Transcript Saturable absorption and optical limiting in semicontinuous gold

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
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”
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.
Isolated nanoparticles in a dielectric matrix
εi
Maxwell Garnett theory:
εh
 MG     h  
     h  
 f i
 MG    2 h  
 i    2 h  
(for spherical inclusions)
resonance close to Re i    2 h    0
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)
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
(  3  1010 esu )
Interband contribution: at 530 nm, saturation of the interband absorption
(  3  10 8 esu )
Hot electron contribution: the optical pulse modifies the equilibrium
distribution of electrons (“Fermi smearing”)
Largest contribution
(  3  107 esu )
Balance: gold is an induced absorber for ps pulses at 530 nm
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.
 MG   h

 MG  2 h


 MG  f
 i with
Maxwell Garnett
i  h
 MG
 i

 i  2 h
Letting
3 
Ei 
 i  12i Ei
with
(nonlinear inclusions)
2
 MG
3 
 fqi qi  i
2
2
3 
 MG  2 h
E  qi E
 i  2 h
Nonlinear optics of metal-dielectric composites
At the plasmon resonance Re i  2 h   0 and qi is mainly imaginary
 MG 3   fqi 2 qi  i 3 
2
Gold: induced opacity
the effective susceptibility changes sign
Gold nanoparticles: induced
transparency
Absorption in the nanoparticles grows
less intensity in the
nanoparticles
the resonance is smaller
less overall absorption
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. SiO2 and gold from AIP handbook; 3 of gold from Smith D. D. et al.,
2
J. Appl. Phys. 86, 6200 (1999), taken as independent from l (?)
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.
Samples and experimental technique
Two series of samples
1) Gold-silica cosputtered on quartz, f = 0.04 to 0.56
continuously variable across the sample (D. D. Smith, NASA
Marshall flight center)
2) 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.
Our results so far
Nonlinear absorption coefficient b in the cosputtered sample at
λ = 532 nm.
 I    0  b I
 4 12 2
3  
b  Im
 
 l n0 Ren0 c

The nonlinearity first grows nonlinearly in the fill fraction then
decreases. The sign is never positive.
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 redshifted.
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.