Mechanisms of perfect absorption in nanocomposite systems

Recently, it was noted that losses in plasmonics can also enable several useful optical functionalities. One class of structures that can maximize absorption are metal insulator metal systems. Here, we study 3-layer systems with a nano-composite metal layer as top layer. These systems can absorb almost 100% of light at visible frequencies, even though they contain only dielectrics and highly reflecting metals. We elucidate the underlying physical phenomenon that leads to this extraordinary high and broadband absorption. A comprehensive study of the particle material and shape, mirror material and dielectric spacer thickness is provided to identify their influence on the overall absorption. Thus, we can provide detailed design guidelines for realizing optical functionalities that require near-perfect absorption over specific wavelength bands. Our results reveal the strong role of lossy FabryPerot interference within these systems despite their thickness being well below half a wavelength. © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement


Introduction
For decades, losses associated with plasmonics were seen as detrimental; however, it was recently noted that losses can also enable several useful optical functionalities and are also related to strong local field enhancements [1].Thus, they can assist one in improving the performance of various applications including solar power [2] and sensing [3], e.g.Raman scattering [4].One particular class of structures that can maximize absorption in the visible spectrum (VIS) are metal insulator metal (MIM) systems [5].Such 3-layer systems consist typically of a metallic base layer (mirror layer), a dielectric spacer layer and an at least partially metallic top layer.Although, dielectric top layers are also explored to maximize absorption bandwidth and strength [6].
Several well-ordered and defined MIMs have been manufactured [7][8][9][10][11][12][13][14].They have typically periodic top layers and can achieve broad-band absorption levels in the range of 60-80% for the case of thoroughly optimized systems [7], while certain systems can even absorb up to 100% in the infrared spectrum [8].The periodicity and the generally well-defined geometry assists analysis, including their dipolar and quadrupolar resonances [9].It is also possible to quantitatively study the coupling of the localized surface plasmon (LSP) mode of the individual nanostructures with the surface plasmon polariton (SPP) of the metallic mirror layer [10].Recently, MIMs were proposed that are oriented vertically and can even reach nearly 100% absorption over a broad spectrum [11].All these well-ordered structures require however high precision manufacturing processes, such as ebeam lithography, which limits manufacturing throughput and structured area size.Additionally, the achievable maximum absorption and bandwidth of periodic systems is limited compared to systems where at least one layer contains random elements.Typically, the top layer contains randomly sized and arranged metal nano particles that are usually embedded in a dielectric matrix (in this article we will call such a layer a nano-composite layer).
Nano-composite layers can be created by direct thin layer evaporation [15][16][17][18], thermal annealing [19][20][21], laser-induced dewetting [22], co-evaporation [23][24][25][26], spin-coating [27] or even through simple drop-casting [28].The MIM realization of Hedayati et al. in 2011 exceeded 95% absorption across the entire VIS, thus realizing a very strong and broad absorbing MIM system with a relatively simple and scalable co-evaporation technique of gold and SiO 2 , which produces a gold nano-composite layer [25].Contrary to the needs for high precision machining of periodic systems, in this approach one must only control two evaporation rates.A similar optical performance was observed for gold, silver and copper based nano-composites [29].
It is fascinating that a system consisting only of transparent and highly reflective materials can absorb almost 100% of the incident light and the objective of this paper is to elucidate the underlying physical phenomenon.
The random nature and nanometer dimensions of the composite layer obscure an insightful analytical analysis of the system's optical properties that lead to this performance.Thus, other authors resorted to studying this system numerically using finite difference time domain (FDTD) algorithms [30,31].Etrich et al. focused on retrieving the optical parameters of the nano-composite layer through simulations and optimized the dielectric spacer thickness to enhance absorption [30].This optimization was carried out with a transfer matrix algorithm, which results agreed very well with those obtained by FDTD.Feng et al. researched the optical parameters required to achieve high and broadband absorption [31].They identified for example that perfect absorbers require a dielectric spacer layer at least 20 nm thick to assure modest requirements on the nano-composite layer permittivity.
Both research groups treated the metallic nano-composite layer as a homogenous, dispersive and isotropic material and focused on its "macroscopic" properties.In contrast, we focus here on understanding the microscopic absorption mechanisms of the system described in [25], which was not undertaken yet to the best of our knowledge.In particular, we address the question of the broad bandwidth light absorption and where it is absorbed locally.Possible resonance broadening mechanisms associated with variations of the gold particles shape, size, position or plasmonic coupling to the metal mirror were suggested in [25,29]; however, we rule out that latter mechanism, as discussed in Section 3. Instead we propose that the resonance broadening effect is based on lossy Fabry-Perot interferences in combination with plasmonic inter-particle coupling.
The paper is organized as follows: Section 2 describes the simulation model used; the optical response of single particles at some distances above a mirror layer is discussed in Section 3; while the response of many particle systems is discussed in Section 4, followed by a conclusion.

