Erik Jørgensen

Chief Scientist

Education: PhD, MSc in Electrical Engineering Specialization: Moment method, electromagnetic theory With TICRA since: 2003

Phone: +45 3330 6752

Erik is involved in formulating and efficiently implementing new EM modelling algorithms in user-friendly product environments. With his background within full-wave analysis, he has significantly contributed to the method of moments implementation in ESTEAM. Erik used to be TICRA’s CTO (2018-2024).

Analysis and Design of Large Array Antennas Using a Fast Direct Solver

This paper presents the application of TICRA’s recent full-wave analysis advancements for antenna arrays, with a particular emphasis on the use of the Fast Direct Solver (FDS). We showcase the effectiveness of this method through real-world examples, including a 10×10…

Extended Higher-Order Array Decomposition Method for Fully Populated or Thinned Array Antennas and Scatterers with Connected Elements

The Higher-Order Array Decomposition Method (HO-ADM) is extended to handle fully populated or thinned finite array antennas and scatterers which can be modeled as arrays with connected elements lying on a regular lattice. The Discontinuous Galerkin Method (DGM) is employed…

Higher-Order Array Decomposition Method for Arrays with Dielectric Substrates

The Higher-Order Array Decomposition Method (HO-ADM) has been extended to regular arrays with dielectric substrates. To maintain the multi-level block-Toeplitz Method of Moments (MoM) matrix structure, internal equivalent currents are introduced, ensuring an FFT-accelerated matrix vector product (MVP). Results demonstrate…

Design and RF Testing of Reflectarray for Cubesat at X-band

A reflectarray has been designed and measured. The reflectarray is intended for use as downlink antenna on the 2-by-3 unit surface of 6U and 12U CubeSats in the X band from 8.025 GHz to 8.4 GHz. A main design requirement…

Efficient Full-Wave Computation of the Monostatic Radar Cross Section

A full-wave solver for computing monostatic radar cross sections of electrically large structures is proposed. The solver is based on method of moments. It uses the multilevel fast multipole method in combination with higher-order basis functions, a blocked iterative solver,…

Higher-Order Array Decomposition Method for Array Antennas with Connected Elements

The Higher-Order Array Decomposition Method (HO-ADM) is extended to handle regular array antennas with interconnected elements. The Discontinuous Galerkin Method (DGM) is used to retain the multi-level block-Toeplitz Method of Moments (MoM) matrix structure, even for connected elements. The presented…

Full-Wave Monostatic Radar Cross Section using the Multilevel Fast Multipole Method

An efficient full-wave solver for the computation of monostatic Radar Cross Section (RCS) for electrically large structures using the method of moments is developed. This is accomplished by utilizing higher-order basis functions, to reduce the number of unknowns, and the…

Advanced Antenna Modelling Tool for Performance Verification and Diagnosis

A development project of a new software tool for uncertainty quantification (UQ) of an antenna’s performance caused by the stochastic behaviour of design variables of the system has been performed within the ESA Contract No. AO/1-10116/19/NL/AS. The mathematical algorithms implemented…

Fast Source Reconstruction of Large Reflector Antennas for Space Applications

In this work, a method for diagnostics of large reflector antennas for space applications is presented. By using a Calderón projection together with a Higher-Order (HO) Method of Moments (MoM) discretization, the inverse electromagnetic scattering problem is solved in an…

A Fast Source Reconstruction Method for Radiating Structures on Large Scattering Platforms

We present a fast source reconstruction method suitable for antenna diagnostic applications of radiating structures on electrically large platforms. The method is based on a novel implementation of a recent reformulation of the inverse electromagnetic scattering problem, and is solved…

Design of a dual circularly polarized elliptical feed horn for CubeSat reflectarray applications

A low loss dual circularly polarized feed antenna for a high gain deployable K-band reflectarray antenna on a CubeSat platform is designed. The feed consists of an elliptical horn antenna and its feed network, which will be optimized alongside with…

Full-wave scattering from reflector antennas on electrically large platforms using low-memory computers

We consider the use of full-wave integral equation techniques on scattering problems from reflector antennas on electrically large structures, and consider how an implementation of such techniques could use an inexpensive solid-state drive (SSD) rather than costly random access memory…

