Finite Difference Beam Propagation Method Research Articles

Planar and Channel Waveguide Structures in CdS Crystals at 633 and 1539 nm

We report on the fabrication and optical properties of planar and channel waveguides in a CdS crystal using a C ion implantation technique combined with a standard photolithographic technique. The prism-coupling and the end-face coupling methods separately measure the guiding modes and the near-field intensity distribution of the light at 633 and 1539 nm. The refractive index profiles of the planar and channel waveguides are reconstructed at 633 and 1539 nm. The finite difference beam propagation method is used to simulate the guided mode profiles. There is excellent agreement between the measured and simulated modes at 633 and 1539 nm.

Finite-Difference Beam Propagation Method for Graphene-Based Devices

We propose a novel finite-difference beam propagation method capable of dealing with the discontinuity of the tangential component of the magnetic field induced by bi-dimensional graphene layers, which can be arbitrarily placed within dielectric media. In stark contrast with conventional numerical solvers, this approach does not require a discretization step as small as a fraction of the atomic thickness of graphene, allowing ultrafast simulation times. The validity of the method is proved by propagating the plasmonic supermodes of two coupled graphene layers, and the evaluated beat length exhibits excellent agreement with respect to analytical results.

Oxygen-implanted optical planar waveguides in Er3+/Yb3+-codoped silicate glasses for integrated laser generation

Er 3+ /Yb 3+ -codoped silicate glasses are good candidates for the application of laser actions and signal amplification. Optical planar waveguides in Er 3+ /Yb 3+ -codoped silicate glasses are fabricated by 6.0-MeV oxygen-ion implantation with a dose of 6.0×10 14 ions/cm 2 at room temperature. The SRIM 2010 code is carried out to simulate the energy losses during the implantation process in order to obtain a better understanding of the waveguide formation. The guiding modes and near-field intensity distributions of the waveguide are characterized by the prism-coupling and end-face coupling methods. The refractive index profile and light propagation mode of the planar waveguide are numerically calculated by the reflectivity calculation method and finite difference beam propagation method. The waveguide has a “well+barrier ” refractive index distribution and its optical loss is ∼1.02 dB/cm . The microluminescence and absorption investigation reveal that fluorescent and transmission properties in the waveguide are well preserved with respect to the bulk, suggesting promising potential for waveguide amplifiers and lasers.

To analyse the performance of tapered and MMI assisted splitter on the basis of geographical parameters

A literal model using geometric examination was formulated to calculate the optimum width and length of multimode interference structure used in the 1×2 power splitter and plot electric field intensity for input and each output signal. Designing and simulation of the wavelength response of 1×2 splitter using Tapered and MMI assisted structure. Mechanism on the critical geographical parameters like length and width of MMI structure, separation distance between output ports ‘S’, arm angle ‘α’ which give the optimum power and electric field intensity for the considered necessary wavelength. Finite difference beam propagation methods have been used to simulate the conventional and tapered MMI device behaviour.

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.

Cylindrical beam propagation modelling of perturbed whispering-gallery mode microcavities

We simulate light propagation in perturbed whispering-gallery mode microcavities using a two-dimensional finite-difference beam propagation method in a cylindrical coordinate system. Optical properties of whispering-gallery microcavities perturbed by polystyrene nanobeads are investigated through this formulation. The light perturbation as well as quality factor degradation arising from cavity ellipticity are also studied.

Coherent beam combination of fiber lasers with a strongly confined tapered self-imaging waveguide: theoretical modeling and simulation

Coherent beam combination (CBC) of fiber lasers based on self-imaging properties of a strongly confined tapered waveguide (SCTW) is studied systematically. Analytical formulas are derived for the positions, amplitudes, and phases of the N self-images at the output of a SCTW, which are important for quantitative analysis of waveguide-based CBC. The formulas are verified with numerical examples by a finite difference beam propagation method (FDBPM) and the errors of the analytical expressions are studied. This study shows that the analytical formulas agree well with the FDBPM simulation results when the taper angle is less than 1.4° and the phase distortion is less than λ/10. The relative errors increase as the taper angle increases. Based on the theoretical model and the FDBPM, we simulated the CBC of fiber laser array and compared the CBC based on the tapered waveguide with that based on the nontapered one. The effects of input beam number, aperture fill factor, and taper angle on the combination performance have been studied. The study reveals that a beam which has near-diffraction limited beam quality (M2≤1.41) and a single beam without side lobe in the far field can be achieved with tapered-waveguide-based CBC. It is shown that beam quality depends on input beam number, aperture fill factor, and taper angle. There exists a best fill factor which will increase as input beam number increases. The tolerance of the system on the fill factor and the taper angle is studied, which is 0.45<t<0.67 and θ<0.8°, respectively. The results may be useful for practical, high-power fiber laser systems.

