ResearchArticle Thin Metal Superlens Imaging in ...downloads.hindawi.com/journals/ijo/2019/6513836.pdfInternationalJournalofOptics 0 0.51 1.5 2 2.5 3 3.5 4 4.5 5 0 2 4 6 8 10 12 14

Research ArticleThin Metal Superlens Imaging in Nanolithography

JingWang and Yunlong Sheng

Departement de Physique de Genie Physique et dOptique Centre dOptique Photonique et Laser (COPL)Universite Laval Quebec G1V 0A6 Canada

Correspondence should be addressed to Yunlong Sheng shengphyulavalca

Received 31 January 2019 Accepted 26 March 2019 Published 2 May 2019

Academic Editor John T Sheridan

Copyright copy 2019 JingWang andYunlong ShengThis is an open access article distributed under theCreativeCommonsAttributionLicense which permits unrestricted use distribution and reproduction in anymedium provided the originalwork is properly cited

Superlens imaging system in nanolithography can be regarded as a cascade of two F-P cavities ie a superlens cavity and a dielectriccavity between superlens and introduced mask of high loss and the transfer function of system is obtained by considering multiplereflections inside the two cavities For the range of wavevector of interest the typical high peak of transmission coefficient ofsuperlens coincides with a local minimum of transmission coefficient of dielectric cavity The peak of transfer function of systemcorresponds to the peak of transmission coefficient of dielectric cavity Thin superlens imaging system in nanolithography isanalyzed based on transfer function which can be flattened by simply tuning transmission coefficient of dielectric cavity andsuperlens cavity The results are further validated by Finite Element Method (FEM) simulations

1 Introduction

The metal planar superlens with a negative permittivity atoptical frequency and a positive permeability was proposedby Pendry in 2000 [1] as an alternative to negative indexmedia (NIM) by Veselago in 1967 [2] to break the diffrac-tion limit The principle of superlens is to compensate theexponential decay of the evanescent field away from theobject by amplifying the evanescent waves through surfaceplasmons (SP) resonances Since then many research effortshad been devoted into superlens imaging [3ndash15] includ-ing theoretical models numerical simulations experimentaldemonstrations and applications

The silver superlens was demonstrated experimentallywith the resolution of one-sixth of the illumination wave-length by Zhang et al in 2005 [3] In their experiment 35nm thick silver slab was used because it gives the optimumtransfer function Thinner sliver slabs show higher butnarrow enhancement bands and thicker slabs show smallerenhancements in reference to zero-order transmission [4]In order to eliminate the sharp peak of transfer functionSheng et al proposed designing the metallic superlens closeto the cutoff condition of the long-range SP mode to balancethe amplification by the SP resonance and the flatness of thetransfer function [5 6] Moore et al suggested a performancewindow for superlens with total thickness range from 120

nm to 140 nm in order to get a flatter transfer function [7]Those were reported by considering transfer functions ofthe imaging system with three-layer structure a superlenssandwiched by two semi-infinite dielectrics [4ndash7]

Normally when dealing with the imaging system aperfectly absorbing thin screen with slit(s) has been widelyadopted The transmission of the idealized screen will be1 in the slit or 0 otherwise While in real nanolithographyapplications there exists a metallic object mask The metallicmask itself exists mainly for constructing a perfect objectfunction in the object plane just behind the mask for theimaging system To obtain a good enough object functionwhich means as close as the ideal case ie 1 in the slit and0 otherwise a thick mask with intrinsic high loss such asChrome (Cr) is usually applied Due to the introductionof mask a dielectric cavity is naturally formed between themask and superlens Blaikie et al approximately consideredthe neglected recursive reflections in the dielectric cavitybetween the superlens and the mask and modified transferfunction by an improved transfer-matrix model [8] Shenget al further took possible SPR by mask itself in some casesinto account and gave a more general model with its transferfunction which is optimized by genetic algorithm (GA) [9]

For the superlens imaging system in nanolithography weregarded it as two cascaded F-P cavities a superlens cavity

HindawiInternational Journal of OpticsVolume 2019 Article ID 6513836 6 pageshttpsdoiorg10115520196513836

2 International Journal of Optics

Object plane Image planeMask Superlens

x

zＪＩ＞ＭＫ

Figure 1 Metal superlens imaging system for nanolithography

and a dielectric cavity between superlens and introducedmask of high loss and the transfer function of system isobtained by considering multiple reflections inside the twocavities [9 10]We studied the transfer function of system andthe transmission coefficient of two cavities and then revealedsome relations among them It is found that the peak shownin transmission coefficient of superlens always correspondsto the local minimum of transmission coefficient of dielectriccavity Moreover the peak of transfer function of systemcoincides with transmission coefficient of dielectric cavityinstead of that of superlens Based on these we propose thatby simply tuning the transmission coefficient of superlenscavity and dielectric cavity a very thin metal superlensimaging systemcan showwell-balanced transfer function andthus produces improved image which is validated by FEMsimulations

