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

Yixin CHEN; Xiuhua FU; Gong ZHANG; Jing ZHANG; Fei YANG

doi:10.3788/gzxb20215011.1131002

Journals >Acta Photonica Sinica >Volume 50 >Issue 11 >Page 1131002 > Article

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

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

Yixin CHEN¹, Xiuhua FU^1、*, Gong ZHANG¹, Jing ZHANG¹, and Fei YANG²

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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DOI: 10.3788/gzxb20215011.1131002 Cite this Article

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 Copy Citation Text

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Fig. 1. （A B）^N periodic structure of 1-D photonic crystal

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Fig. 2. Dispersion curve of（A B）^N，（A B A）^N and（A B B A）^N

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Fig. 3. Dispersion curve corresponding to thickness d₁，d₂ and 0.5 d₁，d₂

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Fig. 4. Dispersion curve of

n_{a} = 1.38

and

n_{B} / n_{A} = 1.7

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Fig. 5. Band gap of n_A=1.38 and

n_{B} / n_{A} = 1.7

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Fig. 6. The width of the first band gap when

n_{A}

n_{B} / n_{A}

is a fixed value is the fixed value

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Fig. 7. When

n_{A}

is a fixed value，the forbidden band width of the second forbidden band，the third forbidden band and the fourth forbidden band

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$Forbidden band width with constant refractive index ratio$

Fig. 8. Forbidden band width with constant refractive index ratio

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$Dispersion curve when coefficient，center wavelength，incident angle and refractive index ratio are the same$

Fig. 9. Dispersion curve when coefficient，center wavelength，incident angle and refractive index ratio are the same

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Fig. 10. Dispersion curve and band gap width corresponding to center wavelength 300~1 100 nm

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$The width of the band gap of the center wavelength under different refractive index ratios$

Fig. 11. The width of the band gap of the center wavelength under different refractive index ratios

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$The position where each band gap of the center wavelength ends under different refractive index ratios$

Fig. 12. The position where each band gap of the center wavelength ends under different refractive index ratios

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Fig. 13. The dispersion curve and band gap width corresponding to different incident angles

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Fig. 14. Dispersion curve and spectrum comparison of blue and green notch filters

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Fig. 15. Dispersion curve and spectrum comparison of blue and green notch filters

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Material_L	n	Material_H	n
Na₃AlF₆	1.3/1.38	TiO₂	1.9/2.3
MgF₂	1.38	H₄	2.1
SiO₂	1.46	Ta₂O₅	2.16
Al₂O₃	1.54/1.62	Ti₃O₅	2.35
YbF₃	1.52/1.48	ZnS	2.35/2.16
SiO	1.55	Ge	4.4

Table 1. Refractive index of common materials^［7］

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n_A	p₃	p₄	n_B/n_A	p₃	p₄
1.22	195.7	-174.7	1.5	81.79	12.36
1.3	208.9	-187.8	2	170	13.6
1.38	221.9	-201.8	2.5	250	19
1.46	223.2	-214.8	3	332.9	13.01
1.54	247.8	-226	3.5	409.6	10.14
1.62	260.5	-237.8	4	482.9	9.01

Table 2. The value of the fitting coefficient when n_A or n_B/n_A is a fixed value

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$n_{A}$	$n_{B} / n_{A}$ <1.7		$n_{B} / n_{A}$ >1.7
$n_{A}$	p₅	p₆	p₅	p₆
1.22	-23.57	40.14	63.02	-110
1.3	-23.57	40.14	66.79	-117.3
1.38	-27.86	47.71	70.51	-124.1
1.46	-27.86	47.71	74.43	-131.9
1.54	-30.71	52.43	78.78	-140.8
1.62	-33.57	57.14	81.63	-145

Table 3. Fitting coefficient value of the second band gap

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$n_{A}$	a₁	a₂	a₃	b₁	b₂	b₃	c₁	c₂	c₃
1.22	19.14	183.8	186.6	0.369	4.78	4.713	1.246	0.197 4	-9.074
1.3	20.24	135	137.2	0.462 1	4.84	4.744	0.927 4	-0.021 58	-9.227
1.38	22.14	100.6	103.5	0.497 4	4.887	4.757	0.859 1	-0.272 9	-9.401
1.46	22.81	130.7	132.4	0.589 7	4.921	132.4	0.532	-0.337 4	-9.521
1.54	24.17	127.3	129.2	0.691 6	4.819	4.707	0.212 3	-0.036 79	-9.205
1.62	35.62	14	4.808	0.009 035	2.978	7.958	0.540 9	7.478	-3.945

