# Guided Mode Resonance in a Low-Index Waveguide Layer
## 1 Introduction  
Guided mode resonance (GMR) can occur when an incoming wave and output wave interfere in a waveguide [1]. The spectral response depends on both the geometry and material of the waveguide and cladding layers. Both broad-band [2] and narrow-band [3] GMR filters with high transmittance/reflectance can be achieved by careful design. GMR has been used for filters [4], absorbers [5, 6, 7, 8], sensors [9, 10], field enhancement [11, 12], spectrometers [13] and optical communications [14].  
Due to their ability to allow an intensive field enhancement, hybrid GMR systems that integrate plasmonic structures with photonic waveguide layers have also been developed. This property has been used for surface-enhanced Raman scattering (SERS) [15], fluorescence enhancement [16] and photodetectors [17]. A gold nanoparticle array on top of an Indium Tin Oxide (ITO) waveguide layer has achieved strong coupling for bandgap engineering [18]. A metal grating embedded in a high-index waveguide layer could produce an ultra-narrow transmission spectrum that has not been achieved using a single waveguide system or a single plasmonic system [19]. High-index dye-doped polymer combined with metal nanostructures has also been explored [20]. This scheme provides the ability to enhance the photoluminescence of the dye-doped polymer.  
Although various configurations have been developed, almost all GMR structures use high-index materials as the waveguide layers since the Total Internal Reflection (TIR) must be satisfied at the top and bottom interfaces. This restricts GMR application in high-index material regions. Exploring GMR in a low-index waveguide can break the limitation and expand the GMR application into a broader condition. Therefore, it is an interesting question of whether low-index materials can also support a guided mode. While in the hybrid GMR system, the TIR can be replaced by the grating effect. This implies that one may realize the GMR in a low-index waveguide with the help of grating. Obtaining GMR in a low-index waveguide material expands the toolbox, especially for functional materials such as electro-optic polymers and mixed polymers with active materials.  
In this paper, we clearly show that a guided mode resonance could be supported in a low-index waveguide material by adopting a hybrid GMR configuration and the refractive index of the substrate has little influence on the behavior of the guided mode resonance. In this scheme, the periodic metal gratings are embedded in the low-index waveguide layer which is situated on top of a high index substrate, and the air is used as the top cladding layer. The guided mode is supported by the combination of metal grating diffraction and the TIR. The TIR condition can be satisfied at the air-waveguide layer boundary. At the boundary between the low-index layer and the high-index layer, the diffraction of the metal grating couples the light wave into the waveguide and pushes the mode back into the low-index material. The guided mode resonance occurs when the diffracted light wave at the metal grating boundary and the TIR light wave at the top boundary match the waveguide mode supported by the low-index layer. The influence of the geometrical parameters on the GMR is explored with both simulation and experiment. This paper shows that almost all dielectrics no matter how large the refractive index is can be used to support GMR. The ease-of-fabrication makes this platform a promising candidate for many applications including sensing, imaging and fluorescence enhancement.