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Large-scale silicon nanophotonic metasurfaces with polarization independent near-perfect absorption Nils Odebo Länk, Ruggero Verre, Peter Johansson, and Mikael Käll Nano Lett., Just Accepted Manuscript • Publication Date (Web): 30 Mar 2017 Downloaded from http://pubs.acs.org on March 30, 2017

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Large-scale silicon nanophotonic metasurfaces with polarization independent near-perfect absorption Nils Odebo Länk*,†, Ruggero Verre†, Peter Johansson†,‡ and Mikael Käll*,† †

Department of Physics, Chalmers University of Technology, 412 96 Göteborg, Sweden ‡ School of Science and Technology, Örebro University, 701 82 Örebro, Sweden E-mail: *[email protected] (N.O.L.); [email protected] (M.K.)

Keywords: Metasurfaces, high-index nanophotonics, perfect absorption, colloidal lithography

Optically thin perfect light absorbers could find many uses in science and technology. However, most physical realizations of perfect absorption for the optical range rely on plasmonic excitations in nanostructured metallic metasurfaces, for which the absorbed light energy is quickly lost as heat due to rapid plasmon decay. Here we show that a silicon metasurface excited in a total internal reflection configuration can absorb at least 97% of incident near-infrared light due to interferences between coherent electric and magnetic dipole scattering from the silicon nanopillars that build up the metasurface and the reflected wave from the supporting glass substrate. This “near-perfect” absorption phenomenon loads more than 50 times more light energy into the semiconductor than what would be the case for a uniform silicon sheet of equal surface density, irrespective of incident polarization. We envisage that the concept could be used for the development of novel light harvesting and optical sensor devices.

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Electromagnetic (EM) metasurfaces are structured material layers with subwavelength thickness that appears smooth to an impinging EM field because the feature spacing is small compared to the incident wavelength. While many potential applications, such as lenses and other beam-shaping devices based on phase-gradient metasurfaces1-5, benefit from maximum optical transmission or reflection, others, for example solar harvesting devices and photodetectors, instead are based on maximized light absorption6-9. Metamaterials that exhibit close to 100% absorption in the optical wavelength range have become known as “perfect absorbers”10. Optically thin perfect absorbers typically function only in a narrow wavelength range and for a limited range of incidence angles and polarization states because the phenomenon is intrinsically linked to the possibility of generating complete destructive interference between reflected and transmitted wave components, which forces light to be trapped in the thin absorbing layer10. Interference can be induced by two impinging coherent beams, leading to so-called coherent perfect absorption or “anti-lasing”11, but a more common approach has been to place the absorbing metasurface above a mirror such that transmission is blocked and reflection is cancelled through destructive interference12. Over the past few years, a significant number of theoretical and experimental studies devoted to the understanding and design of perfect absorbers have been reported. Examples include studies of metasurfaces composed of multilayers13, different particle designs10,

14

, two-dimensional materials15,

16

and

metallic structures17-19, and of applications in, for example, phase based sensing17, 20, terahertz absorption21, strong coupling22, light harvesting6, 23 and photocatalysis24. It has previously been shown that perfect absorption can be induced in a dilute layer of plasmonic gold nanodisks if the layer is illuminated under total internal reflection (TIR) conditions through a supporting glass substrate18. This “total internal absorption” phenomenon can be interpreted in terms of a


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completely destructive Fano interference between the specular reflection from the glass interface and the coherent scattering from the nanodisk metasurface25. The enhanced near-fields associated with perfect absorption in plasmonic metasurfaces can be highly useful in applications like molecular sensing17,

20

and surface-enhanced spectroscopy26.