Optimized design of a new three branch optical waveguide

A new type of 1×3 Y-branch optical waveguide structure with a cone transitional section is introduced in this paper. The symmetrical branch ratio of the 1×3 Y branch optical waveguide is obtained by changing the width of this waveguide. The loss and the uniformity are obtained by using the finite difference beam propagation methods, and their values are 0.2dB and 0.05dB, respectively. Therefore, it provides some experimental basis for production of three branch optical waveguide.

Characterization of Strongly Coupled Si-Wire Waveguides for High-Density Optical WDM and Sensing Applications

This paper presents theoretical and experimental study of ultra-compact Si-wire Optical Directional Couplers (ODCs) on Silicon-on-Insulator wafer for optical signal processing. The presence of the controllable evanescent light strongly confined in the region bounded by the Si nano-wires has a large impact on the optical power coupling between waveguides. The characteristics of coupling length and power transmission in ODCs based on separation, wavelength, light field propagation distance and geometry of waveguides are described in detail by the coupled mode theory, 3-D finite-difference time-domain analysis and beam propagation method, and are confirmed by experiments. The exponential dependency of coupling length on the separation of coupled waveguides and wavelength shows interesting high-sensitivity optical sensing, switching and multiplexing properties. Custom spectral properties can be achieved by the configuration of coupled nano-wire waveguides based on their separation and lengths. We show that optimization of ODCs based on the physics of the coupled waveguides will lead to short optical devices which can be integrated as building blocks within high-density photonic circuits with the desired spectral characteristics. In the end, two new systems based on Mach-Zehnder structure and Micro-Ring Resonators are proposed in which ODCs are implemented as embedded tunable devices resulting in more functional optical sensing and signal processing devices.

Optical self-switching based on a semiconductor-optical-amplifier-assisted Sagnac interferometer

The self-switching mechanism in a Sagnac interferometer is studied numerically. A new structure of a semiconductor-optical-amplifier (SOA)-based Sagnac interferometer self-switch (SISS) is presented. For analyzing the switching characteristics of the structure, an improved finite-difference beam propagation method is utilized to study counterpropagation pulses in the SOA. All intraband nonlinear gain compression effects in the SOA that have not been considered simultaneously in previous Sagnac switches are considered. The effects of structural and input pulse parameters on the SISS operation are analyzed. Simulation results determine the optimum condition for the maximum switching output power.

TEMPORAL AND SPECTRAL ANALYSIS FOR MID-INFRARED FOUR-WAVE MIXING IN QUANTUM INTERSUBBAND STRUCTURE

We design a quantum cascade (QC) intersubband structure for four-wave mixing (FWM) generation from In 0.53 Ga 0.47 As / In 0.52 Al 0.48 As in the mid-infrared spectral region which can be described by third-order nonlinear optical susceptibility. In this structure, increasing FWM is accomplished by band engineering which modify energy of subbands. To analyze FWM characteristics in a QC structure, the evolution in time and spectral domain of pump and probe input optical pulses with different frequencies during propagation is calculated and simulated by using finite-difference beam propagation method. Central frequencies of pump and probe pulses which are used for driving the amplifier are 37.97 THz and 32.61 THz, respectively. Third order susceptibility responsible for FWM resonance nonlinearity of the structure is enhanced by two orders of magnitude. As power of input pulses rises, the value of the FWM output signal increases but the pulse loses its initial shape. Gain saturation and dispersion play a major role in shaping the output pulse. Results reveal that the FWM optical pulse characteristics are highly sensitive to the pulse power and QC parameters in the time and frequency domains.

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.

