Full-vectorial Beam Propagation Method Research Articles

Design of a 1 × 4 silicon-alumina wavelength demultiplexer based on multimode interference in slot waveguide structures

In this paper we present 1 × 4 wavelength demultiplexer operating at 1.4 μm, 1.45 μm, 1.5 μm and 1.55 μm wavelengths, based on multimode interference (MMI) coupler in slot waveguide structure. Alumina was used as the slot material. The design is based on three cascaded 1 × 2 MMI demultiplexers. Tapered waveguide structures are being in the input/output of the MMI section, for reducing the excess loss. Since the slot waveguide encompasses true guided modes, confined by total internal reflections, there are no noticeable confinement losses. Full vectorial-beam propagation method (FV-BPM) and BPM simulations were used for optimizing the device parameters and assessing its performance. To the best of our knowledge it is the first time that a 1 × 4 demultiplexer is being implemented by a slot waveguide based MMI.

Calculation of coupling length for spatial waveguides using planar waveguides

A simple method to calculate the coupling length of the spatial waveguides is presented in this paper. Spatial waveguides with same center–center separation space and different center–center vertical and horizontal distances are studied using the field matching method. The analysis results indicate that the coupling length strongly depends on the center–center separation space. Therefore, the coupling length of spatial waveguides can be calculated using the existing formula for planar waveguides. The proposed method is verified using the three-dimensional full-vector beam propagation method.

Silicon Optical Modulators Based on Tunable Plasmonic Directional Couplers

For the development of Si-based next generation electronic-photonic integrated circuits, a silicon optical modulator is designed based on tunable plasmonic directional couplers. The characteristics are investigated using numerical simulations with a full-vectorial beam propagation method. The center waveguide in the three-core coupler is a MOS-type hybrid plasmonic waveguide that consists of a Si-ITO-SiO2-Si structure. By electrically tuning the ITO's refractive index, the coupling efficiency of the directional coupler is switchable and, hence, we can obtain modulated optical signals at the outer waveguide, which is configured with a vertical offset. The extinction ratios are 6.7 and 2.3 dB at 1.31- and 1.55-μm wavelength, respectively. The optical modulator can be transformed into a plasmonic absorption modulator based on a two-core directional coupler at the cost of a long coupling length. The proposed silicon optical modulator has the potential to play a key role in complementary metal-oxide-semiconductor-compatible 3-D silicon photonic integrated circuits.

Numerical analysis of pump propagation and absorption in specially tailored double-clad rare-earth doped fiber

We present a numerical analysis of multi-mode pump absorption in recently proposed double-clad fiber with stadium-like cross section of the inner cladding and asymmetrically placed rare-earth doped core. Such a cross section allows easy splicing of the multi-mode pump fiber and single-mode signal fiber to the double-clad fiber. The full-vector finite element beam propagation method was used as a numerical tool. In order to allow excitation of the structure by arbitrary field profile, definite set of functionals satisfying unisolvence condition together with hybrid edge-nodal finite element basis was derived. The flat-top field profile and more realistic speckle pattern were considered in the analysis. The effect of coiling and simultaneous twisting of the fiber was taken into account. It was found that the twisting of the DC fiber significantly improves the pump absorption.

Fiber-laser monolithic coherent beam combiner based on multicore photonic crystal fiber

A monolithic coherent combiner scheme for combining multiple fiber lasers based on a photonic crystal fiber is described. Beam propagation method (BPM) simulations show that the beam combiner efficiency can reach 96% for a 4×1 combiner, 94% for an 8×1 combiner, and 91% for a 16×1 combiner, provided the fiber lasers are phase matched. In addition, a 2×1 intensity polarization combiner is proposed and simulated through full vectorial BPM, yielding a combining efficiency of 95%. This concept can lead to a rugged and efficient combiner for multiple fiber lasers.

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.

