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					Optical Properties of Nanomaterials
                         David G. Stroud,
                   Department of Physics,
        Ohio State University Columbus OH 43210
          Work supported by NSF Grant DMR01-04987, the
                       Ohio Supercomputer Center, and BSF


        Linear Optical Properties of Nanocomposites

        Nonlinear Optical Properties of Nanocomposites

        Surface Plasmons in Nanoparticle Chains

        Gold/DNA Nanocomposites

“Labors of the Months” (Norwich, England, ca. 1480).
    (The ruby color is probably due to embedded
                gold nanoparticles.)
     What is the origin of the color?
     Answer: ``surface plasmons’’
   An SP is a natural oscillation of the electron gas
    inside a gold nanosphere.
   If the sphere is small compared to a wavelength
    of light, and the light has a frequency close to
    that of the SP, then the SP will absorb energy.
   The frequency of the SP depends on the
    dielectric function of the gold, and the shape of
    the nanoparticle. For a spherical particle, the
    frequency is about 0.58 of the bulk plasma
    frequency. Thus, although the bulk plasma
    frequency is in the UV, the SP frequency is in
    the visible (in fact, close to 520 nm)
Sphere in an applied electric field

              Metallic sphere      Incident electric field
                                   is E_0exp(-i w t)
   EM wave

       Surface plasmon is excited when a long-
   wavelength electromagnetic wave is incident on a
                    metallic sphere
Calculation of SP Frequency
         Effective conductivity of
a random metal-insulator composite in the
     effective-medium approximation

     Note the broad ``surface plasmon peak and the
   narrow Drude peak above the percolation threshold.
        [D. Stroud, Phys. Rev. B19, 1783 (1979)]
Effective conductivity of a composite of Drude metal and
insulator: dots, numerical; full curves, effective-medium
       approximation. [From X. Zhang and Stroud,
                   PRB49, 944 (1994).]
Theory and experiment for transmission
        through Ag/SiO2 films

Theory: Maxwell-Garnett approximation (MGA) and effective-medium
  approximation (EMA) [D. Stroud,Phys. Rev. B19, 1783 (1979)] ;
 Experiment [Priestley et al, Phys. Rev. B12, 2121 (1975)]. (f is the
                       volume fraction of Ag.)
      Nonlinear optical properties of
   Suppose we have a suspension of nanoparticles
    in a host (or some other composite which is
    structured on the nanoscale).
    If an EM wave is applied, the local electric field
    may be hugely enhanced near an SP resonance.
    Ifso,one expects various nonlinear
    susceptibilities, which depend on higher powers
    of the electric field, to be enhanced even more.
     The Kerr Susceptibility is
           defined by

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

    If the electric field is locally large, as near an SP
   resonance, then its cube is correspondingly larger.
    Thus, near an SP resonance, one expects a huge
enhancement of the cubic nonlinear (Kerr) susceptibility.
Kerr susceptibility for a dilute
suspension of coated spheres

  Cubic nonlinear (Kerr) susceptibility for a dilute suspension of coated
      metal particles in a glass host, calculated in Maxwell-Garnett
   approximation [X. Zhang, D. Stroud, Phys. Rev. B49, 944 (1994)].
   Inset: linear dielectric function of same composite. Left and right
                  are for two coating dielectric constants.
Kerr enhancement factor for
 metal-insulator composite

Kerr enhancement factor for a random metal-insulator
 composite, assuming (left) metal and (right) insulator
is nonlinear. Calculation is carried out numerically, at
       the metal-insulator percolation threshold.
 Real and imaginary parts of the SHG susceptibility for a dilute
suspension of of metal spheres coated with a nonlinear dielectric
     [Hui, Xu, and Stroud, Phys. Rev. B69, 014203 (2004)]

     Left and right panels show susceptibility enhancement per
     unit volume of nonlinear material for two different ratios of
              coating thickness to metal particle radius.
Real and imaginary parts of the THG susceptibility for a
dilute suspension of coated metal spheres in a dielectric

     Susceptility enhancement per unit volume for third-harmonic
     generation (THG) for coated metal sphere suspension [from
            Hui, Xu, and Stroud, PRB69, 014202 (2004)]
Faraday Rotation in Composites:
 enhanced near SP resonance

                      Real and imaginary
                     parts of the Faraday
                      rotation angle in a
                     composite of Drude
                      metal and insulator
                      in a magnetic field
                     (Xia, Hui, Stroud, J.
                     Appl. Phys. 67, 2736
Faraday rotation in granular

    Frequency-dependence of the real and imaginary parts of the
 Faraday rotation angle for a dilute suspension of ferromagnet in an
insulator at two different temperatures below the Curie temperature
       [Xia, Hui, and Stroud, J. Appl. Phys. 67, 2736 (1990)].
           Nanoparticle chain



Surface plasmons can propagate along a periodic
  chain of metallic nanoparticles (above)
Photon STM Image of a Chain of
Au nanoparticles [from Krenn et
   al, PRL 82, 2590 (1999)]

