Polariton nanophotonics using phase-change materials

Polaritons formed by the coupling of light and material excitations enable light-matter interactions at the nanoscale beyond what is currently possible with conventional optics. However, novel techniques are required to control the propagation of polaritons at the nanoscale and to implement the first practical devices. Here we report the experimental realization of polariton refractive and meta-optics in the mid-infrared by exploiting the properties of low-loss phonon polaritons in isotopically pure hexagonal boron nitride interacting with the surrounding dielectric environment comprising the low-loss phase change material Ge3Sb2Te6. We demonstrate rewritable waveguides, refractive optical elements such as lenses, prisms, and metalenses, which allow for polariton wavefront engineering and sub-wavelength focusing. This method will enable the realization of programmable miniaturized integrated optoelectronic devices and on-demand biosensors based on high quality phonon resonators.


Supplementary Note 2: Lens and metalens design and analysis
The focus of the fabricated plano-convex lenses cannot be computed with the lens-maker's equation, since these lenses cannot be approximated with thin lenses. Therefore, the focal spot is computed by approximating the lens with a hyperbolic lens which has a well-defined analytical formula for the focal spot position (Supplementary Figure 1). The hyperbolic profile has the equation: ( 2 − 1) 2 − 2 − 2 ( − 1) = 0 (S3) where = eff,c / eff,a is known and (i.e. the focal length) is fitted. The focal position found in this way strictly relies on ray optics, which is used to derive the hyperbolic profile in the first place.
Supplementary Figure 1 | Fitting semi-circular lenses with hyperbolic profile. The hyperbolic lens is the exact locus of points that can focus an incoming plane wave in a single point according to geometric optics. The written lens is semi-circular and is fitted by the hyperbolic profile using f as the fitting parameter.
A better description of the focal spot can be obtained by considering that the guided wavelength is comparable to the size of the lens ( ≈ ) and using gaussian optics. According to gaussian optics, the actual beam waist is at a position s (where the focused beam has the smallest lateral size) which is not equal to f. Such an equality holds only in the ray optics limit (R >> ). Following ref. 32: where R is the Rayleigh range of the input beam defined using the radius of the lens as the input beam waist and a is the SPhP wavelength on amorphous GST ( a = eff,a ⁄ ). As expected, for the large lens limit, = as expected for ray optics. For the metalens design, each truncated waveguide element is simulated first in a periodic environment as usually done for metasurface design. The phase delay is found relative to the case where no element is present (length or width equal to zero) and then elements are chosen from the desired phase profile. The differences between the design phase and the desired phase profile in Figure 4d are due to discrepancies in the initial estimation of the layer thicknesses (fixed in the last metasurface) and to the phase discretization of the width in the second metasurface, due to the way the waveguides are written (with several passes at a given distance from each other). Supplementary table 1 summarizes the information on the design of the various lenses.

Supplementary Note 3: Direct laser writing
The patterning of the GST film was carried out using a 405 nm laser diode (disassembled from a Pioneer 16X BDR-209 Blu-Ray writer), which was coupled into a single mode fibre and focused onto the sample through a 0.9 NA objective (Supplementary Figure 2). The laser diode was driven using an Agilent 8114A pulse generator. All structures were written with 50 ns pulse trains at 17 MHz frequency and a beam moving velocity of 1 µm/s. The pulse peak power used for writing ranged from 3.55 mW to 12.2 mW (details for different structures in Supplementary Table 2). For erasing, shorter pulses of 20 ns duration, 17 MHz repetition rate and a peak power of 28 mW were used. The GST film is ablated outside of the hBN covered regions, which were only protected by a 15 nm layer of ZnS:SiO2 to prevent oxidation of the GST film (Supplementary Figure 3). Typically, one would use a layer thickness on the order of 100 nm to carry out the re-write procedure on GST without hBN. Since we do not observe ablating in regions covered by hBN, we conclude that it serves as excellent capping layer for GST by itself. Furthermore, we observed small specks of crystalline GST after erasing in an optical microscope (Nikon) with 150x magnification, which we couldn't resolve during the erasing with the selfbuilt microscope that we used for monitoring the quality of the erasing. We confirmed however, that these small impurities did not affect polariton propagation.
Given that the necessary powers were very low compared to what is in principle available for the laser diode we used (1000 mW), all demonstrated patterns can be achieved by parallel illumination using a spatial light modulator. In this scenario, the amorphization would not suffer from residual crystalline patches as the illumination would be homogenous over a large area. Supplementary Figure 4 is an overview of the hBN flake in its final state.

