Stop bands in magneto-photonic crystal in millimeter waveband
One-dimensional (1D) magneto-photonic crystal (MPC) with tri-layer cell (vacuum-ferrite-quartz) interfaced with wire medium (WM) was investigated at microwave band. The appearance of two stopbands associated correspondingly with wave interference in the MPC and with ferromagnetic resonance absorptio...
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Інститут радіофізики і електроніки ім. А.Я. Усикова НАН України
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irk-123456789-1057462016-09-08T03:02:42Z Stop bands in magneto-photonic crystal in millimeter waveband Khodzitsky, M.K. Радиофизика твердого тела и плазмы One-dimensional (1D) magneto-photonic crystal (MPC) with tri-layer cell (vacuum-ferrite-quartz) interfaced with wire medium (WM) was investigated at microwave band. The appearance of two stopbands associated correspondingly with wave interference in the MPC and with ferromagnetic resonance absorption in ferrite layer was demonstrated. The occurrence of surface waves for the MPC+WM system in the MPC stop band frequency range was shown theoretically and experimentally. The surface wave peak allows the tuning of its position with applied magnetic field. It was shown that the steepness of the curve describing the dependence of surface wave peak position on magnetic field is less than the steepness of the corresponding curve for the left edge of the MPC stop band. The considered effects will make it possible to develop new magneto tunable microwave devices on basis of magneto-photonic crystals for GHz and THz band. Был исследован одномерный магнитофотонный кристалл (МФК) с трехслойной ячейкой (воздух-ферриткварц), ограниченный проволочной средой в миллиметровом диапазоне длин волн. Показано появление двух зон непропускания, связанных соответственно с интерференцией волн в МФК и с ферромагнитно-резонансным поглощением в ферритовом слое. Показано теоретически и экспериментально появление поверхностных волн для системы МФК + проволочная среда в частотном диапазоне зоны непропускания МФК. Показана возможность управления положением пика пропускания, связанного с поверхностной волной в спектре с помощью магнитного поля. Показано, что крутизна кривой, описывающая зависимость положения пика пропускания, связанного с поверхностной волной от магнитного поля, меньше, чем крутизна кривой, описывающая зависимость положения низкочастотного края зоны непропускания МФК от магнитного поля. Рассматриваемые эффекты позволят разработать новые магнитоуправляемые микроволновые устройства на основе МФК в гигагерцевом и терагерцевом диапазонах. Було досліджено одновимірний магнітофотонний кристал (МФК) із тришаровою коміркою (воздух-ферриткварц) обмежений дротовим середовищем у міліметровому діапазоні довжин хвиль. Показано появу двох зон непропускання зв'язаних відповідно з інтерференцією хвиль у МФК і з ферромагнітно-резонансним поглинанням у ферритовом шарі. Показано теоретично й експериментально появу поверхневих хвиль для системи МФК + дротове середовище у частотному діапазоні зони непропускання МФК. Показано можливість керування положенням піка пропускання пов’язаного з поверхневою хвилею в спектрі за допомогою магнітного поля. Показано, що крутизна кривої, що описує залежність положення піка пропускання, пов’язаного с поверхневою хвилею від магнітного поля, менше, ніж крутизна кривої, що описує залежність положення низькочастотного краю зони непропущення МФК від магнітного поля. Розглянуті ефекти дозволять розробити нові магнітокеровані мікрохвильові пристрої на основі МФК у гигагерцевому і терагерцевому діапазонах. 2009 Article Stop bands in magneto-photonic crystal in millimeter waveband / M.K. Khodzitsky // Радіофізика та електроніка. — 2009. — Т. 14, № 2. — С. 177-182. — Бібліогр.: 27 назв. — англ. 1028-821X http://dspace.nbuv.gov.ua/handle/123456789/105746 539.2.029.64:539.9 en Радіофізика та електроніка Інститут радіофізики і електроніки ім. А.Я. Усикова НАН України |
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English |
| topic |
Радиофизика твердого тела и плазмы Радиофизика твердого тела и плазмы |
| spellingShingle |
Радиофизика твердого тела и плазмы Радиофизика твердого тела и плазмы Khodzitsky, M.K. Stop bands in magneto-photonic crystal in millimeter waveband Радіофізика та електроніка |
| description |
