Open Waveguide Research Articles

Prolog to, "Leaky-wave theory, techniques, and applications: From microwaves to visible frequencies"

The theory of electromagnetic leaky waves can explain a variety of electromagnetic phenomena and scenarios, from microwave to visible frequencies. In the field of wave physics, the damping of harmonic oscillations in time and/or space is associated with losses in a dissipative system. Moreover, in open systems, oscillation energy gradually gets lost in the form of radiation toward the remote boundaries of an open region, reducing the amplitude of oscillations, even in a nondissipative system. This effect occurs with radioactive states in quantum mechanics, with damped resonances in open acoustic or electromagnetic cavities, and with leaky-waves in open waveguiding structures. The theory of electromagnetic leaky waves can explain a variety of electromagnetic phenomena and scenarios, from microwave to visible frequencies.

Efficient approximations of dispersion relations in optical waveguides with varying refractive-index profiles.

In this paper we consider the problem of computing the eigen-modes for the varying refractive-index profile in an open waveguide. We first approximate the refractive-index by a piecewise polynomial of degree two, and the corresponding Sturm-Liouville problem (eigenvalue problem) of the Helmholtz operator in each layer can be solved analytically by the Kummer functions. Then, analytical approximate dispersion equations are established for both TE and TM cases. Furthermore, the approximate dispersion equations converge fast to the exact ones for the continuous refractive-index function as the maximum value of the subinterval sizes tends to zero. Suitable numerical methods, such as Müller's method or the chord secant method, may be applied to the dispersion relations to compute the eigenmodes. Numerical simulations show that our method is very practical and efficient for computing eigenmodes.

Fast computation of wave propagation in the open acoustical waveguide with a curved interface

In ocean acoustics, the ocean is considered simply as an open waveguide with a curved interface. To compute the wave propagation in the waveguide, firstly a local orthogonal coordinate transform and an equation transform are applied; secondly a perfectly matched layer (PML) is used to terminate the open waveguide to a bounded one. In this way, the curved interface is turned to a flat one and the equation is also changed to another form in the bounded domain. Based the Dirichlet-to-Neumann (DtN) map, the boundary value problem is reduced to an initial problem. In this paper, a new marching method is provided to solve the initial problem fast. Numerical results show that our treatment is feasible and more efficient.

Leonid Brekhovskikh and his lasting impact on underwater acoustics

This paper will discuss Brekhovskikh’s groundbreaking contributions into physical oceanography and the theory of wave propagation, scattering, and diffraction from the prospective offered by current developments in underwater acoustics. In hindsight, three major contributions stand out in Brekhovskikh’s legacy, which highlight different facets of his personality and his talents. For many decades, ocean acoustics was Leonid’s passion. He developed and promoted an approach to underwater acoustics, which embraced the ocean’s complexity and centered on devising techniques to reliably characterize the uncertain environment by acoustic means. The approach led to creation of an informal but rather productive and enduring “Brekhovskikh’s school.” Leonid worked only briefly on wave scattering by rough surfaces. However, his findings, which became known as the tangent plane approximation, revolutionized the field. Universally recognized are Brekhovskikh’s systematic theoretical studies of underwater sound propagation, which are summarized in his celebrated book Waves in Layered Media. The theory includes spectral representations of wave fields, normal mode theory for open waveguides, and a clear treatment of diffraction phenomena attendant to caustics, lateral waves, and reflection of wave beams and pulses. The book charted the ways forward which have been and are followed by numerous researchers around the globe.

Titanium dioxide slot waveguides for visible wavelengths.

We present the first, to our knowledge, experimental demonstration of a titanium dioxide slot waveguide operating in the visible range of light. Ring resonators based on slot waveguides were designed, fabricated, and characterized for λ≃650 nm. The fabrication method includes atomic layer deposition, electron beam lithography, and reactive ion etching. The required narrow slot widths of a few tens of nanometers were achieved by using a conformal atomic layer re-coating technique. This unique feature-size-reduction technique was applied after the final etching step.

