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This work presents a new analytical transmission line model for microstrip T-resonator dielectric constant measurement method in order to simplify the extraction of the complex dielectric permittivity of the substrate and increase its accuracy. The proposed new formula, which is based on the T -matrix equivalent circuit of the structure, is only dependent on the propagation and attenuation constants of the stub line. Two new formulas to determine the end effect of open-ended stub and the propagation constant parameters are also presented. As an example, a T-resonator is implemented on a 31 mil RO4003C substrate, and it is simulated and measured S-parameter results in the range of 1 MHz–8 GHz are used to calculate a complex dielectric constant of the substrate at each resonance frequency. A full-wave simulation is also used to confirm the accuracy of the proposed model. The comparison between the simulated and the measured S-parameters demonstrates a relative error of

This study examines the analytical and numerical solution of electromagnetic surface waves supported by a resistive metasurface-covered grounded metamaterial structure. To simulate the metamaterial, the Kramers–Kronig relation based on the causality principle is used, while the modeling of the resistive metasurface has been done by implementing the impedance boundary conditions. The analytical expressions for the field phasors of surface waves are developed for the transverse magnetic (TM) polarized mode and transverse electric (TE) polarized mode. The characteristic equations are computed for both modes, and the unknown propagation constant is evaluated numerically in the kernel. After computation, the dispersion curves, electric field profiles, effective mode index ($$N_{eff}$$ N eff ), and phase speeds ($$v_{p}$$ v p ) are presented for both the TM and TE polarized modes. To study the tunability of surface waves, the influence of the thickness of the metamaterial slab ($$d$$ d ), effective permittivity of the metamaterial ($$\varepsilon_{1}$$ ε 1 ), thickness of the resistive metasurface ($$t$$ t ), and effective permittivity of the metasurface ($$\varepsilon_{r}$$ ε r ) on all the numerical results has been studied. However, the geometrical parameters are found to be more sensitive to the effective mode index ($$N_{eff}$$ N eff ) and phase speed ($$v_{p}$$ v p ) of the surface waves. The results are consistent with the published results, which reflects the accuracy of the work. It is concluded that the appropriate choice of parameters can be used to achieve surface waves with the desired characteristics in the GHz range. The present work may have potential applications in surface waveguide design, surface wave speed controllers, surface communication devices, and light trapping configurations.

We propose a method to design compact circularly polarized (CP) antenna using a novel sunshine-shaped slotted radiating patch, which exhibits slow wave and other interesting properties. The structured radiating patch introduces adjustable coupling between a pair of orthogonal modes (TM10 mode and TM01 mode) to facilitate good axial ratio (AR) and reflection parameters of the antenna simultaneously in the radiating frequency band. A $\pi $ /2 balun is employed to excite the TM10 and TM01 modes by using back feeding structure. Based on the proposed method, a compact left-hand CP antenna is designed, fabricated, and measured to verify the feasibility of the design method. The whole antenna is $0.17\lambda _{0}\times 0.17\lambda _{0}$ in dimension ( $\lambda _{0}$ is the wavelength in free space) and the measured maximum gain is 5 dBic in the working band, and 3 dB AR bandwidth is 0.4% for left-hand CP.

In this article, a new transmission-line-based analysis is introduced to design the gradient and Huygens’ metasurfaces. In this method, each unit cell of the gradient and Huygens’ metasurfaces is modeled by a transmission line with a specific characteristic impedance and propagation constant. By using this method, a prototype for each of the gradient and Huygens’ metasurfaces is designed and simulated. Each unit cell in the prototype consists of only one magneto-dielectric slab. Due to the difficulty of realizing the magneto-dielectric materials, a special unit cell structure consisting of three dielectric slabs is introduced. A prototype for each gradient and Huygens’ metasurface is designed and simulated. To verify the designed structure, a Huygens’ metasurface prototype is fabricated using Rogers TMM 13i substrate. The measured results are in good agreement with the theoretical results.

