In this section, we design a one-dimensional (1-D) resonant square holes photonic bandgap (PBG) filter based on plasma effect by BeamPROP.
We simulate the phase shift effect and the filtering wavelength with adding various voltages. The refractive index changes in the modulator mechanism also are calculated with adding various voltages. The total length of the resonant square PBG filter waveguide L and electrode pad L is 112.9µm.
The width of input port Wi and electrode pad Wp is 2.1µm and 60µm, respectively. The three-dimensional (3-D) structure of resonant square holes PBG filter waveguide with electrode pads is shown in Fig. 2-3. The dot regions are the p-type and n-type regions and the dark regions are electrode pads. The electrode pads are above doping regions and the electrode pads Wn is also 60µm.
In our designed 1-D resonant square holes PBG has 36 square holes, which are spaced 4.45µm apart. This square hole-to-hole separation increases to 0.85 (for =3µm) or 2.55µm for the center two square holes, giving rise to the quarter wave-like phase shift that gives the transmission resonance. Where is the distance between neighboring holes center-to-center or called the period of the photonic crystal. The width of each square hole is 0.15a or 0.45µm. The length and the width of the entire waveguide is 112.9µm and 0.7 or 2.1µm, respectively. This small size allows for a compact integration of many wavelength filters on a small chip. A slightly longer version of this structure (one with more air holes) can act as a high microcavity. The main feature of 1-D resonant square holes PBG filter waveguide is exhibited a narrow transmission peak centered at
a a
a
a
λ in a stopband. According to the above condition, we can get
the narrow transmission peak center wavelength at 1536.1nm. This happens in analogy with the effect caused by a defect in an electronic crystal and it is exhibited an allowed energy state inside the crystal energy bandgap.
In this section, our designed structure has two doping regions and that are composed by n-type and p-type in 1-D resonant square holes PBG waveguide regions. The phase modulator we used is the free-carrier dispersion effect in our designed 1-D resonant square holes PBG filter waveguide based on SOI wafer. By injection of carriers through the electrode pads, the refractive index of the horizontal p-i-n SOI structure can be changed. We use p-i-n junction and modulation voltage on the both side of the 1-D resonant square holes PBG filter waveguide to tune the filtering center transmission wavelength at the output port.
The active length of the modulator waveguid L is 112.9µm and the wavelength of the propagating mode λc is 1536.1nm. We can get the phase modulation of the resonant square PBG filter waveguide is 28.05°
follow the Eq. (2-3-6). In this case, we can calculate the average change in refractive index is –1.06×10-3 on the electronic pad region of the resonant square PBG filter waveguide and the center transmission wavelength shifting is 0.4nm. Fig. 2-11 show the relation of the transmittance and wavelength at various widths of the resonant quadrilateral holes PBG waveguide. According to the various width of the quadrilateral hole to design our resonant PBG filter waveguide. The width of the quadrilateral hole is 0.15a or 0.45µm and we can get the optimum value of the transmission wavelength. The center transmission wavelength is 1536.1nm
the maximum transmission of the guided light is 73.12%. Fig. 2-12 show the relation of the transmittance and wavelength at various lengths of the resonant quadrilateral holes PBG filter waveguide. The length of the quadrilateral holes is 0.15a or 0.45µm and we can get the optimum value of the transmission wavelength. The center transmission wavelength is 1536.1nm the maximum transmission of the guided light is 73.12%. Fig.
2-13 show the relation of the transmittance and wavelength at various holes number of the resonant square holes PBG filter waveguide. In the resonant square holes PBG filter waveguide and the holes number is 6, the bandwith and FWHM is larger than other case. In the resonant square holes PBG filter waveguide and the holes number is 56, the transmittance is smaller than other case. These two cases are not suitable to design for our resonant PBG filter waveguide. Hence, we chose the optimum holes number is 36 in resonant square holes PBG filter waveguide. The maximum transmission of the guided light is 73.12% and the transmission wavelength is in the center of the stopband. Both side wavelengths of the center transmission wavelength are not pass through the 1-D resonant square holes PBG filter waveguide. Fig. 2-14 shows the relation of the transmittance/reflectance and wavelength at various photonic crystal periods . According to the various photonic crystal periods to design our resonant square holes PBG filter structure and use the structure to filter various center narrow transmission wavelengths. The optimum value of the photonic crystal period is 3µm and the center transmission wavelength is 1536.1 nm without adding voltage. The transmittance and the width of the square holes as a function of wavelength is shown in Fig. 2-15. When the width of the
a
a
square holes is increased, the center narrow transmission wavelength is shifting. By tuning the width of the input waveguide, the center narrow transmission wavelength is also shifted. Then, we choose the optimum width of the square hole 0.15 a or 0.45µm to design our device. Fig. 2-16 show the relation of transmission/reflectance and wavelength with various waveguide widths, we choose the value of waveguide width is 0.7 or 2.1µm and the structure are conforming to the single mode waveguide.
a
Fig. 2-17 shows the transmittance and wavelength with tuning the phase shift length. Due to the quarter wavelength phase shift structure, we can get the narrow center transmission wavelength at output. According to the various phase shift length such as 4.80µm, 4.82µm, 4.84µm, 4.86µm, 4.88µm, 4.90µm, 4.92µm, 4.94µm, 4.96µm, 4.98µm and 5.00µm to filter various center transmission wavelength. In this section, we use the optimum value of phase shift length Lp=4.90µm to design our device. Fig.
2-18 shows the transmittance/reflectance and the effective refractive index change as a function of wavelength. When the extra voltage is increased, the effective refractive index change is raised. By tuning the refractive index change, the center narrow transmission wavelength and the transmittance is also shifted and decreased. Then, we can use the results to design 32 ports resonant PBG filter waveguide to connect the 32 channels sharp bend PBG waveguide and 32×32 PBG wavelength switch on one chip.
Fig. 2-19 show the transmittance (solid line) and reflectance (dashed line) as a function of wavelength. The wide bandgap is from 1530.5 to 1541.5 nm and a narrow transmission peak is near 1536.1 nm. The
transmittance outside the bandgap is large and the modes remain be guided as the light wave propagate through the resonant square holes PBG filter waveguide. The width (FWHM) of the transmission peak is 0.534 nm and the maximum transmission of the guided light is 73.12%. The factor can be computed directly and using the relation
Q
λ λ ∆
= /
Q , where ∆λ is the width of the resonance and λ is the peak wavelength of the resonance.
We can assign a quality factor of approximately 2876.5 to our λ/4
microcavity. The value is considerably high than other types of waveguide based microcavities. Fig. 2-20 shows transmittance (solid line) and reflectance (dashed line) as a function of wavelength with adding voltage in our designed resonant square holes PBG filter waveguide. In this case, we can calculate the average change in refractive index is –1.06×10-3 on the electronic pad region of the resonant square holes PBG filter waveguide.
The narrow center transmission peak is shifting from 1536.1 to 1535.7 nm and the transmission wavelength shifting (passband) is 0.4 nm.
The optical spectra (wavelength response) at the output port of the designed resonant square holes PBG filter waveguide with adding various voltages to change the refractive index change. Fig. 2-21 shows the transmission spectrum of the 32 phase-shift wavelengths with adding various voltages around the 1550 nm wavelength. The transmittance power uniformity over the 32 phase-shift wavelengths is about 2.5024 dB. The insertion loss is 1.3596 dB on our designed resonant square PBG filter waveguide. The center transmission wavelength is shifting from 1536.1 nm to 1523.7 nm and the channel spacing is 0.4 nm.