Efficient surface plasmon amplification in gain-assisted silver nanotubes andassociated dimersHaiQun Yu, ShuMin Jiang, and DaJian Wu Citation: Journal of Applied Physics 117, 153101 (2015); doi: 10.1063/1.4918310 View online: http://dx.doi.org/10.1063/1.4918310 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/117/15?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Publishers Note: Guided-mode-resonance-coupled plasmonic-active SiO2 nanotubes for surface enhancedRaman spectroscopy [Appl. Phys. Lett. 100, 191114 (2012)] Appl. Phys. Lett. 101, 059901 (2012); 10.1063/1.4738733 Guided-mode-resonance-coupled plasmonic-active SiO2 nanotubes for surface enhanced Raman spectroscopy Appl. Phys. Lett. 100, 191114 (2012); 10.1063/1.4714710 Giant optical resonances due to gain-assisted Bloch surface plasmons Appl. Phys. Lett. 94, 151111 (2009); 10.1063/1.3120564 Hyper-Raman scattering enhanced by anisotropic dimer plasmons on artificial nanostructures J. Chem. Phys. 127, 111103 (2007); 10.1063/1.2786982 Enhanced plasmon coupling in crossed dielectric/metal nanowire composite geometries and applications tosurface-enhanced Raman spectroscopy Appl. Phys. Lett. 90, 093105 (2007); 10.1063/1.2709996 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:182.185.42.45 On: Fri, 17 Apr 2015 15:18:25Efficient surface plasmon amplification in gain-assisted silver nanotubesand associated dimersHaiQun Yu,1ShuMin Jiang,1and DaJian Wu2,a)1Faculty of Science, Jiangsu University, Zhenjiang 212013, China2Jiangsu Key Lab on Opto-Electronic Technology, School of Physics and Technology,Nanjing Normal University, Nanjing 210023, China(Received 14 January 2015; accepted 4 April 2015; published online 16 April 2015)SPASER(surfaceplasmonamplicationbystimulatedemissionofradiation)propertiesinactiveSiO2Ag nanotubes and associated dimers have been investigated by using the scattering theory andthe nite element method. In the active Ag nanotube, as the gain coefcient of the core increases toa critical value, a super-resonance occurs. The SPASER phenomenon also can be found in the activeAgnanotubedimer.ThestrongcouplingsbetweentwonanotubesleadtolargergainthresholdfortheactiveAgnanotubedimercomparedwiththeactiveAgnanotube. Atthesuper-resonance,themaximal surface enhanced Raman scattering factor at the hot spot in the active Ag nanotube dimercanachieve about 8 1018, whichis large enoughfor singlemoleculedetection. Furthermore,withincreasingtheseparationbetweentwoAgnanotubes, thegainthresholdvalueforthesuper-resonanceof theactiveAgnanotubedimer decreases, whilethecorrespondingsuper-resonancewavelength increases rst and then decreases. VC2015 AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4918310]I.INTRODUCTIONTheoptical properties of metallicnanostructures havebeenintensivelystudied inrecentdecadesandvarious metalnanostructures with different shapes have been produced andinvestigated.1It is well known that the surface plasmon (SP)responses inthemetal nanostructuresarestronglydepend-ence on the detailed shape parameters.2,3The specic opticalproperties in different metallic nanostructures canlead tomany applications in functional materials,4surface-enhancedRaman spectroscopy (SERS),5biological sensing,6plasmoniclasers,7etc.Amongmanynovelplasmonicnano-structures, themetal dimerisasimplebut important nano-structure.810Above all, an enormous SERS response can befound in metal nanoparticle dimers when the molecules weretrappedatthegapbetweentwoparticles.11Byadjustingthegeometryparametersofthedimers, thenear-eldenhance-ment, resonancewavelength, scattering, andabsorptionallwill be changedeffectively.12For example, Hucket al.13foundthatthenear-eldcouplingsinthegoldnanoantennasarrangedintip-to-tipcongurationleadtostrongnear-eldenhancements