Open Journal of Antennas and Propagation, 2013, 1, 44-48
Published Online December 2013 (http://www.scirp.org/journal/ojapr)
http://dx.doi.org/10.4236/ojapr.2013.13008
Open Access OJAPr
FDTD Analysis of Millimeter Wave Binary Photon Sieve
Fresnel Zone Plate
I. V. Minin, O. V. Minin
Siberian State Geodesy Academy, Novosibirsk, Russia.
Email: prof.minin@gmail.com
Received October 13th, 2013; revised November 14th, 2013; accepted December 9th, 2013
Copyright © 2013 I. V. Minin, O. V. Minin. This is an open access article distributed under the Creative Commons Attribution Li-
cense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
In the paper, we report about the possibilities to apply the photon sieve principle to binary diffractive lens in millimeter
wave band. The FDTD simulation showing the idea of the photon sieve application to millimeter wave optics does not
allow increasing the resolution power. The reason is the small number of holes in the FZP aperture. But such simulation
results may be used as computational experiments of simple scale in millimeter wave allowing obtaining insight into
physical systems which are characterized by nanometric objects, because the D/f and D/λ are almost the same.
Keywords: Photon Sieve; Fresnel Zone Plate; FDTD Simulation; Millimeter Wave
1. Introduction
According to the IEEE Standard Definition of Terms for
Antennas (IEEE Std 145-1993), Fresnel lens antenna is
an antenna consisted of a feed and a lens; usually Planar
transmits the radiated power from the feed through the
central zone and the alternate Fresnel zones of the illu-
minating field on the lens. The simplest variant of Fres-
nel lens is Fresnel zone plate.
It is well known that Fresnel zone plates (FZP) can be
used to focus and image [1,2]. But it is directly related to
the width of the zone. Spatial resolution of the conven-
tional diffractive lenses, such as Fresnel zone plate, is in
the order of the width of the outmost zone. Therefore,
reducing feature size of the zone plates helps to improve
the spatial resolution. According to the zone plates theory
[1,2], the width of zone from the center to the outer is
decreased gradually, and especially the width of the out-
ermost zone is very small.
To achieve higher resolution of well-known diffractive
optics, Kipp et al. proposed the novel idea of the photon
sieve [3]. Photon sieves (PS) are a type of diffractive
optical elements (DOEs) developed for soft X-ray focus-
ing and imaging. Unlike a zone plate which is composed
of concentric rings, a photon sieve is composed of a great
number of pinholes suitably arranged according to the
ring pattern of a classical Fresnel zone plate. It can over-
come the limitations of Fresnel zone plates in the case of
a big number of pinholes.
For an infinite conjugate, and binary FZP of focal
length
f
at wavelength
, the radial distance to the
center of the bright zone is given by [1,2]:
th
nn
r
22
fn
2
2
n
rn

The width w of each zone is such the area in a paraxial
approximation which is a constant (nf
), so

2n
wfr
.
In its simplest version, the photon sieve is consisted of
holes of diameter w located at a corresponding radial
distance n. The holes can be distributed regularly or
randomly in angle about the zone. According to the
Rayleigh, the angular resolution of this PS will be di-
rectly proportional to the smallest hole (largest ).
r
n
Traditionally, if position is near the Fresnel radii, size
and density of the pinholes can be used as design pa-
rameters. As we know that all the photon sieves reported
so far work in far-field region with macro-scale dimen-
sions and their minimum hole diameter is larger than the
incident wavelength
r
. Optical photon sieves FZP pro-
vide the advantage that the size of the focused spot is not
limited by the size of the smallest zone, as it is the case
for traditional zone plates.
FZP lenses, binary or phase correcting, have already
turned into essential focusing and imaging elements and
FDTD Analysis of Millimeter Wave Binary Photon Sieve Fresnel Zone Plate 45
also in the microwave [4,5] and millimeter wave/tera-
hertz systems [6-8].
The interest to PS FZP in this waveband is determined
by the possibly better resolution power, light weight and
simple design. But taken into account that in millimeter
wave band, the number of Fresnel zones at the FZP ap-
erture is small [4-8], and the effect of photon sieve to
resolution power is not the evidence and has not been
published in the literature yet.
In this paper, we report about the possibilities to apply
the photon sieve principles to diffractive lens in millime-
ter wave band.
2. Calculation Experiment Technology
The amplitude of the radiation passing through a specific
pinhole is given by its area, the phase by its position.
Positions in front of light and dark rings differ in phase
by π. As a rule amplitude photon sieve FZP consisting of
a large number of precisely positioned holes distributed
according to an underlying Fresnel zone plate geometry,
while the holes at transparent and opaque circular rings
of the FZP have a π phase shift. Compared to a conven-
tional photon sieve, the binary photon sieve has a trans-
mission two times more amplitude PS and a diffractive
efficiency approximately four times than amplitude PS.
The focusing characteristics of millimeter wave PS
FZP were examined by numerical experiment with the
following data: diameter of PS FZP = 230 mm, =
D f
150 mm,
= 10 mm, the total number of zones = 8.
n
In this wave band the hole diameter is comparable to
the incident wavelength
. So in our current research, we
intend to use the Finite Difference Time Domain Method
(FDTD) to observe the radiation pattern characteristics of
PS FZP with comparison of classical FZP [8,9].
FDTD is the method of choice for accurate and fast
simulations of electromagnetic wave interaction with
different structures. FDTD analyzes the propagation of
electromagnetic waves in a structure by solving Max-
well’s equations as a function of time at discrete loca-
tions.
Electromagnetic fields can be described in the differ-
ential form by Maxwell equations in a linear medium as
follows:
Faraday’s law:
BEM
t

