Finite-difference Vector Beam Propagation Research Articles

Passive polarization rotator based on silica photonic crystal fiber for 1.31-μm and 1.55-μm bands via adjusting the fiber length

A new polarization rotator based on the silica photonic crystal fiber is proposed. The proposed polarization rotator photonic crystal fiber (PR-PCF) possesses a triangle jigsaw-shape core region. The full-vector finite-element method is used to analyze the phenomenon of polarization conversion between the quasi-TE and quasi-TM modes. Numerical simulations show that the wavelengths of 1.31 μm and 1.55 μm are converted with a nearly 100% polarization conversion ratio with their matched coupling length and has a relatively strong realistic fabrication tolerance −100 nm on the y axis and 50 nm on the x axis. The full vectorial finite difference beam propagation method is used to confirm the performance of the proposed PR-PCF.

Polarization converters in highly birefringent microfibers

A novel type of polarization converters (PCs) based on highly birefringent (Hi-Bi) microfibers is presented. Analytical formulation based on the Jones Matrix method and a numerical code based on the Full Vectorial Finite Difference Beam Propagation Method are developed to analyze the polarization evolutions in such PCs. Two different design configurations, namely the "one-side" and "two-side" perturbation configurations, are studied by use of the two methods, and the results obtained agree well with each others. The PCs can be flexibly designed to have different operating wavelengths, spectral bandwidths, and devices lengths. A particular PC based on an elliptical microfiber demonstrates a bandwidth of ∼ 600 nm around 1550 nm with a device length of ∼ 150 μm.

Analysis of polarisation conversion in cascaded bent photonic crystal fibre

A rigorous analysis of polarisation conversion in a novel design of cascaded bent silica photonic crystal fibre is proposed using full vectorial finite difference method as well as full vectorial finite difference beam propagation method. The influence of different structural geometrical parameters on the polarisation rotator performance is investigated. The numerical results reveal that by a careful adjustment of the structural geometrical parameters and bending radius, nearly a 100% polarisation conversion ratio with nine sections only and low bending losses can be achieved.

Novel Design of Ultra-Compact Triangular Lattice Silica Photonic Crystal Polarization Converter

A novel design of ultra-compact polarization rotator (PR) based on triangular lattice silica photonic crystal fiber is proposed and analyzed. The suggested design has a central air hole which can be shifted in x and y directions to achieve complete polarization rotation. The influence of the different structure geometrical parameters and operating wavelength on the PR performance is investigated. The simulation results are obtained using full vectorial finite difference method as well as full vectorial finite difference beam propagation method. The numerical results reveal that the reported PR can provide nearly 100% polarization conversion ratio with a device length of 206 μm. It is also expected that over the 1.5-1.6 μ m wavelength range, polarization conversion would be more than 99%.

Design Consideration of Polarization Converter Based on Silica Photonic Crystal Fiber

In this paper, the performance of a novel design of passive polarization rotator (PR) based on silica photonic crystal fiber is studied and analyzed using the full vectorial finite difference method along with the full vectorial finite difference beam propagation method. The proposed design has a rectangular core region with a slanted sidewall. The influence of the different structure geometrical parameters and operating wavelengths on the PR performance is investigated. At a wavelength of 1.55 μm, nearly 100% polarization conversion ratio is obtained, with a device length of 2839 μm. In addition, it is expected that over the 1.5 to 1.6-μm wavelength range, polarization conversion would be more than 99%.

Passive Polarization Converters Based on Photonic Crystal Fiber With L-Shaped Core Region

In this paper, novel designs of single and multiple sectioned passive polarization rotators (PRs) based on silica photonic crystal fiber (PCF) are studied and analyzed. The suggested PCF PRs have an L-shaped core region which offers nearly 100% polarization conversion ratio. The simulation results are obtained using the full vectorial finite difference method along with the full vectorial finite difference beam propagation method. The influence of the different waveguide parameters and operating wavelength on the PRs performances are investigated in order to obtain optimum PR designs. The single and multiple sectioned PCF PRs offer nearly 100% polarization conversion ratio with device lengths of 1743 μ m and 1265 μ m, respectively.

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.

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.

Explicit finite-difference vector beam propagation method based on the iterated Crank-Nicolson scheme

We introduce and develop a new explicit vector beam propagation method, based on the iterated Crank-Nicolson scheme, which is an established numerical method in the area of computational relativity. The proposed approach results in a fast and robust method, characterized by simplicity, efficiency, and versatility. It is free of limitations inherent in implicit beam propagation methods, which are associated with poor convergence or uneconomical use of memory in the solution of large sparse linear systems, and thus it can tackle problems of considerable size and complexity. The advantages offered by this approach are demonstrated by analyzing a multimode interference coupler and a twin-core photonic crystal fiber. A possible wide-angle generalization is also provided.

