ObjectiveIn a dense wavelength-division multiplexing (DWDM) system, the narrow-band filter is a core component ensuring the quality of information transmission, and its importance is self-evident. As data transmission continues to develop towards larger capacity and higher density, the DWDM system faces even greater challenges. To improve the utilization rate of optical fiber transmission channels, the number of multiplexing needs to be continuously increased, which leads to a continuous narrowing of the channel spacing. Therefore, the filters with high transmittance, ultra-narrow bandwidth, and large aperture have attracted increasing attention from researchers. Zero-index metamaterial (ZIM) possess a series of unique physical properties, and their zero-index characteristic only exists within a narrow frequency range. This characteristic is extremely beneficial for the design of ultra-narrow-band optical filters. For this purpose, an ultra-narrow-band compsite filter baseed on ZIM is designed.
MethodsFirstly, a ZIM material with a thickness of
d2 is designed to be embedded in the resonant cavity of the filter to compose a composite filter (
Fig.2). The degeneracy frequency
ωd of the ZIM is designed to be equal to the center frequency
ω0 of the resonant cavity with a thickness of
d1, that is,
ω0=
ωd. Subsequently, the COMSOL Multiphysics software is used to simulate the transmission curve (
Fig.3(a)) of the composite filter and the electric-field distribution at the frequency of
ω0 (
Fig.3(b) and
Fig.3(c)). Furthermore, the equivalent permittivity and permeability of the ZIM at the Dirac-like frequency point are calculated (
Fig.4). Finally, in order to analyze the mechanism of the compression of the transmission bandwidth of the composite filter, the influence of the thickness
d2 on the bandwidth of the composite filter is simulataed (
Fig.5).
Results and DiscussionsTo compose a composite filter, a ZIM with a thickness of
d2=2.8 μm is embedded in a resonant cavity with a defect of
d1=0.3 μm (
Fig.2(b)). The simulated results indicate that the resonant frequencies of these two cavities are nearly identical (
Fig.3(a)). This phenomenon suggests that light with resonant frequency experiences almost no phase delay when passing through the ZIM material. Through further calculations and analyses, it is found that the equivalent refractive index of the ZIM approaches zero (
Fig.4(a)). In such a situation, the transmittance of the composite filter is hardly affected by the thickness of the ZIM, which is consistent with that of a single line-defect filter without ZIM. At the resonant frequency of 195.9 THz, the full-width at half-maximum (FWHM) of the proposed composite filter is only 70 GHz (
Fig.4(b)). Compared with the 300-GHz FWHM bandwidth of a sigle line-defect filter, its bandwidth is compressed by a factor of approximately 4.5 (
Fig.4(b)), fully demonstrating the characteristics of ultra-narrowband filtering. Meanwhile, the quality factor of the composite filter is also significantly improved. Finally, by thoroughly calculating the influence of the thickness
d2 on the bandwidth of the proposed composite filter, the simulated results show that the thickness of the ZIM has little effect on the resonance mode of the composite filter. Moreover, the ultra-narrowband characteristics of the composite filter can be optimized through the meticulous design of the ZIM thickness
d2 (
Fig.5).
ConclusionsThe rapid growth in demand for ultra large capacity and high-density information transmission in the era of intelligence has led to increasing attention being paid to the research of ultra narrowband filters. An optical metamaterial with degenerate energy bands and Dirac-like point are introdeced into the traditional resonant cavity structure filter model, and a composite ultra-narrow-band filter that combines zero refractive index effect and resonant effect is proposed. The COMSOL Multiphysics software is used to simulate the transmission rate of the optical filter and its electric-field distribution. The simulation results show that when the Dirac-like frequency point coincides with the resonant frequency of the cavity, the zero-phase-delay characteristic and the strong dispersion characteristic of ZIM will work together, and the filtering bandwidth of the proposed filter can be significantly compressed. Specifically, a composite filter based on ZIM material with a thickness of 2.8 μm and a 0.3 μm-line-defect resonant cavity is designed. At the resonant frequency of 195.9 THz, the FWHM of the composite filter is only 70 GHz. Compared with the 300-GHz bandwidth of a single line-defect filter, its bandwidth is compressed by a factor of approximately 4.5, fully demonstrating the characteristics of ultra-narrowband filtering. An in-depth analysis of the mechanism of bandwidth compression and explores the optimization design of ultra-narrow-band are also provided. The research results provide new technical ideas for the design and application of optical communication devices based on optical metamaterials.