ritika phd final 16 april 2013 - information and library...

63

Chapter 3

Dielectric Resonator and Whispering Gallery

Mode Resonator

“Whispering Gallery” is a acoustical feature associated with few monuments.

This phenomenon of whispering gallery was first explained by Lord Rayleigh in

1910, on the basis of his own observations made in an ancient gallery located under

the dome of St. Paul’s Cathedral in London (figure 3.1) that sound waves graze

through concave surface of the wall and travel circumferentially along it [1]. Among

the ancient Indian whispering galleries great Gol Gumbaz at Bijapur (figure 3.2) is

most remarkable, and its architecture and acoustic features was explained by Sir C.V.

Raman in 1922 [2].

Figure 3.1: (a) Image of whispering gallery at St. Paul’s Cathedral in

London, (b) sound path in circular whispering gallery, (source:

http://www.sonicwonders.org/?p=57)

(a) (b)

Dielectric Resonator and Whispering Gallery Mode Resonator

Chapter 3 64

Acoustics of such enclosed places make them a whispering gallery where even

a negligible sound like a whisper can be heard at diagonally opposite side of the

Gumbaz or dome, moreover at the periphery of these dome are a circular balconies

where any whisper, clap or sound gets echoed for around more than five times. For

Gol Gumbaz, it is said that during the rule of sultan, Ibrahim Adil Shah, musicians

used to sing, seated in the whispering gallery in order that the music produced could

reach every corner of the hall. [1]- [3]

Figure 3.2: Gol Gumbaz [3]

In last few decades, studies based on Whispering Gallery modes (WGM)

became popular due to its applications in optics and microwaves as ultrahigh Q-factor

resonator. WGM resonators are also used for highly sensitive sensing applications by

various researchers. These high-Q sensors are usually used in identification of

biomolecule and components of any material.


Chapter 3 65

3.2 Dielectric Resonators

Dielectric resonator (DR) is a kind of passive component to fix a certain

frequency in the microwave systems. Dielectric resonator was first introduced by

Richtmyer in 1939 [6]. He showed that dielectric materials of definite geometry can

act as an electrical resonator at high frequencies. Richtmyer had also computed their

resonant frequencies and losses for various uncomplicated structures and formulated a

theory for dielectric resonators. In 1960’s, high frequency research was more focused

around DR, with many researchers working on the development and applications of

DR[7]. Okaya et.al showed that pieces of single crystals of rutile exibits high-Q

resonances at microwave frequencies and observed that decrease in the temperature

will lead to increase in both the Quality factor (Q-factor) and the resonant wavelength.

Following this many papers were reported by researchers like Jerzy Krupka, P.

Guillon and Darko Kajfez [8].

3.2.1 Chronological Review of the Work on WGM Dielectric Resonator

Whispering gallery modes (WGM) are higher order modes found in DR and

have similar characteristic as found in dome due to sound waves. Thus, modal fields

confines within the small region near the boundary of DR. In 1967, J.R. Wait studied

the electromagnetic WGM propagation in dielectric rod [9]. WGM in cylindrical

dielectric resonators was first explained by J. Arnaud in 1982 [10]. After this many

researcher had worked on this topic with various applications. This section gives a

brief overview of the important work reported in the literature on dielectric WGM

resonator. In 1987, Jiao et.al had discussed a theoretical method for calculating the

resonant frequencies of WGM dielectric ring resonator [11]. In 1993, Eugene et.al had

presented an analytical method for calculating the resonant frequency and Q-factor of


Chapter 3 66

shielded dielectric disk resonator for higher order modes, at room and at cryogenic

temperatures [12]. Then in 1994, Jerzy Krupka et.al had employed Rayleigh-Ritz

method and finite element method capable of not generating spurious solutions for

analysis of WGMs in cylindrical single crystal anisotropic dielectric resonator [13].

