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Insufficient anti-counterfeiting performance and difficulties in manufacturing lead to performance degradation of the subwavelength rectangular structure grating, when it is applied to the field of optical anti-counterfeiting. To solve the problem, an embedded subwavelength one-dimensional simple periodic sinusoidal grating structure is proposed in this paper to replace the previous structure with a rectangular structure. By using equivalent medium theory, we find that the rectangular structure whose duty ration is 0.5 has the same effective refractive index as the sinusoidal structure. Then equivalent structure parameters of a sinusoidal structure are obtained based on a rectangular structure tricolor-shifting device, and the characteristics of the reflection peak are analyzed. The result shows that the sinusoidal structure gating can realize the same tricolor-shifting properties with a higher reflective efficiency as the rectangular structure gating. When the incidence angle of natural light is 45 for TE and TM polarization, the highest reflectivity values of 90%, 89% and 100% in blue, green and red bands can be obtained at the azimuths of 24, 63 and 90, respectively. Then the azimuth-induced color shifts of blue, green and red are realized. Physical mechanism of the equivalent rectangular structure to sinusoidal structure is explained in non-resonance and resonance conditions. Under the non-resonance condition, both of them can be regarded as a layer of completely equivalent optical film, possessing exactly the same optical properties. Under the resonance condition, they can be regarded as a slab waveguide. So when their effective refractive indexes, periods, film thicknesses and depths are equal, they have the same optical characteristic matrixes, supported guided modes, and resonant peak positions. In addition, we investigate the influences of the deviations of key parameters, including grating period, grating depth, coating film thickness, and incidence angle, and propose the rigorous redundancy of these parameters. When the values of period, depth, thickness, and incidence angle are kept within the ranges of 430-455 nm, 88-160 nm, 10-40 nm, and 40-50, respectively, the device can well keep the color-shifting effects of blue, green and red light. A model structure of the sinusoidal grating is fabricated by two-beam laser interference lithography experimentally. The tricolor-shifting device based on the sinusoidal structure presented in this paper can realize high diffraction efficiency azimuth-induced color shifts of blue, green and red light when natural light is incident, which breaks through the limit of bi-color shifting technology and lowers the difficulties in manufacturing, and may have great applications in the field of the optically variable image security.
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Keywords:
- sub-wavelength /
- sinusoidal structure /
- tricolor-shifting /
- two-beam laser interference lithography
[1] Wang Y, Shi W, Wang X 2015 Opt. Lett. 40 4647
[2] Lin D, Fan P 2014 Science 345 298
[3] Lo Y L, Chen Y B, Yang T Y 2011 Appl. Opt. 50 415