Realization of a broadband terahertz wavelength-selective coupling based on five-core fibers

We propose a novel kind of wavelength-selective coupling for the terahertz range based on solid five-core fiber (FCF). The performances of coupling, propagation characteristics, and confinement loss properties are numerically investigated by using a full vector beam propagation method (BPM). Simulation results show that it is possible to realize a broadband wavelength-selective coupling. The coupling length can reach 1.913 cm, and the confinement loss is better than 1.965 × 10−4 cm−1. Furthermore, a parameter, the power difference, is defined, and it numerically demonstrates the working performance of the wavelength-selective coupler; that is, when the power difference is better than − 15 dB, the frequency located in the range of 0.76 THz–1.00 THz is separated relatively well from the frequency of 0.3 THz. Finally, the effect of the structural parameter on the working performance of the coupler is also investigated. We show that the performance optimization is possible by appropriately tuning the core diameter, and the tunabilities of frequency and bandwidth are possible by appropriately tuning the pitch. The wavelength-selective coupler is of potential application for optical fiber sensing and communication in terahertz wavelength division multiplexer fields.

CMOS-Compatible Polarization Splitter for 3-D Silicon Photonic Integrated Circuits

To achieve intra-chip three-dimensional (3-D) integration of silicon photonic circuits, we design a polarization beam splitter based on complementary metal-oxide-semiconductor (CMOS) platform. With the aid of the polarization-dependent nature of the center waveguide in a three-port directional coupler, the device separates the TM- and TE-polarization modes onto different layers of 3-D silicon photonic circuits. Numerical simulations with a full vectorial beam propagation method exhibit that we can obtain a 10 μm-long polarization splitter with extinction ratio better than 20 dB on the entire C-band. The optical device without the vertical offset can serve as a horizontal polarization splitter with nearly the same optical characteristics. We conclude that the proposed polarization beam splitter is compatible not only with the CMOS structure but also with the CMOS fabrication process.

Symmetric Few-Mode Fiber Couplers as the Key Component for Broadband Mode Multiplexing

All-fiber broadband mode multiplexers (MMUXs) for mode and wavelength division multiplexing transmission systems are designed and analyzed. The MMUXs are based on cascaded 2-D or 3-D symmetric few-mode fiber (FMF) couplers. The MMUXs are optimized for operation over the C band and multiplex modes LP $_{01}$ , LP $_{11a}$ , LP $_{11b}$ , LP $_{21a}$ , LP $_{21b}$ , and LP $_{02}$ with a nearly flat response and an average insertion loss around 1.6 dB, depending on the design approach. The operation of the FMF couplers and the MMUXs is analyzed numerically by means of a full-vectorial beam propagation method. If the two polarization states of each LP mode are further considered, such all-fiber MMUXs can be used to combine 12 spatial channels, supporting an order of magnitude capacity increase—compared to a single spatial channel system—in optical fiber transmission systems through space (mode and polarization) division multiplexing.

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.

Design of a compact polarization splitter composed of a multiple-slotted waveguide and a silicon nanowire

A polarization splitter (PS) based on a directional coupler (DC) composed of a vertical multiple-slotted waveguide (MSW) and a silicon nanowire is proposed and designed by using a modified three-dimensional full-vectorial beam propagation method (BPM). By utilizing the unique modal properties of the slotted waveguide, the coupling of the DC in quasi-TE modes can be almost neglected, and only that in quasi-TM modes is considered, leading to a compact PS. Moreover, the MSW has the advantages of both strong field confinement and high birefringence, which improve the performance of the device. The numerical results show that a PS with a length of 20.5 μm in the coupling region is achieved with a bandwidth of up to 22 nm (ranging from 1.540 to 1.562 μm) with the crosstalk lower than −20 dB. In addition, the fabrication tolerances for the structural parameters are investigated in detail. The evolution of the injected field along the propagation distance through the PS is also demonstrated.

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%.

Simplified Algorithms for the Full-Vectorial ADI-BPM Using a Fundamental Scheme

A fundamental scheme is utilized to efficiently implement the full-vectorial alternating-direction implicit beam-propagation method (ADI-BPM). In the conventional ADI-BPM, four coupled Fresnel equations contain eight derivatives in the right-hand sides (RHSs): four for a specific polarization and four for a polarization coupling. Introduction of the fundamental scheme leads to derivative-free forms for the specific polarization in the RHSs, where only the four mixed derivatives for the polarization coupling are calculated. This results in the computation time reduced by 20%. For further simplification, two out of the four mixed derivatives are replaced with auxiliary variables, where only the remaining two mixed derivatives are taken into account in the RHSs. This reduces the computation time by 34%, with the equivalence to the conventional method.

