Beam Propagation Algorithm Research Articles

Theoretical investigation on the effective coupling optical system between an astigmatic tapered diode laser beam and single-mode optical fibers

In this study, we theoretically investigate the coupling efficiency of tapered diode lasers to single-mode fibers in four different coupling systems using an astigmatic beam propagation algorithm. The fast-axis lens and slow-axis lens have been used to mitigate astigmatism, which is a characteristic of the tapered diode laser and then the beam coupling into different single-mode fibers. Designers should carefully balance the pursuit of high coupling efficiency with the need to minimize astigmatism sensitivity in the design of coupling systems.

Efficient light propagation algorithm using quantum computers

Quantum algorithms can potentially overcome the boundary of computationally hard problems. One of the cornerstones in modern optics is the beam propagation algorithm, facilitating the calculation of how waves with a particular dispersion relation propagate in time and space. This algorithm solves the wave propagation equation by Fourier transformation, multiplication with a transfer function, and subsequent back transformation. This transfer function is determined from the respective dispersion relation, which can often be expanded as a polynomial. In the case of paraxial wave propagation in free space or picosecond pulse propagation, this expansion can be truncated after the quadratic term. The classical solution to the wave propagation requires O(NlogN) computation steps, where N is the number of points into which the wave function is discretized. Here, we show that the propagation can be performed as a quantum algorithm with OlogN2 single-controlled phase gates, indicating exponentially reduced computational complexity. We herein demonstrate this quantum beam propagation method (QBPM) and perform such propagation in both one- and two-dimensional systems for the double-slit experiment and Gaussian beam propagation. We highlight the importance of the selection of suitable observables to retain the quantum advantage in the face of the statistical nature of the quantum measurement process, which leads to sampling errors that do not exist in classical solutions.

Mechanisms of Spontaneous and Amplified Spontaneous Emission in CH3NH3PbI3 Perovskite Thin Films Integrated in an Optical Waveguide

In this paper, the physical mechanisms responsible for optical gain in ${\mathrm{CH}}_{3}{\mathrm{NH}}_{3}{\mathrm{Pb}\mathrm{I}}_{3}$ (MAPI) polycrystalline thin films are investigated experimentally and theoretically. Waveguide structures composed by a MAPI film embedded in between PMMA and silica layers are used as an efficient geometry to confine emitted light in MAPI films and minimize the energy threshold for amplified spontaneous emission (ASE). We show that photogenerated exciton density at the ASE threshold is as low as $(2.4\ensuremath{-}12)\ifmmode\times\else\texttimes\fi{}{10}^{16}\phantom{\rule{0.1em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$, which is below the Mott transition density reported for this material and the threshold transparency condition deduced with the free-carrier model. Such a low threshold indicates that the formation of excitons plays an important role in the generation of optical gain in MAPI films. The rate-equation model including gain is incorporated into a beam-propagation algorithm to describe waveguided spontaneous emission and ASE in MAPI films, while using the optical parameters experimentally determined in this work. This model is a useful tool to design active photonic devices based on MAPI and other metal-halide semiconductors.

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.

Design of Optical Directional Couplers Made of Polydimethysiloxane Liquid Crystal Channel Waveguides

We present numerical simulations of a directional coupler based on three-dimensional waveguides made of a nematic liquid crystal, acting as the waveguide core, infiltrated in polydimethysiloxane channels. Modeling is based on the combination of minimization of Oseen-Frank energy of the liquid crystal molecules with a beam propagation algorithm. Design of the coupler waveguides is optimized to minimize coupling lengths and maximise efficiencies. Such components can be made at low cost on flexible plastic substrates and can be also integrated with optofluidic devices for biomedical applications.

Stability analysis of FD-BPM applied in high power semiconductor laser models

We perform a stability analysis of the Crank-Nicolson based finite difference beam propagation algorithm for a medium with a complex refractive index distribution. We use typical waveguide parameters that correspond to an InGaAs–AlGaAs epitaxy. The results show that selecting the fundamental mode propagation constant as the BPM reference value, even though it allows reducing the errors, makes the FD-BPM scheme unstable when attempting to retrace the propagation.

