Symmetric Waveguide Research Articles

Symmetry‐Induced Selective Excitation of Topological States in Su–Schrieffer–Heeger Waveguide Arrays

The investigation of topological state transition in carefully designed photonic lattices is of high interest for fundamental research, as well as for applied studies such as manipulating light flow in on‐chip photonic systems. Herein, the topological phase transition between symmetric topological zero modes (TZM) and antisymmetric TZMs in Su–Schrieffer–Heeger mirror symmetric waveguides is reported. The transition of TZMs is realized by adjusting the coupling ratio between neighboring waveguide pairs, which is enabled by selective modulation of the refractive index in the waveguide gaps. Bidirectional topological transitions between symmetric and antisymmetric TZMs can be achieved with proposed switching strategy. Selective excitation of topological edge mode is demonstrated owing to the symmetry characteristics of the TZMs. The flexible manipulation of topological states is promising for on‐chip light flow control and may spark further investigations on symmetric/antisymmetric TZM transitions in other photonic topological frameworks.

Spatial differentiation based on resonant absorption on symmetrical metal-cladding waveguide

We propose a new spatial differentiation scheme based on resonant absorption on a symmetrical metal-cladding waveguide (SMCW) with the guiding layer as birefringent crystal. The differentiator consists of a SWCW and two polarizers. When the resonant condition and critical thickness are satisfied for SMCW, the destructive interference between the directedly reflected field and the leaked field makes differentiation in the x-direction possible, and the destructive interference between the left-handed and right-handed circularly polarized field components makes differentiation in the y-direction possible. So, the x-direction, y-direction and two-dimensional spatial differentiation can be obtained just by adjusting the orientation of the first polarizer. The differentiator has the advantages of miniaturization and simple operation.

Miniaturized metallic symmetrical resonator backed CPW inspired dual band filter using Meander line for 5G mm‐wave applications

AbstractAn ultra‐miniaturized symmetrical resonator backed coplanar waveguide based dual band pass filter using Meander line for 5G mm‐wave applications is presented. Meander line CPW structure with ultra miniaturized size was designed, investigated and its equivalent circuit was extracted using theoretical and experimental results to explore basic RF characteristics. The resonator at the back side of the substrate is symmetrical in both horizontal and vertical plane. This resonator is electrically coupled with the Meander line structure in the conducting plane. Symmetrical resonator structure coupled with open stubs on both sides on ground plane and Meander line structure with uniform spacing implemented at the conducting layer constitutes the metallic backed Co‐Planar waveguide based dual band filter. By using Meander line, the overall size of the communication devices has been reduced in large scale. The combination of symmetrical resonator and Meander line structure produces the overall bandwidth from (1 to 30) GHz. 5G mm‐wave filter operates in two bands; Band I operates from (1 to 14.2) GHz with insertion loss −1.8 dB and return loss −34 dB with fractional bandwidth of 73.6%; Band II operates from (16.2 to 30) GHz with insertion loss −1.2 dB, return loss −30 dB and fractional bandwidth of 59.7%. The overall filter circuit geometry is (5 × 5 × 1.6) mm and in terms of wavelength: (0.52 × 0.52) λg.

Propagation of surface magnetoplasmon polaritons in a symmetric waveguide with two-dimensional electron gas

The properties of surface magnetoplasmon polaritons (SMPPs) in a symmetric structure, composed of two semi-infinite regions of high-density two-dimensional electron gas (2DEG) separated by a thin film in Voigt configuration, are investigated. The normal and absorption dispersion relations for the transverse magnetic polarization are derived by correlating Maxwell’s equation and the boundary conditions. It is demonstrated that the features of SMPPs are greatly influenced by the external magnetic field, collision frequency of 2DEG, the dielectric constant, and the thickness of the thin film, suggesting that the locations and propagation lengths of SMPPs can be governed accordingly. It is shown that the symmetry of the physical geometry preserves the symmetry of the dispersion relations of SMPPs. Furthermore, it is discovered that as the external magnetic field increases, the penetration depth of SMPPs decreases, while their energy loss reduces, implying that plasmons can propagate for longer distances. Additionally, it is observed that SMPPs in the symmetric configuration have a longer lifetime than those in the asymmetric configuration.