Design of a transverse electric–pass/transverse magnetic–splitting three-guide directional coupler composed of two slot waveguides and one silicon wire

A three-guide directional coupler composed of two slot waveguides and one silicon wire with a function of transverse electric (TE)-pass/transverse magnetic (TM)-splitting is proposed and designed using a modified 3-D full-vectorial beam propagation method. In our design, quasi-TE modes fed in the middle silicon wire pass through without coupling, whereas quasi-TM modes fed in the same channel are evenly split into the outer slot waveguides. With properly chosen parameters, a TE-pass/TM-splitting directional coupler with a length of 22.6 μm, including the straight coupling region and the S-bends, is achieved with the crosstalk of −31 and −35 dB for quasi-TE and quasi-TM modes, respectively. In addition, the tolerances to the structural parameters and operating wavelength are also investigated in detail.

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%.

The characteristics of the polarization beam splitters based on micro/nano optical fiber

The characteristics of the polarization coupling of two micro/nano optical fibers that are closed to each other were investigated by three dimension full vector beam propagation method(3D FVBPM).The analytical results of their characteristics of the polarization coupling show that a polarization beam splitter(PBS) based on coupled micro/nano optical fiber can be constructed.Considering the polarization splitting performance of the component,the geometric parameters of the PBS,such as the diameter of micro/nano optical fiber and the gap between them are optimized.The optimal parameters are as follows:the diameter of about 0.9 μm,the gap of about 0.5 μm and the length of 218 μm.Numerical simulations show that we can acquire fabrication tolerances for the polarization splitter at a wavelength of 1 550 nm when the extinction ratio of polarization of both output ports of the splitter are larger than 15 dB,such as a bandwidth of about 10 nm,overlapping length of ±2 μm,and about-3～2 nm for the diameter and gap respectively.

Modeling of Nonlinear Beam Propagation in Chiral Nematic Liquid Crystals

In this work three dimensional full-vector beam propagation method derived directly from Maxwell equations and combined with the exact equations describing director reorientation are presented. Molecules reorientation model bases on the Frank-Oseen equation with two angles (twist and azimuthal) describing molecule orientation. Solutions of light propagation in chiral nematic liquid crystals for different input beam polarization are shown. Formation of a soliton-like beam which has been already observed in many experiments is analyzed. Comparison between two-angle model and one-angle model assuming reorientation in a single plane is also provided.

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.

Terahertz switch and polarization controller based on photonic crystal fiber

Theoretical studies on liquid crystal filled photonic crystal fiber (LC-PCF) are presented. The effects of electric birefringence of liquid crystal (LC) in the LC-PCF and the transmitting properties of photonic crystal fiber (PCF) are investigated by using the full vector plane wave expansion and beam propagation method. The simulation results show that the electrically controlled LC-PCF can act as not only a terahertz (THz) switch with about 0.55 THz bandwidth, but also a tunable polarization controller for changing the polarization state of the fundamental mode.

A search-and-track algorithm for controlling the number of guided modes of planar optical waveguides with arbitrary refractive index profiles

A search-and-track algorithm is proposed for controlling the number of guided modes of planar optical waveguides with arbitrary refractive index profiles. The algorithm starts with an initial guess point in the parameter space that supports a specific number of guided modes. Then, it searches for, and tracks, the boundaries of this space or another space supporting different number of modes. It does so by monitoring the sign of a unified cutoff dispersion function. The algorithm is applied to both symmetric and asymmetric silicon-based parabolic-index waveguides. It shows that unlike asymmetric waveguides, the single-mode condition of symmetric waveguides is controlled by TM-, as opposed to TE-, polarization. This abnormal polarization control is strongest for high index contrast waveguides of sub-micrometer core sizes. The results are verified by full-vectorial beam propagation method.