research article self-referenced plasmon waveguide...

Research ArticleSelf-Referenced Plasmon Waveguide Resonance Sensor UsingDifferent Waveguide Modes

Pengfei Zhang12 Le Liu3 Yonghong He12 Yanhong Ji4 and Hui Ma12

1Shenzhen Key Laboratory for Minimal Invasive Medical Technologies Institute of Optical Imaging and SensingGraduate School at Shenzhen Tsinghua University Shenzhen 518055 China2Department of Physics Tsinghua University Beijing 100084 China3Institute of Green Chemistry and Energy Graduate School at Shenzhen Tsinghua University Shenzhen 518055 China4MOE Key Laboratory of Laser Life Science amp Institute of Laser Life Science South China Normal UniversityGuangzhou 510631 China

Correspondence should be addressed to Yonghong He heyhsztsinghuaeducn

Received 21 August 2014 Revised 30 October 2014 Accepted 6 November 2014

Academic Editor Jae Ho Han

Copyright copy 2015 Pengfei Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

We report a plasmon waveguide resonance (PWR) sensing structure supporting two waveguide modes for self-referencedmeasurement We show theoretically the dual mode PWR sensing structure owns unique opportunities for self-referencedmeasurement and the accuracy and cross sensitivity can be optimized by simply varying the gold film thickness or dielectric layerthickness or dielectric film refractive index This structure may provide an approach owning good compatibility with the surfaceplasmon resonance and PWR biosensors for self-referenced biosensing

1 Introduction

Surface plasmon is electromagnetic surface wave propagatingalong the interface of two materials with real dielectric con-stants of opposite signsThe surface plasmon resonance (SPR)is a sensing approach measuring the refractive index (RI)changes within the evanescent field of these waves [1] TheSPR has the advantage of high sensitivity and permits labelfree molecular interaction analysis in real time which hasbecome a central method for characterizing and quantifyingbiomolecular interactions [2ndash4] The variations within theevanescent field can change the SPR propagation constantwhich results in a change in the sensor output and these vari-ations can be divided into the surface and bulk effects corre-sponding to the thickness change of the binding surface layerand bulk RI change respectively [5] In the practical appli-cations the surface effects usually need to be distinguishedfor specific detection which is especially significant for thebiosensing [2 6] However the typical SPR supporting onlyone surface plasmonmode cannot distinguish the surface andbulk effects As a solution to this problem the dual mode SPR

sensors for self-referenced measurement are developed Thedual mode SPR sensors are usually based on the long rangeSPR sensing structure which is constructed by sandwichinga dielectric layer between the prism andmetal film in the SPRstructure The dual mode SPR sensors can simultaneouslysupport the long and short range surface plasmon modeswith different penetration depths where the surface and bulkeffects can be distinguished owing to the different sensitivityfactors to the surface and bulk effect in different surface plas-monmodes [7]The optimal dualmode SPR sensors based onthe wavelength interrogation [8] angular interrogation [9]and bimetallic film [10] were developed recently

Plasmon waveguide resonance (PWR) is an extension ofthe SPR and is usually constructed by sequentially coating adielectric layer on themetal surface in SPR sensorsThe PWRsensors own high stability and enhanced evanescent field dueto the shield and optical amplification effects of dielectriclayer and permit the measurement in both transverse mag-netic (TM) and transverse electric (TE) modes owing to thetransformation of the admittance [11 12] But the PWR sen-sors were usually applied for bulk RI sensing due to the long

Hindawi Publishing CorporationJournal of SensorsVolume 2015 Article ID 945908 10 pageshttpdxdoiorg1011552015945908

2 Journal of Sensors

penetration depth of the evanescent field [13] To improve thePWR sensor performance in the surface sensing recently theself-referenced PWR sensing method was proposed utilizingdifferent penetration depths of the TM and TE modes [14]This self-referenced PWR sensor has better performance thanthe SPR in the RI sensing But compared with the dualmode SPR sensors this sensor cannot allow the simultaneousmeasurement in different modes because the measurementsin the TM and TE modes at one sensor spot need to be time-multiplexed

In this paper we report a PWR structure using differentwaveguide modes with different penetration depths in TMmode for self-referenced measurement We pay attention tothe feasibility of the two waveguide modesrsquo simultaneousexcitation using a monochrome angular interrogation in thissensing film structure In this case one can use the conven-tional angular SPR sensors for self-reference We show thissensing structure can be optimized for high accuracy offinding resonance position and low cross sensitivity betweenthe surface and bulk responses Besides the sensor chip fab-rications are also discussed for suitable materials to constructthis sensor

2 Principle of the Self-Referenced PWR

The key point of the self-referenced measurement is thedifferent sensitivity factors for surface and bulk effects whichis corresponding to different penetration depths in differentmodes Inspired by different waveguide modes existence inthe dielectric layer with different RI [15] we assume there willbe different waveguide modes changing another parameterof the dielectric layer namely the thickness In this studywe employ the typical PWR sensing structure shown inFigure 1(a) where a thin gold film of 50 nm and the silica filmare sequentially coated on a BK7 prismThewater a commonmaterial in nature is employed as the sample and the incidentwavelength is fixed at the 6328 nm After increasing thethickness of dielectric layer to 1000 nm which is thickerthan hundreds of nanometers in the typical PWR [11ndash13] wecalculate the reflection angular spectrum and the electric fieldstrength distribution using the Fresnel formula and Maxwellequations as shown in Figures 1(b) and 1(c) respectively Toshow different penetration depths of TM1 and TM2 modesthe normalized electric field strength distribution in thewateris shown in Figure 1(d) The refractive indices of the prismgold silica and water used in the simulation are 1515 0133+ 3654119894 146 and 133 respectively The accuracy differenceis because the silica film owns different siliconoxygen ratiowith different coating process so the reported RI is different[16 17] and the water RI varies with the density at roomtemperature and fixed incident wavelength so it is not stablein different experiments [18] So the accuracy of refractiveindices of silica andwater is lower than the optical glass prismand gold whose refractive indices are usually stable with agiven incident wavelength at room temperature [19]

It can be seen from Figures 1(b) and 1(c) that there aretwo resonance dips in the TM modes namely the TM1and TM2 modes The TM1 mode exists in the conventionalPWR sensor With the increasing thickness of the silica layer

the resonance angle which is the incident angle affordingthe minimum reflectance intensity in the TM1 mode shiftsto the large value compared with the reported results in [13]That may be caused by the increasing effective RI within theevanescent field due to the silica owning larger RI than thewaterThis can be also seen from the electric field distributionshown in Figure 1(c) where the penetration depth in theTM1 mode in the water is shortened because the electricfield is mostly limited in the silica layer Owing to these thepenetration depths in TM1 and TM2 modes are different inthis sensing structureThismakes this sensor possible for self-referenced measurement Then we will discuss the surfaceand bulk sensitivity factors of this sensor based on the linearsensor response model [7] The resonance angle shifts in theTM1 and TM2 modes Δ120579TM1 and Δ120579TM2 are given by

Δ120579TM1 = 119878S-TM1Δ119889 + 119878B-TM1Δ119899

Δ120579TM2 = 119878S-TM2Δ119889 + 119878B-TM2Δ119899(1)

where the 119878S-TM1 and 119878S-TM2 are the surface sensitivity fac-tors in degree-anglenanometer-thickness for TM1 and TM2modes and the 119878B-TM1 and 119878B-TM2 are the bulk sensitivities indegree-anglerefractive index unit (RIU) for TM1 and TM2modesTheΔ119889 andΔ119899 are the binding layer thickness changein nanometer and the bulk RI change in RIU respectivelyIn the experiment if we know the sensitivity factors andresonance angle shifts the surface layer thickness and bulkRI changes can be calculated as

Δ119889 =Δ120579TM1119878B-TM1 minus Δ120579TM2119878B-TM2119878S-TM1119878B-TM1 minus 119878S-TM2119878B-TM2

Δ119899 =Δ120579TM1119878S-TM1 minus Δ120579TM2119878S-TM2119878B-TM1119878S-TM1 minus 119878B-TM2119878S-TM2

(2)