This paper presents the results of an analysis of the necessary propagation conditions in a step-index optical fiber with a Kerr nonlinearity of two modes, LP01 and LP11, during the transmission of high-power optical pulses. All results were obtained by solving a system of two nonlinear equations for these modes, obtained by the Gauss approximation method, and the subsequent use of a procedure for refining estimates using the mixed finite elements method. The necessary conditions are determined, estimates of the boundaries for the range of normalised frequencies for which they are fulfilled are obtained, and an approximate formula is proposed for estimating the upper limit of this range.

An expression for the propagation constant, cutoff frequency, and associated fields of the first two modes in a waveguide filled with a tilted slab of the dielectric is derived using the variational analysis. The solution to such a problem is divided into two parts. First, the slab is assumed to be parallel with the walls of the waveguide with no tilt. In this part, the effective permittivities of the first two orthogonally polarized modes are derived from two different variational expressions for the transversal resonance frequencies. This results in a diagonal tensorial permittivity that represents an effective uniaxial anisotropic medium. Next, this tensorial permittivity is transformed into a tilted set of coordinates representing the required tilt angle. In the new set of coordinates, a variational expression for the propagation constant is solved using the Rayleigh–Ritz procedure. The resulting analytic expressions are verified using a full-wave analysis and a prototype measurement.

It is formulated a model, within which, regularities for formation of nonlinear surface waves with a specific field structure are described. It is shown that there are two new types of waves of chosen polarization, which propagate along the contact of a photorefractive crystal with diffusion nonlinearity and a nonlinear optical medium with switching. Nonlinearity in this medium is modelled by a stepwise changing the refractive index depending on the field amplitude. The field structure in the obtained surface waves consists of three components in different regions of contacting media. The propagation of a localized light beam along the boundary at the near-boundary region results in formation of an area of a finite width, which has a refractive index that is different from the remaining medium. The field exponentially decreases in the region behind this domain when moving away from the near-boundary region. In a photorefractive crystal, the field can decrease with oscillations or without oscillations. The dependence of the propagation constant on optical characteristics of media and guiding parameters is derived in the explicit analytical form.

A study of the influence of the parameters design, such as the refractive index of the core, the cladding and the radius of the core on propagation constant (β) of single-mode optical fiber in optical communication region (1.2-1.6) m have been investigated. Material, waveguide, and profile dispersions are analyzed and investigated. Three models of optical fibers with different relative refractive indices () (0.004, 0.007, 0.01) at a wavelength equal 1.55 m, and three models of core radius (3,4,5) m is taken in the count. Numerical simulations and modeling are arranged depending on weakly guiding approximation for solving homogeneous wave equation derived from Maxwell’s equations. Our modeling solved by the aid of MATLAB software. Material and profile dispersion have no significant change for various relative refractive index, while waveguide dispersion is affected by the change of relative refractive index. the waveguide dispersion increased by increasing core diameter and the profile dispersion decreased as the core diameter increased. There is no effect on martial dispersion by increasing the core diameter.

The theoretical analysis of transverse electric surface waves in ferrite medium surrounded by isotropic plasma layers is presented in this manuscript. Maxwell’s equations in differential form are used, and we impose the boundary conditions to acquire the dispersion relation to formulate the proposed structure. The influence of number density, separation distance between the layers of plasma, and dielectric permittivity of ferrite film on the normalized propagation constant is studied. It is concluded from the result obtained that if the number density and values of dielectric permittivity of ferrite film increases the propagation constant Re(β) tends to decreases whereas the increase in separation distance between the layers of plasma tends to increase the propagation constant Re(β). Furthermore, to verify the surface waves, the normalized field distribution for plasma medium as well as ferrite medium are also presented in this manuscript. The present work has potential applications in communication, drug delivery, cancer treatment, and ferrite sensing waveguide structures in the GHz frequency regime.