Reflectarrays in future satellite antenna systems application and design

In recent years, there has been a significant interest in reflectarray antennas and the latest research shows that reflectarrays can be used to provide solutions which are not possible when using conventional technologies. This paper presents a general design framework…

Application of the MCS algorithm for antenna optimisation

Key aspects of optimization algorithms when applied to challenging antenna design problems are reviewed. As an example of such an algorithm, the Multi-level Coordinate Search (MCS) global optimization algorithm is highlighted as a good candidate algorithm. We present two comparisons…

Optimization of feed chains and large reflectors

A higher-order Method of Moments formulation, accelerated with the Multi-Level Fast Multipole Method, and dedicated waveguide analysis methods constitute the foundation of efficient direct optimization of antenna systems consisting of feed chains and electrically large reflectors. A numerical example illustrates…

Direct optimization of electrically large reflectors and feed chains

The combination of a higher-order Method of Moments formulation and the Multi-Level Fast Multipole Method constitutes the foundation of an efficient direct optimization of reflector antenna systems consisting of feed chains and electrically large reflectors. Through a numerical example it…

Uncertainty quantification for modern antenna systems

Many modern antenna systems, particularly for applications in telecommunication or earth observation, have significant mechanical complexity. This entails an often lengthy and detailed design process, where the design is carefully revised to ensure the best performance for the intended application….

RF Design Tool for end-to-end Optimisation of High-performance Multibeam Antenna Systems

This paper describes a new integrated RF design tool for analysis and optimisation of reflector-based multibeam antenna systems. The new tool combines several powerful algorithms into a flexible software framework that allows end-to-end optimisation of antenna systems comprising of passive…

Uncertainty quantification for reflectarrays

Reflectarray antennas for space applications involve a large number of elements with varying sizes to be printed on a dielectric substrate. Due to the manufacturing process, the fabricated reflectarray might have significant deviations from the desired design. This paper demonstrates…

Direct optimization of quasi-periodic surfaces in multi-reflector systems

In recent years, there has been an increasing interest in replacing traditional periodic surfaces, e.g., frequency selective surfaces, with quasi-periodic surfaces (non-identical elements) in multi-reflector systems for satellite applications. Quasi-periodic surfaces can be used to improve existing antenna solutions or…

Demonstration of TM01 Circular Waveguide Mode in Matched Feeds for Single Offset Reflectors

Matched-feed horns can be employed to reduce the inherent cross polarization of offset reflector antennas. For circular horns, the traditional method is to excite TE21 modes in the aperture. We recently proposed that TE01 or TM01 modes can be used…

Advances in commercial software for high-gain antennas and electrically large platforms

We present the latest enhancements in the GRASP software package for analysis and design of electrically large antennas and platforms. The focus is on the hybridisation of efficient and accurate methods which allows antenna systems with very high complexity to…

Uncertainty quantification for reflector antennas

Large reflector antennas for telecommunication or space observation purposes often require a lengthy and detailed design process, where the design is carefully revised to ensure the best performance for the intended application. For many modern reflector antennas, quantification of the…

Efficient Monostatic RCS Calculation with Higher-Order MLFMM

The traditional O(f6) computational time scaling when using Method of Moments for monostatic Radar Cross Section calculations is circumvented by applying the Multi-Level Fast Multipole Method (MLFMM) along with a number of modifications. The performance of the modified MLFMM-based algorithm…

Advances on High-Performance Curved Reflectarrays for Telecommunication Applications

The latest advances on the use of curved reflectarrays for telecommunication applications is presented in this paper. For contoured beam applications, the curvature of the reflectarray surface can be used to enhance the bandwidth significantly, yielding reflectarray designs that can…

Metasurface Waveguides Applied to Matched Feeds for Reflector Antennas

Waveguides with anisotropic surface impedance boundaries have been investigated for the purpose of matched feeds for offset reflectors. Matched feeds employ higher order waveguide modes to cancel out cross polarization introduced by the offset geometry. Since the higher order modes…

Monostatic RCS Analysis of Electrically Large Structures using Integral Equations

