high·-q resonator design from microwave to millimetre
TRANSCRIPT
Journal of Physical Science and Application 1(20 1 1)1 5.28
LOW-Loss Dielectric Material CharaCteriZation and
薅 黪 蠛
High·-Q Resonator Design from Microwave to Millimetre
W aves Frequencies
Jean-Michel Le Floch ,M ichael E.Tobar。,Georges Humbert2
,David M ouneyrac。一
,Denis F6rachou2
. Romain
Bara ,M ichel Aubourg ,John G.Hartnett ,Dominique Cros。
,Jean—Marc Blondy。and Jerzy Krupka3
· School ofPhysics,University of Western Australia,35 Stifling Hwy,6009 Crawley,We tern A“ tr日,f。
XLIM,UMR CNRSNo 6172,123 av.A.Thomas,87060Limoges Cedex
. Frn,2ce
3·Institute ofMicroelectronies and Optoelectronics Warsaw University ofTechnology,Ko ykD n 75 Warsnw Pol nd
Received:March 25,20 1 1/Accepted:April 08, 20 1 1/Published:June 1 5,20 1 1
Abstract:Dielectric resonators are key components in many microwave and millimetre wave circuits and applications. including
n。gn‘ rllte s and frequency‘determining elements for precision frequency synthesis. Multilayered and bulk low.1oss single crystal and
polycrystalline dielectric structures haye become very important for designing these devices. Proper design requires careful
electromagnetic characterisation of low loss material properties, This includes exact simulation with precision numerical software and
precise measurements ol resonant modes.For example,we have developed the Whispering Gallery mode technique,which has now
become the standard for characterizing Iow-loss structures. This paper will review some of the common characterisation techniques
used in the microwave to millimetre wave frequency regime.
Key words:Dielectric resonator,Bragg mode,whispering gaUery mode,bulk and thin film characterization
1.IntrOducti0n
Dielectric resonators(DR)are the key element in
most telecommunications systems,which allow for a
better reception and more customers on the same
communication bandwidth.They are also very useful
in many industries that require radar detection,
proximity detection, as well as military based
applications like secure transmissions,remote guiding,
navigation and positioning systems(i.e.,GPS and
Galileo [1,2]).Also,to realize precise time and
frequency references, it is necessary to design
microwave sources with high spectral purity and
precise frequency stability[3—1 31.These characteristics
are directly related to the quality of the resonant
COrresponding author: Jean—Michel Le Floch, Ph.D.,
research fields: dielectric characterisation, thin film,
computational physics, microwave and millimetrewave
technologies.E-mail:lefioch@cyllene.uwa.edu.au
element,such as the cryogenic sapphire oscillator
(cso),which is based on an ultra-high—Q-factor(-10 )
sapphire DR.These oscillators are used as a secondary
frequency reference and are capable of pulsing a
primary standard(caesium fountain clock)at the
quantum noise limit[14,151.CSOs have also been
developed to test fundamental Physics.such as a
modem Michelson-Morley local Lorentz Invariance
tests,using either orthogonal modes or a double
dielectric sapphire resonators[1 6-1 8].The experiment
searches for a difference jn the speed of light in two
orthogonal directions:parallel to,and perpendicular to,
the motion of the Earth around the Sun.
Depending on the application,the requirement on
materiaI properties and size of the dielectric.the make
up of the resonator can vary substantially.To make the
right choice of materiaI and dimensions it is very
important to use precise experimental and numerical
16 Low.Loss Dielectric Material Characterization and High-Q Resonator Design from Microwave to
Millimetre Waves Frequencies
techniques【1 9-26】to properly characterize materials.
In this paper we present some important resonant
techniques to characterize dielectric samples,which
depend on the scale size of the sample.Following this,
we will then describe the design of high—Q dielectric
resonators using a multi—layered structure such as
photonic band—gap and Bragg resonators at microwave
and millimetre wave frequencies.
2. Electromagnetic M odes for M aterial
Property Characterization
Two types of electromagnetic modes in cylindrical
systems are commonly used for dielectric
characterisation of low—loss materials at microwave
frequencies—Whispering Gallery(WG)modes and pure
Transverse Electric(TE)and Transverse Magnetic
(TM)modes.In spherical systems all modes are pure
TE and TM .A class of higher order modes define a
greater set of modes that whisper around the inner
dielectric at the air interface,known as Whispering
Spherical(ws)modes.