A robust and efficient model for transmission of surface plasmon polaritons onto metal–insulator–metal apertures

A simple yet accurate model for the transmission of surface plasmon polaritons (SPPs) in a finite metal–insulator–metal (MIM) waveguide to the sides of the apertures is proposed and demonstrated to be more accurate than the available models. It is as simple as using a magnetic current density across the plane of the aperture whose value is defined by the SPPs with any number of modes in the waveguide through the equivalence principle. Then, the generated SPPs on both sides of the aperture are extracted from the convolution integral of the equivalent current density and Green’s function. As a result, the model provides the transmission coefficients of the SPPs in the MIM waveguide to the side walls of the aperture accurately and efficiently; not only for symmetric MIM waveguides with a single isolating layer but also non-symmetric ones with multi-layered insulating materials. The results are in very good agreement with those obtained by the finite-difference time-domain method and better than the other approximations available in literature for a wide range of aperture widths.

Ultrawideband De-Embedding Calibration for Magnetic Field Probes by Using Symmetric GCPW Calibrators

Microstrip line is commonly used as a calibrator for probe calibration. However, some issues need to be addressed for high frequency application, such as ripple and attenuation caused by the embedded part of the calibrator. In this paper, an ultra-wideband de-embedding calibration method (DCM) for magnetic field probe is proposed. Two symmetric non-soldering grounded coplanar waveguide (GCPW) calibrators, including Through and Line standards, are used to solve the de-embedded <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> -parameter matrix of a 3-port calibration system. Compared with the traditional calibration method (TCM), the proposed method can reduce the influence of the reflection and attenuation caused by the embedded part and preserve the intrinsic properties of the probe itself. By using the DCM with a symmetric and good matched GCPW calibrator, the ripples of the DCM decreases by 6.57 dB, which is 82 % of the TCM with a microstrip line, and the attenuation has been compensated by about 0.7 dB at 10 GHz. In addition, a new characterization method of common mode suppression ratio for H-field probe is also presented, and it is applicable to conducted emissions measurement in which a probe can detect signals without 90° rotation.

Robust and non-robust bound states in the continuum in rotationally symmetric periodic waveguides.

A fiber grating and a one-dimensional (1D) periodic array of spheres are examples of rotationally symmetric periodic (RSP) waveguides. It is well known that bound states in the continuum (BICs) may exist in lossless dielectric RSP waveguides. Any guided mode in an RSP waveguide is characterized by an azimuthal index m, the frequency ω, and Bloch wavenumber β. A BIC is a guided mode, but for the same m, ω and β, cylindrical waves can propagate to or from infinity in the surrounding homogeneous medium. In this paper, we investigate the robustness of nondegenerate BICs in lossless dielectric RSP waveguides. The question is whether a BIC in an RSP waveguide with a reflection symmetry along its axis z, can continue its existence when the waveguide is perturbed by small but arbitrary structural perturbations that preserve the periodicity and the reflection symmetry in z. It is shown that for m = 0 and m ≠ 0, generic BICs with only a single propagating diffraction order are robust and non-robust, respectively, and a non-robust BIC with m ≠ 0 can continue to exist if the perturbation contains one tunable parameter. The theory is established by proving the existence of a BIC in the perturbed structure mathematically, where the perturbation is small but arbitrary, and contains an extra tunable parameter for the case of m ≠ 0. The theory is validated by numerical examples for propagating BICs with m ≠ 0 and β ≠ 0 in fiber gratings and 1D arrays of circular disks.

Frozen mode regime in an optical waveguide with a distributed Bragg reflector

We introduce a glide symmetric optical waveguide exhibiting a stationary inflection point (SIP) in the Bloch wavenumber dispersion relation. An SIP is a third-order exceptional point of degeneracy (EPD) where three Bloch eigenmodes coalesce to form a so-called frozen mode with vanishing group velocity and diverging amplitude. We show that the incorporation of chirped distributed Bragg reflectors and distributed coupling between waveguides in the periodic structure facilitates the SIP formation and greatly enhances the characteristics of the frozen mode regime. We confirm the existence of an SIP in two ways: by observing the flatness of the dispersion diagram and also by using a coalescence parameter describing the separation of the three eigenvectors collapsing on each other. We find that, in the absence of losses, both the quality factor and the group delay at the SIP grow with the cubic power of the cavity length. The frozen mode regime can be very attractive for light amplification and lasing in optical delay lines, sensors, and modulators.

