tested through a temperature range between 20 and 35 °C and the results show that the mode conversion process is achieved at each temperature with different phase matching wavelengths (λPMW) but with quite similar coupling length (LC). The proposed device can therefore be effectively utilized in integrated photonic circuits.

Mixed integer programming with kriging surrogate model technique for dispersion control of photonic crystal fibers

In this paper, mixed integer nonlinear programming (MINLP) optimization algorithm integrated with kriging surrogate-model is newly formulated to optimize the dispersion characteristics of photonic crystal fibers (PCFs). The MINLP is linked with full vectorial finite difference method (FVFDM) to optimize the modal properties of the PCFs. Through the optimization process, the design parameters can take real and/or integer values. The integer values can be used to selectively fill the PCF air holes to control its dispersion characteristics. However, the other optimization techniques deal with real design parameters where the PCF can be optimized using none or predefined infiltrated air holes. The MINLP algorithm is used to obtain an ultra-flat zero dispersion over a broadband of wavelength range from 1.25 to 1.6 μm using silica PCF selectively infiltrated with Ethanol material. To show the superiority of the proposed algorithm, nematic liquid crystal selectively infiltrated PCFs are also designed with high negative flat dispersion over wide range of wavelengths from 1.25 to 1.6 μm for the quasi transverse magnetic (TM) and the quasi transverse electric (TE) modes. Such designs have negative flat dispersions of − 163 ± 0.9 and − 170 ± 1.2 ps/Km nm, respectively over the studied wavelength range. Therefore, the MINLP algorithms could be used efficiently for the design and optimization of selectively filled photonic devices.

Compact TE-pass polarizer based on silicon-on-insulator platform with bimetallic rhodium–silver grating

An ultra-compact hybrid plasmonic grating based transverse electric (TE) pass polarizer using SOI platform is proposed and analyzed. The reported structure utilizes bi-metallic grating of noble metals; rhodium (Rh) and silver (Ag) as plasmonic materials to get benefit from their attractive properties. The rhodium is a corrosion-free, nonoxidizing, and chemically inert against aggressive chemicals noble metal. In conjunction with the use of Ag, Rh ensures better plasmonic response. The bi-metallic combination Ag/Rh exhibits large coupling between the quasi transverse magnetic mode confined in the silicon core and the surface plasmon mode constructed at the dielectric/metal interface, while the TE-mode can propagate with minimal losses. The modal characteristics of the proposed device are numerically investigated using full vectorial finite difference method, while the propagation analysis is performed using finite difference time domain method via Lumerical software package. The numerical results show that the TE-pass polarizer of a compact device length (LD) = 3.5 μm offers an extinction ratio (ER) of 36.6 dB and an insertion loss (IL) of about 0.8 dB at λ = 1.55 μm. Additionally, the reported polarizer is robust to fabrication errors keeping the ER larger than 20 dB and the IL less than 1 dB despite changing the geometrical parameters by pm hspace{0.17em}10% in the wavelength range of 1.4 to 1.7 μm.

Numerical analysis of a strip-loaded silicon rich nitride-thin film lithium niobate hybrid waveguides

Hybrid integration of silicon rich nitride and lithium niobate on insulator (SRN-LNOI) is an emerging material platform for photonic integrated circuits (PIC). In this paper, we present a systematic numerical investigation of the mode properties of a strip-loaded SRN-LNOI hybrid waveguide at 1550 nm wavelength using the full-vectorial finite difference method. Considering the anisotropic nature of the lithium niobate (LN) crystal, the effective refractive indices of the transverse electric and transverse magnetic modes of strip-loaded SRN-LN hybrid waveguides were analyzed. The single-mode condition, zero-birefringence, effective mode area, and power distribution in terms of the geometrical parameters of the strip-loaded SRN-LN hybrid waveguide are discussed in detail. Furthermore, the optical power transmission in both straight and bent waveguides, as well as the different characteristics of the optical power confinement of the fundamental modes in the SRN and LN layers were analyzed. This study provides useful information for designing high-performance photonic devices on a hybrid SRN-LNOI platform for future PIC applications.

Tunable liquid crystal asymmetric dual-core photonic crystal fiber mode converter.