It can be seen that the 119878S-TM1 119878S-TM2 119878B-TM1 and 119878B-TM2are the dominant performance indices in the self-referencedmeasurement So the self-referenced sensor characteristic isusually evaluated with the difference in the sensitivity ratiosas

120594 =

10038161003816100381610038161003816100381610038161003816

119878S-TM1119878S-TM2

minus119878B-TM1119878B-TM2

10038161003816100381610038161003816100381610038161003816

(3)

where the figure of merit 120594 is inversely proportional to thecross sensitivity [7] The higher figure of merit 120594 indicatesbetter ability to distinguish the surface and bulk effects Wesuppose the RI of the binding layer is 148 (proteins) andcalculate the sensitivity factors in two modes The bulk andsurface sensitivity factors can be calculated with

119878B =120597120579

120597119899 119878S =

120597120579

120597119889 (4)

where 120579 is the resonance angle 119899 is the RI of sample and119889 is the thickness of binding layer [5] The bulk sensitivityfactors in TM1 and TM2 modes are calculated to be 66 and

Journal of Sensors 3

Prism

Gold film

Silica layer

Water

(a)

TM1TM2

10

08

06

04

02

00

60 62 64 66 68 70 72

Nor

mal

ized

refle

ctan

ce

Incident angle (deg)

(b)

Gold Silica Water

TM1

TM2

0 1000 2000 3000

0

20

40

60

80

100

120

Relat

ive e

lect

ric fi

eld

stren

gth

Distance from prism surface (nm)

(c)

TM1

TM2

10

05

00

Nor

mal

ized

elec

tric

fiel

d str

engt

h

Distance from filmwater interface (nm)0 1000500 1500 2000

(d)

Figure 1 (a)The schematic of the plasmon waveguide resonance sensing structure (b)The angular reflectance spectrumThe gold and silicafilms have the thickness of 50 and 1000 nm respectively The refractive indices of the prism gold silica and water are 1515 0133 + 3654119894146 and 133 respectivelyThe incident wavelength is 6328 nm (c)The electric field strengths in different waveguidemodes under resonancecondition are plotted against the distance from the prism surface (d) The normalized electric field strengths in different waveguide modesunder resonance conditions are plotted against the distance from the filmwater interface

392 degrees per RIU and the surface sensitivity factors inTM1 and TM2 modes are calculated to be 00083 and 00144degrees per nanometer respectively So the120594 is approximately4 in the simulation which is comparable with the reportedvalues [7ndash10] Considering this we believe that we proposea PWR sensing structure which is feasible for self-referencedmeasurement

3 Numerical Analysis ofthe Self-Referenced PWR

The angular reflectance spectrum in the transverse magnetic(TM) mode can be calculated using the multiple reflectancetheory and Fresnel formula with

119877119901=

10038161003816100381610038161003816100381610038161003816

11990312+ 1199032sdotsdotsdot119896

exp(21198941205732)

1 + 119903121199032sdotsdotsdot119896

exp(21198941205732)

10038161003816100381610038161003816100381610038161003816

2

1199032sdotsdotsdot119896=11990323+ 1199033sdotsdotsdot119896

exp (21198941205733)

1 + 119903231199033sdotsdotsdot119896

exp (21198941205733)

119903119894119895=

119883119894minus 119883119895

119883119894+ 119883119895

119883119894=120576119894

119896119894119911

119896119894119911=120596

119888radic120576119894minus 1205760sin2120579

(5)

where 119896 is the total layer number 120576119895and 119889

119895are the dielectric

constant and thickness of the 119895th layer120596 and 120579 are the angular


frequency and incident angle of the incident light and 119888 is thelight speed in the vacuum respectively [20 21]

In this study the electric field strength distribution in theself-referenced PWR sensing film structure can be calculatedusing the algorithm proposed by Hansen [22] and Tien andUlrich [23] Firstly the field components of the electromag-netic wave propagating in each layer can be calculated with

(1198981111989812

1198982111989822

) = (cos (120573

119892) minus

sin (120573119892)

119901119901119892

minus119901119901119892times sin (120573

119892) cos (120573

119892)

)

sdot (cos (120573

119889) minus

sin (120573119889)

119901119901119889

minus119901119901119897times sin (120573

119889) cos (120573

119889)

)

(119867119910119892

119864119909119892

) = (cos (119896119911

119892times 119911)

sin (119896119911119892times 119911)

119901119901119892

119901119901119892times sin (119896119911

119892times 119911) cos (119896119911

119892times 119911)

)

sdot (1198981111989812

1198982111989822

) sdot (119905119867

119901119901119904times 119905119867

) sdot 119899119901sdot 119864119894

(119867119910119889

119864119909119889

)

= (cos (119896119911

119889(119911 minus 119889

119892))

sin (119896119911119889(119911 minus 119889

119892))

119901119901119897

119901119901119889times sin (119896119911

119889(119911 minus 119889

119892)) cos (119896119911

119889times (119911 minus 119889

119892))

)

sdot (cos (120573

119889) minus

sin (120573119889)

119901119901119889

minus119901119901119897times sin (120573

119889) cos (120573

119889)

)

sdot (119905119867

119901119901119904times 119905119867

) sdot 119899119901sdot 119864119894

119896119911119892=

2120587119899119892

120582cos (120579

119892) 119896119911

119889=2120587119899119889

120582cos (120579

119889)

120573119892= 119896119911119892times 119889119892 120573

119889= 119896119911119889times 119889119889

119901119901119901=

cos (120579119901)

119899119901

119901119901119892=

cos (120579119892)

119899119892

119901119901119889=cos (120579

119889)

119899119889

119901119901119904=cos (120579

119904)

119899119904

119899119892sin (120579

119892) = 119899119901sin (120579) 119899

119889sin (120579119889) = 119899119901sin (120579)

119899119904sin (120579119904) = 119899119901sin (120579)

119905119867 =

2119901119901119901

(11989811+ 11989812times 119901119901119904) 119901119901119901+ (11989821+ 11989822times 119901119901119904)

119905119864 =

119899119901

119899119904

119905119867

(6)

where 119899119901 119899119892 119899119889 and 119899

119904are the refractive indices of the prism

gold film dielectric film and samples 119911 is the distance fromthe prism surface 119889

119892and 119889

119889are the thickness of the gold

film and dielectric film and 120579 and 119864119894are the incident angle

and electric field strength of the incident light respectivelyThen the electric field strength in the gold film 119864

119892 dielectric

film 119864119889 and samples 119864

119904can be calculated using

119864119892= radic(119864119909119892)

2

+

119899119901

2times sin (120579)

(119899119892)4

(119867119910119892)2

119864119889= radic(119864119909

119889)2

+

119899119901

2times sin 120579

(119899119889)4

(119867119910119889)2

119864119904= 119864119894 times radic[(cos 120579

119904times 119905119864)2

+ (

119899119901sin(120579)119899119904

times 119905119864)

2

]

times radicexp(minus4120587 (119911 minus 119889

119892minus 119889119889) Im (119899

119904times cos 120579

119904)

120582)

(7)

In the multilayer system the thicknesses of differentlayers are of importance for the sensor characteristics So wediscuss the influence of the thickness of layer on the figureof merit and accuracy of finding resonance position Theaccuracy of finding resonance position is estimated using thecombined sensitivity factor (CSF) [24] as

CSF = 119878 times119877max minus 119877minFWHM

(8)

where the 120579 is the incident angle 119877max and 119877min are themaximum and minimum normalized reflectance FWHM isthe full width at half maximum and 119878 is the sensitivity factorThe surface and bulk CSFs are calculated using the surfaceand bulk sensitivities respectively

We study the effect of the thickness change of the gold filmfirstly The thickness of the silica film is fixed to be 1000 nmThe figure of merit surface CSF and bulk CSF with the goldfilm of 40 45 50 55 60 65 and 70 nm are calculated andshown in Figures 2(a) 2(b) and 2(c) respectively It can beseen that all three performance indices do not respond to thegold film thickness monotonouslyThe figure of merit whichis themost important estimate function in the self-referencedmeasurement gets the maximum value at the gold film ofapproximately 65 nm But the surface and bulk CSFs in theTM1 and TM2 modes all achieve the best values at the rangeof approximately 55 nm to 60 nm While the figure of meritat the gold film of 55 nm or 60 nm is a little lower than thevalue at the gold film of 65 nm the CSFs at the gold film of65 nm are worse than the values at the gold film of 55 nm and60 nm obviously After trading off the cross sensitivity andthe accuracy of finding the resonance position we considerthat the 55 or 60 nm should be the optimization thickness forthe gold film in this structure For further confirmation theangular reflectance spectra at the gold film of 55 and 60 nmare calculated and shown in Figure 2(d) It can be seen that