The monostatic Radar Cross Section (RCS) is an important design parameter for many applications but accurate RCS prediction of an electrically large structure continues to be a challenging task. High accuracy demands and a complicated geometry often mean that asymptotic…

High-Performance Curved Contoured Beam Reflectarrays with Reusable Surface for Multiple Coverages

An investigation of curved contoured beam reflectarrays with reusable surface for multiple coverages is presented. The main advantage of curved reflectarrays over shaped reflectors is that they allow the possibility of reusing a standard parabolic mold for multiple missions. To…

Efficient Optimization of High-Performance Contoured Beam Reflectarrays with Reusable Surface Shape for Multiple Coverages

This paper describes the design of high-performance contoured beam reflectarrays using a direct optimization technique with an improved optimization engine. In Ku-band, curved reflectarrays allow the reuse of a standard mold for multiple missions and thereby reduce cost and delivery…

High-Performance Curved Reflectarrays for Telecommunication Applications

The use of curved reflectarrays for telecommunication applications is presented in this paper. For contoured beam applications, the curvature of the reflectarray surface can be used to enhance the bandwidth significantly, yielding reflectarray designs that are equivalent in performance compared…

Fast and Memory-Efficient Method for Full-Wave Analysis of Electrically Large Reflector Antennas and Satellite Platforms

We present a method that enables full-wave analysis of electrically large antennas and platforms, e.g., a detailed telecommunication satellite at Ka-band. Owing to the efficient formulation, even large problems can be solved on relatively modest computing platforms such as laptops…

Analytical Modelling of Waveguide Mode Launchers for Matched Feed Reflector Systems

Matched feed horns aim to cancel cross polarization generated in offset reflector systems. An analytical method for predicting the mode spectrum generated by inclusions in such horns, e.g. stubs and pins, is presented. The theory is based on the reciprocity…

Large-scale Optimization of Contoured Beam Reflectors and Reflectarrays

Designing a contoured beam reflector or performing a direct optimization of a reflectarray requires a mathematical optimization procedure to determine the optimum design of the antenna. A popular approach, used in the market-leading TICRA software POS, can result in computation…

Memory-efficient, full-wave analysis of waveguide scattering parameters for multiple reflector feeds mounted on electrically large satellite platforms

A Higher-Order Multilevel Fast Multipole Method (HO MLFMM) is presented for the efficient calculation of waveguide scattering parameters in cases where several reflector feeds are mounted on electrically large satellite platforms. The efficiency is obtained by: 1) using a Block…

New Analysis Capabilities for Electrically Large Antennas and Platforms

We present recent advances in the RF modelling of electrically large antennas and platforms, with an emphasis on reflector antennas and satellite platforms. The Higher-Order Multilevel Fast Multipole Method (HO MLFMM) was introduced recently in the commercial software tool GRASP,…

Full-wave Optimization of Large Compact Antenna Test Ranges

The challenges related to the increasing physical size of satellite platforms carry over to a number of related areas, including the design of Compact Antenna Test Ranges (CATRs) capable of handling such structures. In the present paper, we consider the…

Optimization Procedure for Wideband Matched Feed Design

The inherently high cross polarization of prime focus offset reflector antennas can be compensated by launching higher order modes in the feed horn. Traditionally, the bandwidth of such systems is in the order of a few percent. We present a…

Design and Validation of Compact Antenna Test Ranges using Computational EM

The design of modern Compact Antenna Test Ranges (CATRs) is a challenging task, and to achieve strong performance, simulation using computational electromagnetics is a vital part of the design process. However, the large electrical size, geometrical complexity and high accuracy…

Full-Wave Modeling of the PLANCK Space Telescope

Modeling the optical system on the Planck Space Telescope pre-launch was a very demanding task, with the huge electrical size, the strict accuracy requirements and the complicated feed arrangement all posing complications for efficient modeling. Pre-launch, the only viable option…

Full Wave Simulation of Large Satellite for the Evaluation of Multiple Frequency Antennas Interference

The paper presents a full wave simulation of the spacecraft of JUICE, ESA’s Jupiter Icy moons Explorer mission. Results prove the possibility of simulating the entire spacecraft modelling the instruments of the payload in a realistic environment to predict unwanted…

