Acta Photonica Sinica, Volume. 50, Issue 11, 1131002(2021)

Design Method of Notch Filter Based on One-dimensional Photonic Crystal Band Structure

Yixin CHEN1... Xiuhua FU1,*, Gong ZHANG1, Jing ZHANG1 and Fei YANG2 |Show fewer author(s)
Author Affiliations
  • 1College of Photoelectric Engineering,Changchun University of Science and Technology,Changchun 130022,China
  • 2Changchun Institute of Optics,Fine Mechanics and Physics,Chinese Academy of Sciences,Changchun 130033,China
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    Figures & Tables(26)
    (A B)^N periodic structure of 1-D photonic crystal
    Dispersion curve of(A B)^N,(A B A)^N and(A B B A)^N
    Dispersion curve corresponding to thickness d1,d2 and 0.5 d1,d2
    Dispersion curve of na=1.38 and nB/nA=1.7
    Band gap of nA=1.38 and nB/nA=1.7
    The width of the first band gap when nA or nB/nA is a fixed value is the fixed value
    When nA is a fixed value,the forbidden band width of the second forbidden band,the third forbidden band and the fourth forbidden band
    Forbidden band width with constant refractive index ratio
    Dispersion curve when coefficient,center wavelength,incident angle and refractive index ratio are the same
    Dispersion curve and band gap width corresponding to center wavelength 300~1 100 nm
    The width of the band gap of the center wavelength under different refractive index ratios
    The position where each band gap of the center wavelength ends under different refractive index ratios
    The dispersion curve and band gap width corresponding to different incident angles
    Dispersion curve and spectrum comparison of blue and green notch filters
    Dispersion curve and spectrum comparison of blue and green notch filters
    • Table 1. Refractive index of common materials7

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      Table 1. Refractive index of common materials7

      MaterialLnMaterialHn
      Na3AlF61.3/1.38TiO21.9/2.3
      MgF21.38H42.1
      SiO21.46Ta2O52.16
      Al2O31.54/1.62Ti3O52.35
      YbF31.52/1.48ZnS2.35/2.16
      SiO1.55Ge4.4
    • Table 2. The value of the fitting coefficient when nA or nB/nA is a fixed value

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      Table 2. The value of the fitting coefficient when nA or nB/nA is a fixed value

      nAp3p4nB/nAp3p4
      1.22195.7-174.71.581.7912.36
      1.3208.9-187.8217013.6
      1.38221.9-201.82.525019
      1.46223.2-214.83332.913.01
      1.54247.8-2263.5409.610.14
      1.62260.5-237.84482.99.01
    • Table 3. Fitting coefficient value of the second band gap

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      Table 3. Fitting coefficient value of the second band gap

      nAnB/nA<1.7nB/nA>1.7
      p5p6p5p6
      1.22-23.5740.1463.02-110
      1.3-23.5740.1466.79-117.3
      1.38-27.8647.7170.51-124.1
      1.46-27.8647.7174.43-131.9
      1.54-30.7152.4378.78-140.8
      1.62-33.5757.1481.63-145
    • Table 4. Fitting coefficient value of the third band gap

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      Table 4. Fitting coefficient value of the third band gap

      nAa1a2a3b1b2b3c1c2c3
      1.2219.14183.8186.60.3694.784.7131.2460.197 4-9.074
      1.320.24135137.20.462 14.844.7440.927 4-0.021 58-9.227
      1.3822.14100.6103.50.497 44.8874.7570.859 1-0.272 9-9.401
      1.4622.81130.7132.40.589 74.921132.40.532-0.337 4-9.521
      1.5424.17127.3129.20.691 64.8194.7070.212 3-0.036 79-9.205
      1.6235.62144.8080.009 0352.9787.9580.540 97.478-3.945
    • Table 5. Fitting coefficient value of the fourth band gap