425

420

415

410

40 50 60 70

Figu

re o

f mer

it

Gold film thickness (nm)

Calculated results

(a)

40 50 60 70


TM2

TM1

010

008

006

004

002

Surfa

ce C

SF

(b)

TM2

TM1

40 50 60 70


Bulk

CSF

240

200

160

120

80

40

(c)

Nor

mal

ized

refle

ctan

ce10

08

06

04

02

00

615 620 695 700 705 710 715


55nm60nm

(d)

Figure 2 ((a) (b) and (c))The figure ofmerit surface combined sensitivity factor (CSF) and bulk CSF plotted against the gold film thicknessThe silica films have the thickness of 1000 nm The refractive indices of the prism gold silica and water are 1515 0133 + 3654119894 146 and133 respectively The incident wavelength is 6328 nm (d) The angular reflectance spectra with the gold film of 55 nm and 60 nm

there is better extinction ratio in the angular spectrum at thegold film of 55 nm This will be beneficial for the resonanceangle measurement in the practical terms [25 26] In thisdiscussion we choose the interval of 5 nm changing the goldfilm thickness This is because there are always thicknesserrors in the vacuum film coating that have been studied inour previous work [27] so we think it should be unnecessaryto use smaller interval Considering these we think the opti-mization thickness of the gold film is 55 nm in this structure

The characteristics of the surface plasmon based opticalsensors are usually corresponding to the electric field distri-butions of the evanescent field [28] To illustrate the optimalgold film thickness of 55 nm the electric field strength distri-butions of the evanescent fields in TM1 and TM2 waveguide

modes are calculated and shown in Figures 3(a) and 3(b) withdifferent gold film thickness It could be seen from Figure 3that the electric field strengths are both lower when thegold film thickness is thinner or thicker than the optimalthickness This may be because the incident light couldnot be efficiently coupled to the waveguide modes via thesurface plasmons existing on the gold film surface due tothe matching relations in the multilayer system In summarythis PWR sensor has better characteristics when the gold filmowns optimal thickness

After optimizing the gold film thickness to be 55 nm wediscuss the effect of the silica film thickness on the sensorcharacteristics We should point out that the two waveguidemodes in the silica layer should maintain a large RI range


Gold Silica Water120

100

80

60

40

20

0

0 500 1000 1500 2000


Relat

ive e

lect

ric fi

eld

stren

gth

40nm55nm70nm

(a)

40nm55nm70nm

80

60

40

20

0

0 500 1000 1500 2000 2500 3000


Relat

ive e

lect

ric fi

eld

stren

gth

Gold Silica Water

(b)

Figure 3 (a)The electric field strengths under resonance condition are plotted against the distance from the prism surface with the gold filmthicknesses of 40 55 and 70 nm in TM1 waveguide mode and (b) in TM2 waveguide mode The silica film has the thickness of 1000 nmTherefractive indices of the prism gold silica and water are 1515 0133 + 3654119894 146 and 133 respectivelyThe incident wavelength is 6328 nm

Under room temperature the water RI varies from 133to 134 in the visible light wavelength region [18] So wechange the water RI from 133 to 134 to test the angularreflectance spectrum in this sensor We calculate the angularreflectance spectra with the silica film of 900 nm 950 nmand 1000 nm and show them in Figure 4(a) It can be seenthat the angular reflectance spectra in TM2 mode cannotmaintain good resonance curve in this range until the silicafilm thickness increases to 1000 nm Then we increase thesilica film thickness and the bulk CSFs surface CSFs andfigure of merit in the TM1 and TM2modes are calculated andshown in Figures 4(b) 4(c) and 4(d) respectively Differentfrom the gold film the silica film thickness increase hasnegative effect on all three performance indices It may bebecause the electric fields in two modes are more limited inthe silica film with increasing the silica film thickness Theelectric field distributions of the evanescent fields existingin the water under resonance conditions in TM1 and TM2waveguide modes are calculated as shown in Figures 5(a)and 5(b) respectively It can be seen from Figure 5 that theelectric field strengths of evanescent fields in two waveguidemodes both decrease with increasing the silica film thicknessIn summary the optimization silica film thickness is exactlythe critical thickness where the two waveguide modes justcanmaintain the good resonance curves So the optimizationthickness of the gold and silica films in this structure is 55 and1000 nm respectively

4 Discussion

There are six parameters (eg prism RI metal film thicknessand RI dielectric layer thickness and RI and incident wave-length) in this self-referenced PWR sensor so there will be

more opportunities for minimizing the cross sensitivity andimproving the accuracy of finding the resonance position Ithas been pointed out that the performance of conventionalPWR sensor can be improved by lowering the RI of dielectriclayer [29]Then we employ magnesium fluoride (MgF

2) with

RI of 138 which has also been used in the PWR sensor [12]instead of the silica with the RI of 146 as the dielectric layerWe have known that the optimization dielectric layer thick-ness is the critical thickness The gold film of 55 nm is alsoemployed as the metal film To confirm the critical thicknessof MgF

2layer the angular reflectance spectra with the MgF

2

layer thickness of 1600 nm and 1650 nm measuring the RI of133 and 134 are calculated and shown in Figure 6(a) It can beseen fromFigure 6(a) that the critical thickness ofMgF

2layer

for the self-referenced measurement is 1650 nm The electricfield distribution with MgF

2layer thickness of 1650 nm is

calculated and shown in Figure 6(b) It can be seen fromFigure 6(b) that the electric field distribution in this system issimilar to the gold-silica systems shown in Figure 1 To com-pare the sensing characteristics of two structures the angularreflectance spectra with the MgF

2film of 1650 nm and silica

film of 1000 nmare calculated and shown in Figure 7(a)Thenwe calculate the electric field distributions of the evanescentfields in the water in the TM1 and TM2 waveguide modes inboth sensing structures and show them in Figure 7(b)

It can be seen that the resonance curves in the gold-MgF2structure are sharper than the gold-silica structure

The surface and bulk CSFs in the TM2 TM1 modes are 013and 528 011 and 136 in the gold-MgF

2structure which are

better than the 0088 and 239 0059 and 47 in the gold-silica structure The figure of merit essential performanceindex in the self-referenced measurement is 531 in the gold-MgF2structure which is better than the gold-silica film


10

08

06

04

02

00

610 615 620 625 65 66 67 68 69 70

Nor

mal

ized

refle

ctan

ce


900nm with 133

950nm with 134

1000nm with 133

1000nm with 134

(a)

240

200

160

120

48

46

44

42

40

Bulk

CSF

TM2

TM1

1000 1050 1100 1150 1200

Silica film thickness (nm)

(b)

009

008

007

006

Surfa

ce C

SF

TM2

TM1

1000 1050 1100 1150 1200


(c)

1000 1050 1100 1150 1200


4

3

2

Figu

re o

f mer

it

Calculated results

(d)

Figure 4 (a)The angular reflectance spectra with different silica film thickness measuring the samples with different refractive indices ((b)(c) and (d)) The bulk combined sensitivity factor (CSF) surface CSF and figure of merit plotted against the silica film thickness The goldfilms have the thickness of 55 nmThe refractive indices of the prism gold silica and water are 1515 0133 + 3654119894 146 and 133 respectivelyThe incident wavelength is 6328 nm

structure with the value of 418 and the reported values of 14[7] 146 [8] 50 [9] 38 [10] and 47 [14] The improvementby the employment of MgF

2can be owing to the enhanced

electric field shown in Figure 7(b) It can be seen that theelectric fields in the analyte are both enhanced in the TM1andTM2modesThere is an additional advantage of the gold-MgF2structure the resonance angle difference between two

waveguide modes is less than 3 degrees which is comparablewith the reported long range SPR structure [9] but muchless than the reported self-referenced PWR using TM andTE modes [14] This will lead to easier detection modulearrangement in the practical terms This discussion shows

this self-referenced PWR sensing structure owns good poten-tial to be improved owing to the multisensor parameters

