Adiabatic Waveguide Research Articles

A methodical approach to design adiabatic waveguide couplers for heterogeneous integrated photonics

Abstract We present an elegant and effective approach for the design of adiabatic waveguide couplers tailored for the heterogeneous integration of photonic building blocks. This method empowers users to incorporate the shortest taper(s) in their designs, while upholding optimal coupling efficiency. The technique assesses mode overlap between a minimum of two waveguides within the cross-section of any heterogeneous material stack, determining the necessary waveguide cross-sectional dimension to achieve optimal coupling efficiency. Two illustrative design applications are showcased and compared to a linear, concave, and convex taper for reference: a SiN-to-polymer structure exhibiting a 40% coupling improvement and a Si-to-GeSi structure having a 2.2 up to 5 times shorter length.

Symbolic-numerical implementation of the model of adiabatic guided modes for two-dimensional irregular waveguides

In this work, a symbolic-numerical solution of Maxwell’s equations is constructed, describing the guided modes of a two-dimensional smoothly irregular waveguide in the zeroth approximation of the model of adiabatic waveguide modes. The system of linear algebraic equations obtained in this approximation is solved symbolically. The dispersion relation is solved numerically using the parameter continuation method.

Ultra-Broadband Integrated Optical Filters Based on Adiabatic Optimization of Coupled Waveguides

Broadband spectral filters are highly sought-after in many integrated photonics applications such as ultra-broadband wavelength division multiplexing, multi-band spectroscopy, and broadband sensing. In this study, we present the design, simulation, and experimental demonstration of compact and ultra-broadband silicon photonic filters with adiabatic waveguides. We first develop an optimization algorithm for coupled adiabatic waveguide structures, and use it to design individual, single-cutoff spectral filters. These single-cutoff filters are 1×2 port devices that optimally separate a broadband signal into short-pass and long-pass outputs, within a specified device length. We control the power roll-off and extinction ratio in these filters using the adiabaticity parameter. Both outputs of the filters operate in transmission, making it possible to cascade multiple filters in different configurations. Taking advantage of this flexibility, we cascade two filters with different cutoff wavelengths on-chip, and experimentally demonstrate band-pass operation. The independent and flexible design of these band edges enables filters with bandwidths well over 100 nm. Experimentally, we demonstrate band-pass filters with passbands ranging from 6.4 nm up to 96.6 nm. Our devices achieve flat-band transmission in all three of the short-pass, band-pass, and long-pass outputs with less than 1.5 dB insertion loss and extinction ratios of over 15 dB. These ultra-broadband filters can enable new capabilities for multi-band integrated photonics in communications, spectroscopy, and sensing applications.

Efficient adiabatic-coupler-based silicon nitride waveguide crossings for photonic quantum computing.

Optical integrated quantum computing protocols, in particular using the dual-rail encoding, require that waveguides cross each other to realize, e.g., SWAP or Toffoli gate operations. We demonstrate efficient adiabatic crossings. The working principle is explained using simulations, and several test circuits are fabricated in silicon nitride (SiN) to characterize the coupling performance and insertion loss. Well-working crossings are found by experimentally varying the coupler parameters. The adiabatic waveguide crossing (WgX) outperforms a normal directional coupler in terms of spectral working range and fabrication variance stability. The insertion loss is determined using two different methods: using the transmission and by incorporating crossings in microring resonators. We show that the latter method is very efficient for low-loss photonic components. The lowest insertion loss is 0.18 dB (4.06%) enabling high-fidelity NOT operations. The presented WgX represents a high-fidelity (96.2%) quantum NOT operation.

Symbolic-Numerical Modeling of the Propagation of Adiabatic Waveguide Mode in a Smooth Waveguide Transition

In this work, the model of adiabatic waveguide modes is studied by means of computer algebra. Within the model, the solution of the system of Maxwell’s equations is reduced to a form expressed via the solution of a system of four ordinary differential equations and two algebraic equations for six components of the electromagnetic field. In the case of multilayer waveguides, by means of a computer algebra system, the equations are reduced to a homogeneous system of linear algebraic equations, which is studied symbolically. The condition for non-trivial solvability of the system defines a dispersion relation, which is solved by the symbolic-numerical method, while the system is solved symbolically. The paper presents solutions that describe adiabatic waveguide modes in the zeroth approximation, taking into account the small slope of the interface of the waveguide layer, which are qualitatively different from solutions that do not take into account this slope.

