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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 52, NO. 3, MARCH 2004
High-Frequency Analysis of Integrated Dielectric
Lens Antennas
Davide Pasqualini, Member, IEEE, and Stefano Maci, Fellow, IEEE
Abstract—A high-frequency method for the three-dimensional
analysis of integrated dielectric lens antennas is presented. This
method consists on improving the physical optics (PO) currents on
the lens surface by modifying, via suitable transition functions, the
spreading factor of those rays from the source point which arrive
at the lens-air interface close to the critical angle of incidence. Invoking the locality principle of the high-frequency phenomena, the
method uses the rigorous canonical solution of the semi-infinite dielectric space locally tangent at the lens surface. A uniform asymptotic evaluation of this canonical solution is provided with the introduction of a new transition function for the TM case. The present
formulation provides significant correction from the PO currents
of an elliptical lens, with a consequent improvement of the radiation pattern prediction, testified by comparisons with results from
a full-wave analysis.
Index Terms—Green’s function of layered media, high-frequency methods, lens antennas.
I. INTRODUCTION
D
IELECTRIC lenses are often used as directive antennas
in millimeter and submillimeter wave receiving systems
[1]. A typical application of this kind of antenna is concerned
with Earth and sky observation space missions, where stringent
requirements are needed such as low sidelobes, polarization
purity, and mechanical robustness. Lens antennas offer capability to be integrated with millimeter and submillimeter
planar feeding structures and the relevant circuitry (e.g., mixer
and local oscillator); therefore, they may be technologically
competitive with respect to the conventional solutions which
use horns or planar antennas. The major drawbacks of planar
antennas (patches or slots), such as low directivity and losses of
power into surface waves, are overcome when a dielectric lens
is leaned against the planar antenna, the latter providing the
primary focal source for the lens itself. In a first approximation,
the lens may be considered as an infinite substrate that does not
support undesired guided modes; furthermore, if the shape of
the lens is elliptical or approximately elliptical (e.g., extended
hemispherical lens) the rays from a focal spherical wave source
are refracted in forward direction, providing high antenna
directivity. In other emerging applications, such as those
concerning broadband wireless communications, dielectric
lenses are becoming increasingly important due to the recent
trend to move the operative frequency into the millimeter wave
range [2]. The attention given to dielectric lens antennas for
wireless applications is essentially relevant to the multiple
Manuscript received November 19, 2002; revised March 20, 2003.
The authors are with the Department of Information Engineering, University
of Siena, 53100 Siena, Italy.
Digital Object Identifier 10.1109/TAP.2004.824676
beam capability obtained with multiple offset primary point
sources, with a mechanism which resembles those employed
in parabolic reflector antennas.
The large dimensions in terms of a wavelength presumably
authorize the use of high-frequency asymptotic approximation
for the lens analysis. The physical optics (PO) method has been
widely used in this context, for far field [1] and, in combination, with multiple geometrical optics (GO) reflections for the
internal region [2]–[5]. The effects of the lens reflection to the
feeding source are remarkable due to the fact that the focus of
the ellipse, where the primary source is located, is a causic of
doubly reflected rays. It has been found that the application of
PO in this case is sufficiently accurate [4]–[6]. On the other
hand, we observed inaccuracy in applying the PO to find the radiation pattern even though internal reflections are introduced.
The purpose of this work is to understand the motivations of the
PO inaccuracy and to find analytical corrections to improve the
prediction.
To this end, we first present a ray description of the problem
(Section II), which serves to introduce the involved physical
mechanism. Next, we describe the PO currents improvement
based on the local canonical dielectric half-space problem (Section III). To improve the efficiency, the Sommerfeld integrals involved in the canonical solution are estimated via a new uniform
asymptotic evaluation, which is valid for every space point, including the lateral wave transition region (Section IV), and even
for TM polarization and high dielectric contrast. After checking
the accuracy of the new uniform asymptotics, numerical results
(Section V) show that our asymptotic process provides a significant refinement to the PO currents, whose amplitude profile is
left free by nonphysical cusps around the critical angle of incidence. The radiation pattern of the refined PO currents exhibits
noticeable corrections even from the first side lobes. To check
the accuracy, the latter results are compared with those obtained
from a full wave analysis provided by commercial software.