5 Conclusion

In this paper we report a PWR sensing structure supportingtwo waveguide modes for self-referenced measurement Bysimply increasing the dielectric layer thickness the sensingstructure supporting two waveguide modes with differentpenetration depths in the analyte can be constructed Wehave optimized the structure in terms of high accuracy andlow cross sensitivity for both modes The optimized dual


Relat

ive e

lect

ric fi

eld

stren

gth

30

20

10

0

0 100 200 300 400 500

Distance from filmwater interface (nm)

1000nm1100nm1200nm

(a)

1000nm1100nm1200nm

0 200 400 600 800 1000


Relat

ive e

lect

ric fi

eld

stren

gth

70

50

30

0

10

20

40

60

(b)

Figure 5 (a) The electric field strengths under resonance condition are plotted against the distance from the filmwater interface with thesilica film thickness of 1000 nm 1100 nm and 1200 nm in TM1 waveguide mode and (b) in TM2 waveguide mode The gold film has thethickness of 55 nmThe refractive indices of the prism gold silica and water are 1515 0133 + 3654119894 146 and 133 respectively The incidentwavelength is 6328 nm

10

08

06

04

02

00

62 63 64

Nor

mal

ized

refle

ctan

ce


1600nm with 133

1600nm with 134

1650nm with 133

1650nm with 134

(a)

Gold MgF2 Water350

300

250

200

150

100

50

0

Relat

ive e

lect

ric fi

eld

stren

gth

0 1000 2000 3000 4000


TM2

TM1

(b)

Figure 6 (a) The angular reflectance spectra with the MgF2film thickness of 1600 nm and 1650 nm measuring the samples with different

refractive indices (b) The electric field strengths in different waveguide modes under resonance condition are plotted against the distancefrom the prism surface The gold film has the thickness of 55 nm The refractive indices of the prism gold silica and water are 1515 0133 +3654119894 146 and 133 respectively The incident wavelength is 6328 nm

mode chip with gold-silica structure owns a figure of meritof 418 After using the gold-MgF

2structure the figure of

merit is improved to 531 The detection operation can beaccomplishedwith only the TMpolarized incident light using

the attenuated total reflection manner so it provides a self-referenced approachwith good compatibility for the commonSPR and PWR sensors Further work is required for experi-mental demonstration of the feasibility of this structure


10

08

06

04

02

00

60 64 68 72

Nor

mal

ized

refle

ctan

ce


SilicaMgF2

(a)

120

100

80

60

40

20

0

Rela

tive e

lect

ric st

reng

th

0 500 1000 1500 2000


MgF2 TM2

MgF2 TM1

Silica TM2

Silica TM1

(b)

Figure 7 (a) The comparison of angular reflectance spectra with silica film and MgF2film as the dielectric layers The gold film silica film

and MgF2film have the thickness of 55 nm 1000 nm and 1650 nmThe refractive indices of the prism gold silica MgF

2 and water are 1515

0133 + 3654119894 146 138 and 133 respectively The incident wavelength is 6328 nm (b) The electric field strengths in different waveguidemodes under resonance condition are plotted against the distance from the filmwater interface

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was made possible with the financial supportfromNSFCChina (61275188 61378089 and 61361160416) the863 project China and the Technology Development Pro-gram of Shenzhen City

References

[1] J Homola S S Yee and G Gauglitz ldquoSurface plasmon reso-nance sensors reviewrdquo Sensors and Actuators B Chemical vol54 no 1 pp 3ndash15 1999

[2] J Homola ldquoSurface plasmon resonance sensors for detection ofchemical and biological speciesrdquoChemical Reviews vol 108 no2 pp 462ndash493 2008

[3] B D Gupta and R K Verma ldquoSurface plasmon resonance-based fiber optic sensors principle probe designs and someapplicationsrdquo Journal of Sensors vol 2009 Article ID 97976112 pages 2009

[4] L Liu S Ma Y Ji et al ldquoA two-dimensional polarization inter-ferometry based parallel scan angular surface plasmon reso-nance biosensorrdquo Review of Scientific Instruments vol 82 no2 Article ID 023109 2011

[5] J T Hastings ldquoOptimizing surface-plasmon resonance sensorsfor limit of detection based on a Cramer-Rao boundrdquo IEEESensors Journal vol 8 no 2 pp 170ndash175 2008

[6] Z Liu L Liu X Wang et al ldquoPolarization-interferometry-based wavelength-interrogation surface plasmon resonanceimager for analysis of microarraysrdquo Journal of BiomedicalOptics vol 17 no 3 Article ID 036002 2012

[7] R Slavık J Homola and H Vaisocherova ldquoAdvanced biosens-ing using simultaneous excitation of short and long rangesurface plasmonsrdquoMeasurement Science and Technology vol 17no 4 pp 932ndash938 2006

[8] J T Hastings J Guo P D Keathley et al ldquoOptimal self-refere-nced sensing using long- and short-range surface plasmonsrdquoOptics Express vol 15 no 26 pp 17661ndash17672 2007

[9] J Guo P D Keathley and J T Hastings ldquoDual-mode surface-plasmon-resonance sensors using angular interrogationrdquoOpticsLetters vol 33 no 5 pp 512ndash514 2008

[10] G Dyankov M Zekriti and M Bousmina ldquoDual-mode sur-face-plasmon sensor based on bimetallic filmrdquo Applied Opticsvol 51 no 13 pp 2451ndash2456 2012

[11] Z Salamon H A Macleod and G Tollin ldquoCoupled plasmon-waveguide resonators a new spectroscopic tool for probingproteolipid film structure and propertiesrdquo Biophysical Journalvol 73 no 5 pp 2791ndash2797 1997

[12] H Shi Z Y Liu X X Wang et al ldquoA symmetrical opticalwaveguide based surface plasmon resonance biosensing sys-temrdquo Sensors and Actuators B Chemical vol 185 pp 91ndash962013

[13] F Bahrami M Maisonneuve M Meunier J Stewart Aitchisonand M Mojahedi ldquoAn improved refractive index sensor basedon genetic optimization of plasmon waveguide resonancerdquoOptics Express vol 21 no 18 pp 20863ndash20872 2013

[14] F Bahrami M Maisonneuve M Meunier J S AitchisonandMMojahedi ldquoSelf-referenced spectroscopy using plasmonwaveguide resonance biosensorrdquo Biomedical Optics Express vol5 no 8 pp 2481ndash2487 2014

[15] Y Fan K Hotta A Yamaguchi and N Teramae ldquoEnhancedfluorescence in a nanoporous waveguide and its quantitativeanalysisrdquo Optics Express vol 20 no 12 pp 12850ndash12859 2012

[16] S Szunerits and R Boukherroub ldquoPreparation and character-ization of thin films of SiO

119909on gold substrates for surface


plasmon resonance studiesrdquo Langmuir vol 22 no 4 pp 1660ndash1663 2006

[17] H Imai M Yasumori H Hirashima K Awazu and H OnukildquoSignificant densification of sol-gel derived amorphous silicafilms by vacuum ultraviolet irradiationrdquo Journal of AppliedPhysics vol 79 no 11 pp 8304ndash8309 1996

[18] P Schiebener J Straub J M H L Sengers and J S GallagherldquoRefractive index of water and steam as function of wavelengthtemperature and densityrdquo Journal of Physical and ChemicalReference Data vol 19 no 3 pp 677ndash717 1990

[19] S K Ozdemir and G Turhan-Sayan ldquoTemperature effects onsurface plasmon resonance design considerations for an opticaltemperature sensorrdquo Journal of LightwaveTechnology vol 21 no3 pp 805ndash814 2003

[20] O S Heavens Optical Properties of Thin Films Dover NewYork NY USA 1955

[21] M Born and E Wolf Principles of Optics ElectromagneticTheory of Propagation Interference andDiffraction of Light CUPArchive 1999

[22] W N Hansen ldquoElectric fields produced by the propagationof plane coherent electromagnetic radiation in a stratifiedmediumrdquo Journal of the Optical Society of America vol 58 no3 pp 380ndash390 1968