intheinfraredregion. Agnanoshell dimershave been reported to be a dual-band photoluminescenceenhancer at the dipole and quadrupole modes of the SPresonances.14In the plasmonic split nanoring dimer, the cou-pling and interference of the dimer SP modes can induce themultiple Fano-like resonances.15In addition, Marinicaet al.16found the strong nonlinear effects in a coupledmetalnanoparticle dimer.Recently, surfaceplasmonamplicationbystimulatedemission of radiation (SPASER) has received extensiveattention because of their potential applications inultrasensing,17scanning near-eld optical microscopy,18bio-medicaltests,19andSP-enhancedphotodetectors.20Thegainmaterialsnearthemetal surfacecouplewiththeplasmonicstructures andtransfer energytocompensatethelosses ofthe SPs. Finally, it will lead to the enormous amplication ofthedesiredSPresponse.2125In2009, Noginovetal.26rstdemonstratedexperimentallythatananoparticlewithagoldcoreanddye-dopedsilicashellcanrealizeaSPASER-basednanolaser. Li et al.27reported an efcient nanorod-basedSPASERwithwavelengthtunabilityandpolarizationsensi-tivity.AFanoresonance-basedSPASERwasfoundinarodand concentric square ring-disk nanostructure.28We alsoproposed a dual-frequency SPASER based on the gain-assisted metallic nanomatryushkas.29However, the SPASERproperties inmetal nanotubes wereseldomreported, espe-cially in their dimers.Inthispaper, wepresent atheoretical investigationforthe SPASER properties of the active Ag nanotubes and asso-ciated dimers. As the gain coefcient increases to the criticalvalues, thesuper-resonancescanbefoundintheactiveAgnanotubesandtheactiveAgnanotubedimers. Wefocusonthefar-andnear-eldpropertiesoftheactiveAgnanotubedimersatthesuper-resonances. Theinuencesofthedimergap on the gain threshold and super-resonance wavelength ofthe active Ag nanotube dimer have been discussed in detail.II.ACTIVE AG NANOTUBE AND ASSOCIATED DIMERThe Ag nanotube comprises a dielectric core with radiusr1andanAgshellwithradiusr2. TheschematicoftheAgnanotubedimerisshowninFig. 1. TheAgnanotubedimeris illuminated by an incident electric eld with K vector nor-mal totheaxisof dimer andelectricvector parallel totheaxisofdimer. Throughoutthepaper,r1andr2aresetas40and50 nm, respectively. The other values of r1andr2ofa)Author towhomcorrespondence shouldbe addressed. Electronic mail:wudajian@njnu.edu.cn0021-8979/2015/117(15)/153101/5/$30.00 VC2015 AIP Publishing LLC 117, 153101-1JOURNAL OF APPLIED PHYSICS 117, 153101 (2015) [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:182.185.42.45 On: Fri, 17 Apr 2015 15:18:25coursecanbeusedforthismodel. However, theinuencesof thestructureparameters of theAgnanotubeontheSPamplicationsarenotthemainpartofthiswork. Wefocuson the effects of the couplings between two Ag nanotubes ontheSPASERproperties of theactiveAgnanotubedimers.Thus, we only study one kind of Ag nanotube. The dielectricfunctions of thecoreandshell aree1ande2, respectively.The separation between two nanotubes is dened as D and Cpoint isthemidpoint inthedimer gap. ADrudemodel isadopted for the complex dielectric function of the Ag shell.29Thegainmaterialssuchasdyemolecules,26rare-earthions,andsemiconductor quantumdots21canbedopedintosilicacoretorealizetheactivenanotubesandassociateddimers.For simplicity, a complex refractive index of the doped SiO2coreissetasn ik.Therealpart nrepresentstherefractiveindexofSiO2(n 1.43)andgaincoefcientkisrelatedtotheamount of optical gaininducedbyexternal pumping.30Theembeddingmediumisassumedasairwithe31. Theincident lightinteractingwithainniteactiveAgnanotubecanbedescribedbythescatteringtheory.31Thescatteringandabsorptionspectraofthenanotubesareshownbyusingthe