Saturable absorption and optical limiting in semicontinuous gold films.

1. Saturable absorption and optical limiting in semicontinuous gold films. Giovanni Piredda1,David D. Smith2,Mark Nelson3, Youngkwon Yoon1, Robert W. Boyd1,Rongfu Xiao4and Bettina Wendling5 1The Institute of Optics, University of Rochester 2NASA Marshall Space Flight Center 3New Mexico State University 4Department of Physics, Hong Kong University of Science and Technology, Hong Kong 5Max Planck Institute for Polymer Science Symposium On Materials Research 2006

2. The nonlinear optical properties of gold-silica composite materials vary greatly as a function of composition and wavelength. • These materials can be both saturable absorbers and optical limiters. • We present our experimental study: • measurement of the imaginary part of the optical Kerr coefficient • connection between the linear and nonlinear properties • connection between the nonlinear properties and the “percolation threshold”

3. One minute course on metal-dielectric composites We study composite materials that can be described by an effective dielectric constant: the size of each grain of material and the distances between them are much smaller than the wavelength of light; a plane wave in these kinds of media is not destroyed by scattering. In certain metal-dielectric composites a resonance appears in the effective dielectric constant: the plasmon resonance. At the plasmon resonance, the nonlinear susceptibility of the material is enhanced.

4. Isolated nanoparticles in a dielectric matrix Maxwell Garnett theory: εi εh (for spherical inclusions) resonance close to High metal concentrations percolation Interactions between nanoparticles Electrodynamic retardation Effective medium theories Exact (quasi-static)results at percolation Brouers – Shalaev theory* Exact calculations *F. Brouers et al., PRB 55, 13234 (1997)

5. Nonlinear optics of gold Three contributions to the nonlinear refractive index of gold nanoparticles with response time < ≈ 1 ps. Intraband contribution (it does not exist in bulk): confinement of the conduction electrons inside the nanoparticles. Contributes a small induced absorption Interband contribution: at 530 nm, saturation of the interband absorption Hot electron contribution: the optical pulse modifies the equilibrium distribution of electrons (“Fermi smearing”) Largest contribution Balance: gold is an induced absorber for ps pulses at 530 nm

6. Nonlinear optics of metal-dielectric composites Nanoparticles: at the plasmon resonance the field in the metal is enhanced; the nonlinearity of the composite is consequently enhanced. In the Maxwell Garnett regime the third order Kerr susceptibility can be calculated assuming that the field distribution is determined by the linear dielectric constants. Maxwell Garnett with Letting with (nonlinear inclusions)

7. At the plasmon resonance and is mainly imaginary the effective susceptibility changes sign Gold nanoparticles: induced transparency Gold: induced opacity Nonlinear optics of metal-dielectric composites Absorption in the nanoparticles grows the resonance is smaller less intensity in the nanoparticles less overall absorption

8. Prediction of Maxwell Garnett theory for the nonlinearity of spherical gold nanoparticles in silica; fgold = 0.2, λ = 532 nm Both the real and the imaginary part of the susceptibility depend strongly on frequency. eSiO22and egoldfromAIP handbook; c(3)of gold from Smith D. D. et al., J. Appl. Phys. 86, 6200 (1999), taken asindependentfrom l (?)

9. Maxwell Garnett model predictions “beyond its validity limits” No complete theory exists for semicontinuous films; the Maxwell Garnett theory gives a good hint to what we can expect.

10. Samples and experimental technique • Two series of samples • Gold-silica cosputtered on quartz, f = 0.04 to 0.56 continuously variable across the sample (D. D. Smith, NASA Marshall flight center) • Gold deposited on glass by laser ablation; a discrete series of samples, f≈ 0.2 to 0.8 (M. Nelson, New Mexico State University) The measurement method we choose is the z-scan, which is easy and distinguishes real and imaginary parts of the nonlinearity. We use pulses of around 20 ps duration.

11. Our results so far Nonlinear absorption coefficient b in the cosputtered sample at λ = 532 nm. The nonlinearity first grows nonlinearly in the fill fraction then decreases. The sign is never positive.

12. Our results so far Nonlinear absorption in one of the samples deposited by laser ablation at λ= 532 nm (second harmonic of Nd:YAG); f≈ 0.42; sample not percolated linear transmittance z-scan There is no sign change in this case; the measurement is taken at a wavelength off the plasmon resonance, which in this sample is red-shifted.

13. Conclusions and future work We confirm that the sign of the nonlinear absorption in a Maxwell Garnett composite is opposite to the sign in the bulk material. We observed both signs of nonlinearity in gold-silica composites, and there is evidence of a link to of the sign change to the plasmon resonance (also outside the regime of validity of the Maxwell Garnett theory). We must now bracket as well as possible the region in which the sign change happens, both in fill fraction and in wavelength.