Narrow Band Filter at 1550 nm Based on Quasi-One-Dimensional Photonic Crystal with a Mirror-Symmetric Heterostructure

In this paper, we present a high-efficiency narrow band filter (NBF) based on quasi-one-dimensional photonic crystal (PC) with a mirror symmetric heterostructure. Similarly to the Fabry-Perot-like resonance cavity, the alternately-arranged dielectric layers on both sides act as the high reflectance and the junction layers used as the defect mode of the quasi-one-dimensional PC, which can be designed as a NBF. The critical conditions for the narrow pass band with high transmittance are demonstrated and analyzed by simulation and experiment. The simulation results indicate that the transmission peak of the quasi-one-dimensional PC-based NBF is up to 95.99% at the telecommunication wavelength of 1550 nm, which agrees well with the experiment. Furthermore, the influences of the periodicity and thickness of dielectric layers on the transmission properties of the PC-based NBF also have been studied numerically. Due to its favorable properties of PC-based NBF, it is can be found to have many potential applications, such as detection, sensing, and communication.


Selection of Materials
In our design, the multilayer film is applied as the narrow band filter (NBF) similarly to the Fabry-Perot cavity. The designed NBF is based on a quasi-one-dimensional photonic crystal (PC) with a structure denoted as (HL) 6 (LH) 6 , for this defective PC, the defect mode is located inside the photonic band gap (PBG), and its spectral position with respect to the PBG center is defined by parameters of the multilayer films (thickness and refractive index). Here the materials composed of multilayer films are Nb2O5 and SiO2, corresponding to the high (H) and low (L) refractive index materials, respectively. The materials selected are due to the following demands for the application of NBF in the infrared communication region: 1) Their transparency range should cover the application infrared communication band (0.8-1.8 m), otherwise the film will absorb, thus reduces transparency.
2) These materials should be easily prepared by using advanced coating technology for achieving high-quality film.
3) Their matching degree of these two kinds of materials should be high, which will directly influence the cohesion and stability between different layers.
The common materials satisfied with the above demands are listed in Table S1. For the experiment, physical vapor deposition (PVD) was used to turn solid materials into gas and deposit them on the substrate. Here, the films were deposited by electron beam gun evaporation (EBD) and ion-beam assisted deposition (IAD) [34,35]. During the process of vacuum coating, the electron gun produces a high-energy electron beam to directly impact the target materials sublimating the solid into gas molecules or atoms, then these gas molecules or atoms, obtaining enough energy from ion-beam assistance, travel through the vacuum chamber to deposit upon the substrate. As shown in Table S1, using EBD with IAD can obtain a high stacking density of Nb2O5, which always matches with SiO2 to fabricate multilayer films due to its small stress. It is well known that the greater the difference between the high and low refractive indices, the wider the forbidden band and the narrower the transmission peak that can be obtained. TiO2 and Ta2O5 as oxide films also have high refractive indices; however, compared with Nb2O5, the quality of the NBF composited with SiO2 will decline slightly. MgF2 and Na3AlF6, as fluoride films have low refractive indices. However, due to stress problems, MgF2 always matches with ZnS to prevent film cracking, and the low firmness of Na3AlF6 is not resistant to the environment. Considering the quality of the filter and the preparation technology, we selected Nb2O5 and SiO2 as suitable materials.

Angular Dependence for Quasi-One-Dimensional PC-Based NBF
In the simulation, the incident wave is of linear polarization, the TE wave has an electric field parallel to the interface and is named as S polarization, while the TM wave with a magnetic field parallel to the interface is named as P polarization. We considered only the condition of light normally incident to the surface of the proposed quasi-one-dimensional PC in the paper, where the S and P polarizations are identical. For further discussion of angular dependence caused by oblique incidence [36,37], we present the transmittance and reflectance of the proposed quasi-one-dimensional PC with different incident angles, θ, changed from 0° to 80°. As shown in Figure S1, it can be observed that the wavelength of the transmission peak and forbidden band is blue-shifted significantly with the increase of the incident angle. Furthermore, S-pol and P-pol (dashed and solid lines) exhibit polarization that gradually separates with the increase of the incident angle. When the angle of incidence increases from 0° to 80°, the detailed data of the properties of the quasi-one-dimensional PC-based NBF are listed in Table S2. For the light of S-Pol, the magnitude of the transmission peak gradually decreases; the central wavelength shift is in the direction of short waves, and the FWHM will become narrower and the Q factor will become larger. For the light of P-Pol, the magnitude of the transmission peak increases firstly, and then decreases, and the central wavelength shift to the direction of short waves; the FWHM will become wider and the Q factor will become smaller. The value of the transmission peak, FWHM and Q factor vary with the increase of incidence angles evidently. There is a serious effect of the oblique incident angle to the performance of the NBF. In practical application, the designed quasi-one-dimensional PC for its miniaturization and integration can be loaded directly into the device port, thus, light usually has perpendicular incidence to the surface. Thus, we discussed only the performance of NBF under normal incident light.    Wavelength, /nm Figure S1. The simulated reflectance and transmittance spectra of the designed 1DPCs with (Nb2O5/SiO2) 6 (SiO2/Nb2O5) 6 when the incident angle is set to 10°, 20°, 30°, 40°, 50°, 60°, 70°, and 80°.