We develop a simple yet rigorous theory of the photoluminescence (PL) enhancement in the vicinity of metal nanoparticles. The enhancement takes place during both optical excitation and emission. The strong dependence on the nanoparticle size enables optimization for maximum PL efficiency. Using the example of InGaN quantum dots (QDs) positioned near Ag nanospheres embedded in GaN, we show that strong enhancement can be obtained only for those QDs, atoms, or molecules that are originally inefficient in absorbing as well as in emitting optical energy. We then discuss practical implications for sensor technology

Khurgin, Jacob B.

Soref, R. A.

Sun, Greg

English

University of Massachusetts Boston: ScholarWorks at UMass

University of Massachusetts BostonScholarWorks at UMass BostonPhysics Faculty Publications Physics3-9-2009Practical enhancement of photoluminescence bymetal nanoparticlesGreg SunUniversity of Massachusetts Boston, greg.sun@umb.eduJacob B. KhurginJohns Hopkins UniversityR. A. SorefAir Force Research Laboratory, Hanscom Air Force BaseFollow this and additional works at: http://scholarworks.umb.edu/physics_faculty_pubsPart of the Physics CommonsThis Article is brought to you for free and open access by the Physics at ScholarWorks at UMass Boston. It has been accepted for inclusion in PhysicsFaculty Publications by an authorized administrator of ScholarWorks at UMass Boston. For more information, please contact library.uasc@umb.edu.Recommended CitationSun, Greg; Khurgin, Jacob B.; and Soref, R. A., "Practical enhancement of photoluminescence by metal nanoparticles" (2009). PhysicsFaculty Publications. Paper 15.http://scholarworks.umb.edu/physics_faculty_pubs/15Practical enhancement of photoluminescence by metal nanoparticlesG. Sun, J. B. Khurgin, and R. A. Soref  Citation: Appl. Phys. Lett. 94, 101103 (2009); doi: 10.1063/1.3097025 View online: http://dx.doi.org/10.1063/1.3097025 View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v94/i10 Published by the American Institute of Physics.  Related ArticlesInfluence of non-radiative recombination on photoluminescence decay time in GaInNAs quantum wells with Ga-and In-rich environments of nitrogen atoms J. Appl. Phys. 111, 063514 (2012) Spontaneous emission control of single quantum dots in bottom-up nanowire waveguides Appl. Phys. Lett. 100, 121106 (2012) Europium location in the AlN: Eu green phosphor prepared by a gas-reduction-nitridation route J. Appl. Phys. 111, 053534 (2012) Extremely long carrier lifetime over 200ns in GaAs wall-inserted type II InAs quantum dots Appl. Phys. Lett. 100, 113105 (2012) Optical observation of single-carrier charging in type-II quantum ring ensembles Appl. Phys. Lett. 100, 082104 (2012)  Additional information on Appl. Phys. Lett.Journal Homepage: http://apl.aip.org/ Journal Information: http://apl.aip.org/about/about_the_journal Top downloads: http://apl.aip.org/features/most_downloaded Information for Authors: http://apl.aip.org/authors Downloaded 29 Mar 2012 to 158.121.194.143. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissionsPractical enhancement of photoluminescence by metal nanoparticlesG. Sun,1,a J. B. Khurgin,2 and R. A. Soref31Department of Physics, University of Massachusetts Boston, Boston, Massachusetts 02125, USA2Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore,Maryland 21218, USA3Sensors Directorate, Air Force Research Laboratory, Hanscom AFB, Massachusetts 01731, USAReceived 22 January 2009; accepted 12 February 2009; published online 9 March 2009We develop a simple yet rigorous theory of the photoluminescence PL enhancement in the vicinityof metal nanoparticles. The enhancement takes place during both optical excitation and emission.The strong dependence on the nanoparticle size enables optimization for maximum PL efficiency.Using the example of InGaN quantum dots QDs positioned near Ag nanospheres embedded inGaN, we show that strong enhancement can be obtained only for those QDs, atoms, or moleculesthat are originally inefficient in absorbing as well as in emitting optical energy. We then discusspractical implications for sensor technology. © 2009 American Institute of Physics.DOI: 10.1063/1.3097025The enhancement of luminescence from various opti-cally active objects of nanoscale dimensions such as atoms,molecules, and quantum dots QDs here we shall use thegeneric term molecule to donate them all when placed inclose proximity to metal nanoparticles1–10 is a phenomenonthat has been conceptually well understood as a product ofstrong