1. Saturable absorption and optical limiting
in semicontinuous gold films.
Giovanni Piredda1, David D. Smith2, Mark Nelson3, Youngkwon Yoon1,
Robert W. Boyd1, Rongfu Xiao4 and 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. εi εh 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, (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. Nonlinear optics of metal-dielectric composites
At the plasmon resonance
and
is mainly imaginary
the effective susceptibility changes sign
Gold: induced opacity
Gold nanoparticles: induced transparency
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. eSiO22 and egold from AIP handbook; c(3) of gold from Smith D. D. et al., J. Appl. Phys. 86, 6200 (1999), taken as independent from 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 (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
z-scan
linear transmittance
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.