Three-dimensional Waveguide Research Articles

Tapered depressed-cladding waveguide lasers modulated by Ag nanoparticles embedded in SiO2

We report on fabrication of tapered circular depressed-cladding waveguides in Nd:YAG crystal by femtosecond laser direct writing (FsLDW). Based on the fabricated waveguides, for the first time to the best of our knowledge, efficient Q-switched mode-locked (QML) lasers are realized by employing silver nanoparticles (NPs) embedded in fused silica as saturable absorber (SA) element. Laser pulses as short as 25 ps with a repetition rate of 7.7 GHz are generated at a wavelength of 1064 nm. We systematically explore the influence of incident-output facet and the reduction factors on guiding properties and laser performance by conducting a comparative study of different tapers, and it has been found that the waveguides with tapered structures can suppress multi-mode guiding while ensure fundamental-mode output for waveguide lasers. Our work paves a new way toward developing three-dimensional (3D) waveguide for applications in on-chip ultrafast laser sources.

Three-Dimensional Compacted Optical Waveguide Mode Converter/Splitter Designed by Invariant Engineering

In this paper we demonstrate an analytical method, basing on the invariant engineering, to solve the relevant coupled mode equations for designing various grating-assisted 3D optical waveguide mode converter/splitter. Our method is based on the quantum-optical analogy, i.e., the Maxwell equation for the electromagnetic wave propagating along a waveguide structure in the spatial domain is formally equivalent to the Schrödinger equation for the evolution of a quantum system in the time domain. It is found that, the spatial domain invariants can be effectively constructed to solve the 3D coupled-mode equations, analogously to solve the dynamical evolution for the quantum systems in the time domain. The present approach overcomes the complication of solving the coupled-mode equation by the usual numerical method. As a consequence, by appropriately setting the coupling parameters between the grating-assisted interconnected waveguides, the desired mode conversion/splitting based on 3D coupler can be designed conveniently. As the invariant method is a natural shortcut to the adiabaticity, the compacted devices designed by the invariant-based engineering are useful for the fabrications of various 3D integrated optical devices.

Broadband energy squeezing and tunneling based on unidirectional modes

Energy squeezing is attractive for its potential applications in electromagnetic (EM) energy harvesting and optical communication. However, due to the Fabry-Perot resonance, only the EM waves with discrete frequencies can be squeezed and, as far as we know, in the previous energy-squeezing devices, stringent requirements of the materials or the geometrical shape are needed. We note that the structures filled with epsilon-near-zero (ENZ) mediums as reported in some works can squeeze and tunnel EM waves at frequencies (e.g. plasma frequency). However, the group velocity is usually near zero, which means little EM information travels through the structures. In this paper, low-loss energy squeezing and tunneling (EST) based on unidirectional modes were demonstrated in YIG-based one-way waveguides at microwave frequencies. According to our theoretical analysis and the simulations using the finite element method, broadband EST was achieved and the EM EST was observed even for extremely bended structures. Besides, similar EM EST was achieved in a realistic three-dimensional remanence-based one-way waveguide as well. The unidirectional mode-based EST paves the way for ultra-subwavelength EM focusing, enhanced nonlinear optics, and the design of numerous functional devices in integrated optical circuits such as phase modulator.

Wave dispersion analysis of three-dimensional vibroacoustic waveguides with semi-analytical isogeometric method

Material and structural non-destructive evaluations using guided-wave (GW) testing techniques rely on the knowledge of wave dispersion characteristics. When studying coupled fluid–solid waveguides having complex geometries using the semi-analytical finite element (SAFE) method, an excessive computational effort may be required, especially at high-frequency ranges. In this paper, we show the robustness of an efficient computational approach so-called the semi-analytical isogeometric analysis (SAIGA) for computing the wave dispersion in 3D anisotropic elastic waveguides coupled with acoustic fluids. This approach is based on the use of Non-Uniform Rational B-splines (NURBS) as the basis functions for the geometry representation as well as for the approximation of pressure/displacement fields. The obtained results are compared with the ones derived from using the conventional SAFE method which uses Lagrange polynomials. It is shown that for computing the dispersion of GWs, using SAIGA leads to a much faster convergence rate than using the conventional SAFE with the same shape function’s order. For hollow prismatic structures immersed in fluids, using high-order NURBS (e.g, p=8) is particularly efficient as it only requires a few elements to achieve solutions having the same precision as the ones obtained by SAFE which requires up to five times of number of DOFs. Moreover, the continuity of normal displacement at fluid–solid interfaces could be significantly improved thanks to the smoothness feature of NURBS, showing the advantage of SAIGA over SAFE in the evaluation of the shape modes of GWs in coupled fluid–solid systems.