2 Metal Superlens Imaging System

Consider an imaging system for nanolithography with ametal superlens of permittivity 120576119904 and a thick metallic maskof permittivity 120576119900 with high intrinsic loss to construct anobject function as shown in Figure 1 For the purpose ofthe image analysis herein a slit of nanosize is perforatedthrough the objectmask A dielectric cavity with permittivity120576119889 is formed between the superlens and the mask Theilluminating light of TM polarization is incident normallyto the object mask from the semi-infinite dielectric medium120576119901 The image plane is placed in a semi-infinite dielectricmedium 120576119902 at a distance 119889119902 from the superlens The incidentplane wave of TM polarization was launched in dielectricmedium 120576119901 and then encountered the object mask 120576119900 In thecase where the lithographic metal mask layer is thick andof high intrinsic loss the incident waves will be dissipatedin the mask medium and can only pass through the slit Atthe exit of the slit the waves labelled as source A will bescattered in the medium 120576119889 launching the Surface PlasmonPolaritons (SPPs) along interfaces of the superlens Boththe homogeneous propagating waves and inhomogeneousSPP waves will reach the image plane and contribute to theimage in dielectric medium 120576119902 The evanescent waves will

simply undergo an exponential delay in the semi-infinitedielectric medium 120576119902 Therefore the imaging system forsource A shown in Figure 1 can be regarded as two cascadedFabry-Perot (F-P) cavities The first cavity is the dielectriclayer 120576119889 with two metaldielectric interfaces 120576119889120576119900 and 120576119889120576119904respectively The second cavity is the metal superlens layerwith two interfaces 120576119904120576119889 and 120576119904120576119902 respectively The transferfunction of the imaging system can be computed as theproduct of transmission coefficients of the two cavities whichare obtained by considering multiple reflections inside thetwo cavities We analyze the mathematical expressions of thetransmission coefficients corresponding to the two cavities inorder to get a flat transfer function of the imaging system

21 Transmission Coefficient of Superlens Cavity The super-lens cavity of permittivity 120576119904 is between two metaldielectricinterfaces of 120576119904120576119889 and 120576119904120576119902 Its transmission coefficient canbe calculated by considering resonance of multiple reflectedfields in the superlens cavity as [1 5]

120591119904 =1198901199041199051198891199041199051199041199021 minus 1198902119904 119903119904119889119903119904119902

(1)

where the Fresnel reflection and transmission coefficientsfrom medium i to medium j with subindices i j = o ds and q are 119903119894119895 = (120576119895119896119911119894 minus 120576119894119896119911119895)(120576119895119896119911119894 + 120576119894119896119911119895) and 119905119894119895 =2120576119895119896119911119894(120576119895119896119911119894 + 120576119894119896119911119895) with 119896119911119894 = radic12057611989411989620 minus 1198962119909 the propagationfactor 119890119894 = exp(119894119896119911119894119889119894) describing the phase change of thepropagating waves with 1198962119909 lt 12057611989411989620 along the distance 119889119894 andthe exponent decay in amplitude of the evanescent waves1198962119909 gt 12057611989411989620 over 119889119894 respectively

According to (1) and for a silver superlens with variablethickness the amplitude of transmission coefficient |120591119904| asa function of normalized wavevector 1198961199090 = 119896119909(radic1205761198891198960) isdepicted in Figure 2(a) Typically for a thin superlens of lessthan 30 nm in thickness a sharp and high peak is shown at alow spatial frequency 11989611990901 slightly larger than 1198961199090 = 1 and arelative broad and low peak is at a high spatial frequency 11989611990902When increasing the thickness only one peak will appear at aspatial frequency between spatial frequency 11989611990901 and 11989611990902 Forlarge thickness of superlens the amplitude of transmissioncoefficient becomes low and flat due to high loss in the thickmetal superlens as shown in Figure 3(a)

According to Maxwellrsquos equations and the boundaryconditions in the Dielectric-Metal-Dielectric (DMD) waveg-uide structure the dispersion relation can be obtained andsolved numerically [5] The effective indices of waveguidemodes are plotted for different thickness of Ag superlens inFigure 2(b) Two modes long-range surface plasmon (LRSP)mode and short-range surface plasmon (SRSP) mode aresupported for DMD waveguide of a thin superlens The twopeaks correspond to such two excited SP modes a LRSPmode associated with a narrow peak located at lower spatialfrequencies 11989611990901 and a SRSP mode associated with a broadpeak at higher spatial frequencies 11989611990902 When the thicknessof the metal superlens increases location of the peak at lowfrequency (LRSP mode) tends to shift to higher frequencyand location of the peak at high frequency (SRSPmode) tends

International Journal of Optics 3

0 20 40 60 80 100 120

0

1

2

3

4

5

6

7

8

9

102

4

68

10

1214

16

18

20

Thickness of superlens dＭ

Nor

mal

ized

wav

evec

tork

Ｒ0

(a)

0 20 40 60 80 100 120 1400

2

4

6

8

10

12

14

LRSP modeSRSP mode


Nor

mal

ized

wav

evec

tork

Ｒ0

(b)

Figure 2 For Ag superlens of thickness ranging from 5 nm to 120 nm sandwiched by two dielectricmediums 120576119889 = 120576119902 = 234 (a) the amplitudeof transmission coefficient |120591119904| lt 1 for propagating waves with 1198961199090 lt 1 while for evanescent waves with 1198961199090 gt 1 it can be amplified (b) Modeeffective index of DMD waveguide

to lower frequency At a certain thickness of the superlensonly one mode will be supported which accounts for onlyone peak of the transmission coefficient