2 1 Whispering Gallery fWG》Modes in Cylindrical
Resonators
WG modes in a cylindrical resonator may be
visualized as a superposition of two rays,one moving
clockwise the other anticlockwise,propagating around
the peripheral cylinder with an integer
乙 Fig.1 Field density plot of a W hispering Gallery mode
with 2m azimuthal variations.In this ease m :1 1.
Hr Ho Ez
蛋 碧
number of reflections along the azimuthal( direction
(Fig. 1). clockwise the other anticlockwise,
propagating around the peripheral cylinder with an
integer number of reflections along the azimuthal(
direction(Fig.1).
There are two different types of WG modes-those
with an electric field polarization parallel(WGH)and
perpendicular(WGE)to the z-axis.Each polarization
has three main electromagnetic field components,as
shown in Fig.2.
The fields may be solved for using M axwell’s
equations.Assuming a separation of variables along
the axial component of the electromagnetic field we
can write the following approximate expressions[22】:
WGEmode, :o : J,(krr cosq~z)(1)
WGHmode,H~=0 = r) cosq~z) (2)
Here js the BesseI function of order m,and and
;c=are the卜 and z-direction propagation constants or
wave—numbers in the dielectric,respectively.The other
components ofthe field are directly calculable from the
z—components using M axwell’s equations.In genera1.
in dielectric cavities exact solutions are not possible
(but only approximations[261).Thus for precise
calculations of the field components numerical
techniques must be used.For example,the field density
plots shown in Fig.2 were calculated using the Method
ofLines[19].
2.2 Whispering Spherical s)Modes in Spherical
Resonators
Spherical systems possess similar modes to the
cylindrical system that whisper around the inner
surface ofthe sphere.W e call these modes W hispering
(WS)modes.General exact solutions for and are
given by Eqs.(3a)and(3b)for Transverse Magnetic
(TM)and Transverse Electric(TE)modes respectively:
Er E9 耋_lz
j婪]誉 j !. l 。.。i 。 . .i
Fig·2 (1eft)Half dielectric loaded cavity field density plot of a WGH or E-mode,(right)Half dielectric loaded cavity density
plot of a WGE or H-mode(1eft),as calculated using the Method of Lines I191.
Low·Loss Dielectric Material Characterization and High-Q Resonator Design from Microwave to
Millimetre Waves Frequencies
=0,£,= +1) : + ( r) (c。s co s伸(m O)(3a)
=q = +lJ丁,/k,r
。( (c。 _Ac os㈣~a)(3b)
where n is the mode number, is the wave number and
m is the azimuthaI mode number in the 0 direction. and
the number of 2万variations in the direction varies
from 0 to .The wave number takes discrete values
corresponding to an integer number of variations in the
radial direction,denoted by P.Modes that correspond
to P = 1 are the fundamental W S mode families.In
order to find a specific solution the composition ofthe
system must be taken into account by solving the radial
boundary value problem.In the case of spherically
symmetric dielectrically loaded cavities, the
dimensions of the system,permittivity of the dielectric
and the shielding effect of the cavity walls set by the
boundary conditions in the radial direction lead to the
complete solmion.
A field density plot for the = 4 fundamental W S
mode family is shown in Fig.3.We distinguish the W G
mode when 胛 fpropagation occurs mainly along
O-direction)and Whispering Longitude(WL)mode
when m 0(propagation occurs mainly along the
一 direction).The rest of the resonance modes
propagate around both dimensions。
The higher the azimuthal mode number the more
the field is concentrated in the crystal and the less the
cavity walls affect the properties of the resonance.
The use of high order whispering gallery modes
permits very high precision measurement of the
l7
sample dielectric properties for azimuthal mode
numbers related to the high confinement of the
electromagnetic energy in the dielectric resonator。
However the higher azimuthal mode number means a
higher frequency and as a result we see a higher
density of spurious modes in the vicinity of the
desired mode.Therefore in some cases we use an
open cavity[21,221.