Nonreciprocal guided waves in the presence of swift electron beams

Breaking the reciprocity of electromagnetic interactions is of paramount importance in photonic and microwave technologies, as it enables unidirectional power flows and other unique electromagnetic phenomena. Here we explore a method to break the reciprocity of electromagnetic guided waves utilizing an electron beam with a constant velocity. By introducing an effective dynamic conductivity for the beam, we theoretically demonstrate how nonreciprocal guided waves and a one-way propagating regime can be achieved through the interaction of swift electrons with electromagnetic waves in two-dimensional (2D) parallel-plate and three-dimensional (3D) circular-cylindrical waveguides. Unlike the conventional electron beam structures such as traveling wave tubes and electron accelerators, here the goal is neither to generate and/or amplify the wave nor to accelerate electrons. Instead, we study the salient features of nonreciprocity and unidirectionality of guided waves in such structures. The relevant electromagnetic properties such as the modal dispersion, the field distributions, the operating frequency range, and the nonreciprocity strength and its dependence on the electron velocity and number density are presented and discussed. Moreover, we compare the dispersion characteristics of waves in such structures with some electric-current-based scenarios in materials reported earlier. This broadband tunable magnet-free method offers a unique opportunity to have a switchable strong nonreciprocal response in optoelectronics, nanophotonics, and THz systems.

Efficient bidirectional marching solver for optical propagation in three-dimensional waveguide structures.

A novel bidirectional operator marching method based on the Dirichlet-to-Neumann (DtN) mapping for three-dimensional optical waveguide structures is developed and implemented using iterative methods. The backward propagation wave is integrated into the classical operator marching approach which represents the forward propagating wave. The bidirectional range marching formulas are exact for each range-independent piece and a large range step is possible in both directions. The validity and effectiveness of our proposed method are verified by analyzing uniform waveguides and longitudinal waveguides with varying refractive indices.

Improved multimodal formulation of the wave propagation in a 3D waveguide with varying cross-section and curvature.

An efficient method is proposed to solve the multimodal wave propagation within a three-dimensional waveguide bounded by a hard wall with varying cross section and curvature. This is achieved by first turning the original problem, in a complex-shaped waveguide, into a cylindrical waveguide with unit radius, by means of an adapted and flexible geometrical transformation. Then supplementary modes are defined to enrich the standard modal basis that is usually considered in such methods and to help restore the right boundary condition. It is shown through various numerical applications that the introduction of these supplementary modes, whatever the complexity of the waveguide geometry, significantly enhances the multimodal method, notably by increasing its convergence rate, whether one's aim is to solve the wavefield or the scattering problem.

Multisector Parabolic Equation Method for Scattering From Impenetrable Objects in Fluid Waveguides

Parabolic equation methods are a robust and efficient tool for modeling long-range acoustic propagation in range-dependent waveguides. A lesser known, but equally effective, application of parabolic equations is to the scattering problem. In this paper, we study the applicability and accuracy of the multisector parabolic equation approach to scattering from impenetrable objects - first developed approximately two decades ago for convex objects and recently extended to more complex scatterers - in waveguides in two and three dimensions. We benchmark the method in two dimensions in a range-dependent waveguide consisting of two different fluid media and find very good agreement with finite element methods for both forward scattering and backscattering, including the case where the scatterer is located at the interface between the media. Finally, we provide an example of scattering in a large three-dimensional waveguide, which would be extremely computationally intensive using alternate approaches, but is practical using the parabolic equation method.

Recrystallization Behavior of a Pure Cu Connection Interface with Ultrasonic Welding

Three-dimensional metal waveguide components are key components in the next generation of radio telescopes. Ultrasonic additive manufacturing technology combining ultrasonic welding and micro electrical discharge machining (micro-EDM) provides a new method for the overall manufacturing of waveguide elements, and the effective welding of Electrolytic Tough Pitch copper (Cu-ETP) sheets is the key process of this method. This study demonstrates that the orthogonal test optimization method is used to conduct ultrasonic welding tests on Cu-ETP. Specifically, electron backscattered diffraction (EBSD) technology is used to analyze the crystal grains, grain boundary types and texture changes during interface recrystallization. In addition, the finite element software ABAQUS 6.13 is employed to calculate the temperature field in order to determine the possibility of recrystallization of the welding interface. The results showed that the average grain size of the welding interface decreased from 20 to 1~2 μm. The Cu-ETP matrix is mainly composed of coarse grains with high-angle grain boundaries (HAGBs), while a large number of low-angle grain boundaries (LAGBs), subcrystals and fine equiaxed grains appear in the welded joint. At the same time, discontinuous dynamic recrystallization (DDRX) occurs in the less strained area, and continuous dynamic recrystallization (CDRX) is predominant in the greater strain area. The temperature field calculation shows that the peak temperature of the welding interface exceeds the recrystallization temperature of Cu-ETP from 379.05 to 433.2 °C.

