Perfect magnetic mirror and simple perfect absorber in the visible spectrum

Known experimental artificial magnetic conductors for terahertz and optical frequencies are formed by arrays of nanoparticles of various shapes. In this paper, we show that artificial magnetic conductors for the visible spectrum can be realized as simple, effectively quasistatic resonating structures, where the effective inductance is due to the magnetic flux inside a uniform metal substrate, and the effective capacitance is due to electric polarization of a thin uniform dielectric cover. To illustrate the main potential application of artificial magnetic conductors, we concentrate on the perfect-absorption regime, achieved by adjusting the loss factor of the artificial magnetic conductor to match its real input impedance to free space. We provide approximate analytical design formulas and introduce a simple equivalent circuit to explain the physical mechanism of emulation of magnetic response and perfect absorption of light. A prototype of a nearly perfect absorber for optical (from green to ultraviolet) frequencies is designed and experimentally tested. The results confirm the theoretical predictions and show polarization insensitivity and angular independence of response in a wide range of incidence angles.

Figure 1

An artificial magnetic mirror formed by a thin dielectric layer with the relative permittivity $\mathrm{Re}\left({\varepsilon }_{\mathrm{r}}\right)>1$ and thickness $h$ on a bulk metal substrate [the relative permittivity $\mathrm{Re}\left({\varepsilon }_{\mathrm{rs}}\right)<0$] excited by a plane wave $(\mathbf{E},\mathbf{H},\mathbf{k})$ traveling along a direction that forms an angle $\theta$ with the normal axis. The equivalent lossless resonant circuit is also depicted, illustrating the reactive components in the corresponding materials: capacitor for the layer, inductor for the substrate.

Figure 2

Schematic of the normalized complex input admittance plane $Y_{\mathrm{in}}{\eta }_0$ showing two alternative ways of realizing a perfect absorber for normal incidence. One can start from a lossless metallic substrate (purple dot) and with a lossless dielectric layer to obtain (via the deep blue arrow) a perfect magnetic-wall regime (the blue dot); to this end, the addition of a matched resistive sheet can lead (via the gray arrow) to a perfect-absorber regime (the red dot). More realistically, one can start from a lossy metallic bulk (the green dot) and by adding a suitably selected lossy layer (or layers) can reach again (via the brown arrow) the perfectly absorbing regime (the red dot).

Figure 3

The physical configuration of the resonant absorbing structure. Two semiconducting layers of thicknesses $h_1,h_2$ and relative permittivities ${\varepsilon }_{\mathrm{r}1},{\varepsilon }_{\mathrm{r}2}$ are installed on a metallic substrate with the permittivity ${\varepsilon }_{\mathrm{rs}}$ illuminated by an obliquely incident plane wave $(\mathbf{E},\mathbf{H},\mathbf{k})$ at the angle $\theta$. The corresponding transmission-line circuit (voltage $V$, current $I$) is also shown with a lossy capacitor $(C,r)$ representing the role of the dielectric layers and a lossy inductor $(L_{\mathrm{s}},r_{\mathrm{s}})$ representing the effect of the metallic substrate.

Figure 4

The flow chart describing how alternative material combinations leading (with the optimal thicknesses) to perfect absorbers are being derived. The thickness parameters $(h_1,h_2)$, the material parameters $({\varepsilon }_{\mathrm{r}1},{\varepsilon }_{\mathrm{r}2},{\varepsilon }_{\mathrm{rs}}),$ and the reflection coefficient $R^{\mathrm{TE},\mathrm{TM}}$ as function of the incidence angle $\theta$ are again defined in the inset.

Figure 5

The schematic layer sequence for the grown prototype. A thin adhesion layer of Cr, 150 nm of gold, and $h_2=6$ nm of Ge were first grown onto a silicon substrate using the standard $e-\mathrm{beam}$ evaporation technique. Finally, the sample was transferred to a plasma-enhanced vapor phase deposition (PECVD) system with Oxford Plasmalab 80 for growth of $h_1=28$ nm of ${\mathrm{SiN}}_x$.

Figure 6

The (a) real and (b) imaginary parts of the relative permittivities of silicon nitride, ${\varepsilon }_{\mathrm{r}1}$, germanium, ${\varepsilon }_{\mathrm{r}2}$ (as measured by our ellipsometric procedure), and gold, ${\varepsilon }_{\mathrm{rs}}$, with respect to the operating free-space wavelength ${\lambda }_0$. Normal incidence: $\theta =0$.

Figure 7

(a) The squared magnitude of the reflection coefficient ${\left|R\right|}^2$ for the prototype absorber (various versions of theoretical evaluations and experimental measurements) and in the case of a common quarter-wavelength (Dallenbach) absorber centralized at ${\lambda }_0\cong 400$ nm with the permittivity ${\varepsilon }_{\mathrm{r}}=40+i8$ and (b) the optical thickness of the two aforementioned absorbers, for varying operating free-space wavelength ${\lambda }_0$. Normal incidence: $\theta =0$. The two alternative configurations are depicted in the insets of Fig. 7.

Figure 8

The magnitude of the squared reflection coefficient $|R^{\text{TE,TM}}{|}^2$ (expressed in dB) in contour plots with respect to the operating free-space wavelength ${\lambda }_0$ and the incidence angle $\theta$ for (a) TE excitation (theory), (b) TM excitation (theory), (c) TE excitation (experiment), and (d) TM excitation (experiment).

Figure 9

A demonstration of the absorbing efficiency of the prototype. Blue light (${\lambda }_0\cong 500$ nm) illuminates at the angle $\theta ={60}^{\circ }$ both our prototype (left) and a gold reference sheet (right). Our device even at the extreme limits of its operation (very large wavelength and very oblique incidence) appears working nicely. The two alternative configurations are depicted in the insets.

Figure 10

A demonstration of the absorbing efficiency of the present prototype with respect to various frequencies. The reflection of a colored text on a black surface (a piece of paper in this case) has been captured (i) when only the gold substrate is present, (ii) when a silver mirror is posed on the top, and (iii) when using our prototype sample. It is clear that our absorber is very efficient for blue, violet, and ultraviolet radiation but reflects strongly at smaller frequencies (green, yellow, red).

Figure 11

The (real and imaginary) normalized admittances of the capacitive layers (${\mathrm{SiN}}_x$, Ge) and inductive substrate (Au) as functions of the operating free-space wavelength ${\lambda }_0$. Normal incidence: $\theta =0$. The definitions of the input admittance $Y_{\mathrm{in}}$, the admittance of the semiconducting layers $Y$, and the admittance of the metallic bulk $Y_{\mathrm{s}}$ are given in the inset of the transmission-line circuit (voltage $V$, current $I$).