Imtiaz U Khairuddin et.al had explained a mathematical model of coupling between

WGM-DR and a transmission line for application in millimetre wave monolithic

integrated circuit (MMIC) [14]. In 1996, Darko Kajfez et.al had presented a

comparison of analytical and numerical methods for higher order modes in dielectric

resonator [15]. Tobar et.al had developed a composite DR with competing

temperature dependent permittivity for possible applications in oscillators for

reference[16]. They had successfully annulled the frequency–temperature coefficient

of a composite sapphire–strontium titanate (Al2O3–SrTiO3) microwave resonator at

108 K with a resulting Q-factor of 20,000–50,000 below 150 K. In 2001, S.L

Badnikar et.al had investigated resonant frequencies of dielectric disc utilizing the

ring resonator model and results were used to generate a numerical expression for

describing the operational frequencies for computer aided design applications [17].

3.2.2 WGM mode in cylindrical DR

Among theoretically investigated configurations, cylindrical shape has been

commonly accepted as the most advantageous one. Therefore, in this section theory of

WGM in cylindrical dielectric resonators, its basic properties and application of of

higher order mode resonator is discussed. Realistic circuit applications often require

mounting of resonator in the proximity of conducting walls or other dielectric

materials. Thus, for accurate prediction of the resonant frequency it is essential to

consider all these boundary perturbations in the theoretical analysis.


Chapter 3 67

Dielectric constant of DR is usually taken very high as compared to air, due to

which the reflection coefficient � of the interface between DR body and air will go to

unity thereby reflecting most of the energy inside the DR. Mathematically, as, �� ≫ 1

for DR reflection coefficient given by:

� = �� − �� + � = √�� − 1√�� + 1 ≈ 1 3.1

where, �� is characteristic impedance of air, Z is characteristic impedance of

dielectric material and �� is relative permittivity of this material. Due to these

reflections in DR, the standing waves are formed and EM resonance occurs. Resonant

frequency of DR depends on following properties:

i Resonance mode

ii Size of DR

iii Dielectric constant

In WGM of cylindrical DR resonators, the modal field is confined within the

small region near the resonator boundary. Ray optics, suggests that cause of this

energy confinement is total internal reflection of a ray at the dielectric-air interface,

and its movement is tangential to an inner caustic circle. Therefore, the ray moves

only within a small region near the cylinder boundary, as shown in Fig. 3.3.

From analytical approach, all waves guided in a dielectric cylinder can be

described by Bessel functions ��(��) where, argument �� will be of n order and for

WGM case n >> 5. In WGM, modal field is oscillatory between the boundaries and a

slightly smaller radius, while it decays exponentially elsewhere.


Chapter 3 68

Figure 3.3: WGM by ray optics.

3.2.3 Advantages of using WGM –DR

As stated by N.D Kataria et.al [18] in 2004:

“In WG mode, EM energy is confined around the dielectric-air interface inside

the crystal because of total internal reflection that minimizes the radiation and

conduction loss there by increasing the Q-value”.

With this understanding following are the broad advantages of WGM resonator:

i. Good suppression of spurious modes.

ii. Very high quality factor.

iii. Sensitivity to the presence of absorbing and conducting materials etc.

WGM are higher order modes of large azimuthal mode number n > 5 these modes

are described as WGEnml and WGHnml mode. Where n represents azimuthal variations,

m represents the radial variations and l represents axial variations. [9]-[11],[18]

Boundary

Modal caustic

Modal ray

O a

ai


Chapter 3 69

3.3 Mathematical model of WGM cylindrical DR

Mathematical model for the determination of resonant frequencies of the

whispering-gallery modes of cylindrical dielectric resonator was proposed by Jiao,

Guillon, and Bermudez [11], this model is known as JGB model. The advantage of

this model is that it needs only real argument of the Bessel functions having integral

order. Arrangement for solving JGB model is shown in figure 3.4. For the wave

propagation in this circular cylinder, only regions 1, 2, and 3 are required however for

cavity method region 4 should be considered due to truncation effects. Note that

region 1 and 2 will be of same material in case of solid DR.