However, harvesting of the absorbed light energy, for example through plasmon-induced hot electron transfer27, is in general inefficient due to the ultrafast decay of plasmons. Perfect absorption in plasmonic metasurfaces therefore mostly results in heat through Ohmic dissipation18. This issue can in principle be addressed by replacing the metal by a high-index semiconductor material, which can support excitations with much longer lifetime than plasmons. In this work, we show that the concept demonstrated in reference18 can be rendered polarization independent and readily extended to silicon metasurfaces excited in the deep red, that is, just above the optical bandgap. Here, the optical penetration depth is very large, of the order 10 µm, but the absorbed light energy can, at least in principle, be harvested by well-known concepts employed in silicon photovoltaics and photodetectors. To achieve this, we utilize the fact that silicon nanoparticles can support spectrally overlapping dipolar modes of both electric and magnetic character28-30. This concept is illustrated in Figure 1. In fact, as will be shown, perfect absorption in a metasurface of such particles excited in TIR can be thought of as a generalization of the so-called Kerker conditions31, which can be used to direct emission from single dielectric particles and metasurfaces in a highly specific manner32-35. The experimental results are based on an original and cost-effective fabrication method. We analyze the electric and magnetic character of the experimentally observed resonances and demonstrate that the optical response can be tuned by varying the nanostructure size. In particular, we show that polarization independent


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absorption >97% can be achieved. Finally, we demonstrate that fabrication method can extended more complex particle morphologies, such as silicon dimers.

Figure 1. Schematic illustration of the perfect absorption phenomenon. (a) A dielectric material reflects light according to the standard Fresnel equations. (b) When high-index nanostructures are patterned on top of a glass slide, scattering from the electric and magnetic resonances contribute to the reflection. (c) At a particular illumination angle in total internal reflection geometry all reflections can interfere destructively, realizing a completely absorbing material irrespective of the incident polarization.

First consider a bare dielectric interface between media with refractive indices and . Specular reflection of s- and p-polarized light incident from the high index side at a certain angle of incidence is described by the standard Fresnel reflection coefficients, yielding, for example,

the angle of polarization from tan

and the critical angle from sin (Fig.

1a). We now cover the interface with a layer of subwavelength particles with surface density . The particles need to be close enough for a metasurface description to be valid, but we neglect inter-particle interactions. Each particle is polarizable in the plane of the interface and has a characteristic complex and wavelength dependent electric polarizability ∥ and magnetic

∥ polarizability (Fig 1b). To generate perfect absorption in the layer at a certain incident


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vacuum wavelength , the coherent electric and magnetic dipole scattering in the specular direction needs to cancel out the reflection from the bare interface at an angle (Fig. 1c).

To analyze this problem, we start from modified Fresnel coefficients developed to describe an interface with an infinitesimally thin layer of electrically polarizable islands36. This theory can be further developed to take into account islands with both an electric and a magnetic polarizability (Supporting Information, section I). This yields a set of boundary conditions for the electromagnetic fields at the interface, which in turn can be used to deduce the following modified Fresnel reflection coefficients:

-

cos − cos 1 −

cos + cos 1 −

cos − cos 1 −

cos + cos 1 −

! ! ∥ ∥

4#

! ! ∥ ∥

4#

$−%

! ! ∥ ∥

4#

$−%

$−%

! ! ∥ ∥

4#

$−%

&

∥ cos cos −

) cos

∥ &− ∥ )

∥ cos +

∥ # ' ∥*

# +

+ cos cos

+ cos cos

∥ # '

∥*

Here is the angle of refraction, which is given by through Snell’s law,

wavenumber of the exciting field and # is the vacuum permittivity.

, 1

# +

. 2

is the vacuum

We study the numerator of Eq. (1) to gain a deeper understanding of the analytical model. The

first term, cos − cos , is independent of the particle polarizabilities and we can therefore loosely think of this term as representing the contribution from the substrate to the ∥ ∥ reflection. The three remaining terms are proportional to either , ∥ or ∥ . A similar

analysis is valid for Eq. (2). The total reflection from the system thus depends on the combined


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interferences between the reflection from the glass substrate and the coherent scattering from the electric and the magnetic dipoles. It is particularly interesting to note that if one assumes

and normal incidence, 0, the requirement that Eqns. (1) and (2) vanish coincide with the first Kerker condition,

∥ 31 ∥ # , which indeed implies that back-scattering is cancelled . In

order to extract a condition for vanishing reflection at arbitrary polarization and incidence angle

, which implies perfect absorption, we set Eq. (1) and (2) to zero and solve for the required resonance constraints (see Supporting Information II). This yields: ∥ ∥ # 1 , , ,

∥ # 2 , , .

