Wide-angle Beam Propagation Research Articles

Multiple-pathways light modulation in Pleurosigma strigosum bi-raphid diatom.

Ordered, quasi-ordered, and even disordered nanostructures can be identified as constituent components of several protists, plants and animals, making possible an efficient manipulation of light for intra- and inter- species communication, camouflage, or for the enhancement of primary production. Diatoms are ubiquitous unicellular microalgae inhabiting all the aquatic environments on Earth. They developed, through tens of millions of years of evolution, ultrastructured silica cell walls, the frustules, able to handle optical radiation through multiple diffractive, refractive, and wave-guiding processes, possibly at the basis of their high photosynthetic efficiency. In this study, we employed a range of imaging, spectroscopic and numerical techniques (including transmission imaging, digital holography, photoluminescence spectroscopy, and numerical simulations based on wide-angle beam propagation method) to identify and describe different mechanisms by which Pleurosigma strigosum frustules can modulate optical radiation of different spectral content. Finally, we correlated the optical response of the frustule to the interaction with light in living, individual cells within their aquatic environment following various irradiation treatments. The obtained results demonstrate the favorable transmission of photosynthetic active radiation inside the cell compared to potentially detrimental ultraviolet radiation.

Physics-based multistep beam propagation in inhomogeneous birefringent media.

We present a unified theoretical framework for paraxial and wide-angle beam propagation methods in inhomogeneous birefringent media based on a minimal set of physical assumptions. The advantage of our schemes is that they are based on differential operators with a clear physical interpretation and easy numerical implementation based on sparse matrices. We demonstrate the validity of our schemes on three simple two-dimensional birefringent systems and introduce an example of application on complex three-dimensional systems by showing that topological solitons in frustrated cholesteric liquid-crystals can be used as light waveguides.

Ultrahigh sensitivity with different taper geometries of thin-core fiber modal interferometer for refractive index sensing

A highly sensitive refractive index sensor based on a fiber in-line Mach–Zehnder interferometer sensor based on single-mode–tapered thin-core–single-mode fiber is proposed. We developed a theoretical model using wide-angle beam propagation method in cylindrical coordinates to simulate light propagation performance of such fiber devices. Tapered structures using different taper geometries (linear, exponential, and parabolic taper) with waist diameters as low as 30 μm are presented. The proposed sensor has an ultrahigh sensitivity of 996.4 nm/refractive index unit in glycerin solution with different concentrations in water using the linear taper geometry. The designed structure presents the merits of high sensitivity, which is 6 times higher than that of the thin-core fiber modal interferometer and makes it an excellent candidate for biochemical sensing applications.

Utilizing multimode interference effects in integrated graded-index optical waveguides for efficient power splitting

PurposeFor the realization of optical waveguide components, needed for photonic integrated circuits, multimode-interference based (MMI-based) devices are an excellent component class for the realization of low loss optical splitters. A promising approach to the manufacturing of these components is their embedding in thin glass sheets by ion-exchange diffusion processes, which has not yet been extensively studied. This study aims to significantly enhance the modeling of the diffusion process to support manufacturing of graded-index, MMI-based optical splitters.Design/methodology/approachThe methods of design and analysis of MMI-based components are based on a step-index refractive index profile. In this work, fundamental correlations between the properties of the manufacturing ion-exchange process and the characteristics of the graded-index, MMI-based components are established. The refractive index profile is calculated with a proprietary solver based on the finite element method. Any further investigation with respect to parameter influence is based on the beam propagation method, specifically a finite difference based, semi-vectorial, wide-angle beam propagation algorithm. The influence of the parameters of the self-imaging effect is investigated. On this basis, different approaches for efficient power splitting with graded-index, MMI-based waveguide components are evaluated.FindingsEasy approximations – mostly linear – can be found to model the dependencies of the investigated parameters. The resulting graded-index splitters are characterized by their low excess and insertion loss.Originality/valueThese findings are the first step in the direction of the semi-analytical modeling of the respective waveguide components to reduce the numerical effort.

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.

