Optical Properties of Optical Properties of NanomaterialsNanomaterials

David G. StroudDavid G. Stroud, ,

Department of PhysicsDepartment of Physics,,

Ohio State University Columbus OH 43210Ohio State University Columbus OH 43210

Work supported by NSF Grant DMR01-04987, the Work supported by NSF Grant DMR01-04987, the Ohio Supercomputer Center, and BSFOhio Supercomputer Center, and BSF OUTLINEOUTLINE

Linear Optical Properties of NanocompositesLinear Optical Properties of Nanocomposites

Nonlinear Optical Properties of NanocompositesNonlinear Optical Properties of Nanocomposites Surface Plasmons in Nanoparticle ChainsSurface Plasmons in Nanoparticle Chains

Gold/DNA NanocompositesGold/DNA Nanocomposites ConclusionsConclusions

““Labors of the Months” (Norwich, England, ca. Labors of the Months” (Norwich, England, ca. 1480).1480).

(The ruby color is probably due to embedded(The ruby color is probably due to embeddedgold nanoparticles.)gold nanoparticles.)

What is the origin of the color? What is the origin of the color? Answer: ``surface plasmons’’ Answer: ``surface plasmons’’

An SP is a natural oscillation of the electron gas An SP is a natural oscillation of the electron gas inside a inside a goldgold nanospherenanosphere..

If the sphere is small compared to a If the sphere is small compared to a wavelength of light, and the light has a wavelength of light, and the light has a frequency close to that of the SP, then the SP frequency close to that of the SP, then the SP will absorb energy. will absorb energy.

The frequency of the SP depends on the The frequency of the SP depends on the dielectricdielectric functionfunction of the gold, and the of the gold, and the shapeshape of of the nanoparticle. For a spherical particle, the the nanoparticle. For a spherical particle, the frequency is about frequency is about 0.580.58 of the of the bulkbulk plasmaplasma frequencyfrequency. Thus, although the bulk plasma . Thus, although the bulk plasma frequency is in the UV, the SP frequency is in frequency is in the UV, the SP frequency is in the visible (in fact, close to 520 nm)the visible (in fact, close to 520 nm)

Sphere in an applied electric Sphere in an applied electric field field

Surface plasmon is excited when a long-Surface plasmon is excited when a long-wavelength electromagnetic wave is wavelength electromagnetic wave is

incident on a metallic sphereincident on a metallic sphere

Metallic sphere

EM wave

Incident electric field is E_0exp(-i w t)

Calculation of SP FrequencyCalculation of SP Frequency

Effective conductivity ofEffective conductivity ofa random metal-insulator composite in the a random metal-insulator composite in the

effective-medium approximationeffective-medium approximation

Note the broad ``surface plasmon peak and the Note the broad ``surface plasmon peak and the narrow Drude peak above the percolation narrow Drude peak above the percolation

threshold. [D. Stroud, Phys. Rev. B19, 1783 threshold. [D. Stroud, Phys. Rev. B19, 1783 (1979)](1979)]

Effective conductivity of a composite of Drude metal Effective conductivity of a composite of Drude metal and insulator: dots, numerical; full curves, effective-and insulator: dots, numerical; full curves, effective-medium approximation. [From X. Zhang and Stroud,medium approximation. [From X. Zhang and Stroud,

PRB49, 944 (1994).]PRB49, 944 (1994).]

Theory and experiment for transmissionTheory and experiment for transmissionthrough Ag/SiO2 filmsthrough Ag/SiO2 films

Theory: Maxwell-Garnett approximation (MGA) and effective-Theory: Maxwell-Garnett approximation (MGA) and effective-medium approximation (EMA) [D. Stroud,Phys. Rev. B19, medium approximation (EMA) [D. Stroud,Phys. Rev. B19,

1783 (1979)] ;1783 (1979)] ;Experiment [Priestley et al, Phys. Rev. B12, 2121 (1975)]. (f Experiment [Priestley et al, Phys. Rev. B12, 2121 (1975)]. (f

is the volume fraction of Ag.)is the volume fraction of Ag.)

