Beam Propagation Method Simulations Research Articles

Broadband silicon nitride integrated polarization rotators at 780 nm

Polarization management, and in particular polarization rotation, is becoming increasingly important for photonic integrated circuits (PICs). While fiber-optic networks are generally polarization insensitive, the large aspect ratio of high-index-contrast PIC waveguides leads to a large polarization-dependent response of integrated components such as waveguides, optical cavities, couplers, etc. Although foundry-processed polarization rotators operating at telecom and datacom wavelengths (C- and O-band) have been demonstrated, to date, there have been few reports of devices operating at shorter wavelengths. This work demonstrates silicon nitride (SiN) polarization rotators operating from λ=700-1000 nm (the I/Z-band) that take advantage of optical coupling between two waveguiding layers in a standard foundry process. We demonstrate a broadband white-light polarization measurement setup that enables precise characterization of the polarization-dependent transmission of photonic waveguide devices. Measurements on foundry-processed devices confirm full TE-to-TM rotation exhibiting a maximum polarization extinction ratio (PER) approaching 20 dB (limited by our measurement setup), and an exceptionally large bandwidth of up to 160 nm with an insertion loss less than 0.2 dB. Beam propagation method (3D-BPM) simulations show good agreement with experimental data and enable the device parameters to be adjusted to accommodate different operating wavelengths and geometries with no changes to the existing foundry process. This work opens up opportunities for applications in quantum information and bio-sensing where operation at λ<1000nm is needed.

Block paralleled BPM simulation of an optical waveguide with cross-sectional random refractive index distribution

Image transport mediated by transverse Anderson localization requires an optical waveguide to have high contrasted indices and subwavelength feature size in random distribution. Super-fine mesh therefore needs to be adopted in numerical solution techniques. Existing numerical simulation approaches such as the conventional beam propagation method (BPM), however, shows low efficiency and is often unstable with fine mesh and high contrasted random index distribution. In this work, we propose a block algorithm based on a 3D finite-difference full-vector BPM, which is appealing as a reliable tool in numerical simulation of optical waveguides with random refractive index distribution.

Adiabatically focusing X-rays to the nanometer scale by one dimensional long kinoform lenses: comparison between an ideal Cartesian oval refocusing lens and a parabolic lens.

The nano-focusing performance of adiabatically designed Cartesian oval refocusing lenses is compared with other well known compound refractive lenses with parabolic profiles (both simple concave and kinoform types). Using beam propagation method (BPM) simulation, it is shown that our design based on oval lenses does significantly improve the focusing properties compared to other parabolic lens based designs, e.g. adiabatically focusing lenses (AFLs), which doesn't take into account of the refocusing effect. This points to the importance of optimizing complex lens design in improving nano-focusing lens performance.

Asymmetric Si-Slot Coupler With Nonreciprocal Response Based on Graphene Saturable Absorption

We present the study of a proof-of-concept integrated device that can be used as a nonlinear broadband isolator. The device is based on the asymmetric loading of a highly-confining silicon-slot photonic coupler with graphene layers, whose ultrafast and low-threshold saturable absorption can be exploited for nonreciprocal transmission between the cross-ports of the coupler. The structure is essentially a non-Hermitian system, whose exceptional points are briefly discussed. The nonlinear device is modeled with a coupled Schrodinger equation system whose validity is checked by full-vector finite element-based beam-propagation method simulations in CW. The numerically computed performance reveals a nonreciprocal intensity range (NRIR) in the vicinity of 100 mW peak power with a bandwidth spanning tens of nanometers, from CW down to ps-long pulses. Finally, the combination of saturable absorption and self-phase modulation (Kerr effect) in graphene is studied, indicating the existence of two NRIR with opposite directionality.

Optical microprism cavities based on dislocation-free GaN

Three-dimensional growth of nanostructures can be used to reduce the threading dislocation density that degrades III-nitride laser performance. Here, nanowire-based hexagonal GaN microprisms with flat top and bottom c-facets are embedded between two dielectric distributed Bragg reflectors to create dislocation-free vertical optical cavities. The cavities are electron beam pumped, and the quality (Q) factor is deduced from the cavity-filtered yellow luminescence. The Q factor is ∼500 for a 1000 nm wide prism cavity and only ∼60 for a 600 nm wide cavity, showing the strong decrease in Q factor when diffraction losses become dominant. Measured Q factors are in good agreement with those obtained from quasi-3D finite element frequency-domain method and 3D beam propagation method simulations. Simulations further predict that a prism cavity with a 1000 nm width will have a Q factor of around 2000 in the blue spectral regime, which would be the target regime for real devices. These results demonstrate the potential of GaN prisms as a scalable platform for realizing small footprint lasers with low threshold currents.

