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

0鹪

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

赤 4 『-l

i J商 2004 00l5臻i 0巷

囊： 穆棼O0翻器 氛 0谚嵇棼谚秘 秘棼零 尊辩嚣

圆 Hz ( o～ 1 05 ，000 器 巷鼋张群

霪

妻毒

． 、

7 ⋯ F

、

。

H 一 )

CH1卷辩N鬟~ k盛童e 嚣

棼 蛰2495 霉 巷瓣嚣

瓢 2黪≯盏8誊叠 3臻拇z

臻 置臻 嚣蠢虢

铸巷嘻{～42 §：旗霉 堪嚣

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．

3土摊种 2瓣S t9~44i42

窭 Hz

益 ㈨ _

、 j

＼

》 II l

|

m {

镶 i器 瓣艇 麓8鹣 鞲

：．{裁l{∞辩 辅2

嚣瓣鲢?，

l0§彗*§麓?瓣

盍

瓤 H 2蛳g j4 ∞

l m 、

}

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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