[23] P K Tien and R Ulrich ldquoTheory of prism-film coupler andthin-film light guidesrdquo Journal of the Optical Society of Americavol 60 no 10 pp 1325ndash1337 1970

[24] A Abbas M J Linman and Q Cheng ldquoSensitivity comparisonof surface plasmon resonance and plasmon-waveguide reso-nance biosensorsrdquo Sensors and Actuators B Chemical vol 156no 1 pp 169ndash175 2011

[25] P F Zhang L Liu Y H He et al ldquoNon-scan and real-time multichannel angular surface plasmon resonance imagingmethodrdquo Applied Optics vol 53 no 26 pp 6037ndash6042 2014

[26] Y F Zhou P F Zhang Y H He et al ldquoPlasmon waveguideresonance sensor using an Au-MgF

2structurerdquo Applied Optics

vol 53 no 28 pp 6344ndash6350 2014[27] L Liu X Chen Z Liu et al ldquoPolarization interference inter-

rogation of angular surface plasmon resonance sensors withwide metal film thickness tolerancerdquo Sensors and Actuators BChemical vol 173 pp 218ndash224 2012

[28] A Lahav M Auslander and I Abdulhalim ldquoSensitivityenhancement of guided-wave surface-plasmon resonance sen-sorsrdquo Optics Letters vol 33 no 21 pp 2539ndash2541 2008

[29] N Skivesen R Horvath and H C Pedersen ldquoOptimizationof metal-clad waveguide sensorsrdquo Sensors and Actuators BChemical vol 106 no 2 pp 668ndash676 2005

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



penetration depth of the evanescent field [13] To improve thePWR sensor performance in the surface sensing recently theself-referenced PWR sensing method was proposed utilizingdifferent penetration depths of the TM and TE modes [14]This self-referenced PWR sensor has better performance thanthe SPR in the RI sensing But compared with the dualmode SPR sensors this sensor cannot allow the simultaneousmeasurement in different modes because the measurementsin the TM and TE modes at one sensor spot need to be time-multiplexed

In this paper we report a PWR structure using differentwaveguide modes with different penetration depths in TMmode for self-referenced measurement We pay attention tothe feasibility of the two waveguide modesrsquo simultaneousexcitation using a monochrome angular interrogation in thissensing film structure In this case one can use the conven-tional angular SPR sensors for self-reference We show thissensing structure can be optimized for high accuracy offinding resonance position and low cross sensitivity betweenthe surface and bulk responses Besides the sensor chip fab-rications are also discussed for suitable materials to constructthis sensor

2 Principle of the Self-Referenced PWR

The key point of the self-referenced measurement is thedifferent sensitivity factors for surface and bulk effects whichis corresponding to different penetration depths in differentmodes Inspired by different waveguide modes existence inthe dielectric layer with different RI [15] we assume there willbe different waveguide modes changing another parameterof the dielectric layer namely the thickness In this studywe employ the typical PWR sensing structure shown inFigure 1(a) where a thin gold film of 50 nm and the silica filmare sequentially coated on a BK7 prismThewater a commonmaterial in nature is employed as the sample and the incidentwavelength is fixed at the 6328 nm After increasing thethickness of dielectric layer to 1000 nm which is thickerthan hundreds of nanometers in the typical PWR [11ndash13] wecalculate the reflection angular spectrum and the electric fieldstrength distribution using the Fresnel formula and Maxwellequations as shown in Figures 1(b) and 1(c) respectively Toshow different penetration depths of TM1 and TM2 modesthe normalized electric field strength distribution in thewateris shown in Figure 1(d) The refractive indices of the prismgold silica and water used in the simulation are 1515 0133+ 3654119894 146 and 133 respectively The accuracy differenceis because the silica film owns different siliconoxygen ratiowith different coating process so the reported RI is different[16 17] and the water RI varies with the density at roomtemperature and fixed incident wavelength so it is not stablein different experiments [18] So the accuracy of refractiveindices of silica andwater is lower than the optical glass prismand gold whose refractive indices are usually stable with agiven incident wavelength at room temperature [19]

It can be seen from Figures 1(b) and 1(c) that there aretwo resonance dips in the TM modes namely the TM1and TM2 modes The TM1 mode exists in the conventionalPWR sensor With the increasing thickness of the silica layer

the resonance angle which is the incident angle affordingthe minimum reflectance intensity in the TM1 mode shiftsto the large value compared with the reported results in [13]That may be caused by the increasing effective RI within theevanescent field due to the silica owning larger RI than thewaterThis can be also seen from the electric field distributionshown in Figure 1(c) where the penetration depth in theTM1 mode in the water is shortened because the electricfield is mostly limited in the silica layer Owing to these thepenetration depths in TM1 and TM2 modes are different inthis sensing structureThismakes this sensor possible for self-referenced measurement Then we will discuss the surfaceand bulk sensitivity factors of this sensor based on the linearsensor response model [7] The resonance angle shifts in theTM1 and TM2 modes Δ120579TM1 and Δ120579TM2 are given by

Δ120579TM1 = 119878S-TM1Δ119889 + 119878B-TM1Δ119899

Δ120579TM2 = 119878S-TM2Δ119889 + 119878B-TM2Δ119899(1)

where the 119878S-TM1 and 119878S-TM2 are the surface sensitivity fac-tors in degree-anglenanometer-thickness for TM1 and TM2modes and the 119878B-TM1 and 119878B-TM2 are the bulk sensitivities indegree-anglerefractive index unit (RIU) for TM1 and TM2modesTheΔ119889 andΔ119899 are the binding layer thickness changein nanometer and the bulk RI change in RIU respectivelyIn the experiment if we know the sensitivity factors andresonance angle shifts the surface layer thickness and bulkRI changes can be calculated as

Δ119889 =Δ120579TM1119878B-TM1 minus Δ120579TM2119878B-TM2119878S-TM1119878B-TM1 minus 119878S-TM2119878B-TM2

Δ119899 =Δ120579TM1119878S-TM1 minus Δ120579TM2119878S-TM2119878B-TM1119878S-TM1 minus 119878B-TM2119878S-TM2

(2)

It can be seen that the 119878S-TM1 119878S-TM2 119878B-TM1 and 119878B-TM2are the dominant performance indices in the self-referencedmeasurement So the self-referenced sensor characteristic isusually evaluated with the difference in the sensitivity ratiosas

120594 =

10038161003816100381610038161003816100381610038161003816

119878S-TM1119878S-TM2

minus119878B-TM1119878B-TM2

10038161003816100381610038161003816100381610038161003816

(3)

where the figure of merit 120594 is inversely proportional to thecross sensitivity [7] The higher figure of merit 120594 indicatesbetter ability to distinguish the surface and bulk effects Wesuppose the RI of the binding layer is 148 (proteins) andcalculate the sensitivity factors in two modes The bulk andsurface sensitivity factors can be calculated with

119878B =120597120579

120597119899 119878S =

120597120579

120597119889 (4)

where 120579 is the resonance angle 119899 is the RI of sample and119889 is the thickness of binding layer [5] The bulk sensitivityfactors in TM1 and TM2 modes are calculated to be 66 and


Prism

Gold film

Silica layer

Water

(a)

TM1TM2

10

08

06

04

02

00

60 62 64 66 68 70 72

Nor

mal

ized

refle

ctan

ce


(b)

Gold Silica Water

TM1

TM2

0 1000 2000 3000

0

20

40

60

80

100

120

Relat

ive e

lect

ric fi

eld

stren

gth


(c)

TM1

TM2

10

05

00

Nor

mal

ized

elec

tric

fiel

d str

engt

h


(d)





119877119901=

10038161003816100381610038161003816100381610038161003816

11990312+ 1199032sdotsdotsdot119896

exp(21198941205732)

1 + 119903121199032sdotsdotsdot119896

exp(21198941205732)

10038161003816100381610038161003816100381610038161003816

2


exp (21198941205733)

1 + 119903231199033sdotsdotsdot119896

exp (21198941205733)

119903119894119895=

119883119894minus 119883119895

119883119894+ 119883119895

119883119894=120576119894

119896119894119911

119896119894119911=120596

119888radic120576119894minus 1205760sin2120579

(5)







(1198981111989812

1198982111989822

) = (cos (120573

119892) minus

sin (120573119892)