II. RAY DESCRIPTION
The dielectric lens antenna is constituted by a primary feed
source and a dielectric lens mounted on the feed plane. In this
paper, by referring to the most popular feed source constituted
by slots on a ground plane, we will assume a magnetic dipole
source placed in the focus. This may also be regarded as an
elementary constituent for finding the response to actual feed
arrangement (e.g., double slot fed by coplanar waveguides) via
a Green’s function convolution process.
The shape of the lens may be elliptical, hemispherical, hyperhemispherical, or extended hemispherical [1], [6]. The latter is
0018-926X/04$20.00 © 2004 IEEE
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841
Fig. 1. GO ray field from a focused point source inside an elliptical dielectric
lens with " = 4. Rays emanating from a spherical wave source at the focus F
which impinge on the interface above the maximum waist are all refracted in a
direction parallel to the lens axis, thus realizing an in-phase aperture. Dashed
line represents the equiphase surface of all the rays. is the critical angle of
incidence, associated to the dielectric contrast ( = sin (1= " )).
p
the most used, due to the capability to approximate the ellipse
while simplifying the technological fabrication process. Here,
we will refer to the basic elliptical shape for conceptual simplicity; however, the rather general method presented here can
be applied to the other various shapes.
The refraction mechanism of an elliptical dielectric lens optically transforms a spherical wave-front phase centered at the
focus in a plane wave front, with similarity to what happens in
the reflection process in parabolic reflectors. The ray-refraction
mechanism is represented in Fig. 1. In a GO ray approximation,
this spherical-to-plane wave transformation is obtained when
of the
the ellipse eccentricity and the relative permittivity
. Under this assumption, those
lens are related by
rays launched by a focal source that impinge on the lens surface
above the plane of maximum waist (dashed-dotted line in Fig. 1)
are transmitted in free space in the broadside direction, thus providing a uniform phase aperture distribution. Those rays that
impinge on the interface below the maximum waist are not focused on the aperture, thus producing spillover of energy which
may be parameterized through a proper spillover efficiency, like
in reflector antennas. Those rays that impinge exactly at the
maximum waist are associated to a critical angle of incidence
, due to the condition
. Overcoming critical angle, that would imply total reflection, never
for any incident ray). For
occurs for the ellipse (i.e.,
other kinds of lens shapes or for non focal sources, there may
be large supercritical angle zones.
For the elliptical lens, the critical angle regime produces an
increase of the ray density approaching the edge of the aperture,
and a consequent caustic of refracted rays on a cylindrical surface at the aperture rim, where the GO must be appropriately
corrected.
The presence of critical angles complicates the ray description. On the exterior side, the critically incident ray, beside the
refracted ray tangent at its impact point, excite surface guided
waves. Near the point of impact, the surface guided wave resembles the conventional lateral wave occurring for flat interface,
except for surface-induced leakage into the external medium.
When the observer moves further into the shadow region beyond the critically refracted (tangent) ray, it is converted into a
creeping wave of the type encountered on a perfectly conducting
object.
Fig. 2. Profile of the parallel Fresnel’s coefficient for parallel polarization.
Critical angle ( ) and Brewster angle ( ) of incident rays are related to the
null of transmission and reflection coefficient, respectively.
A complete ray description for the two-dimensional (2-D)
case is presented in [7] and comprises the various (creeping
wave, lateral wave) interaction and treatment of refracted ray
caustic. The extension for the 3-D case, however, would imply
complicated transition phenomena to render extremely difficult
a practical applicability. For this reason, a method based on
equivalent current integration at the interface may be convenient, as discussed next.
