Cavity resonators of metal-coated dielectric nanorodsJ. J. Diao, Shuogang Huang, and M. E. Reeves Citation: The Journal of Chemical Physics 122, 146101 (2005); doi: 10.1063/1.1869393 View online: http://dx.doi.org/10.1063/1.1869393 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/122/14?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Terahertz surface plasmons excitation by nonlinear mixing of lasers in over ultrathin metal film coated dielectric J. Appl. Phys. 114, 053101 (2013); 10.1063/1.4817091 Non Linear Optical Characterization of MetalDielectric SubmicroSpheres AIP Conf. Proc. 960, 231 (2007); 10.1063/1.2825125 Manipulation of dielectric particles using photonic crystal cavities Appl. Phys. Lett. 89, 253114 (2006); 10.1063/1.2420771 The resonant electromagnetic fields of an array of metallic slits acting as Fabry-Perot cavities J. Appl. Phys. 99, 124903 (2006); 10.1063/1.2204818 Adjustable resonant cavity for measuring the complex permittivity of dielectric materials Rev. Sci. Instrum. 71, 3207 (2000); 10.1063/1.1304865

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:

128.83.63.20 On: Wed, 26 Nov 2014 20:21:39

Cavity resonators of metal-coated dielectric nanorodsJ. J. Diao and Shuogang HuangDepartment of Physics, The George Washington University, Washington, DC 20052

M. E. Reevesa!

Department of Physics, The George Washington University, Washington, DC 20052Materials and Sensors Branch, Code 6363, Naval Research Laboratory, Washington, DC 20375

sReceived 29 November 2004; accepted 18 January 2005; published online 8 April 2005d

Metallic nanoparticles bridge the length scale between atoms and crystals, exhibiting mesoscopicproperties unique to their size. Thus, they have generated much interest for their potentialapplications as chemical or biological sensors and particularly as waveguides for light in nanoscalestructures.fY. W. C. Cao, R. C. Jin, and C. A. Mirkin, Science297, 1536s2002d; H. J. Lezecet al.,Science297, 820 s2002d; S. A. Maier, P. G. Kik, and H. A. Atwater, Appl. Phys. Lett.81, 1714s2002d; J. M. Oliva and S. K. Gray, Chem. Phys. Lett.379, 325 s2003dg. One important directionof research into the properties of individual metal nanoparticles involves the controlled variation oftheir geometry, which can yield new and tunable optical properties that simple sphericalconfigurations do not possess.fT. S. Ahmadi, Z. L. Wang, T. C. Green, A. Henglein, and M. A.Ei-Sayed, Science272, 1924s1996dg. A prime example of this is the core-shell nanostructure thathas a central material surrounded by differing cladding layer. ©2005 American Institute of Physics.fDOI: 10.1063/1.1869393g

In this paper, we will discuss our theoretical investiga-tion of cylindrical nanostructures that have been demon-strated to have unique, tunable optical properties.1–8 Muchwork, to date, has emphasized the role of the surface plas-mon resonance of spherical metal-coated nanoshells basedon Mie’s scattering theory.9–12Thus, our work stands in con-trast by focussing on the bulk resonance arising from a me-tallic shell surrounding a dielectric nanorod. Our resultsshow that in addition to a plasmon resonance, a cavity-typeresonance contributes to the electromagnetic response ofnanoparticles, and both can be tuned to give a desired elec-tromagnetic response. These effects have been observed inthe optical response of gold-coated TiO2 and SiO2 nanorods.7

The model geometry of the metal-coated nanorod isshown in Fig. 1, i.e., a miniature classical cylindrical reso-nator. We find the dominant cutoff modesthe lowest fre-quency moded by solving wave equations for the electric andmagnetic fields. In a cylindrical, as opposed to a coaxialresonator, no TEM wave is found; and only TE and TMmodes are predicted. For a classical cylindrical waveguidecavity, the resonant frequency of the TEnml mode is given by

fnml =c

2pÎm1e1

ÎSpnm8

r1D2

+ S lp

LD2

. s1d

The resonant frequency of theTMnml mode is given by

fnml8 =c

2pÎm1e1

ÎSpnm

r1D2

+ S lp

LD2

, s2d

wherec is the speed of light in vacuum,r1 is the radius, andL is the length of the cavity,m1 is the relative permeability,ande1 is the relative permittivity of the dielectric nanorods.Pnm andPnm8 are themth root of thenth Bessel’s function andits derivative.13 By checking values ofPnm andPnm8 , we findthe dominant TE mode is TE111 with P118 =1.841, while thedominant TM mode is the TM010 with P01=2.405. Under thecondition of 2r1,L, the cutoff mode is TE111.

13 Thus, for acylindrical cavity resonator, the frequency of the main,TE111, mode is obtained

f111=c

2pÎm1e1

ÎS1.841

r1D2

+ Sp

LD2

. s3d

Equations3d shows that the cavity’s resonance can be con-trolled by adjusting the radius and the length of the nano-rod’s dielectric core. Of particular interest are gold-coatednanorods, which are actually wirelike structures, 100–200nm in diameter and,10 mm in length. For nanowires withL@ r1, the resonant frequency can be written compactly as

f111<1.841c

2pr1Îm1e1

. s4d

Thus, a nanowire’s resonant frequency depends only on theradius of its dielectric core.

