Search Results(14113)

2026-06-13
PIER M
Vol. 138, 65-74
Gain Enhancement and Reduced Isolation of 4-Port Orthogonal Multiple-Input-Multiple-Output Antennas Based on Metamaterial for 5G Applications
Boddapati Naga Prasanna and Thokala Kalpalatha Reddy
As the need for rapid data transmission and dependable wireless networks grows, so does the need for advanced antenna technology. This has become a major focus of modern communication technologies. This paper describes the design of a 4-port multiple-input multiple-output (MIMO) microstrip patch working at 28 GHz in the Ka-band. This antenna is fabricated on a substrate measuring 21 × 21 × 3.97 mm3, composed of FR4, foam, and RT/Duroid 5880. It uses a microstrip feed. Performance enhancements are achieved by positioning the feeds orthogonally, incorporating a U-shaped slot into the MIMO antennas, and implementing a superstrate made of metamaterial (MTM) elements. Additionally, a single-layer MTM superstrate with rectangular slots is created to improve gain while keeping good impedance matching. The design process systematically improves gain and mutual coupling while keeping the overall size compact. The specific challenge addressed by the design is to improve peak gain and radiation efficiency by employing MTM elements operating at 28 GHz. The 4-port MIMO antenna achieves an impedance bandwidth (IB) of 27.11-29.21 GHz, with a peak gain of 14.05 dB, respectively. This antenna is used in next-generation communication systems, vehicular networks, and 5G systems.
2026-06-12
PIER C
Vol. 171, 189-199
Safety Constrained Sparse Radiation Therapy via Efficient Optimization Approach for Biomedical Phased Array Applications
Ahmed Jameel Abdulqader , Huda A. Al-Tayyar and Yessar Ezzaldeen Mohammed Ali
The development of interventional radiotherapy techniques has become one of the most important concerns for antenna designers worldwide. In this study, an efficient optimization approach based on a hybrid algorithm derived from exploiting the quantitative concept, along with the theory of reinforcement convexity, called the quantitative-convex approach (QCA), to produce a high-performance electromagnetic radiation pattern is presented. The novelty of this study lies in shaping patterns that mimic the shape of the targeted human organ in radiotherapy by steering a flat main beam of a square antenna array, along with optimal control of the sidelobe level. The proposed approach works by identifying the diseased organ captured from medical imaging, converting it into a binary image (black and white colors), and then feeding it into the antenna system to form a radiation pattern that accurately mimics the diseased organ. To reduce the systemic and computational complexity of the therapeutic antenna system, a sparsity technique was added to the hybrid algorithm. The computer simulation results showed high efficiency in generating robust patterns with sharp boundary profiles, such as those used for isolating diseased and undiseased tissues and measuring the tissue-specific absorption rate (TSAR), making it suitable for use in radiotherapy.
2026-06-12
PIER M
Vol. 138, 55-64
Broadband and Switchable VO2-Based BI-Functional THz Polarization Converter Combined with a Deep-Learning-Assisted Design Method
Haohan Xie , Shuning Wei , Wenting Qu , Xinlei Zhang , Chenshan Le , Jinlin Li and Jun Dong
This study presents a broadband, switchable, and bi-functional terahertz device based on the phase transition of vanadium dioxide (VO2). When VO2 is in the metallic state, the device operates as a linear polarization converter (LPC). When VO2 transitions to the insulating state, the device functions as a broadband linear-to-circular polarization converter (LTC-PC). Numerical simulations are conducted to verify the device performance. To further optimize metamaterial performance and accelerate the design process, a deep learning framework that integrates convolutional neural networks (CNNs) and the Transformer architecture via an adaptive mechanism is proposed. Numerical simulations indicate that this LPC achieves a polarization conversion ratio (PCR) exceeding 90% across the 1.92-2.93 THz band and maintains angular stability for incidence angles up to 50°. The LTC-PC operates effectively within the 2.40-4.33 THz range. Featuring broadband operation and bi-functional capabilities, the converter holds significant potential for applications in terahertz imaging, sensing, solar energy harvesting, and communications.