(3)

(4)

Here 1 and 2 are complex valued functions (see Supporting Information II), as are the two polarizabilities, which means that four conditions need to be fulfilled simultaneously for perfect absorption to occur. Eq. (3) can be thought of as a generalized Kerker condition and specifies the

Figure 2. Numeral analysis of the perfect absorption phenomenon. (a) Electric (red) and magnetic (blue) complex polarizabilities satisfying Equation (3). The electric polarizability has been divided by 34 to match the units of the magnetic polarizability. (b) Reflectance for s- and p-polarized light for a metasurface calculated from Eqns. (1) and (2) using the polarizabilities in (a), at 56 78° and assuming a density of : ;. < particles/µm2. At = >44 nm perfect absorption is observed irrespective of the incident polarization. (c) Reflection at = >44 nm as a function of the illumination angle. ACS Paragon Plus Environment

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ratio between the electric and magnetic dipole polarizabilities while Eq. (4) specifies the particle density for a given vacuum wavelength (note that

2?⁄ and always appears as a

product in Eqns. (1,2)). Since we have five free particle parameters ( and the real and imaginary ∥ parts of ∥ and ) for fixed , , , , the four conditions given by Eqns. (3,4) can be

fulfilled in principle. As an indication that this is possible also in practice, we show in Figure 2 a

calculation for a metasurface sandwiched between air ( 1 and glass ( 1.52 illuminated at = 800 nm for 63°, which is well above the critical angle for the air-glass

interface. Since the particle density, , does not enter directly into Eq. (3), it can be used as a tuning parameter in order for Eq. (4) to be fulfilled. In anticipation of the experimental results, we set 7.5 particles/µm2 and then use analytical Lorentzian polarizabilities with feasible

values tuned to fulfill Eq. (3). This yields perfect absorption at 800 nm, which is close to what is observed experimentally, as shown below.


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Figure 3. Silicon metasurfaces. (a) A photograph of the 1.8 F 1.8 cm2 metasurfaces arranged from left to right according to increasing diameter. A Swedish 10 crown coin is included for scale (b) Tilted SEM view of a typical metasurface. (c) SEM images of samples of silicon nanopillars with different diameters, 120 nm, 180 nm, 200 nm and 300 nm. The average height of the nanopillars is 185 nm in all samples. The scale bar corresponds to 500 nm. (d) Experimental extinction spectra for metasurfaces composed of silicon nanopillars with varying diameter. We fabricated metasurfaces composed of silicon nanopillars using a modified version of the hole-mask colloidal lithography (HCL) technique37. This method yields homogeneous macroscopic areas of nanostructures with short-range translational order (see methods in Supporting Information VI for details). In brief, PMMA was first spin coated on silica wafers coated by a thin polycrystalline silicon film. Polystyrene beads were then dispersed across the surface, a thin gold mask was evaporated, and the beads were removed by tape stripping. The exposed PMMA was then etched, generating a hole-mask, after which 40 nm of nickel was


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evaporated at normal incidence. After lift-off, the silicon was vertically etched and the nickel was removed. The resulting samples exhibit distinct colors depending on the bead size chosen (Fig. 3a). Scanning electron microscope (SEM) images reveal surfaces homogenously decorated with Si nanopillars (Fig. 3b, c). The metasurfaces were characterized by extinction measurements at normal incidence and found to exhibit distinct spectral resonances depending on nanopillar diameter D (Fig. 3d). The

D = 120 nm sample shows two almost overlapping resonances at around = 600 nm. These are generally attributed to the electric dipole (short wavelength) and the magnetic dipole (long wavelength) geometric resonances28,

38, 39

. The resonance wavelengths scale approximately

linearly with D but with different proportionality constants, resulting in increasing mode splitting for increasing D in accordance with previous reports38. For the largest nanopillar diameter, the magnetic dipolar resonance is found at 1000 nm while additional multipolar resonances appear at shorter wavelengths. The data thus indicate that by precisely engineering the nanoparticle size, it should be possible to enter the perfect absorption regime. We now focus on the D = 200 nm case, which shows the highest extinction at normal incidence. The electric and magnetic character of the resonances was first investigated using finite difference time-domain (FDTD) simulations of an isolated particle (Fig. 4a). The discrepancy between the relative intensities of the resonances in simulation and experiment is primarily due to inhomogeneous broadening caused by the slight polydispersity of the beads used in the HCL fabrication process and the fact that we are modeling an isolated particle instead of a short-range ordered array of nanoparticles40.


