ABCD Matrix Research Articles

Proposal of Technique for Analysis of Complementary Frequency Selective Surfaces

AbstractA specific class of frequency selective surface (FSS) is the complementary frequency selective surface (CFSS) that has interesting characteristics such as high angular stability, multiple transmission and/or reflection bands, and the possibility of miniaturization. The analysis and design of this sort of structure are commonly performed using commercial software, which demands a high computational effort, impacting a longer optimization time. The equivalent circuit model combined with a cascading technique emerges as an alternative method to the use of these softwares, in the optimization of the physical dimensions of these structures, as they model the behavior of a CFSS with low computational effort and optimization time, in addition to being able to be implemented in various programming languages. Thus, this work proposes a CFSS analysis technique that combines the equivalent circuit method with the ABCD matrix. To the best of our knowledge, this is the first reported research on approximate techniques for CFSS analysis. The chosen geometry was the circular ring, due to high angular stability and polarization independence. The modeling of the equivalent circuit for patch and aperture geometries is presented. Some structures are simulated, and the results are compared with results obtained with the HFSS software. Finally, two prototypes are built to validate the analyses performed.

Structurally Stable Astigmatic Vortex Beams with Super-High Orbital Angular Momentum (ABCD Matrix Approach)

We have demonstrated efficiency of employing the ABCD matrix approach to transform higher-order structured Laguerre–Gaussian (sLG) beams into structurally stable astigmatic sLG (asLG) beams, highlighting their dynamics at propagating. Radical transformations of the beam structure by a cylindrical lens form not only orbital angular momentum (OAM) fast oscillations and bursts, but also make the asLG beams structurally unstable in propagation through cylindrical and spherical lenses when focusing paraxially. But, if the spherical lens performs a Fourier transform of the asLG beam after a cylindrical lens, the symmetric beam emerges at the lens focal plane with a sharp OAM dip; then, the OAM restores its former astigmatism, becoming structurally stable at the far diffraction domain. By investigating the beam structure at the focal area, we have showed that the OAM sharp dip is associated with nothing less than the process of dividing the OAM into the vortex and astigmatic constitutes predicted by Anan’ev and Bekshaev.

Periodical properties of the ray transfer matrix and generation of sideband modes in a stable laser resonator.

The paper describes a subclass of stable laser cavities, periodic stable laser cavities, in which perturbations consisting of deviations of the mode axis from the ideal direction are of a strictly periodic oscillatory nature. In such resonators, in addition to unperturbed longitudinal-transverse spatial modes with an ideal direction of the optical axis, additional modes can appear at sideband frequencies, associated with the resonant buildup of perturbation oscillations. These modes have approximately the same spatial structure as those of the unperturbed fundamental modes, and their frequency detuning from the frequencies of the fundamental modes is governed by the resonator geometry and the periodicity parameter, i.e., the number of passes in the resonator in one period of perturbation oscillations. For many repetitively pulsed laser systems emitting comb spectrum structures, such as free electron lasers, modern frequency standards using femtosecond lasers, and various comb spectrometers, it is desirable to avoid such periodic stable cavities in order to preserve the purity of the comb spectrum used in them. This may also be important for CW lasers with extreme radiation monochromaticity. In some repetitively pulsed lasers, on the contrary, it may be desirable to use such periodic stable laser cavities for a more complete frequency filling and higher quasi-continuity of their emission spectra.

Simple method to suppress n = −2 harmonic for periodic leaky-wave antennas with open-stopband suppression

Periodic leaky-wave antennas (PLWAs) suffer two main issues limiting their scanning ability. The first one is n= −2 spatial harmonic radiation, generating high grating-lobe levels. In this paper, a simple technique by introducing glide-symmetry structure to the PLWA is analysed and used to reduce n = −2 space harmonic level and enhance n = −1 harmonic radiation, subsequently. The other issue is open-stopband (OSB), preventing PLWAs from scanning through broadside. By analysing the ABCD matrix of the cascaded equivalent circuit for the unit cell, a conjugate match condition to counteract the susceptance of the radiation element to suppress the OSB is obtained, which is simple without extracting any parameters. A half-mode substrate integrated waveguide-based prototype is designed and manufactured to demonstrate the proposed methods. The measured results show that the proposed antenna achieves gain fluctuation lower than 1 dB and sidelobe level less than −12 dB, indicating OSB and n = −2 harmonic suppression well, which demonstrates the validity of the proposed method.