Adiabatic guided modes of a three-layer integral optical waveguide

The numerical solution of the problem of guided propagation of polarized light in a smooth junction of a planar waveguide is considered. Within the framework of the model of adiabatic guided modes, the system of Maxwell equations is reduced to a system of four ordinary differential equations and two algebraic equations for six components of the electromagnetic field in the zeroth approximation and the same number of equations in the first approximation. The multilayer structure of waveguides makes it possible to reduce the problem to a homogeneous system of linear algebraic equations, whose nontrivial solvability condition yields the dispersion equation. Auxiliary eigenvalue problems for describing the adiabatic modes of the waveguide are solved. Keywords: smoothly irregular integrated-optical multilayer waveguides, eigenvalue and eigenvector problems, single-mode propagation of adiabatic waveguide modes.

Profile thickness synthesis of thin-film waveguide Luneburg lens

In the work the link between the focusing inhomogeneity of the effective refractive index of waveguide Luneburg lens and the irregularity of the waveguide layer thickness generating this inhomogeneity is demonstrated. For the dispersion relation of irregular thin-film waveguide in the model of adiabatic waveguide modes the problem of mathematical synthesis and computer-aided design of the waveguide layer thickness profile for the Luneburg thin-film generalized waveguide lens with a given focal length is being solved. The calculations are carried out in normalized (in a special way) coordinates to adapt the used relations to computer calculations. The obtained solution is compared with the same solution within the cross-section’s method. The performance of the algorithm implemented in Delphi, was demonstrated by plotting the dispersion curves and plotting a family of dispersion curves, demonstrating a critical convergence. As an additional result, the thickness profiles of additional (irregular in thickness) waveguide layer, forming a thin film generalized waveguide Luneburg lens were synthesized. This result generalizes Southwell’s results.

Adiabatic operation slope-loss algorithm for ultrashort and broadband waveguide taper

In this paper, an adiabatic operation slope-loss algorithm (AO-SLA) is developed for designing efficient adiabatic waveguide tapers. The algorithm can compute the efficient adiabatic guided-wave shape of the waveguide taper. A well-studied case of an adiabatic waveguide taper is used to show how it can readily generate a guided-wave shape that gives the same mode-connection power transfer with a much shorter length compared with the linear shape. In the waveguide taper design, it is shown that the device efficiency designed with AO-SLA is better than that based on the parabolic case and the SLA case, and the adiabatic taper designed can give a broad operating bandwidth. Moreover, the adiabatic condition α for AO-SLA can be very large.

Investigation of adiabatic waveguide modes model for smoothly irregular integrated optical waveguides

The model of adiabatic waveguide modes (AWMs) in a smoothly irregular integrated optical waveguide is studied. The model explicitly takes into account the dependence on the rapidly varying transverse coordinate and on the slowly varying horizontal coordinates. Equations are formulated for the strengths of the AWM fields in the approximations of zero and first order of smallness. The contributions of the first order of smallness introduce depolarization and complex values characteristic of leaky modes into the expressions of the AWM electromagnetic fields. A stable method is proposed for calculating the vertical distribution of the electromagnetic field of guided modes in regular multilayer waveguides, including those with a variable number of layers. A stable method for solving a nonlinear equation in partial derivatives of the first order (dispersion equation) for the thickness profile of a smoothly irregular integrated optical waveguide in models of adiabatic waveguide modes of zero and first orders of smallness is described. Stable regularized methods for calculating the AWM field strengths depending on vertical and horizontal coordinates are described. Within the framework of the listed matrix models, the same methods and algorithms for the approximate solution of problems arising in these models are used. Verification of approximate solutions of models of adiabatic waveguide modes of the first and zero orders is proposed; we compare them with the results obtained by other authors in the study of more crude models.

Mode coupling in a coastal wedge due to quasi crossing of range-dependent modal eigenvalues and spatial sound field variability

In the paper sound waves propagation in a coastal wedge with sound speed profile (the presence of thermocline) is studied. In down- and up-slope propagation each adiabatic waveguide mode is transformed from the “bottom—surface reflected” shape to the “bottom-bottom refracted” one at some distance from the edge, depending on mode number. Analysis of mode composition and the corresponding spatial variability of the sound field is carried out using Parabolic Equation with the following decomposition of the field over adiabatic modes. It is shown, that there is significant change of amplitudes of adiabatic modes which is interpreted as manifestation of mode coupling. It is shown that mode coupling has local character, at the definite distance from the source, where two range dependent eigenvalues convergent to each other. This phenomenon is analog to the so called quasi crossing of states in atomic physics (Landau–Zener theory of nonadiabatic transitions in two-level system). This leads to sequential excitation of more and more higher modes in down-slope propagation and even creation of higher modes which did not exist at the position of the source. Results of modeling are presented, possible experimental observations are discussed. [Work was supported by RFBR, Grant 20-55-S52005.]