Competitiveness of the BPM in studying the optical beams at critical incidence on dielectric interfaces

We investigate the usefulness of the wide-angle Fast Fourier Transform-based beam propagation method (FFT-BPM) to investigate important and quite involved problems in the propagation of optical beams. The incident transverse electric (TE) and transverse magnetic (TM) optical beams at the critical angle on a dielectric interface are investigated. Major numerical difficulties associated with the singularity of the transverse derivative of the step-like refractive index at the interface plane (for the TM case) are circumvented via an “equivalent-index” formalism. An arc-tangent function is used to approximate the abrupt change of the refractive index at the interface, such that the singular derivative is eliminated, and the TM problem is transformed to an equivalent TE one with no singular behavior. Further, the propagation of a rectangular incident pulse on an interface at the critical angle is also studied. In this investigation, the large shift of the lateral field and the standing wave pattern resulting from the incident and reflected fields are investigated and justified by simple calculations. A new phenomenon, called “spatial transient” is discussed, concerning the substantial spatial evolution of the pulse over very short propagation distance (fraction of the wavelength). Finally, a parametric study of a plasmonic-type sensor in the Kretschmann configuration is presented using the proposed FFT-BPM to ensure its validity in studying such subwavelength-based phenomenon.

An Efficient 3-D Semivectorial Horizontally Wide-Angle Beam-Propagation Method

An efficient 3-D semivectorial horizontally wide-angle beam-propagation method (WA-BPM) based on the alternating direction implicit (ADI) scheme is proposed, where only the paraxial term in the vertical direction is considered. The present formulation reduces the splitting error to the second order and shows good compatibility with previously developed WA-BPMs. A block matrix decomposition process and a simulation window-cutting scheme are utilized to further improve the efficiency of the WA-BPM. Then, by applying Pade approximation to the resulting operator, an efficient ADI scheme that can be solved by the Thomas algorithm is constructed. Alternatively, the resulting operator can be approximated by the Denman–Beavers iterative scheme, leading to an ADI scheme with faster convergence rate and reasonable efficiency. Results from several numerical examples show the effectiveness of the present WA-BPM.

A Locally Modal B-Spline Based Full-Vector Finite-Element Method with PML for Nonlinear and Lossy Plasmonic Waveguide

AbstractIn this paper, we develop a B-spline finite-element method (FEM) based on a locally modal wave propagation with anisotropic perfectly matched layers (PMLs), for the first time, to simulate nonlinear and lossy plasmonic waveguides. Conventional approaches like beam propagation method, inherently omit the wave spectrum and do not provide physical insight into nonlinear modes especially in the plasmonic applications, where nonlinear modes are constructed by linear modes with very close propagation constant quantities. Our locally modal B-spline finite element method (LMBS-FEM) does not suffer from the weakness of the conventional approaches. To validate our method, first, propagation of wave for various kinds of linear, nonlinear, lossless and lossy materials of metal-insulator plasmonic structures are simulated using LMBS-FEM in MATLAB and the comparisons are made with FEM-BPM module of COMSOL Multiphysics simulator and B-spline finite-element finite-difference wide angle beam propagation method (BSFEFD-WABPM). The comparisons show that not only our developed numerical approach is computationally more accurate and efficient than conventional approaches but also it provides physical insight into the nonlinear nature of the propagation modes.

A Wide-Angle Beam Propagation Method Using Denman–Beavers Iterative Scheme

A new algorithm for the wide-angle beam propagation method (BPM) is proposed, where the propagation propagator in the Helmholtz equation is approximated by the Denman-Beavers iterative scheme. By rotating the propagator into the complex plane, the generally concerned problem, incorrect evolution of the evanescent waves, in the conventional BPM is well solved, greatly improving the computational stability and convergent behaviors. Numerical results from several typical tests show that the present approach has reasonable efficiency and high accuracy with the convergence rate faster than the widely used Pade-based BPM.