119901119901119892

minus119901119901119892times sin (120573

119892) cos (120573

119892)

)

sdot (cos (120573

119889) minus

sin (120573119889)

119901119901119889

minus119901119901119897times sin (120573

119889) cos (120573

119889)

)

(119867119910119892

119864119909119892

) = (cos (119896119911

119892times 119911)

sin (119896119911119892times 119911)

119901119901119892

119901119901119892times sin (119896119911

119892times 119911) cos (119896119911

119892times 119911)

)

sdot (1198981111989812

1198982111989822

) sdot (119905119867

119901119901119904times 119905119867

) sdot 119899119901sdot 119864119894

(119867119910119889

119864119909119889

)

= (cos (119896119911

119889(119911 minus 119889

119892))

sin (119896119911119889(119911 minus 119889

119892))

119901119901119897

119901119901119889times sin (119896119911

119889(119911 minus 119889

119892)) cos (119896119911

119889times (119911 minus 119889

119892))

)

sdot (cos (120573

119889) minus

sin (120573119889)

119901119901119889

minus119901119901119897times sin (120573

119889) cos (120573

119889)

)

sdot (119905119867

119901119901119904times 119905119867

) sdot 119899119901sdot 119864119894

119896119911119892=

2120587119899119892

120582cos (120579

119892) 119896119911

119889=2120587119899119889

120582cos (120579

119889)

120573119892= 119896119911119892times 119889119892 120573

119889= 119896119911119889times 119889119889

119901119901119901=

cos (120579119901)

119899119901

119901119901119892=

cos (120579119892)

119899119892

119901119901119889=cos (120579

119889)

119899119889

119901119901119904=cos (120579

119904)

119899119904

119899119892sin (120579

119892) = 119899119901sin (120579) 119899

119889sin (120579119889) = 119899119901sin (120579)

119899119904sin (120579119904) = 119899119901sin (120579)

119905119867 =

2119901119901119901

(11989811+ 11989812times 119901119901119904) 119901119901119901+ (11989821+ 11989822times 119901119901119904)

119905119864 =

119899119901

119899119904

119905119867

(6)

where 119899119901 119899119892 119899119889 and 119899



119892and 119889




119892 dielectric

film 119864119889 and samples 119864


119864119892= radic(119864119909119892)

2

+

119899119901

2times sin (120579)

(119899119892)4

(119867119910119892)2

119864119889= radic(119864119909

119889)2

+

119899119901

2times sin 120579

(119899119889)4

(119867119910119889)2

119864119904= 119864119894 times radic[(cos 120579

119904times 119905119864)2

+ (

119899119901sin(120579)119899119904

times 119905119864)

2

]


119892minus 119889119889) Im (119899

119904times cos 120579

119904)

120582)

(7)



(8)




425

420

415

410

40 50 60 70

Figu

re o

f mer

it


Calculated results

(a)

40 50 60 70


TM2

TM1

010

008

006

004

002

Surfa

ce C

SF

(b)

TM2

TM1

40 50 60 70


Bulk

CSF

240

200

160

120

80

40

(c)

Nor

mal

ized

refle

ctan

ce10

08

06

04

02

00

615 620 695 700 705 710 715


55nm60nm

(d)








100

80

60

40

20

0

0 500 1000 1500 2000


Relat

ive e

lect

ric fi

eld

stren

gth

40nm55nm70nm

(a)

40nm55nm70nm

80

60

40

20

0

0 500 1000 1500 2000 2500 3000


Relat

ive e

lect

ric fi

eld

stren

gth

Gold Silica Water

(b)



4 Discussion



2) with



2


2layer











10

08

06

04

02

00

610 615 620 625 65 66 67 68 69 70

Nor

mal

ized

refle

ctan

ce


900nm with 133

950nm with 134

1000nm with 133

1000nm with 134

(a)

240

200

160

120

48

46

44

42

40

Bulk

CSF

TM2

TM1

1000 1050 1100 1150 1200


(b)

009

008

007

006

Surfa

ce C

SF

TM2

TM1

1000 1050 1100 1150 1200


(c)

1000 1050 1100 1150 1200


4

3

2

Figu

re o

f mer

it

Calculated results

(d)







5 Conclusion



Relat

ive e

lect

ric fi

eld

stren

gth

30

20

10

0

0 100 200 300 400 500


1000nm1100nm1200nm

(a)

1000nm1100nm1200nm

0 200 400 600 800 1000


Relat

ive e

lect

ric fi

eld

stren

gth

70

50

30

0

10

20

40

60

(b)


10

08

06

04

02

00

62 63 64

Nor

mal

ized

refle

ctan

ce


1600nm with 133

1600nm with 134

1650nm with 133

1650nm with 134

(a)

Gold MgF2 Water350

300

250

200

150

100

50

0

Relat

ive e

lect

ric fi

eld

stren

gth

0 1000 2000 3000 4000


TM2

TM1

(b)








10

08

06

04

02

00

60 64 68 72

Nor

mal

ized

refle

ctan

ce


SilicaMgF2

(a)

120

100

80

60

40

20

0

Rela

tive e

lect

ric st

reng

th

0 500 1000 1500 2000


MgF2 TM2

MgF2 TM1

Silica TM2

Silica TM1

(b)







Acknowledgments


References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Prism

Gold film

Silica layer

Water

(a)

TM1TM2

10

08

06

04

02

00

60 62 64 66 68 70 72

Nor

mal

ized

refle

ctan

ce


(b)

Gold Silica Water

TM1

TM2

0 1000 2000 3000

0

20

40

60

80

100

120

Relat

ive e

lect

ric fi

eld

stren

gth


(c)

TM1

TM2

10

05

00

Nor

mal

ized

elec

tric

fiel

d str

engt

h


(d)





119877119901=

10038161003816100381610038161003816100381610038161003816

11990312+ 1199032sdotsdotsdot119896

exp(21198941205732)

1 + 119903121199032sdotsdotsdot119896

exp(21198941205732)

10038161003816100381610038161003816100381610038161003816

2


exp (21198941205733)

1 + 119903231199033sdotsdotsdot119896

exp (21198941205733)

119903119894119895=

119883119894minus 119883119895

119883119894+ 119883119895

119883119894=120576119894

119896119894119911

119896119894119911=120596

119888radic120576119894minus 1205760sin2120579

(5)







(1198981111989812

1198982111989822

) = (cos (120573

119892) minus

sin (120573119892)

119901119901119892

minus119901119901119892times sin (120573

119892) cos (120573

119892)

)

sdot (cos (120573

119889) minus

sin (120573119889)

119901119901119889

minus119901119901119897times sin (120573

119889) cos (120573

119889)

)

(119867119910119892

119864119909119892

) = (cos (119896119911

119892times 119911)

sin (119896119911119892times 119911)

119901119901119892

119901119901119892times sin (119896119911

119892times 119911) cos (119896119911

119892times 119911)

)

sdot (1198981111989812

1198982111989822

) sdot (119905119867

119901119901119904times 119905119867

) sdot 119899119901sdot 119864119894

(119867119910119889

119864119909119889

)

= (cos (119896119911

119889(119911 minus 119889

119892))

sin (119896119911119889(119911 minus 119889

119892))

119901119901119897

119901119901119889times sin (119896119911

119889(119911 minus 119889

119892)) cos (119896119911

119889times (119911 minus 119889

119892))

)

sdot (cos (120573

119889) minus

sin (120573119889)

119901119901119889

minus119901119901119897times sin (120573

119889) cos (120573

119889)

)

sdot (119905119867

119901119901119904times 119905119867

) sdot 119899119901sdot 119864119894

119896119911119892=

2120587119899119892

120582cos (120579

119892) 119896119911

119889=2120587119899119889

120582cos (120579

119889)

120573119892= 119896119911119892times 119889119892 120573

119889= 119896119911119889times 119889119889

119901119901119901=

cos (120579119901)

119899119901

119901119901119892=

cos (120579119892)

119899119892

119901119901119889=cos (120579

119889)

119899119889

119901119901119904=cos (120579

119904)

119899119904

119899119892sin (120579

119892) = 119899119901sin (120579) 119899

119889sin (120579119889) = 119899119901sin (120579)