In this study, a compact mode converter based on an asymmetric dual-core photonic crystal fiber (ADC-PCF) infiltrated with nematic liquid crystal (NLC) is reported. The full vectorial finite difference method is used to compute the modal characteristics of the studied transverse magnetic (TM) mode. In this investigation, the geometrical and material parameters of the proposed mode converter are studied to achieve high wavelength selectivity with a compact device length. The proposed mode converter has a compact device length of 403.6 µm at λ=1.3µm. In addition, the reported device is simulated under different temperature levels from 15°C to 45°C to show the thermal tunability. Therefore, the proposed design can be used efficiently in integrated photonic circuits.

Mid-infrared broadband all-optical wavelength converter in Ge20Sb15Se65 photonic crystal fiber with flattened dispersion

A chalcogenide photonic crystal fiber (PCF) with flattened dispersion and high nonlinearity in mid-infrared (mid-IR) based on a triangular and circular lattice hybrid cladding structure is proposed. The structural parameters of the PCF are optimized by the full-vectorial finite-difference method. The numerical simulation results show: when d1 = 0.4 µm, d2 = 0.16 µm, d3 = 0.04 µm, Ʌ1 = 0.88 µm, Ʌ2 = 0.8 µm, Ʌ3 = 0.5 µm, the flatten and low dispersion is obtained in the wavelength range of 3.8–5 µm. The dispersion value is between ± 1.2 (ps/nm/km), and the maximum nonlinear coefficient is as high as 2464.2 km-1 W-1 at 2.5 µm. Based on the four-wave mixing (FWM) effect in the proposed PCF, the all-optical wavelength conversion performance is numerically analyzed. When the pumping wavelength is 4.02 µm, the 3 dB conversion bandwidth can reach 4833 nm (from 2.737 µm to 7.57 µm), and the maximum wavelength conversion efficiency is 12.12 dB. The proposed all optical wavelength converter is having large bandwidth and high conversion efficiency in mid-IR band due to the flat dispersion and high nonlinearity of the PCF, which has potential application in future space optical communication network and mid-IR photonic.

Tunable polarization splitter based on asymmetric dual-core liquid photonic crystal fiber

Tunable photonic crystal fiber polarization splitter is proposed and analyzed. The proposed splitter has a dual asymmetric cores where one core is only filled with a nematic liquid crystal (NLC). The birefringence is also increased between the two polarized modes due to the NLC material which improves the splitting performance. The coupling between the two asymmetric cores occurs at a specific wavelength which can be controlled by the NLC material. Additionally, the splitting between the two polarized modes can be tuned by rotating the NLC molecules using an external electric field. Further, the matching wavelength where the power coupling occurs between the two asymmetric cores can be controlled thermally due to the NLC dependence on the temperature. The analysis of the proposed splitter is carried out using full vectorial finite difference method. The reported polarization splitter has a compact device length of 602 µm at λ = 1.3 μm with high wavelength selectivity. In addition, large bandwidth of 60 nm is obtained with crosstalk lower than − 20 dB which ensures the superiority of the reported device.

Compact and broadband 3D mode (de)multiplexer via displacement of an asymmetric slot-strip coupler

A compact and broadband three-dimensional (3D) quasi- T E 0 and quasi- T E 1 mode (de)multiplexer [(De)MUX] is proposed via an asymmetric slot-strip coupler, in which the optimally lateral displacement between the bottom silicon slot waveguide and the upper poly-silicon strip-waveguide can enable the vertical mode-coupling efficiently. The design of the proposed 3D mode (De)MUX is based on the full-vectorial finite-element method, 3D full-vectorial finite-difference time-domain method, and mode expansion method. The optimized 3D mode (De)MUX is with a compact coupling length of only 5.65 µm, a broad 3 dB bandwidth of 231.5 nm, a low insertion loss of 0.3 dB, and a mode cross talk of − 27.54 d B . The fabrication tolerance is also studied with a width error of ± 20 n m for both the upper and lower layers.

Analysis of Photonic Crystal Fibers Using Full Vectorial Finite Difference Method (Dept.P)

The full-vectorial finite difference method (FV-FDM) is applied to perform modal solution to photonic crystal fibers (PCFs). The effects of geometrical parameters of the circular and elliptical holes on the effective index, the dispersion and the effective mode area of the fundamental mode have been studied. PCF structure showing dispersion of 0+1.288 ps/nm.km over the wavelength range from 1.3 um to 1.8 um has been reported. The applicability of using PCF as a pressure sensor has been discussed.