Observation of the Gouy phase anomaly in astigmatic beams

The Gouy phase anomaly, well established for stigmatic beams, is validated here for astigmatic beams. We simulate the predicted Gouy phase anomaly near astigmatic foci using a beam propagation algorithm integrated within lens design software. We then compare computational results with experimental data acquired using a modified Mertz-Sagnac interferometer. Both in simulation and in experiment, results show that a π/2-phase change occurs as the beam passes through each of the astigmatic foci, experimentally validating results derived in a recent paper by Visser and Wolf [Opt. Commun. 283, 3371-3375 (2010)].

Finite element optical modeling of liquid crystal waveguides

A finite element modesolver and beam propagation (BPM) algorithm are applied to the optical analysis of liquid crystal waveguides. Both approaches are used in combination with advanced liquid crystal calculations and include a full dielectric tensor in solving the Helmholtz equation to model the liquid crystal behavior properly. Simulation of the beam propagation in a waveguide with tunable liquid crystal cladding layer illustrates the coupling of a Gaussian beam to the fundamental waveguide mode obtained with the modesolver. Excellent quantitative agreement between both approaches illustrates the potential of these methods for the design of advanced devices. The high accuracy of the BPM algorithm for wide angle propagation, essential in the analysis of high index contrast waveguides, is illustrated for angles up to 40 deg.

Nonparaxial Split-Step Method With Local One-Dimensional Scheme for Three-Dimensional Wide-Angle Beam Propagation

A wide-angle, split-step finite-difference method with the classical local one-dimensional scheme is presented to analyze the three-dimensional scalar wave equation. Its essence is to convert the three-dimensional scalar wave equation into two two-dimensional equations that can be solved without using slowly varying envelope or one-way propagation approximations. To validate the effectiveness, numerical results for the Gaussian beam propagation in vacuum and the eigen-mode propagation in tilted step-index channel waveguide are compared with other beam propagation algorithms. Results show that the method has high accuracy and numerical efficiency compared with other known split-step methods. The perfectly matched layer boundary condition can be implemented easily.

Focus on software

Focus on software

A Novel Three-Dimensional Wide-Angle Beam Propagation Method Based on Split-Step Fast Fourier Transform

A novel three-dimensional wide-angle beam propagation method based on the split-step fast Fourier transform is developed. The formulation is based on the three-dimensional Helmholtz wave equation. Each propagation step is performed by utilizing both the FFT and split-step scheme. The solution of Helmholtz wave equation does not make the slowly varying envelope and one-way propagation approximations. To validate the efficiency and accuracy, numerical results for a propagation beam in a tilted step-index optical waveguide are compared with other beam propagation algorithms.

Generalized rectangular finite difference beam propagation method

A method is proposed that allows for significant improvement of the numerical efficiency of the standard finite difference beam propagation algorithm. The advantages of the proposed method derive from the fact that it allows for an arbitrary selection of the preferred direction of propagation. It is demonstrated that such flexibility is particularly useful when studying the properties of obliquely propagating optical beams. The results obtained show that the proposed method achieves the same level of accuracy as the standard finite difference beam propagation method but with lower order Padé approximations and a coarser finite difference mesh.

Coupling and cross-talk effects in 12-15 μm diameter single-mode fiber arrays for simultaneous transmission and photon collection from scattering media

We examine signal degradation effects in fiber arrays from fiber-to-fiber coupling and from cross talk attributable to backscatter from the sample medium originating from adjacent fibers in the array. An analysis of coupling and cross talk for single-mode fibers (SMFs) operating at 1310 nm with different core diameters, interaction lengths, core center spacing, and numerical apertures (NAs) is evaluated. The coupling was evaluated using beam propagation algorithms and cross talk was analyzed by using Monte Carlo methods. Several multimode fiber types that are currently used in fiber image guides were also evaluated for comparative purposes. The analysis shows that an optimum NA and core diameter can be found for a specific fiber center separation that maximizes the directly backscattered signal relative to the cross talk. The coupling between fibers can be kept less than -35 dB for interaction lengths less than 5 mm. The calculations were compared to an experimentally fabricated SMF array with 15 microm center spacing and showed good agreement. The experimental fiber array without a lens was also used in a coherent detection configuration to measure the position of a mirror. Accurate depth ranging up to a distance of 250 microm from the tip of the fiber was achieved, which was five times the Rayleigh range of the beam emitted from the fiber.