Discrete spectrum of waveguide modes of a linearly graded-index film introduced into a medium with a stepwise nonlinearity

Even and odd modes propagating along the symmetrical planar waveguide, which is a film embedded in a nonlinear medium, are described analytically. The dielectric function of the film is characterized by a linear spatial profile symmetrical about its center in transverse direction. The dielectric function of the nonlinear medium changes stepwise its value when the electric field amplitude exceeds the threshold value. Exact solutions of even and odd symmetry to the wave equation with such compound dielectric function are found. The solutions describe the waveguide modes existing with the discrete spectrum of the effective refractive index. Waveguide modes can be excited at certain discrete values of the angle of incidence of the exciting beam. Low-order modes are excited at large angles of incidence, and high-order modes are excited at small ones. The number of excited modes is limited and is determined by the parameters of the waveguide system, in particular, by the film thickness and the wavelength of the exciting radiation. Excitation of an even mode of certain order requires a wavelength longer than that of an odd mode of the same order. The intensity of the mode increases with an increasing film thickness, and it decreases with an increasing wavelength. The power flux and the radiation confinement factor are calculated analytically. The radiation confinement factor behaves in the same way as the intensity of the waveguide mode. It is shown that the minimum value of the radiation power required to excite the mode is reached at the critical value of the film thickness (or the critical wavelength), at which the radiation confinement factor is equal to a half.

Regrowth-free AlGaInAs MQW polarization controller integrated with a sidewall grating DFB laser

Polarization control is at the heart of high-capacity data optical communication systems, such as polarization-division multiplexers and Stokes vector modulation transmitters. Despite passive polarization control being mature, the realization of monolithically integrated polarization controllers and single longitudinal mode light sources, such as distributed-feedback (DFB) lasers, is of importance. In this research, we report an AlGaInAs multiple-quantum-well photonic integrated circuit device which can control the state of polarization of the output light source, consisting of a polarization mode converter (PMC), a differential phase shifter (DPS), and a sidewall grating DFB laser. We demonstrate an asymmetrical stepped-height ridge waveguide PMC to realize TE to TM polarization conversion and a symmetrical straight waveguide DPS to enable polarization rotation from approximately counterclockwise circular polarization to linear polarization. Based on the identical epitaxial layer scheme, all the PMC, DPS, and DFB lasers can be integrated monolithically using only a single step of metalorganic vapor-phase epitaxy and two steps of III-V material dry etching. For the DFB-PMC device, a high TE to TM polarization conversion efficiency (98.4%) over a wide range of DFB injection currents is reported at 1555 nm wavelength. For the DFB-PMC-DPS device, a nearly 60° rotation of the Stokes vector on the Poincaré sphere was obtained with a range of bias voltage from 0 to −3.0 V at a laser drive current of 170 mA.

Development of a three-dimensional semi-coherent energy flux propagation model

The classic energy flux propagation model integrates an averaged intensity distribution over elevation angle for an azimuthally symmetric waveguide, and the method has also been extended to reincorporate some of the coherence in the mode-sum cross product, producing caustic features and convergence zones. Some ocean environments with asymmetric range-dependent bathymetry and acoustic medium properties can refract the acoustic wave horizontally which N-by-2D models cannot capture due to their assumed symmetry. Fully three-dimensional models can capture horizontal refraction but are typically computationally expensive to execute. Further development and study of the energy flux method is worthwhile since it avoids root-finding, is not a marching solution, and it invokes mode number invariance under the adiabatic modes assumption to map propagation angles and directly integrate the intensity distribution at the receiver location. A first-pass at analytically deriving a generalizable three-dimensional energy flux model was presented previously, and this current study focuses on further analytical development, numerical implementation, and efforts to verify the model using other three-dimensional acoustic propagation models.

Bistable Reflection Assisted by Fano Resonance in DMDMW With Low-Threshold and Large Modulation Depth

Owing to an additional thinner planar waveguide with micron scale is attracted to the symmetrical metal cladding waveguide (SMCW) with sub-millimeter scale, the interference interaction between different Q-value guided modes would generate a Fano reflectivity curve. In our double metal-dielectric-metal waveguides (DMDMW) structure, a Kerr nonlinear medium is located in the guiding layer of the SMCW where the excited oscillating wave is enormously enhanced. Numerical calculations show that a minute variation of the incident light intensity will give rise to a change in the dielectric constant of the Kerr nonlinear medium and lead to positive feedback. A bistable reflection can be achieved with a low threshold and a large modulation depth because of the sharpness and the asymmetricity of the Fano reflectivity curve.