One-dimensional (1D) magneto-photonic crystal (MPC) with tri-layer cell (vacuum-ferrite-quartz) interfaced with wire medium (WM) was investigated at microwave band. The appearance of two stopbands associated correspondingly with wave interference in the MPC and with ferromagnetic resonance absorption in ferrite layer was demonstrated. The occurrence of surface waves for the MPC+WM system in the MPC stop band frequency range was shown theoretically and experimentally. The surface wave peak allows the tuning of its position with applied magnetic field. It was shown that the steepness of the curve describing the dependence of surface wave peak position on magnetic field is less than the steepness of the corresponding curve for the left edge of the MPC stop band. The considered effects will make it possible to develop new magneto tunable microwave devices on basis of magneto-photonic crystals for GHz and THz band. |
| format |
Article |
| author |
Khodzitsky, M.K. |
| author_facet |
Khodzitsky, M.K. |
| author_sort |
Khodzitsky, M.K. |
| title |
Stop bands in magneto-photonic crystal in millimeter waveband |
| title_short |
Stop bands in magneto-photonic crystal in millimeter waveband |
| title_full |
Stop bands in magneto-photonic crystal in millimeter waveband |
| title_fullStr |
Stop bands in magneto-photonic crystal in millimeter waveband |
| title_full_unstemmed |
Stop bands in magneto-photonic crystal in millimeter waveband |
| title_sort |
stop bands in magneto-photonic crystal in millimeter waveband |
| publisher |
Інститут радіофізики і електроніки ім. А.Я. Усикова НАН України |
| publishDate |
2009 |
| topic_facet |
Радиофизика твердого тела и плазмы |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/105746 |
| citation_txt |
Stop bands in magneto-photonic crystal in millimeter waveband / M.K. Khodzitsky // Радіофізика та електроніка. — 2009. — Т. 14, № 2. — С. 177-182. — Бібліогр.: 27 назв. — англ. |
| series |
Радіофізика та електроніка |
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2025-07-07T17:19:32Z |
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1837009494286008320 |
| fulltext |
__________
ISSN 1028-821X Радиофизика и электроника, том 14, № 2, 2009, с. 177-182 ИРЭ НАН Украины, 2009
РАДИОФИЗИКА ТВЕРДОГО ТЕЛА И ПЛАЗМЫ
УДК 539.2.029.64:539.9
STOP BANDS IN MAGNETO-PHOTONIC CRYSTAL IN MILLIMETER WAVEBAND
M. K. Khodzitsky
A. Usikov Institute of Radiophysics and Electronics of the national Academy of Science of Ukraine
12, Ac. Proscury St., 61085, Kharkov, Ukraine
Е-mail: khodzitskiy@yandex.ru
One-dimensional (1D) magneto-photonic crystal (MPC) with tri-layer cell (vacuum-ferrite-quartz) interfaced with wire me-
dium (WM) was investigated at microwave band. The appearance of two stopbands associated correspondingly with wave interference in
the MPC and with ferromagnetic resonance absorption in ferrite layer was demonstrated. The occurrence of surface waves for the
MPC+WM system in the MPC stop band frequency range was shown theoretically and experimentally. The surface wave peak allows the
tuning of its position with applied magnetic field. It was shown that the steepness of the curve describing the dependence of surface
wave peak position on magnetic field is less than the steepness of the corresponding curve for the left edge of the MPC stop band. The
considered effects will make it possible to develop new magneto tunable microwave devices on basis of magneto-photonic crystals for
GHz and THz band. Figs. 5. Ref.: 27 titles.
Key words: magneto-photonic crystal, wire medium, stop band, surface wave, Tamm state, ferromagnetic resonance.
During the last decade, structures with peri-
odic refraction index (known also as photonic crys-
tals (PCs) or photonic band gap materials [1]) have
been a subject of experimental and theoretical re-
search due to their prominent spectral properties and
possibilities of promising applications in microwave
and optoelectronics [2–6]. The PCs possess band
gaps in which electromagnetic wave propagation is
prohibited in any direction. Characteristics of band
gap can be described by energy band structure or stop
band (forbidden band) in transmission spectrum.
Substantially, PCs are artificially made from dielec-
tric (organic) or metallic materials for band gap elec-
tronic control [7–8]. Up to the present, magnetic ma-
terials for PCs have not attracted much attention be-
cause permeability of magnetic materials in the opti-
cal frequency range equals to unity. But for ferrites,
yttrium iron garnets, granular magnetic films and
other magnetic materials the permeability differs
from unity at microwave frequencies because of fer-
romagnetic resonance (FMR) [9]. So, ferrites can be
exploited for microwave magnetic photonic crystals
(MPCs) [10]. The ferrites in saturation state have a
tensor permeability tuned by a static magnetic field.
