Full-vectorial Beam Propagation Method Research Articles

Chirally-coupled-ring fibers for arbitrary-order orbital angular momentum mode generation and detection.

A novel chirally-coupled-ring fiber (CCRF) is proposed for efficiently generating and detecting arbitrary-order orbital angular momentum (OAM) modes in ring-core fibers (RCFs). The CCRF comprises inner and outer cores, N angularly uniformly distributed dielectric rods, and a cladding layer. These rods, twisted along the fiber axis between the cores, introduce angular geometry perturbations to manipulate the core modes. Through meticulous theoretical modeling and systematic analysis grounded in coupled-mode theory, we reveal CCRF eigenmodes carrying spin-entangled OAM, elucidate the mode coupling and power transfer in CCRFs, and present the CCRF design principle. Utilizing the full-vector beam propagation method, we carry out a proof-of-principle experimental system to demonstrate the capability of CCRFs in OAM mode manipulation and their feasibility and superiority in system-level applications. Additionally, we generate OAM modes across a wide range of topological charges from ℓ = -8 to ℓ = 8 using CCRFs, with conversion efficiencies from 92.10% to 99.63% and mode purities from 90.28% to 99.48%. Attributed to a coaxial dual-core structure with core-separated geometry perturbations, CCRFs enable flexible manipulation of arbitrary-order OAM modes without altering core geometry parameters, effectively solving design flexibility and compatibility problems in conventional single-core fiber devices. The proposed CCRF holds great promise for fiber-based OAM applications, especially for RCF-based OAM multiplexing communications.

A Compact Polarization MMI Combiner Using Silicon Slot-Waveguide Structures.

The study of designing a compact transverse electric (TE)/transverse magnetic (TM) polarization multimode interference (MMI) combiner based on silicon slot-waveguide technology is proposed for solving the high demands for high-speed ability alongside more energy power and minimizing the environmental impact of power consumption, achieving a balance between high-speed performance and energy efficiency has become an important consideration in an optical communication system. The MMI coupler has a significant difference in light coupling (beat-length) for TM and TE at 1550 nm wavelength. By controlling the light propagation mechanism inside the MMI coupler, a lower order of mode can be obtained which can lead to a shorter device. The polarization combiner was solved using the full-vectorial beam propagation method (FV-BPM), and the main geometrical parameters were analyzed using Matlab codes. Results show that after a short light propagation of 16.15 μm, the device can function as TM or TE combiner polarization with an excellent extinction ratio of 10.94 dB for TE mode and 13.08 dB for TM mode with low insertion losses of 0.76 dB (TE) and 0.56 dB (TM) and the combiner function well over the C-band spectrum. The polarization combiner also has a robust MMI coupler length tolerance of 400 nm. These attributes make it a good candidate for using this proposed device in photonic integrated circuits for improving power ability at the transmitter system.

Combining Four Gaussian Lasers Using Silicon Nitride MMI Slot Waveguide Structure.

Transceivers that function under a high-speed rate (over 200 Gb/s) need to have more optical power ability to overcome the power losses which is a reason for using a larger RF line connected to a Mach–Zehnder modulator for obtaining high data bitrate communication. One option to solve this problem is to use a complex laser with a power of over 100 milliwatts. However, this option can be complicated for a photonic chip circuit due to the high cost and nonlinear effects, which can increase the system noise. Therefore, we propose a better solution to increase the power level using a 4 × 1 power combiner which is based on multimode interference (MMI) using a silicon nitride (Si3N4) slot waveguide structure. The combiner was solved using the full-vectorial beam propagation method (FV-BPM), and the key parameters were analyzed using Matlab script codes. Results show that the combiner can function well over the O-band spectrum with high combiner efficiency of at least 98.2% after a short light coupling propagation of 28.78 μm. This new study shows how it is possible to obtain a transverse electric mode solution for four Gaussian coherent sources using Si3N4 slot waveguide technology. Furthermore, the back reflection (BR) was solved using a finite difference time-domain method, and the result shows a low BR of 40.15 dB. This new technology can be utilized for combining multiple coherent sources that work with a photonic chip at the O-band range.