Adiabatic propagation algorithm for photonic lanterns

Photonic lanterns are adiabatically tapered waveguiding structures which are used for loss-less coupling of light between modes of multiple single mode fibers (SMF) to specific modes or mode groups of a few mode fiber (FMF). In this paper, we demonstrate a propagation algorithm that can be used for modelling, design and analysis of such structures. Specifically, the algorithm describes the 3D scalar beam propagation in structures with an adiabatic transition along the propagation direction. It is based on the eigenmode expansion method and exploits the property of adiabaticity. The algorithm is an invaluable tool for designing application specific photonic lanterns without running tedious finite difference beam propagation method (FDBPM) simulations. On prior reported structures, we demonstrate the applicability of our propagation algorithm, thus highlighting its advantages, efficiency and comparing it with the more common FDBPM.

General formulae of designing novel photonic digital sensors with arbitrary levels of directional couplers for testing liquids

High sensitivity and rapid detecting photonic sensors are essential devices such as in medical diagnostics and biological test. Conventional biochemical sensors based on the directional couplers need other apparatus to measure the precise output power intensities. Conversely, a digital sensor is more efficiently utilized to determine the refractive index of the liquid sample. By simple mathematics induction, the formulae of designing a general photonic digital sensor, which comprises k (k ≥ 1) levels of the directional couplers composed of the ridge waveguides, are obtained in this paper. The performance of the sensor resembles an analog-to-digital converter and distinguishes 2k liquid samples. As long as k is large enough, the sensor can lower the quantization error and precisely determine the refractive index of the liquid sample. To demonstrate the validity of our formulae and design rules, we present the beam propagation method simulation results in this paper.

Femtosecond Laser-inscribed Non-volatile Integrated Optical Switch in Fused Silica based on Microfluidics-controlled Total Internal Reflection

We demonstrate a non-volatile optical power switch, fabricated by femtosecond laser inscription in a fused silica substrate, with switching operation based on microfluidics-controlled total internal reflection. The switch consists of crossed waveguides and a rectangular, high aspect ratio microfluidic channel, located at the waveguide crossing. The switching between total internal reflection and transmission at the channel wall is determined by the refractive index of the medium inside the channel. Femtosecond laser inscription allows for co-integration of low-loss optical waveguides and channels with smooth sidewalls and thus the fabrication of low insertion loss switches that are broadband and show low polarization dependent losses. The measured total internal reflection loss of the fabricated switch is about 1.5 dB at the wavelength 1550 nm. The loss due to transmission through the channel filled with refractive index matching liquid is about 0.5 dB. Detailed finite difference time domain and beam propagation method simulations of the switch's performance indicate that the losses can be further reduced by optimizing its geometry, together with further adjusting the inscription parameters.

Implementation of reversible Peres gate using electro-optic effect inside lithium-niobate based Mach-Zehnder interferometers

Power dissipation is an important consideration in digital design. Reversible logic is an unconventional form of computing in which the computational process is bijective and can efficiently reduce power dissipation problem. Peres gate is a basic reversible logic gate used in various reversible circuit. In this paper, design of Peres gate using electro-optic effect inside lithium-niobate based Mach-Zehnder interferometer is proposed. The various applications of Peres gate such as full-adder circuit and flip-flop is also explained. A theoretical description along with mathematical formulation of device is elaborated. The device is analyzed through Beam propagation method and MATLAB simulations.

Design of highly mode group selective photonic lanterns with geometric optimization.

