Transmission Gratings relying on Huygens Metasurfaces for short-wave to long-wave infrared applications

. In many spectroscopic applications, diffraction gratings are the pivotal optical component which is used to decompose white light into its spectrum. However, design and manufacturing of diffraction gratings for the infrared spectral domain operating in transmission bares its own challenges, i.e. a very limited choice of transparent materials. Here we present our effort on exploiting Huygens-metasurface structures for design and manufacturing of diffraction gratings intended for operation in the short-wave (around 2µm) up to the long-wave infrared region (>10µm). Silicon nano-pillars are the material system of choice since they exhibit the best compromise between optical performance and manufacturing feasibility. We present specific designs as well as measurement results of a demonstrator sample.


Introduction
Spectroscopic techniques are widely used and wellestablished in very different kinds of applications.Such applications stretch from everyday chemical analysis of foods and biological samples up to scientific instrumentation in astronomy and physics.If you look at the landscape of commercially available spectrometers, you will notice that in the VIS or NIR they are mostly realized based on diffraction gratings, whereas in the long-wave infrared region Fourier transform spectrometers are the standard.The reason for this distinction in design and concept is, among others, the limited choice of transparent materials for the infrared which complicates the suitable design of broadband grating-based IR spectrometers.The former classification and reasoning mostly apply to commercial products, however, in the field of scientific instrumentation (e.g. in astronomy or space-and airborne earth observation), the realization of grating-based imaging and non-imaging IR spectrographs can bare important benefits such as the absence of any sensitive mechanically moving components.
In this contribution we present a novel design for diffraction gratings which rely on the implementation of Huygens-metasurfaces [1,2].We concentrate on the wavelength domain between ~2µm and ~13µm.We will show that gratings composed of gradually sized siliconnano-pillars achieve large diffraction efficiencies above 90% while at the same time being perfectly suited in terms of transparency and manufacturability with standard lithographic techniques.

Grating Design and Performance
Surface relief diffraction gratings do exist in several topographic versions.There are, e.g., simple binary gratings composed of an alternating arrangement of only two features, i.e. ridge&groove.They are well suited for narrow-band applications requiring high spectral dispersion [3,4,5].On the contrary, there are saw-tooth profiled gratings or effective medium gratings which typically offer lower spectral dispersion, but achieve considerably larger bandwidths [6,7].In what follows, we focus on the latter scenario, and we present a grating design which is similar to effective medium gratings (at least in topology), however, the fundamental physical working mechanism is different, and it is inherited from those of so-called Huygens metasurfaces [2].The diffraction grating's microstructure is schematically depicted in Fig. 1.In general, quadratically shaped silicon nano-pillars of gradually increasing diameter are arranged in a periodic manner.Optionally, a spacer layer of lowrefractive index material (in green) is additionally implemented.The silicon pillars locally modify the phase of the incoming wavefront such that a blazing effect, i.e. a phase gradient, is achieved.Overall, the phase difference between the smallest and largest silicon pillars in the lattice amounts to 2π. Figure 2 presents the optical performance relying on the above approach for two completely different gratings and intended application scenarios.The first grating (Fig. 2 top) covers the short-wave-IR region, and it is optimized to be used within a gas-sensing imaging spectrometer for the measurement of atmospheric CO2 und CH4 concentrations.The latter grating operates in the mid-IR region and is evaluated for operation in an astronomical instrument for stellar science.The peak diffraction efficiency is close to 90% for both gratings and the drop in when moving to the spectral edges is quite moderate, i.e., ~70%.All performances are calculated relying on full Maxwell solvers taking into account realistic material properties.

Demonstrator Manufacturing
A demonstrator grating for the short-wave-IR application was manufactured relying in electron beam lithography.The entire sample has a lateral size of 150mm squared and the substrate's material is (IR-grade) fused silica.The silicon layer was directly deposited on the glass substrate via sputtering technology and the whole sample was exposed to thermal annealing directly afterwards to minimize absorption losses.The actual patterning of the pillar structures was performed in a two-step workflow.First, the pattern is exposed into a resist layer which is then transferred into a metallic masking layer via ionbeam-etching.Then, again a reactive ion etching process is used to transfer the pattern into the underlying silicon layer which finally defines the grating (see Fig. 4).The details of grating design as well as optical performance measurements of the sample grating will be discussed in detail in the full contribution.

Conclusion
We have presented novel design rules for diffraction gratings in the IR domain relying on the implementation of resonant Huygens metasurfaces, i.e., silicon nanopillars.The typical structure depth is λ/2 and maximum required aspect ratios do not exceed 1:5.At the same time we achieve peak efficiencies up to 90%.Overall, the proposed grating structures present a good compromise between manufacturing feasibility and optical performance and might be an interesting alternative to classical echelle-type gratings which are manufactured using completely different technologies, e.g., mechanical ruling or non-binary photolithographic technologies.

Fig. 1 .
Fig. 1.Layout of the grating's nanostructure and composition of pillars of different size.

Fig. 2 .
Fig. 2. Calculated diffraction efficiency of a grating composed of silicon nano-pillars for the short-wave-IR (top) and midwave-IR (bottom) domain.Substrate materials are assumed to be fused silica (top) and Germanium (bottom).

Fig. 4 .
Fig. 4. SEM image of the SW-IR grating's nanostructure covering approximately a single period.