O-Band Multimode Interference Coupler Power Combiner Using Slot-Waveguide Structures

Photonic transmitters that operate with a high data transfer rate (over 150 Gb/s) at the O-band range (1260–1360 nm) require at least 100 milliwatts of power to overcome the power losses that are caused by using high-speed modulators. A laser with higher power can probably handle this requirement; however, for the transmitter system, this solution can be problematic due to the nonlinear effects that can happen, which may lead to high noise in the transmitter system. Thus, to solve this issue, we propose a new design of a 2 × 1 multimode interference (MMI) power combiner using silicon nitride (SiN) slot waveguide structures. The MMI power combiner and the SiN slot waveguide structures were optimized using the full-vectorial beam propagation method (FV-BPM) and the finite difference time domain (FDTD) method. After combining two sources, high efficiency was obtained of 94.8–97.6% from the total power after a short coupling length of 109.81 µm over the O-band range with a low back reflection of 44.94 dB. Thus, the proposed device can be very useful for combining two O-band sources to gain a higher power level, which can be utilized to improve performances in transmitter systems.

A four green-light demultiplexer using a multi gallium nitride slot-waveguide structure

In this work, we introduce a four green-light wavelength splitter device, based on six slot-waveguide structures. Silica and gallium nitride materials were chosen for confining the green light inside the slot-waveguide area in a transverse magnetic field mode. The device functioned as a 1 × 4 demultiplexer, which demultiplexes wavelengths in the green-light band with wavelength range of 500–530 nm with an accurate spacing of 10 nm. The coupling between the six slot-waveguide units was analyzed using the classical mode theory and the full vectorial beam propagation method. Simulation results showed that the four wavelengths could be demultiplexed after a short coupling length of 106.5 μm with low losses around 0.108–0.127 dB, full width at half maximum around 8.99–9.39 nm, and excellent crosstalk around −21.13 to −24.1 dB. The device has the potential to increase data bitrate by utilizing the wavelength division multiplexing technique in visible light communication systems.

A Four Green TM/Red TE Demultiplexer Based on Multi Slot-Waveguide Structures.

A four green transverse magnetic (TM)/red transverse electric (TE) light wavelength demultiplexer device, based on multi slot-waveguide (SW) structures is demonstrated. The device aims to demultiplex wavelengths in the green/red light range with wavelengths of 530, 540, 550, and 560 nm; 630, 640, 650, and 660 nm. This means that the device functions as a 1 × 4 demultiplexer for each polarization mode (TE/TM). The controlling of the light switching between two closer segment SWs under the TM/TE polarization mode was studied by designing a suitable SW structure and setting the right segment length to fit the coupling lengths of the operating wavelengths. The device is composed of six-segment SW units and six S-bends (SB) SW. The key SW and SB parameters were optimized and determined by a full vectorial beam propagation method (FV-BPM). Results show power losses better than 0.138 dB, crosstalk better than −21.14 dB, and an optical spectrum smaller than 9.39 nm, with an overall compact size of 104.5 µm. The device can be integrated in wavelength division multiplexing (WDM) for increasing data bit rate in a visible light communication (VLC) system.

An ultracompact 3×1 MMI power-combiner based on Si slot-waveguide structures

Today, photonic integrated circuits (PIC) that work with a high-modulation speed (100Gb/s and beyond) are required to use more optical power to overcome the losses. One solution is to use a high-level laser with a hundred milliwatts power. However, for a microchip circuit, this solution can be problematic due to the nonlinear effects and high cost. Therefore, to solve this issue, we propose a new design of a 3×1 multimode interference (MMI) power combiner based on a slot waveguide structure that can utilize slot-waveguide technology for reducing losses. In this study, the full-vectorial beam propagation method (FV-BPM) was used to find the optimal geometrical parameters of the MMI coupler, inputs/output taper, and the slot waveguide structure. Simulation results show that after light propagation of 9.82 μm the beam combiner efficiency can reach 97.6 % working within the C-band range. Also, to reduce back reflection losses an angled MMI was designed using a finite difference time domain (FDTD) method and results show a low back reflection of 40 dB. This unique design can lead to an efficient and compact combiner for multiple coherent sources that work with PIC chips.

Efficient Shape and Topology Optimization Based on Sensitivity Analysis for Optical Waveguide Devices Utilizing Full-Vectorial BPM

We present a new design approach of shape and topology optimization utilizing the full-vectorial beam propagation method (FV-BPM) so as to achieve efficient design for high-refractive-index contrast optical waveguides and devices based on gradual mode-evolution. In our design approach, material distribution is represented via normalized density parameters, and these design parameters are updated with sensitivity computed based on an adjoint variable method (AVM). The sensitivity analysis method and the design procedure are offered in the specific case where the density method, the AVM, and the FV-BPM based on an alternative direction implicit method (AIDM) are employed. The applicability of our design approach is numerically studied by designing high-refractive-index contrast photonic components which induce polarization rotation: a TM0-to-TE1 mode order converter and a polarization rotator. The results of the design examples indicate that our approach has potential to be suitable for efficient initial design of optical devices based on gradual mode-evolution.

