Full-vectorial finite-difference beam propagation method based on the modified alternating direction implicit method

A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.

Wavelet Beam Propagation Method for Study the Integrated Optical Waveguide

A new numerical technique based on the wavelet derivative operator is presented as an alternative to BPM to study the integrated optical waveguide. The wavelet derivative operator is used instead of FFT/IFFT or finite difference to calculate the derivatives of the transverse variable in the Helmholtz equation. Results of numerically simulating the injected field at z =0 are exhibited with Gaussian distribution in transverse direction propagating through the two dimensional waveguides (with linear and/or nonlinear refractive index) , which are similar to those in the related publications. Consequently it is efficient and needs not absorbing boundary by introducing the interpolation operator during calculating the wavelet derivative operator. The iterative process needs fewer steps to be stable. Also, when the light wave meets the changes of mediums, the wavelet derivative operator has the adaptive property to adjust those changes at the boundaries.

Three-dimensional beam propagation method based on the variable transformed Galerkin's method

A novel three-dimensional beam propagation method (BPM) based on the variable transformed Galerkin's method is introduced for simulating optical field propagation in three-dimensional dielectric structures. The infinite Cartesian x-y plane is mapped into a unit square by a tangent-type function transformation. Consequently, the infinite region problem is converted into the finite region problem. Thus, the boundary truncation is eliminated and the calculation accuracy is promoted. The three-dimensional BPM basic equation is reduced to a set of first-order ordinary differential equations through sinusoidal basis function, which fits arbitrary cladding optical waveguide, then direct solution of the resulting equations by means of the Runge-Kutta method. In addition, the calculation is efficient due to the small matrix derived from the present technique. Both z-invariant and z-variant examples are considered to test both the accuracy and utility of this approach.

An improved three-dimensional full-vectorial finite-difference imaginary-distance beam propagation method

A modified alternating direction implicit approach is proposed to discretize the three-dimensional full-vectorial beam propagation method （3D-FV-BPM） formulation along the longitudinal direction. The cross-coupling terms （CCTs） are neglected at the first substep, and then double used at the second substep. The order of two substeps is reversed for each transverse electric field component so that the CCTs are always expressed in an implicit form, thus the calculation is efficient and stable. Based on the multinomial interpolation, a universal finite difference scheme with a high accuracy is developed to approximate the 3D-FV-BPM formulation along the transverse directions, in which the discontinuities of the normal components of the electric field across the abrupt dielectric interfaces are taken into account and can be applied to both uniform and non-uniform grids. The corresponding imaginary-distance procedure is first applied to a buried rectangular and a GaAs-based deeply-etched rib waveguide. The field patterns and the normalized propagation constants of the fundamental and the first order modes are presented and the hybrid nature of the full-vectorial guided-modes is demonstrated, which shows the validity and utility of the present approach. Then the modal characteristics of the deeply- and shallow-etched rib waveguides based on the InGaAsp/InGaAsP strained multiple quantum wells in InP substrate are investigated in detail. The results are necessary for modeling and the design of the planar lightwave circuits or photonic integrated circuits based on these waveguides.

A Construction of Beam Propagation Methods for Optical Waveguides

This paper presents a systematic method to derive Beam Propagation Models for optical waveguides.The technique is based on the use of the symbolic calculus rules for pseudodifferential operators.The cases of straight and bent optical waveguides are successively considered.

Modified Wide-angle Beam Propagation Method Using Douglas Operators

A modified wide-angle beam propagation based on the Douglas operators is presented.The truncation error in the modified wide-angle beam propagation is reduced to o (Δ x ) 4 in the transverse direction nearly without any increase of the computation time,whereas the error in the ordinary wide-angle beam propagation method is typically o (Δ x ) 2.With trivial programming changes,the accuracy is higher,especially in wide-angle propagation.

Gaussian Beam Propagation in a Kerr Type Metamaterial Medium Using ABCD Matrix Method

In this paper, a split step ABCD matrix method is suggested to investigate Gaussian beam propagation in a Kerr type metamaterial medium. This method is based on dividing the medium interval into subsequent steps.Meanwhile, Gaussian beam profile in every step is obtained by finding the ABCD matrix of that particular step, and is used to find the ABCD matrix of the next step. Results of the suggested matrix method have been compared with the results of numerical split-step Fourier method for a Kerr medium, which indicates a good agreement. Then, we use the ABCD matrix to investigate Gaussian beams propagation in a Kerr type metamaterial, which is also in agreement with pervious results by other methods.

