Full-vectorial Beam Propagation Method Research Articles

Coupling Characteristics of Dual Liquid Crystal Core Soft Glass Photonic Crystal Fiber

In this paper, the coupling characteristics of a novel design of soft glass photonic crystal fiber with dual nematic liquid crystal core (SGLC-PCF) are introduced and analyzed. The index contrast between the core and cladding region ensures the index guiding through the reported coupler. The analysis is carried out using the full vectorial finite difference method along with the full vectorial finite difference beam propagation method. The numerical results reveal that the SGLC-PCF coupler can be used as a polarization splitter of length 6232 μm with low crosstalk better than -20 dB with great bandwidths of 250 nm and 60 nm for the quasi transverse electric and quasi transverse magnetic, modes, respectively. In addition, the proposed splitter has a tolerance of ±3% in its length which makes the design less sensitive to the perturbation introduced during the fabrication process.

Design of passive polarization rotator based on silica photonic crystal fiber

We propose and analyze a novel (to the best of our knowledge) design of a polarization rotator (PR) based on silica photonic crystal fiber. The proposed design has a rectangular core region with a slanted sidewall. The simulation results are obtained using the full vectorial finite difference method as well as the full vectorial finite difference beam propagation method. The numerical results reveal that the suggested PR can provide a nearly 100% polarization conversion ratio with a device length of 3102 μm.

1 × 4 coupler based on all solid five-core photonic crystal fibers

An improved 1 × 4 coupler based on all solid multi-core photonic crystal fiber is proposed and analyzed. The expressions to calculate the coupling length and the coupling efficiency are deduced based on the coupled-mode equations firstly. Then a full-vector finite element method (FEM) is used to calculate the coupling length and the coupling efficiency. Next, the propagation characteristics and the performances of the coupler are analyzed through using a full vector beam propagation method (BPM). Research shows that the results derived by FEM agree with that by BPM. The coupling length of the coupler is 4.1 mm at λ = 1.55 μm. A maximum coupling efficiency of 24.96% can be obtained. The coupling ratio is more than 22.5% over a wavelength range of 100 nm. The polarization-dependent loss at λ = 1.55 μm is equal to 0.73 dB. Finally, the influences of the micro-variation of structure parameters and the material refractive index on the working performances of the coupler are investigated.

Theoretical investigation of band-gap and mode characteristics of anti-resonance guiding photonic crystal fibres

With the full-vector plane-wave method (FVPWM) and the full-vector beam propagation method (FVBPM), the dependences of the band-gap and mode characteristics on material index and cladding structure parameter in anti-resonance guiding photonic crystal fibres (ARGPCFs) are sufficiently analysed. An ARGPCF operating in the near-infrared wavelength is shown. The influences of the high index cylinders, glass interstitial apexes and silica structure on the characteristics of band-gaps and modes are deeply investigated. The equivalent planar waveguide theory is used for analysing such an ARGPCF filled by the isotropic materials, and the resonance and the anti-resonance characteristics can be well predicted.

Proposal for a simple integrated optical ion-exchange waveguide polarizer with a liquid crystal overlay

A simple, compact electro-optic polarizer based on an ion-exchanged glass channel waveguide covered with a nematic liquid crystal (LC) is proposed. A full-vectorial beam propagation method is employed to simulate this device for the first time. For the cases of zero and strong LC surface anchoring, the performance of the proposed polarizer under different applied voltages is analyzed numerically. Analysis indicates that surface anchoring of the liquid crystal is a key issue influencing the performance for the proposed optical polarizer device.

Design and characteristics of a novel narrow-band filter with the dual-core photonic crystal fiber

A novel narrow-band filter based on the dual-core doped photonic crystal fiber is proposed. By optimizing structure parameters of the photonic crystal fiber, the index curves of the fundamental modes for the two cores are crossed at 1.55 μm and the wavelength-selective coupling is achieved. The characteristics of the filter are numerically simulated by the full-vector beam propagation method. And the simulation results show that the coupling length and the bandwidth of the filter are 16.4 mm and 9 nm at −3 dB loss, respectively. It demonstrates the advantages of the filter with a small size, a low transmission loss and the narrow-band width.

Longitudinal polarization stability of near-elliptic inner-cladding polarization-maintaining photonic crystal fiber

A novel theoretical analysis model of fiber birefringence and extinction ratio deterioration induced by longitudinal stochastic variation in diameter of silica capillaries for fiber preform is established based on three-dimensional full-vector beam propagation method (3D-FV-BPM) and Jones Matrix method. The longitudinal polarization stability of near-elliptic inner-cladding polarization-maintaining photonic crystal fiber (NEIC-PM-PCF) is analyzed and compared with near Panda clading photonic crystal fiber (NPC-PCF) and near rectangle photonic crystal fiber (NR-PCF) in detail. The longitudinal diameter tolerance ranges of capillaries could be calculated for a given extinction ratio and a certain fiber length, which shows a good reference for fabricating NEIC-PM-PCFs.