A Fully Numerical Method for Designing Efficient Adiabatic Mode Evolution Structures (Adiabatic Taper, Coupler, Splitter, Mode Converter) Applicable to Complex Geometries

A fully numerical method for designing efficient adiabatic mode evolution structure (AMES) (referred to as NAMES) is introduced, which can be applied to adiabatic taper, coupler, splitter, mode converter, and a wide range of AMES based devices. The method can compute efficient adiabatic waveguiding shapes for these devices, including those with complex waveguiding geometries involving 2D/3D mode connections. We introduce two algorithms for the NAMES, referred to as “maximal mode-power loss at top algorithm” and “mode-power loss at initial slope algorithm”. Both are based on keeping the mode-connection power exchange constant. We use the simple case of a waveguide taper to explain the algorithms, and then apply it to a more complex case of an adiabatic waveguide coupler to show how it can readily generate a waveguiding shape that can give the same mode-connection power transfer with a much shorter length than that based on a linear shape. In the coupler case, we show the device efficiency is equal to that based on an optimized analytical approach developed for a simple geometry, but the NAMES can address many different device types and complex device geometries all with a single numerical approach that would also enable design automation. The algorithms utilize Eigenmode Expansion (EME) simulator for field propagation with functionalities that are particularly efficient for the algorithms. We cross-checked the EME simulator results using finite-difference time-domain method. With sufficiently fine division of the structure, the waveguiding shape generated converges to basically the same shape for both algorithms and the shape is quite insensitive to the starting parameters. Thus, the NAMES given is robust, convergent, efficient, and general (not restricted to a particular device type). The NAMES would have wide applications to designing AMES based devices with complex geometries for photonic integrated circuits.

Adiabatic guided wave optics - a toolbox of generalized design and optimization methods.

Starting from the fully vectorial coupled local-mode theory, a general design rule for adiabatic waveguide design is derived. The design rule guarantees adiabaticity and puts an upper limit on the transmission loss of any guided wave transformation. The rule is applicable to any waveguide geometry, admits multi-dimensional optimization, and accounts for radiative loss to guided and radiation modes. Moreover, the design technique is enhanced with further optimization procedures that eliminate coupling between particular pairs of modes. The utility of this toolbox of design rules and methods is illustrated through the design of a 2×2 coupler and a bilayer waveguide transition. These design procedures can be used to optimize single-mode and multimode photonic devices by varying one or more waveguide parameters.

Single-mode propagation of adiabatic guided modes in smoothly irregular integral optical waveguides

This paper investigates the waveguide propagation of polarized electromagnetic radiation in a thin-film integral optical waveguide. To describe this propagation, the adiabatic approximation of solutions of Maxwells equations is used. The construction of a reduced model for adiabatic waveguide modes that retains all the properties of the corresponding approximate solutions of the Maxwell system of equations was carried out by the author in a previous publication in DCM ACS, 2020, No 3. In this work, for a special case when the geometry of the waveguide and the electromagnetic field are invariant in the transverse direction. In this case, there are separate nontrivial TEand TM-polarized solutions of this reduced model. The paper describes the parametrically dependent on longitudinal coordinates solutions of problems for eigenvalues and eigenfunctions - adiabatic waveguide TE and TM polarizations. In this work, we present a statement of the problem of finding solutions to the model of adiabatic waveguide modes that describe the stationary propagation of electromagnetic radiation. The paper presents solutions for the single-mode propagation of TE and TM polarized adiabatic waveguide waves.

Calibrating Power Meters in the 140–220-GHz Frequency Range Using an Absolute-Power Reference Calorimeter

This study aimed to calibrate power meters in the frequency range of 140–220 GHz (WR-05 band). To this end, a WR-05-waveguide calorimeter is designed as a reference standard. The calorimeter is based on the dc-substitution method in which the absorbed power is substituted for dc power as heat. A detailed thermal analysis is performed on the dc-substitution coefficient and the heat leakage of the adiabatic waveguide, which are the dominant contributors to uncertainty, and measures to decrease the uncertainty are determined. Experiments are performed to clarify the contributions of these factors to the uncertainty. A $W$ -band power meter, to which a tapered waveguide is attached to extend the applicable frequency range from the WR-10 waveguide band to the WR-05 band, is calibrated at 0.38–0.48 mW using the calorimeter. The uncertainty of the calibration is analyzed by the Monte Carlo method. As a result, the calibration factor of the power meter is determined to be 0.15–1.36 in the WR-05 band with an expanded uncertainty of 3.6%–12.7% ( $k = 2$ ).