AlA
BdAAdl MdA
t
 
 
Ampere’s law:
D
H
J
t

AlA
DdA HdlJdA
t

 
Gauss’ law for the electric field:
0
0
A
D
DdA
 

Gauss’ law for the magnetic field:
0
0
A
B
BdA
 

where:
E—the electric field strength; —electric induction; D
H
—the magnetic field strength; —magnetic induction; B
A
surface; l—closed contour bounding surface 3D
A
;
J
—current density;
M
—magnetization.
For linear medium we can write
DEB H
,
and
are the electric permittivity and magnetic permeability of free space, respectively.
First, the device under study is modeled by defining the geometry itself using 3- cells, being each cell properly
characterized with its electrical conductivity, permittivity, and loss tangent [10]. Each cell is referred as a Yee cell, in
honor of Kane S. Yee, who originally developed the FDTD method in 1966 [11,12]. By stacking several Yee cells, an
FDTD volume can be created. The structure under study is fabricated inside this volume. The equations are solved in a
leap-frog manner; that is, the electric field is solved at a given instant in time, then the magnetic field are solved at the
next instant in time, and the process is repeated for the specified number of time steps [10].
D
According to Yee Maxwell equations can be written as follows:
Open Access OJAPr
FDTD Analysis of Millimeter Wave Binary Photon Sieve Fresnel Zone Plate
46
12, 1,12
12, 1,12
12 12
12, 1,1212, 1,12
12, 1, 12
12, 1,12
12, 1,112
12, 1,12
,1,12
,1,12
12
12
12
ijk
ijk
nn
yy
ijk ijk
ijk
ijk
n
xij kxi
ijk
ij k
ij k
t
EE
t
t
HH
t



 


 


















,1,1 ,1,12 1,1,12
source1 2,1,1 2
y
nnn
j kzij kzij kn
ijk
HH
J
zx
 







12, 12, 1
1
,12,1
12 12
2
1 2,12,11 2,12,1
12, 12, 1
12, 12, 1
1,12,1 ,12,1
2
1,12,1
2
12, 12, 1
12
12
12
ijk
ij k
nn
zz
ijk ijk
ijk
ijk
ij kyij k
ij k
ijk
t
EE
t
t
H
t

 

 


 
 


















, 12,112,1,112,, 1
source1 2,12,1
z
nn nn
yijkxijkxijkn
ijk
HH H
J
xy
 








Similarly, we can write finite-difference formulas for
Hx, Hy, and Hz [11,12].
Important considerations in the design of the geometry
include that the ratio of the sides of the cell cannot ex-
ceed two, and that the biggest cell dimension must be at
least 1/20 of the highest frequency of interest. If these
conditions are not met the results are not reliable [10,13].
We also successfully use FDTD methodic mentioned
above for pattern reconstruction in millimeter wave me-
trology [13]. The electric field intensity in our simulation
was determinate according to paper [14].
3. Simulation Results
In the Figure 1 the results of PS FZP and classical FZP
are shown. The red is an air, green—the dielectric with
dielectric constant equal to 3. The holes were distributed
randomly in angle about the zone. The holes diameters
were equal to the width of correspondent Fresnel zones.
The incident wave front was flat.
The field intensity distribution across the focal plane is
shown in the Figu re 2.
The analysis of simulation results and from the Fig-
ures 1 and 2 it is followed:
1) The resolution power for PS FZP and classical FZP
are the same;
2) The first sidelobe level for PS FZP is about 1 dB
less that for classical FZP.
The gain of PS FZP is about 0.83 times less than for
classical FZP.
The structure of the photon sieve is based on FZP, and
therefore, their behavior for the first diffraction order is
similar. The main difference is that the higher-orders
obtained with the FZP are reduced with the sieve. For a
zone plate each ring contributes equally to the amplitude
at the focus. This contribution drops abruptly to zero
beyond the outermost ring which leads to strong intensity
oscillations in the diffration pattern.
With a photon sieve the number of pinholes per ring
can be readily adjusted to yield a smooth transition which
minimizes the secondary maxima.
4. Conclusions
Simulation results of photon sieve FZP investigation in
millimeter wave showing the resolution power of PS FZP
is the same as for classical FZP. The reason is the small
number of holes in the FZP aperture. But the first side
lobes suppressed conveniently. So the idea of the photon
sieve application to millimeter wave optics does not al-
low increasing the resolution power.
Another advantage of PS FZP over the FZP arises
from the fabrication point of view: the PS FZP can be
constructed in a single structure without any supporting
substrate.
But as it is known that nano-optics dealing with optical
effects occurs if light interacts with matter which has
artificially structured features with sizes comparable to
the wavelength [15]. From this point of view, we detailed
how the use of simple scale computational experiments
Open Access OJAPr
FDTD Analysis of Millimeter Wave Binary Photon Sieve Fresnel Zone Plate 47
(a)
(b)
Figure 1. Field intensity distribution near the focus: (a) the
PS; (b) the classical FZP.
Figure 2. The field intensity distribution in dB in the focal
plane for classical FZP (red) and PS FZP (blue).
in millimeter wave allows obtaining insight into physical
systems which are characterized by nanometric objects,
because the D/f and D/λ are almost the same.
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FDTD Analysis of Millimeter Wave Binary Photon Sieve Fresnel Zone Plate
Open Access OJAPr
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