Waveguide-integrated black phosphorus photodetector with high responsivity and low dark current

Layered two-dimensional materials have shown novel optoelectronic properties and are well suited to be integrated in planar photonic circuits. For example, graphene has been utilized for wideband photodetection. Because graphene lacks a band gap, however, graphene photodetectors suffer from very high dark current. In contrast, layered black phosphorous, the latest addition to the family of 2D materials, is well-suited for photodetector applications due to its narrow but finite band gap. Here, we demonstrate a gated multilayer black phosphorus photodetector integrated on a silicon photonic waveguide operating in the near-infrared telecom band. In a significant advantage over graphene devices, black phosphorus photodetectors can operate under a bias with very low dark current and attain intrinsic responsivity up to 135 mA/W and 657 mA/W in 11.5nm and 100 nm thick devices, respectively, at room temperature. The photocurrent is dominated by the photovoltaic effect with a high response bandwidth exceeding 3 GHz.

Numerical modeling of three-dimensional open elastic waveguides combining semi-analytical finite element and perfectly matched layer methods

Among the numerous techniques of non-destructive evaluation, elastic guided waves are of particular interest to evaluate defects inside industrial and civil elongated structures owing to their ability to propagate over long distances. However for guiding structures buried in large solid media, waves can be strongly attenuated along the guide axis due to the energy radiation into the surrounding medium, usually considered as unbounded. Hence, searching the less attenuated modes becomes necessary in order to maximize the inspection distance. In the numerical modeling of embedded waveguides, the main difficulty is to account for the unbounded section. This paper presents a numerical approach combining a semi-analytical finite element method and a perfectly matched layer (PML) technique to compute the so-called trapped and leaky modes in three-dimensional embedded elastic waveguides of arbitrary cross-section. Two kinds of PML, namely the Cartesian PML and the radial PML, are considered. In order to understand the various spectral objects obtained by the method, the PML parameters effects upon the eigenvalue spectrum are highlighted through analytical studies and numerical experiments. Then, dispersion curves are computed for test cases taken from the literature in order to validate the approach.

Dispersion Modeling and Analysis for Multilayered Open Coaxial Waveguides

This paper presents a detailed modeling and analysis regarding the dispersion characteristics of multilayered open coaxial waveguides or cables. The electromagnetic model is based on a layer recursive computation of axial-symmetric fields in connection with a magnetic frill generator excitation that can be calibrated to the current measured at the input of the cable. The layer recursive formulation enables a stable and efficient numerical computation of the related dispersion functions, as well as a detailed analysis regarding the analytic and asymptotic properties of the associated determinants. Modal contributions as well as the contribution from the associated branch-cut (nondiscrete radiating modes) are defined and analyzed. Measurements and modeling of pulse propagation on an 82-km-long HVDC power cable are presented as a concrete example. In this example, it is concluded that the contribution from the dominating axial-symmetric transverse magnetic mode is sufficient, and that the contribution from the branch-cut is negligible for all practical purposes, and in particular if the exterior domain is lossy. The main contribution of this paper is to provide the necessary modeling and analysis tools for a quantitative study of these phenomena.

A Planar and Subwavelength Open Guided Wave Structure Based on Spoof Surface Plasmons

A planar and compact open waveguiding structure based on spoof surface plasmon polaritons (SPPs) was demonstrated. For practicality, instead of the well-known wire medium, the uniaxial strip medium (USM) was proposed and used as the effective bulk material with a negative dielectric constant to support the spoof SPP modes. The relevant formulations, including the modal dispersion relations and the formulation for the waves in a multilayer anisotropic structure, are analytically presented in this paper. Interestingly, instead of taming and suppressing the spatial dispersion (SD), which had been done in most past studies, SD was exploited in the proposed structure to enhance the field confinement of the spoof SPP mode by approximately 41%. Moreover, the thickness of the USM slab could be reduced by 50%, using conductor backing and without perturbing the odd mode. This method and SD can help avoid electromagnetic interactions among various components of a multilayer printed circuit board structure and help miniaturize sensors or surface-wave waveguides in the microwave regime. In this study, the subwavelength thickness of the proposed structure was only 0.09 λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> at 1.34 GHz. Additionally, the propagation loss for such slow-wave structures has seldom been discussed analytically and quantitatively. In this study, through calculations and simulations, low attenuation constants in the spoof SPP propagation direction of the proposed structures were investigated. Finally, an experiment was conducted, and an extraction method for obtaining the required reflection spectrum from the measured S-parameter was developed.