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In order to elucidate the character of the resonances, the in-plane electric and magnetic dipole moments of the structure were calculated and the corresponding electric and magnetic polarizabilities were extracted from the total electric field in the whole structure according to41 GH I # #H − 1JKH H dM , 5 and

1 −%P N KKH I H F OHH dM I # #H − 1 H F JKH H dM . 6 2 2

We then identified the corresponding polarizabilities from the relations GH Q ∙ JKHexc and

KHexc , where JKHexc and U KHexc are the fields in the absence of the nanostructure but in the N KKH Q ∙ U presence of the substrate. Figure 4b shows the resulting electric dipole polarizability and magnetic dipole polarizability. The short wavelength resonance is clearly electric dipole dominated while the long wavelength resonance has primarily magnetic dipole character. However, the modes are obviously not pure. We interpret this as an effect of a magnetoelectric coupling induced when a high-index dielectric nanoparticle is placed on top of a glass substrate, which results in an electric dipole moment on the particle at the magnetic resonance wavelength29. This justifies the inclusion of two Lorentzian resonances to describe the electric polarizability in Figure 2. This substrate-induced (bi-anisotropic) coupling could in principle be handled by extracting the single-particle superpolarizability tensor of the structure42 and then inserting this into appropriately modified Fresnel formulas43, but the simplicity of the theory would then be lost. Here we instead take this effect approximately into account by calculating polarizabilities in the presence of the substrate. The near field patterns in Figure 4c further support the modal decomposition analysis. In the case of the short wavelength resonance (Fig. 4c, left), both the electric field enhancement


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Figure 4. FDTD simulation and characterization of silicon nanopillars. (a) Measured extinction of the 200 nm-metasurface along with simulated extinction cross section for this structure. (b) The electric (red) and magnetic (blue) dipole polarizabilities of the silicon nanopillars. The real parts are shown in dashed lines and the imaginary parts are shown in solid lines. Here, the electric polarizability is normalized by 34 . (c) Electric field lines (green contours) and intensity enhancement (color coded) for the electric (left) and magnetic (right) mode of the silicon nanopillar, the outline of which is shown in black dashed lines. The wavelengths corresponding to these modes, =V ;4> nm and =W >X> nm, are marked with red and blue lines respectively in (a), (b). distribution and the electric field lines are consistent with electric dipole response in the middle of the structure, though there is also clear signs of a magnetic quadrupole contribution. For the long wavelength resonance (Fig. 4c, right), the electric field lines clearly show the circular currents indicative of a magnetic dipole resonance. The strong magnetic field enhancement in the center of the structure further illustrates this point.


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We now turn our attention to the perfect absorption phenomenon for the Y 200 nm sample. The sample was illuminated from the glass side and the specular reflection was measured as indicated in Fig. 5a for a range of incidence angles ∈ [0\ , ~75\ ^ using p- and s-polarized

light. At low incidence angles, the two resonances induce peaks in the reflection spectra similar to what is seen in extinction. However, for ≈ 41\ , the peaks turns into dips in the uniform white reflectance that would be present for a bare glass-air interface (Fig. 5c upper panel). Increasing the incidence angle further results in almost total extinction of the reflected

beam within a narrow wavelength range. In particular, for 69° and ~855 nm, we found a reflection less than 3% independent of polarization (Fig. 5b). This corresponds to absorption above 97 % since the diffuse scattering at this wavelength is smaller than 0.3% (see Supporting Information, Fig. S3). For comparison, the absorption at the same angle for a single homogenous layer of silicon with a thickness of 33 nm, corresponding to the same surface averaged volume density as the 200 nm-metasurface, was calculated44 to be around 2% at 855 nm (see Supporting Information, Fig. S4). Thus, the effective intensity enhancement (or, equivalently, the effective path length) in the silicon metasurface for the near-perfect absorption condition is about 50 times higher than in such a uniform Si layer. This strong absorption is quite remarkable considering the low imaginary part of the refractive index of silicon in this spectral region.


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Figure 5. Near-perfect absorption in a Si metasurface (a) Sketch of the experimental set-up. (b) Measured absorbance (1 - R) spectra of the 200 nmmetasurface for p- and s-polarized light at 7ao. The inset shows the angular dependence for =4 >

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