localized electric field induced by the surface plas-mons SPs.11 This enhancement with important applicationsin sensing has been attributed primarily to the increase inradiative decay rate caused by the Purcell12 effect associatedwith the tightly confined high-density SP modes. That treat-ment is adequate in estimating the enhancement factor forelectroluminescence where the excitation energy in the formof an electric dipole gets coupled directly into the SP modes.But for photoluminescence PL, the situation is more com-plicated. There are two enhancement mechanisms at work.One takes place during the optical excitation stage and theother during the stage of light emission. In the absence ofmetal nanoparticles, the optical excitation typically in theform of a focused laser beam is being absorbed by the mol-ecules. With a metal nanoparticle placed in the vicinity of themolecules, the beam can now get coupled first into thetightly confined SP mode enhancing the optical energy den-sity near the molecule field, which enhances the absorptionrate. The same SP modes albeit at different frequencies canalso enhance the energy-emission efficiency of the excitedmolecules through the Purcell12 effect. A proper estimate ofPL enhancement by metal nanoparticles therefore has to in-clude both energy absorption and emission processes that areenhanced simultaneously by the associated SP modes. Tomake the matter even more complicated, all of these pro-cesses depend on the wavelength relationships between theoptical excitation, the molecule emission, and the SP mode.A clear understanding of the enhancement mechanism is ob-viously important for improving the performance of sensorsrelying upon PL. Based on the “effective mode volume”approach,13 we have previously developed analytical modelsthat rigorously treated the enhancement effects of light emis-sion by molecules in the presence of a metal sheet14 andmetal nanoparticles,15 as well as light absorption by mol-ecules in the proximity of metal nanoparticles.16 Combiningthe models for light absorption16 and emission by metalnanoparticles,15 we are now in position to calculate howmuch total enhancement one can realistically obtain in mea-sured PL for a given metal embedded in a given dielectricmedium. We can also provide an analytical approach for op-timizing the metal nanostructure in order to achieve maxi-mum enhancement. The salient feature of our approach isthat it shows the attainable PL enhancement that can be op-timized for each particular molecule—characterized by theabsorption cross section at the excitation frequency aex,the radiative efficiency radPL, and their product—the PLcross section PLex ,PL=aexradPL.The enhancement of a PL process is illustrated in Fig. 1.Optical excitation at the frequency of ex in the form of alaser beam is focused into the region where a metal nano-sphere with a radius r and a molecule separated by a distanced are located. The excitation beam couples into the highlyconfined SP mode around the metal sphere with an incou-pling coefficient in. Energy inside the SP mode is then ab-sorbed by the active molecule with an absorption cross sec-tion a. This process competes with radiative rad andnonradiative decays nrad of the SP mode. The excited mol-aElectronic mail: greg.sun@umb.edu.FIG. 1. Color online Illustration of the enhancement of a PL process bythe incoupling of the optical excitation into the SP mode surrounding ametal sphere and by the outcoupling of the SP mode into the radiative mode.APPLIED PHYSICS LETTERS 94, 101103 20090003-6951/2009/9410/101103/3/$25.00 © 2009 American Institute of Physics94, 101103-1Downloaded 29 Mar 2012 to 158.121.194.143. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissionsecule with the original radiative decay rate 1 /rad subse-quently relaxes by emitting energy at the frequency PL intothe SP mode at the rate of FP /rad, which is enhanced by thePurcell12 factor FP. Simultaneously, the molecule also re-laxes into nonradiative modes at its original nonradiative rateof 1 /nrad. The observed PL power depends on the outcou-pling efficiency of the SP mode pr=rad / rad+nrad. It isclear that strong PL enhancement occurs when the frequen-cies of both optical excitation and emission are close to theSP resonance. It is thus optimal to have the frequency rela-tionship ex0PL for PL measurement.Following our previous work,16 we first treat the en-hancement of absorption by a metal nanosphere. In the ab-sence of the metal nanosphere, the optical excitation willsimply be focused