Supporting information

Broadband absorption engineering of hyperbolic metafilm patterns

Dengxin Ji, Haomin Song, Xie Zeng, Haifeng Hu, Kai Liu, Nan Zhang, Qiaoqiang Gan*

Department of Electrical Engineering, University at Buffalo,The State University of New York, Buffalo, NY 14260.

*email: .

  1. Mode distribution in the multi-layered HMM waveguide taper

Here we model the mode distribution in an 8-pairHMM waveguide taper as an example to interpret the broadband absorption observed in Fig. 2. As shown in Fig. S1,four different wavelengths (i.e. 3.4 μm, 3.8 μm, 4.2 μm and 4.6 μm) are trapped at four different positions along the vertical direction of the structure, agreeing well with the theoretical prediction shown in Fig. 1.

Figure S1| Modeled E-field distributions in the 8-paired HMM waveguide taper (i.e. sample 3).

  1. Surface roughness of alternating multi-layered Ag/SiO2 films

To fabricate the proposed HMM waveguide taper, we prepared multi-layered Ag/SiO2 films with different pairs (e.g. 1, 4 and 8 pairs). According to the atomic force microscopic characterization shown in Figure S2 (characterized by an AIST-NTSmartSPM™ 1000 system), the top surface roughness increases with more alternating layers, which is one mechanism resulting in the difference between theoretical modeling and experimental observation shown in Figs. 2 and 3.

Figure S2| Surface roughness of multi-layered films with (a) 1-pair, (b) 4-pair, (c) 8-pair Ag/SiO2 layers. The root mean square roughness data for thesefilms are 2.9 nm in (a), 3.6 nm in (b) and 3.9 nm in (c), respectively.

  1. The effect of fabrication errors on side walls of HMM waveguide tapers

Due to the fabrication error of FIB milling process, the designed waveguide taper structure cannot be reproduced perfectly, leading to the mismatch between modeling and measured results. The most significant mismatch is that the width of the top Ag strip is slightly smaller than the designed value. For instance, as shown in Figure 2 (sample 2), the bottom width and designed top width are 950nm and 530 nm, respectively. However, the observed top width isapproximately 500nmas shown in the SEM image. By considering the width of each layer measured from the SEM image, the top two layers of the simulation model are therefore adjusted accordingly, as shown in Figure S3 (a). One can see from Figure S3(b) that the adjusted modeling result (see the black curve) fits better to the measurement (see the blue curve) than the ideal HMM waveguide taper structure (see the red curve).For samples 3, 4, 6, 7 and 8, the fabricated top widths are 500nm, 850nm, 500nm, 580nm and 780nm, and 630nm and 760nm, respectively, instead of predesigned 550nm, 880nm, 530nm, 600nm and 800nm, and 660nm and 790nm. In addition, the cross-sectional profile of sample 5 is in a curved shape, which is different from ideal waveguide taper. Consequently, in the modeling shown in Figure 2, all geometric parameters of modeling were adjusted based on the cross-sectional SEM images.

Figure S3| (a) Schematic of the adjusted model for the simulation. (b) Simulated absorption of ideal (the red curve) and adjusted (the black curve) HMM waveguide taper structures compared with the measured absorption spectrumof sample 2(the blue curve).

  1. Effect of the surface roughness

According to a recent report (see ref. [40] of the main text), it was believed that the scattered light fromroughened HMM structures constructed by nanowire arrays will couple stronger to the high-k modes. However, when the incident light is within the resonance wavelength band of the proposed patterned HMM waveguide taper array, the roughness near the degeneracy point will reduce the resonant absorption, which is different from previously reported non-resonant HMM structures. To validate this explanation, we numerically introduced random roughness into the bottom four pairs of an 8-pair HMM waveguide taper, as shown in Fig. S4a. The top and bottom widths of the pattern are 550 nm and 1.14 µm, respectively. The absorption spectra before and after adding roughness are shown by red and black curves in Fig. S4b, respectively. Since the top 4-pair metal-dielectric layers were not affected by the roughness, the optical absorption in the wavelength range of 3-4 μm is approximately unchanged. In contrast, the absorption spectrum in the wavelength range of 4-5 μm is reduced obviously due to the extra roughness which re-radiated the coupled light to free space. In addition, compared with the ideally planar structure, the roughened one has higher absorption beyond the resonant wavelength region, which agreed well with our experimental observation for sample 3 and 2 as shown in Figs. S4c and S4d, respectively. One can see that the absorption of the real sample is lower within the resonant band but higher than the modeled one beyond this wavelength region. This phenomenon should be attributed to the mechanism proposed by ref. [40] of the main text, i.e. scattered light will couple stronger to the high-k modes of the HMM.

Figure S4| (a) Schematic of 8-pair HMM waveguide taper modelwith roughness in the bottom 4 pairs. (b) Comparison of the absorption spectra of the 8-pair structure without (red curve) and with roughness (black curve). (c) and (d) are comparison of modeled (red curves)and measured absorption spectra (black curves) for (c) sample 3 and (d) sample 2, respectively.

  1. Discontinuity in the multi-unit pattern design

If sample C in Fig. 2 of the main text (i.e. an 8-pair structure) is separated into two components at its central position along the vertical direction and placed in parallel in the same period (P=2.26 μm), its absorption is shown in Fig. S5a. Compared with the absorption spectrum of sample C (see the red curve), an obvious dip at the wavelength of ~3.9 μm can be observed (see the black curve), which is introduced by the discontinuity at the separation position. To reveal the mechanism of this absorption gap, we model the electrical field distribution at different wavelength (i.e. 3.4 μm, 3.8 μm, 4.2 μm, and 4.6 μm, respectively) in both 8-pair and 4-pair HMM waveguide tapers. As shown in Fig. S5b and S5c, one can see that the localized field intensity at the wavelength of 3.8 μm in the two-unit pattern (in Fig. S5b) is obviously weaker than that in the 8-pair structure (see Fig. S5c) since the efficient coupling from the taper tip to this position is not maintained. Therefore, the absorption decreases significantly in this wavelength region. As shown in Fig. 4c in the main text, the absorption gap was successfully compensated by introducing an overlap between the bottom and top widths of the two-pattern unit.

Figure S5| (a) Comparison of the absorption spectra of an 8-pair structure and a 4-pair double unit structure. (b) and (c) are modeled E-field distributions in (b) the 4-pair double unit HMM waveguide taper and (c) the 8-pair single unit structure.

  1. Scattering of the HMM waveguide taper array

It is necessary to analyze the scattering property of the proposed HMM waveguide taper array due to the finite numerical aperture of the collection lens in our experiment system (i.e. NA=0.4 corresponding to the collection angle of 23.6˚). If a significant part of the light is scattered into higher order modes beyond the collection angle, the measurement result cannot describe the absorption properties of the structure accurately. As shown in Fig. S6, we model the zero-order reflection spectra of all 8 samples (see dots) and compare them with theircorresponding total reflection spectra (see solid curves). One can see that these two spectra are approximately identical, indicating that the high order scattering/reflection are negligible for all samples analyzed in this work.

Figure S6| Comparison between the zero-order reflection spectra (see dots) and total reflection spectra (see solid curves)for all 8 samples.