A periodically patterned metal-dielectric composite material is designed, fabricated and characterized that spatially splits incoming microwave radiation into two spectral ranges, individually channeling the separate spectral bands to different cavities within each spatially repeating unit cell. Further, the target spectral bands are absorbed within each associated set of cavities. The photon sorting mechanism, the design methodology, and experimental methods used are all described in detail. A spectral splitting efficiency of 93–96% and absorption of 91–92% at the two spectral bands is obtained for the structure. This corresponds to an absorption enhancement over 600% as compared to the absorption in the same thickness of absorbing material. Methods to apply these concepts to other spectral bands are also described.
© 2012 Optical Society of America
Composite optical structures composed of periodic arrays of metals and dielectrics have been attracting considerable interest due to their ability to control light in unusual and compelling ways. These composite structures include dielectric-based photonic crystals [1, 2], plasmonic structures composed of both patterned metals and dielectrics [3, 4], metamaterials with constituent “meta-atoms” that are much smaller than the wavelength of light [5,6], transformational optical structures [7, 8], and periodic subwavelength aperture or cavity arrays (SAAs) [9–13]. These structures exhibit extraordinary optical phenomena and behavior including negative index of refraction [5, 6, 14], lensing of light , and light concentration and trapping [16–18] to name a few.
The ability of a material to combine the functionalities of photon sorting, localization, and absorption opens up numerous applications, including horizontally-oriented multi-junction solar cells, antenna improvement, multi-wavelength micro-bolometers and other sensors. There has been some prior research on multi-band frequency selective surfaces to increase the capabilities of multi-frequency microwave antennas by adding subreflectors capable of operating at multi-frequency bands [19–21], and in bimetallic nanoantennas , or plasmonic gratings for the visible regime . The devices demonstrated in these studies lack any multi-functional properties (i.e., photon sorting, localization and absorption), unlike the structures described in this work. Our previous work on polarization-splitting  and wavelength-selective compound grating structures [9–13, 24] dealt primarily with transmission properties, and the devices were not optimized for absorption. While there is some work involving periodic grating structures for frequency selective absorption of electromagnetic radiation [16, 25, 26], these devices are highly polarization-dependent, a limitation that is not shared by the device described in this work.
In this work, the method to design a device that locally splits radiation according to its frequency is described. A SAA is designed, fabricated and tested that has, within each repeating unit cell, two differently-sized cavities that are designed to resonantly localize and absorb radiation of different, nonoverlapping spectral bands. The device is designed to operate in the microwave spectral region, yet the general concept can be applied to any spectral region by appropriate scaling of the geometric sizes of the device features and appropriate selection of materials. Yet, issues such as increased optical loss within the metals for the visible and IR spectral range and larger relative skin depth (relative to the wavelength) should be taken into account when scaling the device to operate at shorter wavelengths.
2. Material Design
The structure designed and demonstrated in this paper is a compound subwavelength cavity array. The cavities themselves are not deeply subwavelength in size; feature sizes are approximately where ε = ε′ +iε″ is the complex dielectric permittivity within the cavities. Thus from the perspective of incident radiation of wavelength λ, the material does not appear to be of homogenous composition with spatially-independent, effective values of ε.
The mechanism responsible for the light channeling towards, and into the cavity is explained if one considers the time-reversed situation of light exiting an aperture. For linear materials (see  for exceptions), Maxwell’s equations and its solutions are invariant under complex conjugation . In a lossless structure this simply amounts to time reversal symmetry (i.e. a eiωt time dependence transforms to e−iωt), while a lossy dielectric transforms to a gain material, in addition to time-reversal. Considering the time-reversed version of our structure, light generated at resonance by a gain material within an individual cavity, upon exiting, will spread out and form a diffuse beam . Now, for an infinitely periodic array of apertures with gain media, in which radiation is generated with well-defined phase relationships, the light exiting each aperture diffracts in the same way as a single aperture, and will constructively interfere with the light exiting all the other apertures to create an outgoing plane wave. Note that each array of identical cavities will resonate (and radiate) light at their own resonant frequencies, independent from the (different) resonances of the other-sized cavities. A full discussion of the properties of the outgoing beams, which are dependent on the cavity’s shape and size, as well as the structure’s periodicity, is beyond the scope of this paper. Nevertheless, the overall effect of this phenomenon is that the collective effect of light radiating from each aperture results in plane waves in the far field. Thus, transforming back to the forward-time with a lossy material, it is expected that light will converge towards (i.e. be channeled into) the cavities as it approaches the entrances to the apertures, and ultimately be absorbed.