We present a simplified Nicolson–Ross–Weir (NRW) material characterization procedure that employs only a single-port network analyzer for data collection. This approach is particularly attractive for mmW and THz applications, as it eliminates the need for costly two-port instrumentation required in the conventional NRW method. Akin to the well-known adapter removal techniques, we use two successive calibrations of the defined measurement ports and deduce the two-port response of the sample under test. Subsequently, the conventional NRW procedure can be employed to simultaneously determine permittivity and permeability of the material under test. We demonstrate our approach for the WR8.0 waveguide band (90–140 GHz) using a multioffset-short calibration method. Similar to the two-port through–reflect–line calibration, the multioffset-short process determines the propagation constant of the waveguide, which provides additional verification of the quality of the collected measurements and the validity of the NRW procedure. We demonstrate that the simplified one-port NRW method is as effective in performance as the conventional two-port procedure. To our knowledge, this is the first-time realization of the single-port NRW method for mmW and THz bands.

[EN] Optical fibers featuring multi-layer refractive index profiles have been widely investigated and developed in a variety of scenarios, including space-division multiplexing transmission, fiber sensing, loss and dispersion management, as well as high-power amplifiers and lasers. For the first time to our knowledge, we present in this paper a general model deriving the universal characteristic equation for multi-layer optical fibers that comprise a set of concentric layers with arbitrary radial dimensions and refractive index values, considering both stepped (as step-index) or continuous (as graded-index) profiles. Expressions for the main fiber propagation parameters are also derived. We validate the model by comparing our results to the ones provided by numerical software tools with excellent matching for a series of particular optical fibers comprising step-index trench-assisted, ring-core, triangular-index and four-cladding profiles. This compact universal characteristic equation serves as a useful tool for optical fiber designers, where one can get valuable physical insights without the need to resort to numerical software tools, and even evaluate the effect of a single layer in isolation without the need to evaluate the whole refractive index structure., This work was supported in part by the European Research Council (ERC) under Consolidator Grant Project 724663, and in part by the Spanish MINECO under TEC2016-80150-R project, BES-2015-073359 scholarship for S. Garcia and Ramon y Cajal fellowship RYC-2014-16247 for I. Gasulla.

The relative average inter-core crosstalk (IC-XT) among wavelength-division multiplexed (WDM) optical channels in a quasi-homogeneous two-core fiber system exhibiting slight differences on the propagation constant, inverse group-velocity, and the group-velocity dispersion (GVD) between cores is numerically investigated. This analysis is performed using a theoretical formalism that includes fiber nonlinearities in the presence of random perturbations. The results show oscillations on the average IC-XT of WDM channels that mainly depend on the walk-off between cores. These oscillations arise superimposed to the linear wavelength-dependence of the IC-XT caused by the core-coupling coefficient. As transmission power increases, the nonlinearities do not reduce the presence of these oscillations, but slightly modify their amplitudes and periods. These results provide valuable information to fully understand the wavelength dependence of the average IC-XT of real multi-channel MCF systems, especially those of very short reach.

In this study, a novel quasi-transverse electromagnetic (TEM) transmission line (TL) on a single-layer substrate is presented. The proposed structure comprises bilateral metalised vias and two longitudinal slots on the top and bottom plates, respectively. This two-conductor TL separated by the two slots allows the quasi-TEM mode and guarantees high isolation due to the vias which constrain the electromagnetic field. Additionally, the proposed structure provides a remarkable high range of the characteristic impedance, enabling a more flexible design. Furthermore, an empirical analytical formula is derived to calculate the characteristic impedance of the proposed TL adopting conformal mapping, and modified by a polynomial fraction. The transitions to the double-sided parallel-strip line and the microstrip line are proposed with which the propagation constant of this TL is extracted. The comparisons of the far-end couplings of several types of microwave TLs have been provided by the simulation and measurement to verify the isolation property of the proposed TL. Finally, the proposed TL is applied to the T-junction wideband power divider design to demonstrate its practicability. A prototype is fabricated and measured with a wide operating bandwidth from 6.8 to 17.6 GHz.

