URSI Commission B
International Symposium on Electromagnetic Theory (EMTS 2019)

27–31 May 2019 San Diego, CA, USA

2019 URSI Commission B School for Young Scientists

The sixth edition of the URSI Commission B School for Young Scientists is arranged on the occasion of the EMTS 2019. This one-day School is sponsored jointly by URSI Commission B and the EMTS 2019 Local Organizing Committee. The School offers a short, intensive course, where a series of lectures will be delivered by a leading scientist in the Commission B community. Young scientists are encouraged to learn the fundamentals and future directions in the area of electromagnetic theory from these lectures.

Field and Potential Based Methods in Anisotropic and Bianisotropic Electromagnetics


Date: Monday, May 27, 2019
Venue: Westin San Diego Hotel, San Diego, CA, USA (EMTS 2019 venue)

Schedule (Coffee breaks are also included):

0800-0845       Lecture 1        Maxwell’s Equations and Constitutive Relations

0900-0945       Lecture 2        Factors that Influence Anisotropy and Bianisotropy

1000-1045       Lecture 3        Field and Potential-Based Methods of Analysis

1100-1145       Lecture 4        Field-Based Examples – Sources Not Present


1200-1300       LUNCH


1300-1345       Lecture 5        Field-Based Examples – Sources Present

1400-1445       Lecture 6        Potential-Based Examples – Sources Not Present

1500-1545       Lecture 7        Potential-Based Examples – Sources Present

1600-1645       Lecture 8        Conclusion and Future Research



Recent advances in rapid prototyping techniques, such as 3D printing, have made the manufacturing of complex media such as anisotropic and bianisotropic media possible. This capability has subsequently placed a greater need to incorporate the teaching of complex media into the advanced undergraduate and graduate educational curricula.  The goal of this short course is to develop and demonstrate both field and potential based analytical techniques for the solution of electromagnetic problems involving complex media. First, it will be shown how symmetry has a profound influence on material tensor properties and how this symmetry can be utilized to fabricate anisotropic and bianisotropic media. Next, it will be shown how these material tensor properties influence the method of analysis; either a field-based or potential-based technique.  Field-based techniques, which are directly based upon Maxwell’s equations, will be discussed first.  Examples, including the analysis of plane waves in general bianisotropic media and the analysis of a parallel-plate waveguide filled with a uniaxial medium, will be provided to demonstrate the field-based methodology. It will also be shown why the well-known vector potential method for isotropic media becomes invalid for complex media. This subsequently leads to a scalar potential formulation that is valid for gyrotropic anisotropic or gyrotropic bianisotropic media. Examples of the scalar potential formalism are given, including the analysis of a parallel-plate waveguide filled with a uniaxial medium. A comparison between the field and potential-based formalisms is provided to better understand the advantages and limitations of each method. A conclusion and future recommendations are also provided.


Overall Goals of the Course

·         Gain a deeper appreciation of Maxwell’s equations and the regimes of validity.

·         Develop a better understanding of the constitutive relations and learn about some of the recent and fascinating areas of electromagnetic materials research subsequently being inspired.

·         Understand the profound influence symmetry has on material property tensors and how symmetry can be infused into designs to create anisotropic and bianisotropic media.

·         Learn how to solve Maxwell’s equations using both field and potential-based techniques for various complex media with and without sources present.

·         Obtain deeper physical insight into electromagnetic field behavior in complex media.

·         Apply knowledge learned in your own personal research.


Overview of lectures

Lecture 1 presents an overview of Maxwell’s equations and constitutive relations. The microscopic and macroscopic form of Maxwell’s equations are discussed first. This review will help better understand the regimes of validity of the traditional form of Maxwell’s equations implemented in engineering practice, especially when used to analyze complex media (e.g., metamaterials). The quantum and general relativistic forms of Maxwell’s equations are also briefly reviewed since nanotechnologies are encroaching upon quantum regimes and cloaking can be understood in the general framework of curved spacetime. Constitutive relations are subsequently discussed since they are vital for obtaining a well-posed mathematical model. In general, these relations depend on space, time and field strength, and can be nonlinear, nonlocal, inhomogeneous, time varying, non-reciprocal and non-isotropic (i.e., bi-isotropic, anisotropic or bianisotropic). The review of these properties is important to better understand the affects of these materials on electromagnetic fields and to better appreciate current trends in material research (e.g., spacetime modulated metamaterials, gyrotropic and hyperbolic media, topological insulators, etc.). Understanding these properties is also important since the particular form of the constitutive relations has a strong influence on analysis methods in solving a given problem.  The review of the constitutive relations also provide the overall context of how anisotropic and bianisotropic media provides a basis into the broad classification of electromagnetic materials.