Adiabatic Performance Evaluation System for Waveguide Transmission Lines

In a temperature-controlled radio frequency (RF) power measurement system, there is a temperature difference between the system and the environment temperature. If a metal waveguide is used in the system, heat can reach the core of the system and affect the measurement. An adiabatic waveguide is utilized to reduce this heat flow. This article introduces several WR10 rectangular waveguides that are used in the Korea Research Institute of Standards and Science (KRISS) microcalorimeter and an evaluation system that can measure the adiabatic performance of the waveguides via a thermostat. The basic concept and measurement setup for the evaluation system are briefly introduced, and the structure and the function of the waveguide heat source and heat sense modules of the thermostat are presented. The test results of the adiabatic performance of several WR10 rectangular waveguides are compared and the electromagnetic performance is presented. We also tested preliminary dielectric waveguides that have been co-studied with Physikalisch-Technische Bundesanstalt (PTB), Germany recently. We propose an index to characterize the adiabatic performance of the waveguides. Based on the index results, we improve the adiabatic performance of our newly electroforming-processed adiabatic waveguide with a thick resin coating, which is forty times higher than that of the prototype KRISS microcalorimeter adiabatic waveguide. Finally, we fabricated and investigated dielectric waveguides that have a superb adiabatic property for the microcalorimeter application.

Implementation of on-chip multi-channel focusing wavelength demultiplexer with regularized digital metamaterials

Abstract Adiabatic waveguide taper and on-chip wavelength demultiplexer are the key components of photonic integrated circuits. However, these two kinds of devices which were designed by the traditional semi-analytic methods or the brute-force search methods usually have large size. Here, based on the regularized digital metamaterials, a two-channel focused wavelength demultiplexer with a footprint of 2.4 × 10 μm2 has been proposed. The designed demultiplexer can directly connect to a grating coupler under the absence of a long adiabatic waveguide taper. The objective first method and the modified steepest descent method are used to design the demultiplexer which splits 1520 nm and 1580 nm light. Experimental results show that the insertion loss of the upper (lower) channel of the demultiplexer is −1.77 dB (−2.10 dB) and the crosstalk is −25.17 dB (−12.14 dB). Besides, the simulation results indicate that the fabrication tolerance of the device can reach ±20 nm in etching depth and ±10 nm in plane size changing. Benefitted from the extensibility of the design method, other types of ultra-compact “focused” devices, like mode splitters, mode converters, and power splitters can also be designed. Most importantly, this design method can be used to design devices with more complicated functionalities, such as multi-channel focused wavelength demultiplexers.

Sub-wavelength grating-assisted polarization splitter-rotators for silicon-on-insulator platforms.

We propose and demonstrate broadband, entirely mode-evolution-based, polarization splitter-rotators (PSR) using sub-wavelength grating (SWG) assisted adiabatic waveguides for two SOI platforms. Our PSRs are more compact than previously demonstrated entirely mode-evolution-based designs. The devices were fabricated using two fabrication processes and, in both cases, the measured spectra show close matches to the simulation results. One of the processes uses standard optical lithography and, hence, this is the first time that an SWG-based PSR has been experimentally implemented using such a process. Finally, measurements for arbitrary input polarizations on an active, automated polarization receiver, that uses one of our PSRs, are also presented.

Adiabatic and Ultracompact Waveguide Tapers Based on Digital Metamaterials

Adiabatic waveguide taper is one of the fundamental building blocks in photonic integrated circuits, but it is challenging to achieve high efficiency and compact size simultaneously. Here we demonstrate efficient, compact, and adiabatic on-chip spot-size converters using inversely designed tapers based on digital metamaterials. Ultracompact tapers with only 3- μ m length between single-mode and few-mode waveguides are demonstrated with 90% efficiencies over 80 nm wavelength range. For another scenario of interconnection between a 0.5- μ m-wide waveguide and a 10- μ m-wide slab waveguide, an efficiency of 76% is experimentally achieved by 5- μ m long taper. Using such a compact taper, the grating coupler footprint is reduced to even smaller than a focusing coupler. The nanostructured tapers have mode rejection ratios of >20 dB and fabrication tolerance to ±5 nm variations of the pixel dimension without efficiency drop.

Broadband and Temperature Tolerant Silicon Nitride Liquid Controlled Waveguide Coupler

A broadband and temperature tolerant liquid-controlled adiabatic waveguide coupler (LCC) is realized. The LCC with silicon nitride waveguides is designed to be compatible with liquids that can be actuated by an electrowetting-on-dielectric system. This proof-of-principle demonstration with manual actuation paves the way toward the realization of non-voloptical switch systems. A 630- ${\mu }$ m-long LCC configured as a $1\times 2$ switch has a measured insertion loss less than 1.5 dB and a crosstalk less than $-14$ dB for both bar and cross state over the telecommunication wavelength range 1260 to 1630 nm. Furthermore, the LCC is tolerant to variations in temperature. The measured excess insertion loss over the temperature range 21 to 73 $^\circ$ C is less than 0.3 dB for bar and cross state, over the same wavelength range.

绝热耦合超对称光波导结构

绝热耦合超对称光波导结构