Therefore, magnetic materials included in MPCs
make it possible to design the magneto-tunable mi-
crowave devices on basis of MPCs [11]. Recently,
some papers have been devoted to the MPCs investi-
gation. Sigalas et al. [12] have studied theoretically
the effect of permeability on the photonic band gaps
of MPCs. A. Saib et al. [13] have studied experimen-
tally magnetic photonic band-gap material based on
ferromagnetic nanowires at microwaves. S. Cher-
novtsev et al. [14, 15] have experimentally and theo-
retically studied the tuning of frequency stop bands
for 1D MPC on basis of ferrite in K and Ka frequen-
cy band. Jie Xu et al. [16] have experimentally and
theoretically investigated the transmission characte-
ristics of 2D MPC in X frequency band. However, in
all these works, it has not considered the possibility
of appearance of two stopbands: the stop band asso-
ciated with wave interference in MPC (further let’s
call it as MPC stopband) and the stop band associated
with resonance absorption in magnetic layer con-
nected with FMR (further let’s call it as FMR zone).
The origin of the usual PC stop bands is the
same as in the solid state periodical lattice, where the
diffraction of electron wave on periodical potential
make it impossible for electron with certain energy to
move through the crystal. If we proceed with this
analogy further we can anticipate the existence of
some surface waves (SW), (analogous to so named
«Tamm states» (TS) in solid state physics) [17] on
the interface between the PC and the medium, where
electromagnetic wave cannot propagate (ideally con-
ducting metals, medium with negative permittivity
and permeability, another PC or MPC). The frequen-
cy of such surface wave should lie in a forbidden gap
of PC. The electromagnetic wave vector is directed
along the crystal axis, the field being uniform in
transversal direction and do not transfer energy. The
surface wave can be detected by studying transmis-
sion and reflection spectra of the system – a narrow
peak appears in the transmission spectrum together
with a dip in the reflection spectrum. These surface
waves have been theoretically and experimentally
studied by Vinogradov et all. for PC as well as MPC
with bi-layered cell in optical frequency range
[18–19]. The research of these waves in the micro-
wave band has a very short history is started only
recently [20, 21].
In this paper we have experimentally studied
appearance of two stopbands with various physical
origins in the MPC transmission spectrum and occur-
М. К. Ходзицкий / Зоны непропускания в магнитофотонном…
_________________________________________________________________________________________________________________
178
rence of the surface waves in these stopbands in mi-
crowave band (22–40 GHz). This frequency band
displays certain advantage over the optical band be-
cause we can experimentally observe the field distri-
bution near the PC interface. Experimental results are
in good agreement with theoretical results.
1. Theory. Let us consider the finite struc-
ture consisting of MPC and WM, loaded in a rectan-
gular waveguide (Fig. 1).
1D MPC consisted of tri-layer primitive
cells (vacuum-ferrite-quartz). The MPCs is restricted
by a rectangular waveguide along the y and x axes.
A static magnetic field is applied along the y axis.
Fig. 1. Schema of structure consisting of the MPC and WM,
loaded in a rectangular waveguide
It is well known that the ferrite layers, mag-
netized under the external magnetic field have a ten-
sor permeability derived from the Landau-Lifshitz
equations [22]:
.
100
0
0
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
−= μμ
μμ
μ a
a
j
j
(1)
For saturated ferrite with dissipation we
have
( ) ;22
2
ωω
ωωωωμ
−
−+
=
H
MHH (2)
,22 ωω
ωωμ
−
=
H
M
a (3)
where αωγω jHH += 0 is the ferromagnetic reso-
nance frequency; γ is the gyromagnetic ratio; H0 is
the dc magnetic field in ferrite layers; fπω 2= is the
circular frequency of the alternating electromagnetic
field; α is the damping coefficient of ferrites;
SM Mπγω 4= is the characteristic frequency of fer-
rite; MS is the ferrite saturation magnetization.
Let us consider the propagation of a plane
wave through ferrite. The wave vector is normal to
the applied static magnetic field H0 (this case is
called transverse magnetization), the tensor of effec-
tive permeability can reduce to a scalar as [22]:
.