This paper introduces a prospective material for photonic laser applications. Different high purity samples of olive oil were subjected to a spectrophotometer to determine the absorption spectra. The transmission behavior of olive oil is about (44.28) % at a wavelength of 532 nm, while it is (62.94) % at 1064 nm. Then, the nonlinear optical properties represented by the nonlinear refractive index and nonlinear absorption coefficient are determined using a highly sensitive method known as the Z-scan technique. Z-Scan experiment was performed using 1064 nm CW Nd:YAG and 532 nm SHG Nd:YVO4 lasers. n2 = 3.99×10-6W/cm2 and beta = -0.0017 m/W for 1064nm wavelength and n2 = 2.45×10-7W/cm2 and beta =-7.26×10-4 m/W for 532nm wavelength. This paper gives simulation results for a liquid-core optical fiber (LCOF) filled with olive oil. The nonlinear propagation constant and group velocity dispersion (GVD) properties are estimated. The simulation of the generation of LCOF is also obtained. The calculations show that LOCF can provide huge nonlinear parameters and a large span of slow varying GVD characteristics in the visible and infrared region, which have potential applications in optical communications and nonlinear optics. The material is olive oil which is classified as an organic compound, having good nonlinear optical properties making it a potential candidate to be for photonic applications.

—The article studies eigenwaves of an electromagnetic crystal in the form of a two-dimensionally periodic lattice of metal cylinders with capacitive gaps between two metal screens forming a plane waveguide. The standard system of electrodynamic modeling is used to study the dispersion characteristics of eigenwaves propagating in a structure in the first and second transparency bands in the self-oscillation mode. In the plane-wave excitation mode, the authors study the characteristics of an electromagnetic crystal layer infinite in one coordinate in its transparency bands. It is shown that the fundamental eigenwave of the structure in the first transparency band is a slow wave, the deceleration coefficient of which increases at the boundary of the first band gap. It has been established that in the second transparency band, under certain conditions, backward waves can occur with anomalous frequency dispersion of the propagation constant. The relationship between the conditions of the occurrence of backward waves and the frequency of the series resonance of the capacitive cylinder is shown.

In this paper, a novel technology based on double-layer metasurfaces is proposed in order to broaden the bandwidth of microstrip antennas, which has been verified in X-band linearly polarised and circularly polarised antennas. Referring to the conventional metasurface antenna that employs slot-coupled feeding, these designs add an extra metasurface between the radiation patch and the ground plane so as to establish dual resonance modes, TM10 and TM20. Following the adoption of the composite right/left-handed transmission lines principle, this technique aims to adjust the propagation constant in the right-hand region by introducing parallel inductors and capacitors to widen the dual resonant frequencies' interval, thereby realising a broadband antenna. In addition, the interlayer metasurface may also be utilised as a director to balance the E-field of the radiation patch. A linearly polarised double-layer metasurface antenna with a size of 0.8 0.8 0.058 (wavelength in free space at the centre frequency) is filled with F4B substrate with a dielectric constant of 2.2. It finally realises an impedance matching bandwidth (VSWR 2) from 8.41 to 11.67 GHz, occupying about 32.47 of the centre frequency. This circularly polarised antenna attains both an impedance matching bandwidth of 32.44 (i.e. 8.29–11.5 GHz) and an axial-ratio bandwidth of 19.72 (i.e. 9.6–11.7 GHz).

In this article, a periodic leaky wave antenna (LWA) is presented for fixed frequency beam scanning in microstrip line technology. Both the beam angle and the beamwidth can be controlled electronically. The unit cell of the antenna is loaded with shunt stubs, which are either short or open-circuited, using p-i-n diodes as a switch. The switching of the stub alters the impedance loading of the antenna, leading to a change in the propagation constant and thus the main beam angle. The input impedance of the stubs is chosen for symmetrical beam scanning through the broadside direction. A total of 50 distinct main beam positions with an angular separation of approximately 1° are selected from the different switching states using an iterative process. The second set of p-i-n diodes are inserted between the consecutive unit cells to control the leakage and, hence, the beamwidth. The antenna is fabricated and measured at 2.45 GHz. The measured main beam angle scans from −26° in the backward direction to +24° in the forward direction, through broadside, with an overall measured gain variation of 1.2 dB. Also, the beamwidth can be continuously tuned up to a maximum of 204%, keeping the gain variation within 1.2 dB.