Semi-vectorial analysis of a compact wavelength demultiplexer based on the tapered multimode interference coupler

Based on a parabolically tapered multimode interference （MMI） coupler with a deep-etched SiO2/SiON rib waveguide, a compact wavelength demultiplexer operating at 1.30 and 1.55 μm wavelengths is proposed and analysed by using three-dimensional semi-vectorial finite-difference beam propagation method （3D-SV-FD-BPM）. The results show that a MMI section of 330.0 μm in length, which is only 76% length of a straight MMI coupler, is achieved with the contrasts of 42.3 and 39.2dB in quasi-TE mode, and 38.4 and 37.8dB in quasi-TM mode at wavelengths 1.30 and 1.55μm, respectively, and the insertion losses below 0.2dB at both wavelengths and in both polarization states, The alternating direction implicit algorithm with the Crank-Nicholson scheme is applied to the discretization of the 3D-SV-FD-BPM formulation along the longitudinal direction. Moreover, a modified FD scheme is constructed to approximate the resulting equations along the transverse directions, in which the discontinuities of the derivatives of magnetic field components Hy and Hx along the vertical and horizontal interfaces, respectively, are involved.

Theoretical investigation of band-gap and mode characteristics of anti-resonance guiding photonic crystal fibres

With the full-vector plane-wave method （FVPWM） and the full-vector beam propagation method （FVBPM）, the dependences of the band-gap and mode characteristics on material index and cladding structure parameter in anti- resonance guiding photonic crystal fibres （ARGPCFs） are sufficiently analysed. An ARGPCF operating in the near- infrared wavelength is shown. The influences of the high index cylinders, glass interstitial apexes and silica structure on the characteristics of band-gaps and modes are deeply investigated. The equivalent planar waveguide theory is used for analysing such an ARGPCF filled by the isotropic materials, and the resonance and the anti-resonance characteristics r：~n h~ w~｜] r^r~dlrtpd

Design of novel three port optical gates scheme for the integration of large optical cavity electroabsorption modulators and evanescently-coupled photodiodes

This paper presents a novel scheme to monolithically integrate an evanescently-coupled uni-travelling carrier photodiode with a planar short multimode waveguide structure and a large optical cavity electroabsorption modulator based on a multimode waveguide structure. By simulation, both electroabsorption modulator and photodiode show excellent optical performances. The device can be fabricated with conventional photolithography, reactive ion etching, and chemical wet etching.

Elliptical Gaussian solitons in synthetic nonlocal nonliear media

This paper studies analytically and numerically the dynamics of two-dimensional elliptical Gaussian solitons in a ＂double-self-focusing＂ synthetic nonlocal media featuring elliptical and circular Gaussian response with different degrees of nonlocality. Based on the variational approach, it obtains the approximately analytical solution of such Gaussian elliptical solitons. It also computes the stability of the solitons by numerical simulations.

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.

Effect of interstitial air holes on Bragg gratings in photonic crystal fibre with a Ge-doped core

The effect of interstitial air holes on Bragg gratings in photonic crystal fibre （PCF） with a Ge-doped core is numerically investigated by using the beam propagation method （BPM）. It is shown that the interstitial air holes （IAHs） can make Bragg resonance wavelength λB shift a little towards short wavelengths and increase λB -λ1 （the wavelength spacing between the main peak with Bragg resonance wavelength λB and the first side peak with wavelength λ1） and the coupling coefficient κ of Bragg resonance. Moreover, when the ratio of air hole diameter （d） to pitch （∧）, d/∧, is small, IAHs can suppress the cladding mode resonance. When d/∧ is large, IAHs increase the number of mode that could strongly interact with the fundamental mode. By comparing the transmission spectral characteristics of PCF-based fibre Bragg grating （FBG） with IAHs with those without IAHs at the same air-filling fraction, it is clarified that the change of transmission spectral characteristics of PCF-based FBG with IAHs is not due to a simple change in air-filling fraction. It is also closely related to the distribution of interstitial air holes.

The Notched Filtering Characteristics of Stratified Volume Holographic Grating

Utilizing the tool of beam propagation method (BPM) to calculate the zeroth order diffraction beam intensity, we find SVHG displays notched diffraction response as a function of the readout wavelength. Using the method of SA and considering the variance of refractive index as the readout wavelength changes, a practiced notch filter can be designed and the period of the filter is discussed.