III. EQUIVALENT CURRENTS AT LENS-AIR INTERFACE
By invoking the equivalence principle on the lens surface, the
field outside the lens can be calculated by radiation in free space
of equivalent electric and magnetic current distributions established by the total field at the external interface. These currents
may be approximated at different levels of accuracy, as shown
next.
A. PO Currents
PO approximates the equivalent currents by GO applied to a
local flat interface, i.e., by resorting to the local Fresnel transmission coefficients. For the case of an elliptical dielectric lens
fed by a single directed magnetic focal dipole, the plane
profile of the parallel polarization Fresnel reflection
and
transmission
coefficients are presented in Fig. 2; actually,
the latter is multiplied by the cosine of the incidence angle to
obtain a quantity proportional to the PO currents. The equivalent current profile presents an unphysical cusp at the critand not
ical angle (note that Fig. 2 presents strictly
its amplitude).
vanishes at the maximum waist of the lens,
i.e., for critical incidence;
vanishes at the intersection of the
lens surface with the plane passing trough the upper focus
and normal to the vertical axis. This null is associated to the
Brewster angle of incidence, but no discontinuity occurs there.
The nonphysical behavior of the reflection coefficient
in the
neighborhood of the maximum diameter is due to the lack of
PO in describing the transition wave mechanism at the critical angle, thus requiring the asymptotic improvement discussed
next.
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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 52, NO. 3, MARCH 2004
where
(3)
(4)
(5)
and
denotes the transpose of . Note that ,
, and
are related as follows:
,
, and
where
. In (1) and (2),
are derived from the classical
Sommerfeld’s integrals by approximating the Hankel functions
inside the integrals with the asymptotic values for large arguments
(6)
in which
of the source from the interface,
,
. By introducing
and
the various spectra
is the distance
, and
,
in (6) are defined as
(7)
(8)
Fig. 3. (a) Canonical semi-infinite dielectric problem for the definition of the
equivalent currents for an arbitrary tangential point P on an elliptical lens. (b)
Same problem for a tangential point P on the maximum perimeter. For this case,
the tangent point is under the critical angle of incidence.
B. Local Canonical Semi-Infinite Dielectric Currents
By referring to the ray field theory for the homogeneous halfspaces problem [8], [10], the field launched by a source embedded into the denser medium is asymptotically represented
as the sum of a GO wave and a lateral wave. The latter exists
only for the incidence angle greater than the critical angle. When
the angle of incidence approaches the critical angle, whether
greater or smaller, a transition field occurs, which produces a
significant deformation of GO fields and relevant PO currents.
Let us, therefore, consider [Fig. 3(a)] the canonical problem of
a semi-infinite dielectric medium locally tangent to the curved
lens surface, which is illuminated by a magnetic dipole located
in the neighborhood of the lower focus of the elliptical lens. Let
the magnetic dipole
us denote by
source. A local
coordinate system is introduced with
its origin at the dipole and its axis perpendicular to the flat
and cylindrical
colocal interface; spherical
ordinate systems are also introduced. The equivalent currents
defined through the canonical problem at the tangential point
are then distributed on the lens surface.
and magnetic currents
The electric currents
at are given by
(1)
(2)
(9)
The application of the equivalence principle requires the definition of the field at the limit to the surface from the external side.
We have indeed used a representation of the field in the denser
medium; this is appropriate due to the continuity of the tangential field at the interface.
IV. UNIFORM ASYMPTOTIC EVALUATION OF THE
SOMMERFELD INTEGRALS
The absence of literature for robust uniform asymptotics
for treating the Sommerfeld integral in (6) motivates the new
uniform asymptotic formulation presented here. Indeed, while
the asymptotic solution uniformly valid everywhere is given for
the TE case in the classical works of Bleistein and Handelsman
[9] and Brekhovskikh [10], the TM case is not yet fully exploited. The difficulty arises from the presence of leaky-wave
pole located on an improper Riemann sheet of the complex
integration plane. In the absence of losses, the residue of this
pole is not associated to any physical wave, since this pole is
never captured by any steepest descent path (SDP) deformation.