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.

Improving triangular-lattice photonic-crystal-fiber couplers by introducing geometric nonuniformities

The coupling characteristics of newly proposed photonic-crystal-fiber couplers are rigorously analyzed using a 3-D finite-difference vector beam propagation method. The coupling length and efficiency of the couplers are investigated as a function of their geometrical parameters at different wavelengths. Size variability of the central hole is considered as a means of improving the coupling between the two cores. A determination of the guiding properties of the couplers, such as the propagation constants and the effective indices, is performed using a mode solver based on the plane-wave method. We show that it is possible to design very short photonic-crystal-fiber couplers with submillimeter coupling lengths. Nonuniformities are deliberately introduced in the coupler pattern to decrease the coupling length in comparison with the ideal structures. This study confirms that the designed coupler can act as an efficient ultrasmall-wavelength splitter or polarization-preserving directional coupler for wavelength division multiplexing systems.

Analysis of GaN-based single-mode rib waveguide with large cross section

A GaN-based optical single-mode rib waveguide with a large cross section is systematically designed and analyzed using the finite-difference vector beam propagation method (FD-VBPM). The method is a combination of numerical aperture and FD-VBPM, which is used to determine the single-mode conditions for a GaN/AlxGa1-xN optical rib waveguide. We analyze the optical propagation properties and loss characteristics of the designed waveguides. The analysis illustrates that optical power increases with an increase of the rib width or a decrease of the slab height. Therefore, our analysis results can be helpful in the process of designing a GaN-based rib waveguide for optical communications.

A three-wavelength Mach–Zehnder optical demultiplexer by one step ion-exchange in glass

A three-wavelength optical demultiplexer based on Mach–Zehnder interferometer parameters is presented. The combination of the effective index technique based Rung–Kutta method and a finite difference vector beam propagation method (FD-VBPM) provide for a computational design tool that yields useful results. The demultiplexer device is fabricated by a one-step K + ion-exchange in glass. The total device length obtained is 1.49 cm. The measured output light–power extinction ratios for the three wavelengths, 980, 1310 and 1550 nm are 19, 24 and 24 dB, respectively, and agree reasonably well with the FD-VBPM simulation.

Electromagnetic field in a slab of photonic crystal by BPM

The finite-difference vector beam propagation method is used to simulate propagation of Gaussian light beam in a finite slab of photonic crystal. A possibility to control light flow by the change of symmetry and polarisation of the incident light beam is demonstrated.

Investigation of acceleration of a vectorial beam propagation method

Acceleration of a vectorial finite difference beam propagation method is investigated. Several steps, including use of a modified Crank-Nicholson scheme, a decreased initial error, a reduced iteration parameter and a transparent boundary condition, are discussed. The resulting program has a speed fast enough for calculations of intricate structures on a conventional workstation.

An explicit and stable finite difference 2-D vector beam propagation method

The DuFort-Frankel method is used to replace the Crank-Nicolson method in a two-dimensional finite-difference vector beam propagation method (VBPM). This new method is explicit, stable, and very efficient, and is particularly good for adaptation in a three dimensional finite-difference VBPM.

An improved finite-difference vector beam propagation formulation for graded-index waveguides

An improved finite-difference vector beam propagation formulation for graded-index waveguides is presented. The modification over the existing version involves a more accurate representation of the Fresnel operator in finite-difference form that accounts for the gradient of the refractive index in the vector Hehmholtz equation. The modified scheme is assessed by calculating the TM mode propagation constants of single-mode planar guides that yield better agreement to the exact values over the existing scheme. Furthermore, the calculated coupling lengths of a vertical directional coupler show improved comparison to experimental data.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Fast three-dimensional split-step algorithm for vectorial wave propagation in integrated optics

An efficient split-step modification of the finite-difference vector beam propagation methods (BPM) based on transverse magnetic fields is presented. Two substeps are introduced by separately treating and alternating the transverse directions, resulting in a tridiagonal system matrix. The novel scheme reduces calculation effort considerably by maintaining accuracy. To demonstrate this, a circular test structure is chosen of which the exact modal field solution is known. In addition, performance of the algorithm is illustrated by launching a linear polarized Gaussian field into a buried rectangular waveguide where the generation of a stationary field distribution is observed during the propagation process.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Efficient and accurate vector mode calculations by beam propagation method

An in-depth study of the beam propagation method for the vector mode calculation of optical waveguides is presented. It is established that the imaginary-distance propagation method may be generalized to vectorial modes for arbitrary structures by combining it with the finite-difference vector beam propagation method (FD-VBPM). A simple, unified theory and analysis are developed. An assessment of the accuracy and efficiency is carried out by comparing the simulated results with the analytical solutions for well-known structures.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>