2026-06-09
PIER C
Vol. 171, 180-188
Design and Optimization of a Flux Reversal Machine with Double-Layer Dual-PM Halbach Array
Jiahao Zhang , Bingnan Feng , Runqing Su and Libing Jing
The flux reverse machine (FRM) has the advantages of high utilization rate of permanent magnet (PMs) and wide speed range. However, it still suffers from low output torque and large torque ripple. In this study, an FRM with a double-layer dual-PM Halbach array (DLDPMH-FRM) is proposed. The PMs are arranged in a double layer at the stator slot, and a Halbach array is employed at the rotor slot openings. The stator and rotor PMs together form a dual-PM structure. The response surface method (RSM) and multi-objective genetic algorithm (MOGA) were combined for global optimization. Compared with the dual-PM FRM (DPM-FRM), the torque of the DLDPMH-FRM reaches 7.75 N·m, which is 35.72% higher than DPM-FRM, while the torque ripple is reduced by 86.01%. This model provides a feasible solution for the design and optimization of high-performance FRM.
2026-06-09
PIER C
Vol. 171, 171-179
A Miniaturized 2 × 2 Orthogonal MIMO Antenna for 5G NR Mid-Band Applications (N77/N78/n79 )
Shraddha , Mohammad Arshad , Kamakshi and Jamshed Aslam Ansari
The proposed prototype miniaturizes a two-port wideband multi-input multi-output (MIMO) antenna structure to operate over a specified frequency spectrum from 2.6 to 5.1 GHz and exhibits an impedance bandwidth of 64.93% to support 5G mid-band (n77/n78/n79) applications. The antenna design incorporates a pair of spoon-shaped radiating units configured orthogonally to achieve polarization diversity. To improve inter-port isolation (S21), T-shaped slots along with a diagonally oriented rectangular slot are employed in the ground plane, while the isolation value remains better than −15 dB within the prescribed limit. The developed MIMO antenna was implemented in a compact configuration on an FR4 substrate, with physical dimensions of 30 × 30 mm2. The antenna exhibits a gain ranging from 3.5 to 3.9 dB with radiation efficiency varying from 94% to 96% and a stable radiation pattern within the targeted frequency band. The diversity performance metrics across the operating frequency range were validated by the envelope correlation coefficient (ECC < 0.01), diversity gain (DG < 9.99 dB), and mean effective gain (MEG) close to −3 dB. Experimental findings show close correlation with simulated data, confirming the effectiveness of the developed MIMO antenna structure for 5G New Radio (NR) mid-band operation.
2026-06-09
PIER C
Vol. 171, 156-170
Research on the Performance of Permanent Magnet Synchronous Motors with Optimized Stator-Rotor and Hybrid Permanent Magnet Structure
Han Lin , Huawei Liu and Zhonggen Wang
To address the trade-off between increasing output torque and reducing torque ripple and cogging torque in interior permanent magnet synchronous motors (IPMSMs), this study proposes a structure incorporating stator-rotor auxiliary slots and rotor damping holes. Additionally, a hybrid permanent magnet configuration combining N35 and N30 grades was adopted to maintain high performance while further reducing costs. First, an analytical expression for the cogging torque was derived, and a finite element model of the motor was established. Subsequently, a parametric sweep and optimization of the stator and rotor auxiliary slots were conducted to obtain the optimal combination of auxiliary slot dimensions. Furthermore, a multi-objective optimization algorithm was proposed to optimize the motor parameters. Finally, radial electromagnetic force analysis was performed on the optimized motor model. The results demonstrate that the proposed structure effectively suppresses the torque ripple, cogging torque, and amplitude of the radial electromagnetic force, thereby reducing motor vibration amplitude while ensuring that the electromagnetic torque remains unaffected. The proposed design achieves a favorable balance between output torque enhancement and torque ripple/cogging torque reduction, with cost control through hybrid permanent magnets, demonstrating comprehensive performance improvements for IPMSMs.
2026-06-09
PIER C
Vol. 171, 144-155
Microwave Scattering from a Ship on a Sea Surface: Incoherent Matrix and Coherent Intensity Computed from Single and Double Bouncing PO and MoM -EPILE
Christophe Bourlier , Prisca Le Dily , Nicolas Pinel and Romain Bocheux
Scattering from a deterministic object in the presence of a randomly rough surface, such as a ship on a sea surface, can be characterized by statistical moments. Full-wave methods, such as the method of moments (MoM), provide accurate results but can be time-consuming. To account for both the gravity and capillary waves, a full sea spectrum is used, which constrains the consideration of a one-dimensional sea surface to include all roughness scales. Asymptotic methods are a good compromise between the computation time and accuracy of the results. In this study, the field scattered by a trapezoidal ship on a 1D sea surface is calculated by iterating the physical optics approximation and incorporating evanescent waves. In addition, the resulting closed-form expressions allow us to derive the associated coherent components analytically by considering a finite and infinite sea surface length. They are validated by comparison to the MoM combined with the extended propagation-insidelayer-expansion (EPILE) method, which can separate bounce orders. The results of the incoherent components, evaluated using a Monte Carlo process, are also shown by introducing a novel concept, based on the centered inter-correlation matrix between the single and double bounces, to quantify the different incoherent contributions. This concept highlights the ``backscattering enhancement'' phenomenon, only observed for a single rough surface with high slopes.
