Measuring the electronic third-order susceptibility of the silicon phthalocyanine-monomethacrylate molecule with quadratic electroabsorption spectroscopy

Robert J. Kruhlak; Mark G. Kuzyk

doi:10.1364/JOSAB.22.000643

Journal of the Optical Society of America B
Vol. 22,
Issue 3,
pp. 643-654
(2005)
•https://doi.org/10.1364/JOSAB.22.000643

Measuring the electronic third-order susceptibility of the silicon phthalocyanine–monomethacrylate molecule with quadratic electroabsorption spectroscopy

Robert J. Kruhlak and Mark G. Kuzyk

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Robert J. Kruhlak and Mark G. Kuzyk, "Measuring the electronic third-order susceptibility of the silicon phthalocyanine-monomethacrylate molecule with quadratic electroabsorption spectroscopy," J. Opt. Soc. Am. B 22, 643-654 (2005)

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Abstract

We report on a quadratic electroabsorption measurement of the electronic third-order molecular susceptibility of silicon phthalocyanine–monomethacrylate-doped poly(methyl methacrylate) thin films. The results are compared with homogeneously broadened (Lorentzian) and inhomogeneously broadened theories of the second hyperpolarizability. For the first time to our knowledge the effect of distribution of sites in the polymer is taken into account and is found to be negligible on its effects on $χ^{(3)} .$ We show that a three-level model of the third-order susceptibility is sufficient to characterize the electronic states of these dye-doped thin films in the visible regime. The limited spectral range of the experiment allows us to estimate only the zero-frequency third-order molecular susceptibility, which we find is below the quantum-mechanical limit.

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Analysis	State n	$ℏ ω_{ng} (λ)$ [eV (nm)]	$ℏ Γ_{ng}$ (meV)	$ℏ γ_{ng}$ (meV)	$μ_{ng}$ D
IB	1	1.85 $(670 \pm 1)$	$5 \pm 2$	$19 \pm 3$	$7.3 \pm 0.5$
IB	3	1.94 $(640 \pm 2)$	$10 \pm 4$	$20 \pm 3$	$2.1 \pm 0.3$
IB	5	2.05 $(605 \pm 2)$	$12 \pm 4$	$20 \pm 3$	$2.3 \pm 0.3$
IB	7	2.008 $(617 \pm 2)$	$12 \pm 4$	$20 \pm 3$	$1.4 \pm 0.5$
L	1	1.85 $(670 \pm 1)$	$18 \pm 2$	—	$7.9 \pm 1.5$
L	3	1.94 $(640 \pm 2)$	$18 \pm 2$	—	$1.9 \pm 0.4$
L	5	2.05 $(605 \pm 2)$	$18 \pm 2$	—	$2.3 \pm 0.4$
L	7	2.008 $(617 \pm 2)$	$18 \pm 2$	—	$1.1 \pm 0.3$

Analysis	State		$ℏ ω_{ng} (λ)$ [eV (nm)]	$ℏ Γ_{ng}$ (meV)	$ℏ γ_{ng}$ (meV)	$μ_{mn}$ D
Analysis	m	n	$ℏ ω_{ng} (λ)$ [eV (nm)]	$ℏ Γ_{ng}$ (meV)	$ℏ γ_{ng}$ (meV)	$μ_{mn}$ D
IB	1	2	3.0–3.7 (335–400)	∼40	∼80	$9.25 \pm 0.85$
L	1	2	2.7–3.5 (350–460)	∼40	—	$8.75 \pm 1.45$

SiPc–MMA	$γ_{max}$ b (positive)	$γ_{max}$ b (negative)	QEA		OKEc L
SiPc–MMA	$γ_{max}$ b (positive)	$γ_{max}$ b (negative)	L	IB	OKEc L
$γ (10^{- 34} {cm}^{6} / erg)$	199	-50	$- 3.5 \pm 4.5$	$- 1 \pm 2$	5.2

	IB
L	$(β ⩽ 1)$		$(β = 1)$
$\frac{C_{1}}{ω_{ng} \mp i Γ_{ng} \mp ω}$	$\frac{i \sqrt{π} C_{1}}{γ_{ng}} W_{β}^{(1)} (\frac{- ω_{ng} \pm i Γ_{ng} \pm ω}{γ_{ng}})$	$\frac{i \sqrt{π} C_{1}}{γ_{ng}} W (\frac{- ω_{ng} \pm i Γ_{ng} \pm ω}{γ_{ng}})$
$\frac{C_{2}}{(ω_{ng} \mp i Γ_{ng} \mp ω)^{2}}$	$\frac{i \sqrt{π} C_{2}}{γ_{ng}} [\frac{- 1}{γ_{ng}} W_{β}^{(2)} (\frac{- ω_{ng} \pm i Γ_{ng} \pm ω}{γ_{ng}})]$	$\frac{i \sqrt{π} C_{2}}{γ_{ng}} [\frac{2 (ω_{ng} \mp i Γ_{ng} \mp ω)}{γ_{ng}^{2}} W (\frac{- ω_{ng} \pm i Γ_{ng} \pm ω}{γ_{ng}}) + \frac{2 i}{\sqrt{π} γ_{ng}}]$
$\frac{C_{3}}{(ω_{ng} \mp i Γ_{ng} \mp ω)^{3}}$	$\frac{i \sqrt{π} C_{3}}{γ_{ng}} [\frac{1}{γ_{ng}^{2}} W_{β}^{(3)} (\frac{- ω_{ng} \pm i Γ_{ng} \pm ω}{γ_{ng}})]$	$\frac{i \sqrt{π} C_{3}}{γ_{ng}} \{[\frac{2 (ω_{ng} \mp i Γ_{ng} \mp ω)^{2} - γ_{ng}^{2}}{γ_{ng}^{4}}] W (\frac{- ω_{ng} \pm i Γ_{ng} \pm ω}{γ_{ng}})$ $+ \frac{2 i (ω_{ng} \mp i Γ_{ng} \mp ω)}{\sqrt{π} γ_{ng}^{3}}\}$

Analysis	State n	$ℏ ω_{ng} (λ)$ [eV (nm)]	$ℏ Γ_{ng}$ (meV)	$ℏ γ_{ng}$ (meV)	$μ_{ng}$ D
IB	1	1.85 $(670 \pm 1)$	$5 \pm 2$	$19 \pm 3$	$7.3 \pm 0.5$
IB	3	1.94 $(640 \pm 2)$	$10 \pm 4$	$20 \pm 3$	$2.1 \pm 0.3$
IB	5	2.05 $(605 \pm 2)$	$12 \pm 4$	$20 \pm 3$	$2.3 \pm 0.3$
IB	7	2.008 $(617 \pm 2)$	$12 \pm 4$	$20 \pm 3$	$1.4 \pm 0.5$
L	1	1.85 $(670 \pm 1)$	$18 \pm 2$	—	$7.9 \pm 1.5$
L	3	1.94 $(640 \pm 2)$	$18 \pm 2$	—	$1.9 \pm 0.4$
L	5	2.05 $(605 \pm 2)$	$18 \pm 2$	—	$2.3 \pm 0.4$
L	7	2.008 $(617 \pm 2)$	$18 \pm 2$	—	$1.1 \pm 0.3$

Abstract

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Journal of the Optical Society of America B