Gain characteristics of the hybrid slot waveguide amplifiers integrated with NaYF4:Er3+ NPs-PMMA covalently linked nanocomposites.

Waveguide amplifiers based on slot waveguide have enormous capacity due to their ability to confine light strongly to a narrow slot waveguide. NaYF4:Er3+ nanoparticles-polymeric methyl methacrylate covalently linked nanocomposites were synthesized and filled into the slot. The stability and the Er3+ concentration doped in this novel material were improved. The slot waveguide was designed accurately. The rigorous numerical method, full-vector finite difference method, was used to analyze the modal characteristics and optimize the slot combined with the maximum power confinement in the slot and the minimum effective mode area of the slot. A four-level spectroscopic model pumped at 1480 nm was presented. The rate equations and propagation equations were solved and the gain characteristics of the slot waveguide amplifier were numerically simulated. The primary parameters were optimized. A net gain of 5.78 dB was achieved when the signal power was 0.001 mW at 1530 nm, pump power was 20 mW, Er3+ concentration was 1.3 × 1027 m−3, and the waveguide length was 1.5 cm.

Highly tunable compact polarization rotator based on silicon on insulator platform

A novel design of an ultra-compact polarization rotator (PR) based on silicon on insulator platform infiltrated with liquid crystal is reported and studied. The anisotropic property of the liquid crystal material leads to a high modal hybridness, which improves the power exchange between the two orthogonal polarized modes. Therefore, tunable and high polarization conversion can be achieved over a short propagation distance. The proposed PR is analyzed by using full-vectorial finite-difference method and full-vectorial finite-difference beam propagation method. At an operating wavelength of 1.55 μm, the PR has a compact device length of 5.4 μm with 14 dB extinction ratio (ER) and 0.15 dB insertion loss. Moreover, the suggested PR offers a relatively broad bandwidth of (1340–1685) nm with an overall ER better than 10 dB. Further, the polarization conversion ratio can be tuned by controlling the rotation angle of the nematic liquid crystal molecules via an external electric field. Furthermore, the fabrication tolerance study shows that the reported PR has high robustness to the fabrication errors.

Reconfigurable Mode (De)Multiplexer Using Ge2Sb2Se4Te1 Based Triple-Silicon-Waveguide

A reconfigurable mode (de)multiplexer [(De)MUX] is proposed based on a triple-silicon-waveguide directional coupler, consisting of a central waveguide with a Ge2Sb2Se4Te1 (GSST) upper layer and two outer silicon waveguides. The output mode states can be switched by the self-holding phase transition between the amorphous and crystalline states of the GSST layer, and a low loss of the proposed device can be achieved benefiting from the low propagation losses of the GSST at both states. The proposed reconfigurable mode (De)MUX is optimized by using the full-vectorial finite-element method and the thee-dimensional full-vectorial finite-difference time-domain method. The numerical results reveal that the proposed reconfigurable mode (De)MUX is with a compact length of 17.65 $\mu \text{m}$ , insertion losses of 0.16 and 0.96 dB, and mode crosstalk of −15.91 and −26.97 dB at ON and OFF states, respectively. The proposed reconfigurable mode (De)MUX can operate over the S + C + L band with high performance. The fabrication tolerances are also studied in detail.

Supercontinuum generated high power highly nonlinear photonic crystal fiber for medical and optical communications applications

This paper investigates a supercontinuum generated high power highly nonlinear photonic crystal fiber for medical and optical communication applications. The full vector finite difference method with perfectly matched layer is used as an analysis tool. Numerical simulation results show that it is possible to achieve high nonlinear coefficient, near zero ultra-flattened dispersion, low confinement loss and supercontinuum spectrum with high power. Moreover, numerical results show that short length of the proposed photonic crystal fiber is achieved. The numerical simulation results of supercontinuum generation is conducted by solving the generalized nonlinear Schrödinger equation with the split-step Fourier method. It is observed adequate supercontinuum spectrum that broaden from 960 to 1870 nm by considering center wavelengths of 1.06, 1.31, and 1.55 μm into silica based index guiding photonic crystal fiber. This simulation results prove that the proposed design of a highly nonlinear photonic crystal fiber is a great solution for broad supercontinuum generation with high power.