If the imaging system is considered as a superlensbetween two semi-infinite dielectrics without presence of themetal lithographic mask as that in [4ndash7] then the very thinsuperlens is usually inappropriate for imaging due to theexistence of sharp peak of |120591119904| resulting from excitation of

LRSPmodeThe LRSPmode can be cutoff [5] if 119903119889119904+1198902119904 119903119904119902 asymp 0is met which means the reflection of metal layer is around 0

22 Transmission Coefficient of Dielectric Cavity The dielec-tric slab of 120576119889 is sandwiched by the metal superlens andthe metal mask constituting a dielectric F-P cavity Itstransmission coefficient can be calculated [9 10] by takinginto account the recursive reflections in the cavity as

120591119889 =119890119889

1 minus 1198902119889((119903119889119904 + 1198902119904 119903119904119902) (1 minus 1198902119904 119903119904119889119903119904119902)) ((119903119889119900 + 1198902119900119903119900119901) (1 minus 1198902119900119903119900119901119903119900119889))

(2)

For a thick mask with high loss used in the superlens imagesystem for nanolithography 119903119900119901 = 0 then (2) can be furtherwritten as

120591119889 =1

1119890119889 minus 119890119889 ((119903119889119904 + 1198902119904 119903119904119902) (1 minus 1198902119904 119903119904119889119903119904119902)) 119903119889119900

= 11119890119889 minus ((119903119889119904 + 1198902119904 119903119904119902) 119903119889119900119890119889 (119890119904119905119889119904119905119904119902)) 120591119904

(3)

For evanescent waves with 1198962119909 gt 12057611988911989620 119890119889 =exp(119894radic12057611988911989620 minus 1198962119909119889119889) = exp(minusradic1198962119909 minus 12057611988911989620119889119889) is realThe denominator in (3) can be evaluated based on||119886| minus |119887|| le |119886 plusmn 119887| le |119886| + |119887| and |119886119887| = |119886||119887| as

10038161003816100381610038161003816100381610038161003816100381610038161003816

10038161003816100381610038161003816100381610038161003816100381610038161003816

(119903119889119904 + 1198902119904 119903119904119902) 119903119889119900119890119889119890119904119905119889119904119905119904119902

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161205911199041003816100381610038161003816 minus1119890119889

10038161003816100381610038161003816100381610038161003816100381610038161003816

le100381610038161003816100381610038161003816100381610038161003816100381610038161119890119889minus(119903119889119904 + 1198902119904 119903119904119902) 119903119889119900119890119889119890119904119905119889119904119905119904119902

12059111990410038161003816100381610038161003816100381610038161003816100381610038161003816

le10038161003816100381610038161003816100381610038161003816100381610038161003816

(119903119889119904 + 1198902119904 119903119904119902) 119903119889119900119890119889119890119904119905119889119904119905119904119902

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161205911199041003816100381610038161003816 +1119890119889

(4)

Thus when the amplitude of transmission coefficient of thesuperlens |120591119904| shows a very high peak associated with theexcitation of LRSP mode at a low spatial frequency 11989611990901slightly larger than 1198961199090 = 1 the amplitude of transmissioncoefficient of the dielectric cavity |120591119889| will fall to a localminimum Meanwhile |120591119889| will reach a maximum when theabsolute value of denominator of (3) approaches 0 ie


0 05 1 15 2 25 3 35 4 45 50

2

4

6

8

10

12

14

16

18

Am

plitu

de

Normalized wavevector kx0

s

A

d

(a)

0 05 1 15 2 25 3 35 4 45 50

5

10

15

20

25

Am

plitu

de


s

A

d

(b)

Figure 3 The amplitude of transmission efficient of superlens and dielectric and transfer function of the system as a function of normalizedwavevector (a) 119889119889 = 40nm 119889119904 = 30 nm (b) 119889119889 = 10nm and 119889119904 = 15nm

100381610038161003816100381610038161003816100381610038161003816100381610038161119890119889minus(119903119889119904 + 1198902119904 119903119904119902) 119903119889119900119890119889119890119904119905119889119904119905119904119902

12059111990410038161003816100381610038161003816100381610038161003816100381610038161003816997888rarr 0 (5)

Besides it is interesting to notice that if 119903119889119904 + 1198902119904 119903119904119902 asymp 0 in(3) then the transmission coefficient 120591119889 asymp 119890119889 implying anexponential decay of the evanescent waves in the dielectriccavity just as that in the free space without any resonancesand is independent of the cavity thickness

23 Transfer Function of Imaging System As the imagingsystem for source A is a cascade of two F-P cavities the totaltransfer function 120591119860 is calculated by

120591119860 = 120591119889 sdot 120591119904

= 11 (119890119889120591119904) minus (119903119889119904 + 1198902119904 119903119904119902) 119903119889119900119890119889 (119890119904119905119889119904119905119904119902)

