Graphene multilayers for coherent perfect absorption: effects of interlayer separation

TL;DR

This study models how the optical absorption of multilayer graphene for coherent perfect absorption depends on interlayer separation, revealing critical limits and providing analytical expressions to predict absorption behavior.

Contribution

It introduces a semi-analytical model accounting for interlayer separation effects on graphene's absorption, improving predictions over previous models that neglect this factor.

Findings

Maximum absorption of 50% for real conductivities, achievable with enough layers.

Upper bounds on absorption decrease with increasing interlayer separation.

Analytical expression for infinite layers derived, highlighting the importance of interlayer distance.

Abstract

We present a model study to estimate the sensitivity of the optical absorption of multilayered graphene structure to the subnanometer interlayer separation. Starting from a transfer-matrix formalism we derive semi-analytical expressions for the far-field observables. Neglecting the interlayer separation, results in upper bounds to the absorption of 50% for real-valued sheet conductivities, exactly the value needed for coherent perfect absorption (CPA), while for complex-valued conductivities we identify upper bounds that are always lower. For pristine graphene the number of layers required to attain this maximum is found to be fixed by the fine structure constant. For finite interlayer separations we find that this upper bound of absorption only exists until a particular limiting value of interlayer separation which is less than the realistic interlayer separation in graphene multilayers. Beyond this value, we find a strong dependence of absorption with the interlayer separation. For an infinite number of graphene layers a closed-form analytical expression for the absorption is derived, based on a continued-fraction analysis. Our comparison with experiments illustrates that multilayer Van der Waals crystals suitable for CPA can be more accurately modelled as electronically independent layers and more reliable predictions of their optical properties can be obtained if their subnanometer interlayer separations are carefully accounted for.