In this letter, a wideband transition for exciting the second higher order mode on microstrip line is presented. Different from the traditional excitation method, a systematical design approach is first conducted. The field distribution of higher order modes could be well matched and transformed into quasi-TEM mode by a taper structure. Based on the study of the orthogonal principle of different modes, each mode could be effectively excited by a specific amplitude/phase condition of the feeding network. To meet the wideband amplitude and phase radio requirements among different ports of the feeding network, a multimode resonator-based phase shifter could be utilized to achieve 180° phase difference. To validate this proposal, a wideband EH0-to-EH2 mode transition with 60% bandwidth is proposed, designed, and implemented. Both the extracted propagation constant and the back-to-back S -parameters show good wideband response over the concerned frequencies.

The hybrid modes in the plasmonic quantum dot (QD) laser are modeled using the Marctili method. The model is then used to study the mode characteristics. The modes are going to cutoff point at zero propagation constant, while it goes to surface plasmon polaritons (SPPs) mode at higher photon energy. This behavior was different from that of waveguide modes shown in the dielectric waveguide. At plasmon resonance, hybrid mode is exactly one mode: surface plasmon polariton mode (perfect electric conductor).

An ultra-broadband mode splitter is proposed based on the phase controlling of the bridged subwavelength grating (BSWG) waveguides. An asymmetric directional coupler composed of two BSWG waveguides with an identical waveguide-width but two different bridge-widths is introduced to split the TM0 and TM1 modes based on the mode-sensitive phase-matching condition. The proposed mode splitter is optimized by utilizing the 3D full-vectorial finite difference time domain method. The results indicate that the proposed mode splitter can achieve a compact coupling length of 5.75 μm, the insertion losses of 0.41 dB and 0.53 dB, and the mode crosstalks of −19.6 dB and −27.8 dB for the TM0 and TM1 modes, respectively. The broad bandwidths of 430 nm and 372 nm can be achieved with the mode crosstalk of ≤−15 dB for the TM0 and TM1 modes, respectively. The fabrication tolerances are also studied in detail. The proposed mode splitter could be employed for signal selection and routing in the mode division multiplexing networks.

In this letter, a symmetrical periodic leaky-wave antenna is proposed using an annular-elliptical-shaped unit cell loaded with balanced shorting pins across the E -plane. The proposed structure is a series-fed antenna array with a microstrip feed-line. The even symmetry field distribution across the longitudinal plane of the unit cell has the controllable propagation constant feature. With excitation of double symmetry (even TM21) mode of an annular elliptical patch at broadside frequency, the open stopband is suppressed. Thus, the antenna shows a wideband and a wide scanning capability of 105° (−78° to 27°). The measured results validate the proposed antenna with a maximum realized gain of 16 dB. The possibility of independent control of the directivity and the main beam direction is also presented at a fixed frequency by simultaneously varying two geometrical parameters.

We present a new method to design miniaturized antennas using a corrugated microstrip (CM) line, which shows good slow wave characteristic in the required frequency band. To achieve good radiating behavior and low profile simultaneously, CM is employed as the resonating part of the antenna. The impact of the CM propagation constant on the antenna is discussed in detail. The miniaturized antenna is designed and measured to verify the feasibility of the design method. The measured results show that the proposed antenna can achieve a beamwidth of 70° in E-plane and 75° in H-plane with a gain tolerance of 3 dB, and the realized peak gain level at the central frequency is 5.15 dBi, which have good agreements to the expected designs. Such results indicate that the proposed antenna exhibits excellent radiation characteristics at the resonant mode. The effective size of the proposed miniaturized antenna is $0.16\lambda _{0}\times 0.16 \lambda _{0}\times 0.04 \lambda _{0}$ at 9 GHz, in which $\lambda _{0}$ is the wavelength of the central frequency.