(6)

and when condition (5) is satisfied |120591119860| and |120591119889| will bothreach their maximums according to (3) and (6) at thesame spatial frequency 11989611990903 This reveals that the peak ofthe total transfer function |120591119860| for source A in the imagingsystem corresponds to the peak of transmission coefficientof dielectric cavity |120591119889| at 11989611990903 instead of that of superlens|120591119904| at 11989611990901 Actually the value of |120591119860| at 11989611990901 is alwaysbalanced as the transmission coefficient of the superlens|120591119904| can be suppressed by the local minimum of |120591119889| at11989611990901 The transfer function for source A is defined as thetransmission coefficients of the system described in (6) asa function of the spatial spectral frequency According toSPP waveguide theory the LRSP mode is cutoff when thepropagation constant 120573 is purely real which occurs when thenature of the mode changes from attenuating (Im[120573] gt 0)to growing (Im[120573] lt 0) with the propagation along themetal layer [5 6] If the cutoff condition for LRSP mode

ie 119903119889119904 + 1198902119904 119903119904119902 asymp 0 is fulfilled the transfer function 120591119860 =120591119889 sdot 120591119904 asymp 119890119889 sdot 120591119904 In this case a relative flat transfer function canbe expected when considering together the well-controlledproper amplification of SPP by superlens and an exponentialdecay of amplitude of evanescent waves in dielectric cavity

3 Imaging by Thin Superlens Imaging System

Wefirst consider anAg superlens imaging systemwith typicalparameters the metallic mask is chrome with permittivity120576119900 = minus855 + 119894896 and thickness of 119889119900 = 50nm and thesilver slab with permittivity 120576119904 = minus26 + 119894025 with incidentwavelength of 365 nm and thickness 119889119904 = 30 nm the dielectriclayer between superlens and mask has the permittivity 120576119889 =234 and thickness of 119889119889 = 40 nm and the dielectric 120576119902= 234as shown in Figure 1 From Figure 3(a) the sharp peak of|120591119904| corresponds to the local minimum of |120591119889| at 11989611990901 asymp 13which is the effective index of LRSP mode excited in DMDwaveguide The broad peak of |120591119904| at 11989611990902 asymp 36 is shownbecause of the excitation of SRSP modeThe value of transferfunction |120591119860| at 11989611990901 asymp 13 is balanced by the multiplicationof |120591119904| and |120591119889| which indicates that we cannot judge theimaging system only by transmission coefficient of superlensThe peak of transfer function |120591119860| locates at 11989611990903 asymp 16 whichis the same as that of transmission coefficient of dielectriccavity |120591119889| We change the thickness of Ag to 119889119904 = 15 nmand thickness of dielectric 119889119889 =10 nm which form a thinnersuperlens imaging systemThe transmission coefficient |120591119904| of15 nm thick superlens has a shaper and higher peak as shownin Figure 3(b) than that of superlens of 30 nm thickness inFigure 3(a) Still the peak of |120591119904| corresponds to the localminimum of |120591119889| at 11989611990901 asymp 11 and thus the value of |120591119860|at 11989611990901 asymp 11 is balanced in the same manner The peakof transfer function |120591119860| and transmission coefficient of thedielectric cavity |120591119889| is obtained around 11989611990903 asymp 14 as depicted


0 02 04 06 08 10

10

20

30

40

50

60

70

80

90

100(a)

(b)

Am

plitu

de o

f Hz

Length (um)

min max

0 02 04 06 08 10

10

20

30

40

50

60

70

80(c)

(d)A

mpl

itude

of H

zLength (um)

min max

Figure 4 Simulation results of the superlens imaging system by FEM (a) Hz field distributions of system with 119889119889 = 40nm and 119889119904 = 30 nm(b) image of two-slit object in the imaging plane in (a) (c) Hz field distributions of system with 119889119889 = 10nm and 119889119904 = 15 nm (d) image oftwo-slit object in the imaging plane in (c)

in Figure 3(b) The very thin superlens imaging system canshow a flatter transfer function over a broader range of spatialfrequency by simply tuning the transmission coefficient ofsuperlens cavity and dielectric cavity

For further validations 2DFinite ElementMethod (FEM)by commercial software package COMSOL Multiphysics 44was employed to simulate the imaging system in (x y) planeas shown in Figure 4 A TM (Ex Ey Hz) plane wave withwavelength of 365 nm was launched along y direction fromthe input port on the top boundary in the FEM simulationsA perfectly matched layer (PML) was applied at the bottomboundary and periodical boundary conditions (PBC) wereimposed on the left and right sides A chrome mask with twoslits of 40 nm was used The centre-to-centre distance of twoslits was 120 nm The lateral length along x direction of eachlayer was 1 um To clearly show the Hz fields after the mask ofhigh loss the incident waves before and in the mask and themask itself are removed in Figures 4(a) and 4(c) The imageof the two spaced slits is recorded at the imaging plane placedat a distance of 10 nm away from the superlens as shown inFigures 4(b) and 4(d) Obviously the image in Figure 4(d) bythin superlens system with transfer function in Figure 3(b) isbetter than the one in Figure 4(b) with the transfer functionshown in Figure 3(a) because the side lobes of the image inFigure 4(d) were largely suppressed compared with that inFigure 4(b) However the amplitude of the unwanted centrepeak is still high as shown in Figures 4(b) and 4(d)