On the absence of trapped modes in locally perturbed open waveguides

This paper presents a new approach for proving that the presence of a bounded defect in a uniform open waveguide cannot produce trapped modes, contrary to the case of a closed waveguide. The originality of the proof lies in the fact that it relies on a modal decomposition. It shows in particular that the absence of trapped modes results from a strong connection between the various modal components of the field. The case of the three-dimensional scalar wave equation is considered.

Active terahertz two-wire waveguides.

We demonstrate, by generating a THz electric field directly within the guiding structure, an active two-wire waveguide operating in the terahertz (THz) range of wavelengths. We compare the energy throughput of the active configuration with that of a radiatively coupled semi-large photoconductive antenna, in which the radiation is generated outside the waveguide, reporting a 60 times higher energy throughput for the same illumination power and applied voltage. This novel, active waveguide design allows to have efficient coupling of the THz radiation in a dispersion-less waveguide without the need of involved radiative coupling geometries.

СПЕКТРАЛЬНЫЙ ПОДХОД К ОЦЕНКЕ РЕЗОНАНСОВ ОТРАЖЕНИЯ В ПРЯМОУГОЛЬНОЙ ВОЛНОВОДНОЙ СЕКЦИИ С ПРЯМОУГОЛЬНЫМ ШТЫРЕМ

Revealing the physical phenomena causing various resonant phenomena is a key to successful design of frequency selective structures. Within the frames of the spectral theory of open waveguide resonators, the nature of the total reflection resonance formed by a rectangular waveguide section with a rectangular post inside is studied. The waveguide section is considered as a single-channel multimode resonator. An interpretation of the total reflection resonance is suggested as a result of excitation of natural oscillations in the resonator. Transformation phenomenon for the resonant mode explaining the resonant reflection of the incident wave by symmetric structures is revealed. It is established that the resonant frequency and quality-factor are estimated precisely by the complex frequency of a single natural oscillation. It is shown that quantitative estimations for the reflection resonance obtained within the spectral theory of open waveguide resonators are in order of magnitude more precise than those obtained within the classical approach. The results obtained make synthesis of bandstop filters, possessing complicated frequency behavior, to be more efficient. Key words: resonance of reflection, rectangular waveguide, natural vibration Manuscript submitted 06.05.2014 Radio phys. radio astron. 2014, 19(3): 258-266 REFERENCES 1. ROSENBERG, U. and AMARI, S., 2007. A novel band-reject element for pseudoelliptic bandstop filters. IEEE Trans. Microwave Theory Tech . vol. 55, no. 4, pp. 742–746. DOI: https://doi.org/10.1109/TMTT.2007.893653 2. KIRILENKO, A. A., KULIK, D. Yu, MOSPAN, L. P., and RUD', L. A., 2013. Reflection Resonances in a Waveguide Section with Two Different Height Posts. Radiophysics and Electronics , vol. 13, no. 2, pp. 154–158 (in Russian). 3. POLITI, M. and FOSSATI, A., 2010. Direct coupled waveguide filters with generalized Chebyshev response by resonating coupling structures. In: Proc. of European Microwave Conference . Roma, Itali. pp. 966–969. 4. TOMASSONI, C. and SORRENTINO, R., 2013. A new class of pseudoelliptic waveguide filters using dual-post resonators. IEEE Trans. Microwave Theory Tech . vol. 61, no. 6, pp. 2332–2339. DOI: https://doi.org/10.1109/TMTT.2013.2258171 5. SHESTOPALOV, V. and SHESTOPALOV, Yu., 1996. Spectral Theory and Excitation of Open Structures . London: Peter Peregrinus Publ. DOI: https://doi.org/10.1049/PBEW042E 6. RUD', L. A., SIRENKO, YUu. K., YATSIK, V. V., and YASHINA, N. P., 1988. A Spectral method of analyzing the effects of total wave transformation by open-periodic and waveguide resonators. Radiophys. Quantum Electron . vol. 31, no. 10, pp. 894–899.DOI: https://doi.org/10.1109/TMTT.2013.2258171 7. KIRILENKO, A.. A., YASHINA, N. P., 1980.On the relationship between resonances in the "locked" modes with the excitation modes of quasi non-closed volume. Pis'ma v ZHTF , vol. 6, no. 12, pp. 1512–1515. 8. KIRILENKO, A. A. and TYSIK, B. G., 1993. Connection of S-matrixof wave guide and periodical structures with complex frequency spectrum. Electromagnetics . vol. 13, no. 3,pp. 301–318. DOI: https://doi.org/10.1080/02726349308908352 9. PRIKOLOTIN, S. A., STESHENKO, S. A., KULIK, D. YU., RUD, L. A., and KIRILENKO, A. A., 2012. Fast full 3D EM CAD of wave guideunits based on the generalized mode-matching technique. In: Proc of Int. Conf. on MMET . Kharkov, Ukraine. pp. 109–112. 10. MOSPAN, L. P., PRIKOLOTIN, S. A., STESHENKO, S. A., and KIRILENKO, A. A., 2013. Spectral Properties of a Rectangular Waveguide Section with Two Uneven Rectangular Posts. Radio Phys. Radio Astron . vol. 18, no. 4, pp. 349–356 (in Russian).

