The electromagnetic effects of conventional dielectrics, anisotropic dielectrics, and metamaterials were modeled in a terahertz-frequency folded-waveguide slow-wave circuit. Results of attempts to utilize these materials to increase efficiency are presented

Smith, Nathan D.

Starinshak, David P.

Wilson, Jeffrey D.

NASA Technical Reports Server

David P. Starinshak and Nathan D. Smith
Ohio Aerospace Institute, Brook Park, Ohio
Jeffrey D. Wilson
Glenn Research Center, Cleveland, Ohio
Using COMSOL Multiphysics Software to Model 
Anisotropic Dielectric and Metamaterial Effects 
in Folded-Waveguide Traveling-Wave 
Tube Slow-Wave Circuits
NASA/TM—2008-215267
July 2008
P1.35
https://ntrs.nasa.gov/search.jsp?R=20080030373 2019-08-30T05:05:17+00:00Z
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David P. Starinshak and Nathan D. Smith
Ohio Aerospace Institute, Brook Park, Ohio
Jeffrey D. Wilson
Glenn Research Center, Cleveland, Ohio
Using COMSOL Multiphysics Software to Model 
Anisotropic Dielectric and Metamaterial Effects 
in Folded-Waveguide Traveling-Wave 
Tube Slow-Wave Circuits
NASA/TM—2008-215267
July 2008
P1.35
National Aeronautics and
Space Administration
Glenn Research Center
Cleveland, Ohio 44135
Prepared for the
Ninth International Vacuum Electronics Conference (IVEC 2008)
sponsored by the IEEE Electronic Device Society
Monterey, California, April 22–24, 2008
Acknowledgments
     This work was supported by the NASA Glenn Research Center’s Independent R&D Fund.
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NASA/TM—2008-215267 1
Using COMSOL Multiphysics Software to Model Anisotropic  
Dielectric and Metamaterial Effects in Folded-Waveguide  
Traveling-Wave Tube Slow-Wave Circuits 
 
David P. Starinshak and Nathan D. Smith 
Ohio Aerospace Institute 
Brook Park, Ohio 44142 
 
Jeffrey D. Wilson 
National Aeronautics and Space Administration 
Glenn Research Center 
Cleveland, Ohio 44135 
 
 
Abstract 
The electromagnetic effects of conventional dielectrics, 
anisotropic dielectrics, and metamaterials were modeled in a 
terahertz-frequency folded-waveguide slow-wave circuit. 
Results of attempts to utilize these materials to increase 
efficiency are presented. 
Introduction 
COMSOL Multiphysics (ref. 1) is a versatile commercial 
software package that solves systems of coupled three-
dimensional partial differential equations. Thus it can be used 
to model physical phenomena in a wide range of applications 
including electromagnetics. With the finite element method of 
solution, it can easily model complex material properties that 
cannot readily be modeled with finite difference codes. For 
our interests in particular, it can solve for the electromagnetic 
fields in devices that include anisotropic dielectrics or meta-
materials with negative values for electric permittivity and/or 
magnetic permeability. 
We will confirm that COMSOL Multiphysics can accu-
rately determine the dispersion and interaction impedance for 
slow-wave circuits. We will then show that it can be used to 
investigate electromagnetic effects of both conventional 
dielectrics and unconventional materials such as anisotropic 
dielectrics and metamaterials. In particular, we will show 
results of attempts to improve the design power and efficiency 
of a terahertz-frequency folded-waveguide slow-wave circuit.  
Background 
There is much interest in using vacuum electronic amplifi-
ers in the terahertz regime of the electromagnetic spectrum 
because of their superior power and efficiency capabilities 
compared to solid state power amplifiers (SSPA’s) at high 
frequencies (ref. 2). However, power and efficiency levels 
with conventional vacuum electronics devices are still quite 
low at these frequencies because of the small size of the circuit 
dimensions and high attenuation (ref. 3).  
In attempts to reduce the attenuation and improve power 
and efficiency at terahertz frequencies, we modeled and 
investigated the effects of conventional dielectrics, anisotropic 
dielectrics, and metamaterials with negative values of electric 
permittivity and/or magnetic permeability (refs. 4 and 5) in a 
metallic folded-waveguide slow-wave circuit. The COMSOL 
Multiphysics finite element software package was utilized 
because its flexibility enables it to model material properties 
that are difficult to model with finite difference codes. 
Analysis and Results 
To test its accuracy, COMSOL Multiphysics’s RF Module 
was used to compute the dispersion and interaction impedance 
for ferruleless and ferruled coupled-cavity slow-wave circuits. 
The agreement with experiment was comparable to that 
obtained previously with other software (refs. 6 and 7). It was 
then used to model the dispersion, interaction impedance, and 
attenuation for the folded-waveguide slow-wave circuit shown 
in figure 1 operating at a frequency of 0.4 THz. Figure 2 
shows the computed surface current densities on the conduct-
ing waveguide walls for half of a geometric period. Because 
the current density and corresponding ohmic loss is strongest 
along the inside curves of the waveguide, we experimented 
with replacing the metal with nonconducting materials in these 
regions.  
We first modeled the dielectric silicon on the inner curve 
surfaces. Although it would be difficult, in principle this 
structure could be fabricated with a dielectric-metal layered 
structure. At 0.4 THz, the computed attenuation dropped  
45 percent, but unfortunately the interaction impedance 
dropped by 60 percent, resulting in a decrease in estimated 
circuit efficiency. We next investigated the effects of anisot-
ropic dielectrics in which the permittivity is directionally 
dependent. However, scanning over the permittivity tensor 
components showed no improvement over the isotropic case.  
NASA/TM—2008-215267 2
 