The imaging performance of thin superlens imaging sys-tem can be further improved by approaching the LRSP modecutoff condition as we demonstrated Change the dielectric120576119889 = 234 to 120576119889 = 408 and keep all others unchanged as those

in Figure 4(c) The transfer function |120591119860| and transmissioncoefficient |120591119889| and |120591119904| are plotted in Figure 5(a) from whichwe can see that the high peak of |120591119904| associated with LRSPmode is mainly removed and |120591119889| approximately followsan exponential decay for evanescent waves and thus thetransfer function |120591119860| is balanced to show flatness The Hzfield by a FEM simulation in this superlens system is shownin Figure 5(b) and the image is notably improved as shown inFigure 5(c) in which both the side lobes and the centre peakare greatly suppressed compared with those in Figures 4(b)and 4(d)

4 Conclusions

We investigated the imaging performance of the metal planarsuperlens for nanolithography considering the superlensimaging system as a cascade of two F-P cavities a super-lens cavity and a dielectric cavity between superlens andintroduced mask of high loss By analyzing the transmissioncoefficient of superlens and dielectric cavity and the transferfunction of whole system we found that the peak of thetransmission coefficient of the superlens always coincideswith the local minimum of that of the dielectric cavity andthe peak of the whole transfer function of system actuallycorresponds to that of dielectric cavity instead of superlensThen we show that very thin superlens imaging systemwhich was usually believed to be improper for superlensimaging has an improved imaging performance by simplytuning the transmission coefficient of superlens cavity anddielectric cavity All the results are analyzed based on transferfunctions and further confirmed by FEM simulations


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

Am

plitu

de


s

A

d

0 02 04 06 08

(b)

(a) (c)

10

10

20

30

40

50

60

70

80

Am

plitu

de o

f Hz

Length (um)

min max

Figure 5 (a) Amplitude of transmission coefficient of superlens and dielectric and transfer function of the system as a function of normalizedwavevector (a) LRSP mode cut-off condition is approached with 119889119889 = 10nm 119889119904 = 15nm and 120576119889 = 408 (b) Hz field distributions in superlensimaging system (c) image of two-slit object in the imaging plane in (b)

Data Availability

The data used to support the findings of this study areincluded within the article

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The authors acknowledge the support from the Natural Sci-ence and Engineering Research Council (NSERC) of CanadaDiscovery Grant to this research program

References

[1] J B Pendry ldquoNegative refraction makes a perfect lensrdquo PhysicalReview Letters vol 85 no 18 pp 3966ndash3969 2000

[2] V G Veselago ldquoThe electromagnetics of substances with simul-taneously negative values of epsilon and murdquo Soviet PhysicsUspekhi vol 10 no 4 pp 509ndash514 1968

[3] N Fang H Lee C Sun and X Zhang ldquoSub-diffraction-limitedoptical imaging with a silver superlensrdquo Science vol 308 no5721 pp 534ndash537 2005

[4] H Lee Y Xiong N Fang et al ldquoRealization of optical superlensimaging below the diffraction limitrdquoNew Journal of Physics vol7 no 255 2005

[5] G Tremblay and Y Sheng ldquoImproving imaging performanceof a metallic superlens using the long-range surface plasmon

polariton mode cutoff techniquerdquo Applied Optics vol 49 no 7pp A36ndashA41 2010

[6] G Tremblay and Y Sheng ldquoDesigning the metallic superlensclose to the cutoff of the long-range moderdquo Optics Express vol18 no 2 pp 740ndash745 2010

[7] C PMoore andR J Blaikie ldquoRobust design of a silver-dielectricnear-field superlens for photolithographyrdquo Journal of theOpticalSociety of America B Optical Physics vol 30 no 12 pp 3272ndash3277 2013

[8] C P Moore R J Blaikie and M D Arnold ldquoAn improvedtransfer-matrix model for optical superlensesrdquo Optics Expressvol 17 no 16 pp 14260ndash14269 2009

[9] G Tremblay and Y Sheng ldquoModeling and designing metallicsuperlens with metallic objectsrdquo Optics Express vol 19 no 21pp 20634ndash20641 2011

[10] F Xu G Chen CWang B Cao andY Lou ldquoSuperlens imagingwith a surface plasmon polariton cavity in imaging spacerdquoOptics Expresss vol 38 no 19 pp 3819ndash3822 2013

[11] B Zhang and J B Khurgin ldquoEigen mode approach to the sub-wavelength imaging with surface plasmon polaritonsrdquo AppliedPhysics Letters vol 98 no 26 p 263102 2011

[12] X Zhang and Z Liu ldquoSuperlenses to overcome the diffractionlimitrdquo Nature Materials vol 7 no 6 pp 435ndash441 2008

[13] S Kawata Y Inouye and P Verma ldquoPlasmonics for near-fieldnano-imaging and superlensingrdquoNature Photonics vol 3 no 7pp 388ndash394 2009

[14] CWangW Zhang Z Zhao et al ldquoPlasmonic structures mate-rials and lenses for optical lithography beyond the diffractionlimit a reviewrdquoMicromachines vol 7 no 7 p 118 2016

[15] K A Willets A J Wilson V Sundaresan and P B JoshildquoSuper-resolution imaging and plasmonicsrdquo Chemical Reviewsvol 117 no 11 pp 7538ndash7582 2017

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components


Shock and Vibration


High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Acoustics and VibrationAdvances in