Planar waveguide structure formed on Nd:YVO4 by Kr8+ ion irradiation at ultralow fluences

We report on the fabrication of a planar waveguide structure on Nd:YVO4 laser crystal. The waveguide structure was formed by Kr8+ ion irradiation with energy of 30MeV at fluences of 2×1012cm−2. The guiding modes of the planar waveguide were measured by the prism-coupling method at wavelengths of 633nm and 1539nm. The reflectivity calculation method (RCM) was used to reconstruct the refractive index profiles. Relatively large positive changes in the ordinary refractive index occur in the waveguide region. The refractive index profile of the planar waveguide was a typical “well”+“barrier” distribution, and we used the finite-difference beam propagation method (FD-BPM) to simulate light propagation in the waveguide. Using the Stopping and Range of Ions in Matter (SRIM 2008) software, the energy loss during ion irradiation was simulated to obtain a better understanding of the formation of the waveguide structure. The investigation of the absorption bands demonstrated that the transmission properties of the bulk Nd:YVO4 crystal have been preserved after ion irradiation.

Estimation of the performance of a 3-dB Y-junction optical coupler with a channel profile of proton-exchanged lithium niobate

A 3-dB optical coupler (power splitter) based on a Y-junction waveguide with a channel profile of proton-exchanged lithium niobate has been modeled. Finite difference beam propagation method has been used to investigate light wave propagation in axially varying waveguides. It is found that the structure splits the input power equally at the Y-junction with an efficiency of 99% and an average excess loss ⩽0.04 dB. The novelty of the coupling structure proposed is its capability to function as a wavelength-independent 3-dB coupler while maintaining very low-power imbalance for widespread optical communication wavelengths of 1.3 and 1.55 µm.

Nanometer-Scale SOI Based Y-Branch Couplers for High Density Optical Integrated Circuits

SOI Ridge nanowire waveguide (RNW) has advantages of strong confinement of optical mode, low propagation loss, small bend radius and fully compatible with CMOS technique, etc. An ultra-compact Y-branch coupler based on SOI RNW was designed and fabricated. Based on the finite-difference beam propagation method (FD-BPM), key parameters of the coupler were analyzed. Then the device was fabricated by electron beam lithography (EBL) and inductively coupled plasma (ICP) reactive ion etching. Results showed that the propagation loss of RNW was 1.89 dB/mm, and the radiation loss of the coupler with branch angle of 30° was only 0.66 dB. Compared with traditional Y-branch coupler, the proposed structure were more promising for high density optical integrated circuits.

Investigation of LPG-SPR sensors using the finite element method and eigenmode expansion method

As compared to the well-known traditional couple-mode theory, in this study, we proposed a visual, graphical, and simple numerical simulation method for long-period fiber-grating surface-plasmon-resonance (LPG-SPR) sensors. This method combines the finite element method and the eigenmode expansion method. The finite element method was used to solve for the guided modes in fiber structures, including the surface plasmon wave. The eigenmode expansion method was used to calculate the power transfer phenomenon of the guided modes in the fiber structure. This study provides a detailed explanation of the key reasons why the periodic structure of long-period fiber-grating (LPG) can achieve significantly superior results for our method compared to those obtained using other numerical methods, such as the finite-difference time-domain and beam propagation methods. All existing numerical simulation methods focus on large-sized periodic components; only the method established in this study has 3D design and analysis capabilities. In addition, unlike the offset phenomenon of the design wavelength λ(D) and the maximum transmission wavelength λ(max) of the traditional coupled-mode theory, the method established in this study has rapid scanning LPG period capabilities. Therefore, during the initial component design process, only the operating wavelength must be set to ensure that the maximum transmission wavelength of the final product is accurate to the original setup, for example, λ = 1550 nm. We verified that the LPG-SPR sensor designed in this study provides a resolution of ~-45 dB and a sensitivity of ~27000 nm/RIU (refractive index unit). The objective of this study was to use the combination of these two numerical simulation methods in conjunction with a rigorous, simple, and complete design process to provide a graphical and simplistic simulation technique that reduces the learning time and professional threshold required for research and applications of LPG-SPR sensors.