 
Figure 1.—Section of folded-waveguide slow-wave cir-
cuit. Electron beam passing through square aperture 
interacts with electromagnetic wave passing through 
serpentine waveguide. 
 
 
 
 
 
 
Figure 2.—Computed surface current densities for half of a 
geometric period of folded-waveguide slow-wave circuit. 
 
 
 
 
Finally we investigated metamaterials. These engineered 
non-natural materials have been shown recently to exhibit 
effective negative values for permittivity and permeability at 
microwave frequencies (refs. 4 and 5). We did determine that 
the efficiency could be improved for small conductivity values 
when permittivity and permeability have opposite signs and 
small values. It is possible that future developments in meta-
material theory and nanofabrication could make such material 
characteristics possible in the future. However present meta-
materials have high attenuation and there is as of yet no 
known method of fabricating such a hypothetical low-loss 
metamaterial.  
Conclusion 
We were not able to design for a significant improvement in 
computed power or efficiency by utilizing either conventional 
dielectrics, non-isotropic dielectrics, or existing metamaterials 
in terahertz folded-waveguide slow-wave circuit designs. 
Barring future major advances in metamaterial theory and 
nanofabrication, it appears that this is not a useful path toward 
efficiency and power improvement. However, we were able to 
show that COMSOL Multiphysics is a useful tool for investi-
gating unconventional materials in electromagnetic devices. In 
the future, this modelling capability may be able to show that 
such materials can provide significant advantages in other 
applications. 
References 
1. http://www.comsol.com.  
2. J. Booske, D. Whaley, W. Menninger, R. Hollister, and C. 
Armstrong, “Traveling-Wave Tubes,” in Modern Microwave 
and Millimeter-Wave Power Electronics, R. Barker et al., eds. 
New York: Wiley-Interscience, chap. 4, 2005. 
3. G. Scheitrum, “Microfabricated MVEDs,” in Modern Micro-
wave and Millimeter-Wave Power Electronics, R. Barker et al., 
eds. New York: Wiley-Interscience, chap. 7, 2005. 
4. D. Smith, et al., “Composite Medium with Simultaneously 
Negative Permeability and Permittivity, Phys. Rev. Letters, May 
1, 2000. 
5. J. Wilson and Z. Schwartz, “Multifocal Flat Lens With Left-
Handed Metamaterial,” Applied Physics Letters, Jan. 10, 2005. 
6. D. Schroeder and J. Wilson. “Ferruleless Coupled-Cavity 
Traveling-Wave Tube Cold-Test Characteristics Simulated with 
Micro-SOS,” NASA TP–3306, Aug. 1993. 
7. J. Maruschek, C. Kory, and J. Wilson. “Generalized Three-
Dimensional Simulation of Ferruled Coupled-Cavity Traveling-
Wave Tube Dispersion and Impedance Characteristics,” NASA 
TP–3389, Nov. 1993. 
 
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Using COMSOL Multiphysics Software to Model Anisotropic Dielectric and Metamaterial 
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The electromagnetic effects of conventional dielectrics, anisotropic dielectrics, and metamaterials were modeled in a terahertz-frequency 
folded-waveguide slow-wave circuit. Results of attempts to utilize these materials to increase efficiency are presented. 
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Using COMSOL Multiphysics Software to Model Anisotropic Dielectric and Metamaterial Effects in Folded-Waveguide Traveling-Wave Tube Slow-Wave Circuits

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