Higher-Order Method of Moments Analysis for Unconnected Quadrilateral Meshes

A higher-Order (HO) quadrilateral mesher is presented along with a HO method of moments formulation for unconnected meshes. A numerical example is presented to validate the new formulation. Publication: Proc. 2015 IEEE AP-S Symposium on Antennas and Propagation Place: Vancouver, British…

Design and Optimization of a Single-Layer Planar Transmit-Receive Contoured Beam Reflectarray with Enhanced Performance

This paper presents the design and optimization of a 1.2-meters single-layer planar contoured beam reflectarray in Ku-band. The reflectarray is optimized to fulfill the requirements of a Direct Broadcast Satellite mission, which covers a South American coverage in both transmit…

Analysis and Optimization of a Curved Transmit-Receive Contoured Beam Reflectarray

This paper presents the analysis and optimization of a 1 meter single-layer curved contoured beam reflectarray in Kuband. The curved reflectarray is designed to radiate a contoured beam over a European coverage in both transmit and receive frequency bands for…

New Fast and Robust Modelling Algorithms for Electrically Large Antennas and Platforms

This paper presents two new modelling algorithms that were recently added to the commercially available GRASP software package for electrically large antenna and scattering problems. In particular, a new higher-order multilevel fast multipole solver (HO-MLFMM) provides very high simulation accuracy…

Fast and Accurate Analysis of Reflector Antennas with Struts and Satellite Platform Scattering

This paper presents two methods related to modelling of reflector antenna struts and surrounding structural features such as satellite platforms. One method is a MoM-based strut model and represents an improvement of an existing PO-based model, thus enabling analysis of…

Detailed Pattern Computations of the UHF Antennas on the Spacecraft of the ExoMars Mission

This paper describes the pattern computations of the UHF antennas mounted on the spacecraft of the EXOMARS mission. The analyses are made by the higher-order Method of Moments (MoM) add-on to GRASP and are computed twice. In the first computation,…

Efficient Body of Revolution Method of Moments for Rotationally Symmetric Antenna Systems with Offset Illumination

An efficient Body of Revolution Method of Moments formulation is presented in which the unknown surface current density on the generatrix of the rotationally symmetric scatterer is expanded in terms of higher-order hierarchical Legendre basis functions. Careful attention has been…

Integral Equation Modelling of Reverberation Chambers using Higher-Order Basis Functions

Reverberation chambers (RCs) are important measurement facilities, and thus it is often required to simulate their behaviour numerically. However, due to their special characteristics, especially for high Q factors, they are often considered too challenging for application of standard numerical…

Adaptive Grouping for the Higher-Order Multilevel Fast Multipole Method

An alternative parameter-free adaptive approach for the grouping of the basis function patterns in the multilevel fast multipole method is presented, yielding significant memory savings compared to the traditional Octree grouping for most discretizations, particularly when using higher-order basis functions….

Multilevel Fast Multipole Method for Higher Order Discretizations

The multi-level fast multipole method (MLFMM) for a higher order (HO) discretization is demonstrated on high-frequency (HF) problems, illustrating for the first time how an efficient MLFMM for HO can be achieved even for very large groups. Applying several novel…

Gaussian Translation Operator for Multi-Level Fast Multipole Method

Results using a new translation operator for the Multi-Level Fast Multipole Method are presented. Based on Gaussian beams, the translation operator allows a significant portion of the plane-wave directions to be neglected, resulting in a much faster translation step. Publication:…

Reflector Antenna Analysis using Physical Optics on Graphics Processing Units

The Physical Optics approximation is a widely used asymptotic method for calculating the scattering from electrically large bodies. It requires significant computational work and little memory, and is thus well suited for application on a Graphics Processing Unit. Here, we…

Generalized Admittance Matrix Method for Fast Full-Wave Analysis of Integrated Lens Antennas

This paper presents an efficient technique for full-wave analysis of dielectric lenses with integrated feeding. The feeding section is analysed with a higher-order 3D-MoM algorithm, while the rotationally symmetric lens is analysed with a higher-order BoR-MoM. Each method allows the…

Design and Optimization of Multi-Faceted Reflectarrays for Satellite Applications