The optical properties of gold-coated TiO2 and SiO2 na-norods have been measured by Cao’s group.7 Some of thespectra exhibit two peaks, consistent with a surface plasmonresonance and with a bulk, geometric resonance. For ex-

adAuthor to whom correspondence should be addressed. Electronic mail:reevesme@gwu.edu

THE JOURNAL OF CHEMICAL PHYSICS122, 146101s2005d

0021-9606/2005/122~14!/146101/2/$22.50 © 2005 American Institute of Physics122, 146101-1

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:

128.83.63.20 On: Wed, 26 Nov 2014 20:21:39

ample, Fig. 1sad depicts the absorbtion spectrum of 180 nmTiO2 nanorods coated with 4 nm Au. We fit the apparentpeak and broad shoulder to two peaks: one at 549±1 nm andthe other at 626±3 nm. The bulk resonance is predicted byEq. s4d to lie between 613 and 686 nm with the range brack-eted by the uncertainty in the dielectric constant of the po-rous nanostructure of TiO2, 4,e1,5.14,15The shorter wave-length peak, at 549±1 nm, is attributed to Mie scattering bysurface plasmon as described in the original experimentalpaper, Ref. 7.

The same effect is shown in Fig. 1sbd for 200 nm SiO2

nanorods coated with 6 nm of Au. The spectrum shows two

peaks, one at 484 nm and one clearly below 400 nmsfittedwith a centroid of 300±112 nmd. The peak at 484±13 nm isvery close to our prediction for the bulk cavity resonance,and the 300 nm peak is likely due to Mie scattering. In amacroscopic system, the thickness of the metal shell wouldexceed the electromagnetic skin depth. However, fornanoshells, the metallic shell is much thinner, a few nanom-eters. Thus, the incident electromagnetic wave can penetrateinto the cavity, but only for cases in which the metallic coat-ing is less than the electromagnetic skin depth,,10 nm forgold. This fact is consistent with Cao’s experiments, inwhich only one Mie scattering peak is observed for goldshells thicker than 10 nm.7 The fact that the peak is broad islikely due to the nonuniform radii of the nanorodssgiving astatistical spread in frequenciesd7 but also attributable to en-ergy lost by radiating through ultrathin or incomplete shells.6

Thus, in this paper, we present a study of mini cylindri-cal resonators, formed by dielectric nanorods coated by thinmetallic shells. These core-shell structures act as cylindricalelectromagnetic cavities, whose resonance displays tunabil-ity controlled by their geometry. Our theoretical results de-scribe previously unexplained peaks in the electromagneticspectrum of gold-coated TiO2 and SiO2 nanorods.

This work was supported by the Army Research Officeunder Grant No. DAAD19-01-1058.

1Y. W. C. Cao, R. C. Jin, and C. A. Mirkin, Science297, 1536s2002d.2H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J.Garcia-Vidal, and T. W. Ebbesen, Science297, 820 s2002d.

3S. A. Maier, P. G. Kik, and H. A. Atwater, Appl. Phys. Lett.81, 1714s2002d.

4J. M. Oliva and S. K. Gray, Chem. Phys. Lett.379, 325 s2003d.5T. S. Ahmadi, Z. L. Wang, T. C. Green, A. Henglein, and M. A. Ei-Sayed,Science272, 1924s1996d.

6S. J. Oldenburg, R. D. Averitt, S. L. Westcott, and N. J. Halas, Chem.Phys. Lett. 288, 243 s1998d.

7S. J. Limmer, T. P. Chou, and G. Cao, J. Phys. Chem. B107, 13313s2003d.

8J. J. Diao and G. D. Chen, J. Phys. D34, L79 s2001d.9S. J. Oldenburg, G. D. Hale, J. B. Jackson, and N. J. Halas, Appl. Phys.Lett. 75, 1063s1999d.

10R. D. Averitt, S. L. Westcott, and N. J. Halas, J. Opt. Soc. Am. B16, 1824s1999d.

11C. Radloff and N. J. Halas, Nano Lett.4, 1323s2004d.12E. Hao, S. Li, R. C. Bailey, S. Zou, G. C. Schatz, and J. T. Hupp, J. Phys.

Chem. B 108, 1224s2004d.13P. M. Pozar,Microwave Engineering, 2nd ed.sWiley, New York, 1998d.14D. Mardare and P. Hones, Mater. Sci. Eng., BB68, 42 s1999d.15D.-J. Won, C.-H. Wang, H.-K. Jang, and D.-J. Choi, Appl. Phys. A: Mater.

Sci. Process.A73, 595 s2001d.

FIG. 1. Experimental absorbance datasopen circlesd and multipeak fitssolidlined for Au-coated TiO2 and SiO2 nanorodssRef. 7d. The dotted lines rep-resent the deconstruction of the multipeak fit.sad Results for 180 nm TiO2nanorods coated with 4 nm thick Au andsbd for 200 nm SiO2 nanorodscoated with 6 nm of gold. The inset shows the idealized geometry uponwhich our calculation is based:r1 is the core radius andL is the length of thenanorod.

146101-2 Diao, Huang, and Reeves J. Chem. Phys. 122, 146101 ~2005!

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:

128.83.63.20 On: Wed, 26 Nov 2014 20:21:39