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With the development of the microstructure fabrication process and the integration of micro-optical elements, diffractive micro-optical elements are widely used in broadband light sources, such as the integrated light guide plate (ILGP). And with the structural feature size of the ILGP decreasing from tens of microns to microns and even sub-microns, the diffraction dispersion phenomenon will inevitably become a prominent problem in research and design of non-dispersion elements. Nevertheless, under the broadband light source illumination, the analysis of the dispersion characteristic of diffraction spectrum of the microstructure array has not been reported in detail. Therefore a theoretical model of micro-optical element with a typical one-dimensional rectangular phase grating (RPG) and a widely used white LED source is established in this paper. The dispersion characteristic of the diffraction spectrum is studied, that is, with the increase of period of the RGP or the cone angle of incident beam, the dispersion of diffraction spectrum weakens. Dispersion parameter C and its formula are proposed, which can precisely measure the chromatic dispersion degree of the diffraction spectrum. Furthermore, the boundary criterion point of non-dispersion C = 0.3 is given explicitly. It is explored that no matter whether the cone angle of incident beam or the RPG period increases, the non-dispersion output light can be obtained only by matching the two parameters to make the dispersion parameter C less than 0.3. Then an RPG sample, of which the structural parameters are consistent with the designed ones, is fabricated by using micro-nano processing technology. By changing the cone angle of incident beam, the luminance and the chromaticity coordinates of the diffraction beam are tested. The analyses of the test results of the fabricated RPG sample show that the spectrum dispersion regularity is in accord with the theoretical analysis. The consistency verifies the correctness of dispersion parameter C, its formula and the non-dispersion boundary criterion point. The dispersion parameter C and non-dispersion boundary criterion point presented in this paper provide a guidance for analyzing the dispersion characteristics when the structural parameters of the integrated light guide plate and other broadband micro-optical element are designed.
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Keywords:
- micro-optical element /
- broadband light source /
- non-dispersion /
- integrated light guide plate
[1] Xu P, Huang H X, Wang K, Ruan S C, Yang J, Wan L L, Chen X X, Liu J Y 2007 Opt. Express 15 809
Google Scholar
[2] Xu P, Hong C Q, Cheng G X, Zhou L, Sun Z L 2015 Opt. Express 23 6773
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Google Scholar
[4] 黄海漩, 徐平, 阮双琛, 杨拓, 袁霞, 黄燕燕 2015 物理学报 64 154212
Google Scholar
Huang H X, Xu P, Ruan S C, Yang T, Yuan X, Huang Y Y 2015 Acta Phys. Sin. 64 154212
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[7] Thomschke M, Reineke S, Lüssem B, Leo K 2012 Nano Lett. 12 424
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[12] 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
Google Scholar
[13] Xu P, Huang Y Y, Su Z J, Zhang X L, Luo T Z, Peng W D 2015 Opt. Express 23 4887
Google Scholar
[14] Xu P, Yan Z L, Wan L L, Huang H X 2004 Proceedings of SPIE Holography Diffractive Optics and Applications Ⅱ Beijing, China, November 8−11, 2004 p66
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Google Scholar
[16] Yang X P, Yan Y B, Jin G F 2005 Opt. Express 13 8349
Google Scholar
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Google Scholar
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Google Scholar
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Zhang Y M 2008 Applied Optics (Beijing: Publishing House of Electronics Industry) Chapter 7 (in Chinese)
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Lü N G 2006 Fourier Optics (Beijing: China Machine Press) pp70−113 (in Chinese)
[21] 苏显渝, 李继陶 1999 信息光学 (北京:科学出版社) 第44页
Su X Y, Li J T 1999 Information Optics (Beijing: Science Press) p44 (in Chinese)
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图 1 宽带光源微光学元件衍射理论模型图(宽带光源为白光LED, 微光学元件为矩形位相光栅)
Figure 1. Diffraction theoretical model under the broadband light source illumination. The broadband light source is a white LED, and the microstructure array is the RPG.
图 2 零级、± 1级三衍射级次的相对光强分布 (a)−(e)入射光束锥角θ和光栅周期d分别分别为(7.5°, 4 μm), (7.5°, 8 μm), (7.5°, 40 μm), (14.5°, 4 μm), (102.5°, 4 μm); 图中红色、绿色、蓝色线分别代表三原色的红光、绿光、蓝光; 零级、+1级、–1级分别用粗横线、竖短线、细横线表示
Figure 2. Relative light intensity distributions of zero, positive and negative one order of diffraction beams of three primary colors, where the RPG period d and the cone angle of incident beam θ of (a)−(e) are (7.5°, 4 μm), (7.5°, 8 μm), (7.5°, 40 μm), (14.5°, 4 μm) and (102.5°, 4 μm) respectively. The red, green, blue line represents the red, green, blue light of three primary colors respectively. The zero, positive and negative one order beam is represented by the thick horizontal, vertical short and thin horizontal line respectively.
图 3 色散量C的相关定参量示意图, 其中红线、黑线分别代表红色光束、零级光束
Figure 3. Relevant parameters of the dispersion parameter C. Where the red, black line respectively represents the red, zero order light beam.