ρ= aρ= aiρ= 0

z=d

z=0

z=-d

Region 4

εr4

Region 4

εr 4

Region 2

εr2

Region 1

εr1

Region 3

εr3

ρ

ρ= c

Metallic

wall

z=h

z=-h

Figure 3.4: Configuration of JGB model for Dielectric resonator.

DR Model shown in Figure 3.4 have diameter 2a and height 2d, which is kept

separated from wall of cavity and this cavity, is of diameter 2c and height 2h. In

WGM-DR most of the energy is confined in region 1, between the cylindrical


Chapter 3 70

dielectric-air boundary of radius a and the inner modal caustic of radius ai. Here,

inner radius ai is an artificial "boundary" which divides the cylinder into the

propagating and evanescent regions along radial direction.

By solving the differential Bessel equation, the radius of the modal caustic can

be estimated by

�� = �� − �� 3.2

where, n is the modal variation in the azimuthal direction, β the propagation constant

and εr the relative dielectric constant of the resonator. For the present study radial

variation m and axial variation l are kept fixed whereas n is variable.

Figure 3.5: (a) 3D view of Dielectric Resonator. (b) Components of fields

for WGE and (b) WGH modes.


Chapter 3 71

Figure 3.5 represents the 3D view of DR to get a better understanding of

model given in figure 3.4 and also shows the direction of field’s components for both

WGE and WGH modes. Thus, by considering JGB model shown in figure 3.4

expressions for the electromagnetic field of WG modes can be establish. As usual, the

longitudinal components of the field are obtained by solving the Helmholtz equation

�� + �� = 0 3.3

where,

� = ��

In equation 3.3 � can be either *+ or -+.

Let, the solution of wave equation is given by

�(., 0, 1) = 2(.). 4(0). �(1)

hence, by using method separation of variable we will get three independent equations

as solutions are given by

�(1) = 5678+ + 967:8+

here, ; = < + =�, we know that ; = < for evanescent m

odes and ; = =� for propagating mode.

4(0) = 5� cos �0 + 9� sin �0

2(.) = 5? ��(�. .) + 9? @�(�. .)


Chapter 3 72

here, �� = ;� + �� whereas �� and @� represents the Bessel function of first kind

and second kind respectively. If �� = − ;� − �� then solution of 2(.) will be

given by

2(.) = 5′? B�(�. .) + 9′? C�(�. .)

here, C� and B� are known as modified Bessel functions of first and second kind

respectively.

For WGE modes, the electric field is essentially transverse and Ez may be

neglected. Similarly, Hz = 0 for WGH modes. Thus, for WGEn,m,l modes

D+ = 0 3.4

E+6 = [5G��(�6.) + 9G@�(�6.)] sin �0 cos �1 3.5

E+� = IGC�(��.) sin �0 cos �1 3.6

E+? = JGB�(�?.) sin �0 cos �1 3.7

E+K = [5GL ��(�K.) + 9GL@�(�K.)] sin �0 7:M+ 3.8

and for WGHn,m,l modes

E+ = 0 3.9

D+6 = [5N��(�6.) + 9N@�(�6.)] sin �0 cos �1 3.10

D+� = INC�(��.) sin �0 cos �1 3.11

D+? = JNB�(�?.) sin �0 cos �1 3.12


Chapter 3 73

D+K = [5NL ��(�K.) + 9NL @�(�K.)] sin �0 7:M+ 3.13

with

�� = ��

�6 = ��6 − ��

�� = �� − ��

�? = ��? − ��

< = ��6� − ��

�� = ��6

Transverse components can be deduced from Ez and Hz by

*O = 1�� P−=�Q 1. R-SR0 + R�*SR1R.T *U = 1�� P=�Q R-SR. + 1. R�*SR1R0T

-O = 1�� P=�� 1. R*SR0 + R�-SR1R.T

-U = 1�� P=�� R*SR. + 1. R�-SR1R0T


Chapter 3 74

with

�� = �� − ��

Boundary conditions for the calculation of resonant frequency, by matching

the tangential components at . = a and . = ai, are as follows:

*VW = *VX

-SW = -SX

*VW = *VY

-SW = -SY

*VY = 0

-SY = 0

for WGEn,m,l modes and

*SW = *SX

-VW = -VX

*SW = *SY

-VW = -VY

-VY = 0

*SY = 0

for WGHn,m,l modes.

at . = ��

at . = �

at . = ��

at . = �

at . = �

at . = �


Chapter 3 75

By solving these equations, following equation obtains:

ZZ ��(�6. �� ) @�(�6. ��) −C�(��. ��) 0�� L (�6. ��) �� @�L(�6. ��) −�6 C�L (��. ��) 0��(�6. �) @�(�6. �) 0 −B�(�?. �)�? ��L (�6. �) �? @�L(�6. �) 0 −�6 B�L (�?. �) ZZ = 0

3.14

also B�(�?. �) = 0 and B�L (�?. �) = 0 due to metallic cavity of radius c for WGEn,m,l

modes.

ZZ ��(�6. ��) @�(�6. ��) −C�(��. ��) 0�� 6 ��L (�6. ��) �� 6 @�L(�6. ��) −�6�� C�L (��. ��) 0��(�6. �) @�(�6. �) 0 −B�(�?. �)�? ��6 ��L (�6. �) �? ��6 @�L(�6. �) 0 −�6��? B�L (�?. �) ZZ= 0

3.15

From boundary conditions, fields become zero at metallic boundary for WGEn,m,l

modes and for WGHn,m,l modes therefore B�(�?. �) = 0 and B�L (�?. �) = 0 due to

metallic cavity in determinant 3.15. To obtain correct resonant frequency, we must

take into consideration the axial energy confinement in region |1| < d. From above

field equation’s longitudinal field components Ez and Hz respectively for TM and TE

mode are proportional to

G6(z) = C6 cos �1

in the region 1 and in region 4 it is

GK(z) = C� 7:M+

here, C6 and C� are proportionality constants. Now by applying following boundary

conditions in axial direction by matching the longitudinal field components and their

first derivatives at the discontinuity of the resonator radius:


Chapter 3 76

_6(1) = _K(1)

`_6(1)`1 = `_K(1)`1

and

_K(1) = 0

`_K(1)`1 = 0 Thus, obtained equations are as follows:

C6 cos �` = C� 7:Ma

C6 � sin �` = C� < 7:Ma and,

C� 7:MN = 0

C�(−<)7:MN = 0

thus, following equations will obtained:

tan �` = <� 3.16

and

7:MN = 0

Thus, from equations 3.5 and 3.10 it is observed that Bessel equation inside the

dielectric resonator disc is oscillating for . > �� and . < � , and from equations 3.6

at z = d

at z = h


Chapter 3 77

and 3.11 monotonically decreasing for . < �� while in region 3 and 4 from fields

equation 3.7, 3.8, 3.12 and 3.13 will decay exponentially.

Final step is to solve and calculate the resonant frequency of WGM by solving

simultaneously the equations 3.14 and 3.16 or 3.15 and 3.16 for the case of WGE and

WGM mode correspondingly. Here, the values of c and h should be three times

greater as comparison to dimensions of dielectric resonator according to the paper

[12]. And this can also be verified by solving equations obtained from boundary

conditions at the metallic cavity.

3.4 Application of WGM-DR’s

Dielectric resonators are widely used in oscillators, in filter designing and in

complex permittivity measurement of dielectric materials. Due to these advantages of

WGM-DR many researchers are using this technique in different applications some of

which are as follows:

In 1995, Taber and Flory had reported work on development of commercially-

viable high purity X-band signal source, by integrating a WGM cryogenic sapphire

dielectric resonator. WGM are used due to its tremendous electromagnetic field

confinement capability and using this they had developed microwave oscillators.[19]

WGM DR are also used in oscillator applications, In 1998, Tobar et.al had

reported a method to determine the dielectric properties of a single crystal rutile

(TiO2) resonator using whispering gallery modes [20]. This work gave impetus to

research on determining dielectric properties of various types of materials and fluids:

In 1999, Krupka et.al had reported a work in which whispering gallery modes were


Chapter 3 78

used for very accurate measurement of permittivity and dielectric loss of ultralow loss

isotropic and uniaxially anisotropic single crystals at cryogenic temperatures [21].

