Composite structures for the enhancement of nonlinear-optical susceptibility

A. E. Neeves; M. H. Birnboim

doi:10.1364/JOSAB.6.000787

Journal of the Optical Society of America B
Vol. 6,
Issue 4,
pp. 787-796
(1989)
•https://doi.org/10.1364/JOSAB.6.000787

Composite structures for the enhancement of nonlinear-optical susceptibility

A. E. Neeves and M. H. Birnboim

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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)

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Abstract

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.

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Model					Conjugate Signal $χ_{eff}^{(3)} (esu)$	Absorption

Core	Shell	Medium	r₁/r₂	λ (nm)		γ (cm⁻¹)	η (esu-cm)
PS	–	water	1.0	500^b	3 × 10⁻⁶	30^c	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
PS	Au	water	0.8	628	9 × 10⁻³	3 × 10⁴	9 × 10⁻⁶
PS	Au	water	0.9	942	2 × 10⁻²	3 × 10⁴	2 × 10⁻⁶
Al	PS	water	0.5	500^b	9 × 10⁻⁵	1 × 10²	3 × 10⁻⁶
PS	Al	water	0.92^d	500	1 × 10⁻²	8 × 10⁴	4 × 10⁻⁶
Al	silica	organic	0.5^e	200	2 × 10⁻⁵	1 × 10⁴	6 × 10⁻⁸

Model					Conjugate Signal $χ_{eff}^{(3)} (esu)$	Absorption

Core	Shell	Medium	r₁/r₂	λ (nm)		γ (cm⁻¹)	η (esu-cm)
PDA composite
ρ = 1%, λ = 673 nm at PDA resonant χ⁽³⁾
–	–	PDA	–	673	1 × 10⁻⁷	1 × 10^4a	3 × 10⁻¹⁰
Au	–	PDA	1.0	673^b	1 × 10⁻⁷	1 × 10⁴	3 × 10⁻¹⁰
linear	Au	PDA	0.83	673	6 × 10⁻⁷^c	4 × 10⁴	4 × 10⁻¹⁰
Au	PDA	linear	0.5	673^b	3 × 10⁻¹⁰	1 × 10²	9 × 10⁻¹¹
PDA	Au	linear	0.83	673	1 × 10⁻⁵	3 × 10⁴	1 × 10⁻⁸
PDA	Au	linear	0.86	725	2 × 10⁻⁵	3 × 10⁴	2 × 10⁻⁸
Al	–	PDA	1.0	673^b	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	673^b	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
ρ = 1%, λ = 992 nm at PDA nonresonant χ⁽³⁾
–	–	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 PBT^d 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

Model					Conjugate Signal $χ_{eff}^{(3)} (esu)$	Absorption

Core	Shell	Medium	r₁/r₂	λ (nm)		γ (cm⁻¹)	η (esu-cm)
PS	–	water	1.0	500^b	3 × 10⁻⁶	30^c	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
PS	Au	water	0.8	628	9 × 10⁻³	3 × 10⁴	9 × 10⁻⁶
PS	Au	water	0.9	942	2 × 10⁻²	3 × 10⁴	2 × 10⁻⁶
Al	PS	water	0.5	500^b	9 × 10⁻⁵	1 × 10²	3 × 10⁻⁶
PS	Al	water	0.92^d	500	1 × 10⁻²	8 × 10⁴	4 × 10⁻⁶
Al	silica	organic	0.5^e	200	2 × 10⁻⁵	1 × 10⁴	6 × 10⁻⁸

Model					Conjugate Signal $χ_{eff}^{(3)} (esu)$	Absorption

Core	Shell	Medium	r₁/r₂	λ (nm)		γ (cm⁻¹)	η (esu-cm)
PDA composite
ρ = 1%, λ = 673 nm at PDA resonant χ⁽³⁾
–	–	PDA	–	673	1 × 10⁻⁷	1 × 10^4a	3 × 10⁻¹⁰
Au	–	PDA	1.0	673^b	1 × 10⁻⁷	1 × 10⁴	3 × 10⁻¹⁰
linear	Au	PDA	0.83	673	6 × 10⁻⁷^c	4 × 10⁴	4 × 10⁻¹⁰
Au	PDA	linear	0.5	673^b	3 × 10⁻¹⁰	1 × 10²	9 × 10⁻¹¹
PDA	Au	linear	0.83	673	1 × 10⁻⁵	3 × 10⁴	1 × 10⁻⁸
PDA	Au	linear	0.86	725	2 × 10⁻⁵	3 × 10⁴	2 × 10⁻⁸
Al	–	PDA	1.0	673^b	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	673^b	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
ρ = 1%, λ = 992 nm at PDA nonresonant χ⁽³⁾
–	–	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 PBT^d 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

Abstract

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Equations (56)

Journal of the Optical Society of America B