2.3Pure TransverseElectricandM agneticModes
There are two types of modes,TE,and TM,as
shown in Fig.4,which have an azimuthal mode
number m 0 and only 3 field components. The
cylindrical structures shown in Fig. 4 use these
conventional modes and offer be~er frequency
isolation than the whispering gallery modes.That is,
they have a much smaller spurious mode density near
their resonance frequency.However their quality factor
is generally limited by the confining cavity metallic
wall losses due to a much lower confinement of the
electromagnetic energy in the dielectric sample than in
the case of W G modes.
3.M aterial Characterization Using W Gs and
TE M odes
W e can distinguish between the method to
characterize dielectric samples by their thickness.
Depending on their thicknesses we employ the
Whispering Gallery mode technique or a lower order
TE or TM mode.Typically we will use the following
techniques depending on the sample dimensions:
m ‘3 m =4
Fig.3 Field density plot ofW hispering Spherical modes for azimuthal mode numbers from /,n equals 0 to 4.
I8 Low.Loss Dielectric Material Characterization and High·Q Resonator Design fr0m Microwave to
Millimetre Waves Frequencies
TEo,1,1
TMo,1,1
Ee H Hz I E E, Ha
麟 l鐾 黜 Fig.4 Field density plot of a fundamental TE and TM mode
·The whispering gallery mode technique [20,
22.271 for thicknesses from a cm to a feW mm.This iS
the most accurate technique for lOW.1oss material;
·TE modes can be used for any thickness[28,29]
and iS suitable for measuring lossy materials or
material samples below a few mm n thickness.
Mode excitation is achieved by using probes with
coaxial cables or with waveguides.The latter iS more
difficult to set up but this iS the only kn own solution at
high frequencies of millimetre waves(Fig.51.
Loop Probe
Coupling to magnetic field
3.1 Whispering GalleryMode Technique
The WG technique is suitable for both topologies
shown in Fig.6.
In both cases the sample is supported with a spring
1oaded system in order to hold it tightly and ensure
good thermal contact.The cavity may be closed or
open depending of the chosen azimuthal mode number
and the losses in the dielectric sample.However the
higher the azimuthal mode number.the higher the field
concentration in the sample.which iS determined by
Probe
Coupling to electric field
Fig.5 Coupling methods to excite electromagnetic modes into a cavity with the associated field pattern.
Copper
Cavity
Fig.6 (1eft)Design for a spherical topology,(right)Design for a cylindrical topology to characterize the dielectric sample.
Low-Loss Dielectric Material Characterization and High—Q Resonator Design from Microwave to
Millimetre Waves Frequencies
the electric filling factor ).This is the fraction of
electric field energy in the dielectric sample compared
to the total electric energy in the cavity.A geometric
factor(G)is defined by the magnetic energy density
applied tangential to the metallic walls compared to the
total magnetic energy in the resonator volume.These
parameters, necessary to determine the dielectric
properties of the sample under test,are calculated with
rigorous electromagnetic simulation software.In our
case we use the Method ofLines[19].The formulas for
both pe and G are given below in Eqs.(4)and(5)and
also their dependence on azimuthal mode number is
shown in Fig.7.
pe
G =
(I) poH dV
v
Wemn_erl
WeT0tdi
H H:dS
m E ·E dV
静( ) ·E dV (5)
The general form ulas to determine the intrinsic
properties of the material are as follows:
Q =Q +Q +Q :
(6)
Q。=Q上+( + :)Q
where Qo is the unloaded Q—factor,QL is the loaded
o eom etric tactor
E;!;i ; i ; ; i; 。 ; j!;j ;: ; ! ! j ;j_一一 。! !j j ; i i ;
— ri i !
i ;; ㈡ ; — ; :i i i i: i:.-,I ! i;!
! i i ! ; —
, j i : ;
; ! ; , : i ! ; j; ; i j ; i; j;i i;i; ; ;;!
l j ;i ;i ■ j i; i i ;;i! i; —I ; ㈡ ;;; { !i: : ;: 。i i ; ;; ;: ;!
i ! 。- !; !㈠ ; ! 二● ; i; i ! j i i i!
! J i i i!
! j , j ;;; ; i ㈡ ;i :!: ;; ; ㈡ ; i
!;一 : ; : ;; ;i ! ; i ;; ;!