2026-06-07
PIER B
Vol. 117, 198-213
Analytical Modeling and Full-Wave Simulation of Metal and Dielectric Trihedral Corner Reflectors and Their Arrays
Denys I. Zaikin
This work presents a unified analytical and full-wave investigation of the monostatic radar cross section (RCS) of trihedral corner reflectors (TCRs) and their arrays, covering both metallic and dielectric configurations. Accurate analytical prediction of the monostatic RCS of trihedral corner reflector arrays (TCRAs), particularly for tightly packed mosaic geometries and dielectric materials, remains challenging due to the lack of general closed-form models accounting for multiple reflector orientations and array effects. To address this gap, closed-form RCS expressions are derived for single reflectors and mosaic arrays incorporating two distinct reflector orientations. The proposed formulation extends classical geometrical-optics models through a corrected complex-target phase treatment and explicit inclusion of multi-orientation effects. The analytical results are validated using full-wave finite-element simulations in COMSOL Multiphysics®. For metallic reflectors, geometrical optics is shown to be accurate for electrically large elements, whereas diffraction, resonance, and phase-distortion effects emerge as the reflector size decreases. Dielectric TCRAs exhibit strongly non-symmetrical scattering and reversed boresight offsets in the φ = π/2 plane; nevertheless, grating-lobe locations remain predictable using the metal-array analytical model. The study concludes with practical design guidelines for mosaic TCRAs, including peak-RCS scaling, grating-lobe placement, and the transition from corner-reflector to plate-like scattering.
2026-06-06
PIER C
Vol. 171, 134-143
Gold Nanowire-Enhanced Quasi-D-Shaped SPR-PCF Biosensor for High-Sensitivity Phase-Matched Cancer Cell Detection
Prarthana Madhusoodanan , Neville Philips Jommy , Joel Tiji , Sangeetha Natarajan and Ashish Patwari
The present paper suggests a structurally optimized photonic crystal fiber (PCF) for a surface plasmon resonance (SPR) based biosensors, in which a gold nanowire is embedded within a U-shaped open microchannel to detect with refined accuracy the presence of cancer cells. The proposed nanowire-based architecture is capable of providing localized enhancement of the electromagnetic field confinement and phase matching between the core mode and localized surface plasmon resonance (LSPR) compared to conventional thin-film SPR architectures. The given SPR-based PCF biosensor was mathematically studied using the finite element method (FEM) to optimize its performance within the near-infrared wavelength range. Systematic variation of parameters, such as nanowire diameter, air-hole diameter, number of air holes, and channel dimensions, optimized the sensor performance. The sensor proposed has a top wavelength sensitivity of 42,857 nm/RIU and an amplitude sensitivity of 189 RIU-1 within a range of refractive index 1.39-1.376 between healthy and cancer cells. The architecture has a higher confinement loss peak and good phase matching, which has proven to be superior to traditional thin-film configurations. The suggested SPR-based PCF biosensor can be a promising label-free and realtime biomedical diagnostic solution because of the relatively easy fabrication process, high mechanical strength, and high accuracy.
2026-06-05
PIER Letters
Vol. 131, 9-17
A Compact Four-Port Circularly Polarized MIMO Antenna Using a Polarization Conversion Superstrate
Jingchang Nan , Siyao Zhao and Yifei Wang
A compact four-port circularly polarized multiple-input multiple-output (CP-MIMO) antenna with a dual-layer architecture is proposed for low-altitude communication applications. In compact MIMO arrays of CP-capable monopole elements, strong mutual coupling makes stable CP radiation difficult to achieve. To address this issue, the proposed antenna uses a lower layer for dual-polarized MIMO generation and an upper layer for polarization conversion. The antenna is fabricated on two FR-4 substrates with an overall size of 0.85λ × 0.85λ × 0.084λ. In the lower layer, a dual-polarized feed backplane (DPFB) forms a ±45° dual-polarized MIMO array with port isolation exceeding 17 dB. In the upper layer, a polarization conversion superstrate (PCS) converts the incident dual-polarized waves into CP radiation. The PCS extends the impedance bandwidth by 36%, from 7.55 to 10.08 GHz, and enables LHCP radiation with a 3 dB AR bandwidth of 8.22-8.89 GHz. A gain enhancement of 48% is also achieved. Measured results verify the design and show good MIMO diversity performance.