Focal properties of an underwater acoustic Fresnel zone plate lens

Fresnel zone plate (FZP) lenses provide thin alternatives to conventionally sized acoustic lenses. We present experimental characterization of an underwater acoustic FZP lens fabricated at the Naval Research Laboratory. This diffractive lens has a short focal length (numerical aperture angle of θ = 62°) which provides a narrow focal spot with a diffraction limited first-null radius 0.61λ/sinθ. The 13 in diameter FZP consists of opaque rubber foam rings attached to a thin PDMS rubber substrate. Ultrasonic measurements of transmission were made using a scanning needle hydrophone and a 200 kHz piston source. Measured focal gain varied between 20 and 15 dB for incidence angles between 0 and 12°, respectively. These gains agreed with predictions computed using a wide-angle beam propagation method. Measured transverse focal shift agreed with geometrical constructions used in conventional lens theory. Axisymmetric finite-element computations using Fourier decomposition of the oblique incident field are also pres...

A reflective fiber-optic refractive index sensor based on multimode interference in a coreless silica fiber

A reflective fiber-optic refractive index (RI) sensor based on multimode interference (MMI) is presented and investigated in this paper. The sensor is made by splicing a small section of coreless silica fiber (CSF) to the standard single mode fiber (SMF). A wide-angle beam propagation method (WA-BPM) is employed for numerical simulation and design of the proposed RI sensor. Based on the simulation results, a RI sensor with a length of 1.7cm of CSF is fabricated and experimentally studied. Experimental results show that the characteristic wavelength shift has an approximately linear relationship with the RI of the sample. A sensitivity of 141nm/RIU (refractive index unit) and a resolution of 2.8×10−5 are obtained in the RI range from 1.33 to 1.38. As the RI value is higher than 1.38, the sensitivity of the sensor increase rapidly as the RI increase and a maximum sensitivity of 1561nm/RIU can be achieved, corresponding to a resolution of 2.6×10−6. The experimental results fit well with the numerical simulation results.

Fourier Expansion of the Beam Propagation Operator in the Eigenvalue Domain

Propagation methods in the frequency domain are powerful tools for the analysis of electromagnetic field propagation within photonic waveguide devices. They can be classified as wide angle beam propagation or eigenvector expansion methods. In comparison to the wide angle beam propagation methods, eigenvector expansion methods inherently include an accurate computation of radiation waves, guided modes, and evanescent waves. Common numerical methods rely on the solution of eigenvalue problems or the solution of matrix equations of high order. Consequently, the computation time needed can be tedious. A method is proposed, which exploits the inherent advantage of eigenvector expansion methods, but reduces the computation time considerably as the resulting propagation algorithm is based on simple matrix vector multiplications, allowing a large number of discretization points. The method takes advantage of the compact eigenvalue spectrum of the system matrix. The operator can be periodically expanded so that a Fourier decomposition can be applied. The expansion is carried out under consideration of the physical interpretation of eigenvalues for radiation waves, guided modes, and evanescent waves.

A Novel Finite Element Method Based Beam Propagation Method without Using Slow Varying Envelope Approximation

A novel finite element method (FEM) based wide-angle (WA) beam propagation method (BPM) was presented whereby the scalar Helmholtz equation was solved without using the slow varying envelope approximation (SVEA) and was more general and precise than the previous well-known WA-BPM proposed by Hadley. The accuracy of this novel scheme was demonstrated in comparison with the existing approach.

Simulation of spectral stabilization of high-power broad-area edge emitting semiconductor lasers

The simulation of spectral stabilization of broad-area edge-emitting semiconductor diode lasers is presented in this paper. In the reported model light-, temperature- and charge carrier-distributions are solved iteratively in frequency domain for transverse slices along the semiconductor heterostructure using wide-angle finite-difference beam propagation. Depending on the operating current the laser characteristics are evaluated numerically, including near- and far-field patterns of the astigmatic laser beam, optical output power and the emission spectra, with central wavelength and spectral width. The focus of the model lies on the prediction of influences on the spectrum and power characteristics by frequency selective feedback from external optical resonators. Results for the free running and the spectrally stabilized diode are presented.