图 4 色散量C与矩形位相光栅周期d, LED入射光束锥角θ的关系 (a)矩形位相光栅周期d; (b) LED入射光束锥角θ; 其中红圆圈表示零色散的边界点
Figure 4. Influences of grating period d and incident light cone angle θ on the dispersion parameter C. (a), (b) is the calculated relationship curve between C and d, or θ respectively, where the red circles represent the zero-dispersion boundary points.
图 5 矩形光栅样品的结构测试图 (a)光刻显影后; (b)紫外线压印后
Figure 5. Structural testing diagrams of the RPG sample: (a) After being developed; (b) the structural testing diagrams of the final sample after UV stamping.
图 6 实验光束观测图 (a)零色散边界点(θ = 34.71°, d = 4 µm); (b) θ = 3.58°, d = 4 µm
Figure 6. Observation diagram of the diffraction beam: (a) At zero-dispersion boundary point (θ = 34.71°, d = 4 µm); (b) θ = 3.58°, d = 4 µm.
图 7 色散量C的理论值和测试值与入射光束锥角θ关系曲线的对比
Figure 7. Contrast curves of the relationship between the test and theoretical value of C with θ.
表 1 不同入射光束锥角θ在观察平面中点所对应的衍射光谱的亮度值和色坐标
Table 1. Luminance and chromaticity coordinate of the center diffraction spectrum with different θ.
θ 102.68º 64.01º 45.24º 34.71º Luminance L (cd/m2) 6105.6 5161.2 4018.2 3262.1 Chromaticity Coordinate x = 0.2978
y = 0.2828x = 0.3024
y = 0.2798x = 0.3074
y = 0.2779x = 0.3025
y = 0.2770
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[1] Xu P, Huang H X, Wang K, Ruan S C, Yang J, Wan L L, Chen X X, Liu J Y 2007 Opt. Express 15 809
Google Scholar
[2] Xu P, Hong C Q, Cheng G X, Zhou L, Sun Z L 2015 Opt. Express 23 6773
Google Scholar
[3] Huang H X, Ruan S C, Yang T, Xu P 2015 Nano-Micro Lett. 7 177
Google Scholar
[4] 黄海漩, 徐平, 阮双琛, 杨拓, 袁霞, 黄燕燕 2015 物理学报 64 154212
Google Scholar
Huang H X, Xu P, Ruan S C, Yang T, Yuan X, Huang Y Y 2015 Acta Phys. Sin. 64 154212
Google Scholar
[5] 徐平, 袁霞, 杨拓, 黄海漩, 唐少拓, 黄燕燕, 肖钰斐, 彭文达 2017 物理学报 66 124201
Google Scholar
Xu P, Yuan X, Yang T, Huang H X, Tang S T, Huang Y Y, Xiao Y F, Peng W D 2017 Acta Phys. Sin. 66 124201
Google Scholar
[6] 徐平, 唐少拓, 袁霞, 黄海漩, 杨拓, 罗统政, 喻珺 2018 物理学报 67 024202
Google Scholar
Xu P, Tang S T, Yuan X, Huang H X, Yang T, Luo T Z, Yu J 2018 Acta Phys. Sin. 67 024202
Google Scholar
[7] Thomschke M, Reineke S, Lüssem B, Leo K 2012 Nano Lett. 12 424
Google Scholar
[8] Siitonen S, Laakkonen P, Vahimaa P, Kuittinen M, Tossavainen N 2006 Appl. Opt. 45 2623
Google Scholar
[9] Zhao X N, Hu J P, Lin Y, Xu F, Zhu X J, Pu D L, Chen L S, Wang C H 2016 Sci. Rep. 6 28319
Google Scholar
[10] Xue C X, Cui Q F 2010 Opt. Lett. 35 986
Google Scholar
[11] Tsukamoto H, Nishiyama M 2006 Jpn. J. Appl. Phys. 45 6678
Google Scholar
[12] 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
Google Scholar
[13] Xu P, Huang Y Y, Su Z J, Zhang X L, Luo T Z, Peng W D 2015 Opt. Express 23 4887
Google Scholar
[14] Xu P, Yan Z L, Wan L L, Huang H X 2004 Proceedings of SPIE Holography Diffractive Optics and Applications Ⅱ Beijing, China, November 8−11, 2004 p66
[15] Park S R, Kwon O J, Shin D, Song S H, Lee H S, Choi H Y 2007 Opt. Express 15 2888
Google Scholar
[16] Yang X P, Yan Y B, Jin G F 2005 Opt. Express 13 8349
Google Scholar
[17] Caputo R, Sio L D, Jak M J J, Hornix E J, Boer D K G, Cornelissen H J 2007 Opt. Express 15 10540
Google Scholar
[18] Xu M, Urbach H P, Boer D K G 2007 Opt. Express 15 5789
Google Scholar
[19] 张以谟 2008 应用光学 (北京:电子工业出版社) 第7章
Zhang Y M 2008 Applied Optics (Beijing: Publishing House of Electronics Industry) Chapter 7 (in Chinese)
[20] 吕乃光 2006 傅里叶光学 (北京:机械工业出版社)第70−113页
Lü N G 2006 Fourier Optics (Beijing: China Machine Press) pp70−113 (in Chinese)
[21] 苏显渝, 李继陶 1999 信息光学 (北京:科学出版社) 第44页
Su X Y, Li J T 1999 Information Optics (Beijing: Science Press) p44 (in Chinese)
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