Department of Mechanical Engineering, Aeronautical Engineering and Mechanics, Rensselaer Polytechnic Institute, Troy, New York 12180-3590 USA
A Neeves
M Birnboim
A. E. Neeves and M. H. Birnboim, "Composite structures for the enhancement of nonlinear-optical susceptibility," J. Opt. Soc. Am. B 6, 787-796 (1989)
Calculations of the nonlinear-optical behavior are developed for model composites of nanospheres with a metallic core and nonlinear shell or with a nonlinear core and metallic shell suspended in a nonlinear medium. Optical phase conjugation is shown to be enhanced from each nonlinear region because the optical field can be concentrated in both the interior and the exterior neighborhoods of the particle and magnified at the surface-mediated plasmon resonance. For the model composite with a metallic core, a limited range of resonance tunability can be achieved by adjustment of shell thickness; the frequency range is dependent on the dielectric dispersion of the metal. For the composite with a metallic shell instead of a metallic core, this restriction is reduced so that tunability from ultraviolet to infrared can be attained. Enhancement of the phase-conjugate signal is calculated for the electrostrictive mechanism dominant in the microsecond time scale and for the electronic mechanism dominant in the picosecond time scale. Calculations based on the dielectric functions for gold and for aluminum indicate that phase-conjugate reflectivity enhancements of 108 can be achieved. The imaginary components of the composite dielectric functions are shown to limit the magnitude of the field enhancement at the surface-plasmon resonance and determine the absorption and figure of merit of the composite.
Composite Model Calculations for Electrostrictive Mechanism in Polystyrene Compositea
Conjugate Signal χ eff ( 3 ) ( esu )
η (esu-cm)
PS – water 1.0 500b 3 × 10−6 30c 3 × 10−6
Au PS water 0.5 500 6 × 10−5 1 × 103 2 × 10−6
PS Au water 0.6 500 2 × 10−3 2 × 104 3 × 10−6
Al PS water 0.5 500b 9 × 10−5 1 × 102 3 × 10−6
PS Al water 0.92d 500 1 × 10−2 8 × 104 4 × 10−6
Al silica organic 0.5e 200 2 × 10−5 1 × 104 6 × 10−8
a 2r2 = 100 nm, ρ = 1%. For (3.7°) coarse grating τ = 33 msec; for (176°) fine grating τ = 50 μsec. For r2 = 100 nm, all electrostrictive χeff(3) are increased by 103, and both τ’s are increased by 10.
b Nonresonant.
c γs dominant; otherwise γm dominates γ.
d Particle, 2r2 = 50 nm.
e Particle, 2r2 = 10 nm.
Composite Model Calculations for Electronic Mechanism
PDA composite
ρ = 1%, λ = 673 nm at PDA resonant χ(3)
– – PDA – 673 1 × 10−7 1 × 104a 3 × 10−10
Au – PDA 1.0 673b 1 × 10−7 1 × 104 3 × 10−10
linear Au PDA 0.83 673 6 × 10−7c 4 × 104 4 × 10−10
Au PDA linear 0.5 673b 3 × 10−10 1 × 102 9 × 10−11
PDA Au linear 0.83 673 1 × 10−5 3 × 104 1 × 10−8
Al – PDA 1.0 673b 1 × 10−7 1 × 104 3 × 10−10
linear Al PDA 0.955 673 9 × 10−7 8 × 104 3 × 10−10
Al PDA linear 0.5 673b 3 × 10−10 1 9 × 10−11
PDA Al linear 0.955 673 2 × 10−4 7 × 104 5 × 10−7
ρ = 1%, λ = 400 nm at PDA nonresonant χ(3)
– – PDA – 400 1 × 10−9 8 × 102 4 × 10−11
linear Al PDA 0.87 400 1 × 10−6 2 × 105 1 × 10−10
PDA Al linear 0.87 400 4 × 10−5 2 × 105 6 × 10−9
– – PDA – 992 1 × 10−9 1 3 × 10−9
linear Au PDA 0.93 992 1 × 10−8 3 × 104 1 × 10−11
PDA Au linear 0.93 992 4× 10−7 3 × 104 4 × 10−10
PBT composite
ρ = 1%, λ = 633 nm at PBTd nonresonant χ(3)
– – PBT – 633 5 × 10−11 9 × 102 1 × 10−12
PBT Al linear 0.95 633 5 × 10−8 1 × 104 1 × 10−10
Urea composite
ρ = 0.2%, at urea nonresonant χ(3)
– – urea – 200 1 × 10−12 1 3 × 10−11
Al Urea silica 0.9 200 1 × 10−7 9 × 104 3 × 10−11
a Particle size chosen so that γm dominates.
c Both shell and outer medium contribute equally.
d PBT n0 = 1.75, ∊″ = 0.15.