Full-vectorial mode solver for anisotropic optical waveguides using multidomain spectral collocation method

A full-vectorial mode solver in terms of the transverse magnetic field components for optical waveguides with transverse anisotropy is described by using the multidomain spectral collocation method based on Chebyshev polynomials. The waveguide cross section surrounded by the perfectly matched layers is divided into suitable number of homogeneous rectangles, and then connected with by imposing the continuities of the longitudinal field components at the dielectric interfaces shared by the adjacent rectangles, resulting in a generalized matrix eigenvalue problem. To validate the established method, results of an anisotropic square waveguide and a magnetooptic rib waveguide are presented and compared with those from the full-vectorial finite difference method, full-vectorial beam propagation method, and the experimental data.

Beam Propagation Analysis of Polarization Rotation in Soft Glass Nematic Liquid Crystal Photonic Crystal Fibers

In this letter, a novel design of high tunable polarization rotator (PR) based on nematic liquid crystal (NLC) photonic crystal fiber is proposed and analyzed. The tunability of the proposed PR results from the change of the optical properties of the NLC with the temperature or external electric field. The simulation results are obtained using the full vectorial finite-difference method as well as the full vectorial finite-difference beam propagation method. The numerical results reveal that the suggested PR can provide a strong polarization conversion ratio of 99.81% with a device length of 1072 ?m.

Numerical simulation of beam propagation in a layer filled with chiral nematic liquid crystals

Simulation of light beam propagation in chiral nematic liquid crystals, which are anisotropic media, requires the use of full-vector methods. One of them is FV-BPM (Full-Vector Beam Propagation Method). In the present work an application of FV-BPM to simulate light propagation, in the linear case, is shown. Calculations are carried out for various values of incident beam full width at half maximum, position of the launched beam and the pitch of the cholesteric. Full Text: PDF

Coupling characteristics of a soft glass nematic liquid crystal photonic crystal fibre coupler

This study presents the coupling characteristics of a novel soft glass photonic crystal fibre (PCF) coupler infiltrated with a nematic liquid crystal (NLC–PCF). The soft glass provides optical properties that cannot be obtained by silica such as high refractive index, high rare earth solubility and mid-infrared transmission. In addition, the nematic liquid crystal (NLC) offers high tunability with the temperature and external electric field, and increases the birefringence between the two fundamental polarised modes in the proposed coupler. Therefore the NLC–PCF coupler has stronger polarisation dependence than the low birefringence conventional silica PCF coupler. The effects of the coupler geometrical parameters, rotation angle of the director of the NLC and temperature on the coupler performance are investigated. The analysis is carried out using the full vectorial finite difference method and the beam propagation study is performed by the full vectorial finite difference beam propagation method. The numerical results reveal that the polarisation dependence of NLC–PCF coupler is approximately 2.5 times that of the conventional silica PCF coupler with shorter coupling length. In addition, the NLC–PCF coupler has strong potential to offer practical design for short polarisation splitter as well as multiplexer–demultiplexer.

Design of miniaturized silicon wire and slot waveguide polarization splitter based on a resonant tunneling

We propose an ultra-small polarization splitter based on a resonant tunneling phenomenon. This polarization splitter consists of two identical horizontally oblong silicon wire waveguides separated by a vertical slot waveguide. The structural parameters of the central resonant slot waveguide are designed to couple only the TM-like mode between the left and right side silicon wire waveguides. Results from numerical simulation with the full-vectorial beam propagation method show that a 16-mum-long polarization splitter with extinction ratio better than -20 dB on the entire C-band is achieved.

Polarization Coupling Between Strongly Guiding Waveguides Stacked Laterally

The full-vectorial beam-propagation method is applied to the assessment of the coupling characteristics between strongly guiding waveguides stacked laterally. The polarization crosstalk behavior of square waveguides stacked laterally is demonstrated by the eigenmode and beam-propagation analyses. In order to make use of the polarization crosstalk constructively, we determine the vertical spacing between the two square waveguides. Almost complete conversion can be obtained, when the two waveguides are stacked diagonally. Another coupler composed of two rectangular waveguides is studied to realize the polarization conversion without exchanging the power with the same polarization. A crossing-waveguide-type polarization converter is also developed, with a short device length of less than 80 mum at a wavelength of 1.55 mum.

Polarization beam splitter based on photonic crystal fibers

Polarization beam splitters (PBSs) are a special kind of coupler. They can split incoming light from a single fiber into two orthogonally polarized beams. They are usually used in coherent optical communication systems, optical sense systems and optical measurement systems. In this paper, two kinds of mechanisms of the PBSs based on photonic crystal fibers (PCFs) are discussed. The full-vector finite element method (FEM) was employed to analyze propagating properties, while the full-vector beam propagation method (BPM) was applied to analyze preferences of the splitters. The results show that it is possible to achieve a compact PBS with high extinction ratio.

