Gradient refractive index square lenses. I. Fabrication and refractive index distribution

Hao Lv; Aimei Liu; Jufang Tong; Xunong Yi; Qianguang Li

doi:10.1364/JOSAA.26.001085

Journal of the Optical Society of America A
Vol. 26,
Issue 5,
pp. 1085-1089
(2009)
•https://doi.org/10.1364/JOSAA.26.001085

Gradient refractive index square lenses. I. Fabrication and refractive index distribution

Hao Lv, Aimei Liu, Jufang Tong, Xunong Yi, and Qianguang Li

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Hao Lv, Aimei Liu, Jufang Tong, Xunong Yi, and Qianguang Li, "Gradient refractive index square lenses. I. Fabrication and refractive index distribution," J. Opt. Soc. Am. A 26, 1085-1089 (2009)

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Abstract

An equation for the distribution of refractive index of a gradient refractive index square lens has been established, and such a lens has been fabricated using ion exchange. The distributions of refractive indices at different angles of incidence are discussed. Experimental and theoretical data are compared and show good agreement.

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Angle $(θ)$	Fitting Coefficient $(a)$	Polynomial [ $n (r) = n_{0} (1 - a r^{2})$ , $n_{0} = 1.612$ ]
0	0.0659	$n (r) = n_{0} (1 - 0.0659 r^{2})$
$π ∕ 12$	0.1188	$n (r) = n_{0} (1 - 0.1188 r^{2})$
$π ∕ 6$	0.0968	$n (r) = n_{0} (1 - 0.0968 r^{2})$
$π ∕ 4$	0.0890	$n (r) = n_{0} (1 - 0.0890 r^{2})$

Coordinates $(x, y)$	Experimental Data	Theoretical Data	Error
(1.131,1.000)	1.6142	1.6127	0.093
(1.525,1.000)	1.5844	1.5798	0.290
(1.511,1.137)	1.5840	1.5813	0.170
(1.657,1.176)	1.5612	1.5561	0.330
(1.065,1.113)	1.6141	1.6127	0.087
(1.272,1.471)	0.5844	1.5838	0.004
(1.093,1.093)	1.6145	1.6127	0.011
(1.391,1.391)	1.5844	1.5854	0.063
(1.535,1.535)	1.5613	1.5624	0.070

Angle $(θ)$	Fitting Coefficient $(a)$	Polynomial [ $n (r) = n_{0} (1 - a r^{2})$ , $n_{0} = 1.612$ ]
0	0.0659	$n (r) = n_{0} (1 - 0.0659 r^{2})$
$π ∕ 12$	0.1188	$n (r) = n_{0} (1 - 0.1188 r^{2})$
$π ∕ 6$	0.0968	$n (r) = n_{0} (1 - 0.0968 r^{2})$
$π ∕ 4$	0.0890	$n (r) = n_{0} (1 - 0.0890 r^{2})$

Coordinates $(x, y)$	Experimental Data	Theoretical Data	Error
(1.131,1.000)	1.6142	1.6127	0.093
(1.525,1.000)	1.5844	1.5798	0.290
(1.511,1.137)	1.5840	1.5813	0.170
(1.657,1.176)	1.5612	1.5561	0.330
(1.065,1.113)	1.6141	1.6127	0.087
(1.272,1.471)	0.5844	1.5838	0.004
(1.093,1.093)	1.6145	1.6127	0.011
(1.391,1.391)	1.5844	1.5854	0.063
(1.535,1.535)	1.5613	1.5624	0.070

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Equations (27)

Journal of the Optical Society of America A