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      Table 5. Fitting coefficient value of the fourth band gap

      nAa1a2a3b1b2b3c1c2c3
      1.2230.8722.713.8240.886 61.4272.764-0.416 81.9427.032
      1.3377.63642.8250.8070.8883.2150.850 13.8276.142
      1.38396.7388.11.7150.826 70.889 93.5490.77023.7964.953
      1.4641.7634.822.9850.846 61.3543.25-0.0162.355.766
      1.5427.449.2383.7960.5962.5323.408-0.549-0.4975.888
      1.6235.4311.17.7830.588 33.9754.598-0.787 5-3.8093.906
    • Table 6. The corresponding nA and nB/nA when the third forbidden band disappears

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      Table 6. The corresponding nA and nB/nA when the third forbidden band disappears

      nAnB/nA
      1.223.26
      1.33.288
      1.383.316
      1.463.344
      1.543.72
      1.623.4
    • Table 7. Fitting coefficient values of the second,third,and fourth band gaps

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      Table 7. Fitting coefficient values of the second,third,and fourth band gaps

      nB/nASecond band gapThird band gapFourth band gap
      p7p8p7p8p7p8
      1.50712.5-3.250.13
      20.415239.3-280.50.28
      2.522.518.5525-11.512.52.75
      352.514.9512.5-6.2522.5-3.45
      3.577.517.45-12.523.2525-6.5
      41002002725-12.5
    • Table 8. Fitting coefficient values of the four band gaps

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      Table 8. Fitting coefficient values of the four band gaps

      nB/nAFirst band gapSecond band gapThird band gapFourth band gap
      p1p2p1p2p1p2p1p2
      1.40.262 51.650.018 5-0.350.026 5-0.150.0071.1
      1.50.304 59.250.022 50.450.031-0.30.011 5-0.45
      20.519 50.150.047 5-1.650.045-0.50.022 5-0.95
      2.50.6810.50.062-0.60.054-0.20.029-0.7
      30.819 5-0.450.071 50.550.0600.0310.9
      3.50.940 50.250.0800.064 50.450.036 51.45
      41.052-0.20.087 5-0.450.0690.30.040
    • Table 9. Fitting coefficient values of the four band gaps

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      Table 9. Fitting coefficient values of the four band gaps

      nB/nAFirst band gapSecond band gapThird band gapFourth band gap
      p1p2p1p2p1p2p1p2
      1.40.8500.3180.350.02550.850.1960.225
      1.50.8420.6
      20.8010.35
      2.50.780
      30.7730.9
      3.50.7650.35
      40.751 50.35
    • Table 10. Fitting coefficient values of the four band gaps

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      Table 10. Fitting coefficient values of the four band gaps

      Coefficienp9p10p11
      First band gap0.015 19-0.100 5186.1
      Second band gap0.007 725-0.050 790.047 62
      Third band gap0.002 828-0.006 06120.01
      Fourth band gap0.000 529 10.066 67-0.119
    • Table 11. The forbidden band(cut-off zone)required by the design of RGB notch filter and the corresponding actual results

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      Table 11. The forbidden band(cut-off zone)required by the design of RGB notch filter and the corresponding actual results

      RGB notch filterDesign requirements/nmDispersion curve/nmTransmittance spectrum/nm
      Bule notch filter385~505385~505386~504
      Green notch filter525~575525~575526~575
      Red notch filter600~700600~654/650~700601~653/651~700
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    Yixin CHEN, Xiuhua FU, Gong ZHANG, Jing ZHANG, Fei YANG. Design Method of Notch Filter Based on One-dimensional Photonic Crystal Band Structure[J]. Acta Photonica Sinica, 2021, 50(11): 1131002

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    Paper Information

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    Received: May. 6, 2021

    Accepted: Aug. 18, 2021

    Published Online: Dec. 2, 2021

    The Author Email: FU Xiuhua (goptics@163.com)

    DOI:10.3788/gzxb20215011.1131002

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