2026-06-05
PIER B
Vol. 117, 182-197
Design and Analysis of a Novel Switched Reluctance Motor Utilizing Embedded Permanent Magnets for Torque Enhancement
Matin Rahimi , Seyed Hamid Shahalami and Esmaeil Fallah Choolabi
This research presents a high-performance 24/22 hybrid-excited switched reluctance motor (HESRM) featuring a modular C-core, dual-tooth topology engineered for superior torque density and efficiency. The proposed architecture utilizes a strategic flux-concentration mechanism by embedding permanent magnets (PMs) exclusively within the inter-tooth spaces. This targeted integration establishes a dual-path flux enhancement that intensifies air-gap flux density while suppressing stator yoke saturation. To ensure methodological rigor, structural parameters were optimized using a Multi-Objective Genetic Algorithm (GA) to maximize average torque. Additionally, a Magnetic Equivalent Circuit (MEC) model was derived to analytically interpret the PM-assisted torque enhancement. The design is rigorously validated through Three-Dimensional Finite Element Analysis (3D FEA), accounting for end-leakage effects. The 3D FEA results yield an average torque of 3 Nm, exhibiting excellent agreement with the 2D FEA estimation (2.98 Nm). Detailed evaluations of losses and efficiency mapping reveal that the HSSRM 24/22 achieves a 43% increase in average torque and significantly higher efficiency than the reference HSRM 12/10. Ultimately, this study offers a robust, cost-effective solution with an enhanced torque-per-PM-volume ratio for advanced electric drive applications.
2026-06-03
PIER C
Vol. 171, 125-133
A Fractal-Inspired Owl-Eye Circular Patch Antenna with Polygonal Defected Ground Structure for 3.6 GHz /4.6 GHz 5G and WLAN Applications
Lanka Padmalatha , Satya Nagakishore Bhavanam and Vasuja Devi Midasala
An owl-eye circular patch antenna with a polygonal defected ground structure (DGS) is presented in this paper for dual-band applications. The polygonal defected ground structure improves impedance matching and radiation characteristics, leading to a better gain and more efficient signal radiation. The design is fabricated on a FR-4 substrate measuring 35 × 33 × 1.6 mm3. This is a cheap way to make modern wireless devices. Adding circular fractal features resembling an owl-eye pattern to the radiating element improves the current flow and enables multiple resonant modes. It works at 3.68 GHz and 4.68 GHz, which make it suitable for 5G and WLAN applications. Antenna impedance matching is good, with reflection coefficient values of -24 dB at 3.68 GHz and -16 dB at 4.68\,GHz. As a result, very little signal is reflected. At the frequencies where it operates, it achieves gains of 6.2\,dBi and 5.68\,dBi. Additionally, the antenna has a high radiation efficiency of about 95{\%}, which means that it radiates well. Next-generation wireless communication systems will benefit from the proposed design.
2026-06-03
PIER C
Vol. 171, 117-124
A Miniaturized Long-Read-Range Anti-Metal UHF RFID Tag Antenna for Full-Process Management of Bank Cash Transport Boxes
Bingqing Yao
In this study, a miniaturized long-read-range anti-metal ultra-high frequency (UHF) RFID tag patch antenna for bank cash transport boxes is presented. Short-circuit inductors were loaded on the side of the antenna, and double H-shaped slots were etched on the patch surface. These structures extend the current path and increase the electrical length, which lowers the resonant frequency and enables antenna miniaturization. The antenna impedance can be flexibly tuned by adjusting the position and width of the short-circuit inductors and the length of the double H-shaped slots. Conjugate matching with the RFID chip is therefore achieved to ensure maximum power transfer. In addition, the short-circuit inductors reduce the influence of the metal plate and improve the current distribution. Consequently, the radiation efficiency is enhanced, and a long reading distance is obtained. The proposed antenna was fabricated and measured, and good agreement between the simulation and measurement results was observed. The measured results show that the antenna occupied an area of 615 mm2 and achieved a maximum reading distance of 12.4 m when mounted on a metal cash-in-transit box. The presented antenna is suitable for the full-process management of bank cash transport boxes in different application scenarios.