scattering efciency Qsca and absorption efciency Qabs.For the Ag nanotube dimer, using scattering theorydirectly to deal with the near- and far-eld properties isdifcult and complex. Thus, the nite element method (FEM)is used to study the near and far-eld optical properties of thepassiveandactiveAgnanotubedimers. TheFEMhasbeenproved to be a exible and efcient numerical tool to analyzethe inhomogeneous and complex structures. The FEM has theadvantageofdeningthematerial interfacesaccuratelyandcanuseanunstructuredadaptivemeshtoimprovethehighnumerical resolution wherever necessary. Therefore, theFEMhasbeenwidelyusedintheresearchesof theopticalproperties of themetallicnanostructures.32,33Our 2D-FEMmodel consists of an Ag nanotube dimer, the embedding me-dium, andaperfectlymatchedlayer(PML). ThecylindricalPMLaroundtheAgnanotubedimeractsasanabsorberofthescatteredelds. Theplanwaveforexcitationisdenedthrough the background eld with the polarization parallel totheaxisofthedimer. Thescattererandembeddingmediumare meshed with free triangular elements and the PMLdomain is meshed with quadrilateral elements by mapping.III.RESULTS AND DISCUSSIONFirstly, weinvestigatetheopticalpropertiesofasingleAgnanotube. Figure2showstheabsorptionandscatteringspectraoftheAgnanotubeswithdifferentgaincoefcients.It is found that the scattering and absorption of the Ag nano-tubecanbeadjustedbychangingthegaincoefcientofthecore. InFig. 2(a), ask 0, astrongpeakappearsat about632 nm, which is dueto the dipole plasmon resonancein thepassive Ag nanotube. The line width of the scattering peak isabout80 nmandthecorrespondingqualityfactorisabout8.Thequalityfactor Qis evaluatedfromQk/Dk, wherekandDk are the central emission wavelength and the fullwidthat half maximum, respectively.34Asthegaincoef-cient k increases to 0.0715, the absorption at the SPresonance wavelengthbecomes zero, while the Qsca-valueincreasesto8.5,asshowninFig.2(b).Atthispoint,theSPlosses in the Ag nanotube are compensated by gain media. InFIG. 1. Schematic diagram of the Ag nanotube dimer.FIG. 2.Scattering and absorption spec-tra of the active Ag nanotubes withgaincoefcientkof(a)0, (b)0.0715,(c) 0.1753, and (d) 0.1816.153101-2 Yu, Jiang, and Wu J. Appl. Phys. 117, 153101 (2015) [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:182.185.42.45 On: Fri, 17 Apr 2015 15:18:25Fig. 2(c), as k-value increases to the critical point ofkc0.1753, a super-resonance occurs in the active Ag nano-tubeatabout620.7 nm.Thepeakvalueof Qscasignicantlyincreases to about 4.04 107, which is about 1.3 107timesthevalueforthepassiveAgnanotube.Meanwhile,thepeakvalue of Qabsdecreases dramatically to a minimum4.04 107. The line width of the SP peak reduces to about0.5 nm and the extinction efciency QextQscaQabsreaches zero. It is well known that the SP amplication arisesfrom theinteractionsamongthegainmedium, Agnanotube,and incident light. As the gain coefcient reaches the criticalvalue, thelight amplicationanddissipationof thesystemkeep a dynamic balance and the net amplication of theSPASERbecomeszero.23Then, astableSPASERisestab-lished. Under this condition, the quality factor of the SPresonanceis greatlyincreased(about 1240) andhencethestrengthoftheSPresonanceissignicantlyenhanced.Withfurther increasingthegaincoefcient, thestrengths of thescattering and absorption peaks decrease rapidly and thesuper-resonance disappears.30InFig. 