However, its vicinity to the branch point affects the ordinary
saddle-point evaluation during the saddle-point/branch-point
coalescence. This fact invalidates, especially for high dielectric
contrast, a conventional uniform asymptotics based on mapping
saddle-point/branch-point interactions onto canonical parabolic
cylinder functions. In this section, while modifying the procedure with respect to the work of Bleistein for the TE case, we
formulate the TM case with the use of new canonical functions.
The asymptotic output blends more neatly and gradually into
the nonuniform GO-plus-lateral-wave ray description. This
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843
desirable property, although in a different formulation, is also
preserved in the work of Ishihara and Miyagawa [11].
Before proceeding further, let us first note that the problem
of a dipole on a grounded dielectric stratification, which was
treated by several authors [12], [13], is similar to the present
one; there, the interaction between the surface (leaky)-wave
and space-wave contributions is parameterized in terms of
(pole)-(saddle-point) interaction in place of (branch-point)(saddle-point) interaction. This implies the description of the
transitional behavior in terms of the erfc function, at variance
with the cylinder parabolic functions we will obtain next.
For the sake of simplicity in the notation, from here
on we suppress the superscript
in the quantities
and
. By using the angular change of variable
, with
, the original real axis
plane is mapped into the contour
contour of the
. Integral (6) is then transformed into
(10)
where
and
.
The plane, shown in Fig. 3, exhibits a saddle point at
and a branch point singularity on
(critical angle), the
in the original spectral plane; the
latter coming from
branch point corresponding to
disappears, due to the
. In order to isolate asymptotic contribuchoice
tions, the original path is deformed into the SDP passing through
the saddle point . The asymptotic evaluation on the SDP leads
to the GO contribution. When
, no branch-cut contribu[Fig. 4(b)] an
tions are intercepted [Fig. 4(a)], while for
additional integration around the branch cut must be included,
which asymptotically leads to the lateral wave contribution. For
far away from , GO and lateral wave contributions are distinct, thus allowing a nonuniform asymptotic evaluation by expanding in Taylor series the amplitude function close to the
respective critical points. This approximation fails when the
branch point is close to a saddle point (i.e., approaching the
critical angle), thus imposing more sophisticated asymptotics.
As a consequence of the SDP deformation, the original integral in (10) can be represented as
A. TE Case
(12)
The uniform asymptotics for the TE case start from the identity
(13)
and
and
circumvents the branch cut at . This branch cut
varies from
to in the top
is such that the phase of
Riemann sheet. As described next, depending on the TE or TM
case, a different mapping onto canonical functions is chosen for
the uniform asymptotic evaluation.
(11)
,
is the unit step
where
function, and
or
where
and
denote
the SDP and the path around the branch cut, respectively (see
Fig. 4).
It is now useful to perform the further change of variable
, which maps the saddle point in
and the branch point in
. The integral in (12) then becomes
where
(see Fig. 4),
Fig. 4. Integration paths in the spectral angular plane. (a) Angle of incidence
smaller than the critical angle. (b) Angle of incidence greater than the critical
angle.
maps in the plane. In particular
is along the real axis of the plane,
(14)
which is obtained just multiplying and dividing by the left-hand
. Identity (14) applies to any TE
side of (14) by
spectra in (8) and (9). The integrand in (13) is then approximated
as
(15)
where the constants
,
, and
are found in such a
at the critical points of the
way to match the value of
domain. In particular, let us denote by
and
the
, which comes from the mapping of
contributions to
and
in (14), respectively. Since during the first change of
variable in the plane the branch point corresponding to
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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 52, NO. 3, MARCH 2004
disappears,
does not present any branch point in the
plane. Thus, the constant
is found by the value obtained by
at the saddle point; i.e.,
. The constant
and are found indeed by matching the value of
at both the saddle point and the branch point; i.e., by solving
and
the linear equations
.