Design of Power-Splitter With Selectable Splitting-Ratio Using Angled and Cascaded MMI-Coupler

A concept of power splitter with selectable splitting-ratios is proposed based on two multimode interference (MMI) sections connected by a phase-shifting region, in which phase-matching conditions can be fulfilled by using a simple angled section or alternatively using matched phase-shifters. The design example of an asymmetrical splitter (10:90) is optimized by using the transfer matrix method and 3-D full-vectorial beam propagation method. The numerical results reveal that a simple 1.2° angled section can yield a 10:90 splitter with an insertion loss of 0.74 dB and a total length of $192~\mu \text{m}$ . It is also shown that, for the cascaded MMI couplers-based splitter, a more compact length of $58~\mu \text{m}$ with a lower insertion loss of 0.41 dB can be achieved. The fabrication tolerances are also investigated for the proposed asymmetrical power splitter.

Study on High Precision and Stable Finite Element Beam Propagation Method Based on Incomplete Third Order Hybrid Edge/Nodal Element

It has been reported that the full vectorial finite element beam propagation method (FV-FE-BPM) is not always stable. In this paper, we propose a stabilized FV-FE-BPM using a linear filter to suppress unstable modes. Moreover, aiming for improving the computational accuracy of FV-FE-BPM for longitudinally varying optical waveguides, we employ incomplete third order hybrid edge/nodal elements to reduce interpolation error which occurs in finite element mesh update process at each propagation step. The validity and effectiveness of this approach are verified through several numerical examples of uniform waveguides and longitudinally varying waveguides.

Full-Vector Finite-Element Beam Propagation Method for Helicoidal Waveguides and Its Application to Twisted Photonic Crystal Fibers

A full-vector beam propagation method based on a finite-element scheme for a helicoidal system is developed. The permittivity and permeability tensors of a straight waveguide are replaced with equivalent ones for a helicoidal system, obtained by transformation optics. A cylindrical, perfectly matched layer is implemented for the absorbing boundary condition. To treat wide-angle beam propagation, a second-order differentiation term with respect to the propagation direction is directly discretized without using a conventional Pade approximation. The transmission spectra of twisted photonic crystal fibers are thoroughly investigated, and it is found that the diameters of the air holes greatly affect the spectra. The calculated results are in good agreement with the recently reported measured results, showing the validity and usefulness of the method developed here.

Design of novel SOI 1 × 4 optical power splitter using seven horizontally slotted waveguides

In this paper, we demonstrate a compact silicon on insulator (SOI) 1×4 optical power splitter using seven horizontal slotted waveguides. Aluminum nitride (AIN) surrounded by silicon (Si) was used to confine the optical field in the slot region. All of the power analysis has been done in transverse magnetic (TM) polarization mode and a compact optical power splitter as short as 14.5μm was demonstrated. The splitter was designed by using full vectorial beam propagation method (FV-BPM) simulations. Numerical investigations show that this device can work across the whole C-band (1530–1565nm) with excess loss better than 0.23dB.

An 8-Channel Wavelength MMI Demultiplexer in Slot Waveguide Structures.

We propose a novel 8-channel wavelength multimode interference (MMI) demultiplexer in slot waveguide structures that operate at 1530 nm, 1535 nm, 1540 nm, 1545 nm, 1550 nm, 1555 nm, 1560 nm, and 1565 nm. Gallium nitride (GaN) surrounded by silicon (Si) was found to be a suitable material for the slot-waveguide structures. The proposed device was designed by seven 1 × 2 MMI couplers, fourteen S-bands, and one input taper. Numerical investigations were carried out on the geometrical parameters using a full vectorial-beam propagation method (FV-BPM). Simulation results show that the proposed device can transmit 8-channel that works in the whole C-band (1530–1565 nm) with low crosstalk (−19.97–−13.77 dB) and bandwidth (1.8–3.6 nm). Thus, the device can be very useful in optical networking systems that work on dense wavelength division multiplexing (DWDM) technology.

All fiber M-Z interferometer for high temperature sensing based on a hetero-structured cladding solid-core photonic bandgap fiber.