! i i i i j ; j
O 10 2O 3O 40 50
Azimuthal mode nutuber lm,
Fig.7 (1eft)Evolution of the Geometric factor(G)
(Pe)vs the azimuthal mode number(m).
19
Q—factor,pl,2 the probe coefficients.
To ensure the measurement of the intrinsic
material properties the cavity needs to be well
under—coupled(13<<1).That means the contribution
from the probes(ie.external losses)to the total losses
is negligible.Then the measurement given by the
loaded cavity Q-factor( )will be equal to the
unloaded Q—factor(Qo),which is essentially only the
contribution from the dielectric( ,)and the cavity
wall losses(Q ).
≈0 Q ≈Q =Q二 +Q (7)
Q :∑N tan + (8) l U
The dielectric Q—factor is given by the electric
energy filling factor PP,and the material loss tangent.
The metallic Q-factor Om is determined from the
Geometric factor G and the surface resistivity Rs[Units
Ohms]ofthe material used to make the metallic cavity.
The latter is related to the conductivity(o)of the metal
and the chosen mode resonance frequency co/2rc[Hz】
(see Eq.(8)).
尺 : w = (9)
The surface resistivity is obtained by measuring
the empty cavity,i.e.,the cavity without the sample.
Then it is straight forward to deduce the loss tangent of
the materia1.Determination of the permittivity of the
1
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O 舀0
0 g7
O 95
o 94
lIl 孽 F箨ctor
鼬 商舞端掷 n t i“H 0
:
勰:
* 叫盘蚺一
:黜
一
静;
60 0 辔 蛙 0站 40 囝 国
AzlmuthaI mode I1umber《mJ
vs the azimuthal mode number(m)'(right)Evolution ofthe filling factor
,
~
一 器嚣饔 :I 矗鞲‰
l。lJ暑篙!1 笛基
20 Low-Loss Dielectric Material Characterization and High-Q Resonator Design from Microwave to
Millimetre W aves Frequencies
sample is achieved by retro—simulation using Finite
Element Analysis,Mode M atching or,in our case,the
Method ofLines[191.
The W G method can be used for both isotropic and
uniaxially anisotropic materials with a thickness of a
few cm to a few mm.This is the most accurate
technique to determine the intrinsic properties of the
sample due to the fact that the electric energy fil ling
factor P in the dielectric tends to unity for a large
azimuthal mode number.However,this method is not
applicable to samples with thicknesses below a few
mm,because the excitation of whispering gallery
modes is not possible with flat aspect ratios.
3.2 Transverse Electric Mode Technique
In this section, we present the technique for
characterizing dielectric samples from a few gm to a
few mn【28,29].The measurement is done in three
steps using the fundamental transverse electric mode
(TE0 1 0.The method consists of inserting a dielectric
sample through a slot into a cylindrical cavity where
the electric field is maximum,and then measuring the
perturbations in frequency and Q—factor.In this case we
may want to characterize a substrate with a dielectric
deposition only nm thick.
Step 1 consists of measuring the properties of the
cavity itselfi This allows us to know the conductivity of
the metal and calibrate the simulation software for the
successive measurements.These determine the initial
conditions for the measurement.The initial Q—factor
has to be very high in case of measuring very low loss
materials and therefore should not being limited by the
cavity.This calculation is related by the previous Eqs.
(5)一(8).
Step 2,we insert the substrate carefully and slowly to
be sure to track the resonance mode frequency shift in
order to deduce the right permi~ivity by
retro simulation.The drop in the value of the Q—factor
indicates the lOSS contribution from the dielectric
substrate used in the next step to measure the properties
of the thin film deposition.Hence we can deduce the
loss tangent of the substrate from
Q..一—R—
s
tan :— — (10) pe
Finally the step 3,we insea the same substrate with a
thin layer of material deposited only a few nm thick.In
the same way we determine the permi~ivity and the
loss tangent ofthe thin film materia1.
This technique is not as accurate as using a
Whispering Gallery mode because ofthe lower electric
energy filling factor in the sample(Fig.8).However it
is the only method available for thick and thin films
characterization.It is also limited to isotropic materials
but is not limited by the sample thicknesses.This
technique may also be used on lossy materials.