Nonlinear wide-angle beam propagation method using complex Jacobi iteration in the Fourier domain

An alternative wide-angle beam propagation method (WA-BPM) using a reformulated Fourier-based complex Jacobi iterative (CJI) technique for modeling nonlinear Kerr-type optical devices is presented. Making use of basic concepts of relaxation iterative methods, the CJI approach is modified to be incorporated as longitudinal solving strategy in WA-BPMs with transverse discretization schemes based on Fourier decomposition. After explaining the fundamentals of the resultant CJI-WA-BPM in the domain of Fourier coefficients, examples are given to show the significant improvements that are obtained, in terms of convergence rate and runtime, with respect to previous finite difference approaches.

Investigation of single-mode–multimode–single-mode and single-mode–tapered-multimode–single-mode fiber structures and their application for refractive index sensing

All-fiber in-line single-mode—multimode—single-mode (SMS) and single-mode—tapered-multimode—single-mode (STMS) fiber structures are investigated. A wide-angle beam propagation method in cylindrical coordinates is developed and employed for numerical simulations of the light propagation performance of such fiber devices. The effect of strong mode interference on the performance of the devices is studied and verified numerically; results indicate that the proposed STMS structure can be exploited for measuring a broad refractive index range with reasonable high resolution, compared with the conventional SMS structure.

Optimization design for polymeric S-shaped ridge waveguide

The dispersion characteristics and transverse field distribution of the fundamental and higher order modes are analyzed for polymeric ridge multimode waveguide by a new technique which is based on the combination of the effective index method and the variational method. An algorithm is implemented to study the effect of the structure parameters and dimensions on the dispersion curves. The optical field distribution of the fundamental and higher order modes for TM modes are computed. The single mode conditions of polymeric ridge waveguide are obtained. The relationship between the curvature radius and the bending loss of S-shaped ridge waveguide are studied with wide-angle finite-difference beam propagation method and effective index method. The conclusion is: when the curvature radius is larger than 5000 μm, the bending loss will not decrease distinctly even if the curvature radius increases, and the light can propagate stably in the S-shaped ridge waveguide.

Ultracompact TM-Pass Silicon Nanophotonic Waveguide Polarizer and Design

An ultracompact transverse magnetic (TM)-pass polarizer based on silicon nanophotonic waveguides is proposed, which contains two tapered waveguides sandwiching a narrow waveguide section only supporting TM-mode propagation. A full-vectorial eigenmode solver is employed to determine the appropriate cross section of the silicon nanophotonic waveguide. The device is first designed in a 2-D approximate model using a wide-angle beam propagation method, and numerical verification is carried out afterward using a parallel full-vectorial 3-D finite-difference time-domain simulation. Both approaches indicate that the finite thickness of the buried SiO2 layerand the reflection at the substrate play important roles on the extinction ratio of the device. A designed numerical example shows an extinction ratio of ~26 dB for the waveguide polarizer with a length of ~10 ?m, while the insertion loss for the TM mode is negligible.

Three-dimensional higher-order Padé approximant-based wide-angle beam propagation method using complex Jacobi iteration

Wide-angle scalar beam propagation methods (BPMs) for effective modelling of optical propagation in three-dimensional (3D) waveguides are usually limited to the low-order-accurate Padé(1,1) approximant. Presented is a 3D wide-angle scalar BPM based on higher-order Padé approximant operators which is factored into a series of simpler first-order Padé(1,1) approximants. This results in a multistep method where each step can be cast in terms of a 2D Helmholtz equation with source term, which can be treated accurately and effectively by the new complex Jacobi iterative technique.

Corrections to “Slanted-Wall Beam Propagation”

Recently, a new algorithm for wide-angle beam propagation was reported that allowed grid points to move in an arbitrary fashion between propagation planes and was thus capable of modeling waveguides whose widths or centerlines varied with propagation distance. That algorithm was accurate and stable for TE polarization but unstable for wide-angle TM propagation. This deficiency has been found to result from an omission in one of the wide-angle terms in the derivation of the finite-difference equation and is remedied here, resulting in a complete algorithm accurate for both polarizations.