119899119904sin (120579119904) = 119899119901sin (120579)

119905119867 =

2119901119901119901

(11989811+ 11989812times 119901119901119904) 119901119901119901+ (11989821+ 11989822times 119901119901119904)

119905119864 =

119899119901

119899119904

119905119867

(6)

where 119899119901 119899119892 119899119889 and 119899



119892and 119889




119892 dielectric

film 119864119889 and samples 119864


119864119892= radic(119864119909119892)

2

+

119899119901

2times sin (120579)

(119899119892)4

(119867119910119892)2

119864119889= radic(119864119909

119889)2

+

119899119901

2times sin 120579

(119899119889)4

(119867119910119889)2

119864119904= 119864119894 times radic[(cos 120579

119904times 119905119864)2

+ (

119899119901sin(120579)119899119904

times 119905119864)

2

]


119892minus 119889119889) Im (119899

119904times cos 120579

119904)

120582)

(7)



(8)




425

420

415

410

40 50 60 70

Figu

re o

f mer

it


Calculated results

(a)

40 50 60 70


TM2

TM1

010

008

006

004

002

Surfa

ce C

SF

(b)

TM2

TM1

40 50 60 70


Bulk

CSF

240

200

160

120

80

40

(c)

Nor

mal

ized

refle

ctan

ce10

08

06

04

02

00

615 620 695 700 705 710 715


55nm60nm

(d)








100

80

60

40

20

0

0 500 1000 1500 2000


Relat

ive e

lect

ric fi

eld

stren

gth

40nm55nm70nm

(a)

40nm55nm70nm

80

60

40

20

0

0 500 1000 1500 2000 2500 3000


Relat

ive e

lect

ric fi

eld

stren

gth

Gold Silica Water

(b)



4 Discussion



2) with



2


2layer











10

08

06

04

02

00

610 615 620 625 65 66 67 68 69 70

Nor

mal

ized

refle

ctan

ce


900nm with 133

950nm with 134

1000nm with 133

1000nm with 134

(a)

240

200

160

120

48

46

44

42

40

Bulk

CSF

TM2

TM1

1000 1050 1100 1150 1200


(b)

009

008

007

006

Surfa

ce C

SF

TM2

TM1

1000 1050 1100 1150 1200


(c)

1000 1050 1100 1150 1200


4

3

2

Figu

re o

f mer

it

Calculated results

(d)







5 Conclusion



Relat

ive e

lect

ric fi

eld

stren

gth

30

20

10

0

0 100 200 300 400 500


1000nm1100nm1200nm

(a)

1000nm1100nm1200nm

0 200 400 600 800 1000


Relat

ive e

lect

ric fi

eld

stren

gth

70

50

30

0

10

20

40

60

(b)


10

08

06

04

02

00

62 63 64

Nor

mal

ized

refle

ctan

ce


1600nm with 133

1600nm with 134

1650nm with 133

1650nm with 134

(a)

Gold MgF2 Water350

300

250

200

150

100

50

0

Relat

ive e

lect

ric fi

eld

stren

gth

0 1000 2000 3000 4000


TM2

TM1

(b)








10

08

06

04

02

00

60 64 68 72

Nor

mal

ized

refle

ctan

ce


SilicaMgF2

(a)

120

100

80

60

40

20

0

Rela

tive e

lect

ric st

reng

th

0 500 1000 1500 2000


MgF2 TM2

MgF2 TM1

Silica TM2

Silica TM1

(b)







Acknowledgments


References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












(1198981111989812

1198982111989822

) = (cos (120573

119892) minus

sin (120573119892)

119901119901119892

minus119901119901119892times sin (120573

119892) cos (120573

119892)

)

sdot (cos (120573

119889) minus

sin (120573119889)

119901119901119889

minus119901119901119897times sin (120573

119889) cos (120573

119889)

)

(119867119910119892

119864119909119892

) = (cos (119896119911

119892times 119911)

sin (119896119911119892times 119911)

119901119901119892

119901119901119892times sin (119896119911

119892times 119911) cos (119896119911

119892times 119911)

)

sdot (1198981111989812

1198982111989822

) sdot (119905119867

119901119901119904times 119905119867

) sdot 119899119901sdot 119864119894

(119867119910119889

119864119909119889

)

= (cos (119896119911

119889(119911 minus 119889

119892))

sin (119896119911119889(119911 minus 119889

119892))

119901119901119897

119901119901119889times sin (119896119911

119889(119911 minus 119889

119892)) cos (119896119911

119889times (119911 minus 119889

119892))

)

sdot (cos (120573

119889) minus

sin (120573119889)

119901119901119889

minus119901119901119897times sin (120573

119889) cos (120573

119889)

)

sdot (119905119867

119901119901119904times 119905119867

) sdot 119899119901sdot 119864119894

119896119911119892=

2120587119899119892

120582cos (120579

119892) 119896119911

119889=2120587119899119889

120582cos (120579

119889)

120573119892= 119896119911119892times 119889119892 120573

119889= 119896119911119889times 119889119889

119901119901119901=

cos (120579119901)

119899119901

119901119901119892=

cos (120579119892)

119899119892

119901119901119889=cos (120579

119889)

119899119889

119901119901119904=cos (120579

119904)

119899119904

119899119892sin (120579

119892) = 119899119901sin (120579) 119899

119889sin (120579119889) = 119899119901sin (120579)

119899119904sin (120579119904) = 119899119901sin (120579)

119905119867 =

2119901119901119901

(11989811+ 11989812times 119901119901119904) 119901119901119901+ (11989821+ 11989822times 119901119901119904)

119905119864 =

119899119901

119899119904

119905119867

(6)

where 119899119901 119899119892 119899119889 and 119899



119892and 119889




119892 dielectric

film 119864119889 and samples 119864


119864119892= radic(119864119909119892)

2

+

119899119901

2times sin (120579)

(119899119892)4

(119867119910119892)2

119864119889= radic(119864119909

119889)2

+

119899119901

2times sin 120579

(119899119889)4

(119867119910119889)2

119864119904= 119864119894 times radic[(cos 120579

119904times 119905119864)2

+ (

119899119901sin(120579)119899119904

times 119905119864)

2

]


119892minus 119889119889) Im (119899

119904times cos 120579

119904)

120582)

(7)



(8)




425

420

415

410

40 50 60 70

Figu

re o

f mer

it


Calculated results

(a)

40 50 60 70


TM2

TM1

010

008

006

004

002

Surfa

ce C

SF

(b)

TM2

TM1

40 50 60 70


Bulk

CSF

240

200

160

120

80

40

(c)

Nor

mal

ized

refle

ctan

ce10

08

06

04

02

00

615 620 695 700 705 710 715


55nm60nm

(d)








100

80

60

40

20

0

0 500 1000 1500 2000


Relat

ive e

lect

ric fi

eld

stren

gth

40nm55nm70nm

(a)

40nm55nm70nm

80

60

40

20

0

0 500 1000 1500 2000 2500 3000


Relat

ive e

lect

ric fi

eld

stren

gth

Gold Silica Water

(b)



4 Discussion



2) with



2


2layer











10

08

06

04

02

00

610 615 620 625 65 66 67 68 69 70

Nor

mal

ized

refle

ctan

ce


900nm with 133

950nm with 134

1000nm with 133

1000nm with 134

(a)

240

200

160

120

48

46

44

42

40

Bulk

CSF

TM2

TM1

1000 1050 1100 1150 1200


(b)

009

008

007

006

Surfa

ce C

SF

TM2

TM1

1000 1050 1100 1150 1200


(c)

1000 1050 1100 1150 1200


4

3

2

Figu

re o

f mer

it

Calculated results

(d)







5 Conclusion



Relat

ive e

lect

ric fi

eld

stren

gth

30

20

10

0

0 100 200 300 400 500


1000nm1100nm1200nm

(a)

1000nm1100nm1200nm

0 200 400 600 800 1000


Relat

ive e

lect

ric fi

eld

stren

gth

70

50

30

0

10

20

40

60

(b)


10

08

06

04

02

00

62 63 64

Nor

mal

ized

refle

ctan

ce


1600nm with 133

1600nm with 134

1650nm with 133

1650nm with 134

(a)