Again in 1999 Krupka et.al had published similar work in which they had obtained

the relationship between resonant frequencies and calculated the permittivity of the

sample under test with a radial mode-matching technique [22] and Ratheesh et.al had

published a paper on the microwave dielectric properties of Ba(Mg1/3,Ta2/3)O3 (BMT)

ceramic resonators by utilizing the WGM and conventional methods in the frequency

range 6–18 GHz [23].

Then in year 2000, Annino et.al had characterized dielectric properties of

materials using whispering gallery dielectric resonators and the field distribution in

the different WG resonant modes was obtained by an analytical calculation under the

mode matching method approximation [24]. Prokopenko et.al had presented their

paper on WGM dielectric resonators for the millimetre wave near field sensing

applications in 2001. According to them resonant parameters of both the isotropic and

anisotropic DR depends on the resonant frequency, Q-factor, slow-down factor and

electric energy filling factor of the modes [25].

Then in 2003, Krupka had discussed on various resonant measurement

methods for complex permittivity determination of lossy dielectrics [26]. Then in

2006, his review article was published on microwave frequency domain measurement

techniques of the complex permittivity, in which he had mentioned all various

methods including WGM method [27].

In 2008, Shaforost et.al had presented a paper on fingerprint detection and

analysis of biochemical (lossy) liquids of pico-to-nanoliter volumes using open

whispering-gallery-modes resonator with local inhomogeneities by using a liquid


Chapter 3 79

droplet. According to authors, this liquid droplet causes a small perturbation of the

electromagnetic field distribution which will lead to change in Q-factor and resonant

frequency of resonator [28]. Then they had published similar work in October 2008

[29]. After this in 2009, Shaforost et.al had presented a paper on WGM resonators for

evanescent sensing of nanolitre liquid substances [30] and published a paper on

similar work in which a microwave resonator composed of a sapphire cylinder and a

quartz plate with a 400 nano litre cavity was introduced for the determination of the

complex permittivity of liquids at 10 GHz [31].

In 2010, Mohamed S. Kheir et.al. presented a paper in which a WGM

dielectric resonator was proposed as a biological material sensor, for this they had

created a 2mm*2mm cavity in dielectric resonator for calculating the permittivity

value [32]. In 2010, another paper was published on WGM resonance sensor for

dielectric sensing of drug tablets, by Mohammad Neshat et.al. In this they had used

two methods for measuring the properties of drug tablet by putting it on top of a

dielectric disk resonator and inside a dielectric ring resonator, on the basis of

resonance frequency and Q-factor of the composite sample tablet and resonator

arrangement [33].


Chapter 3 80

References

[1] C. V. Raman and G. A. Sutherland, “On the Whispering Galleries Phenomenon”, Proceedings of Royal Society London A, vol. 100, pp. 424-428,

1922.

[2] C.V Raman, “On Whispering Galleries”, Bulletin of Indian Association for the

Cultivation of Science, vol. 7, pp. 159-172, 1922.

[3] “Gol Gumbaz”, [Online] Available: http://en.wikipedia.org/wiki/Gol_Gumbaz

[Nov 11, 2011].

[4] A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki,

“Review of Applications of Whispering-Gallery Mode Resonators in

Photonics and Nonlinear Optics”, IPN Progress Report 42-162, August 15,

2005.

[5] Frank Vollmer and Stephen Arnold, “Whispering-Gallery-Mode Biosensing

Labelfree Detection Down To Single Molecules”, Nature Methods, vol.5, no.7, July 2008.