4.Design of High—Q Dielectric Resonators
Using the Bragg Effect
The Bragg effect occurs with the help of one or
several spherical or cylindrical reflectors.The reflector
is defined from two dielectric layers of different
permi~ivities.In our case.the reflector will be defined
by a dielectric layer and a layer of free—space(Fig.9).
In our case,the central region is free-space.The
combination of several reflectors allows a larger
concentration of the electromagnetic field inside the
low 1oss centra1 free—space area.However the Q.factor
一 一 一 Fig.8 Field density plot for the three different characterization steps.(From left to right)empty cavity,substrate,substrate+
deposition.
Low-Loss Dielectric Material Characterization and High-Q Resonator Design from Microwave to
Millimetre Waves Frequencies
Spherical case Cylindrical case Fig.9 Spherical and cylindrical Bragg resonators design for a,m layer structure.
enhancement iS not SO significant after the addition of
the first three Bragg reflectors.This is due to the
dielectric loss added by the Bragg reflectors[7—1 2].
The order of the field confinement within the central
area with this type of structure by using three Bragg
reflectors iS about 9O%.
The design of high-Q dielectric resonators using a
Bragg effect is significant for room temperature
resonators as the field trapped in the free—space inner
region of the structure does not increase the Q—factor.
In the following we summarize the work done on the
design of Bragg resonators with two different
topologies, spherical and cylindrical cases
respectively.
4.1 Spherical Bragg Resonator
In order to realize a spherical Bragg resonator,we
impose boundary conditions between layers.First we
A
础 谤
21
study the fundamental TE mode without azimuthal
variation,without taking into account the propagating
mode in the dielectric.W e assume the separation of
variables jn spherical coordinates is valid and the field
pattern can be decomposed along one propagation
direction.The spherical Bessel function goes to zero at
the interface of the reflector and the edge of the cavity
and has a maximum value at the interface
dielectric/flee—space interface in the reflector,region 2
and 3(see Figs.10 and 1l、.The region 1 is free space.
The right.hand side of Fig.1 0 illustrates the one
dimensional representation[1 1,1 2].The left—hand side
figure shows the field pattern ofthe fundamental Bragg
mode in a spherical cavity with anti—resonance in the
reflector and resonance in the centraI region.
The frequency and wave number of the resonator iS
determined in a similar way to a mode in an empty
cavity and iS given by:
0 .薹
噻
—
。慧
八 凰 豳 囡
o 2 4 & 8
Fig.10 (1eft)Density plot of the spherical Bragg cavity where the field is highly confined in region 1 with an anti。resonance
between 2 and 3,defined as a resonator.The right figure shows the simple modeling of the field pattern in 1D.
22 Low’Loss Dielectric Material Characterization and High-Q Resonator Design from Microwave to
Millimetre W aves Frequencies
Fig·1 1 Realisations of spherical Bragg resonators made with Teflon and YAG crystal(right picture).
where 一
r
here xl is the first root ofthe spherical Bessel function.
The wave number also may be calculated in all the
other regions subject to the“qua~er wavelength”
analogy.For evenly numbered regions we calculate:
k2,= +、一
|
一
H
) for i:1 to J 02)
For odd numbered regions,we calculate
』}2,+.= Z +1一 l ( 卜̈一 ,) for i:1 to j(13)
Here J is the number of Bragg reflector pairs.For
example iU 1 there is one Bragg reflector pair given
by region 2 and 3,and-f,=2 the second pair will be
given by region 4 and 5.The reflectors must c0me in
pairs to ensure the cancellation of the field in the
reflectors.Also, ’,iS the ith root ofthe derivative ofthe
Fig.
Sch
Bessel function and is the fth root of the Bessel
function.To calculate the ~equency and necessary
dimensions the wave number in all regions must be
equated.
Experimentally a Q·factor of about 22,000 was
measured with a single Teflon layer Bragg resonator at
1 3.8 GHz which by scaling the parameters to a sapphire
crystal,should result in a Q.factor of about 260。000
(Fig.1 2,Table 1).This is similar for a sapphire
dielectric W G mode resonator at this frequency.
The comparison between simulation and the
measured results clearly shows that the concept of the
spherical Bragg resonator has been successfully
demonstrated.The main limitation on the Q..factor is
the dielectric loss of the Teflon, An enhancement Of
Q—factor was obtained with respect to a dielectric
resonator limited by the loss tangent of the materia1.