22
μ
μμμ a
eff
−
= (4)
The midgap frequencies of usual MPC stop
bands are defined as [23]:
C
C m
cf
λ
= ; ),(2 qqffvvC dndndnm ++=λ (5)
where c is the speed of light; m is the number of
MPC stop band; dv, df, dq are thicknesses of vacuum,
ferrite and quartz layers correspondingly; nv, nf, nq
are refraction indexes of vacuum, ferrite and quartz
layers correspondingly which are evaluated as
;1=vn ;effffn με= ,qqn ε= (6)
where ,qε fε are the permittivity of quartz and fer-
rite layers correspondingly.
The MPC is adjacent through the quartz
layer to WM. WM represents the arrays of thin copper
wires on polystyrene substrate. The metallic wires
were structured on a scale much less than the wave-
length of radiation. When the wavelength of the inci-
dent radiation is much larger than the size and spac-
ing of scatterers, the response of the scatterers to the
incident fields can be treated by way of the effective
medium theory. Therefore, an effective permittivity
effε can be used to define the permittivity of the me-
dium. Negative permittivity of WM can be achieved
at microwave frequencies (permittivity is negative
below plasma frequency pω ). The WM effective
permittivity and the plasma frequency are given by
formula [24]:
;2
2
ω
ω
εε p
hosteff −= ,
)ln(
2
2
2
2
r
aa
c
p
πω = (7)
where a is the lattice parameter (the distance between
the nearest wires); r is the radius of the wires; hostε –
host medium.
To obtain the surface wave (analogous to
so-called Tamm state) it is necessary that a MPC stop
band overlaps the frequency range where effective
permittivity of WM has negative sign.
The well-known transfer matrix technique
[15, 23] was used to find the transmission (reflection)
coefficient for periodical MPC structure (Fig. 1). The
finite-difference-time-domain method (FDTD) well-
described anywhere [25–27] was used to calculate
the transmission (reflection) spectra of WM and
x
z
y H0
М. К. Ходзицкий / Зоны непропускания в магнитофотонном…
_________________________________________________________________________________________________________________
179
MPC+WM and to evaluate the field profile of the
surface wave as well.
2. Experiment. To carry out the experimen-
tal investigations, the MPC and the WM were de-
signed and fabricated. The ferrite layer (brand
1SCH4) has complex permittivity of about
0008,01,11 jf +=ε , saturation magnetization of
GsM S 382= , damping coefficient of 024,0=α and
thickness of )02,05,0( ±=d mm. The quartz layer
has permittivity of about 5,4=qε and thickness of
)02,01( ±=d mm. The vacuum layer has thickness
of )02,05,1( ±=d mm. The MPC has 4 tri-layered
cells and interfaced with WM by quartz layer. Ac-
cording to equations (5), (6) for given parameters the
midgap frequency of the first MPC stop band asso-
ciated with wave interference in MPC is about of
28,37 GHz at zero applied magnetic field ).1( =effμ
The WM consists of polystyrene substrate (thickness
of 2,1 mm, permittivity 53,2=hostε ) with thin cop-
per wires on one side. The gap between the polysty-
rene substrates is 0,5 mm. The polystyrene substrate
has wires with length of 3,3 mm and diameter of
0,15 mm. The distance between two nearest wires is
of 1 mm along x axis. The WM has 6 polystyrene
substrates with 8, 8, 8, 6, 5, 3 wires accordingly. Ac-
cording to equations (7) such WM has negative effec-
tive permittivity till plasma frequency of 74,36 GHz.
The experimental setup includes mainly the
vector network analyzer (VNA), waveguide transmis-
sion line, waveguide segment with structure under
study and electromagnet controlled by power supply
unit (the magnetic field range is about of 0–7000 Oe)
[14, 15]. The composite structure was loaded in a
rectangular waveguide segment with cross-section of
7,2×3,4 mm2. The segment with structure under
study was placed between poles of electromagnet
where a uniform static magnetic field was provided.
An EM wave propagates along the z axis with an
electric field along the y axis and magnetic field
along the x axis (Fig. 1). The static magnetic field
was applied normally to alternating magnetic field.
The transmission spectra were automatically meas-
ured by the VNA in the frequency range of
22–40 GHz.
3. Results and discussions. Let’s consider
transmission spectra for various structures namely:
for MPC; for WM; for MPC+WM.
