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Abstract
The optical absorption enhancement of graphene is of significant interest due to its remarkable applications in optical devices. One of the most useful methods is placing graphene in an asymmetric Fabry–Perot cavity made of one-dimensional dielectric multilayers forming two mirrors. In that regard, using the transfer matrix method, we have explicitly calculated the required periodicity of the front photonic multilayer mirror to maximize the absorption in the graphene for any given combination of material types and number of layers. Then we studied the equivalence between these structural configurations and those with arbitrary periodicity but with defects, where the equivalence holds when $\omega = \xi {\omega _0},\xi \in {\mathbb{Z}_{\ge 0}}$. These defects are introduced via layer position alterations, based on which we propose an optimization algorithm to maximize absorption in structures having a cavity with an arbitrary periodicity. Numerical calculations are given for dielectric material combinations of ${\text{Ti}}{{\text{O}}_2}/{\text{Si}}{{\text{O}}_2}$ and ${\text{T}}{{\text{a}}_2}{{\text{O}}_5}/{\text{Si}}{{\text{O}}_2}$, and to understand the behavior of these optimized structures for any general combination of material types, the mapping of their calculated front mirror periodicity for a range of refractive indices of the two material types has been studied.
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