Analysis of Waveguides on Lithium Niobate Thin Films

Waveguides formed by etching, proton-exchange (PE), and strip-loaded on single-crystal lithium niobate (LN) thin film were designed and simulated by a full-vectorial finite difference method. The single-mode condition, optical power distribution, and bending loss of these kinds of waveguides were studied and compared systematically. For the PE waveguide, the optical power distributed in LN layer had negligible change with the increase of PE thickness. For the strip-loaded waveguide, the relationships between optical power distribution in LN layer and waveguide thickness were different for quasi-TE (q-TE) and quasi-TM (q-TM) modes. The bending loss would decrease with the increase of bending radius. There was a bending loss caused by the electromagnetic field leakage when the neff of q-TM waveguide was smaller than that of nearby TE planar waveguide. LN ridge waveguides possessed a low bending loss even at a relatively small bending radius. This study is helpful for the understanding of waveguide structures as well as for the optimization and the fabrication of high-density integrated optical components.

Highly wavelength-selective asymmetric dual-core liquid photonic crystal fiber polarization splitter

An asymmetric dual-core photonic crystal fiber (ADC-PCF) wavelength-selective polarization splitter is reported and analyzed. The left core of the DC-PCF is surrounded by nematic liquid crystal infiltrated holes in order to control the wavelength at which coupling occurs between the dual cores of the proposed design. Moreover, the suggested structure can be tuned to split out the x- and y-polarized modes at the two telecommunication wavelengths λ=1.3 μm and λ=1.55 μm. The geometrical parameters of the reported splitter are studied by the full vectorial finite difference method via the Lumerical software package to achieve high wavelength selectivity with device length of 5.678 mm at λ=1.3 μm. Further, the power coupling characteristics of the reported device are studied, which ensures that the ADC-PCF splitter has a very narrow bandwidth of approximately 3 nm around wavelengths of 1.3 μm and 1.55 μm. Therefore, the suggested design can be considered as a very good candidate to be used in the integrated photonic devices.

Amorphous silicon-lithium niobate thin film strip-loaded waveguides

The heterogeneous integration of an amorphous silicon (a-Si) film with a lithium niobate (LN) thin film combines both the mature micro-processing technology of Si and the excellent optical properties of LN. An a-Si thin film was deposited on an LN thin film, and strip-loaded waveguides were designed, fabricated, and characterized. A full-vectorial finite difference method was used to explore the single-mode conditions and appropriate dimensions for the strip-loaded waveguides. The waveguide mode size could be as small as 0.36 μm2. By adjusting the thickness and width of the a-Si loading strip, the distribution of light power could be mainly confined in the LN layer. The maximal light power that could be confined in LN was 91%, which was obtained at an a-Si thickness of 65 nm. A set of waveguides with widths of 2‒7 μm were prepared by inductively coupled plasma (ICP) etching of the a-Si thin film. Following annealing at 300°C in air for 1 hour, light transmission was observed in the waveguide. The 2-μm-wide waveguide showed propagation losses of 20 dB/cm for the quasi-TM (q-TM) mode and 42 dB/cm for the quasi-TE (q-TE) mode at 1550 nm. The root-mean-square (RMS) surface roughness of the a-Si thin film before and after annealing was 1.04 and 0.35 nm, respectively. High-resolution transmission electron microscopy (HRTEM) was performed to investigate the interface morphologies. A well-defined interface was clearly observed, and the structure of the a-Si thin film was proved to be amorphous.

Modified Trust Region Algorithm for Dispersion Optimization of Photonic Crystal Fibers

In this paper, a modified derivative-free surrogate-based trust region optimization algorithm is proposed for optimizing the dispersion properties of photonic crystal fibers (PCFs) for the first time to the best of our knowledge. The modal analysis of the PCF is made using the full vectorial finite difference method with perfect matched layer boundary condition. The numerical results are compared with another trust region algorithm and other metaheuristic techniques to show the strength of the reported technique. Further, the modified algorithm is also used to achieve a nearly ultra-flattened zero dispersion over a wide range of wavelengths from 1.45 $\mu {\rm{m}}$ to 1.6 $\mu {\rm{m}}$ using an index guiding soft glass PCF selectively infiltrated with a nematic liquid crystal. In order to show the strength of the reported algorithm, a highly negative flat dispersion compensation PCF is also designed over wavelength range from 1.4 $\mu {\rm{m}}$ to 1.6 $\mu {\rm{m}}$ . Such a design has a negative dispersion of −155 ± 0.5 ps/Km·nm over the studied wavelength range. The trust region algorithms show a strong potential as an efficient tool for the design and optimization of different photonic devices. Further, these algorithms can be used as powerful techniques for solving the inverse problems.

