The hexagonal arranging structures of cylinder, hexagon and square pillar are analyzed and compared below. Fig. 2-17 shows hexagonal arranging structures of cylinder pillar. Fig. 2-18 shows that TE mode and TM mode Photonic Band Gap (PBG) in cylinder respectively. Fig. 2-19 shows hexagonal arranging structures of hexagon pillar. Fig. 2-20 show that TE mode and TM mode Photonic Band Gap (PBG) in hexagon
respectively. Fig. 2-21 shows hexagonal arranging structures of square pillar. Fig. 2-22 show that TE mode and TM mode Photonic Band Gap (PBG) in square respectively.
It is an optical communication time now so optical sensor is applied to the optical communication system hopefully. And it is set a monitor point at receiver of the sensor assembled in various structures, Fig. 2-23 shows that it has the best transmittance in cylinder arranging at TE mode for 1.55 μm of wavelength and it is the same for TM mode showed in Fig. 2-24. We take1.55 μm wavelength of light as incident light and set x-axis at receiver port to monitor the change of transmittance as shown Fig. 2-25. It shows that it has the best transmission and uniform transmittance density in cylinder for TE mode in Fig. 2-26. And it shows that it has the best transmittance at x-axis and uniform transmittance density in cylinder for TM mode in Fig. 2-27. And utilize the sensor to soak in the solution of sample and come to do the Simulation and analysis as shown Fig.2-28. We monitor the change of transmittance by adjusting refractive index slightly.
Because refractive index of liquid or lived being’s DNA is about between 1 and 2, it can be simulated the transmittance in such a refractive index
Fig. 2-29 showed that transmittance in cylinder arranging for TE mode is
the largest and has the largest response according to the change of refractive index, the relation of refractive index and transmittance is linear.
And the transmittance for TM mode is the largest and has largest change according refractive index in cylinder or square pillar showed in Fig. 2-30.
2-6 Summy
According to the various analysis of 2-D silicon array with cubic and hexagonal lattice of several shapes are compared in this chapter. The several shapes are included cylinder, square and hexagon. The author will make some discussions and conclusions in follow texts. Accord to compare and analysis of the various structures in section 2-5, Fig. 2-31 shows that it has the best transmission in hexagonal structures of cylinder arranging at TE mode for optical communication always used 1.55 μm of wavelength and it is the same for TM mode showed in Fig. 2-32. We take 1.55 μm wavelength of light as incident light and set x-axis at receiver port to monitor the change of transmittance. It shows that it has the best transmittance and uniform transmittance density in hexagonal structures of
cylinder arranging for TE mode in Fig. 2-33 and it is the same for TM mode showed in Fig. 2-34. And we monitor the change of transmission by adjusting refractive index slightly. From Fig. 2-35, Fig. 2-36, we can obtain the TE mode and TM mode has large change in refractive index in hexagonal structures of cylinder. There are linear relative in transmission and refractive curve. The grade difference of TE, TM mode curve in Fig.
2-37 show the trend of polarization. Our sensors were very sensitive. From the comparison of the results, hexagonal structures of cylinder are the best arrange of sensor design.
Fig. 2-1 Working Principle of the Sensor Using Si-Nanopillar Array
Hy
Ez
Hx
Hx
Hy
Hz
Hz
Ey
Hz
z
Hx
Ex
y
x (i, j,k)
Hy
Fig. 2-2Position of the electric and magnetic field vector components about a cubic unit cell of the Yee space lattice[51]
) ) (b
(a
Fig. 2-3 The cubic arranging structures of cylinder. (a) Vertical view (b) Side view
Γ X
M
Γ X
M
) ) (b
(a
Fig. 2-4 The cubic arranging structures of cylinder of (a) TE band
)
(a (b)
Fig. 2-5 The cubic arranging structures of hexagon. (a) Vertical view (b) Side view
Γ X
M
Γ X
M
)
(a (b)
Fig. 2-6 The cubic arranging structures of hexagon of (a) TE band structure, (b) TM band structure.
)
(a (b)
Fig. 2-7 The cubic arranging structures of square. (a) Vertical view (b) Side view
Γ X
M
Γ X
M
)
(a (b)
. 2-8 The cubic arranging structures of square of (a) TE band structure, (b)
1.5 1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59 1.6 0
0.2 0.4 0.6 0.8
Normalized Transmittance
Wavelength (μm)
Fig. 2-9 Simulation resules in cubic arranging structure at TE mode for 1.55 μm of wavelength.
1.5 1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59 1.6 0
0.2 0.4 0.6 0.8 1
Cubic-Cylinder Cubic-Hexgon Cubic-Square
Normalized Transmittance
Wavelength (μm)
Fig. 2-10 Simulation resules in cubic arranging structure at TM mode for 1.55 μm of wavelength.
0 2.5
0 2.5 0 2.5
LIGHT
LIGHT LIGHT
) ) (c
(a (b)
Fig. 2-11 We take1.55 μm wavelength of light as incident light and set x-axis at receiver port to monitor the change of transmittance, the cubic arranging structures of (a) cylinder (b) hexagon (c) square.
0 0.5 1 1.5 2 2.5
0 0.2 0.4 0.6 0.8 1
Cubic-Cylinder Cubic-Hexagon Cubic-Square
Normalized Transmittance
χ position (μm)
Fig. 2-12 Simulation resules that we take1.55 μm wavelength of light as
0 0.5 1 1.5 2 2.5 0
0.2 0.4 0.6
Normalized Transmittance
χ position (μm)
Fig. 2-13 Simulation resules that we take1.55 μm wavelength of light as incident light and set x-axis at receiver port to monitor the change of transmittance at TM mode.