Using (15) in the integral in (13) leads to
(16)
where
Fig. 5. Integration paths in the spectral s angular plane used for the definition
of the canonical function in (18) and (22). For the TM case, an improper pole
at s =
j 2 sin[(
)=2] with = sin (1= " + 1) is located on
the bottom Riemann sheet.
p0
0
p
where
and
(see Fig. 5). Use of (19) in the
integral in (13), along with (22) and (18), leads to the final uniform asymptotic expression
(23)
(17)
and
with
(24)
(18)
with
,
, . This latter function can be
rewritten in terms of ordinary one-parameter cylinder parabolic
and
.
functions for both the contours
B. TM Case
An identity equivalent to (14) is not applicable for the
TM-type denominator so that the previous procedure cannot
be repeated. This is really due to the presence of an additional
leaky wave pole on the bottom Riemann sheet of the plane.
This pole is located at
with
. (A discussion on the meaning of this
pole is outside the scope of this paper; the reader may refer
to [8, pp. 508–509] for details.) Here, we will concentrate on
including in our asymptotic evaluation the influence of this
pole on the SDP integration. Indeed, although this pole is
never captured by any SDP contour deformation in the lossless
case, its presence may affect the asymptotics when the branch
point is close to the saddle point, especially for high dielectric
contrast. For this reason, the following representation of the
integrand in (13) is suggested:
(19)
where the constants
and
are found in such a way
at both the saddle point and the
to match the value of
branch point, i.e., by solving the two equations
(20)
(21)
The term which multiplies
in (19) implies within the integral in (13) the same special function as that in (18) with
. The term multiplying
leads to new canonical
functions defined as
(22)
The numerical calculation of the special function in (22) can
be given in terms of a series expansion similar as that normally
used for cylinder parabolic functions. The analytical derivation
of this series expansion will be the subject of a dedicated work.
Here, we only notice that the overall numerical process is dramatically accelerated also when using the numerical integration
(22) to calculate the new function.
V. ILLUSTRATIVE EXAMPLES
A. Validation of the Asymptotics
Numerical calculations have been carried out to test accuracy
and effectiveness of the asymptotic solution given in (16) and
(17) (TE) and in (23) and (24) (TM), as well as to highlight
the effects of the transition between space and lateral waves.
A reference solution is constructed via accurate numerical integration of the Sommerfeld integral in (6), after extraction of the
(we maintained
asymptotic value of the spectrum for large
the Hankel function in the kernel during the numerical calculation). The presented results have been normalized by the dependent constant . Fig. 6(a) and (b) is relevant to the TE and
TM case with specific reference of the spectra
in (7) and
in (8); similar results have been found for the other spectral components. The reference solution (dashed line) is successfully compared with our uniform asymptotics (continuous line)
as a function of along the interface of the canonical half-space
,
,
). The space wave contributions
(
and the lateral wave contribution
are also drawn individually (dashed-dotted and dashed-double-dotted lines, respectively), together with the conventional GO approximation
(small dots). Both these two contributions exhibit a transitional
behavior close to the critical angle which compensate for the
reciprocal discontinuities. Note that the space wave gradually
blends into the GO field far from the transition region, while
the lateral wave produces expected oscillations by interference
.
with the space wave in the supercritical angular region
The good agreement obtained for the TM case is implied by the
new transition function (22); we did not obtain such a result by
applying the same uniform asymptotics as that for the TE case.
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845
Fig. 7. Principal planes amplitude of the magnetic currents on the lens surface:
comparison between PO (dashed line) currents and currents derived from this
formulation (continuous line).
Fig. 6. Uniform asymptotic evaluation of (a) TE and (b) TM fields at the
dielectric-air interface between two semi-infinite media. Source is a horizontal
magnetic dipole embedded into a dense medium (" = 4) at a distance 4
from the interface with the vacuum, where is the free-space wavelength.
