Identifying the perfect absorption of metamaterial absorbers

We present a detailed analysis of the conditions that result in unity absorption in metamaterial absorbers to guide the design and optimization of this important class of functional electromagnetic composites. Multilayer absorbers consisting of a metamaterial layer, dielectric spacer, and ground plane are specifically considered. Using interference theory, the dielectric spacer thickness and resonant frequency for unity absorption can be numerically determined from the functional dependence of the relative phase shift of the total reflection. Further, using transmission line theory in combination with interference theory we obtain analytical expressions for the unity absorption resonance frequency and corresponding spacer layer thickness in terms of the bare resonant frequency of the metamaterial layer and metallic and dielectric losses within the absorber structure. These simple expressions reveal a redshift of the unity absorption frequency with increasing loss that, in turn, necessitates an increase in the thickness of the dielectric spacer. The results of our analysis are experimentally confirmed by performing reflection-based terahertz time-domain spectroscopy on fabricated absorber structures covering a range of dielectric spacer thicknesses with careful control of the loss accomplished through water absorption in a semiporous polyimide dielectric spacer. Our findings can be widely applied to guide the design and optimization of the metamaterial absorbers and sensors.

Figure 1

The retrieved reflection and transmission parameters from simulation. (a) Amplitude spectra and (b) phase spectra. The inset shows the geometry of the SRR unit cell with period of 45 μm for the array. The perfect absorption spectrum is plotted in (a) for a spacer thickness of 5 μm.

Figure 2

The (a) phase and (b) amplitude spectra of the first (dashed line) and secondary reflection (solid lines) with different spacer thicknesses. The absorption peak frequency points are labeled with circles. (c) Phase spectra of the total reflection for different spacer thicknesses with the inset showing the corresponding absorption. (d) Color plot of the calculated total phase shift as a function of frequency and spacer thickness. The white dashed lines show the spacer thickness (5 μm) and the corresponding frequency (1.28 THz) for the perfect absorption.

Figure 3

Experiment (solid lines) and simulation (dashed lines). (a) Absorption spectra and (b) total reflection phase spectra for metamaterial absorbers with different spacer thicknesses of 3.8, 5.3, and 6.0 μm. The insets in (a) and (b) show the image of a fabricated sample and the unit cell structure.

Figure 4

Absorption diagram based on the reflection and transmission parameters retrieved from (a) transmission line model and (b) simulation.

Figure 5

Perfect absorption frequencies determined from simulations, analytical calculations based on Eqs. (1, 2, 3, 4, 5), and the explicit values from Eqs. (6)–(8). The lines are to guide the eye. (a) Varying ${\varepsilon }_r$ while keeping ${\varepsilon }_i=0.0843$. (b) Varying ${\varepsilon }_i$ while keeping ${\varepsilon }_r=2.81$.

Figure 6

Experiment (solid lines) and simulation (dashed lines). (a) Absorption spectra and (b) total reflection phase spectra for treated metamaterial absorbers with different spacer thicknesses. Results should be compared to Fig. 3.