Performance Estimation of Defected Ternary Photonic …
33
2 Objective
In this chapter, author proposed an optimum design of ternary photonic crystal
based Butterworth filter by calculating transmissivity of the structure under normal
(Banerjee et al. 2017) and slanted incidences of incident radiation [4]. For analytical method, well-known transfer matrix technique (TMT) is preferred over other
existing numerical procedures due to its first-principle advantages. Though Plane
wave expansion method is the choice of theoretical engineers, but this method can
be initially set to get almost the desired range which can be later fine-tuned using
the PWE. Effect of structural parameters and incidence angle are analyzed on the
device, and point defects are considered (Banerjee et al. 2017; [45]) to analyze the
bandwidth and ripple in passband. The work is carried around 1.55 µm for the sole
purpose of utilizing the findings in high-frequency communication.
3 Results and Discussions
Based on the mathematical formulation as described in Sect. 2, transmissivity of
the bandpass filter is evaluated and schemed as a function of the wavelength of the
propagating electromagnetic wave. At first, ideal (defectless) structure is considered
and both normal and oblique incidences are taken into account for filter design,
and next, intentionally point defects are considered within a limit to estimate the
performance of the optical filter.
At first, results for normal incidence are exhibited in Figs. 1 and 2. For simulation, SiO 2 /air/TiO 2 compositions are considered. In Fig. 1, result is graphically
shown by varying SiO 2 layer thicknesses, whereas Fig. 2 represents for various TiO 2
dimensions (Banerjee et al. 2016). Increasing thickness of either of the layer causes
a redshift of the spectrum around the passband. In both the cases, amount is ripple
in passband is non-negligible.
Figures 3 and 4 show the transmissivity profile for TM and TE waves, respectively, for the SiO 2 /air/TiO 2 structure with various layer dimensions of SiO 2 material
(Banerjee et al. 2016). A vis-à-vis relative analogy reveals that ripple is more for TM
wave propagation than obtained for TE wave. Conclusion may be drawn from the
result that TE mode of wave transmission is favorable inside ternary PhC if considered along the refractive indices change. But notch length in transmissivity variation
scale (Y-axis) is much higher for p-polarized wave which converses for enhanced
noise rejection. Hence trade-off is required.
Similarly, calculation is made for different TiO 2 thickness as exhibited in Figs. 5
and 6, respectively. The result is almost same like Figs. 3 and 4, but the difference is
that more passbands exist close to the desired wavelength region which allows the
designer to shift the operating region as per requirement. Another comparison with
the obtained data for normal incidence reveals that filter spectrum is more asymmetric
33
2 Objective
In this chapter, author proposed an optimum design of ternary photonic crystal
based Butterworth filter by calculating transmissivity of the structure under normal
(Banerjee et al. 2017) and slanted incidences of incident radiation [4]. For analytical method, well-known transfer matrix technique (TMT) is preferred over other
existing numerical procedures due to its first-principle advantages. Though Plane
wave expansion method is the choice of theoretical engineers, but this method can
be initially set to get almost the desired range which can be later fine-tuned using
the PWE. Effect of structural parameters and incidence angle are analyzed on the
device, and point defects are considered (Banerjee et al. 2017; [45]) to analyze the
bandwidth and ripple in passband. The work is carried around 1.55 µm for the sole
purpose of utilizing the findings in high-frequency communication.
3 Results and Discussions
Based on the mathematical formulation as described in Sect. 2, transmissivity of
the bandpass filter is evaluated and schemed as a function of the wavelength of the
propagating electromagnetic wave. At first, ideal (defectless) structure is considered
and both normal and oblique incidences are taken into account for filter design,
and next, intentionally point defects are considered within a limit to estimate the
performance of the optical filter.
At first, results for normal incidence are exhibited in Figs. 1 and 2. For simulation, SiO 2 /air/TiO 2 compositions are considered. In Fig. 1, result is graphically
shown by varying SiO 2 layer thicknesses, whereas Fig. 2 represents for various TiO 2
dimensions (Banerjee et al. 2016). Increasing thickness of either of the layer causes
a redshift of the spectrum around the passband. In both the cases, amount is ripple
in passband is non-negligible.
Figures 3 and 4 show the transmissivity profile for TM and TE waves, respectively, for the SiO 2 /air/TiO 2 structure with various layer dimensions of SiO 2 material
(Banerjee et al. 2016). A vis-à-vis relative analogy reveals that ripple is more for TM
wave propagation than obtained for TE wave. Conclusion may be drawn from the
result that TE mode of wave transmission is favorable inside ternary PhC if considered along the refractive indices change. But notch length in transmissivity variation
scale (Y-axis) is much higher for p-polarized wave which converses for enhanced
noise rejection. Hence trade-off is required.
Similarly, calculation is made for different TiO 2 thickness as exhibited in Figs. 5
and 6, respectively. The result is almost same like Figs. 3 and 4, but the difference is
that more passbands exist close to the desired wavelength region which allows the
designer to shift the operating region as per requirement. Another comparison with
the obtained data for normal incidence reveals that filter spectrum is more asymmetric