Study of coupling optics of cylindrical microlens fabricated on tips of graded index fibers having different profile exponents

Abstract With the help of ABCD matrix concept, we examine the coupling efficiency of a single mode circular core graded index fiber (GIF) excited by laser diode via cylindrical micro lens on the fiber tip. We investigate the efficiencies for refractive index distribution of some specific profile exponents such as g = 4.0, 8.0, 10.0 and 20.0. The refractive index distribution for GIFs had been studied earlier. The efficiency is calculated along the vertical plane as the efficiency is very poor along the horizontal plane. For two very common wavelengths 1.3 μm and 1.5 μm the efficiencies have been calculated and for 1.3 μm wavelength the refractive index distribution of profile exponent (g) having the value g = 4 is found to be most efficient in this context. The results are very much important in the design of optical optimization.

A Review of Variable-Beam Divergence Angle FSO Communication Systems

Free-space optical (FSO) communication is widely used in satellites, ships, aircraft, and ground stations due to its advantages of high speed, large capacity, good confidentiality, and strong anti-interference ability. Variable-beam divergence angle (VBDA) technology makes FSO systems more flexible; this has the benefits of higher acquisition probability, stronger tracking ability, wider communication link range, and lower energy consumption. In other words, the study of VBDA has both theoretical significance and practical relevance. This paper conducts a comprehensive search of relevant scientific databases, journals, conference proceedings, patents, and books to identify publications related to VBDA technology. We analyze these publications, classify and organize various VBDA techniques based on their respective methods. To the best of our knowledge, this is the first review of VBDA technology. In this paper, we first explain the basic principle of changing the beam divergence angle by employing the ABCD matrix, and further furnish a detailed overview of the methods used for VBDA along with their corresponding advantages and disadvantages. In addition, we provide a comprehensive summary of the research conducted using VBDA technology across different link types. Lastly, we identify the challenges and potential future research directions for VBDA technology.

Beyond the ABCDs: A better matrix method for geometric optics by using homogeneous coordinates

Geometric optics is often described as tracing the paths of non-diffracting rays through an optical system. In the paraxial limit, ray traces can be calculated using ray transfer matrices (colloquially, ABCD matrices), which are 2 × 2 matrices acting on the height and slope of the rays. A known limitation of ray transfer matrices is that they only work for optical elements that are centered and normal to the optical axis. In this article, we provide an improved 3 × 3 matrix method for calculating paraxial ray traces of optical systems that is applicable to how these systems are actually arranged on the optical table: lenses and mirrors in any orientation or position (e.g., in laboratory coordinates), with the optical path zig-zagging along the table. Using projective duality, we also show how to directly image points through an optical system using a point transfer matrix calculated from the system's ray transfer matrix. We demonstrate the usefulness of these methods with several examples and discuss future directions to expand the applications of this technique.

ABCD transfer matrix model of Gaussian beam propagation in plano-concave optical microresonators.

Plano-concave optical microresonators (PCMRs) are optical microcavities formed of one planar and one concave mirror separated by a spacer. PCMRs illuminated by Gaussian laser beams are used as sensors and filters in fields including quantum electrodynamics, temperature sensing, and photoacoustic imaging. To predict characteristics such as the sensitivity of PCMRs, a model of Gaussian beam propagation through PCMRs based on the ABCD matrix method was developed. To validate the model, interferometer transfer functions (ITFs) calculated for a range of PCMRs and beams were compared to experimental measurements. A good agreement was observed, suggesting the model is valid. It could therefore constitute a useful tool for designing and evaluating PCMR systems in various fields. The computer code implementing the model has been made available online.

Analytical method for single and coupled nonuniform guiding structures

An analytical method is developed to analyze single and coupled nonuniform TEM or Quasi-TEM guiding lines. In some cases, the solution can be extended to some nonuniform waveguides. First, the differential equations describe the nonuniform structures, and the eigenfunction of voltage and current is obtained versus the square root of the per-unit-length impedance and admittance. The general formulas describing the voltage and current are obtained from the eigenfunction. The ABCD matrix of a non-uniform structure is determined in a closed-form expression. The proposed method is expanded for the coupled nonuniform structures. In addition, the procedure is applied to some special cases of waveguides. Several theoretical and practical single and coupled structures are studied to validate the proposed method's performance. The proposed approach results are compatible with exact solutions and measurements in all cases.

Study of coupling efficiency of a laser diode to a cylindrical microlens tipped single-mode circular core dispersion-shifted and dispersion-flattened fibers using ABCD matrix formalism

Study of coupling efficiency of a laser diode to a cylindrical microlens tipped single-mode circular core dispersion-shifted and dispersion-flattened fibers using ABCD matrix formalism

Control of Frequency Combs with Passive Resonators.