Highly mode group selective photonic lanterns (PLs) are desired for mode-division multiplexing transmission systems. Usually, mode selectivity is achieved by using input fibers with different core diameters or refractive indices to break degeneracy between mode groups. We demonstrate that mode group selectivity can be greatly improved by optimizing core geometry of PLs. For three-mode PLs with optimized core geometry, based on beam propagation method (BPM) simulation results, mode selectivity is improved from 23.8dB to 43.9dB for LP01 mode, and mode selectivity of LP11 mode is improved from 26.8dB to 45.5dB. The reason is the optimized core geometry can significantly slow down the changing of mode profile along the taper of the PL; thus adiabatic tapering requirement can be greatly alleviated. It can also be observed that the simulation results by the BPM are in good agreement with calculation of coupled-mode theory.

Novel Design of Photonic Digital Sensors for Distinguishing Uniformly-Distributed Refractive Indices of Fluids

Abstract The authors propose a novel structure of k-level (k is an arbitrary integer) photonic digital sensor based on directional couplers with specific structural parameters. Its function is similar to an analog-to-digital converter (ADC) in electronic system, and capable of distinguishing 2k+1-1 discrete and uniformly-distributed refractive indices of the fluidic samples. In this paper, the principle of designing the photonic digital sensor is described, and the beam propagation method (BPM) simulation results are presented for demonstrating the validity of our design.

Evanescent field boundary conditions for modelling of light propagation

In this work, we introduce a straightforward and original approach for evanescent field boundary conditions (EBCs), which can be, in principle, applied in both Beam Propagation Method (BPM) and Finite Difference Time Domain Method (FDTD) numerical simulations. Importantly, suggested method may serve as an efficient alternative to typically applied ones, such as transparent boundary conditions (TBCs), absorbing boundary conditions (ABCs) or perfectly matched layer (PML) boundary conditions, giving comparable or even better results in terms of smaller reflections and of shorter computation time. Definition of proposed evanescent function, a way of its practical implementation, as well as an influence of its parameters on the light beam propagation in the free-space and in exemplary photonic structures are described in detail. In addition, results of EBCs application are compared with those achieved for Dirichlet, TBC and PML boundary conditions used in analogous arrangement of the physical systems.

GaN-based integrated photonics chip with suspended LED and waveguide

We propose a GaN-based integrated photonics chip with suspended LED and straight waveguide with different geometric parameters. The integrated photonics chip is prepared by double-side process. Light transmission performance of the integrated chip verse current is quantitatively analyzed by capturing light transmitted to waveguide tip and BPM (beam propagation method) simulation. Reduction of the waveguide width from 8 μm to 4 μm results in an over linear reduction of the light output power while a doubling of the length from 250 μm to 500 μm only results in under linear decrease of the output power. Free-space data transmission with 80 Mbps random binary sequence of the integrated chip is capable of achieving high speed data transmission via visible light. This study provides a potential approach for GaN-based integrated photonics chip as micro light source and passive optical device in VLC (visible light communication).

High-speed waveguide photodetector for 64 Gbaud coherent receiver.

A high-speed waveguide photodetector has been successfully fabricated for an integrated coherent receiver. Dual laterally tapered structures are introduced for a spot-size converter. We optimize the responsivity and the polarization-dependent loss of the spot-size converter-integrated waveguide photodetector through the beam propagation method simulation. The waveguide photodetector is designed with electrical as well as optical optimizations. The photodetector provides sufficient alignment tolerance, high responsivity of 0.73A/W, and low polarization-dependent loss of 0.27dB, which is in good agreement with the simulation results. By increasing the thickness of the matching layer and the n-doped upper taper, the electrical properties of the photodetector are enhanced. The photodetector has a 3dB bandwidth of 45GHz, providing high-speed operation. Through the electrical and optical optimizations, we successfully obtain the high-speed waveguide photodetector for a 64Gbaud integrated coherent receiver.

Generation of optical vortices in an integrated optical circuit

In this work, the generation of optical vortices in an optical integrated circuit is numerically demonstrated. The optical vortices with topological charge m = ±1 are obtained by the coherent superposition of the first order modes present in a waveguide with a rectangular cross section, where the phase delay between these two propagating modes is Δφ = ±π/2. The optical integrated circuit consists of an input waveguide continued with a y-splitter. The left and the right arms of the splitter form two coupling regions K1 and K2 with a multimode output waveguide. In each coupling region, the fundamental modes present in the arms of the splitter are selectively coupled into the output waveguide horizontal and vertical first order modes, respectively. We showed by employing the beam propagation method simulations that the fine tuning of the geometrical parameters of the optical circuit makes possible the generation of optical vortices in both transverse electric (TE) and transverse magnetic (TM) modes. Also, we demonstrated that by placing a thermo-optical element on one of the y-splitter arms, it is possible to switch the topological charge of the generated vortex from m = 1 to m = −1.

