Low-order aberration corrections of multilayer flat lenses using negative-index materials

Zhili Lin; Yongzhuo Zou

doi:10.1364/AO.45.006925

Applied Optics
Vol. 45,
Issue 27,
pp. 6925-6931
(2006)
•https://doi.org/10.1364/AO.45.006925

Low-order aberration corrections of multilayer flat lenses using negative-index materials

Zhili Lin and Yongzhuo Zou

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Zhili Lin and Yongzhuo Zou, "Low-order aberration corrections of multilayer flat lenses using negative-index materials," Appl. Opt. 45, 6925-6931 (2006)

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Abstract

A study of the corrections for some low-order aberrations of multilayer flat lenses based on the introduction of negative-index materials is presented. With the aberration coefficients of a multilayer flat lens that we provided, numerical solutions for the parameters of the double-layer three-layer, and four-layer flat lenses are investigated, respectively, to correct the aberrations, under some conditions, up to orders as high as possible. We find that with the increment of the layer number, the spherical and oblique aberrations can be corrected up to higher orders though the corresponding ranges of the refractive indices and working distances become narrower.

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Coefficient and Name		Expression
$W_{40}$	Fourth-order spherical aberration	${(NA)}^{4} \sum_{i = 1}^{k} (\frac{{n_{i}}^{2} - 1}{8 {n_{i}}^{3}}) d_{i}$
$W_{31}$	Third-order linear coma	$- {(NA)}^{3} α \sum_{i = 1}^{k} (\frac{{n_{i}}^{2} - 1}{2 {n_{i}}^{3}}) d_{i}$
$W_{22}$	Third-order astigmatism	${(NA)}^{2} α^{2} \sum_{i = 1}^{k} (\frac{{n_{i}}^{2} - 1}{4 {n_{i}}^{3}}) d_{i}$
$W_{60}$	Sixth-order spherical aberration	${(NA)}^{6} \sum_{i = 1}^{k} (\frac{{n_{i}}^{4} - 1}{16 {n_{i}}^{5}}) d_{i}$
$W_{51}$	Fifth-order linear coma	$- {(NA)}^{5} α \sum_{i = 1}^{k} (\frac{{n_{i}}^{4} + 2 {n_{i}}^{2} - 3}{8 {n_{i}}^{5}}) d_{i}$
$W_{42}$	Fifth-order astigmatism	${(NA)}^{4} α^{2} \sum_{i = 1}^{k} \frac{3 ({n_{i}}^{2} - 1)}{8 {n_{i}}^{5}} d_{i}$
$W_{33}$	Fifth-order cubic coma	$- {(NA)}^{3} α^{3} \sum_{i = 1}^{k} (\frac{{n_{i}}^{2} - 1}{8 {n_{i}}^{5}}) d_{i}$
$W_{80}$	Eighth-order spherical aberration	${(NA)}^{8} \sum_{i = 1}^{k} \frac{5 ({n_{i}}^{6} - 1)}{128 {n_{i}}^{7}} d_{i}$
$W_{71}$	Seventh-order linear coma	$- {(NA)}^{7} α \sum_{i = 1}^{k} \frac{({n_{i}}^{6} + {n_{i}}^{4} + 3 {n_{i}}^{2} - 5)}{16 {n_{i}}^{7}} d_{i}$
$W_{62}$	Seventh-order astigmatism	${(NA)}^{6} α^{2} \sum_{i = 1}^{k} \frac{15 ({n_{i}}^{2} - 1)}{32 {n_{i}}^{7}} d_{i}$
$W_{53}$	Seventh-order cubic coma	$- {(NA)}^{5} α^{3} \sum_{i = 1}^{k} \frac{3 ({n_{i}}^{4} - 6 {n_{i}}^{2} + 5)}{16 {n_{i}}^{7}} d_{i}$
$W_{44}$	—	${(NA)}^{4} α^{4} \sum_{i = 1}^{k} \frac{3 ({n_{i}}^{4} - 6 {n_{i}}^{2} + 5)}{64 {n_{i}}^{7}} d_{i}$
$W_{100}$	Tenth-order spherical aberration	${(NA)}^{10} \sum_{i = 1}^{k} \frac{7 ({n_{i}}^{8} - 1)}{256 {n_{i}}^{9}} d_{i}$

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Applied Optics