The structure discussed in this paper is a two-dimensional square array of subwavelength cylindrical cavities embedded in aluminum. Each unit cell contains two cavities of different radii and identical heights, arranged in a rhombic lattice, see Fig. 1. The individual cavities within the unit cell are designed to support an effective-cavity resonance or cavity mode (CM) with amplified electromagnetic fields, where the lowest order mode’s frequency dependence is approximately given by:30]. Thus, the structure’s resonance response is tuned by adjusting the radii and heights of the cavities, and the periodicity of the array. The two individual-cavity periodic structures are then combined, placing two cavities within one unit cell and their dimensions are optimized to maximize photon sorting and absorption, and to minimize coupled cavity effects that can occur within cavity arrays of this sort.
Because the purpose of the device is to absorb the spectrally-sort photons, an absorbing material is placed within the cavities; this material is an absorbing silicone elastomer dielectric (Sylgard 184), doped with graphite (which is responsible for the absorption), whose dielectric value, ε, can be adjusting by controlling the concentration of graphite inside the material, see Fig. 2.
It is important to note that as the dielectric loss tangent (ε″/ε′) of the material increases, the resonances broaden, essentially overdamping the CM resonance. By choosing a lower graphite concentration we are able to maximize the absorption and maintain independent cavity resonances. We found that a graphite concentration of 8.36%, which gives a complex dielectric permittivity of ε = 4.33 + 0.22i was able to absorb the maximum quantity of incident power, while still maintaining clearly defined resonances, see Fig. 3. Optimum coupling occurs when the probability of radiative decay (i.e. lifetime of the mode) is equal to that of nonradiative decay.  Our optimized result was found numerically by maximizing the absorption in both cavities by varying the permittivity within a range of experimentally realizable values. Future study is required to develop a complete analytical model of this effect.
The goal of this device was to have two absorption peaks that are well separated with respect to each other, while maintaining absorption peaks with as large of a bandwidth as possible for each peak. The target frequencies of the absorption peaks were chosen to be below the onset of far-field diffraction, as these diffraction modes carry energy away from the material surface, and thus compete with the CMs for the energy of the incident beam. This competition between back-scattered far-field diffracted modes and CMs imposes an important constraint on the design that ultimately limits the number of different cavities that can fit within one unit cell. Taking these considerations into account, the fabricated device has a periodicity of Λ = 26 mm, and the two cavities with identical heights of h = 7 mm, but different radii of a1 = 8.03 mm and a2 = 5.74 mm.
Once the preliminary design was obtained using Eq. (1), the device was further optimized and analyzed using HFSS, which is a full-wave, finite element, electromagnetic simulation software. With HFSS, the structures were simulated using periodic boundary conditions in the transverse directions and a Floquet port for the incident beam. We simulated the metal using the aluminum material parameters from the HFSS library with a surface boundary condition, and used the experimentally determined dielectric properties for the elastomer. It is important to note that there is some degree of uncertainty in the measurements of dielectric constants, which can cause a substantial deviation from the results of simulations.
The resonant properties of the cavity modes can be analyzed using direct and indirect methods. In the direct method, the volume loss density (i.e. the fraction of incident energy absorbed in a particular region) derived from the solved electromagnetic fields can be directly integrated over the volume of each of the cavities. At cavity resonance this quantity will exhibit a maximum. Off resonance, the field in the cavities are not excited and the total volume loss will be minimized. This metric is useful for determining where in a structure the fields are localized, however this is difficult to measure experimentally.
Alternatively, the cavity resonances can be determined indirectly from the reflection intensity. In the absence of absorbing materials, the total reflection remains essentially constant, decreasing slightly due to small amounts of surface loss at the metal surfaces. However, with absorption, we can characterize a resonance in frequency-space by a dip in reflection intensity. In practice, we utilize the simulated S-parameters to determine the reflection. This metric is useful for a simple comparison to experimental measurements, however it does not, by itself, determine where, spatially, in a structure the absorption occurs.
An Anritsu M4640A vector network analyzer (VNA) was used to record the measured complex S-parameters of the graphite loaded elastomers in an 8–12 GHz waveguide. The dielectric properties of the elastomer composites were subsequently extracted using the Nicholson-Ross-Weir algorithm [32, 33]. An aluminum plate was machined by CNC to the requisite design, and pre-formed tablets of the selected elastomer composite were inserted into the cavities.