High-performance evanescently-coupled uni-traveling-carrier photodiodes

A new evanescently-coupled uni-traveling-carrier photodiode （EC-UTC PD） based on a multimode diluted waveguide （MDW） structure is fabricated, analysed and characterized. Optical and electrical characteristics of the device are investigated. The excellent characteristics are demonstrated such as a responsivity of 0.36 A/W, a bandwidth of 11.5 GHz and a small-signal 1-dB compression current greater than 18 mA at 10 GHz. The saturation current is significantly improved compared with those of similar evanescently-coupled pin photodiodes. The radio frequency （RF） bandwidth can be further improved by eliminating RF losses induced by the cables, the probe and the bias tee between the photodiode and the spectrum analyzer.

Simulation of Tunable Power Multimode Interference Couplers with Deep Rib Structure

The muhimode interference （MMI） couplers, which operate at 1. 55 microns in deep rib InGaAsP/InP waveguide with large lateral confinement and tunable power splitting ratios, are of high interest in integrated optics. The gold contacts are applied on the top of waveguides where tuning is desired and the plasma effect will lead to negative refractive index change. The three-dimensional （3D） finite difference beam propagation method（FD-BPM） is used to model the tunable MMI couplers. The length of a 2 × 2 overlap-MMI is determined by FD-BPM, so the longitudinal position of tuning spots is obtained. The position of gold contacts with two types, the edge-pads or center-pad, are also determined. In our design, the length of MMI is 180 microns. If the width of pads is 50 microns and the refractive index is tuned from 0 to -0. 027, the power ratio is tuned from 50 ： 50 to the maximum 88.5 ： 11.4. For deep rib structure, the effective index（EI） method can not be used to simplify the 3D waveguide to plane waveguide because of its lower precision, and so the direct 3D FD-BPM simulation is necessary for the design of 3D MMI couplers.

Study and Design of Spiral Bent Waveguide Configuration

A new version of the scalar transverse electric(TE) wave equation in the bent waveguide is introduced. Then, TE polarized field in curved single-mode waveguides is analyzed by using the finite-difference beam propagation method(FD-BPM). The bending loss in bent waveguides is gotten for the optical fields obtained from BPM and comparisons are made among losses of the waveguides with various curvature radiuses, refractive index differences and cross sections. Based on the results, the design of spiral bent waveguide configuration is proposed as follows: refractive index difference being of 0.007, both width and thickness of waveguides being of 6 μm, the curvature radius in the spiral centre being of 4 mm, and the bending loss coefficient of the designed spiral bent waveguide being of 0.302 3 dB/cm.

Numerical Spectral Model Based on BPMfor Er-doped Waveguide Amplifiers

A spectral numerical analysis method to analyze the Er-doped waveguide amplifiers(EDWA) in wavelength division multiplexing is presented. This model is based on finite difference beam propagation method modified by Douglas scheme, which can efficiently reduce the truncation error and time consumption. By superposing the Lorentzian function for the experimental curves, the spectral properties of EDWA can be investigated. Results show that the pump efficiency of EDWA pumped at 980nm is higher than that at 1480nm. Meanwhile, by rationally increasing the pump length and the erbium concentration, larger signal gains can be acquired. Taking account of the up-conversion and cross-relaxation effects of cooperation, the spectrum analysis of highly doped EDWA is carried out over a wider frequency band.

Some Techniques for Computing Wave Propagation in Optical Waveguides

Optical wave-guiding structures that are non-uniform in the propagation direction are fundamental building blocks of integrated optical circuits.Numerical simulation of lightwaves propagating in these structures is an essential tool to engineers designing photonic components.In this paper,we review recent developments in the most widely used simulation methods for frequency domain propagation problems.

Incoherently coupled spatial soliton families in biased two-photon photorefractive crystals with both the linear and quadratic electro-optic effect

Different from the cases discussed preciously, nonlinear changes of refractive index in the photorefractive materials are influenced by both the linear and quadratic electro-optic effect simultaneously now. Here we present the evolution equations of one-dimension incoherently coupled spatial soliton families due to two-photon effect in biased photorefractive crystals with both the linear and quadratic electro-optic effect and discuss their existence conditions and properties in detail. Our analysis indicates that these soliton families can exist in all three possible realizations： dark-dark, bright-bright and dark-bright provided that the incident beams have the same polarization, wavelength and are mutually incoherent. Finally, the stabilities of these soliton families have been discussed by means of beam propagation methods.