Relation construction of transverse magnetic modes and its application for nonhomogeneous waveguides terminated by perfectly matched layers

Modal computation with high precision is an important issue for wave propagation in optical waveguides when the eigenmode expansion method is applied. This numerical study of an open waveguide is accomplished by terminating the unbounded regions with perfectly matched layers. Then, by the differential transfer matrix method (DTMM), two nonlinear relations of modes for the TM case are proposed for complex waveguides with varied refractive indexes along the transverse direction. For the gradually varied waveguides, a higher approximation is provided and some asymptotic formulas of leaky modes are created, which may be used as better initial values for some iteration methods. Numerical examples illustrate that our treatment is highly feasible and effective.

Electromagnetic field and dispersion characteristic analysis of absorbing onion-like carbon tube waveguides

Here, we present our calculation results of the electromagnetic field distributions and the dispersion characteristics of open cylindrical tube waveguides. The analyzed waveguides are made of the onion-like carbon (OLC) material. The solution of the boundary problem was fulfilled by the partial area method (Nickelson et al. in electrodynamical analysis of open lossy metamaterial waveguide and scattering structures. InTech, UK, pp 27–58 [1]). We have determined the complex roots of the dispersion equation using of the Muller method. It discovered the very complicated dependencies of the phase and attenuation constants on the waveguide radii. Such dependencies arise because the OLC material is the highly dispersive and absorbing one. We have investigated the high-frequency cutoff frequency of the propagating hybrid modes HE11 and HE12 dependent on the tube waveguide external and internal radii. We found that it is possible to reach the one-mode regime of OLC tube waveguide.

Analysis of Scan Blindness in a Linearly Polarized Tapered-Slot Phased Array in Triangular Lattice—Performance Improvement With Parasitic Notches

Various types of scan blindness are analyzed in a single-polarized tapered-slot phased array with triangular lattice arrangement, and a scan blindness removal strategy is proposed. In the presented analysis, two types of scan blindness are observed which have not been previously reported. First, a special case of parallel plate cavity resonance is demonstrated to cause scan blindness at a fixed frequency for E-plane scanning. Second, another cause for E-plane scan blindness is extended from previous observations, by including the fundamental mode of a half-mode open waveguide. This type of leaky-wave-induced scan blindness is limited to triangular lattices and can occur at lower frequencies compared to other types of leaky-wave blindness. In the second part of this paper, parasitic notches are proposed as an effective measure to significantly improve the E-plane scanning characteristics of the considered array by reducing the magnitude of the leaky modes. As a beneficial side-effect, these parasitic notches are also proven to improve the H-plane scanning characteristics by suppressing resonances within the stripline substrate cavity of the individual tapered-slot elements. Numerical simulations and measurements performed on a 169-element array prototype validate the analysis and confirm the effectiveness of the proposed concept for scan blindness suppression.

THz Field Enhancement by Antenna Coupling to a Tapered Thick Slot Waveguide

We demonstrate experimentally the coupling of a THz beam into a laser-machined double-tapered thick slot waveguide operating between 0.3 and 2 THz. Simulation reveals that the THz field generated by a standard photoconductive antenna coupled to an undoped aspheric HRFZ-silicon focusing lens can be enhanced by 30 dB in the 40 ${\bf \mu }$ m taper waist, relative to a traditional Gaussian beam waist (at 1 THz). Analysis of the 8 dB insertion loss reveals positive implications for coupling between THz transceivers and in-plane-emitting antennas or low-loss THz waveguides.