NonlinearNonlinear opticaloptical propertiesproperties ofof nanomaterialsnanomaterials

SupposeSuppose wewe havehave a suspensiona suspension ofof nanoparticlesnanoparticles inin a hosta host (or(or somesome otherother compositecomposite whichwhich isis structuredstructured onon thethe nanoscale).nanoscale).

IfIf anan EMEM wavewave isis appliedapplied, , thethe locallocal electricelectric fieldfield maymay bebe hugelyhugely enhancedenhanced near an SP near an SP resonanceresonance. .

Ifso,one expects various nonlinearIfso,one expects various nonlinear susceptibilitiessusceptibilities, , whichwhich dependdepend onon higherhigher powerspowers of the electric field, to be of the electric field, to be enhancedenhanced eveneven moremore. .

The Kerr Susceptibility is The Kerr Susceptibility is defined bydefined by

where D is the electric displacement, E is the where D is the electric displacement, E is the electric field, and epsilon and chi are the linear electric field, and epsilon and chi are the linear

and nonlinear electric susceptibilities.and nonlinear electric susceptibilities.

If the electric field is locally large, as near an SP If the electric field is locally large, as near an SP resonance, then its cube is correspondingly resonance, then its cube is correspondingly

larger. Thus, near an SP resonance, one expects larger. Thus, near an SP resonance, one expects a huge enhancement of the cubic nonlinear (Kerr) a huge enhancement of the cubic nonlinear (Kerr)

susceptibility.susceptibility.

Kerr susceptibility for a dilute Kerr susceptibility for a dilute suspension of coated spheressuspension of coated spheres

Cubic nonlinear (Kerr) susceptibility for a dilute suspension Cubic nonlinear (Kerr) susceptibility for a dilute suspension of coated metal particles in a glass host, calculated in of coated metal particles in a glass host, calculated in

Maxwell-Garnett approximation [X. Zhang, D. Stroud, Phys. Maxwell-Garnett approximation [X. Zhang, D. Stroud, Phys. Rev. B49, 944 (1994)]. Inset: linear dielectric function of Rev. B49, 944 (1994)]. Inset: linear dielectric function of

same composite. Left and right are for two coating same composite. Left and right are for two coating dielectric constants.dielectric constants.

Kerr enhancement factor for Kerr enhancement factor for metal-insulator compositemetal-insulator composite

Kerr enhancement factor for a random metal-Kerr enhancement factor for a random metal-insulator composite, assuming (left) metal and insulator composite, assuming (left) metal and

(right) insulator is nonlinear. Calculation is (right) insulator is nonlinear. Calculation is carried out numerically, at the metal-insulator carried out numerically, at the metal-insulator

percolation threshold.percolation threshold.

Real and imaginary parts of the SHG susceptibility for a Real and imaginary parts of the SHG susceptibility for a dilute suspension of of metal spheres coated with a dilute suspension of of metal spheres coated with a

nonlinear dielectricnonlinear dielectric[Hui, Xu, and Stroud, Phys. Rev. B69, 014203 (2004)][Hui, Xu, and Stroud, Phys. Rev. B69, 014203 (2004)]

Left and right panels show susceptibility Left and right panels show susceptibility enhancement per unit volume of nonlinear material enhancement per unit volume of nonlinear material for two different ratios of coating thickness to metal for two different ratios of coating thickness to metal

particle radius. particle radius.

Real and imaginary parts of the THG Real and imaginary parts of the THG susceptibility for a dilute suspension of coated susceptibility for a dilute suspension of coated

metal spheres in a dielectric hostmetal spheres in a dielectric host

Susceptility enhancement per unit volume for third-Susceptility enhancement per unit volume for third-harmonic generation (THG) for coated metal sphere harmonic generation (THG) for coated metal sphere

suspension [from Hui, Xu, and Stroud, PRB69, 014202 suspension [from Hui, Xu, and Stroud, PRB69, 014202 (2004)](2004)]