Advances in Condensed Matter Physics

OpticsInternational Journal of



AstronomyAdvances in

Antennas andPropagation

International Journal of




Geophysics

Advances inOpticalTechnologies

Hindawiwwwhindawicom

Volume 2018

Applied Bionics and BiomechanicsHindawiwwwhindawicom Volume 2018

Advances inOptoElectronics


Volume 2018


Mathematical PhysicsAdvances in


ChemistryAdvances in


Journal of

Chemistry


Advances inPhysical Chemistry


RotatingMachinery



Journal ofEngineeringVolume 2018

Submit your manuscripts atwwwhindawicom


Object plane Image planeMask Superlens

x

zＪＩ＞ＭＫ

Figure 1 Metal superlens imaging system for nanolithography

and a dielectric cavity between superlens and introducedmask of high loss and the transfer function of system isobtained by considering multiple reflections inside the twocavities [9 10]We studied the transfer function of system andthe transmission coefficient of two cavities and then revealedsome relations among them It is found that the peak shownin transmission coefficient of superlens always correspondsto the local minimum of transmission coefficient of dielectriccavity Moreover the peak of transfer function of systemcoincides with transmission coefficient of dielectric cavityinstead of that of superlens Based on these we propose thatby simply tuning the transmission coefficient of superlenscavity and dielectric cavity a very thin metal superlensimaging systemcan showwell-balanced transfer function andthus produces improved image which is validated by FEMsimulations

2 Metal Superlens Imaging System

Consider an imaging system for nanolithography with ametal superlens of permittivity 120576119904 and a thick metallic maskof permittivity 120576119900 with high intrinsic loss to construct anobject function as shown in Figure 1 For the purpose ofthe image analysis herein a slit of nanosize is perforatedthrough the objectmask A dielectric cavity with permittivity120576119889 is formed between the superlens and the mask Theilluminating light of TM polarization is incident normallyto the object mask from the semi-infinite dielectric medium120576119901 The image plane is placed in a semi-infinite dielectricmedium 120576119902 at a distance 119889119902 from the superlens The incidentplane wave of TM polarization was launched in dielectricmedium 120576119901 and then encountered the object mask 120576119900 In thecase where the lithographic metal mask layer is thick andof high intrinsic loss the incident waves will be dissipatedin the mask medium and can only pass through the slit Atthe exit of the slit the waves labelled as source A will bescattered in the medium 120576119889 launching the Surface PlasmonPolaritons (SPPs) along interfaces of the superlens Boththe homogeneous propagating waves and inhomogeneousSPP waves will reach the image plane and contribute to theimage in dielectric medium 120576119902 The evanescent waves will

simply undergo an exponential delay in the semi-infinitedielectric medium 120576119902 Therefore the imaging system forsource A shown in Figure 1 can be regarded as two cascadedFabry-Perot (F-P) cavities The first cavity is the dielectriclayer 120576119889 with two metaldielectric interfaces 120576119889120576119900 and 120576119889120576119904respectively The second cavity is the metal superlens layerwith two interfaces 120576119904120576119889 and 120576119904120576119902 respectively The transferfunction of the imaging system can be computed as theproduct of transmission coefficients of the two cavities whichare obtained by considering multiple reflections inside thetwo cavities We analyze the mathematical expressions of thetransmission coefficients corresponding to the two cavities inorder to get a flat transfer function of the imaging system

21 Transmission Coefficient of Superlens Cavity The super-lens cavity of permittivity 120576119904 is between two metaldielectricinterfaces of 120576119904120576119889 and 120576119904120576119902 Its transmission coefficient canbe calculated by considering resonance of multiple reflectedfields in the superlens cavity as [1 5]

120591119904 =1198901199041199051198891199041199051199041199021 minus 1198902119904 119903119904119889119903119904119902

(1)

where the Fresnel reflection and transmission coefficientsfrom medium i to medium j with subindices i j = o ds and q are 119903119894119895 = (120576119895119896119911119894 minus 120576119894119896119911119895)(120576119895119896119911119894 + 120576119894119896119911119895) and 119905119894119895 =2120576119895119896119911119894(120576119895119896119911119894 + 120576119894119896119911119895) with 119896119911119894 = radic12057611989411989620 minus 1198962119909 the propagationfactor 119890119894 = exp(119894119896119911119894119889119894) describing the phase change of thepropagating waves with 1198962119909 lt 12057611989411989620 along the distance 119889119894 andthe exponent decay in amplitude of the evanescent waves1198962119909 gt 12057611989411989620 over 119889119894 respectively

According to (1) and for a silver superlens with variablethickness the amplitude of transmission coefficient |120591119904| asa function of normalized wavevector 1198961199090 = 119896119909(radic1205761198891198960) isdepicted in Figure 2(a) Typically for a thin superlens of lessthan 30 nm in thickness a sharp and high peak is shown at alow spatial frequency 11989611990901 slightly larger than 1198961199090 = 1 and arelative broad and low peak is at a high spatial frequency 11989611990902When increasing the thickness only one peak will appear at aspatial frequency between spatial frequency 11989611990901 and 11989611990902 Forlarge thickness of superlens the amplitude of transmissioncoefficient becomes low and flat due to high loss in the thickmetal superlens as shown in Figure 3(a)