Here, the critical angle is at = 30 .
B. Equivalent Currents on the Lens Profile
Here, we compare the conventional PO currents on the lens
surface with the currents derived from the local canonical halfspace problem, as depicted in Fig. 7. We consider an elliptical
and major axis length
, fed by a unit
lens with
amplitude magnetic dipole placed at its lower focus. The equivalent magnetic currents are presented as a function of the scan
angle measured from the center of the ellipse (see the inset).
The and plane cuts are shown in Fig. 9(a) and (b), respectively. As expected, the PO currents significantly deviate from
those derived from the canonical problem, especially in the
plane, where the PO currents vanish improperly at the critical
angle.
Fig. 8. Normalized radiation far-field pattern for a 3 semiaxis elliptical
quartz lens (" = 4). Comparison among conventional PO (dots), this method
(continuous line), and reference results from a full-wave analysis (dashed line,
from FEKO™). Lens is excited by a small focal magnetic dipole: (a) H plane
and (b) E plane.
C. Radiation Pattern
The radiation integral of the PO currents is now compared
with the one associated to the improved currents. To estimate
the accuracy, a reference solution has been produced via a
full-wave method of moments (MoM) analysis provided by the
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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 52, NO. 3, MARCH 2004
with respect to our asymptotic solution may be attributed to the
following reasons. First, the internal reflections and the relevant
induced currents have not been included in the asymptotic
calculation, and this may have a certain influence especially for
the silicon lens (we note, however, that internal reflections play a
fundamental role for the prediction of the feed-source impedance
more than for the radiation pattern [4], [5], [15]). A second reason
for inaccuracy is the lack of description of current contributions
associated with creeping waves [7]. For introducing these contributions, one should start from a different canonical solution
to estimate the currents, i.e., from a locally tangent dielectric
cylinder. The integration of current contribution associated to
creeping waves leads to a weak contribution near broadside but
may be the main cause of inaccuracy for side-lobes up to 40 .
Finally, our approach does not properly include the diffraction
mechanisms that are induced by the lens truncation at the ground
plane. Indeed, although the integration end point provides per
se a rough estimate of the space wave diffraction, the additional
wave mechanisms excited at the truncation are not described.
VI. CONCLUSION
Fig. 9. Normalized radiation far-field pattern for a silicon elliptical lens with
semiaxis 3 (see Fig. 8 for the legenda).
commercial software FEKO1 [14]. The major semi-axis of the
(this corresponds to a maximum diameter
lens is equal to
of approximately six free-space wavelengths). Two different dielectric lenses have been considered relevant to relative dielectric permittivity equal to 4 (quartz, Fig. 8) and to 11.7 (silicon,
Fig. 9). A significant improvement with respect to the PO prediction is obtained by using our method especially for the lower
dielectric constant; this improvement is concerned with the position of the radiation nulls and with the level of the side lobes,
, the PO
particularly for the plane pattern. For
, while the present solution imstarts to be inaccurate at
and to
proves the prediction up to
in the
and
planes, respectively. Note that the PO nulls
and maxima can also be in counterphase with the corresponding
ones of the improved solution. Using larger dimensions of the
lenses, we have seen that the absolute angular range of accuracy
does not change being the permittivity equal.
In obtaining the results for comparison, we noted that the
numerical solution from the full-wave solver was nicely stable
despite the large lens dimensions in terms of wavelengths. In fact,
this stability has been obtained by using properly the symmetry
of the structure in order to reduce the unknown number. Giving
reliability to the reference solution, the residual discrepancy
1Trademarked.