Optical propagation of exciton polaritons in ultrathin van der Waals microcrystals down to few monolayers

The exciton polariton is a kind of quasiparticles and provides a promising opportunity to explore fundamental quantum phenomena for photonic applications. Transition-metal dichalcogenide (TMD) materials provide the platform of nanophotonics that supports the propagative exciton polaritons even at room-temperature. Previously, real space studies on thin flakes of TMDs by scattering-type scanning nearfield optical microscopy (s-SNOM) were limited to waveguide thickness down to 30 nm. In this work, we present the nano-optical imaging of ordinary transverse electric modes of exciton polaritons in MoS2 and WSe2 down to a few atomic layers, measured by atomic force microscope-based s-SNOM. Surprisingly, the interference fringe patterns can be observed clearly at the prepared ultrathin TMD flakes with thickness down to ~3 nm (4 ML) and ~8 nm (12 ML) for MoS2 and WSe2, respectively, which breaks greatly the previous measurement limitation. The wavevectors stay around 1.6k0−1.7k0 constantly when the thickness approaching to a few MLs, instead of 1k0 according to the theory. These modes are supported by the nearly-freestanding TMD microflakes in the form of three-layer symmetric waveguide to confine the exciton polaritons. Our results provide in-depth understanding and open new avenues to explore the polaritonic devices operating at the near infrared region based on ultrathin TMD materials.

Modal analysis of planar waveguides by the immersed interface method

Modal analysis of optical waveguides is a basic task in the design of advanced waveguide devices and optical circuits. How to deal with the problem of electromagnetic heterogeneous interface and absorption boundary condition are two major difficulties in implementing efficient numerical analysis of optical waveguides. Existing high-order accurate finite-difference modal analysis methods do not take into consideration the absorption boundary problem, which, thus, makes it difficult to accurately simulate leakage and radiation modes. Based on the immersed interface method and perfectly matched layer absorption boundary condition, a finite-difference method with the second- and fourth-order accuracy is proposed in this work. By using this method, the single-interface plasmonic waveguide mode, planar symmetric waveguide mode, and one-dimensional photonic crystal waveguide mode are analyzed. Numerico-experimental results show that the convergence rate of the second- and fourth-order algorithm are consistent with the anticipated order of the guided mode, leakage mode and radiation mode. The second-order algorithm provides an ultimate accuracy of about &lt;inline-formula&gt;&lt;tex-math id="M5"&gt;\begin{document}$10^{-9}$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20230595_M5.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20230595_M5.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; for the relative error of effective refractive index, when the normalized step size is &lt;inline-formula&gt;&lt;tex-math id="M6"&gt;\begin{document}$10^{-4}$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20230595_M6.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20230595_M6.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;. The fourth-order algorithm provides an ultimate accuracy of about &lt;inline-formula&gt;&lt;tex-math id="M7"&gt;\begin{document}$10^{-10}$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20230595_M7.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20230595_M7.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; for the relative error of effective refractive index, when the normalized step size is &lt;inline-formula&gt;&lt;tex-math id="M8"&gt;\begin{document}$10^{-3}$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20230595_M8.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20230595_M8.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;. Through the study of field distribution of guided mode and cladding mode in a one-dimensional photonic crystal waveguide, we show that the continuity of the field of transverse electric mode and its first derivative across the interface, and the continuity of the field of transverse magnetic mode and the discontinuity of its first derivative across interface, can be analyzed accurately. The method proposed in this paper can be used to calculate any mode for any refractive index profile, only by using the value of refractive index, independent of the specific functional representation of modal fields. The method provides a simple and efficient tool for implementing the modal analysis of step-index planar waveguides.

Coupling Performance Enhancement of GaSb-Based Single-Transverse-Mode Lasers with Reduced Beam Divergence Obtained via near Field Modulation

Symmetric narrow waveguide structure has been developed and fabricated to achieve low beam divergence and improved coupling performance of the 1.95 μm GaSb-based single-transverse-mode diode lasers. The near-field expansion effect of the narrowed 150 nm vertical waveguide design leads to a reduced fast-axis beam divergence of 44.2° full width at half maximum (FWHM) as well as 62% single-mode fiber (SMF) coupling efficiency, which has 55% relative promotion compared to the 40% efficiency of the conventional 270 nm waveguide design with 60.4° FWHM. The highest SMF coupling power of 113 mW was obtained by the 210 nm narrow waveguide lasers with lower internal optical loss at a 55% coupling efficiency, which performed balanced optimal performance with a narrowed divergence of 53.4° and a relatively high optical power of 206 mW. The high coupling efficiency and power will provide more promising prospects for the GaSb-based single-transverse-mode lasers in the widespread fiber-based and external-cavity applications.