Tailored optical frequency combs are generated by nesting passive etalons within mode-locked oscillators. In this work, the oscillator generates a comb of 6.8 GHz with 106 MHz side-bands. This tailored comb results from the self-synchronized locking of two cavities with precision optical frequency tuning. In this manuscript, it is demonstrated that these combs can be precisely predicted utilizing a temporal ABCD matrix method and precise comb frequency tuning by scanning over the D1 transition line of 87Rb and observing the fluorescence.

A Comprehensive Review on Microstrip Couplers

In this work, several types of microstrip couplers are investigated in terms of structure, performance and design methods. These planar 4-ports passive devices transmit a signal through two different channels. Designers' competition has always been in miniaturizing and improving performance of couplers. Some couplers have been offered with a novel structure, which is a special feature. A high-performance coupler should have high isolation and low losses at both channels. The channels are usually overlapped so that the common port return loss in these channels should be low. Among the couplers, those with balanced amplitude and phase are more popular. The popular mathematical analysis methods are even/odd mode analysis, extracting the information from the ABCD matrix and analyzing the equivalent LC circuit of a simple resonator. According to the phase shift value, couplers are classified as 90º and correct multiples of 90º, where a microstrip 0º coupler can be used as a power divider. Some couplers have filtering and harmonic elimination features that are superior to other couplers. However, few designers paid attention to suppressing the harmonics. If the operating frequency is set in according to the type of application, the coupler becomes particularly valuable.ABCD Matrix

Spin-orbit interactions of a circularly polarized vortex beam in paraxial propagation.

Spin-orbit interactions (SOIs) of circularly polarized beam and circularly polarized vortex beam during paraxial propagation in a radial gradient-index (GRIN) fiber are analyzed using the generalized Huygens-Fresnel principle and the GRIN fiber's ABCD matrix. SAM is only associated with polarized light helicity and OAM is only associated with topological charge m. SAM and OAM do not crosstalk or convert between each other; SOIs did not occur at the GRIN fiber's focal plane. SOIs of partially coherent circularly polarized beam and partially coherent circularly polarized vortex beam in the GRIN fiber are also studied and show the same characteristics as the perfectly polarized beam.

Method of Designing a Planar Scan Angle Enhancing Metalens Featuring Lossless Wide Scanning at mmWave

For the first time, a method to design a planar scan angle enhancing lens with minimum beam distortion for automotive radar at millimeter-wave is presented. The proposed lens is not only advantageous regarding its planar topology but also offers a solution to the chronic problem surrounding planar phased array antenna and planar lenses: scan loss. In this article, ray optics and ray transfer matrix are applied to Galilean lens configuration from which the concept of scan enhancement and compensating parameters are conceived. The basic idea of compensating lies in re-focusing the portion of the beams and suppressing transmission at extreme angles. Visual analysis of the wave refraction and designing of the lens system is conducted using 2-D ray-tracing code. Full-wave simulation validates the effectiveness of the proposed idea by extending the limited scan range of the phased array antenna from 45° to 58° with gain fluctuation below 1.1 dB at E-band. The radiation efficiency is calculated to be 0.86 at 76.5 GHz. Furthermore, the proposed lens system is fabricated using low-temperature co-fired ceramic (LTCC) technology and experimentally verified. Series-fed array antennas integrated with scan angle enhancing meta lens (SAEMLs) confirmed the shift of the gain peak from 46° to 58°, proving that SAEML can effectively extend the scanning range of phased arrays with small gain variation.

Harmonic grounding impedance of rods in horizontally stratified soils using ABCD-matrix approach

Grounding electrodes play a fundamental role in the operation of power systems. In this context, precise computation of grounding impedance must consider the frequency-dependence of the soil parameters and the ground organized in stratified layers of soil. This paper proposes an ABCD matrix approach to compute the harmonic grounding impedance of rods buried in frequency-dependent stratified soils directly in the frequency domain. This technique is based on the traditional ABCD matrix used for overhead multi-phase transmission lines extended to grounding systems. In this approach, each rod segment is modeled as a short transmission line where the equivalent harmonic grounding impedance is calculated. Then, the Ground Potential Rise (GPR) waveforms are computed by lightning currents injected into the rods buried in different scenarios. Results indicated that the ABCD matrix approach has shown a good agreement with those obtained using a full-wave electromagnetic software FEKO. The frequency-dependence of the soil electrical parameters causes a significant modification in the harmonic impedance of grounding rods which reduces the GPR peaks considerably, being this reduction more pronounced in homogeneous and 2-layer soils. The proposed technique is an attractive tool since that considers the frequency dependence on each layer of soil, with a low computational cost and good accuracy from 100 Hz up to 1 MHz.