Electro-optic mode-selective switch based on cascaded three-dimensional lithium-niobate waveguide directional couplers

We propose an electro-optic mode-selective switch based on cascaded three-dimensional lithium-niobate waveguide directional couplers fabricated with a single-step annealed proton-exchange process. To compensate for discrepancies due to uncertainties in the fabrication process, we develop a post-tuning technique to improve the performance of the coupler by means of depositing a layer of titanium oxide (TiO2) onto one of the waveguides of the coupler. By integrating two cascaded dissimilar directional couplers, we experimentally demonstrate switchable (de)multiplexing of the LP01, LP11a, and LP11b modes, where the LP11a mode can be switched at an efficiency over 75% from 1530 nm to 1612 nm with an applied voltage varying between -9 V and +30 V, and the LP11b mode can be switched at an efficiency higher than 90% from 1534 nm to 1577 nm with an applied voltage varying between -21 V to 0 V. The switching times are 230-300 ns. Our proposed waveguide platform could be employed to develop advanced switches for applications in areas where high-speed switching of spatial modes is required, such as reconfigurable mode-division-multiplexing communication.

Imaging in Three-Dimensional Waveguides with Partial Aperture Data

We consider the problem of imaging extended reflectors in three-dimensional acoustic waveguides using a planar array that is parallel to the waveguide’s cross-section. Our data consist of the multiple-frequency array response matrix. To form an image, we back-propagate a projection of the data on the propagating modes in the waveguide. The projection operator is adequately defined for any array-aperture size and shape that cover fully or partially the waveguide cross-section. The properties of the imaging method are analyzed theoretically and its effectiveness is assessed by numerical experiments for scatterers and arrays of varying shape and size.

Three-dimensional waveguide interconnects for scalable integration of photonic neural networks

Photonic waveguides are prime candidates for integrated and parallel photonic interconnects. Such interconnects correspond to large-scale vector matrix products, which are at the heart of neural network computation. However, parallel interconnect circuits realized in two dimensions, for example, by lithography, are strongly limited in size due to disadvantageous scaling. We use three-dimensional (3D) printed photonic waveguides to overcome this limitation. 3D optical couplers with fractal topology efficiently connect large numbers of input and output channels, and we show that the substrate’s area and height scale linearly. Going beyond simple couplers, we introduce functional circuits for discrete spatial filters identical to those used in deep convolutional neural networks.

Function-expansion-based topology optimization of three-dimensional optical waveguide devices with multi-layered structure considering layer thickness

So far, as an optimal design method for 2D and 3D design of optical waveguide devices, topology optimization based on a function expansion method has been reported. In this paper, we improve the conventional function-expansion-based topology optimization method to design three-dimensional photonic devices with structural variation in the depth direction. In order to design realistic 3D optical waveguide devices, we consider a layered structure and design each layer by using function-expansion-based topology optimization method. In this approach, undesired floating structures are avoided and layer thickness can be optimized. The validity of this method is verified through design examples of a polarization splitter and rotator (PSR) and a crossing waveguide which have two-layer structure.

Three-Dimensional Broadband Acoustic Waveguide Cloak**Supported by the National Natural Science Foundation of China (Grant No. 11874311) and the Natural Science Foundation of Fujian Province, China (Grant No. 2017J05015).

The propagation of acoustic waves is a fundamental topic in shallow ocean acoustics. We numerically demonstrate a three-dimensional zone of silence consisting of a circular tube with gradient index metamaterials attached to its rigid wall. The cloaking effect is verified by fine agreement with analytical calculations.

Low-cost and high-efficiency single-mode-fiber interfaces to silicon photonic circuits

A high-efficiency and large-alignment-tolerance fiber interface to silicon-on-insulator wire waveguides is introduced. A spot-size converter is built through a full three-dimensional polymer waveguide and a silicon inverse taper is employed to expand the optical mode field from a silicon sub-micro waveguide to a normal cleaved single-mode fiber with a mode size of about 10μm. The fabrication for the three-dimensional structure relies on simple spin-coating processes. The coupling loss from the fiber to the silicon waveguide through the proposed structure reaches -1.0dB for both transverse electrical and transverse magnetic modes, respectively. The polarization-dependent loss for the best coupling case is kept within -0.6dB in the whole measured wavelength range. The coupling facet of the proposed fiber interface structure is polishable and facilitates an easy package procedure with standard fiber arrays.