Propagation constant versus frequency curves are obtained after processing S-parameters measured to several lines differing only in length. The proposed method can be easily implemented once the thru-reflect-line (TRL) eigenvalues are calculated considering different combination of line pairs. The noticeable simplicity of the approach when compared to the original multiline algorithm makes it an attractive alternative to improve the determination of the complex propagation constant in practical applications by using experimental data collected to more than two lines. Here, applicability is demonstrated up to 110 GHz for printed circuit board (PCB) microstrip lines. Furthermore, it is provided an improved equation to determine the effective relative permittivity once the complex propagation constant is determined.

In this article, two novel efficient leaky-wave antennas (LWAs) with stable radiation patterns operating in the 60 GHz band are proposed. The LWAs are implemented in groove-gap waveguide (GGW) technology. To mitigate the beam squint due to the dispersive nature of LWAs, complementary-dispersive prisms are coupled to the LWA radiation aperture. The antennas are implemented in fully metallic purely holey periodic structures, resulting in a more cost-effective and robust manufacturing process compared to previously reported pin-based structures. Two prisms are proposed, one with mirror symmetry and one with glide symmetry. When the prism possesses a glide symmetry, much fewer holes are required while maintaining a similar performance, which even further decreases the fabrication costs. The complex propagation constant is optimized for low sidelobe levels (SLLs) with tailored hole diameters and waveguide dimensions, thus for the first time demonstrating the capability of using glide-symmetric holes to control the leakage rate. Two prototypes with mirror- and glide-symmetric prisms are theoretically synthesized and validated by the simulated and experimental results. A frequency bandwidth of 11% is achieved for both prototypes with the beam squint within ±0.9° (mirror) and ±1.7° (glide), SLLs below −15 dB (mirror) and −13 dB (glide), total efficiency almost 90%, and realized gain of 17 ± 0.5 dB at a fixed observing angle. The developed antennas are intended for mm-wave point-to-point communications.

We consider the propagation of surface TM waves in a three-layer structure the inner layer of which is formed by a plate of a crystal with a Kerr type focusing nonlinearity, while its outer layers are uniaxial photorefractive crystals with the diffusion nonlinearity formation mechanisms. Nonlinear surface waves that differ in the character of their decay can propagate along the interfaces between the layers. The amplitudes of waves of one type decrease without oscillations with increasing distance from the interface as the waves propagate into the depth of the outer layers of the photorefractive crystals, while the amplitudes of waves of the other type decrease with oscillations. The wave profiles can be either symmetric or antisymmetric with respect to the center of the three-layer structure. The waves with the symmetric profile distribution, the amplitudes of which decrease into the depth of the photorefractive crystals either with or without oscillations, can be of two types, while those with the antisymmetric distribution can be only of one type. For the long-wavelength propagation regime of surface waves, explicit analytical dependences of the propagation constant on the characteristics of the layered structure are found and the conditions for their existence are determined.

This letter proposes a dielectric helical antenna made of three-dimensional (3-D) printed zirconia ceramic, which possesses a better performance than the conventional metal one. On the one hand, the radiation principle of the proposed antenna is investigated by regarding its structure as a dielectric waveguide. It is found that a dielectric waveguide operating at the cut-off state of higher mode, here is TM01 mode, can radiate electromagnetic (EM) waves. The propagation constant of EM waves in waveguide is extracted to demonstrate that the dielectric waveguide indeed works as a fast-wave status at this moment. On the other hand, both the far-field and scattering performances between the proposed and conventional helical antennas are comparatively studied. It is observed that the structure composed of dielectric helix and metal ground can achieve similar radiation gain, axial ratio (AR), and AR bandwidth as the conventional all-metal helical antenna, but possessing lower radar cross section at high frequency. Benefited from a ceramic stereolithography apparatus, the proposed structure can be fabricated precisely, and measured results have reasonably validated the simulated ones.