onto a diffraction limited spot at the apexof the cone characterized by a far field half angle  with aspot radius at the waist w0=	ex /, where 	ex is the excita-tion wavelength in the dielectric medium. The electric fieldin the focal spot Efoc is related to the power s+2 carried bythe incident wave as s+2=nw02Efoc2 /4Z0, where Z0 is theimpedance of free space and n is the index of refraction. Inthe presence of a metal sphere with radius r, the incidentlight gets coupled into the SP mode with an incoupling co-efficient in3rad /8.17 The SP mode has a maximumfield Emax at the surface of the sphere that is related to itsenergy a2= 120DEmax2 Veff, where 0 is the permittivity offree space, D is the dielectric constant of the medium, andVeff= 4r3 /31+ 2D−1 is the effective mode volume atthe resonant frequency 0 wavelength 	D in thedielectric.15 The field enhancement is then found from thesteady-state solution of the rate equation for the amplitude aof the SP mode that describes the incoupling of the incidentwave at the excitation frequency ex and the various decaymechanisms,13dadt= jex − 0a −12rad + nrad + absa + ins+, 1where nrad is the rate due to the Ohmic loss in the Drudemodel approximation, rad= 0 / 1+2D2r /	D3 is theradiative decay rate in the dipole approximation,15 and abs= cNaa /nVeffr / r+d6 is the decay rate due to energyabsorption by Na molecules placed near the sphere. Introduc-ing the Q-factors for the nonradiative decay as Qn=0 / 1+2Dnrad, for absorption as Qa=0 / 1+2Dabs, andthe normalized excitation detuning as ex=21+2Dex−0 /0, and taking into account that molecules are situatedat a distance d away from the metal sphere, we arrive at theenergy density and thus absorption enhancement factorFa =9D2  0ex	2 1ex2 + 3 + Qn−1 + Qa−12  + d	6, 2where we have used the normalized radius =2r /	D anddistance d=2d /	D.Let us now turn our attention to the enhancement of theemission process. The energy in a molecule with an originalradiative efficiency rad=rad−1 / rad−1 +nrad−1  can be coupledinto the SP mode at the PL frequency PL into the SP modeaccording to the rate FPPL /rad where the Purcell factorFPPL as the ratio of the SP effective density of SP modesSP= LPL /Veff / +d6 to that of the radiation con-tinuum rad=8 / 3	PL3 PL with the Lorentzian linewidthfactor L= rad+nrad /2 / −02+ rad+nrad2 /4is given as15FPPL =9D3 0PL	2 3 + Qn−1PL2 + 3 + Qn−12  + d	6, 3in which the normalized PL detuning PL=21+2DPL−0 /0. The enhancement factor can now be evaluated asFe =1 + FPpr1 + FPrad, 4where the radiative outcoupling efficiency of the SP modepr=Qn3 / 1+Qn3. Finally, combining the two sequentialenhancement processes given by Eqs. 2 and 4, we arriveat the total PL enhancement factor FPL=FaFe that showsa rather complicated dependence on one adjustableparameter—the size of nanoparticle . This dependence canbe traced to the fact that nanoparticles play two mutuallyexclusive roles—that of antenna for efficient in- and outcou-pling of energy and that of a nanocavity for energy concen-tration. An efficient antenna requires a large dipole, while ahigh concentration of energy calls for a small nanocavity.Therefore, for each combination of d, Na, a, and rad, thereexists an optimum size  that maximizes PL enhancement.It is not difficult to see that the largest enhancement canbe obtained only for a small number of molecules placedvery close to the metal sphere, d, with a small absorp-tion cross section, QaQn, and a small original radiativeFIG. 2. Color online Absorption Fa, emission Fe, and total enhancementfactors FPL vs metal sphere radius for Ag/GaN.FIG. 3. Color online Optimized PL enhancement factor vs frequency de-tuning ratio of the optical excitation ex /0 and PL emission PL /0.101103-2 Sun, Khurgin, and Soref Appl. Phys. Lett. 94, 101103 2009Downloaded 29 Mar 2012 to 158.121.194.143. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissionsefficiency, FPrad1, when both excitation and PL frequen-cies are close to SP resonance, ex,PL0. Under thesefavorable conditions, we obtain FPL81D2 / 23+Qn−14,indicating that for a small metal sphere, 3Qn1, the maxi-mum enhancement factor FPL,max81D2 Qn4 /2 in line withwhat a simple electrostatic analysis predicts. For a Ag nano-sphere embedded in GaN Qn=2.77, D=5.81, and 0=2.344 eV, FPL,max8.0104. This is a huge enhance-ment, but in reality, the PL enhancement is not nearly assignificant when the finite absorption cross section and origi-nal radiative efficiency of the molecules that are spaced afinite distance away from the metal sphere are taken