We proposed and experimentally demonstrated a high temperature fiber sensor using a hetero-structured cladding solid-core photonic bandgap fiber (HCSC-PBGF) for the first time to our knowledge. A hetero-structured cladding solid-core photonic bandgap fiber is designed and fabricated that supports vibrant core mode and cladding mode transmission. Then, an all fiber M-Z interference sensor is constructed by splicing single mode fiber at both ends of HCSC-PBGF without any other micromachining. The transmission characteristics of HCSC-PBGF are analyzed with a full-vector beam propagation method and a full-vector finite element method, and the simulation results are consistent with experiment results. The sensitivity of this fiber sensor is as high as 0.09 nm/°C when operating from room temperature to 1000 °C, and the fringe contrast keeps stable and clear. It is obvious that this all fiber sensor will have great application prospects in fiber sensing with the advantages of a compact structure, high sensitivity, and cost-effectiveness.

Ultrabroadband polarization splitter based on three-core photonic crystal fiber with a modulation core.

We design an ultrabroadband polarization splitter based on three-core photonic crystal fiber (PCF). A modulation core and two fluorine-doped cores are introduced to achieve an ultrawide bandwidth. The properties of three-core PCF are modeled by using the full-vector finite element method along with the full-vector beam propagation method. Numerical results demonstrate that an ultrabroadband splitter with 320 nm bandwidth with an extinction ratio as low as -20 dB can be achieved by using 52.8 mm long three-core PCF. This splitter also has high compatibility with standard single-mode fibers as the input and output ports due to low splicing loss of 0.02 dB. All the air holes in the proposed structure are circular holes and arranged in a triangular lattice that makes it easy to fabricate.

A Photonic 1 × 4 Power Splitter Based on Multimode Interference in Silicon-Gallium-Nitride Slot Waveguide Structures.

In this paper, a design for a 1 × 4 optical power splitter based on the multimode interference (MMI) coupler in a silicon (Si)–gallium nitride (GaN) slot waveguide structure is presented—to our knowledge, for the first time. Si and GaN were found as suitable materials for the slot waveguide structure. Numerical optimizations were carried out on the device parameters using the full vectorial-beam propagation method (FV-BPM). Simulation results show that the proposed device can be useful to divide optical signal energy uniformly in the C-band range (1530–1565 nm) into four output ports with low insertion losses (0.07 dB).

Ultra‐compact liquid crystal dual core photonic crystal fibre multiplexer–demultiplexer

In this study, the authors propose a novel design of ultra-compact multiplexer–demultiplexer (MUX–DEMUX) based on silica photonic crystal fibre coupler. The suggested design has two large holes infiltrated with nematic liquid crystal of type E7. The reported MUX–DEMUX has short device length of 436 µm with low crosstalk better than −20 dB with bandwidths of 35 and 10 nm around operating wavelength of 1.3 and 1.55 μm, respectively. The simulation results are obtained using full-vectorial finite-difference method together with full-vectorial beam propagation method.

Mode conversion in magneto-optic rib waveguide made by silica matrix doped with magnetic nanoparticles

The TE-TM mode conversion is an important requirement for magneto-optical waveguide devices. It has been analyzed by means of a full-vectorial beam propagation method. The present work is based on the study of the influence of diagonal and off-diagonal elements of the complex dielectric tensor on the conversion efficiency in magneto-optical rib waveguide. We have found that in the presence of the absorption (taking into account the imaginary part of diagonal tensor) the conversion efficiency is affected by the absorption and these latter increases as the volume fraction of nanoparticles increases.

Design of an InGaAsP/InP compact integrated optical depolarizer

In this paper, we propose and demonstrate two integrated optics InGaAsP/InP depolarizer circuits. The first one is based on the Lyot depolarizer configuration, while the second one is based on the Mach-Zehnder configuration. Detailed simulation, using three-dimensional full vectorial beam propagation method, shows that a high-index contrast material allows the design of a compact polarization insensitive depolarizer. For the first design, an output degree of polarization (DOP) less than 0.1 is obtained for light sources with spectral widths larger than 25nm, while for the second one, output DOP less than 0.06 is obtained for light sources with spectral widths larger than 40nm.

Design of a low cost and high sensitivity sensor for curve measurement

In the dual-core optical fiber, the two beams are launched into two cores simultaneously, the solution of coupled mode equations is derived. It is shown that the slight change of the refractive index can affect the coupling between the cores, which causes the change of power of two cores. Based on this idea, the low-cost, high-sensitivity curve sensor based on the dual-core optical fiber is proposed. Numerical simulations with a full vectorial beam propagation method demonstrate that it allows highly accurate curve angle detection. The sensitivity of the curve sensor can reach 1.1405mW/deg. Moreover, by optimizing the pitch and choosing the different propagation direction and the output power of light source, we can obtain the higher sensitivity.