Supplementary Figure 2 | Optical beam path of writing setup.
A laser diode operating at 405 nm is focused into a single mode optical fibre and subsequently focused onto the sample through a 0.9 NA objective (O2). The sample is mounted on a programmable stage and the writing is monitored through a microscope consisting of objective O2 and tube lens T1. The writing and microscope arms are combined using a dichroic mirror (P).

Supplementary Note 4: s-SNOM image processing
The images shown in the main paper have been processed to enhance the mode launched by the edge and coupled in the written structures. The raw data (collected with a commercial s-SNOM from NeaSpec, GmbH) consists of amplitude and phase images obtained via pseudo-heterodyne demodulation. The system performs the demodulation at several pseudo heterodyne harmonics, though only the first two harmonics were used in this work. The s-SNOM images are obtained by shining light on a tip scanning the sample and collecting the demodulated near field optical amplitude and phase for each pixel. Therefore, each pixel contains a complex number that represents phase and amplitude of the near field in that position. The interpretation of the s-SNOM images is not obvious in samples that can support guided modes or standing resonances as explained in our previous works 8, 12,18 . When studying the propagation of guided waves, the complex s-SNOM maps are the superposition of several contributions, each due to a possible light path between the s-SNOM laser source and the detector. These dominant contributions are: • The material contrast contribution, which is associated to photons interacting with the local polarizability of the material just below the tip and which are not coupled into the guided modes. This contribution exists for any sample, even when no guided modes exists.
• The direct coupling contribution, in which guided modes launched by edges or discontinuities propagate until they reach the s-SNOM tip, which probes them locally and scatters them to the detector. For guided modes, this contribution appears as fringes with periodicity approximately equal to the guided wavelength. The approximation comes into play because the exciting incident light is at an angle, and thus affects the periodicity of the observed fringes. This effect can be neglected in strongly confined modes. • The round-trip contribution, in which the guided mode is excited by the tip, reflected by an edge or by a discontinuity and reaches back to the tip. For guided modes, this contribution also appears as fringes, but the periodicity is exactly half of the guided wavelength. This is due to the fact that polaritons propagate twice between the tip and the discontinuity.
In our work, we use the round-trip contribution to determine the effective index of the measured samples (Figure 3h) since the fringe spacing is exactly half of the guided wavelength regardless of the incident light.
This provides more precise measurements than the direct coupling. For imaging the fields, we use the direct contribution instead, which provides the most faithful representation of light propagation on the sample. To excite the direct contribution, the hBN edge must be oriented perpendicularly to the light polarization, while the roundtrip contribution does not depend on the edge orientation. Therefore, the edge orientation can be used to control which of the contributions is dominant in the image. Supplementary table 1 lists the orientation of the edge and the corresponding dominant contribution for all figures in the paper. The table also lists in detail the image processing methods used for each image in the main article. The material contrast contribution is a constant complex number on all the hBN flakes and can be removed by calculating the average of the fields on the flake and subtracting this number from all pixels in the image. After that, the wavefronts can be visualized by taking the real part of the field. For lenses we implement an additional image processing which allows to remove the vertical fringes launched by the opposite edge of the flake and to remove the fields diffracting around the lens. This is achieved by subtracting column by column the fringes launched by the edges which do not interact with the lens (see Supplementary Figure 5 for details). The result is the portion of direct contribution that is transmitted through the lens. The dot is formed by focusing the diode laser in a single position to locally crystallise GST. The dot has a diameter of approximately 800 nm, and these s-SNOM images were taken at 1500 cm -1 (scan area is 5 µm × 5 µm). The response is clearly visible both in the amplitude and in the phase.