Analysis of Connection Loss for a GI Waveguide Based Optical Link Using the Finite Difference Beam Propagation Method

The connection loss which occurs when light transfers from one medium to another attracts additional attention in high-speed and low-power optical links. In this paper, we not only experimentally apply graded index polymer optical waveguide (GI-POW) in the optical link, but also theoretically address some key parameters which largely influence on the connection loss. The experimental setup of this optical link is composed of a VCSEL module, a GI polymer optical waveguide for the transmitter side (WGTx), a GI multimode fiber (GI-MMF), a GI polymer optical waveguide for the receiver side (WGRx), and a detector. We assume that WGTx is launched by a single mode fiber and then measure the connection losses at the interface between any two components. The results show the connection loss between the GI-MMF and the WGRx is approximately 0.4 dB higher than that of the WGTx to the GI-MMF. For the theoretical modeling, we start from the fundamental scalar wave equation, and apply the finite difference beam propagation method (FD-BPM) to simulate the behavior of light inside the waveguide. Furthermore, Fresnel reflection between two media and the scattering effect within polymer optical waveguides are also taken into account. The simulated results show a similar trend to the measured values. Finally, we conclude that the scattering effect could be one of the key issues of GI-POW for maintaining low connection losses with other wave guides and fibers.

Designing LPG-OADM Based on a Finite Element Method and an Eigenmode Expansion Method

This study proposes a visual, graphical, and simplistic numerical simulation method for a long period fiber gratings optical add-drop multiplexer (LPG-OADM), as opposed to the well-known traditional mode-coupled theory. This method combines the finite element method and the eigenmode expansion method, where the finite element method is used to solve all existing guided modes. The eigenmode expansion method was used to calculate the energy transfer phenomenon of the guided modes in the LPG-OADM. This study provides a detailed explanation of the key reasons why the periodic structure of the LPG-OADM can achieve significantly superior results for our method compared to those obtained using other numerical methods, such as the finite-difference time-domain and beam propagation methods. All existing numerical simulation methods focus on large-sized periodic components; only the method established in this study has 3-D design and analysis capabilities. This study used actual examples to verify that, under the operating wavelength of λ = 1550 nm, the LPG-OADM designed using this method would have the full-width half-maximum of 0.2846 nm, and an insertion loss and homo-dyne crosstalk of nearly 0. That is, the LPG-OADM designed using this method can reach the ITU specification for the dense wavelength-division multiplexer bandwidth. The primary objective of this study is to use the combination of these two numerical simulation methods in conjunction with a rigorous, simple, and comprehensive design flow to provide a graphical and simplistic simulation technique that reduces the learning time and professional threshold requirements for the design and application of LPG-OADM.

Enhanced four-wave mixing in quantum cascade semiconductor optical amplifier

We designed a quantum cascade semiconductor optical amplifier (QCSOA) structure for enhanced four-wave mixing (FWM) of short optical pulses in midinfrared. To analyze FWM characteristics in a QCSOA, the evolution in the time and spectral domains of two input optical pulses with different frequencies during propagation is calculated using the finite-difference beam propagation method. Calculated third-order susceptibility responsible for FWM resonance nonlinearity of the modified structure is enhanced by two orders of magnitude. Simulation results reveal that quantum cascade structure parameters and injected pump and probe powers are extremely important in determining the amplified FWM optical pulse characteristics in both the time and frequency domains.

Demonstration and optimisation of an ultrafast all-optical AND logic gate using four-wave mixing in a semiconductor optical amplifier

We have proposed an all-optical AND logic gate based on four-wave mixing (FWM) in a semiconductor optical amplifier (SOA) integrated with an optical filter. In the scheme proposed, the preferred logical function can be performed without using a continuous-wave (cw) signal. The modified nonlinear Schrödinger equation (MNLSE) is used for the modelling wave propagation in a SOA. The MNLSE takes into account all nonlinear effects relevant to pico- and sub-picosecond pulse durations and is solved by the finite-difference beam-propagation method (FD-BPM). Based on the simulation results, the optimal output signal with a 40-fJ energy can be obtained at a bit rate of 50 Gb s-1. In the simulations, besides the nonlinearities included in the model, the pattern effect of the signals propagating in the SOA medium and the effect of the input signal bit rate are extensively investigated to optimise the system performance.