The design and optimization of multi-faceted reflectarrays for satellite applications are presented. The objective of this work is to investigate the performance of a multi-faceted reflectarray designed using a direct optimization technique. To this end, a single-layer multi-faceted reflectarray, that…

Improved Multilevel Fast Multipole Method for Higher-Order Discretizations

The Multilevel Fast Multipole Method (MLFMM) allows for a reduced computational complexity when solving electromagnetic scattering problems. Combining this with the reduced number of unknowns provided by Higher-Order discretizations has proven to be a difficult task, with the general conclusion…

The Generalized Direct Optimization Technique for Printed Reflectarrays

A generalized direct optimization technique (GDOT) for the design of printed reflectarrays using arbitrarily shaped elements with irregular orientation and position is presented. The GDOT is based on the spectral domain method of moments (SDMoM) assuming local periodicity (LP) and…

Array Diagnostics, Spatial Resolution, and Filtering of Undesired Radiation with the 3D Reconstruction Algorithm

This paper focuses on three important features of the 3D reconstruction algorithm of DIATOOL: the identification of array elements improper functioning and failure, the obtainable spatial resolution of the reconstructed fields and currents, and the filtering of undesired radiation and…

Diagnostics of the BIOMASS Feed Array Prototype

The 3D reconstruction algorithm is applied to the prototype feed array of the BIOMASS synthetic aperture radar, recently measured at the DTU-ESA Spherical Near-Field Antenna Test Facility in Denmark. Careful analysis of the measured feed array data has shown that…

Efficient Optimization of Large Reflectarrays Using Continuous Functions

Two new efficient optimization schemes for direct optimization of printed reflectarrays are presented. Instead of optimizing directly on the geometry of the array elements, continuous functions are envoked to represent the aperture field from which the geometry of the array…

Domain-Decomposition Technique for Efficient Analysis of Rotationally Symmetric Reflector Systems Containing 3D Structures

An efficient algorithm for analysis and optimization of rotationally symmetric reflector antennas, possibly including 3D support structures and/or waveguide components, is presented. The high efficiency is obtained by using a domain decomposition approach where each region of space is characterized…

Direct Optimization of Printed Reflectarrays for Contoured Beam Satellite Antenna Applications

An accurate and efficient direct optimization technique for the design of contoured beam reflectarrays is presented. It is based on the spectral domain method of moments assuming local periodicity and minimax optimization. Contrary to the conventional phase-only optimization techniques, the…

Design Tool for High-Performance Rotationally Symmetric Reflector Antennas

In this paper, we present an efficient higher-order BoR-MoM in which the unknown surface current is discretized using hierarchical Legendre basis functions, that are adapted to the circular symmetric geometry. Furthermore, the shape of the generatrix is represented by up…

Array Antenna Diagnostics with the 3D Reconstruction Algorithm

The 3D reconstruction algorithm is applied to a slotted waveguide array measured at the DTU-ESA Spherical Near-Field Antenna Test Facility. One slot of the array is covered by conductive tape and an error is present in the array excitation. Results…

Fast and Accurate Design Tool for Rotationally Symmetric Reflector Antennas with 3D Waveguide Components and Support Structures

We present a new efficient design tool for rotationally symmetric reflector antennas, possibly including 3D support structures and waveguide components. The tool is based on a combination of four solvers: Mode-Matching (MM) for cylindrical wave-guiding structures, a newly developed higher-order…

An Accurate and Efficient Design Tool for Large Contoured Beam Reflectarrays

An accurate and efficient tool for the design of contoured beam reflectarrays is presented. It is based on the Spectral Domain Method of Moments, the Local Periodicity approach, and a minimax optimization algorithm. Contrary to the conventional phase-only optimization techniques,…

Accurate and Efficient Analysis of Printed Reflectarrays With Arbitrary Elements Using Higher-Order Hierarchical Legendre Basis Functions

It is demonstrated that nonsingular higher-order hierarchical Legendre basis functions are capable of accounting for the singularities of the electric currents at the edges of the reflectarray elements, thus yielding good convergence properties and very accurate results. In addition, the…

Design of Dual-Polarized Contoured Beam Reflectarrays with Cross-Polar and Sidelobe Suppression