Theoretical study on fabrication of sub-wavelength structures via combining low-order guided mode interference lithography with sample rotation

Abstract Guided mode interference lithography based on a symmetric metal-cladding dielectric waveguide structure (a resist between two metal layers), is studied. The low-order guided modes in the waveguide structure excited by 325 nm laser, and then sub-wavelength gratings with half-periods of 47 nm ( λ /6.91) and 60 nm ( λ /5.42) can be obtained by excited TM0 and TE0 guided modes, respectively. Among them, the period of the sub-wavelength grating fabricated by TM0 guided mode interference is smaller, but it is limited by the thickness of resist. TE0 guided mode interference is more suitable for thick resist. On this basis, taking TM0 guided mode as an example, periodic sub-wavelength structures, such as square lattice and quasi-hexagonally close-packed structure, can be obtained by rotating and exposing the sample in different ways. The proposed method of combining guided mode interference lithography with sample rotation has simple operation and low cost, and provides a theoretical reference for fabricating two-dimensional sub-wavelength structures.

Polarization-Reconfigurable Compact Wideband Slot Antenna by Using Liquid Metal

In this letter, a compact, low-profile, and wideband slot antenna with polarization reconfigurability is presented by using liquid metal (LM). A small rectangular ring placed below the microstrip line of a symmetric coplanar waveguide (CPW) is used for bandwidth enhancement. Three horizontal currents performed by LM injection are inserted for wide circular polarized excitation. The channel realized by three-dimensional printed technique is loaded on the antenna to provide reconfiguration conditions. By injecting the LM into the left or right channels, the radiation of right-hand circular polarization or left-hand circular polarization is achieved. While when the two channels are empty or both LM injections, the linear polarization (LP) radiations at two operating frequency bands are obtained. A prototype was fabricated and measured. Measurements show that the proposed antenna exhibits a wide impedance bandwidth (IBW) of 67% and an overlapped axial ratio bandwidth of 39.2% for the CP modes. While in the LP states, the overall reconfigurable IBW is 39.7%. Besides, the size of the antenna is 0.30 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> × 0.32 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> × 0.03 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> , which is quite compact and low-profile.

A Compact and Simply-Constructed All-Metal Circularly Polarized Ridge-Waveguide Slotted Antenna Array for Vehicle Mounted Satcom on the Move (SOTM) Communication Application

In this paper, a novel circularly polarized (CP) ridge-waveguide slotted antenna array is proposed for vehicle used Satcom on the Move (SOTM) applications. The antenna array is designed closely following the required factors for generating the circular polarization. The proposed antenna array is constructed on a symmetrical single-ridge slotted waveguide. Each antenna element consists of a pair of inclined slots opened on the narrow walls, and longitudinal slots opened on the bottom of the U-shaped wall of the waveguide. The inclined slots and the longitudinal slots are able to radiate orthogonal electric-fields independently with a phase-difference of 90°. After a vector superposition in the far-field by using this design, the circular polarization could be realized with extremely low axial ratio theoretically. Several essential parameters affecting the CP performance are also studied in this paper. To verify the feasibility of the proposed approach, a four-element CP antenna array is simulated, fabricated and measured. Results show that the obtained prototype achieves a measured impedance bandwidth of 14.74% from 9.24 GHz to 10.71 GHz with S11 <−10 dB, and a 3-dB axial ratio bandwidth of 19.1% from 9.0 GHz to 10.9 GHz.

Experimental Verification of Backscattering Protection in PTD-Symmetric Bifilar Edge Waveguides

This article presents the design and experimental characterization of microwave structures based on parity time-reversal duality symmetric bifilar edge waveguides (PTD-BEWs) realized through a parallel plate waveguide (PPW) loaded by a metasurface. The analyzed structures include transmission lines with bends and multiple line arrangements. Due to their unique symmetry properties, these structures are robust against backscattering, thus resembling the behavior of topological WGs, despite the fact they are reciprocal. This makes it possible to guide the electromagnetic (EM) waves along the edge with low insertion losses and unique matching properties. Measurements, performed in the frequency range between 24 and 32 GHz, have confirmed the feasibility of the theoretical concept.

High-order mode interaction structure for a W-band CW sheet beam extended interaction klystron

To solve the problem of mode competition in high-order working modes, this paper presents a fast design method based on the TM31-2π mode for the dumbbell shaped extended interaction cavity. Based on the equivalent circuit theory, the high-frequency characteristics of the structure are studied. In addition, we propose a W-band continuous wave sheet beam extended interaction klystron high-frequency circuit. The circuit was driven by a 20 kV and 0.85 A sheet electron beam, with a 3.2 × 0.3 mm2 section. The beam was focused by a 0.8 T permanent magnet system. The high-frequency system adopts five dumbbell shaped five-gap cavities, and the output system adopts a symmetrical output waveguide. The 3D particle-in-cell simulation shows that more than 1.5 kW power can be obtained at an input power of 0.12 W, and the electron efficiency and gain are 9.2% and 41.2 dB, respectively.