The transmission spectra of the MPC have
been measured and calculated using transfer matrix
technique [15, 23] and effective permeability has
been calculated using the equation (4). The results
are shown in Fig. 2, a–c. For small applied magnetic
field: )1,0()Re( ∈effμ the transmission spectra of the
MPC have a shape of smooth upturned dome and
represent stop-band associated with Bragg interfe-
rence in periodical MPC (MPC stop band). The bot-
tom value of stop-bands depth (the difference be-
tween transmission coefficient in pass-band and one
in stop-band) equals approximately to –40 dB. As the
magnetic field increases the position of stop band
edges shifts weakly to higher frequencies. The simu-
lation corroborates the experimental results, though
with some discrepancy, associated with an error in
the simulation parameters choice: the module of
transmission coefficient is defined by imaginary part
of both constitutive parameters ),( με of each MPC
layer while the positions of MPC stop-band edges are
defined by real part of parameters.
30 40 50 60
35
30
25
20
15
10
5
0
e1
e3
e2
t3
t2Tr
an
sm
is
si
on
, d
B
Frequency, GHz
t1
–
–
–
–
–
–
MPC
stop band
MPC
stop band
MPC
pass band
–
a)
30 40 50 60
10
0
10
20
MPC
Frequency, GHz
Tr
an
sm
is
si
on
, d
B
ferrite
30 40 50 60
60
40
20
0
–
–
–
FMR
zone
MPC
stop band
Pe
rm
ea
bi
lit
y FMR
–
1
2
c)
Fig. 2. Transmission spectrum of the MPC for various applied
magnetic fields at Re( μeff
) ∈ (0,1), theory: t1 – H = 1130 Oe, t2 –
H = 2290 Oe, t3 – H = 3370 Oe; experiment: e1 – H = 1130 Oe,
e2 – H = 2290 Oe, e3 – H = 3370 Oe (a); frequency dispersion of
effective permeability of ferrite at H = 6840 Oe (b); experimental
(black line) and simulated (grey line) transmission spectrum of the
MPC for H=6840 Oe at Re( μeff
) ∈ (–6,8) correspondingly (c)
For large magnetic field (H = 6840 Oe) the
permeability becomes negative )8,6()Re( −∈effμ in
the investigated frequency range. The depth of expe-
rimental MPC transmission spectrum drops down to
–70 dB see Fig. 2, c. The frequency position of the
valley coincides with ferromagnetic resonance fre-
b)
М. К. Ходзицкий / Зоны непропускания в магнитофотонном…
_________________________________________________________________________________________________________________
180
quency. We can conclude that a new absorption
process connected with FMR in ferrite was engaged.
Hence we have two deep valleys and correspondingly
two stop-bands with various origins. The first band
(the FMR zone) in the range from 23 to 31 GHz cor-
responds to the FMR absorption (Fig. 2, b). In this
frequency range the real part of effective permeabili-
ty of the ferrite is negative and imaginary part is dif-
ferent from zero, therefore electromagnetic wave can
not propagate in ferrite. The position of mid-gap fre-
quency in this band is defined by ferromagnetic re-
sonance frequency and varies linearly with the static
magnetic field. The second band (MPC stop band) in
the range from 31 to 41 GHz corresponds to known
Bragg interference in MPC. In this frequency range
the electromagnetic power is not absorbed. The posi-
tion of mid-gap frequency in this band is defined by
the equation (5) and remains almost unchanged at
variations of the magnetic field. This behavior is due
to small variation (from 0 to 1 at 32 GHz) of the ef-
fective magnetic permeability throughout the whole
interval of static magnetic field change (0–7000 Oe).
Next we consider the transmission spectra
for the WM (experimental (solid line) and simulated
(dash line)) (Fig. 3, a).
25 30 35 40
80
60
40
Tr
an
sm
is
si
on
, d
B
Frequency, GHz
WM
–
–
Cutoff waveguide
frequency
1
2
–
a)
25 30 35 40
8
6
4
2
0
–
–
–W
M
p
er
m
itt
iv
ity
Frequency, GHz
–
b)
Fig. 3. Transmission spectrum of the wire medium: 1 – experi-
ment; 2 – simulation (a); frequency dispersion of effective wire
medium permittivity for following parameters: a = 1 mm;
r = 0,075 mm; εhost = 2,53 (polystyren) (b)
The deep valley with the bottom level of the
order of –70 dB shows the frequency band where the
electromagnetic wave can not propagate through the
WM. Naturally this is connected with negative effec-
tive permittivity of the WM. The experimental and
theoretical curve coincide well within 21–28 GHz.