An efficient power pattern synthesis of contoured beam reflectarrays is presented. Using the presented synthesis technique, an offset dual-polarized contoured beam reflectarray to cover an European region with cross-polar and sidelobe suppression has been designed. Simulations show that the presented…

Higher-Order Basis Functions Applied to the Inverse Method of Moments for Inverse-Source Problems

Higher-order basis functions are commonly used for discretization of surface integral equations, which are typically solved by the Method of Moments (MoM). This leads to higher accuracy and lower memory requirements when compared to a simple piecewise linear discretization, e.g.,…

Design and Analysis of Printed Reflectarrays with Irregularly Positioned Array Elements

The design and analysis of printed reflectarrays with irregularly positioned array elements is presented. An accurate and efficient power pattern synthesis procedure, based on the Local Periodicity approach (LP) and the minimax optimization algorithm has been implemented. The analysis accuracy…

New Modelling Capabilities in Commercial Software for High-Gain Antennas

This paper presents an overview of selected new modelling algorithms and capabilities in commercial software tools developed by TICRA. A major new area is design and analysis of printed reflectarrays where a fully integrated design environment is under development, allowing…

Antenna Diagnostics on Planar Arrays Using a 3D Source Reconstruction Technique and Spherical Near-Field Measurements

In this paper, we apply a recently developed 3D source reconstruction algorithm to perform antenna diagnostics on a planar array configuration. The test case is a planar X-band slot array measured in a spherical near-field facility and two slots were…

Application of Advanced Field-Reconstruction Algorithms

A general, accurate, and efficient stand-alone commercial program for antenna diagnostics, DIATOOL, has been developed by TICRA. The software reconstructs the field or the equivalent currents on a plane or an arbitrary 3D surface enclosing the antenna. The fundamental properties…

Processing of Measured Fields Using Advanced Inverse Method of Moments Algorithm

A higher-order inverse method of moments algorithm, employing smooth current and geometry representations, as well as a very noise-robust solution algorithm, was presented at last year’s ESA workshop. The fundamental properties of the algorithm, including quantitative results for the RMS…

Recent Developments and Challenges for Reflector Antenna EM-Modelling

This paper concerns the EM-modelling of high-accuracy reflector antenna systems, and in particular of reflectors for space antenna systems. Recent modelling developments are exemplified ranging from general software enhancements to meet customer needs, over specific developments on a particular demanding…

Efficient Analysis of Reflector Antennas using GRASP

GRASP has for many years constituted the de facto standard in the space community for advanced reflector antenna modeling. The tool has furthermore found widespread use in the earth station segment and within the VSAT industry, as well as for…

An Accurate Technique for Calculation of Radiation From Printed Reflectarrays

The accuracy of various techniques for calculating the radiation from printed reflectarrays is examined, and an improved technique based on the equivalent currents approach is proposed. The equivalent currents are found from a continuous plane wave spectrum calculated by use…

Analysis of Printed Reflectarrays Using Extended Local Periodicity

An analysis technique for improved modeling of a printed reflectarray is proposed. The technique is based on a periodic approach where periodicity is applied on an extended unit cell, which includes the actual elements surrounding the element under consideration. An…

Advanced Processing of Measured Fields using Field Reconstruction Techniques

This contribution deals with the problem of reconstructing the extreme near-field of an antenna starting from the field measured at a larger distance. The presented method has several applications, including but not limited to antenna diagnostics, suppression of spurious contributions…

Latest Achievements in Antenna Diagnostics and Processing of Measured Fields

A stand-alone commercial program, performing advanced electromagnetic processing of measured data, is being developed by TICRA. The program reads the measured field and computes the extreme near field or the currents on the antenna surface. From the inspection of the…

Improved Source Reconstruction Technique for Antenna Diagnostics

This paper presents an improved inverse Method of Moment technique that allows surface currents to be reconstructed on the surface of an antenna. The input to the algorithm is measured near- or far-fields and the method therefore allows antenna engineers…

Higher Order Hierarchical Legendre Basis Functions for Electromagnetic Modeling

This paper presents a new hierarchical basis of arbitrary order for integral equations solved with the method of moments (MoM). The basis is derived from orthogonal Legendre polynomials which are modified to impose continuity of vector quantities between neighboring elements…

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