囤 }川{z 黼 #船 :
i
/ \
. \ .
gg spherical resonator made in Teflon,(right)
Low-Loss Dielectric Material Characterization and High·Q Resonator Design from Microwave to 23
Millimetre Waves Frequencies
Table 1 Results from simulation and measurement ofa single Bragg spherical resonator.
This Q—factor of 22.000 is 3.5 times greater than the
loss tangent limit and is due to the trapping ofthe field
in the vacuum of the inner free—space region.
The Q.fproduct for a crystal YAG is about 6×10 .
Using this parameter we carl determine the
enhancement of Q—factor obtained(Fig.1 3),which is
3.9 times greater than the lOSS tangent limit.
.2 Cylindrical Bragg Resonator
W e also investigated cylindrical Bragg resonator
structures.To establish the design model we assume
the fundamental transverse electric mode.We also
assume that separation of variables iS valid in
cylindrical coordinates SO the field pattern can be
decomposed into both propagation directions.r and z.
The solutions require a Bessel function in the radial
direction and a sine function in the axiaI direction.Both
鞯
是8
f
嚣麓羹 臻臻 鑫 臻棼, 辩£ 一4釜 礴 d棼
functions go to zero at the interface ofthe reflector and
at the edge of the cavity.They are maximized within
the Bragg reflector at the interface ofthe dielectric and
free—space[8,9].The field density plot shows both
anti—resonance in the reflectors and high field
confinement in the central part of the resonator(Figs.
14 and 15、.
A linear combination of modes was discovered,
which links both directions with the following
parameter),.
7/"
2
厶 , ’J6
1i /~,1,1
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霪
妻毒
. 、
7 ⋯ F
、
。
H 一 )
CH1卷辩N鬟~ k盛童e 嚣
棼 蛰2495 霉 巷瓣嚣
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臻 置臻 嚣蠢虢
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Fig.13 M easurement in transmission at room ternperature of a single Bragg spherical resonator made in crystal YAG·
一.一 ll
屯
24 Low.Loss Dielectric Material Characterization and High-Q Resonator Design from Microwave to
Millimetre Waves Frequencies
1、、
.
‘
Fig.1 4 (1eft)Field density plot of the cylindrical Bragg resonator where the field is highly confined in the centre with
anti.resonance in the reflectors in both directions.(right)Simple modeling ofthe field pattern in 2D on a quarter ofa structure.
圈 囹岛 匕 I lp d_e 口"reflml s=RTet'~ Fig.15 Pictures ofthe single Bragg resonator realisations followed by a schematic ofthe assembly ofthe different pieces.
The simultaneous equations above are used to solve
for i axial Bragg reflectors andj radial Bragg reflectors
where t2i..1 and a2j..1 define the dielectric layers of the
Bragg resonator in Z—and r—directions respectively.
A one layer cylindrical sapphire Bragg resonator
with O.factor of 230,000 has been achieved at 9.7 GHz
抟 帮 :辩e { 辩 啦
萋 鼢 辣 登攥5赣 黧 #燕 # 鲢 氅
辩∥ 3密 .秘辅 ?氍 辅
⋯ 碰i‰ 鹞 群甜
: 积 j
/ . ‘
一 \
§ 糍 畦e搴萼 秘 融
This is higher than in a W hispering Gallery mode
resonator at room temperature (QwGH--200,000,
QWGE--1 00,000)and equivalent to a single spherical
Bragg resonator。However the machining is much
easier in the spherical case(Fig.1 6).
During measurements we noticed higher order more
}# , 日
蕊 赫 《
{ 》
; 郾 s蠢
ll
篱
{
§%蠊 }{《
0 ,i; *
Fig.16 (1eft)Measurement in transmission at room ternperature ofa single cylindrical Bragg resonator,(right)the plot shows
a clear spectrum of modes 500 M Hz around the resonance.
Low·Loss Dielectric Material Characterization and High·Q Resonator Design from
Millimetre Waves Frequencies
confined modes existed,and by combining modeling
and machining different size cavities we observed the
following modes as shown in Figs.17 and 18.
The mode properties shown in Fig.1 8 have two
variations in the central region and one in the reflectors.
