The sketch of the waveguide structure designed was shown in Fig. 1. In the figure, the distance w of the main waveguide cavity with the transparent dielectrics (n=1.0) was set as 50 nm which was far less than the wavelength λ of incident wave from 600 nm to 2700 nm so that the electromagnetic wave could be excited to form SPPs propagation mode in MIM waveguide structure. After that, a j-order (j=1, 2 and 3) resonance formed when the coupled cavity was excited by the main waveguide, whose width Lof the coupled cavities was also set as 50 nm. Our simulation results indicated that Fano resonance was independent of the horizontal distance between the two cavities and dependent on the height H1 (H2). In addition, the relative far-field intensity I was defined as the area under the far-field curve and was proportional to the height h of the curve in this paper.
Fig.2a showed the transmission spectra under different InP structures without air cavity A. It could be observed redshift of the resonance peaks of mode mj (j=1,2,3) with the increase of H2 from 240 nm to 350 nm. The resonant wavelengths of mode mj (j=1, 2, 3) were a function of the height H2. Take H2=350 nm as an example, it was observed three resonance valleys at 998 nm, 1302 nm and 2079 nm, respectively. The resonance valleys at 1302 nm and 2079 nm were first and second order resonance modes, shown in Fig. 2(c-d). However, the resonance valley at 998 nm was located at the critical point of the second and third order resonance and was regarded as third-order resonance, seen in Fig. 2(a-b). In other words, the resonance mode in Fig. 2a could directly be reflected by the distribution of magnetic field in Fig. 2(b-d).
In addition, when the zero order dark mode from the Air cavity and j-order bright modes (j=1, 2 and 3) from the InP cavity were superimposed, some Fano resonance of the modes mj (j=1, 2 and 3) could be obtained in Fig.3a, which showed the transmission spectra of different InP-Air structures whose structural parameters were H1=300 nm and various H2. In the case of only air cavity, it could be observed that the transmission spectrum was very wide passband, which covered the resonance wavelengths of the modes mj (j=1, 2 and 3) and whose central wavelength was at about 1710 nm. Therefore, for the mode m1, it was observed no Fano resonance when H2=280 nm and 300 nm, two slightly obvious Fano resonances when H2=320 nm and 350 nm in the range from 1800 nm to 2700 nm (not marked), and more obvious Fano resonance when H2=240 nm and 260 nm. However, the most obvious Fano resonance came from the mode m2 whose resonance valley shifted to the long wavelength with the H2 increase. According to the main resonance peak [22-23] of the mode m2 in the figure 3a, the quality factor (QF) and the extinction ratio (ER) could be calculated. A high-quality factor was meant to be lower light energy loss in a resonant cavity. Moreover, the lager extinction ratio was implied the better quality of the resonator. For the different InP-Air structures with the length H2 from 240 nm to 350 nm (240 nm, 260 nm, 280 nm, 300 nm, 320 nm and 350 nm), the quality factor QFs calculated were about 44, 30, 29, 28, 34 and 37 respectively. The ERs obtained were around 13, 18, 15, 14, 31 and 12 dB, respectively.
These results showed that the QFs and the ERs were a function of the length H2. There was lower light energy loss in a resonant cavity and the better quality of the resonator for the length H2=240nm and 320nm. In other words, when the height H2 was not higher than 240 nm and not less than 320 nm, the waveguide structure with InP-Air cavities had good filtering performance. In addition, it was obtained that the addition of air cavity did not change the position of the resonant valleys which was dependent on structure sizes of the cavity InP. Take H2=350 nm as an example, for the three resonance valleys at 998 nm, 1302 nm and 2079 nm, it was observed the magnetic field distribution did not change before and after the addition of air cavity. Additionally, it was obtained that the magnetic field distribution of the zero-order resonance in the air cavity where no standing wave was observed, as shown in Fig. 3(b-d).
Figure 4 showed the relationship between transmission and the height H1. The structural parameter was H2=260 nm. It was observed that the resonance position of the mode mj (j=1, 2 and 3) was independent of the height H1. The broadband resonances between 1500nm and 2100nm were considered to originate zero-order resonance of air cavity, which moved to the long wavelength with H1 increasing. In addition, because of strong resonance of the zero-order mode the resonance of mode m1was barely observed when H1<280nm. However, the intensity of resonance peak at about 1645nm gradually decreased with the increment of H1 (>300nm). The QF and the ER were about up to 37 and 16 dB when H1=350nm. Nevertheless, by the simulation, we obtained that the QF and ER decreased to 29 and 14dB when H1=360 nm.
Before the addition of air cavity, under 1302.87 nm monitoring, the relative farfield intensities I were various with the height H2 change from 240 nm to 350 nm and was a function of height H2, namely, I = I(H2), as shown in Fig.5a. The shape of the curve was Guassian Spot with periodic structure, whose symmetric center was located at about θ = -2.20, as shown in the black dash. The relative farfield intensity I gradually decreased with the height H2 from 260 nm to 350 nm. The maximum relative intensity I(260) was about three times that of the minimum I(350), I(260)=3I(350) . After the addition of air cavity, it was observed that the relative farfield intensities I was also a function of height H2, as shown in Fig. 5b. The symmetric center of the curve with periodic structure was located at about θ = 00, as seen in the black dash. The relative farfield intensity I gradually increased with the height H2 from 240 nm to 320 nm. The maximum relative intensity I(320) was about four times that of the minimum I(350), namely, I(320)=4I(350). Therefore, the change of structural parameters could be obtained according to the change of far-field relative intensity [20].