Lecture 2 discusses the various factors that lead to a bianisotropic material response. These factors include naturally-occurring bianisotropic materials, relative motion, weak nonlocality and symmetry. The aspects of symmetry are emphasized due to its profound influence on material tensor properties and due to the ability to infuse symmetry into material design using, for example, 3D printing.


Lecture 3 provides a brief overview of the various factors and techniques that aid in the direct solution of Maxwell’s field equations, including; symmetry, invariance, electromagnetic theorems, computational electromagnetics, asymptotic analysis and analytical methods.  Indirect methods for solving Maxwell’s equations using scalar and vector potentials are discussed in detail, as they are an important part of this short course.


Lecture 4 provides various examples of directly solving Maxwell’s equations in source-free regions. Examples include the analysis of biaxial and gyrotropic media in a source-free rectangular waveguide and the interaction of plane waves with bianisotropic materials using the kEH and kDB systems. These examples are very relevant in current research, especially in applications requiring polarization control.


Lecture 5 provides examples of directly solving Maxwell’s equations when sources are present. Examples include a line source above a conductor-backed gyrotropic medium and a source-excited parallel-plate waveguide filled with a uniaxial material. The example for the gyrotropic medium is relevant to topological insulators which support unidirectional surface wave propagation. And the waveguide example is important for nondestructive characterization of uniaxial and hyperbolic media.


Lectures 6 and 7 include examples of potential-based methods for solving Maxwell’s equations with and without the presence of sources. Solutions for a source-free waveguide filled with complex media are presented. A potential-based solution of a source-excited parallel-plate waveguide filled with a uniaxial media is also examined and subsequently compared to the field-based solution of Lecture 5. This comparison reveals the advantages of the potential-based approach, namely, mathematical simplicity and enhanced physical insight.


Course Instructor

Michael J. Havrilla received B.S. degrees in Physics and Mathematics in 1987, the M.S.E.E degree in 1989 and the Ph.D. degree in electrical engineering in 2001 from Michigan State University, East Lansing, MI.  From 1990-1995, he was with General Electric Aircraft Engines, Evendale, OH and Lockheed Skunk Works, Palmdale, CA, where he worked as an electrical engineer. He is currently a Professor in the Department of Electrical and Computer Engineering at the Air Force Institute of Technology (AFIT), Wright-Patterson AFB, OH. He is a member of URSI Commission B, a senior member of the IEEE, a senior member and current Vice President of the Antenna Measurement Techniques Association (AMTA), and a member of the Eta Kappa Nu and Sigma Xi honor societies. Dr. Havrilla has received various teaching and research awards, including the AFIT Instructor of the Quarter Award and the Air Force John L. McLucas Basic Research Award. His current research interests include electromagnetic and guided-wave theory, electromagnetic propagation and radiation in anisotropic and bianisotropic materials, electromagnetic characterization of complex media, quantum field theory and general relativity.

Registration Fees for the School

The registration fees for the School are as follows:

It is strongly recommended that the recipients of the EMTS 2016 Young Scientist Award (YSA) participate in the School.

For any inquiries on the School, please contact:

Professor Kazuya Kobayashi, Chair, URSI Commission B
Chuo University, Tokyo, Japan
Email: kazuya@tamacc.chuo-u.ac.jp

Professor John L. Volakis, Vice-Chair, URSI Commission B
Florid International University, Miami, FL, USA

Important dates

Deadline for paper submission: October 22, 2018

Notification of acceptance: January 10, 2019

Early-bird and author registration ends: March 30, 2019