A comparative study of propagation delay applied on varieties carbon nanotubes Bundles interconnects using the FDTD and the ABCD matrix method

Due to their hilarious properties, carbon nanotubes (CNTs) with their different varieties have been suggested as potential alternatives for interconnects in many industrial applications related to Artificial Intelligence. This work made an overview of the various models of the resistive effect inside several CNT based interconnects. In addition, it has studied the propagation delay inside the CNT interconnect varieties by comparing two validated transient analysis methods, namely the FDTD and the ABCD matrix. The work has concluded the superiority of the ABCD-matrix method since it has given a better performance.

Development of a New Backward Directional Coupler Based on Perforated Substrates

In this paper, two wideband 10 dB backward directional couplers based on artificial perforated substrates over the frequency range of 25-35 GHz and 32-38 GHz are developed. An analytical method is proposed to design the coupler geometrical parameters. The theoretical modeling is established based on the coupled version of the transmission line (TL) theory using the extended version of the ABCD matrix for four ports microwave network. It is shown that using the proposed method, all required parameters of the directional coupler are determined using the per-unit-length of the applied lines. The geometrical parameters of primary designed couplers are optimized using the particle swarm optimization (PSO) procedure to improve the performance of couplers. The designed couplers are also simulated using High Frequency Structure Simulator (HFSS) software. Moreover, sensitivity analysis is carried out to investigate the effect of fabrication imperfections of the proposed couplers. The obtained results show that the simulated results agree well with the theoretical ones and a low insertion loss (IL) with high return loss is obtained over a wide frequency range bandwidth.

Advances in multipass cell for absorption spectroscopy-based trace gas sensing technology [Invited

In the field of absorption spectroscopy, the multipass cell (MPC) is one of the key elements. It has the advantages of simple structure, easy adjustment, and high spectral coverage, which is an effective way to improve the detection sensitivity of gas sensing systems such as tunable diode laser absorption spectroscopy. This invited paper summarizes the design theory and the research results of some mainstream types of MPCs based on two mirrors and more than two mirrors in recent years, and briefly introduces the application of some processed products. The design theory of modified ABCD matrix and vector reflection principle are explained in detail. Finally, trends in its development are predicted.

A Compact 10–14.5 GHz Quadrature Hybrid with Digitally Reconfigurable I/Q Phase in SiGe BiCMOS Process

In this article, the development of a compact 10–14.5 GHz quadrature hybrid with digitally reconfigurable I/Q phase in 130 nm SiGe BiCMOS process is presented. Thanks to the switched capacitance loaded on I/Q path of the quadrature hybrid, the I/Q phase difference can be optimized and digitally reconfigured. The equivalent model is analyzed with even/odd mode theory, and the ABCD matrix is used for the circuit derivation. In order to obtain high coupling coefficient, the broadside coupled line sections are utilized, and compact hybrid size can be realized accordingly. Measured results show that the compact quadrature hybrid has optimized phase difference of 90 ± 1.0° and amplitude difference less than ±0.5 dB for 10–14.5 GHz, with an ultra-compact size of 460 µm × 151 µm, or 0.031λ0 × 0.011λ0. Meanwhile, with the seven reconfigurable phase states, the quadrature hybrid I/Q phase can be digitally reconfigured for a range of 3 degrees to compensate the I/Q phase imbalance in the quadrature system, without DC power consumption.

A circuit level analysis of power distribution network on a PCB layout exposed to intentional/unintentional electromagnetic threats

In this article a circuit level analytic approach is proposed for radiated susceptibility analysis of a system power distribution network (PDN). For this purpose, electromagnetic wave impacts a two-layer printed circuit board (PCB). This external wave can be radiated from the antenna of a wireless communication device or an intentional electromagnetic interference source. The radiated susceptibility of the PDN is studied by decomposing the stochastic voltage sources for vertical and horizontal transmission lines. The effect of distribution network on the individual induced signal are considered using ABCD matrix for handling the disturbance propagation entire system. The PDN self voltage fluctuation is considered using a simple mathematic model. A measurement procedure is proposed for evaluating the performance degradation without loading effect. Analytic conclusion and simulation results disclose that the induced voltage from external electromagnetic threat on the PDN is comparable with the operating PDN self fluctuation. The results show that the PDN is a susceptible section of the PCB and is an accessible target for interferer systems. This can be a potential susceptibility concern and should be considered in design procedure.