According to Maxwellrsquos equations and the boundaryconditions in the Dielectric-Metal-Dielectric (DMD) waveg-uide structure the dispersion relation can be obtained andsolved numerically [5] The effective indices of waveguidemodes are plotted for different thickness of Ag superlens inFigure 2(b) Two modes long-range surface plasmon (LRSP)mode and short-range surface plasmon (SRSP) mode aresupported for DMD waveguide of a thin superlens The twopeaks correspond to such two excited SP modes a LRSPmode associated with a narrow peak located at lower spatialfrequencies 11989611990901 and a SRSP mode associated with a broadpeak at higher spatial frequencies 11989611990902 When the thicknessof the metal superlens increases location of the peak at lowfrequency (LRSP mode) tends to shift to higher frequencyand location of the peak at high frequency (SRSPmode) tends


0 20 40 60 80 100 120

0

1

2

3

4

5

6

7

8

9

102

4

68

10

1214

16

18

20


Nor

mal

ized

wav

evec

tork

Ｒ0

(a)

0 20 40 60 80 100 120 1400

2

4

6

8

10

12

14

LRSP modeSRSP mode


Nor

mal

ized

wav

evec

tork

Ｒ0

(b)






120591119889 =119890119889


(2)


120591119889 =1

1119890119889 minus 119890119889 ((119903119889119904 + 1198902119904 119903119904119902) (1 minus 1198902119904 119903119904119889119903119904119902)) 119903119889119900

= 11119890119889 minus ((119903119889119904 + 1198902119904 119903119904119902) 119903119889119900119890119889 (119890119904119905119889119904119905119904119902)) 120591119904

(3)


10038161003816100381610038161003816100381610038161003816100381610038161003816

10038161003816100381610038161003816100381610038161003816100381610038161003816

(119903119889119904 + 1198902119904 119903119904119902) 119903119889119900119890119889119890119904119905119889119904119905119904119902

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161205911199041003816100381610038161003816 minus1119890119889

10038161003816100381610038161003816100381610038161003816100381610038161003816

le100381610038161003816100381610038161003816100381610038161003816100381610038161119890119889minus(119903119889119904 + 1198902119904 119903119904119902) 119903119889119900119890119889119890119904119905119889119904119905119904119902

12059111990410038161003816100381610038161003816100381610038161003816100381610038161003816

le10038161003816100381610038161003816100381610038161003816100381610038161003816

(119903119889119904 + 1198902119904 119903119904119902) 119903119889119900119890119889119890119904119905119889119904119905119904119902

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161205911199041003816100381610038161003816 +1119890119889

(4)



0 05 1 15 2 25 3 35 4 45 50

2

4

6

8

10

12

14

16

18

Am

plitu

de


s

A

d

(a)

0 05 1 15 2 25 3 35 4 45 50

5

10

15

20

25

Am

plitu

de


s

A

d

(b)


100381610038161003816100381610038161003816100381610038161003816100381610038161119890119889minus(119903119889119904 + 1198902119904 119903119904119902) 119903119889119900119890119889119890119904119905119889119904119905119904119902

12059111990410038161003816100381610038161003816100381610038161003816100381610038161003816997888rarr 0 (5)



120591119860 = 120591119889 sdot 120591119904

= 11 (119890119889120591119904) minus (119903119889119904 + 1198902119904 119903119904119902) 119903119889119900119890119889 (119890119904119905119889119904119905119904119902)

(6)






0 02 04 06 08 10

10

20

30

40

50

60

70

80

90

100(a)

(b)

Am

plitu

de o

f Hz

Length (um)

min max

0 02 04 06 08 10

10

20

30

40

50

60

70

80(c)

(d)A

mpl

itude

of H

zLength (um)

min max






4 Conclusions



0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

Am

plitu

de


s

A

d

0 02 04 06 08

(b)

(a) (c)

10

10

20

30

40

50

60

70

80

Am

plitu

de o

f Hz

Length (um)

min max


Data Availability




Acknowledgments


References




















Shock and Vibration





Volume 2018














Geophysics



Volume 2018




Volume 2018






Journal of

Chemistry




RotatingMachinery






0 20 40 60 80 100 120

0

1

2

3

4

5

6

7

8

9

102

4

68

10

1214

16

18

20


Nor

mal

ized

wav

evec

tork

Ｒ0

(a)

0 20 40 60 80 100 120 1400

2

4

6

8

10

12

14

LRSP modeSRSP mode


Nor

mal

ized

wav

evec

tork

Ｒ0

(b)






120591119889 =119890119889


(2)


120591119889 =1

1119890119889 minus 119890119889 ((119903119889119904 + 1198902119904 119903119904119902) (1 minus 1198902119904 119903119904119889119903119904119902)) 119903119889119900

= 11119890119889 minus ((119903119889119904 + 1198902119904 119903119904119902) 119903119889119900119890119889 (119890119904119905119889119904119905119904119902)) 120591119904

(3)


10038161003816100381610038161003816100381610038161003816100381610038161003816

10038161003816100381610038161003816100381610038161003816100381610038161003816

(119903119889119904 + 1198902119904 119903119904119902) 119903119889119900119890119889119890119904119905119889119904119905119904119902

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161205911199041003816100381610038161003816 minus1119890119889