The Q—factor iS about 94.000 at 1 2.4 GHz.which iS
equivalent to a W GE mode resonator at room
temperature.However the spectrum 500 M Hz around
the resonance iS overmoded.
Following the modeling of simple Bragg resonator,
we added a second reflector.This was made from
alumina in order to prove the principle.However the
field is SO confined into the centre it has been impossible
for US to couple to the high—Q mode(estimated to be
500,ooo).During the characterization ofthe alumina we
have discovered a high Q—mode at 1 3.4 GHz(Fig.1 9)
which is a hybrid and Bragg like mode with an
azimuthal number )different to =2)[7】.
要 n :Radlalm odenum ber
聪l:矗 娃出 l {o e nt=l f
P :Axialt3"lod~ lumber
:Ra磁盘lmodenm啦》erintothe reflecto~
s; m odenumberintothe reflect0r
Fig.17 Electric field density plots calculated using the method of lines software I19J of the three different Bragg modes.
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l 黼 ; = i ’
j f { ⋯
淫 锺 瓣 i 髓$《辩 《 献 。§帮 弱9§辕甚
Fig.18 (1eft)Measurement in transmission at room temperature of the second Bragg mode of the Fig.18,(right)500 MHz
span around the resonance.
1
26 Low-Loss Dielectric Material CharacterjzatiOn and High-Q Resonator Design from Microwave to
Millimetre Waves Frequencies
0, St 2∞ £ iel{S;22
麓嚣 L赫 《#/ 蓼 螓爨 曼0 璺尊 警i黪
umina 麓 绀 n 0辅 e《躺 0§鞲{z
i越8j‰
国回画 Fig.19 (1eft)Measurement in transmission at room ternperature ofthe Hybrid Bragg mode,(right}density plot ofthis WGE and Bragg like mode.
The unloaded Q—factor obtained is about 1 90,000 at
1 3.4 GHz which is six times above the loss tangent
limit of the alumina.
5. Photonic Band Gap Resonator
(PBGR)-Step to Millimetre Wave High—Q Design
The High—Q Bragg mode design has been very
Successful in the microwave and lower millimetre
wave frequency bands.W e are now able to make
Bragg resonators at different frequencies and
symmetries and we also discovered an enhanced
Bragg mode with azimuthal variations,which is
promising at higher frequencies. However for
'。a4
1 O2
,+00
O 孽8
O.86
coverage across the entire Extremely High
Frequency band this technique is still very difficult
to adapt due to the tiny dimensions as well as
diffi culties of coupling to the Bragg mode.Thus,we
have begun adjusting optical technology and
concepts to the millimetre wave band.For example,
we have designed an out—of-plane photonic band gap
resonator(Fig.20)[30].
The simulation has been realized with the help of
COM SOL software. The density plot shows the
principle for 2 layers of silica rods.W e have then built
the PBGR resonators to prove the concept by confining
the field into the centre of the structure as we did in
Bragg designs(Fig.2 1).
30 40 50
Frequeney(GHz)
· · -
3 rings \
ro娃
4rings
Fig·20 Dispersion diagram of effective indices versus frequency of modes supported by the PBG crystal with one rod
removed in the centre(hollow-core)·Gray areas show domains where the cladding array supports modes delimiting the band
gap.(Inset)The density plot of the fundamental mode shows where the electric field is confined in the boll0w.c0re.
器 一 ≯一 ∞:l熬
Low_Loss Dielectric Material Characterization and High-Q Resonator Design from Microwave to
Millimetre Waves Frequencies
re键uency‘gHz)
Fig.2 1 M easurement in transmission at room temperature of a 3 and 4 rod.1ayers.
The resonator has been made with silica rods.The
resonance has been found at 30 GHz,the 0一factor
obtained was about 5.000 with 4 Iayers of rods.The
Q—factor for a dielectric Ioaded cavity depends on the
electric energy filling factor, the metal surface
resistance,and the geometric factor of the mode.For
our case the Q.factor is mainly limited by the metallic
walllosses rather than the IOSS tangent.
6.Conclusions
This paper has reviewed some of the techniques
achieved at microwave, and millimetre wave
frequencies to design high—Q dielectric loaded
resonators, and to characterize their material
properties.
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