Transmissive filters are usually used to transmit light at a specific wavelength to display the desired color, which have been regarded as vital components in image sensors [[1], [2], [3], [4], [5]]. The spectral filter array methods can be viewed as an extension of bayer filters, which adopt a super-pixel containing a group of spectral filters for spectral recovery. Different filter units exhibit distinctive transmission spectra, and each unit is a periodic array [6,7]. Fabry Perot cavity and subwavelength grating are two commonly used structures for transmissive spectral filters. Filters based on Fabry-Perot cavities offer high scalability and easy manufacturing. However, their pixel size cannot achieve the same scale as that of a subwavelength grating, thus limiting their use in some high-resolution applications [[8], [9], [10], [11]].

Most existing transmissive subwavelength gratings are based on metal gratings. The sub-wavelength metal structure induces local heating in both the structure and the surrounding environment due to Joule heat generated by light absorption, which results in inherent Ohmic losses. This, in turn, leads to low transmittance (below 80%), high sidebands (exceeding 20%) [[12], [13], [14], [15], [16]], and an inability to cover the entire visible range, or fewer channels available when applied in the field of multispectral image sensors [[17], [18], [19]].

In order to reduce the impact of Ohmic losses, most existing schemes aim to replace metal materials with all dielectric materials (non-metallic materials), but the resulting structures are usually based on reflection or scattering to manipulate light and are not suitable for transmissive gratings [[20], [21], [22]]. At the same time, we found that the aforementioned subwavelength metal structures only generate one resonant mode, with the electromagnetic field energy primarily converging in a specific layer (either the metal layer or the waveguide layer) [[13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23]]. Through a review of the literature, we learned that Heming Yang et al. proposed a multi-layer films structure composed of metal and dielectric layers which allows for coupling between surface plasmon polaritons and waveguide modes, resulting in the formation of multi-hybrid plasmonic wave-guide modes (HPWG). Compared to a single SPP mode, HPWG has higher energy and lower ohmic loss [24]. This has inspired us to explore whether can we realize Multi-Mode Coupling by stacking gratings (the stacked subwavelength grating) instead of thin films, to reduce Ohmic losses and improve transmittance while reducing sidebands.

In this paper, a scheme for stacked grating structure is introduced, which uses BK7 glass as the substrate, adding a layer of polydimethylsiloxane (PDMS) thin film on the substrate. The configurations on the thin films are stacked grating structures composed of different materials, from top to bottom are Ag-MgF2-BK7-Ag. By coupling the resonance modes generated by different layers, high transmission resonant peak can be selected throughout the entire visible spectrum with sideband less than 10%.

The remainder of this article is organized as follows: the proposed scheme and simulation results are detailed in the 'Modeling and simulation' section. In the 'Results and discussions' section, we use the mode matching method [[25], [26], [27]] to analyze the structure. Lastly, the 'Conclusion' section provides a summary of our work.