Table 4. Fitting coefficient value of the third band gap

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$n_{A}$	a₁	a₂	a₃	b₁	b₂	b₃	c₁	c₂	c₃
1.22	30.87	22.71	3.824	0.886 6	1.427	2.764	-0.416 8	1.942	7.032
1.3	377.6	364	2.825	0.807	0.888	3.215	0.850 1	3.827	6.142
1.38	396.7	388.1	1.715	0.826 7	0.889 9	3.549	0.7702	3.796	4.953
1.46	41.76	34.82	2.985	0.846 6	1.354	3.25	-0.016	2.35	5.766
1.54	27.44	9.238	3.796	0.596	2.532	3.408	-0.549	-0.497	5.888
1.62	35.43	11.1	7.783	0.588 3	3.975	4.598	-0.787 5	-3.809	3.906

Table 5. Fitting coefficient value of the fourth band gap

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$n_{A}$	n_B/n_A
1.22	3.26
1.3	3.288
1.38	3.316
1.46	3.344
1.54	3.72
1.62	3.4

Table 6. The corresponding n_A and n_B/n_A when the third forbidden band disappears

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n_B/n_A	Second band gap		Third band gap		Fourth band gap
n_B/n_A	p₇	p₈	p₇	p₈	p₇	p₈
1.5	0	7	12.5	-3.25	0.1	3
2	0.4	15	239.3	-280.5	0.2	8
2.5	22.5	18.55	25	-11.5	12.5	2.75
3	52.5	14.95	12.5	-6.25	22.5	-3.45
3.5	77.5	17.45	-12.5	23.25	25	-6.5
4	100	20	0	27	25	-12.5

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

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n_B/n_A	First band gap		Second band gap		Third band gap		Fourth band gap
n_B/n_A	p₁	p₂	p₁	p₂	p₁	p₂	p₁	p₂
1.4	0.262 5	1.65	0.018 5	-0.35	0.026 5	-0.15	0.007	1.1
1.5	0.304 5	9.25	0.022 5	0.45	0.031	-0.3	0.011 5	-0.45
2	0.519 5	0.15	0.047 5	-1.65	0.045	-0.5	0.022 5	-0.95
2.5	0.681	0.5	0.062	-0.6	0.054	-0.2	0.029	-0.7
3	0.819 5	-0.45	0.071 5	0.55	0.06	0	0.031	0.9
3.5	0.940 5	0.25	0.08	0	0.064 5	0.45	0.036 5	1.45
4	1.052	-0.2	0.087 5	-0.45	0.069	0.3	0.04	0

Table 8. Fitting coefficient values of the four band gaps

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n_B/n_A	First band gap		Second band gap		Third band gap		Fourth band gap
n_B/n_A	p₁	p₂	p₁	p₂	p₁	p₂	p₁	p₂
1.4	0.85	0	0.318	0.35	0.0255	0.85	0.196	0.225
1.5	0.842	0.6
2	0.801	0.35
2.5	0.78	0
3	0.773	0.9
3.5	0.765	0.35
4	0.751 5	0.35

Table 9. Fitting coefficient values of the four band gaps

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Coefficien	p₉	p₁₀	p₁₁
First band gap	0.015 19	-0.100 5	186.1
Second band gap	0.007 725	-0.050 79	0.047 62
Third band gap	0.002 828	-0.006 061	20.01
Fourth band gap	0.000 529 1	0.066 67	-0.119

Table 10. Fitting coefficient values of the four band gaps

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RGB notch filter	Design requirements/nm	Dispersion curve/nm	Transmittance spectrum/nm
Bule notch filter	385~505	385~505	386~504
Green notch filter	525~575	525~575	526~575
Red notch filter	600~700	600~654/650~700	601~653/651~700

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

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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