[4] Feng J, Zhou C, Wang B, Zheng J, Jia W, Cao H, Lv P 2008 Appl. Opt. 47 6638
[5] Lee H S, Yoon Y T, Lee S S, Kim S H, Lee K D 2007 Opt. Express 15 15457
[6] Oonishi T, Konishi T, Itoh K 2007 J. Opt. Soc. Am. A 46 5019
[7] Feng J, Zhou C, Zheng J 2009 Appl. Opt. 48 2697
[8] Uddin M J, Khaleque T, Magnusson R 2014 Opt. Express 22 12307
[9] Yoon J W, Lee K J, Magnusson R 2015 Opt. Express 23 28849
[10] Grann E, Moharam M 1996 J. Opt. Soc. Am. A 13 988
[11] Feng J, Zhou C, Cao H, Lu P 2010 Appl. Opt. 49 5697
[12] Chen Y L, Liu W X, Liao N F 2010 Spectroscopy and Spectral Analysis 30 1922 (in Chinese)[陈永利, 刘文霞, 廖宁放 2010 光谱学与光谱分析 30 1922]
[13] Bai B, Laukkanen J, Kuittinen M 2010 Appl. Opt. 49 5454
[14] Berthod L, Gate V 2016 Opt. Mater. Express 6 2508
[15] Cui W, Wang H 2017 Opt. Express 25 4097
[16] Xu P, Yuan X, Huang H X, Yang T, Zhu T F, Tang S T, Peng W D 2016 Nanoscale Res. Lett. 11 485
[17] Xu P, Hong C Q, Cheng G X, Zhou L, Sun Z L 2015 Opt. Express 23 6773
[18] Xu P, Huang Y Y, Su Z J, Zhang X L, Luo T Z, Peng W D 2015 Opt. Express 23 4887
[19] Huang H X, Ruan S C, Yang T, Xu P 2015 Nano-Micro Lett. 7 177
[20] Xu P, Huang Y Y, Zhang X L, Huang J F, Li B B, Ye E, Duan S F, Su Z J 2013 Opt. Express 21 20159
[21] Xu P, Huang H X, Wang K, Ruan S C, Yang J, Wang L L, Chen X X, Liu J Y 2007 Opt. Express 15 809
[22] Cormier G, Boudreau B, Thriault S 2001 J. Opt. Soc. Am. A 18 1771
[23] Wang S, Magusson R 1990 J. Opt. Soc. Am. A 7 1470
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[1] Wang Y, Shi W, Wang X 2015 Opt. Lett. 40 4647
[2] Lin D, Fan P 2014 Science 345 298
[3] Lo Y L, Chen Y B, Yang T Y 2011 Appl. Opt. 50 415
[4] Feng J, Zhou C, Wang B, Zheng J, Jia W, Cao H, Lv P 2008 Appl. Opt. 47 6638
[5] Lee H S, Yoon Y T, Lee S S, Kim S H, Lee K D 2007 Opt. Express 15 15457
[6] Oonishi T, Konishi T, Itoh K 2007 J. Opt. Soc. Am. A 46 5019
[7] Feng J, Zhou C, Zheng J 2009 Appl. Opt. 48 2697
[8] Uddin M J, Khaleque T, Magnusson R 2014 Opt. Express 22 12307
[9] Yoon J W, Lee K J, Magnusson R 2015 Opt. Express 23 28849
[10] Grann E, Moharam M 1996 J. Opt. Soc. Am. A 13 988
[11] Feng J, Zhou C, Cao H, Lu P 2010 Appl. Opt. 49 5697
[12] Chen Y L, Liu W X, Liao N F 2010 Spectroscopy and Spectral Analysis 30 1922 (in Chinese)[陈永利, 刘文霞, 廖宁放 2010 光谱学与光谱分析 30 1922]
[13] Bai B, Laukkanen J, Kuittinen M 2010 Appl. Opt. 49 5454
[14] Berthod L, Gate V 2016 Opt. Mater. Express 6 2508
[15] Cui W, Wang H 2017 Opt. Express 25 4097
[16] Xu P, Yuan X, Huang H X, Yang T, Zhu T F, Tang S T, Peng W D 2016 Nanoscale Res. Lett. 11 485
[17] Xu P, Hong C Q, Cheng G X, Zhou L, Sun Z L 2015 Opt. Express 23 6773
[18] Xu P, Huang Y Y, Su Z J, Zhang X L, Luo T Z, Peng W D 2015 Opt. Express 23 4887
[19] Huang H X, Ruan S C, Yang T, Xu P 2015 Nano-Micro Lett. 7 177
[20] Xu P, Huang Y Y, Zhang X L, Huang J F, Li B B, Ye E, Duan S F, Su Z J 2013 Opt. Express 21 20159
[21] Xu P, Huang H X, Wang K, Ruan S C, Yang J, Wang L L, Chen X X, Liu J Y 2007 Opt. Express 15 809
[22] Cormier G, Boudreau B, Thriault S 2001 J. Opt. Soc. Am. A 18 1771
[23] Wang S, Magusson R 1990 J. Opt. Soc. Am. A 7 1470
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