Faraday Rotation in Faraday Rotation in Composites:Composites:

enhanced near SP resonanceenhanced near SP resonance

Real and Real and imaginary parts of imaginary parts of

the Faraday the Faraday rotation angle in a rotation angle in a

composite of composite of Drude metal and Drude metal and

insulator in a insulator in a magnetic field magnetic field

(Xia, Hui, Stroud, (Xia, Hui, Stroud, J. Appl. Phys. 67, J. Appl. Phys. 67,

2736 (1990)2736 (1990)

Faraday rotation in granular Faraday rotation in granular ferromagnetsferromagnets

Frequency-dependence of the real and imaginary parts of Frequency-dependence of the real and imaginary parts of the Faraday rotation angle for a dilute suspension of the Faraday rotation angle for a dilute suspension of

ferromagnet in an insulator at two different temperatures ferromagnet in an insulator at two different temperatures below the Curie temperature [Xia, Hui, and Stroud, J. Appl. below the Curie temperature [Xia, Hui, and Stroud, J. Appl.

Phys. 67, 2736 (1990)].Phys. 67, 2736 (1990)].

Nanoparticle chainNanoparticle chain

Surface plasmons can propagate along a periodic Surface plasmons can propagate along a periodic chain of metallic nanoparticles (above)chain of metallic nanoparticles (above)

a

d

Photon STM Image of a Chain Photon STM Image of a Chain of Au nanoparticles [from of Au nanoparticles [from Krenn et al, PRL 82, 2590 Krenn et al, PRL 82, 2590

(1999)](1999)]

Individual particles: 100x100x40 nm, separated Individual particles: 100x100x40 nm, separated by 100 nm and deposited on an ITO substrateby 100 nm and deposited on an ITO substrate

Calculation of SP modes in Calculation of SP modes in nanoparticle chainnanoparticle chain

In the dipole approximation, there are In the dipole approximation, there are threethree SP SP modes on each sphere, two polarized modes on each sphere, two polarized perpendicularperpendicular to chain, and one polarized to chain, and one polarized parallelparallel. . The propagating waves are linear combinations The propagating waves are linear combinations of these modes on different spheres. of these modes on different spheres.

In our calculation, In our calculation, wewe includeinclude allall multipolesmultipoles, not , not just dipoles. Then there are a infinite number of just dipoles. Then there are a infinite number of branches, but only lowest three travel with branches, but only lowest three travel with substantial group velocity.substantial group velocity.

Can be compared to Can be compared to nanoplasmonicnanoplasmonic experimentsexperiments, , as discussed by Brongersma et al [Phys. Rev. as discussed by Brongersma et al [Phys. Rev. B62, 16356 (2000) and S. A. Maier et al [Nature B62, 16356 (2000) and S. A. Maier et al [Nature Materials 2, 229 (2003)]Materials 2, 229 (2003)]

Surface plasmon dispersion Surface plasmon dispersion relations, nanoparticle chainrelations, nanoparticle chain

Calculated surface plasmon dispersion relations (left) and Calculated surface plasmon dispersion relations (left) and group velocity of energy for the lowest two bands in a metal group velocity of energy for the lowest two bands in a metal nanoparticle chain. nanoparticle chain. SolidSolid curves: Lcurves: L modesmodes; ; dotteddotted curves: Tcurves: T

modesmodes. Light curves; . Light curves; dipoledipole approximation; dark curves, approximation; dark curves, including including allall multipolesmultipoles. a/d=0.45 [from S. Y. Park and D. . a/d=0.45 [from S. Y. Park and D. Stroud , Phys. Rev. B (in press); a= Stroud , Phys. Rev. B (in press); a= particleparticle radiusradius; d= ; d=

particleparticle separationseparation]]

Composites of Au Composites of Au nanoparticles and DNA strandsnanoparticles and DNA strands

Suppose we put Au nanoparticles and DNA Suppose we put Au nanoparticles and DNA strands in an acqueous suspension.strands in an acqueous suspension.

Certain DNA strands (capped with thiol Certain DNA strands (capped with thiol groups) can attach to Au.groups) can attach to Au.

At high T, Au particles float in suspension, At high T, Au particles float in suspension, with DNA strands attached.with DNA strands attached.

At low T, strands on different grains react At low T, strands on different grains react to form links. Particles agglomerate to to form links. Particles agglomerate to form a gel-like structure.form a gel-like structure.