Multiplexer–Demultiplexer based on nematic liquid crystal photonic crystal fiber coupler

A novel design of Multiplexer–Demultiplexer (MUX–DEMUX) based on index guiding soft glass nematic liquid crystal (NLC) based photonic crystal fiber coupler is proposed and analyzed. The simulation results are obtained using the full vectorial finite difference method as well as the full vectorial finite difference beam propagation method. The numerical results reveal that the proposed MUX–DEMUX of length 3.265 mm can provide low crosstalk better than −20dB with great bandwidths of 40 and 24 nm around the wavelengths of 1.3 and 1.55 μm, respectively. In addition, the reported MUX–DEMUX has a tolerance of ±3% in its length which makes the design more robust to the perturbation introduced during the fabrication process.

Investigation on Guided-Mode Characteristics of Hollow-Core Photonic Crystal Fibre at Near-Infrared Wavelengths

Guided-mode characteristics of hollow-core photonic crystal fibre (HC-PCF) are experimentally and theoretically investigated. The transmission spectrum in the range from 755 to 845 nm is observed and the loss is measured to be 0.12 dB/m at 800 nm by cut-back method. Based on the full-vector beam propagation method and the full-vector plane-wave method, the characteristics of mode field over propagation distance 1 m are simulated, and the results show that the propagation efficiency can be above 80%. Compared with the fundamental guided mode well confined in air core within shorter propagation distance, the second-order guided mode leaks into the cladding region and gradually attenuates due to larger refractive index difference. The primary loss factors in HC-PCF and the corresponding solutions are elementarily discussed.

Characteristic investigation of 2D photonic crystals with full material anisotropy under out-of-plane propagation and liquid-crystal-filled photonic-band-gap-fiber applications using finite element methods

To effectively investigate the fundamental characteristics of two-dimensional (2D) photonic crystals (PCs) with arbitrary 3D material anisotropy under the out-of-plane wave propagation, we establish a full-vectorial finite element method based eigenvalue algorithm to perform related analysis correctly. The band edge diagrams can be conveniently constructed from the band structures of varied propagation constants obtained from the algorithm, which is helpful for the analysis and design of photonic ban gap (PBG) fibers. Several PCs are analyzed to demonstrate the correctness of this numerical model. Our analysis results for simple PCs are checked with others' ones using different methods, including the transfer matrix method, the finite-difference frequency-domain (FDFD) method, and the plane-wave expansion method. And the validity of those for the most complex PC with arbitrary 3D anisotropy is supported by related liquid-crystal-filled PBG fiber mode analysis, which demonstrates the dependence of transmission properties on the PBGs, employing a full-vectorial finite element beam propagation method (FE-BPM).

Simulation of optical waveguides by novel full-vectorial pseudospectral-based imaginary-distance beam propagation method

This work presents a novel full-vectorial imaginary-distance beam propagation method based on the multidomain pseudospectral scheme, for the first time, to study the modal characteristics of dielectric optical waveguides. The proposed method divides the transverse plane into several subdomains with uniform refractive indices, and expands the optical field in each subdomain in terms of a set of suitable basis functions. Accordingly, the complicated cross-coupling terms, which are required by the finite difference or finite element schemes, can be removed from the full-vectorial formulations. However, the coupling effect can be restored by matching the physical interface conditions. Moreover, to identify the higher-order modes, the residual traces of the preceding lower-order modes are subtracted from the calculated optical fields in each propagation step to suppress the rapid growth of the lower-order modes. Numerical examples of the two-dimensional slab waveguides demonstrate that the present approach yields a highly accurate propagation constant. When applied to three-dimensional rib waveguides the present scheme yields results that remarkably agree with the reliable values obtained from the modal transverse resonance method and finite element scheme.

Calculation of the coupling coefficients for spatial waveguides using the field matching method

Spatial waveguides consisting of waveguides on different but parallel layers have been incorporated into many three-dimensional integrated optical devices. The coupling coefficients between two spatial waveguides are calculated in this paper. The calculation is based on the field matching method (FMM), and the three-dimensional full-vector beam propagation method (3D-BPM) is used to verify the computed results. Comparison of the coupling lengths obtained by the 3D-BPM and FMM shows that the maximum relative error is 1.0%, and the average relative error is 0.5%. The coupling coefficients are important parameters for three-dimensional integrated optical devices.

Design of polarization-independent optical couplers composed of three parallel slot waveguides

The characteristics of directional couplers and power splitters based on three-guide optical couplers in slot waveguide structures are analyzed in detail by a three-dimensional full-vectorial beam propagation method. The numerical results show the achievement of a compact three-guide directional coupler operating as polarization independent with a length of 58.0 microm and having almost evenly spaced propagation constants of the three lowest order modes for quasi-TE and quasi-TM modes. Thus, a high coupling efficiency from one outside waveguide to the other outside waveguide is demonstrated and is over 99.5% for both polarization states. For a three-guide power splitter, multiple sets of waveguide parameters for achieving polarization-independent operation are presented. Tolerances to operating wavelength and structural parameters are also analyzed, and the evolution of the injected field along the propagation distance through the proposed devices is demonstrated.