Non-proximity resonant tunneling in multi-core photonic band gap fibers: An efficient mechanism for engineering highly-selective ultra-narrow band pass splitters

The objective of the present investigation is to demonstrate the possibility of designing compact ultra-narrow band-pass filters based on the phenomenon of non-proximity resonant tunneling in multi-core photonic band gap fibers (PBGFs). The proposed PBGF consists of three identical air-cores separated by two defected air-holes which act as highly-selective resonators. With a fine adjustment of the design parameters associated with the resonant-air-holes, phase matching at two distinct wavelengths can be achieved, thus enabling very narrow-band resonant directional coupling between the input and the two output cores. The validation of the proposed design is ensured with an accurate PBGF analysis based on finite element modal and beam propagation algorithms. Typical characteristics of the proposed device over a single polarization are: reasonable short coupling length of 2.7 mm, dual bandpass transmission response at wavelengths of 1.339 and 1.357 mum, with corresponding full width at half maximum bandwidths of 1.2 nm and 1.1 nm respectively, and a relatively high transmission of 95% at the exact resonance wavelengths. The proposed ultra-narrow band-pass filter can be employed in various applications such as all-fiber bandpass/bandstop filtering and resonant sensors.

A novel wide-angle beam propagation method based on the spectral collocation scheme for computing titled waveguides

A multidomain spectral collocation beam propagation method that uses an oblique coordinate transformation is proposed for analyzing a beam propagating in dielectric optical waveguides. Relying on the high accuracy of spectral collocation scheme in transverse discretization, the proposed method achieves extremely small power loss (<10/sup -4/, for the tilt angle of a tilted waveguide up to 20/spl deg/) but considerably save the computational resources. Furthermore, by means of introducing the oblique coordinate system, not only is a significant difficulty arising from staircased approximation of refractive index completely avoided, but the implementation of the present scheme becomes easier. To validate the effectiveness, numerical results for propagating beam in a tilted step-index optical waveguide are compared with other beam propagation algorithms.

The nonunitarity of finite-element beam propagation algorithms

We examine the intrinsic nonunitarity of one-way finite-element propagation techniques in order to clarify the results of previous authors.

A closed-form solution for wave propagation in optical waveguides of longitudinally invariant structures without using beam propagation algorithm

In this paper, we propose a different method to study wave propagation in longitudinally invariant waveguides with arbitrary index profile. In our method, both the electric field and the refractive index profile are expanded into two Fourier cosine series. With these series substituted into the wave equation, a differential matrix equation can then be obtained. We show here that such a matrix equation can be solved and an explicit expression for the wave field at any longitudinal position along an optical waveguide can be obtained. The solution proposed in this method can thus exclude the use of the beam propagation algorithm. This study demonstrates that our approach yields the same results as those obtained by using commercial softwares in which a beam propagation method with the Padé approximation is used.

Design of narrow band-pass filters based on the resonant-tunneling phenomenon in multi-core photonic crystal fibers

The objective of the present paper is to introduce and numerically demonstrate the operation of a novel band-pass filter based on the phenomenon of resonant tunneling inmulti-core photonic crystal fibers (PCFs). The proposed PCF consists of two identical cores separated by a third one which acts as a resonator. With a fine adjustment of the design parameters associated with the resonant-core, phase matching at a single wavelength can be achieved, thus enabling very narrow-band resonant directional coupling between the input and the output cores. The validation of the design is ensured with an accurate PCF analysis based on finite element and beam propagation algorithms. The proposed narrow band-pass filter can be employed in various applications such as all fiber and pass/bandstop filtering.

Impact of exposure induced refractive index changes of photoresists on the photolithographic process

In many commercial and noncommercial photoresists the real and the imaginary parts of the refractive index are changed during exposure. Using a finite-difference beam-propagation algorithm, we analyze the impact of these nonlinear optical effects on the photolithographic process. Changes of the real part of the refractive index have a considerable impact on dose latitudes, sidewalls, swing curves, iso-dense bias and other process parameters. These effects become more dominant as the thickness of the resist layer increases.

Determining reflections for beam propagation algorithms

Reflections occur whenever different waveguide sections are concatenated. In this paper, we will give approximate formulas for determining the reflection coefficient. Starting with generalized transmission line equations we will derive general formulas where suitable approximations are introduced. These approximations allow the determination of the reflections with low numerical effort. The expressions were implemented in an FD-BPM algorithm to determine the field distribution in waveguide devices. For an application in CAD systems the reflection coefficient of the fundamental mode was computed with the approximate formulas. Numerical results were obtained for various concatenations of different waveguide sections. A comparison with the method of lines, a semi-analytic algorithm, shows a good agreement.