Fig. 2-14 Utilize the cubic structure sensor to soak in the solution of sample and come to do the simulation and analysis.
Refractive index variation
Fig. 2-15 The change of transmittance by adjusting refractive index slightly at TE mode.
Fig. 2-16 The change of transmittance by adjusting refractive index
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 0
0.2 0.4 0.6 0.8
Normalized Transmittance
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 0
0.2 0.4 0.6 0.8 1
Cubic-Cylinder Cubic-Hexagon Cubic-Square
Normalized Transmittance
Refractive index variation
) ) (b
(a
Fig. 2-17 The hexagonal arranging structures of cylinder. (a) Vertical view (b) Side view
)
(a (b)
Fig. 2-18 The hexagonal arranging structures of cylinder of (a) TE band structure, (b) TM band structure.
)
(a (b)
Fig. 2-19 The hexagonal arranging structures of hexagon. (a) Vertical view (b) Side view
)
(a (b)
Fig. 2-20 The hexagonal arranging structures of hexagon of (a) TE band structure, (b) TM band structure.
)
(a (b)
Fig. 2-21 The hexagonal arranging structures of square. (a) Vertical view (b) Side view
)
(a (b)
Fig. 2-22 The hexagonal arranging structures of square of (a) TE band structure, (b) TM band structure.
1.5 1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59 1.6 0
0.2 0.4 0.6 0.8
Fig. 2-23 Simulation resules in hexagonal arranging structure at TE mode for 1.55 μm of wavelength.
1.5 1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59 1.6 0
0.2 0.4 0.6 0.8 1
Hexagonal-Cylinder
Normalized Transmittance
Hexagonal-Hexgon Hexagonal-Square
Wavelength (μm)
Wavelength (μm)
Normalized Transmittance
Fig. 2-25 We take1.55 μm wavelength of light as incident light and set x-axis at receiver port to monitor the change of transmittance, the hexagonal arranging structures of (a) cylinder (b) hexagon (c) square.
Fig. 2-26 Simulation resules that we take1.55 μm wavelength of light as incident light and set x-axis at receiver port to monitor the change of transmittance at TE mode.
) (a
LIGHT
LIGHT LIGHT
)
(b (c)
0 0.5 1 1.5 2 2.5
0 0.4 0.8
0.2 0.6 1
Hexagonal-Cylinder Hexagonal-Hexagon Hexagonal-Square
Normalized Transmittance
χ position (μm)
Fig. 2-27 Simulation resules that we take1.55 μm wavelength of light as incident light and set x-axis at receiver port to monitor the change of transmittance at TE mode.
Fig. 2-28 Utilize the hexagonal structure sensor to soak in the solution of
0 0.5 1 1.5 2 2.5
0 0.4 0.8
0.2 0.6
Normalized Transmittance
χ position (μm)
Fig. 2-29 We monitor the change of transmittance by adjusting refractive index slightly at TE mode.
Fig. 2-30 We monitor the change of transmittance by adjusting refractive index slightly at TM mode.
Refractive index variation
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 0
0.4 0.8
0.2 0.6
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
Normalized Transmittance Normalized Transmittance
2 0
0.4 0.8
0.2 0.6 1
Hexagonal-Cylinder Hexagonal-Hexagon Hexagonal-Square
Refractive index variation
1.5 1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59 1.6 0
0.2 0.4 0.6 0.8 1
1.2 Cubic-Square
Fig. 2-31 Simulation resules in various structures at TE mode for 1.55 μm of wavelength.
1.5 1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59 1.6 0
0.2 0.4 0.6 0.8 1 1.2 1.4
1.6 Hexagonal-Cylinder
Normalized Transmittance Normalized Transmittance
Wavelength (μm)
Hexagonal-Hexgon Hexagonal-Square Cubic-Cylinder Cubic-Hexagon Cubic-Square
Wavelength (μm)
Fig. 2-33 Simulation resules that we take1.55 μm wavelength of light as incident light and set x-axis at receiver port to monitor the change of transmittance at TE mode.
Fig. 2-34 Simulation resules that we take1.55 μm wavelength of light as incident light and set x-axis at receiver port to monitor the change of transmittance at TE mode.
0 0.5 1 1.5 2 2.5
0 0.4 0.8
0.2 0.6 1
0 0.5 1 1.5 2 2
Normalized Transmittance
χ position (μm)
.5 0
0.4 0.8 1.2
0.2 0.6 1
Hexagonal-Cylinder Hexagonal-Hexagon Hexagonal-Square Cubic-Cylinder Cubic-Hexagon Cubic-Square
Normalized Transmittance
χ position (μm)
Fig. 2-35 We monitor the change of transmittance by adjusting refractive index slightly at TE mode.
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 0
0.4 0.8
0.2 0.6
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
Normalized Transmittance
Refractive index variation
2 0
0.4 0.8 1.2
0.2 0.6 1
Hexagonal-Cylinder Hexagonal-Hexagon Hexagonal-Square Cubic-Cylinder Cubic-Hexagon Cubic-Square
Normalized Transmittance
Refractive index variation
Fig. 2-34 We monitor the change of transmittance by adjusting refractive
1.2 1.3 1.4 1.5 1.6 0
0.2 0.4 0.6 0.8
0 0.2 0.4 0.6 0.8
Normalized Transmittance
Refractive index variation
Fig. 2-37 We can obtain the TE mode and TM mode has large change in refractive index in hexagonal structures of cylinder. There are linear relative in transmission and refractive curve.