Tapered Spot Size Converter by Mask-Transfer Self-Written Technology for Optical Interconnection

A compact spot size converter (SSC) is the key to the future of optical interconnection. Hence, we proposed a tapered SSC using mask-transfer self-written (MTSW) technology with UV-curable resin. MTSW technology guarantees an easy and fast fabrication concept that makes it a promising technology for SSC devices. A prototype SSC adopting this technology was successfully fabricated. It was also confirmed that a tapered shape could be prepared from diffraction effect. A numerical calculation performed using the beam propagation method simulation shows that radiation loss decreases as SSC length increases. Comparison between the simulation and actual fabrication results shows acceptable value. Thus, this approach is reliable and has potential in the future of optical interconnection.

Study of a single-frequency retrodirective system with a beam pilot signal using dual-mode dielectric resonator antenna elements

A terrestrial microwave power transmission system is considered as an effective method for collecting natural energy. In this system, frequency dependence of the refractive index and multipath propagation due to the ground surface poses problems. In the study, a single-frequency retrodirective system was proposed with a beam pilot signal using dual-mode dielectric resonator antenna elements. The results confirmed that the beam pilot signal radiated from the entire surface of the receiving antenna and accurately used the same propagation space as that of microwave power by beam propagation method simulation. A dual-mode dielectric resonator antenna was proposed as a common array antenna element for the beam pilot signal and microwave power. This involves a cross-shaped hemispherical dielectric resonator structure, and an isolation level exceeding 60 dB was experimentally measured between the orthogonal ports of the fabricated antenna. The dual-mode dielectric resonator antenna with an isolation exceeding 60 dB was successfully developed as an enabling device to realize a single-frequency retrodirective system with a beam pilot signal.

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.

Domain engineering algorithm for practical and effective photon sources.

We introduce a method for shaping the spectral response of nonlinear light sources by tailoring the quasi-phase matching. Our algorithm relies on engineering the poling to accurately trace a generated target signal field amplitude to determine the desired nonlinearity profile. The proposed poling algorithm results in a poling pattern that is more robust to manufacture, as all domain inversions are of equal width. The poling pattern is verified using a nonlinear beam propagation method simulation. This approach is applied to achieve Gaussian-shaped phase matching along a potassium titanyl phosphate (KTP) crystal in order to generate pure heralded single photons of spectral purity ~0.996-this is highly desirable for heralded single photon quantum optics.

Planar microlens with front-face angle: design, fabrication, and characterization

This paper studies the effect of microlens front-face angle on the performance of an optical system consisting of a planar-graded refractive index (GRIN) lens pair facing each other separated by a free-space region. The planar silica microlens pairs are designed to facilitate low-loss optical signal propagation in the free-space region between the opposing optical waveguides. The planar lens is fabricated from a 38-μm-thick fluorine-doped silica layer on a silicon substrate. It has a parabolic refractive index profile in the vertical direction, which is achieved by controlled fluorine incorporation in the silica film to collimate the optical beam in the vertical direction. Horizontal beam collimation is achieved by incorporating a horizontal curvature at the front face of the lens defined by deep oxide etch. A generalized 3×3ABCDGH transformation matrix method has been derived to compute the coupling efficiency of such microlens pairs to take front-face angles that may be present due to fabrication variations or limitations and possible input/output optical fiber offset/tilt into considerations. Pairs of such planar GRIN lens with various free-space propagation distances between them ranging from 75 to 2500 μm and with front-face angles of 1.5 deg, 2 deg, and 4 deg have been fabricated and characterized. Beam propagation method simulations have been carried out to substantiate the theoretical and experimental results. The results indicate that the optical loss is reasonably low up to 1.5 deg of front-face angles and increases significantly with further increase in the front-face angle. Analysis shows that for a given system with specific microlens front-face angle, the optical loss can be significantly reduced by properly compensating the vertical position of the input and output fibers.