Ultracompact Polarization Rotator Based on Liquid Crystal Channel on Silicon

A novel highly tunable polarization rotator (PR) based on channel waveguide on silicon is introduced and analyzed. The proposed SiO2/Si channel is infiltrated with nematic liquid crystal (NLC) material of type E7. The design parameters of the NLC channel PR have been studied to obtain an efficient polarization conversion with an ultrashort device length. Additionally, a tolerance analysis of the structure geometrical parameters, temperature, and operating wavelength is reported in detail. The modal analysis of the NLC PR is carried out using full-vectorial finite-difference method (FVFDM). Further, the propagation characteristics through the suggested design are obtained using full-vectorial finite-difference beam propagation method (FVFD-BPM). The numerical results reveal that the reported PR of compact device length of 4.02 μ m can achieve nearly 100% polarization conversion ratio with insertion loss of 2.19 dB and good crosstalk of –21.73 dB at a wavelength of 1.55 μ m. Further, the crosstalk would be better than –20 dB within the wavelength range of 1.55 ± 0.04 μ m. Moreover, the polarization conversion ratio can be controlled by applying an external electric field. To the best of the authors’ knowledge, it is the first time to introduce ultracompact highly tunable PR based on a channel on silicon platform with simple design and broadband operation.

Full-vectorial analysis of a silicon-based multimode interference mode-order converter for slot waveguide nanowires

Recently, silicon-based photonic integrated circuits (PICs) have attracted considerable interest due to the advantages of high index contrast and complementary metal oxide semiconductor compatible process. Furthermore, to meet the ever-growing bandwidth requirements for data center and supercomputing, several multiplexing on-chip technologies by using silicon PICs are proposed. Among them, the mode division multiplexing (MDM) is widely recognized to be important, where mode-order converters (MOCs) are fundamental building blocks. In addition, slot waveguides can efficiently confine the light in low-index regions, thus forming various kinds of novel photonic devices. In this paper, a compact 12 multimode interference (MMI) mode-order converter (MOC) for silicon-based slot nanowires is proposed, where straight waveguides, as the input/output channels, are connected to a quadratic-tapered multimode waveguide via linear-tapered waveguides. A full-vectorial finite-difference frequency-domain method is used to analyze the modal characteristics of the used silicon-based vertical slot waveguides; from this, quasi-TM mode is chosen as an input optical signal since its field distribution is strongly confined in the slot, i. e., the electric field strength is greatly enhanced in the vertical slot, and with the increase of the width of the slot waveguide, it can support higher-order quasi-TM modes. Compared with the beating length of rectangular MMI structure, the beating length of quadratic-tapered MMI structure can be effectively reduced with transmission loss lowering. From the imaging position of the guided-mode in MMI region via self-imagining effect, the length of quadratic-tapered MMI structure can be determined accurately where first-order and fundamental quasi-TM modes are outputs, respectively, from wider and narrower channels. A three-dimensional finite-difference time-domain method is utilized to assess the performance of the proposed MOC, where the insertion loss and crosstalk are analyzed in detail. The results show that an MOC with an MMI section of 35 m2 is achieved to be an insertion loss and a crosstalk of~0.35 dB and~-16.9 dB, respectively, at a wavelength of 1.55 m by carefully optimizing the key structural parameters. Moreover, the fabrication deviation of the proposed device is also analyzed in detail and the performance is evaluated, where insertion loss and the contrast are considered. To demonstrate the transmission characteristics of the proposed MOC, the evolution of the excited fundamental quasi-TM mode through the MOC is also presented. Numerical results show that the presented MOC realizes the desired function, converting the fundamental quasi-TM mode into first-order one with reasonable performance. We remark that the present MOC has a good potential application in MDM system to improve the capacity of the silicon-based on-chip transmission system.