J. Eur. Opt. Society-Rapid Publ. 22, 1( 2026) 3
Figure 2.( a) Studied resonant structure,( b) Equivalent plane structure,( c) Mode propagation in the equivalent structure.
Figure
3. Excitation of the guided modes by the grating in the dielectric structure.
excited by the reflected waves diffracted by the grating at the angles h res ¼ p = 2 � a, leading to resonance effects. Using the grating equation, the resonant angles h res and the corresponding effective refractive indices n e are defined foreachdiffractedorderm by equation( 5):
n e ¼ sin ðh res
� Þn wg ¼ sin h wg nwg þ m k K
¼ sin ðh s Þn s þ m k K: ð5Þ
h wg is the incident angle on the grating in the waveguide and h s is the incident angle coming from the substrate for the resonance( Fig. 3).
Under appropriate grating geometry, at a small incident angle( yellow), the l = 1 propagating mode( TE 1) canbe excited in the waveguide by the m = + 1 diffracted order and at a higher incident angle( red), the l = 0 propagating fundamental mode( TE 0) can also be excited by the same order m = + 1. The m = �2 evanescent order could also excite the l = 0 counter-propagating mode( TE 0) at a higher angle. The energy transfer arises in between these two last angles.
To summarize, the energy transfer in all-dielectric resonant structure will appear under several conditions linked to the opto-geometrical parameters of the resonant structure: the wavelength, the polarization, the waveguide width, the depth, period and duty cycle of the grating and finally the refractive indices of the materials constituting the resonant structure. The choice of these parameters is discussed in the following section to design a full dielectric optical energy transfer device.
3 Material and methods
3.1 a-Si: H deposition and characterization
To fulfill the required condition of no transmitted orders for the energy transfer, a high refractive index material(> 3) is necessary. Additionally, to achieve the best performance and to obtain high resonances efficiencies, the material should exhibit a high transparency at the operating wavelength due to the specific interrogation of the developed sensor( from the substrate to the resonant grating). With a dielectric constant above 3 and an extinction coefficient below 0.01 in IR wavelength range, hydrogenated amorphous silicon( a-Si: H) meets this criterium. The characterization of a-Si and a-Si: H was largely investigated in the literature [ 16 – 20 ]. This particular material is largely used in the solar cell technology and many techniques can be used to deposit a-Si: H layers( plasma spray, reactive chemical vapor deposition, sputtering,...)[ 21 ]. The passivation of defects, responsible for optical losses in the visible and IR domain, by forming Si-H bonds, enables a high transparency. For instance, a-Si: H layers with refractive index