[6] R.D. Richtmyer, “Dielectric Resonators”, Journal of Applied Physics, vol. 10, pp. 391-398, June 1939.

[7] A. Okaya and L.F. Barash, “The Dielectric Microwave Resonator”,

Proceedings of the IRE, vol. 50, pp. 2081-2092, Oct 1962.

[8] Darko Kajfez and Piere Guillon, Dielectric Resonators, 2nd ed. Georgia, USA:

Noble, 1998.

[9] J.R. Wait, 'Electromagnetic whispering-gallery modes in a dielectric rod', Radio Science, vol.2, pp. 1005-1017, 1967.

[10] C. Vedrenne, and J. Arnaud, 'Whispering-gallery modes of dielectric resonators', IEE Proc. H Microwaves, Antennas and propagation, vol.129, no.

4, pp. 183-187, 1982.


Chapter 3 81

[11] X.H. Jiao, P. Guillon, L.A. Bermudez, “Resonant frequencies of whispering-

gallery dielectric resonator modes”, IEE Proceedings, vol. 134, Pt. H, no. 6,

pp. 497-501, Dec 1987.

[12] Eugene N. Ivanov, David G. Blair, and Victor I. Kalinichev, “Approximate

Approach to the Design of Shielded Dielectric Disk Resonators with Whispering-Gallery Modes”, IEEE Transactions on Microwave Theory And

Techniques, vol. 41, no. 4, pp. 632-638, April 1993.

[13] Jerzy Krupka, Dominique Cros, Michel Aubourg, and Pierre Guillon , “Study

of Whispering Gallery Modes in Anisotropic Single-Crystal Dielectric Resonators”, IEEE Transactions On Microwave Theory And Techniques, vol.

42, no. 1, pp. 56-61, Jan 1994.

[14] Imtiaz U Khairuddin, Ian C Hunter, “A Theoretical Model for Dielectric

Resonators in Whispering Gallery Mode for Application in Millimetre Wave

Monolithic Integrated Circuits”, in IEE Colloquium on Modelling, Design and

Application of MMIC's, 1994, pp. 7/1-7/7.

[15] Darko Kajfez, Atef Elsherbeni, and Asem Mokaddem, “Higher Order Modes

in Dielectric Resonators”, in Antennas and Propagation Society International

Symposium, 1996. AP-S. Digest,1996, vol.1, pp 306-309.

[16] M E Tobar, J Krupka, E N Ivanov and R A Woode , “Dielectric frequency–temperature compensated microwave whispering-gallery-mode resonators”,

Journal of Physics D: Applied Physics, vol. 30, pp. 2770–2775, 1997.

[17] S.L. Badnikar and N. Shanmugam and V.R.K. Murthy, “Resonant frequencies

of whispering-gallery modes dielectric resonator”, Defense Science Journal,

vol. 51, no.2, pp. 189-193, April 2001.

[18] N.D Kataria and Vijay Kumar, “Frequency Temperature Compensated

Whispering Gallery Mode Dielectric Resonator Oscillator”, Chinese Journal

of Physics, vol. 42, no. 4-II, pp. 444-450, Aug 2004.

[19] R. C. Taber and C. A. Flory, “Microwave Oscillators Incorporating Cryogenic Sapphire Dielectric Resonators”, IEEE Transactions On Ultrasonics,

Ferroelectrics, And Frequency Control, vol. 42, no. 1, pp. 111-119, Jan 1995.

[20] Michael Edmund Tobar, Jerzy Krupka, Eugene Nicolay Ivanov, and Richard Alex Woode, “Anisotropic complex permittivity measurements of mono-


Chapter 3 82

crystalline rutile between 10 and 300 K”, Journal of Applied Physics, vol. 83,

no. 3, pp.1604-1609, Feb 1998.

[21] Jerzy Krupka, Krzysztof Derzakowski, Michael Tobar, John Hartnett and

Richard G Geyer, “Complex permittivity of some ultralow loss dielectric

crystals at cryogenic temperatures”, Measurement Science and Technology,

vol. 10, no. 5, pp. 387–392, 1999.