This behavior is easily detected optically.This behavior is easily detected optically.

MethodologyMethodology

To determine structure, we calculate the To determine structure, we calculate the probability that any two bonds on different Au probability that any two bonds on different Au particles form a link, using an equilibrium particles form a link, using an equilibrium condition from simple chemical reaction theory. condition from simple chemical reaction theory.

Structure determined by Structure determined by twotwo differentdifferent modelsmodels: (i) : (i) PercolationPercolation modelmodel; (ii) More elaborate model ; (ii) More elaborate model involving involving reaction-limitedreaction-limited cluster-clustercluster-cluster aggregationaggregation (RLCA) (RLCA)

To treat optical properties (for any given To treat optical properties (for any given structure) use the ``Discrete Dipole structure) use the ``Discrete Dipole Approximation’’ (multiple scattering approach).Approximation’’ (multiple scattering approach).

References: S. Y. Park and D. Stroud, Phys. Rev. References: S. Y. Park and D. Stroud, Phys. Rev. B67, 212202 (2003); B68, 224201 (2003).B67, 212202 (2003); B68, 224201 (2003).

Au/DNA suspension in liquid Au/DNA suspension in liquid statestate

At high T, Au particles float around in aqueous suspension. At high T, Au particles float around in aqueous suspension. Single strands of DNA capped with thiol groups are Single strands of DNA capped with thiol groups are attached.attached.

Melting of Au/DNA cluster, Melting of Au/DNA cluster, two different modelstwo different models

(a), (b) and (c) are a percolation model: all particles on a (a), (b) and (c) are a percolation model: all particles on a cubic lattice. (a): all bonds present; (b) 50% of bonds cubic lattice. (a): all bonds present; (b) 50% of bonds

present; (c) 20% of bonds present. (d) Low temperature present; (c) 20% of bonds present. (d) Low temperature cluster formed by reaction-limited cluster-cluster cluster formed by reaction-limited cluster-cluster

aggregation (RLCA)aggregation (RLCA)

Extinction coefficient, dilute Extinction coefficient, dilute suspensionsuspension

Calculated (full curves) and measured (dashed curves) Calculated (full curves) and measured (dashed curves) extinction coefficient for a dilute Au suspension, plotted extinction coefficient for a dilute Au suspension, plotted

versus wavelengthversus wavelength

Extinction coefficient for Extinction coefficient for compact Au/DNA clusterscompact Au/DNA clusters

Extinction coefficient per unit volume, plotted versus wavelength (in Extinction coefficient per unit volume, plotted versus wavelength (in nm) for LxLxL compact clusters, as calculated using the Discrete nm) for LxLxL compact clusters, as calculated using the Discrete Dipole Approximation (DDA) (from Park and Stroud, 2003)Dipole Approximation (DDA) (from Park and Stroud, 2003)

Calculated extinction Calculated extinction coefficient, RLCA clusterscoefficient, RLCA clusters

Calculated extinction coefficient versus wavelength Calculated extinction coefficient versus wavelength for RLCA clusters with number of monomers varying for RLCA clusters with number of monomers varying

from 1 to 343. from 1 to 343.

Extinction coefficient versus Extinction coefficient versus wavelength, percolation wavelength, percolation

modelmodel

Extinction coefficient versus wavelength for different Extinction coefficient versus wavelength for different fractions p of Au nanoparticles on a 10 x 10 x 10 simple fractions p of Au nanoparticles on a 10 x 10 x 10 simple cubic lattice. ``p=0’’ represents an isolated Au particle. cubic lattice. ``p=0’’ represents an isolated Au particle.

Inset: C, B, and A are isolated particles, compact clusters, Inset: C, B, and A are isolated particles, compact clusters, and RLCA clusters. Melting more closely resembles a and RLCA clusters. Melting more closely resembles a

transition from C to A in experiments.transition from C to A in experiments.

