Generalized theoretical treatment and numerical method of time-resolved radially dependent laser pulses interacting with multiphoton absorbers

Evgueni Parilov; M. J. Potasek

doi:10.1364/JOSAB.23.001894

Journal of the Optical Society of America B
Vol. 23,
Issue 9,
pp. 1894-1910
(2006)
•https://doi.org/10.1364/JOSAB.23.001894

Generalized theoretical treatment and numerical method of time-resolved radially dependent laser pulses interacting with multiphoton absorbers

Evgueni Parilov and M. J. Potasek

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Evgueni Parilov and M. J. Potasek, "Generalized theoretical treatment and numerical method of time-resolved radially dependent laser pulses interacting with multiphoton absorbers," J. Opt. Soc. Am. B 23, 1894-1910 (2006)

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Abstract

We introduce a generalized numerical method to calculate short-pulsed laser propagation in a wide class of multiphoton absorbing materials. The method has no restrictions on the input pulse widths varying from nanosecond to femtosecond, and its numerical solution is both radially and temporarily dependent, enabling us to check numerically the validity of assuming radially constant solutions, which ensures that the true peak intensity falls below the damage causing level. A new feature of our technique enables us to determine quantitatively the contributions to the total absorption due to every electronic energy level. We found excellent agreement between our calculations and experiments using sample materials ranging from reverse saturable absorbers, two-photon absorbers with excited-state absorption to three-photon absorbers. We applied our technique to a two-photon absorber with excited-state absorption and found approximately 1 order of magnitude increase in the absorption when femtosecond pulses were used in place of nanosecond pulses.

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Material Experimental Parameters	$C_{60}$ -Toluene Solution^a	AF455 Chromophore^b	PPAI Dye^c
$σ_{3 PA} ({cm}^{3} ∕ W^{2})$			$3.2 \times 10^{- 21}$
$σ_{TPA} ({cm}^{4} ∕ G W)$		$0.5 \times 10^{- 20}$ ^d
$σ_{01} ({cm}^{2})$	$3.1 \times 10^{- 18}$
$σ_{12} ({cm}^{2})$	$1.6 \times 10^{- 17}$	$1.68 \times 10^{- 17}$
$σ_{34} ({cm}^{2})$	$1.4 \times 10^{- 17}$ ^e	$17.1 \times 10^{- 17}$
$k_{10}^{- 1}$ (ns)	32.5	2.72
$k_{21}^{- 1}$ (ps)	1.0	1.66^f
$k_{13}^{- 1}$ (ns)	1.35	45.3
$k_{30}^{- 1} (μ s)$	40.0	0.368
$k_{43}^{- 1}$ (ns)	1.0	10.0
$z_{\max}$ (mm)	1.0	1.0	10.0
$L_{d f}$	0.09	2.24	0.81
$N_{T} ({nm}^{- 3})$	$1.559 \times 10^{- 3}$ ^h	0.012ⁱ	$0.596 \times 10^{- 3}$ ^j
Energy levels diagram	$B_{0} \cup B_{1} \cup B_{2}$	$B_{1} \cup B_{2} \cup B_{3}$	$B_{4}$
$R_{0} (μ m)$	33.37^k	13.01	53.03
$T_{0}$ (ns)	4.8	1.92	$2.1 \times 10^{- 2}$
$λ_{0}$ (nm)	532	800	1064

Levels	$Φ_{in} = 0.51$ ^a			$Φ_{in} = 2.05$			$Φ_{in} = 14.1$
$⟨ {\hat{p}}_{0} ⟩$ ^b	79.2	23.1	10.4	50.3	4.1	0.4	15.9	0.0	0.0
$⟨ {\hat{p}}_{1} ⟩$	6.7	10.3	1.7	15.2	8.0	0.3	19.0	0.6	0.0
$⟨ {\hat{p}}_{3} ⟩$	14.0	66.2	87.4	41.0	87.7	99.2	64.9	99.3	99.9
$⟨ q ⟩$ ^c	0.06	0.13	0.17	0.08	0.19	0.21	0.14	0.22	0.22

Levels	$E_{in} = 17.0 μ J$			$E_{in} = 93.0 μ J$			$E_{in} = 330.0 μ J$
$⟨ {\hat{p}}_{0} ⟩$	29.4	4.2	0.3	7.8	0.9	0.1	2.7	0.3	0.03
$⟨ {\hat{p}}_{1} ⟩$	65.2	81.4	26.5	89.6	94.6	35.9	96.3	98.0	48.9
$⟨ {\hat{p}}_{3} ⟩$	5.3	14.3	73.0	2.5	4.3	63.9	0.9	1.6	50.9
$⟨ q ⟩$	$1.3 \times 10^{- 5}$	$5.9 \times 10^{- 4}$	$1.0 \times 10^{- 3}$	$2.6 \times 10^{- 4}$	0.01	0.02	$2.6 \times 10^{- 3}$	0.07	0.11

Material Experimental Parameters	$C_{60}$ -Toluene Solution^a	AF455 Chromophore^b	PPAI Dye^c
$σ_{3 PA} ({cm}^{3} ∕ W^{2})$			$3.2 \times 10^{- 21}$
$σ_{TPA} ({cm}^{4} ∕ G W)$		$0.5 \times 10^{- 20}$ ^d
$σ_{01} ({cm}^{2})$	$3.1 \times 10^{- 18}$
$σ_{12} ({cm}^{2})$	$1.6 \times 10^{- 17}$	$1.68 \times 10^{- 17}$
$σ_{34} ({cm}^{2})$	$1.4 \times 10^{- 17}$ ^e	$17.1 \times 10^{- 17}$
$k_{10}^{- 1}$ (ns)	32.5	2.72
$k_{21}^{- 1}$ (ps)	1.0	1.66^f
$k_{13}^{- 1}$ (ns)	1.35	45.3
$k_{30}^{- 1} (μ s)$	40.0	0.368
$k_{43}^{- 1}$ (ns)	1.0	10.0
$z_{\max}$ (mm)	1.0	1.0	10.0
$L_{d f}$	0.09	2.24	0.81
$N_{T} ({nm}^{- 3})$	$1.559 \times 10^{- 3}$ ^h	0.012ⁱ	$0.596 \times 10^{- 3}$ ^j
Energy levels diagram	$B_{0} \cup B_{1} \cup B_{2}$	$B_{1} \cup B_{2} \cup B_{3}$	$B_{4}$
$R_{0} (μ m)$	33.37^k	13.01	53.03
$T_{0}$ (ns)	4.8	1.92	$2.1 \times 10^{- 2}$
$λ_{0}$ (nm)	532	800	1064

Levels	$Φ_{in} = 0.51$ ^a			$Φ_{in} = 2.05$			$Φ_{in} = 14.1$
$⟨ {\hat{p}}_{0} ⟩$ ^b	79.2	23.1	10.4	50.3	4.1	0.4	15.9	0.0	0.0
$⟨ {\hat{p}}_{1} ⟩$	6.7	10.3	1.7	15.2	8.0	0.3	19.0	0.6	0.0
$⟨ {\hat{p}}_{3} ⟩$	14.0	66.2	87.4	41.0	87.7	99.2	64.9	99.3	99.9
$⟨ q ⟩$ ^c	0.06	0.13	0.17	0.08	0.19	0.21	0.14	0.22	0.22

Abstract

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Equations (69)

Journal of the Optical Society of America B