  Individual particles: 100x100x40 nm, separated by 100
          nm and deposited on an ITO substrate
         Calculation of SP modes in
             nanoparticle chain
   In the dipole approximation, there are three SP modes
    on each sphere, two polarized perpendicular to chain,
    and one polarized parallel. The propagating waves are
    linear combinations of these modes on different spheres.
   In our calculation, we include all multipoles, not just
    dipoles. Then there are a infinite number of branches,
    but only lowest three travel with substantial group
   Can be compared to nanoplasmonic experiments, as
    discussed by Brongersma et al [Phys. Rev. B62, 16356
    (2000) and S. A. Maier et al [Nature Materials 2, 229
 Surface plasmon dispersion
relations, nanoparticle chain

  Calculated surface plasmon dispersion relations (left) and group
 velocity of energy for the lowest two bands in a metal nanoparticle
   chain. Solid curves: L modes; dotted curves: T modes. Light
 curves; dipole approximation; dark curves, including all multipoles.
 a/d=0.45 [from S. Y. Park and D. Stroud , Phys. Rev. B (in press);
              a= particle radius; d= particle separation]
Composites of Au nanoparticles and
          DNA strands
   Suppose we put Au nanoparticles and DNA
    strands in an acqueous suspension.
   Certain DNA strands (capped with thiol groups)
    can attach to Au.
   At high T, Au particles float in suspension, with
    DNA strands attached.
   At low T, strands on different grains react to
    form links. Particles agglomerate to form a gel-
    like structure.
   This behavior is easily detected optically.
   To determine structure, we calculate the probability that
    any two bonds on different Au particles form a link,
    using an equilibrium condition from simple chemical
    reaction theory.
   Structure determined by two different models: (i)
    Percolation model; (ii) More elaborate model involving
    reaction-limited cluster-cluster aggregation (RLCA)
   To treat optical properties (for any given structure) use
    the ``Discrete Dipole Approximation’’ (multiple
    scattering approach).
   References: S. Y. Park and D. Stroud, Phys. Rev. B67,
    212202 (2003); B68, 224201 (2003).
    Au/DNA suspension in liquid state

   At high T, Au particles float around in aqueous suspension. Single
    strands of DNA capped with thiol groups are attached.
Melting of Au/DNA cluster, two
       different models

(a), (b) and (c) are a percolation model: all particles on a cubic
 lattice. (a): all bonds present; (b) 50% of bonds present; (c)
20% of bonds present. (d) Low temperature cluster formed by
       reaction-limited cluster-cluster aggregation (RLCA)
Extinction coefficient, dilute

Calculated (full curves) and measured (dashed curves) extinction
coefficient for a dilute Au suspension, plotted versus wavelength
    Extinction coefficient for compact
             Au/DNA clusters

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

  Calculated extinction coefficient versus wavelength for RLCA
   clusters with number of monomers varying from 1 to 343.
 Extinction coefficient versus
wavelength, percolation model

Extinction coefficient versus wavelength for different fractions p of Au
     nanoparticles on a 10 x 10 x 10 simple cubic lattice. ``p=0’’
  represents an isolated Au particle. Inset: C, B, and A are isolated
 particles, compact clusters, and RLCA clusters. Melting more closely
           resembles a transition from C to A in experiments.
  Observed absorptance:
comparison of unlinked and
aggregated Au nanoparticles

Absorptance of unlinked and aggregated Au nanoparticles, as
                measured by Storhoff et al
          [J. Am. Chem. Soc. 120, 1959 (1998)]
Calculated extinction coefficients
 versus temperature at 520 nm

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

Calculated extinction coefficient versus T at wavelength 520 nm for
 particle radius 5, 10, and 20 nm. Inset: comparison of extinction
  for percolation model (open circles) and RLCA model (squares).
   Full line in inset is probability that a given link is broken at T.
Measured extinction at fixed
wavelength vs. temperature

(left) extinction of an aggregate (full curve) and isolated particles
                        (dashed) at 260nm.
 [Storhoff et al, JACS 122, 4640 (2000)]. (right) extinction of an
  aggregate at 260 nm made from Au particles of three different
         diameters [C. H. Kiang, Physica A321, 164 (2003)]
DNA/Au nanocomposite system
                            Linker DNA

                                                         1. Expected phase diagram

                                                                 Gel-sol                        melting
                                                       0         transition                     transition
R. Elghanian, et. al.,                                     gel                 sol                          Ind. particles
Science 277, 1078 (1997).

2. Morpologies from a structural                    3. DDA calculation (left) of extinction
   model                                               cross section (S. Y. Park and D.
                                                       Stroud, Phys. Rev. B68 (224201 (2003)

                     gel                      sol                                            melting

                                     near melting
                                                                                           R. Jin, et. al, J. Am. Chem. Soc. 125, 1643 (2003).
              Work in Progress
   More realistic model for gold/DNA
   Selective detection of organic molecules, using
    gold nanoparticles
   SP dispersion relations in other nanoparticle
   Diffuse and coherent SHG and THG generation
   Control of SP resonances using liquid crystals.
          Current Collaborators

   Dr. Sung Yong Park, Prof. Pak-Ming Hui,
    Kwangmoo Kim, Ivan Tornes, Dr. Ha Youn Lee,
    Prof. Brad Trees, Prof. David J. Bergman, Prof.
    Y. M. Strelniker, Dr. W. A. Al-Saidi, D. Valdez-
    Balderas, Ivan Tornes, K. Kobayashi
   Work Supported by the U. S. National Science
    Foundation, U. S.-Israel Binational Science
    Foundation, and Ohio Supercomputer Center.