Within higher frequency range (28–40 GHz) the dis-
crepancy between experimental and simulated trans-
mission spectra is associated with the shortcomings
of calculation method and wire spacing inaccuracy in
the experiment. The effective permittivity of WM is
negative in the frequency range under study
(21–40 GHz) see in Fig. 3, b.
It was shown in [18] that at interface be-
tween MPC and medium with negative permittivity
surface wave could exist. To study surface wave we
use the composite system MPC+WM in the frequen-
cy band where effective permittivity of the WM is
negative. The surface wave appears as a sharp peak
in the transmission (reflection) spectra in the MPC
stop-band and is detected experimentally (Fig. 4, a).
15 20 25 30 35 40
15
0
15
Pe
rm
ea
bi
lit
y
R
ef
le
ct
io
n
Frequency, GHz
3
0,0
0,5
1,0
ferrite
2
0,5
1,0
MPC MPC
stop band
FMR
zone
SW peak
in FMR zone
SW peak in
MPC stop band
MPC+TWS1
–
a)
20 10 0 10 1
0
1
1
0
1
––
Ey
z, mm
WM
b)
4
3
2
MPC
Ey
1
–
–
c)
Fig. 4. 1 – Simulation of reflection spectrum of the MPC+WM at
H = 4560 Oe, 2 – Simulation of reflection spectrum of the MPC at
H = 4560 Oe, 3 – Frequency dependence of permeability of ferrite at
H = 4560 Oe (a); Calculated Ey field profile along z axis of the SW
peak in MPC stopband at f = 27,04 GHz (b) and SW peak in FMR
zone at f = 23,31 GHz (c) for MPC+WM case at H = 4560 Oe
(1 – ferrite, 2 – quartz, 3 – vaccum, 4 – polystyrene with wires)
М. К. Ходзицкий / Зоны непропускания в магнитофотонном…
_________________________________________________________________________________________________________________
181
It worth noting here that we detected one
more peak in the FMR zone as well. This peak may
correspond also to surface wave (SW). The calculated
Ey field profiles along z axis of both surface waves
are shown in Fig. 4, b, c at H = 4560 Oe. The reflec-
tion spectrum of the MPC+WM structure with sur-
face waves in the MPC and FMR stop bands at mag-
netic field of 4560 Oe are shown in the Fig. 4, a.
To study the «three layer» MPC it is necessary to
derive the corresponding dispersion equation for this
periodical structure and calculate the frequency posi-
tion of the surface wave peak. As can be seen from
the Fig. 4, a the little quasi-pass band occurs between
the MPC and FMR stop band. Indeed it’s the strongly
changed at the left edge of MPC band due to close
neighborhood to the FMR absorption band.
To demonstrate the possibility of magnetic
field to tune of SW peak position, the corresponding
experiment and calculation were carried out. The
experimental and simulated evolution of the SW peak
position in the MPC stop band with variation of the
magnetic field are shown in the Fig. 5.
0 2000 4000 6000
25
30
35
40
3
1
left edge
M
PC
st
op
b
an
d
Fr
eq
ue
nc
y,
G
H
z
Magnetic field, Oe
right edge
SW peak
2
a)
2000 4000 6000
25
30
35
40
1
2
3
left edge
right edge
SW peak
Magnetic field, Oe
Fr
eq
ue
nc
y,
G
H
z
M
PC
st
op
b
an
d
b)
Fig. 5. Experimental frequency dependence of MPC stop band
edges (1, 2) and surface wave peak (3) position on applied magne-
tic field (a); calculated frequency dependence of MPC stop band
edges (1, 2) and surface wave peak (3) position on the magnetic
field (b)
Experimental results are in good agreement
with the results of simulation. The tuning of SW peak
position is about 1 GHz on 3 kOe. It should be noted,
the calculated frequency dependence of surface wave
peak position on magnetic field is shown in the
Fig. 5, b only for corresponding experimental data. It
should be noted that the steepness of the curve describ-
ing the dependence of the SW peak position in change
on magnetic field ( =∂∂ expHfSW 0,42 GHz/kOe,
7,0=∂∂ theorySW Hf GHz/kOe) is less than the cor-
responding steepness of the left edge of the MPC
stop band ( 39,1=∂∂ theoryLeftedge Hf GHz/kOe). The
range of magnetic field is 1880–3370 Oe. Such beha-
vior can be explained by the strong dependence of
SW peak position on the impedance of bounding
medium which is not sensitive in the case of wire
media without magnetic inclusions to the applied
magnetic field.