[22] Jerzy Krupka, Krzysztof Derzakowski, Adam Abramowicz, Michael Edmund

Tobar, and Richard G. Geyer , “Use of Whispering-Gallery Modes for

Complex Permittivity Determinations of Ultra-Low-Loss Dielectric

Materials”, IEEE Transactions On Microwave Theory And Techniques, vol.

47, no. 6, pp. 752-759, June 1999.

[23] R Ratheesh, M T Sebastian, M E Tobar, J Hartnett and D G Blair,

“Whispering Gallery mode microwave characterization of Ba(Mg1=3,Ta2=3)O3 dielectric resonators”, Journal of Physics D: Applied

Physics, vol. 32, no. 21, pp. 2821–2826, 1999.

[24] G. Annino, D. Bertolini, M. Cassettari, M. Fittipaldi, I. Longo, and M.

Martinelli, “Dielectric properties of materials using whispering gallery dielectric resonators: Experiments and perspectives of ultra-wideband

characterization”, Journal of Chemical Physics, vol. 112, no. 5, pp. 2308-2314

, Feb 2000.

[25] Yu. Prokopenko, M. F. Aka, S. N. Kharkovsky, “Whispering Gallery Mode

Dielectric Resonators For The Millimeter Wave Near Field Sensing

Apllications”, in The Fourth International Kharkov Symposium on Physics

and Engineering of Millimeter and Sub-Millimeter Waves, 2001, vol. 2,

pp.699-701.

[26] Jerzy Krupka, “Precise measurements of the complex permittivity of dielectric

materials at microwave frequencies”, Materials Chemistry and Physics, vol. 79, no.1-2, pp. 195–198, 2003.

[27] Jerzy Krupka, “Frequency domain complex permittivity measurements at

microwave frequencies”, Measurement Science and Technology, vol. 17, no. 6, pp. R55–R70, 2006.

[28] Elena N. Shaforost, Alexander A. Barannik, Svetlana Vitusevich, Andreas

Offenhäusser, “Open WGM Dielectric Resonator Technique for

Characterization of nL-Volume Liquids”, in 38th European Microwave

Conference, 2008, pp. 1129-1132.


Chapter 3 83

[29] E. N. Shaforost, N. Klein, S. A. Vitusevich, A. Offenhäusser, and A. A.

Barannik, “Nanoliter Liquid Characterization by Open Whispering-Gallery

Mode Dielectric Resonators at Millimeter Wave Frequencies”, Journal Of

Applied Physics, vol. 104, no.7, pp. 074111-7, 2008.

[30] Elena N. Shaforost, Norbert Klein, Alexey I. Gubin, Alexander A. Barannik,

Alexander M. Klushin, “Microwave-Millimetre Wave WGM Resonators for Evanescent Sensing of Nanolitre Liquid Substances”, in 39th European

Microwave Conference, 2009, pp. 45-48.

[31] E. N. Shaforost, N. Klein, S. A. Vitusevich, A. A. Barannik, and N. T.

Cherpak, “High sensitivity microwave characterization of organic molecule

solutions of nanoliter volume”, Applied Physics Letters, vol. 94, no. 11, pp.

112901-3, 2009.

[32] Mohamed S. Kheir, Hany F. Hammad, and Abbas Omar, “Experimental

Investigation of Whispering-Gallery-Mode Dielectric Resonators for

Biological Material Characterization”, in Conference on Precision

Electromagnetic Measurements, 2010, pp. 285-286.

[33] Mohammad Neshat, Huanyu Chen, Suren Gigoyan, Daryoosh Saeedkia and

Safieddin Safavi-Naeini, “Whispering-gallery-mode resonance sensor for dielectric sensing of drug tablets”, Measurement Science and Technology, vol.

21, no. 1, pp. 015202-11, 2010.

ritika phd final 16 april 2013 - information and library...

Documents