2(d), for k 0.1816,the peakvaluesof Qsca and Qabsreduce to2440 and 2574,respectively, and the line width of the scattering peakincreases toabout 3 nm. Inthis case, theabsorbedenergyoutnumbers the losses, leading to a negative Qext.We further investigate the SPASERproperties of theactiveAgnanotubedimer. Figure3(a) showsthescatteringand absorption spectra of the passive Ag nanotube dimer(k 0). Here, D-value is xed at 5 nm. A strong peak appearsat about 721.5 nm. TheplasmonresonanceoftheAgnano-tubedimerexhibitsanapparent redshift comparedwiththeAg nanotube. According to the plasmon hybridization theory,whentheincident polarizationisparallel tothedimer axis,the couplings between the SP resonances in two Ag nanotubeslead toa bonding mode (lowenergy) andanantibondingmode(highenergy).35Thus, thedipolepeakofthebondingmode of the Ag nanotube dimer will show a redshift. In Fig.3(b), ask-valueincreases to0.1386, theQscaof thedipolepeak of the bonding mode increases to about 13 while the cor-respondingQabs-valuetendstozero.Whenk-valueincreasestothecriticalpointofkc0.5715, asuper-resonanceoccursin the active Ag nanotube dimer. At this super-resonance, theQsca-valuecanreachabout 6.87 107, whichislarger thanthatoftheactiveAgnanotube.Thelinewidthofthescatter-ingpeakbecomesextremelynarrowofabout0.1 nmandthecorrespondingqualityreachesabout6318.WealsonotethatthegainthresholdoftheactiveAgnanotubedimerislargerthan that of the active Ag nanotube. The gain threshold of theactive plasmonic nanostructures depends on the dissipation inthemetal andtheradiationofelectromagneticwaves.36Theplasmonic nanostructure with lower radiation and metalliclosses means asmaller gainthreshold. IntheAgnanotubedimer,thestrong coupling between twoAg nanotubesresultsinaconsiderableenhancement ofthenear-elds. Therefore,themetalliclosses duetotheelectriceldpenetrationintometal layer could be high and hence the large threshold valuefor the active Agnanotube dimer.26,37,38Inaddition, it isfoundthat thesuper-resonancewavelengthoftheactiveAgnanotube dimer shows a blue shift from 721.5 nm to631.8 nm.With increasing the gain coefcient k,the real partof thedielectricconstant of thedopedsilicacore[(n k)2]decreases.Thedecreaseddielectric constantof theinnercorewillincreasethenumberoftheinducedchargesontheinter-nal surfaceof theAgnanotube.39Then, thestrengthof thecollective oscillation of the induced electrons is enhanced andhence the increased resonance energies of the SPmodes.Therefore, theresonanceenergiesofbothbondingandanti-bondingmodesintheAgnanotubedimerwill beincreasedand hence the super-resonance wavelength shows a blue shift.Inaddition, fork 0.5715, theenergytransferredfromgainmedia to the bonding mode is more than that to the antibond-ingmode.Thus,theantibondingmodepeak(Qsca3000)ismuchweakerthanthebondingmodepeak. InFig. 3(d), thesuper-resonanceisdisruptedwhenk-valuefurther increasesto 0.5991.FIG. 3.Scattering and absorption spec-traof theactiveAgnanotubedimerswith gain coefcient k of (a) 0, (b)0.1386, (c) 0.5715, and (d) 0.5991.153101-3 Yu, Jiang, and Wu J. Appl. Phys. 117, 153101 (2015) [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:182.185.42.45 On: Fri, 17 Apr 2015 15:18:25Figures 4(a) and 4(b) show the electric eld distributionsinthepassiveandactiveAgnanotubedimers, respectively.Here, D-valueisxedat 5 nm. InFig. 4(a), thecalculationwavelength is xed at the resonance wavelength of 721.5 nmand k 0. In this passive Ag nanotube dimer, the strong eldenhancementsoccurinthegapbetweentwoAgnanotubes.Whentheincidentpolarizationisparalleltothedimeraxis,the dipole resonance modes of the twoAgnanotubes arealigned and coupled, and hence, the signicant eldenhancements generateinthejunctionbetweentwonano-tubes.40Meanwhile, theelectriceldsaresuppressedelse-where because of the coupling effect. The maximalenhancement (18) of the electric eld is found at C point inthejunctionoftheAgnanotubedimer.InFig.4(b),thecal-culationwavelengthis xedat thesuper-resonancewave-length of 631.8 nm and the gain coefcient