The sample was surrounded by pyramidal absorbers to limit scattering and the free-space p-and s-polarized reflectivity of the sample was measured using the VNA with broadband horns between frequencies of 7.5 and 15.0 GHz, for angles of incidence between 5 and 35 degrees.
We chose to tune the cavities to resonate at target frequencies of 8.10 GHz and 9.25 GHz. Figure 4 shows the simulated and measured reflection intensity of s-polarized microwave radiation specularly reflected from the material surface at an angle of incidence θ = 17 degrees. There is strong agreement between the simulated and experimental results. There are two likely sources of error in the experiment as compared to simulation. First of all, the pre-formed tablets of the elastomer composite fit with different amounts of tightness in the large and small holes, thus leading to a slight dielectric mismatch between the two cavities. Additionally, the elastomer was squeezed into the smaller hole, leading to a small amount of elastomer sticking out above the top of the cavities. Any discrepancies between simulated and experimental results can be accounted for by adjusting these two parameters within a reasonable range.
These results show that the expected photon sorting and absorption is occurring as the theory and modeling predicts. Namely, as 8.1 GHz (9.25 GHz) radiation approaches the structure from above a unit cell, 91% (92%) of the incident energy is absorbed by the structure. Figure 5 shows that the two dips in reflection intensity correspond to maxima in the integrated volume loss density within the two separate cavities. That is, the fields are channeled to and into smaller (larger) of the two cavities, where the resonant fields are strongly, and locally absorbed.
The absorption enhancement can be calculated by normalizing the absorption with respect to the fractional surface area,34]. This corresponds to an enhanced absorption of 303% (600%) at 8.1 GHz (9.25 GHz). Another way of calculating the enhanced efficiency of this device is to compare it to the absorption Es in a 7 mm thick slab of the absorbing dielectric that fills the cavities. This metric gives a enhanced absorption of 610% (452%).
There is a very high spatial selectively to the absorption response at the different resonances. Figure 6 is a pseudo-color plot of the volume loss density in a cut-plane midway through the cavities; the spatially localized nature of the absorption is readily seen. To calculate the photon sorting efficiency, SEn, we use the ratio of total electromagnetic energy absorbed in the desired cavity En to the total energy absorbed by both cavities, ET = E1 + E2Table 1.
We have also studied the dependence of these results on angle of incidence; it is difficult to measure the reflection from this structure for normal incidence. For radiation that is p-polarized, there is a variation in the reflection (and thus, absorption) as a function of angle of incidence, see Fig. 7(b). This is caused by the changes in the properties of evanescent fields above the cavities in this polarization, which extends the effective height in Eq. (1) and decreases the resonant frequency. However, in the s-polarization, where the evanescent fields are largely unaffected, there is negligible variation over a broad range of angles, see Fig. 7(a). At normal incidence the absorption response of this structure is polarization independent, and for shallow angles (< 20°) the response is largely polarization independent. Here, as well, there is strong agreement between simulated values and experimental results, with the differences accounted for when considering variation in material parameters.
We have demonstrated the capability of these compound subwavelength cavity arrays to spatially split, concentrate and absorb microwave radiation, with extremely high efficiency and concentrations. Although this structure was designed to operate in the microwave regime, with appropriate scaling it can be adjusted to other wavelength ranges, where it has applications in multi-junction solar energy absorption. For optical frequencies, however, there are additional difficulties to overcome, including fabrication limitations and increased metal loss. This structure can, in principle, be also extended to absorb additional bands by including additional cavities in each unit cell, as long as the periodicity can stay small. This response is polarization independent for shallow angles. Other structures with narrower bandwith absorption peaks and more absorption peaks are possible and may be useful in developing multi-wavelength bolometers or photodetectors. Furthermore, this device could be improved by shifting the modes further down in frequency, or by reducing the pitch.
This work is supported by the AFOSR Bioenergy project (FA9550-10-1-0350), the NSF Industry/University Cooperative Research Center for Metamaterials (IIP-1068028), and the EPSRC, UK funding through the QUEST project (ref: EP/I034548/1). The design and analysis of the device was done at the The City University of New York, and the fabrication and characterization was done at the Electromagnetics Materials Laboratory at the University of Exeter. We would like to acknowledge Dr. Andrii Golovin, Dr. Thomas James, and Dr. Chris Sarantos for their contributions to the project, and Boyan Penkov for some helpful comments.
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