Tunable Dual‑Band, Polarization‑Insensitive Coherent Perfect Absorber Using Double‑Layer Graphene Hybrid Waveguide

Abstract

Graphene’s intrinsic 2.3 % absorption in the visible and infrared limits its optoelectronic impact. We present a tunable dual‑band, polarization‑insensitive coherent perfect absorber (CPA) operating in the mid‑infrared, built around a silicon‑nanostructure‑coupled double‑layer graphene waveguide. Finite‑difference time‑domain (FDTD) simulations reveal perfect absorption peaks at 9611 nm and 9924 nm. The structure’s central symmetry guarantees polarization independence, while the coherent absorption can be modulated all‑optically by adjusting the relative phase of two counter‑propagating beams. Further, independent tuning of the two graphene layers’ Fermi energies shifts the absorption peaks across a wide spectral range, enabling conversion between dual‑band and narrow‑band operation. These results point to versatile, CMOS‑compatible mid‑IR photonic devices such as switches, logic gates, and coherent photodetectors.

Introduction

Efficient light‑matter interaction in atomically thin materials is pivotal for next‑generation photonics. While transition‑metal dichalcogenides, hexagonal boron nitride, and black phosphorus have shown strong excitonic responses, graphene remains a unique platform due to its broadband optical conductivity and high carrier mobility. Its monolayer form absorbs only ~2.3 % of incident light, but the excitation of surface plasmon polaritons (SPPs) in the terahertz and mid‑infrared can dramatically enhance confinement and absorption. Graphene‑based absorbers, modulators, and sensors have therefore attracted intense research interest.

Coherent perfect absorption (CPA) offers a pathway to eliminate absorption loss by exploiting interference between counter‑propagating waves. In graphene, CPA has been demonstrated in silicon slabs and planar metamaterials, but dual‑band operation in the mid‑infrared has remained largely unexplored. Here we design a symmetry‑engineered CPA that achieves simultaneous perfect absorption at two distinct wavelengths, with full control over polarization, phase, and spectral position.

Methods

The device comprises two continuous graphene monolayers on a silica substrate, separated by a 75‑nm silica spacer (Figure 1). A 160‑nm periodic silicon square array (80‑nm side length, 100‑nm height) sits atop the upper graphene. The lower graphene rests 150 nm below the substrate. Two coherent plane waves (I1 and I2) impinge from opposite sides; their relative amplitude (α) and phase (φ) are defined by I2=αI1 exp(iφ+ikz). The graphene conductivity follows the local random‑phase approximation: \[\sigma(\omega)=\frac{ie^2k_BT}{\pi\hbar^2(\omega+i\tau^{-1})}\Big[\frac{E_f}{k_BT}+2\ln(e^{-E_f/k_BT}+1)\Big]+\frac{ie^2}{4\pi\hbar}\ln\Big[\frac{2E_f-(\omega+i\tau^{-1})\hbar}{2E_f+(\omega+i\tau^{-1})\hbar}\Big]\], where T=300 K, E_f is the Fermi energy, and τ=μE_f/eν_f^2 with μ=10 000 cm^2 V^−1 s^−1 and ν_f=1.1×10^6 m s^−1. The upper and lower layers are set to E_f1=0.66 eV and E_f2=0.31 eV, respectively.

We employ 3‑D FDTD with periodic boundary conditions in the lateral directions and perfectly matched layers along the propagation axis. A non‑uniform mesh (0.1 nm at graphene) ensures numerical accuracy while keeping computational load reasonable.

Results and Discussion

With a single incident beam, the device exhibits dual‑band absorption peaks below the theoretical limit of 50 % (A_max=0.5), confirming that graphene alone cannot reach perfect absorption. When two counter‑propagating beams interfere, the scattering matrix formalism gives the coherent absorption \[A_{co}=1-\frac{|O_1|^2+|O_2|^2}{|I_1|^2+|I_2|^2}=1-\frac{1+\alpha^2-2\alpha\cos\varphi}{2(1+\alpha^2)}.\] Setting α=1 and φ=0 yields perfect absorption (A_co=1) at λ₁=9611 nm and λ₂=9924 nm (Figure 3). The device’s center symmetry renders it polarization‑insensitive; both p‑ and s‑polarized illumination produce identical spectra.

Phase tuning offers all‑optical modulation: varying φ from 0 to π suppresses the absorption peaks to near zero, delivering modulation contrasts above 34 dB (Figure 5). Independently adjusting the Fermi levels of each graphene layer shifts the resonance positions: decreasing E_f2 moves λ₁ red‑shifted while suppressing λ₂; increasing E_f2 has the opposite effect, allowing conversion between dual‑band and narrow‑band operation. Similarly, tuning E_f1 shifts both peaks uniformly across a wide spectral range (Figure 6).

Structural parameter studies reveal that increasing the silicon square width w red‑shifts the resonances and first enhances absorption until the filling factor saturates, after which efficiency drops. Enlarging the period p also red‑shifts the peaks. The spacer thickness d₁ controls interlayer coupling; beyond a critical value the dual‑band behavior collapses into a single peak. Replacing silicon with higher‑index dielectrics (TiO₂, GaSb) red‑shifts the resonances but reduces peak absorption (Figure 7).

Conclusion

We have engineered a CMOS‑compatible, tunable dual‑band CPA in the mid‑infrared that is both polarization‑insensitive and all‑optically controllable. The double‑layer graphene hybrid waveguide, coupled to a silicon nanostructure, achieves perfect absorption at 9611 nm and 9924 nm, with phase‑dependent modulation and wide spectral tunability via Fermi‑level control. The continuous graphene layers preserve high mobility and simplify fabrication compared to patterned structures. This platform opens pathways for mid‑IR photonic devices such as switches, logic gates, and coherent detectors.

Availability of Data and Materials

All data generated or analyzed during this study are included in this published article.

Abbreviations

2D

Two‑dimension

CPA

Coherent perfect absorber

FDTD

Finite‑difference time‑domain

SPPs

Surface plasmon polaritons

TMDCs

Transition‑metal dichalcogenides

a Schematic diagram of the dual‑band graphene‑based perfect absorber. b Side view with dimensions specified. c Top view with dimensions specified

The reflection (R), transmission (T), and absorption (A) spectra of the proposed graphene‑based absorber with Fermi energies E_f1=0.66 eV and E_f2=0.31 eV under the illumination of only one incident beam I1 in the z direction

The absorption spectra of the proposed graphene‑based absorber under the illumination of only one incident beam (red curve), and under coherent illumination with p polarization (blue curve) and s polarization (black curve)

The absorption of proposed CPA with different phase difference at the peaks of a λ1=9611 nm and b λ2=9924 nm, respectively

Absorption spectra as a function of the wavelength and Fermi levels of a lower‑layer graphene and b upper‑layer graphene. The other structural parameters are the same as Fig. 1

Light absorption of proposed CPA with different a p, b w, c d1, and d different dielectric array, respectively. The other parameters are the same as Fig. 2