Conclusions. The transmission and reflec-
tion spectra of one-dimensional MPC with tri-layer
cell interfaced with WM were investigated at micro-
wave band.
The appearance of two stopbands: stopband
connected with wave interference in MPC and one
connected with ferromagnetic resonance absorption
in ferrite layer was demonstrated.
For MPC+WM structure it is shown expe-
rimentally and theoretically the occurrence of surface
waves (analogous to «Tamm states») in the frequen-
cy range corresponding to the MPC stop band.
The tuning of the surface wave peak posi-
tion by magnetic field was demonstrated. The steep-
ness of the curve describing the dependence of the
surface wave peak position on the magnetic field is
less than the corresponding steepness of the left edge
of MPC stop band.
The studied effects make it possible to de-
sign the new magnetotunable devices on basis of
MPCs for GHz and THz bands.
I acknowledge helpful discussions with
Prof. S. I. Tarapov and D. P. Belozorov. This work
was supported by the STCU Project No. 4912 and the
Grant of the President of Ukraine for young scien-
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ЗОНЫ НЕПРОПУСКАНИЯ
В МАГНИТОФОТОННОМ КРИСТАЛЛЕ
В МИЛЛИМЕТРОВОМ ДИАПАЗОНЕ
ДЛИН ВОЛН
М. К. Ходзицкий
Был исследован одномерный магнитофотонный
кристалл (МФК) с трехслойной ячейкой (воздух-феррит-
кварц), ограниченный проволочной средой в миллиметровом
диапазоне длин волн. Показано появление двух зон непро-
пускания, связанных соответственно с интерференцией волн
в МФК и с ферромагнитно-резонансным поглощением в
ферритовом слое. Показано теоретически и эксперименталь-
но появление поверхностных волн для системы
МФК + проволочная среда в частотном диапазоне зоны непро-
пускания МФК. Показана возможность управления положе-
нием пика пропускания, связанного с поверхностной волной в
спектре с помощью магнитного поля. Показано, что крутизна
кривой, описывающая зависимость положения пика пропус-
кания, связанного с поверхностной волной от магнитного
поля, меньше, чем крутизна кривой, описывающая зависи-
мость положения низкочастотного края зоны непропускания
МФК от магнитного поля. Рассматриваемые эффекты позво-
лят разработать новые магнитоуправляемые микроволновые
устройства на основе МФК в гигагерцевом и терагерцевом
диапазонах.
Ключевые слова: магнитофотонный кристалл,
проволочная среда, зона непропускания, поверхностная волна,
Таммовское состояние, ферромагнитный резонанс.
ЗОНИ НЕПРОПУСКАННЯ
В МАГНІТОФОТОННОМУ КРИСТАЛІ
В МІЛІМЕТРОВОМУ ДІАПАЗОНІ
ДОВЖИН ХВИЛЬ
М. К. Ходзицький
Було досліджено одновимірний магнітофотонний
кристал (МФК) із тришаровою коміркою (воздух-феррит-
кварц) обмежений дротовим середовищем у міліметровому
діапазоні довжин хвиль. Показано появу двох зон непропу-
скання зв'язаних відповідно з інтерференцією хвиль у МФК і з
ферромагнітно-резонансним поглинанням у ферритовом шарі.
Показано теоретично й експериментально появу поверхневих
хвиль для системи МФК + дротове середовище у частотному
діапазоні зони непропускання МФК. Показано можливість
керування положенням піка пропускання пов’язаного з повер-
хневою хвилею в спектрі за допомогою магнітного поля. По-
казано, що крутизна кривої, що описує залежність положення
піка пропускання, пов’язаного с поверхневою хвилею від
магнітного поля, менше, ніж крутизна кривої, що описує за-
лежність положення низькочастотного краю зони непропу-
щення МФК від магнітного поля. Розглянуті ефекти дозволять
розробити нові магнітокеровані мікрохвильові пристрої на
основі МФК у гигагерцевому і терагерцевому діапазонах.
Ключові слова: магнітофотонный кристал, дротове
середовище, зона непропускання, поверхнева хвиля, Там-
мовський стан, феромагнітний резонанс.
Рукопись поступила 7 мая 2009 г.
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