2026-06-03
PIER C
Vol. 171, 110-116
A Preprocessing Dimensionality Reduction Framework for Improved Polynomial Chaos Expansion in EMC Uncertainty Quantification
Yitong Lu , Zhengyu Xue and Shenghang Huo
Polynomial Chaos Expansion (PCE) is widely utilized in uncertainty quantification (UQ) for electromagnetic compatibility (EMC) due to its robust global predictive capabilities. However, its computational overhead increases exponentially with stochastic dimensionality, leading to the notorious curse of dimensionality. To address this bottleneck, this paper proposes a generalized preprocessing dimensionality reduction framework designed to enhance the performance of PCE. By decoupling dimensional screening from predictive modeling, the proposed framework first employs low-cost estimators to identify significant random variables. Subsequently, an improved PCE model is constructed within the reduced feature space. Given the prohibitively high computational cost of acquiring EMC simulation samples, this study instantiates a screening module within the framework that integrates Least Squares Support Vector Regression (LSSVR) with Sobol indices. Finally, the proposed framework-based method is applied to a cable crosstalk case study to validate its effectiveness and engineering applicability.
2026-06-03
PIER B
Vol. 117, 165-181
Analytical Modeling of Metamaterial Antennas and Their Equivalent Properties: A Characteristic Mode Approach
Mouad El Moudden , Badiaa Ait Ahmed and Otman Aghzout
This paper examines approaches to improving metamaterial antennas using the Theory of Characteristic Modes (TCM). We investigate the electromagnetic resonant modes of antenna elements, with a focus on how their material properties interact with their geometric configurations. The main goal is to enhance key features, such as bandwidth and radiation efficiency, in the electromagnetic modes of metamaterials. The study also examines how structural features, such as slots and metamaterial shapes, affect antenna performance. Splitring resonators (SRRs) and complementary split-ring resonators (CSRRs) are considered to analyze how electric and magnetic modes can contribute to radiation efficiency using the approaches proposed in this paper. Important parameters, including characteristic angles, current distribution, bandwidth, and radiation patterns, are compared across different designs to identify the most efficient configurations. Notably, the analysis shows that when the SRR and CSRR structures are optimized, they can achieve similar radiation efficiency for electric and magnetic modes, respectively. Consequently, the TCM predictions are strongly corroborated by the S-parameter results. Overall, this paper provides practical insights into the design of compact and efficient metamaterial antennas and offers useful guidance for future wireless communication systems.
2026-06-01
PIER C
Vol. 171, 97-109
Compact Printed UWB Monopole Antenna Employing Coupling and Stub Structure
Nobuyasu Takemura
This paper presents a compact printed ultra-wideband (UWB) monopole antenna employing a coupling structure and a short stub for broadband impedance matching and antenna miniaturization. The proposed antenna is fabricated on an FR-4 substrate with dimensions of 24 × 14 × 1.6 mm3 and fully covers the FCC-defined UWB from 3.1 to 10.6 GHz, achieving a VSWR of ≤ 2. The coupling structure introduces additional capacitive loading, while the short stub provides effective inductive compensation. This enables stable, broadband operation despite significant size reduction. Experimental results demonstrate quasi-omnidirectional radiation characteristics over the entire operating band. In addition to frequency-domain evaluation, time-domain performance is investigated using two identical antennas arranged in face-to-face and side-by-side configurations. The measured correlation coefficients exceed 0.94 in both configurations, and the group delay remains nearly constant at approximately 0.3 ns across the UWB. This indicates high waveform fidelity. These results confirm that the proposed antenna is well-suited for compact UWB communication systems requiring both broadband and time-domain stability.
2026-06-01
PIER C
Vol. 171, 87-96
Accurate Calculation of Mutual Inductance for Rounded Rectangular Coils in Arbitrary Orientations in Wireless Power Transfer Systems
Zhongjiu Zheng , Minghao Zhao , Zhuang Li , Xingfeng Cao and Anran Liu
This paper proposes an analytical method for arbitrary spatial orientations that eliminates systematic errors arising from neglecting rounded corners in planar rectangular coils in wireless power transfer systems. The rounded rectangular coil is decomposed into straight and quarter-arc segments. Using Neumann's formula, mutual inductance expressions for straight-straight, straight-arc, and arc-arc interactions are derived. We establish a unified spatial model using Z-Y-X Euler angle transformations to describe arbitrary translations and rotations in 3D space. We obtain the total mutual inductance by superposition. Results show that neglecting rounded corners increases error as the corner radius grows. Under various conditions, including lateral and axial displacements and composite rotations, the method achieves average relative errors below 1.5% compared with finite element simulations (validated for corner radii up to 12 mm) and below 2.5% compared with experiments (validated for a corner radius of 5 mm), demonstrating high accuracy and robustness.