intoaccount.Consider the example of InGaN QDs situated at d=5 nm away from a Ag sphere in GaN with Naa=1 nm2and rad=0.01. The resulting PL enhancement factor FPL,along with its enhancement contributions from absorption Faand emission Fe, is shown in Fig. 2, where the optical exci-tation and emission frequencies are very close to the reso-nance of SP mode, ex,PL0. There exists an optimizedsize of the metal sphere for which maximum enhancement isachieved. Also, as one can see, the two contributions areroughly of the same order. Figure 3 shows the optimized PLenhancement factor as a function of the detuning of opticalexcitation ex /0 and that of PL emission PL /0 for thesame example—which clearly indicates that it is more criti-cal to have the PL emission frequency near resonance withthe SP mode. This is because, as shown in Fig. 4, the depen-dence of PL enhancement on the original radiative efficiencyrad Fig. 4a is more sensitive than that on the total ab-sorption cross section Naa Fig. 4b. It is clear that PLenhancement is strong only if the active molecules are bothweak absorbers and inefficient emitters being positioned inclose proximity to the metal nanoparticles. Note that the con-dition arad→0 under which the maximum enhancement isachieved is always satisfied for Raman scattering, which canbe seen as nothing but PL with a negligibly small cross sec-tion; hence FRamanFPL,max. Indeed the experimentally veri-fied enhancement of Raman scattering is always significantlylarger than that for PL.In summary, we have analytically treated the PL en-hancement as a product of two equally important factors—one on the absorption stage and another on the emissionstage—and for a given metal-dielectric combination thereexists an optimal nanoparticle size that maximizes the com-bined enhancement. The key conclusion is that metal nano-particles provide large PL enhancement only for small quan-tities of the atoms, molecules, or QDs with originally low PLcross section, hence metal nanoparticles can be indispensablein improving sensors but are of limited use in other applica-tions, where PL is already reasonably a few percentefficient.1P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E.Moerner, Phys. Rev. Lett. 94, 017402 2005.2J.-Y. Wang, Y.-W. Kiang, and C. C. Yang, Appl. Phys. Lett. 91, 2331042007.3S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, Phys. Rev. Lett.97, 017402 2006.4R. Carminati, J.-J. Greffet, C. Henkel, and J. M. Vigoureux, Opt.Commun. 261, 368 2006.5L. Rogobete, H. Schniepp, V. Sandoghdar, and C. Henkel, Opt. Lett. 28,1736 2003.6C. Girard, O. J. F. Martin, and A. Dereux, Phys. Rev. Lett. 75, 30981995.7L. Novotny, Appl. Phys. Lett. 69, 3806 1996.8M. Thomas, J.-J. Greffet, R. Carminati, and J. R. Arias-Gonzalez, Appl.Phys. Lett. 85, 3863 2004.9G. Baffou, C. Girard, E. Dujardin, G. C. des Francs, and O. J. F. Martin,Phys. Rev. B 77, 121101R 2008; G. Colas des Francs, C. Girard, T.Laroche, G. Leveque, and O. J. F. Martin, J. Chem. Phys. 127, 0347012007.10R. M. Bakker, V. P. Drachev, Z. Liu, H.-K. Yuan, R. H. Pedersen, A.Boltasseva, J. Chen, J. Irudayaraj, A. V. Kildishev, and V. M. Shalaev,New J. Phys. 10, 125022 2008.11D. Maystre, in Electromagnetic Surface Modes, edited by A. D. BoardmanWiley, New York, 1982, Chap. 17.12M. Purcell, H. C. Torrey, and R. V. Pound, Phys. Rev. 69, 37 1946.13S. Maier, Opt. Express 14, 1957 2006.14J. B. Khurgin, G. Sun, and R. A. Soref, J. Opt. Soc. Am. B 24, 19682007; G. Sun, J. B. Khurgin, and R. A. Soref, Appl. Phys. Lett. 90,111107 2007.15J. B. Khurgin, G. Sun, and R. A. Soref, Appl. Phys. Lett. 93, 0211202008; G. Sun, J. B. Khurgin, and R. A. Soref, J. Opt. Soc. Am. B 25,1748 2008.16J. B. Khurgin, G. Sun, and R. A. Soref, Appl. Phys. Lett. 94, 0711032009.17H. A. Haus, Waves and Fields in Optoelectronics, 1st ed. Prentice-Hall,Englewood Cliffs, NJ, 1984.FIG. 4. Color online Optimized PL enhancement as a function of aoriginal radiative efficiency rad at fixed Naa=1 nm2 and b absorptioncross section Naa at fixed rad=0.01 for several values of the molecule-metal spacing d and near resonance optical excitation and PL emission.101103-3 Sun, Khurgin, and Soref Appl. Phys. Lett. 94, 101103 2009Downloaded 29 Mar 2012 to 158.121.194.143. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions

Practical enhancement of photoluminescence by metal nanoparticles

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Practical enhancement of photoluminescence by metal nanoparticles

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