Observed absorptance: Observed absorptance: comparison of unlinked and comparison of unlinked and aggregated Au nanoparticlesaggregated Au nanoparticles

Absorptance of unlinked and aggregated Au nanoparticles, Absorptance of unlinked and aggregated Au nanoparticles, as measured by Storhoff et alas measured by Storhoff et al

[J. Am. Chem. Soc. 120, 1959 (1998)][J. Am. Chem. Soc. 120, 1959 (1998)]

Calculated extinction Calculated extinction coefficients versus coefficients versus

temperature at 520 nmtemperature at 520 nm

Normalized extinction coefficient at wavelength 520 nm, calculated Normalized extinction coefficient at wavelength 520 nm, calculated for two different models, plotted vs. temperature in C. Full curves: for two different models, plotted vs. temperature in C. Full curves: percolation model (3 diff. Monomer numbers). Open circles: RLCA percolation model (3 diff. Monomer numbers). Open circles: RLCA

model.model.

Extinction coefficient vs. T at Extinction coefficient vs. T at 520 nm for different particle 520 nm for different particle

sizessizes

Calculated extinction coefficient versus T at wavelength Calculated extinction coefficient versus T at wavelength 520 nm for particle radius 5, 10, and 20 nm. Inset: 520 nm for particle radius 5, 10, and 20 nm. Inset:

comparison of extinction for percolation model (open comparison of extinction for percolation model (open circles) and RLCA model (squares). Full line in inset is circles) and RLCA model (squares). Full line in inset is

probability that a given link is broken at T. probability that a given link is broken at T.

Measured extinction at fixed Measured extinction at fixed wavelength vs. temperaturewavelength vs. temperature

(left) extinction of an aggregate (full curve) and isolated (left) extinction of an aggregate (full curve) and isolated particles (dashed) at 260nm.particles (dashed) at 260nm.

[Storhoff et al, JACS 122, 4640 (2000)]. (right) extinction of [Storhoff et al, JACS 122, 4640 (2000)]. (right) extinction of an aggregate at 260 nm made from Au particles of three an aggregate at 260 nm made from Au particles of three

different diameters [C. H. Kiang, Physica A321, 164 (2003)] different diameters [C. H. Kiang, Physica A321, 164 (2003)]

DNA/Au nanocomposite system

R. Jin, et. al, J. Am. Chem. Soc. 125, 1643 (2003).

R. Elghanian, et. al., Science 277, 1078 (1997).

Linker DNA

1. Expected phase diagram

2. Morpologies from a structural model

3. DDA calculation (left) of extinction cross section (S. Y. Park and D. Stroud, Phys. Rev. B68 (224201 (2003)

gel sol Ind. particles

Gel-sol transition

meltingtransition T0

gel sol

near melting transition

Gel-soltransition

meltingtransition

Experiment

Work in ProgressWork in Progress

More realistic model for gold/DNA More realistic model for gold/DNA nanocompositesnanocomposites

Selective detection of organic molecules, Selective detection of organic molecules, using gold nanoparticlesusing gold nanoparticles

SP dispersion relations in other nanoparticle SP dispersion relations in other nanoparticle geometriesgeometries

Diffuse and coherent SHG and THG Diffuse and coherent SHG and THG generationgeneration

Control of SP resonances using liquid crystals.Control of SP resonances using liquid crystals.

CurrentCurrent CollaboratorsCollaborators

Dr. Sung Yong Park, Prof. Pak-Ming Hui, Dr. Sung Yong Park, Prof. Pak-Ming Hui, Kwangmoo Kim, Ivan Tornes, Dr. Ha Youn Kwangmoo Kim, Ivan Tornes, Dr. Ha Youn Lee, Prof. Brad Trees, Prof. David J. Bergman, Lee, Prof. Brad Trees, Prof. David J. Bergman, Prof. Y. M. Strelniker, Dr. W. A. Al-Saidi, D. Prof. Y. M. Strelniker, Dr. W. A. Al-Saidi, D. Valdez-Balderas, Ivan Tornes, K. KobayashiValdez-Balderas, Ivan Tornes, K. Kobayashi

Work Supported by the U. S. National Work Supported by the U. S. National Science Foundation, U. S.-Israel Binational Science Foundation, U. S.-Israel Binational Science Foundation, and Ohio Science Foundation, and Ohio Supercomputer Center.Supercomputer Center.