k is set as 0.5715.It isobviouslythat thedistributionof theelectriceldsofthe active Ag nanotube dimer at the super-resonance is simi-lartothat inthepassiveAgnanotubedimer. TheSPASERwill not change the distribution of the electric elds.However, The maximal electric eld enhancement in theactive Ag nanotube dimer can reach about 5.37 104, whichis about 3 103times that in the passive Ag nanotube dimer.TheenormouselectriceldenhancementsintheactiveAgnanotubedimeralsobenet bytheenergytransferredfromgainmedia. Figure5showsthelogplot(base10)ofSERSenhancement factor (GjE/E0j4) at C point in the active Agnanotube dimer versus gaincoefcient k. Withincreasingthegaincoefcient k, theSERSGfactor increases at rstandthendecreases. At thecritical point ofkc0.5715, themaximal Gfactor canreachabout 8 1018, whichishighenoughforthesinglemoleculedetection. Nieet al.41havedemonstrated experimentally that the SERS Gfactor of10141015inthemetal nanoparticleaggregatesissufcientfor single-moleculedetection. Li et al.30alsoreportedthatthe active cubic goldnanoboxcangenerate anextremelyhigh SERS G factor on the order of 10161017. They believedthat the single-molecule detection can be readily achieved byusingthis cubicgoldnanobox. IntheactiveAgnanotubedimer,themaximalGfactorofabout8 1018islargerthanthosereportedinpreviousreports. Thus, wethinkthat theactive Ag nanotube dimer can be well used for SERS.Finally, weinvestigatetheinuencesofthedimer gapon the gain threshold and super-resonancewavelength of theactive Ag nanotube dimer. Figure 6(a) shows the dependenceof thegainthresholdof theactiveAgnanotubedimer onD-value. It is foundwithincreasingD-valuethat thegainthresholdvalueoftheactiveAgnanotubedimerdecreases.TheincreasedD-valuemeansthereducedcouplingbetweentwoAgnanotubes, whichreducestheelectriceldsinthegapofthedimer. Thereducedlocalizedelectriceldsindi-catethe decreaseofthemetalliclossandhencethedecreaseofthegainthreshold.38Figure6(b)representsthevariationof the corresponding super-resonance wavelength of theactive Agnanotube dimer withD-values. WithincreasingD-value, thesuper-resonancewavelengthof theactiveAgnanotubedimerincreasesrstfrom600.7 nmat D2 nmto631.8 nmat D5 nmand then decreases to 624.1 nmatD25 nm. The increasedD-value decreases the couplingstrengthbetweentwoAgnanotubesandhencethebondingmode in the Ag nanotube dimer shows a blue shift.FIG. 4. Electricelddistributionsof(a)thepassiveAgnanotubedimeratthe resonance wavelength of 721.5 nm and (b) the active Ag nanotube dimerat the super-resonance wavelength of 631.8 nm (k 0.5715).FIG.5.Logplot(base10)ofthemaximalSERSGfactoroftheactiveAgnanotube dimer as a function of k-value.FIG.6.(a)Gainthresholdvalueand(b)super-resonancewavelengthoftheactive Ag nanotube dimer as a function of the D-value.153101-4 Yu, Jiang, and Wu J. Appl. Phys. 117, 153101 (2015) [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:182.185.42.45 On: Fri, 17 Apr 2015 15:18:25Meanwhile, thedecreaseof thegainthresholdleadstotheincreasedreal part ofe1-value, whichcausesaredshift ofthebondingmodeintheAgnanotubedimer. AsD5 nm,thesuper-resonancewavelengthof theactiveAgnanotubedimer decreases.IV.CONCLUSIONSWe have investigated the SPASERproperties of theactiveAgnanotubesandassociateddimersbymeansofthescatteringtheoryandthe2D-FEM.Asthegaincoefcientkincreasestothecriticalvalues, thesuper-resonancescanbefoundintheactiveAgnanotubesandtheassociateddimers.ThegainthresholdvalueoftheactiveAgnanotubedimerislarger thanthat for theAgnanotubebecauseof thestrongcouplingbetweentwonanotubes.IntheactiveAgnanotubedimer, the maximal SERSGfactor at the hot spot canreachabout8 1018,whichissufcientforsinglemoleculedetection. 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