Nonlinear focal shift due to the Kerr effect for a Gaussian beam focused by a lens

Adrián Aupart-Acosta; Martha Rosete-Aguilar; Jesús Garduño-Mejía; Oscar G. Rodríguez-Herrera; Camilo Ruiz

doi:10.1364/AO.481228

Applied Optics
Vol. 62,
Issue 4,
pp. 1088-1094
(2023)
•https://doi.org/10.1364/AO.481228

Nonlinear focal shift due to the Kerr effect for a Gaussian beam focused by a lens

Adrián Aupart-Acosta, Martha Rosete-Aguilar, Jesús Garduño-Mejía, Oscar G. Rodríguez-Herrera, and Camilo Ruiz

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Adrián Aupart-Acosta, Martha Rosete-Aguilar, Jesús Garduño-Mejía, Oscar G. Rodríguez-Herrera, and Camilo Ruiz, "Nonlinear focal shift due to the Kerr effect for a Gaussian beam focused by a lens," Appl. Opt. 62, 1088-1094 (2023)

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Abstract

When a low-power, monochromatic Gaussian beam is focused by a thin lens in air and the waist of the beam is in the plane of the lens, there is a shift of the focus position if the waist of the beam is much smaller than the size of the lens. The point of maximum intensity relative to the geometrical focal point shifts closer to the lens. We show that for ultra-intense light beams, when the Kerr effect is unavoidable, there is a nonlinear focal shift. The nonlinear focus position shifts closer to the lens for laser powers below the critical power. To avoid the nonlinear focal shift below the critical power, the correct combination of Gaussian beam waist and focal system has to be used in the experimental setup. It will be shown that as the Fresnel number ${N_w}$ associated with the Gaussian beam radius increases, the nonlinear focal shift first increases and then begins to decrease.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Equations (17)

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$w_{0}$	$N_{w}$	$α$	$Δ f_{L}$ $(T E O)$	$Δ f_{L}$ $(N U M)$	$Δ f_{N L}$ $(N U M)$
[mm]	[a.u.]	[a.u.]	[mm]	[mm]	[mm]
1.4	8.17	12.76	0.455	0.461	0.077
2	16.67	6.25	−0.118	−0.160	0.160
4	66.67	1.56	−0.038	−0.034	0.183
6	150	0.69	−0.034	−0.033	0.131
8	266.67	0.39	−0.034	−0.024	0.096
10	416.17	0.25	−0.034	−0.030	0.080

$w_{0}$	$q_{L}$	$q_{N L}$	$I_{L} / I {m a x}_{N L}$	$I_{N L} / I {m a x}_{N L}$
[mm]	[µm]	[µm]	[a.u.]	[a.u.]
1.4	52	37	0.08	0.17
2.0	40	26	0.17	0.34
4.0	24	16	0.44	0.91
6.0	23	14	0.50	1.00
8.0	20	14	0.52	0.99
10.0	20	15	0.52	0.98

$w_{0}$	$N_{w}$	$α$	$Δ f_{L}$ $(T E O)$	$Δ f_{L}$ $(N U M)$	$Δ f_{N L}$ $(N U M)$
[mm]	[a.u.]	[a.u.]	[mm]	[mm]	[mm]
1.4	8.17	12.76	0.455	0.461	0.077
2	16.67	6.25	−0.118	−0.160	0.160
4	66.67	1.56	−0.038	−0.034	0.183
6	150	0.69	−0.034	−0.033	0.131
8	266.67	0.39	−0.034	−0.024	0.096
10	416.17	0.25	−0.034	−0.030	0.080

$w_{0}$	$q_{L}$	$q_{N L}$	$I_{L} / I {m a x}_{N L}$	$I_{N L} / I {m a x}_{N L}$
[mm]	[µm]	[µm]	[a.u.]	[a.u.]
1.4	52	37	0.08	0.17
2.0	40	26	0.17	0.34
4.0	24	16	0.44	0.91
6.0	23	14	0.50	1.00
8.0	20	14	0.52	0.99
10.0	20	15	0.52	0.98

Adrián Aupart-Acosta	https://orcid.org/0000-0002-5956-7592
Martha Rosete-Aguilar	https://orcid.org/0000-0001-6030-5496
Jesús Garduño-Mejía	https://orcid.org/0000-0002-1138-8667
Oscar G. Rodríguez-Herrera	https://orcid.org/0000-0002-4709-1830

Abstract

Data availability

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Figures (9)

Tables (2)

Equations (17)

Applied Optics