On the basis of the observation that the PO is quite inaccurate in describing the field radiated by a dielectric lens antenna,
we have improved the description of the interface equivalent
currents by using the solution of the canonical locally tangent
semi-infinite dielectric problem. To improve the numerical efficiency, a uniform high-frequency solution of the Green’s function of this canonical problem has been presented. In deriving
the asymptotic representation, the integrand has been approximated by rational functions, which preserve the right singularity
and the exact value of the original spectral amplitudes at both
saddle and branch points. The outcome is a representation which
uniformly describes the emergence or disappearance of lateral
waves and that gradually blends into the nonuniform ray-field
structure far from the transition. A new canonical function has
been introduced for the TM case, which accounts for the presence of a pole on the improper Riemann sheet. Accounting for
this pole is particularly important for high-dielectric contrast,
frequently encountered in practical submillimeter wave realizations. Using our asymptotic solution, the PO currents have revealed a strong inaccuracy close to the maximum waist of an
elliptical lens, where the angle of the incident rays from a focal
source approaches the critical angle. The improved solution has
a remarkable positive impact on the prediction of the radiation
pattern, without adding significant computation time to the solution. While the PO starts to be inaccurate at 10 from the lens
axis, the present solution improves the prediction up to 35 –40
and 50 –60 in the and planes, respectively.
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Trans. Microwave Theory Tech., vol. 49, June 2001.
Davide Pasqualini (S’01–M’03) was born in Castel
Del Piano, Italy, in 1972. He received the Laurea degree in telecommunication engineering in 1998 and
the Ph.D. degree in electromagnetics from the University of Siena, Siena, Italy, in 1998 and 2002, respectively.
In 2000, he spent a research period at the Jet
Propulsion Laboratory, NASA-Caltech, Pasadena,
CA, where he worked on EM models for “photomixer” local oscillators for submillimeter
frequencies. Presently, he is employed as a Telecommunication Expert in the company of Monte dei Paschi di Siena. His research
interests include electromagnetic theory and applications, in particular with
high-frequency methods for the analysis and design of printed and lens
antennas.
Dr. Pasqualini has been on the Board of Directors of “Consorzio Terrecablate
Telecomunicazioni,” a new society established for the realization of a public
broadband TLC network in central Italy, since 2002.
847
Stefano Maci (M’92–SM’99–F’04) was born in
Rome, Italy. He received the Laurea degree (cum
laude) in electronic engineering from the University
of Florence, Florence, Italy, in 1987.
From 1990 to 1998, he was with the Department of
Electronic Engineering, University of Florence, as an
Assistant Professor. Since 1998, he has been an Associate Professor at the University of Siena, Siena, Italy.
His research interests include electromagnetic engineering, mainly concerned with high-frequency and
numerical methods for antennas and scattering problems. He was a co-author of an incremental theory of diffraction, for the description of a wide class of electromagnetic scattering phenomena at high frequency,
and of a diffraction theory for the high-frequency analysis of large truncated periodic structures. He has been and presently is responsible for several research
contracts and projects supported by national and international institutions, like
the European Union, the European Space Agency (ESA-ESTEC, Noordvjiik,
The Netherlands), and by industry and research centers. In the sixth EU framework program, he is involved in the Antenna Center of Excellence. In 1997,
he was an Invited Professor at the Technical University of Denmark, Copenhagen. He has been an Invited Speaker at several international conferences and
Ph.D. courses at European universities, industries, and research centers. He is
principal author or coauthor of 40 papers in IEEE Journals, 40 papers in other
international journals, and more than 150 papers in proceedings of international
conferences.
Dr. Maci received the “Barzilai” prize for the best paper at the XI RiNEm
(national conference of electromagnetism) in 1996. He was an Associate Editor
of IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY and Convenor
at the URSI General Assembly. He is presently a member of the Technical Advisory Board of the URSI Commission B and a member of the advisory board
of the Italian Ph.D. School of Electromagnetism. He served as Chairman and
Organizer of several special sessions at international conferences and has been
chairman of two international workshops. He is currently a Guest Editor of the
IEEE TRANSACTIONS ON ANTENNAS PROPAGATION’s Special Issue on Artificial
Magnetic Conductors, Soft Hard Surfaces, and Other Complex Surfaces.