10038161003816100381610038161003816100381610038161003816100381610038161003816

le100381610038161003816100381610038161003816100381610038161003816100381610038161119890119889minus(119903119889119904 + 1198902119904 119903119904119902) 119903119889119900119890119889119890119904119905119889119904119905119904119902

12059111990410038161003816100381610038161003816100381610038161003816100381610038161003816

le10038161003816100381610038161003816100381610038161003816100381610038161003816

(119903119889119904 + 1198902119904 119903119904119902) 119903119889119900119890119889119890119904119905119889119904119905119904119902

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161205911199041003816100381610038161003816 +1119890119889

(4)



0 05 1 15 2 25 3 35 4 45 50

2

4

6

8

10

12

14

16

18

Am

plitu

de


s

A

d

(a)

0 05 1 15 2 25 3 35 4 45 50

5

10

15

20

25

Am

plitu

de


s

A

d

(b)


100381610038161003816100381610038161003816100381610038161003816100381610038161119890119889minus(119903119889119904 + 1198902119904 119903119904119902) 119903119889119900119890119889119890119904119905119889119904119905119904119902

12059111990410038161003816100381610038161003816100381610038161003816100381610038161003816997888rarr 0 (5)



120591119860 = 120591119889 sdot 120591119904

= 11 (119890119889120591119904) minus (119903119889119904 + 1198902119904 119903119904119902) 119903119889119900119890119889 (119890119904119905119889119904119905119904119902)

(6)






0 02 04 06 08 10

10

20

30

40

50

60

70

80

90

100(a)

(b)

Am

plitu

de o

f Hz

Length (um)

min max

0 02 04 06 08 10

10

20

30

40

50

60

70

80(c)

(d)A

mpl

itude

of H

zLength (um)

min max






4 Conclusions



0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

Am

plitu

de


s

A

d

0 02 04 06 08

(b)

(a) (c)

10

10

20

30

40

50

60

70

80

Am

plitu

de o

f Hz

Length (um)

min max


Data Availability




Acknowledgments


References




















Shock and Vibration





Volume 2018














Geophysics



Volume 2018




Volume 2018






Journal of

Chemistry




RotatingMachinery






0 05 1 15 2 25 3 35 4 45 50

2

4

6

8

10

12

14

16

18

Am

plitu

de


s

A

d

(a)

0 05 1 15 2 25 3 35 4 45 50

5

10

15

20

25

Am

plitu

de


s

A

d

(b)


100381610038161003816100381610038161003816100381610038161003816100381610038161119890119889minus(119903119889119904 + 1198902119904 119903119904119902) 119903119889119900119890119889119890119904119905119889119904119905119904119902

12059111990410038161003816100381610038161003816100381610038161003816100381610038161003816997888rarr 0 (5)



120591119860 = 120591119889 sdot 120591119904

= 11 (119890119889120591119904) minus (119903119889119904 + 1198902119904 119903119904119902) 119903119889119900119890119889 (119890119904119905119889119904119905119904119902)

(6)






0 02 04 06 08 10

10

20

30

40

50

60

70

80

90

100(a)

(b)

Am

plitu

de o

f Hz

Length (um)

min max

0 02 04 06 08 10

10

20

30

40

50

60

70

80(c)

(d)A

mpl

itude

of H

zLength (um)

min max






4 Conclusions



0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

Am

plitu

de


s

A

d

0 02 04 06 08

(b)

(a) (c)

10

10

20

30

40

50

60

70

80

Am

plitu

de o

f Hz

Length (um)

min max


Data Availability




Acknowledgments


References




















Shock and Vibration





Volume 2018














Geophysics



Volume 2018




Volume 2018






Journal of

Chemistry




RotatingMachinery






0 02 04 06 08 10

10

20

30

40

50

60

70

80

90

100(a)

(b)

Am

plitu

de o

f Hz

Length (um)

min max

0 02 04 06 08 10

10

20

30

40

50

60

70

80(c)

(d)A

mpl

itude

of H

zLength (um)

min max






4 Conclusions



0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

Am

plitu

de


s

A

d

0 02 04 06 08

(b)

(a) (c)

10

10

20

30

40

50

60

70

80

Am

plitu

de o

f Hz

Length (um)

min max


Data Availability




Acknowledgments


References




















Shock and Vibration





Volume 2018














Geophysics



Volume 2018




Volume 2018






Journal of

Chemistry




RotatingMachinery






0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

Am

plitu

de


s

A

d

0 02 04 06 08

(b)

(a) (c)

10

10

20

30

40

50

60

70

80

Am

plitu

de o

f Hz

Length (um)

min max


Data Availability




Acknowledgments


References




















Shock and Vibration





Volume 2018














Geophysics



Volume 2018




Volume 2018






Journal of

Chemistry




RotatingMachinery








Shock and Vibration





Volume 2018














Geophysics



Volume 2018




Volume 2018






Journal of

Chemistry




RotatingMachinery





Documents

ResearchArticle Thin Metal Superlens Imaging in ...downloads.hindawi.com/journals/ijo/2019/6513836.pdfInternationalJournalofOptics 0 0.51 1.5 2 2.5 3 3.5 4 4.5 5 0 2 4 6 8 10 12 14