Array periodical nanofocusing effect in nanoscale three-dimensional surface plasmon polariton waveguide arrays

In this paper, the array periodical nanofocusing effect in a kind of nanoscale three-dimensional surface plasmon polariton (SPP) waveguide array is introduced. The refractive index of the dielectric layer in the three-dimensional SPP waveguide arrays has a parabolic distribution. The SPPs in the waveguide arrays show a periodical focusing effect as light illuminates on all waveguides. The oscillation propagating effect, which is similar to the photonic spatial Bloch oscillations in waveguide arrays but is fundamentally different from the Bloch oscillation effect in physics, is also realized as light illuminates on part of the waveguides of the arrays. The theoretical work is carried out by the coupled wave theory and is well demonstrated by the finite-difference time-domain numerical simulations.

A scalable photonic computer solving the subset sum problem.

The subset sum problem (SSP) is a typical nondeterministic-polynomial-time (NP)-complete problem that is hard to solve efficiently in time with conventional computers. Photons have the unique features of high propagation speed, strong robustness, and low detectable energy level and therefore can be promising candidates to meet the challenge. Here, we present a scalable chip built-in photonic computer to efficiently solve the SSP. We map the problem into a three-dimensional waveguide network through a femtosecond laser direct writing technique. We show that the photons sufficiently dissipate into the networks and search for solutions in parallel. In the case of successive primes, our approach exhibits a dominant superiority in time consumption even compared with supercomputers. Our results confirm the ability of light to realize computations intractable for conventional computers, and suggest the SSP as a good benchmarking platform for the race between photonic and conventional computers on the way toward "photonic supremacy."

Design and fabrication of three-dimensional single-mode waveguide arrays in bulk diamond through direct focused proton beam implantation

We demonstrate the feasibility of creating three-dimensional photonic devices through the realization of multi-level waveguides inside diamond by a series of systematic combined simulations grounded on Monte-Carlo statistics and Maxwell solver algorithms. Further, we have fabricated the counterparts of the multi-level waveguides buried in single crystalline diamond using a process based on several proton beam irradiation steps with different energies and fluences. On top of that, we draw a thorough comparison between the simulation results and the experimental observations, and find that they are in a good agreement with each other. Moreover, the simulation results also provide additional information such as the working fluence range of single-mode light (1550 nm) wave-guiding, the effective refractive index, and the polarization direction. The proof-of-concept of producing three-dimensional optical and photonic structures by direct focused proton beam implantation would open up a variety of new opportunities in designing and fabricating optical modulators, photonic components and quantum-computing related functional devices in bulk diamond, thus further promoting the development of three-dimensional diamond photonics.

Eigenvalue and Resonance Asymptotics in Perturbed Periodically Twisted Tubes: Twisting Versus Bending

We consider the Dirichlet Laplacian in a three-dimensional waveguide that is a small deformation of a periodically twisted tube. The deformation is given by a bending and an additional twisting of the tube, both parametrized by a coupling constant $\delta$. We expand the resolvent of the perturbed operator near the bottom of its essential spectrum and we show the existence of exactly one resonance, in the asymptotic regime of $\delta$ small. We are able to perform the asymptotic expansion of the resonance in $\delta$, which in particular permits us to give a quantitative geometric criterion for the existence of a discrete eigenvalue below the essential spectrum. In the particular case of perturbations of straight tubes, we are able to show the existence of resonances not only near the bottom of the essential spectrum but near each threshold in the spectrum. We also obtain the asymptotic behavior of the resonances in this situation, which is generically different from the first case.

On the Application of Asymptotic Formulae Based on the Modified Maslov Canonical Operator to the Modeling of Acoustic Pulses Propagation in Three-Dimensional Shallow-Water Waveguides

In this study a technique for the modeling of propagation of acoustic pulses in shallow-water waveguides with three-dimensional bottom inhomogeneities is described. The described approach is based on the ray theory of sound propagation and the method of modified Maslov canonical operator. Representation of acoustical field in terms of the canonical operator gives several important advantages in practical computations. In particular, it is possible to compute the time series of a pulse at a reception point located on the caustics of a family of rays. Besides, a significant part of calculations within the proposed approach can be performed analytically; therefore, overall computational costs are substantially reduced. As an example, sound propagation in a wedge-shaped waveguide representing a shelf area near the coast line is considered. The ray geometry in such a waveguide is discussed both in the isovelocity case and in the presence of the thermocline in the water column. For both cases, the time series of an acoustical pulse propagating along the track aligned along the isobaths (parallel to the apex edge of the wedge) is calculated.