Focal shift of silicon microlens array in mid-infrared regime

ZUO Hai-Jie; YANG Wen; ZHANG Jiang-Yong; YING Lei-Ying; ZHANG Bao-Ping; HOU Zhi-Jin; CHEN Hong-Xu; SI Jun-Jie

doi:10.11972/j.issn.1001-9014.2017.02.005

[1] Kumaresan Y, Rammohan A, Dwivedi P, et al. Large area IR microlens arrays of chalcogenide glass photoresists by grayscale maskless lithography[J]. ACS Appl. Mater. Interfaces, 2013. 5(15):7094.

[2] Zhang L, Ma X Z, Zhuang J L, et al. Microfabrication of a diffractive microlens array on n-GaAs by an efficient electrochemical method[J]. Adv. Mater., 2007. 19(22): 3912-3918.

[3] Deng Z F, Chen F, Yang Q, et al.Dragonfly-eye-inspired artificial compound eyes with sophisticated imaging[J]. Adv. Funct. Mater., 2016. 26(12): 1995-2001.

[4] Agranov G, V Berezin, R H Tsai. Crosstalk and microlens study in a color CMOS image sensor[J]. IEEE Trans. Electron Dev., 2003. 50(1):4-11.

[5] Guo N, Hu W D, Chen X S, et al. Optimization of microlenses for InSb infrared focal-plane arrays[J]. J. Electron. Mater., 2011. 40(8): 1647-1650.

[6] Binnie T D. Fast imaging microlenses[J]. Appl. Opt., 1994. 33(7):1170-1175.

[7] Liu H W, Chen F, Yang Q, et al. Fabrication of bioinspired omnidirectional and gapless microlens array for wide field-of-view detections[J]. Appl. Phys. Lett., 2012. 100(13): DOI: 10.1063/1.3696019.

[8] Huang T F, Hua S H, Hu K C, et al. LED chip having micro-lens structure[P]. 2012, Google Patents.

[9] Stern M B. Binary optics: A VLSI-based microoptics technology[J]. Microelectron. Eng., 1996. 32(1-4): 369-388.

[10] Li Y J, Wolf E. Focal shifts in diffracted converging spherical waves[J]. Opt. Commun, 1981. 39(4): 211-215.

[11] Hu B, Wang Q J, Zhang Y. Systematic study of the focal shift effect in planar plasmonic slit lenses. Nanotechnology, 2012. 23(44): 444002.

[12] Gao Y, Liu J L, Zhang X R, et al.Analysis of focal-shift effect in planar metallic nanoslit lenses[J]. Opt. Express, 2012. 20(2):1320-9.

[13] Hernandez-Aranda R I, Gutierrez-Vega J C. Focal shift in vector Mathieu-Gauss beams[J]. Opt. Express, 2008. 16(8): 5838-48.

[14] Verslegers L, Catrysse P B, Yu Z F, et al. Planar lenses based on nanoscale slit arrays in a metallic film[J]. Nano Lett., 2009. 9(1):235-238.

[15] Aristov V, Grigoriev M, Kuznetsov S, et al. X-ray refractive planar lens with minimized absorption[J]. Appl. Phys. Lett., 2000. 77(24).

[16] Yamazaki R, Obana A, Kimata M. Microlens for uncooled infrared array sensor[J]. Electronics and Communications in Japan, 2013. 96(2):1-8.

[17] Deng Z F, Yang Q, Chen F, et al. Fabrication of large-area concave microlens array on silicon by femtosecond laser micromachining[J]. Opt. Lett., 2015. 40(9):1929-1930.

[18] Liu Y L, Liu H. Analysis of a diffractive microlens using the finite-difference time-domain method[J]. J. Micro-Nanolith Mem, 2010. 9(3).

[19] Gao H W, Hyun J K, Lee M H, et al. Broadband Plasmonic Microlenses Based on Patches of Nanoholes[J]. Nano Lett., 2010. 10(10): 4111-4116.

[20] Li Y. Dependence of the focal shift on Fresnel number and F-Number[J]. J. Opt. Soc. Am., 1982. 72(6).

[21] Arnaud J. Representation of Gaussian beams by complex rays[J]. Appl. Opt., 1985. 24(4):538-539.

[22] Schmitz M, Bryngdahl O. Rigorous concept for the design of diffractive microlenses with high numerical apertures[J]. J. Opt. Soc. Am. A, 1997. 14(4): DOI: 10.1364/JOSAA.14.000901.

[23] Pomme D A, Moharam M G, Grann E B. Limits of scalar diffraction theory for diffractive phase elements[J]. J. Opt. Soc. Am. A, 1994. 11(6):1827-1830.

[24] Prather D W, Shi S Y. Formulation and application of the finite-difference time-domain method for the analysis of axially symmetric diffractive optical elements[J]. J. Opt. Soc. Am. A, 1999. 16(5): DOI: 10.1364/JOSAA.16.001131.

[25] Lin L, Goh X M, McGuinness L P,,et al. Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing[J]. Nano Lett., 2010. 10(5):1936-1940.

[26] Vaillant J, Crocherie A, Hirigoyen F, et al. Uniform illumination and rigorous electromagnetic simulations applied to CMOS image sensors[J]. Opt. Express, 2007. 15(9): 5494-503.

[27] Prather D W, Shi S Y. Combined scalar-vector method for the analysis of diffractive optical elements[J]. Opt. Eng., 2000. 39(7).

[28] Taflove A, Hagness S C. Computational electrodynamics[M]. Artech house, Boston, 2000.

[29] Mait J N. Understanding diffractive optic design in the scalar domain[J]. J. Opt. Soc. Am. A, 1995. 12(10).

[30] Li Y J. A high-accuracy formula for fast evaluation of the effect of focal shift[J]. J. Mod. Opt., 1991. 38(9).

[31] Ruffieux P. On the chromatic aberration of microlenses[J]. Opt. Express, 2006. 14(11):4687-4689.

[32] Szapiel S, Scharf T, Herzig H P, et al. Marechal intensity formula for small-Fresnel-number systems[J]. Opt. Lett., 1983. 8(6).

[33] Niklasson G A, Granqvist C G, Hunderi O. Effective medium models for the optical-properties of inhomogeneous materials[J]. Appl. Opt., 1981. 20(1).