2026-05-31
PIER C
Vol. 171, 75-86
Characteristic Mode-Inspired Ultra-Wideband Dual-Band Notched Four-Port MIMO Antenna
Luyi Ji , Chengzhu Du , Yongkang Yang and Fangrui Zhang
In this paper, a dual-band-notched ultra-wideband MIMO antenna fed by a microstrip line is designed. The ultra-wideband characteristics are obtained by etching a semi-elliptical notch on a circular radiation patch. For the achievement of dual-band-notched features, a U-shaped slot and an inverted U-shaped slot are employed. Additionally, the Characteristic Mode Analysis (CMA) is used to verify and analyze the notch-band and broadband characteristics. Each ground plate is connected by adding a cross-shaped branch, and a circular ring is loaded to further improve antenna isolation (|S21|). This antenna is implemented on an FR4 substrate, and its whole size is 60 mm × 60 mm × 0.8 mm. The measured findings verify that the antenna functions within a broad bandwidth ranging 3.12-21.2 GHz (relative bandwidth 148.6%) and two frequency band rejections of 5.94-7.17 GHz and 12.49-13.92 GHz, effectively suppressing the 6G band, which belongs to the international satellite mobile communication system and the Ku band downlink. The port isolation exceeds 20 dB, the ECC is below 0.04, and the diversity gain (DG) is in excess of 9.97, all of which demonstrate the antenna's excellent diversity performance and superior radiation characteristics. The antenna is a frontrunner for next-generation wireless communication applications.
2026-05-30
PIER C
Vol. 171, 67-74
A Miniaturised Māra Cross-Inspired Fractal Microstrip Sensor for Edible Oil Sensing
Ahmed A. Al-Mudhafar and Sarah J. Ghazi
This work introduces an innovative fractal microstrip sensor, shaped like a Māra cross enclosed within a square, designed and fabricated on a Rogers RT5880 substrate for high-precision detection and characterization of edible oils. The proposed resonant shape enhances electric-field concentration and improves the interaction between the material under test and the electromagnetic field, resulting in improved sensitivity and resonant response. The sensor operates at a frequency of approximately 4 GHz within the S-band, with an area of 50 × 50 mm2, making it suitable for portable and low-cost applications. The results demonstrated clear frequency shifts for various oil types, including coconut oil, olive oil, sunflower oil, and sesame oil. A mathematical model was also developed to extract the complex electrical permittivity with a high coefficient of determination of 0.99, showing excellent agreement between the experimental and theoretical results. The fractal sensor exhibits a remarkable normalized sensitivity of 0.86% and 3.56% per unit dielectric variation and error of 0.03% and 0.13%, with frequency shifts of 163 MHz and 103 MHz for water and ethanol detection, respectively. Maximum sensitivities reached 15.23% for olive oil and 11.32% for sunflower oil, surpassing many previously published studies.
2026-05-29
PIER
Vol. 185, 110-117
An Abbe-Hopkins Unified Formulation of Optical Imaging for Efficient Cross-Model Verification in Computational Lithography
Qi Sun , Ying Wang , Ziyin Ma , Shujie Liu , Degui Li , Zhonglei Mei and David H. Wei
Accurate simulation of partially coherent imaging is crucial for computational lithography, with Abbe and Hopkins as the two main formulations being used. Although the two methods are equivalent in theory, practical simulators making independent choices between Abbe and Hopkins could hardly produce consistent results that match the desired accuracy owing to the inherently different ways of numerically representing, discretizing, and truncating the illumination source and lens pupil function, etc. Moreover, classical Hopkins models require prior construction and/or eigen decomposition of the high-dimensional transmission cross coefficient (TCC), the prohibitive costs of which hinder timely model verification. To address these challenges, we developed a unified Abbe-Hopkins formulation in conjunction with a TCC-free Hopkins pointwise sampler for efficient cross-model validation. Our formulation supports both Abbe and Hopkins modeling in a single unified framework, with the two simulation modes using exactly the same numerical representations of the illumination source and projection lens. Cross-model verification for randomly sampled points is performed efficiently by evaluating the Hopkins quadratic form through a fast Fourier transform of an image and a few pointwise multiplications between images, without ever explicitly constructing a TCC and eigen-analyzing it. Numerical tests show that the Abbe and Hopkins results agree up to the machine precision level.