Gold MgF2 Water350

300

250

200

150

100

50

0

Relat

ive e

lect

ric fi

eld

stren

gth

0 1000 2000 3000 4000


TM2

TM1

(b)








10

08

06

04

02

00

60 64 68 72

Nor

mal

ized

refle

ctan

ce


SilicaMgF2

(a)

120

100

80

60

40

20

0

Rela

tive e

lect

ric st

reng

th

0 500 1000 1500 2000


MgF2 TM2

MgF2 TM1

Silica TM2

Silica TM1

(b)







Acknowledgments


References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










425

420

415

410

40 50 60 70

Figu

re o

f mer

it


Calculated results

(a)

40 50 60 70


TM2

TM1

010

008

006

004

002

Surfa

ce C

SF

(b)

TM2

TM1

40 50 60 70


Bulk

CSF

240

200

160

120

80

40

(c)

Nor

mal

ized

refle

ctan

ce10

08

06

04

02

00

615 620 695 700 705 710 715


55nm60nm

(d)








100

80

60

40

20

0

0 500 1000 1500 2000


Relat

ive e

lect

ric fi

eld

stren

gth

40nm55nm70nm

(a)

40nm55nm70nm

80

60

40

20

0

0 500 1000 1500 2000 2500 3000


Relat

ive e

lect

ric fi

eld

stren

gth

Gold Silica Water

(b)



4 Discussion



2) with



2


2layer











10

08

06

04

02

00

610 615 620 625 65 66 67 68 69 70

Nor

mal

ized

refle

ctan

ce


900nm with 133

950nm with 134

1000nm with 133

1000nm with 134

(a)

240

200

160

120

48

46

44

42

40

Bulk

CSF

TM2

TM1

1000 1050 1100 1150 1200


(b)

009

008

007

006

Surfa

ce C

SF

TM2

TM1

1000 1050 1100 1150 1200


(c)

1000 1050 1100 1150 1200


4

3

2

Figu

re o

f mer

it

Calculated results

(d)







5 Conclusion



Relat

ive e

lect

ric fi

eld

stren

gth

30

20

10

0

0 100 200 300 400 500


1000nm1100nm1200nm

(a)

1000nm1100nm1200nm

0 200 400 600 800 1000


Relat

ive e

lect

ric fi

eld

stren

gth

70

50

30

0

10

20

40

60

(b)


10

08

06

04

02

00

62 63 64

Nor

mal

ized

refle

ctan

ce


1600nm with 133

1600nm with 134

1650nm with 133

1650nm with 134

(a)

Gold MgF2 Water350

300

250

200

150

100

50

0

Relat

ive e

lect

ric fi

eld

stren

gth

0 1000 2000 3000 4000


TM2

TM1

(b)








10

08

06

04

02

00

60 64 68 72

Nor

mal

ized

refle

ctan

ce


SilicaMgF2

(a)

120

100

80

60

40

20

0

Rela

tive e

lect

ric st

reng

th

0 500 1000 1500 2000


MgF2 TM2

MgF2 TM1

Silica TM2

Silica TM1

(b)







Acknowledgments


References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











100

80

60

40

20

0

0 500 1000 1500 2000


Relat

ive e

lect

ric fi

eld

stren

gth

40nm55nm70nm

(a)

40nm55nm70nm

80

60

40

20

0

0 500 1000 1500 2000 2500 3000


Relat

ive e

lect

ric fi

eld

stren

gth

Gold Silica Water

(b)



4 Discussion



2) with



2


2layer











10

08

06

04

02

00

610 615 620 625 65 66 67 68 69 70

Nor

mal

ized

refle

ctan

ce


900nm with 133

950nm with 134

1000nm with 133

1000nm with 134

(a)

240

200

160

120

48

46

44

42

40

Bulk

CSF

TM2

TM1

1000 1050 1100 1150 1200


(b)

009

008

007

006

Surfa

ce C

SF

TM2

TM1

1000 1050 1100 1150 1200


(c)

1000 1050 1100 1150 1200


4

3

2

Figu

re o

f mer

it

Calculated results

(d)







5 Conclusion



Relat

ive e

lect

ric fi

eld

stren

gth

30

20

10

0

0 100 200 300 400 500


1000nm1100nm1200nm

(a)

1000nm1100nm1200nm

0 200 400 600 800 1000


Relat

ive e

lect

ric fi

eld

stren

gth

70

50

30

0

10

20

40

60

(b)


10

08

06

04

02

00

62 63 64

Nor

mal

ized

refle

ctan

ce


1600nm with 133

1600nm with 134

1650nm with 133

1650nm with 134

(a)

Gold MgF2 Water350

300

250

200

150

100

50

0

Relat

ive e

lect

ric fi

eld

stren

gth

0 1000 2000 3000 4000


TM2

TM1

(b)








10

08

06

04

02

00

60 64 68 72

Nor

mal

ized

refle

ctan

ce


SilicaMgF2

(a)

120

100

80

60

40

20

0

Rela

tive e

lect

ric st

reng

th

0 500 1000 1500 2000


MgF2 TM2

MgF2 TM1

Silica TM2

Silica TM1

(b)







Acknowledgments


References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










10

08

06

04

02

00

610 615 620 625 65 66 67 68 69 70

Nor

mal

ized

refle

ctan

ce


900nm with 133

950nm with 134

1000nm with 133

1000nm with 134

(a)

240

200

160

120

48

46

44

42

40

Bulk

CSF

TM2

TM1

1000 1050 1100 1150 1200


(b)

009

008

007

006

Surfa

ce C

SF

TM2

TM1

1000 1050 1100 1150 1200


(c)

1000 1050 1100 1150 1200


4

3

2

Figu

re o

f mer

it

Calculated results

(d)







5 Conclusion



Relat

ive e

lect

ric fi

eld

stren

gth

30

20

10

0

0 100 200 300 400 500


1000nm1100nm1200nm

(a)

1000nm1100nm1200nm

0 200 400 600 800 1000


Relat

ive e

lect

ric fi

eld

stren

gth

70

50

30

0

10

20

40

60

(b)


10

08

06

04

02

00

62 63 64

Nor

mal

ized

refle

ctan

ce


1600nm with 133

1600nm with 134

1650nm with 133

1650nm with 134

(a)

Gold MgF2 Water350

300

250

200

150

100

50

0

Relat

ive e

lect

ric fi

eld

stren

gth

0 1000 2000 3000 4000


TM2

TM1

(b)








10

08

06

04

02

00

60 64 68 72

Nor

mal

ized

refle

ctan

ce


SilicaMgF2

(a)

120

100

80

60

40

20

0

Rela

tive e

lect

ric st

reng

th

0 500 1000 1500 2000


MgF2 TM2

MgF2 TM1

Silica TM2

Silica TM1

(b)







Acknowledgments


References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Relat

ive e

lect

ric fi

eld

stren

gth

30

20

10

0

0 100 200 300 400 500


1000nm1100nm1200nm

(a)

1000nm1100nm1200nm

0 200 400 600 800 1000


Relat

ive e

lect

ric fi

eld

stren

gth

70

50

30

0

10

20

40

60

(b)


10

08

06

04

02

00

62 63 64

Nor

mal

ized

refle

ctan

ce


1600nm with 133

1600nm with 134

1650nm with 133

1650nm with 134

(a)

Gold MgF2 Water350

300

250

200

150

100

50

0

Relat

ive e

lect

ric fi

eld

stren

gth

0 1000 2000 3000 4000


TM2

TM1

(b)








10

08

06

04

02

00

60 64 68 72

Nor

mal

ized

refle

ctan

ce


SilicaMgF2

(a)

120

100

80

60

40

20

0

Rela

tive e

lect

ric st

reng

th

0 500 1000 1500 2000


MgF2 TM2

MgF2 TM1

Silica TM2

Silica TM1

(b)







Acknowledgments


References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










10

08

06

04

02

00

60 64 68 72

Nor

mal

ized

refle

ctan

ce


SilicaMgF2

(a)

120

100

80

60

40

20

0

Rela

tive e

lect

ric st

reng

th

0 500 1000 1500 2000


MgF2 TM2

MgF2 TM1

Silica TM2

Silica TM1

(b)







Acknowledgments


References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article self-referenced plasmon waveguide...

Documents