Finite element computation of trapped and leaky elastic waves in open stratified waveguides

Elastic guided waves are of interest for inspecting structures due to their ability to propagate over long distances. In numerous applications, the guiding structure is surrounded by a solid matrix that can be considered as unbounded in the transverse directions. The physics of waves in such an open waveguide significantly differs from a closed waveguide, i.e. for a bounded cross-section. Except for trapped modes, part of the energy is radiated in the surrounding medium, yielding attenuated modes along the axis called leaky modes. These leaky modes have often been considered in non destructive testing applications, which require waves of low attenuation in order to maximize the inspection distance. The main difficulty with numerical modeling of open waveguides lies in the unbounded nature of the geometry in the transverse direction. This difficulty is particularly severe due to the unusual behavior of leaky modes: while attenuating along the axis, such modes exponentially grow along the transverse direction. A simple numerical procedure consists in using absorbing layers of artificially growing viscoelasticity, but large layers may be required. The goal of this paper is to explore another approach for the computation of trapped and leaky modes in open waveguides. The approach combines the so-called semi-analytical finite element method and a perfectly matched layer technique. Such an approach has already been successfully applied in scalar acoustics and electromagnetism. It is extended here to open elastic waveguides, which raises specific difficulties. In this paper, two-dimensional stratified waveguides are considered. As it reveals a rich structure, the numerical eigenvalue spectrum is analyzed in a first step. This allows to clarify the spectral objects calculated with the method, including radiation modes, and their dependency on the perfectly matched layer parameters. In a second step, numerical dispersion curves of trapped and leaky modes are compared to analytical results.

Highly confined and tunable plasmonic waveguide ring resonator based on graphene nanoribbons

A three-dimensional plasmonic open waveguide ring resonator (WRR) based on graphene nanoribbons, which has high confinement and multiple tunability, is proposed and numerically investigated. The intensity of edge graphene plasmons modes (EGSPs) in a nanoring resonator reaches the maximum at resonant frequencies, which indicates that EGSPs can efficiently propagate along the open graphene nanoring resonator even though in nanoscale. Furthermore, the resonant frequencies can be easily manipulated not only by adjusting the geometric parameters but also by changing the doping level of graphene via chemical doping or electrostatic gating without changing the physical size of the geometric structure. The proposed plasmonic WRR can find important potential applications in optoelectronic integrated circuits.

Statistics of scattered photons from a driven three-level emitter in a one-dimensional open space

We derive the statistics of scattered photons from a $\Lambda$- or ladder-type three-level emitter (3LE) embedded in a 1D open waveguide. The weak probe photons in the waveguide are coupled to one of the two allowed transitions of the 3LE, and the other transition is driven by a control beam. This system shows electromagnetically induced transparency (EIT) which is accompanied with the Autler-Townes splitting (ATS) at a strong driving by the control beam, and some of these effects have been observed recently. We show that the nature of second-order coherence of the transmitted probe photons near two-photon resonance changes from bunching to antibunching to constant as strength of the control beam is ramped up from zero to a higher value where the ATS appears.

Circular Layered Waveguide Use for Wideband Complex Permittivity Measurement of Lossy Liquids

The electromagnetic characteristics of a circular metal waveguide with a coaxial cylindrical dielectric insert and a layer of absorbing liquid that fills the space between the insert and the waveguide wall have been studied. The transverse waveguide dimensions are comparable with the wavelength. Dependences of the attenuation and phase coefficients of waveguide modes on the structure size and material properties of the layers are found by solving the boundary value problem. It is shown that based on the proposed layered waveguide with the HE11 type of wave, a measuring cell can be designed to work at either fixed frequency with high differential sensitivity or in the frequency range of the single-mode waveguide operation. The cell is of class of cells with calculable geometry. In this case, a reference liquid with known dielectric properties is not required for absolute measurements of the complex permittivity (CP) of the absorbing liquid. The method of finding the CP of absorbing liquids are verified using electromagnetic modeling with CST Microwave Studio.