Simulation methodology
Lumerical FDTD, a commercial-grade simulator based on the FDTD method is used to perform all simulations below [32].Figure 1 shows the general simulation layout used here.It consists of a linear polarized light source in the x-z-plane, a metallic nano-composite layer, a dielectric spacer layer and a mirror layer.This MIM structure is embedded in a lossless dielectric background of constant refractive index 1.5.Plane waves first impinge on the nanocomposite layer before they pass the dielectric spacer layer and then hit the 100 nm thick metallic mirror layer.Bloch-type periodic boundary conditions have been used and power detectors were placed at appropriate positions.Figure 2 Both works agree with our finding that interference enhances absorption and in fact, simulations without gold mirror reveal that one needs almost 4 subsequent layers of 8 particles at 150 nm distance in light propagation direction to reproduce the strong enhancement (data not shown).This is another indication for interference as ideal 2 beam interference enhances intensity by a factor of four, which is here the case.Figure 3 shows that the intensity is certainly greater than 3 times the incident intensity at the location of 8 particles 90 nm above a perfect reflector.This makes sense despite the small distance of 90 nm, as the perfect reflector leads to a phase change of 180° and the 90 nm spacing to phase changes from 150° @ 650 nm to 216° @ 450 nm.These phase changes add up to almost 360° within the nano-composite layer, which is required for perfect constructive interference and we can conclude that the enhancement is also significantly influenced by lossy Fabry-Perot interference.Let us note that a similar phase phenomenon has recently been used to build ultrathin planar cavity metasurfaces by Wang et al. [43].
Although manufactured particles at single nanometer length scales tend to be spherical [15,18,25], let us for completeness also report on the response of other possible particle shapes.Figure 4(a) shows the absorption enhancement of a few spherical particles, which was reported in Fig. 2(b) and is included here for easy comparison with the other results.Figures 4(b)-4(d) show the absorption enhancement for three possible particle shapes; hemi-spheres, pillars and cubes, accounting in Eq. ( 1) for the different geometrical cross sections of these particle shapes.We find that other particle shapes lead to higher amplitudes compared to spherical ones.Note that this is also true if we normalize the data to the effective particle volumes.
For non-spherical particles, we also find that increasing the number of particles in a chain aligned with the source polarization leads to a red-shifted and strengthened resonance, as in the case of spherical particles.However, the resonance of a single non-spherical particle is already red-shifted compared to the spherical case and thus one would need to use different materials to absorb strongly in the VIS, especially in the blue and green part of the spectrum.This is an option that is explored in Section 4 for the case of spherical particles.The ratio that for both m of the spectru the blue part case.It is thi aluminum mir of total absorp [33].One cou across the VI nm thick gold The lack i by a proper increase abso silver or alum respectively U enhancement Fig. 6(a), com   light is absorb r this question grate in z-dire as [45]: absorption in is in agreement rption enhance g number of pa center-to-cente whole VIS.In nhancement to is a result of p ystem.These tw aterial properti choice, on ave 6(d).This in ag y dissipation is guration [38].interference.

Conclusion
We have investigated numerically the optical response of MIM systems with a top nanocomposite layer and different mirror materials, particle materials and dielectric spacer thicknesses.We found that small gaps and overlapping particles are required for strong resonance enhancements within the nano-composite layer.In agreement with others, we found the resonance is red-shifted with increasing number of particles.Our data indicate that the distance of the composite layer to the mirror layer is of key importance as the MIM's high and broadband absorption is a consequence of lossy Fabry-Perot interference rather than a pure plasmonic effect.Consequently, interference strength can be maximized with highly reflecting mirror materials.Hence, systems with an aluminum mirror layer can maximize absorption despite their high reflectivity, while other highly reflecting materials would be equally suitable for that purpose.
Most of the light is resonantly absorbed within the particles, just beneath their surface.Thus, one can tune the absorption behavior by modifying particle material as shown here or by changing particle size or density.These results demonstrate the flexibility and versatility of MIM systems to absorb light efficiently over specific wavelength bands and the guidelines provided can assist one in realizing functionalities that require near-perfect absorption over specific wavelength bands.
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