Reversible optical switching of highly confined phonon ...10.1038... · b) c-GST cases. Different GST thicknesses are investigated. The SiC dielectric function is modeled as a Lorentz

Reversible optical switching of highly-confined phonon polaritons with an ultra-thin phase change material

Peining Li, Xiaosheng Yang, Tobias W. W. Maß, Julian Hanss, Martin Lewin, Ann-Katrin U. Michel, Matthias Wuttig, and Thomas Taubner*

1st Institute of Physics (IA), RWTH Aachen University, Aachen 52056, Germany

*Correspondence to: [email protected] Guide of Supplementary Information Figure S1: Dielectric function of quartz.

Figure S2: Dispersion relation of SPhPs hosted by the GST on a SiC substrate.

Figure S3: Simulation of SPhPs excited by an a-/c-GST boundary.

Figure S4: Determination of the SPhP wavelength from the s-SNOM data.

Figure S5: s-SNOM profiles for the cases of 7 and 15 nm a-GST over quartz.

Figure S6: Reflection calculations of the GST/quartz stacks.

Figure S7: Dependence of SPhP wavevectors on GST thickness.

Figure S8: AFM topography of the a-GST SPhP resonators.

Figure S9: Additional s-SNOM data of the a-GST/quartz SPhP resonator.

Figure S10: Results of inverse resonators: c-GST spots in a-GST matrix.

Figure S11: Simulated reflection spectra of the GST/SiC SPhP resonators.

Figure S12: Effects of protection layer and increased resonator density.

Figure S13: Measured reflection spectra of a c-/a-GST grating on quartz.

Figure S14: Additional spectral data of the multiple-time reversible switching

Figure S15: Examples of further improvements and application potential.

Note 1: Determination of SPhP wavelengths from the imaging data.

Note 2: SPhP elliptical resonators.

Movie 1: Multiple-time reversible switching of a-GST spots in c-GST covered with a

protection layer.

Reversible optical switching of highly confined phonon–polaritons with an ultrathin phase-change material

SUPPLEMENTARY INFORMATIONDOI: 10.1038/NMAT4649

NATURE MATERIALS | www.nature.com/naturematerials 1

© 2016 Macmillan Publishers Limited. All rights reserved.

http://dx.doi.org/10.1038/nmat4649

1000 1050 1100 1150 1200

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tz

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Supplementary Figure S1. Real (black) and imaginary part (red) of dielectric permittivity of

quartz used in our work, which were taken from Ref. 32 in the main text. We neglected the

weak anisotropy of the quartz in the wavelength range of interest. The features at around 1160

cm-1 are due to several weak quartz phonons.

2 NATURE MATERIALS | www.nature.com/naturematerials

SUPPLEMENTARY INFORMATION DOI: 10.1038/NMAT4649



Supplementary Figure S2. Calculated SPhP dispersion (slow mode) on SiC covered with (a) a-GST and (b) c-GST cases. Different GST thicknesses are investigated. The SiC dielectric function is modeled as a Lorentz model with LO phonon frequency ωLO = 969 cm-1, TO phonon frequency ωTO = 793 cm-1, ε= 6.7 and damping factor = 4 cm-1. It can be seen that the SPhPs on GST/SiC cases have even larger wavevectors than those of SPhPs on GST/quartz cases (main text Fig.1), which is because SiC has lower damping than quartz. For example, for the case of SiC covered with 30 nm a-GST, the maximum SPhP wavevector kp is over 100k0.





Supplementary Figure S3. Simulation of SPhPs excited by an a-/c-GST boundary. We

simulated the field distribution for the case that a c-GST (x < 0) and an a-GST film (x > 0) are

on a quartz substrate at the frequency of = 1120 cm−1. Both GST films are 30 nm thick. It is

clear that the resulting a-/c-GST boundary (located at x = 0 μm) launches the SPhPs. For the

SPhPs in the a-GST/quartz part, we observe a SPhP wavelength of about λp = 500 nm (kp = 17.9

k0), which nicely agrees with both calculated and experimental results shown in main text (Figs.

1 and 2).





Supplementary Figure S4. Determination of the SPhP wavelength from experimental data. a,

Sketch of the SPhP interference model including boundary-launched SPhP fields Ep,b, tip-

launched SPhP fields Ep,t and tip-launched and boundary-reflected SPhP fields Ep,r. An a-/c-

GST boundary is located at the position x = 0. The incident angle θ of the mid-IR illumination

is about 30 degrees, as in our s-SNOM setup. b and c, Comparison of the modeling and

experimental data at the frequencies of 1120 and 1127 cm-1. Our modeling results show a good

agreement with the experimental data, which reveals that the fringe period almost equals to the

SPhP wavelength λp.





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80 nmSNO

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igna

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Supplementary Figure S5. Line profiles of the s-SNOM signals across the a-/c-GST boundary

for the part of 7 and 15 nm a-GST over quartz. We reveal a half width as small as 40 nm at the

frequency of 1120 cm-1. This indicates the kp is about 70 k0 according to the model described

in Supplementary Note 1.





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Supplementary Figure S6. Reflection calculations of the GST/quartz stacks. The s-SNOM

signal is generally related to the reflection properties of the investigated samples (main text

Refs. 1,2,6). We calculated the reflection coefficients r as a function of the frequency and

the in-plane wavevector kx for both a- and c-GST with the thickness of 7, 15 and 30 nm. We

used the formula 𝑟𝑟 = (𝑟𝑟12 + 𝑟𝑟23𝑒𝑒2𝑖𝑖𝑘𝑘z𝑑𝑑)/(1 + 𝑟𝑟12𝑟𝑟23𝑒𝑒2𝑖𝑖𝑘𝑘z𝑑𝑑) , where r12 and r23 are the

reflection coefficients of the air/GST and the GST/quartz interfaces, respectively. kz is the out-

of-plane wavevector in the GST. d is the thickness of the GST. The reflection peaks found in

the plots (dark color regimes) correspond to the SPhP modes existing in the GST/quartz stacks.

We can see that the thickness of the GST significantly influences the SPhPs. The thicker the

GST layer is over the quartz, the smaller kp and the weaker strength of SPhPs are obtained.





Supplementary Figure S7. Dependence of SPhP wavevectors on GST thickness. We

calculated the reflection coefficients r as a function of the GST thickness d and the in-plane

wavevector kx for both a- and c-GST cases at the fixed wavenumber of 1120 cm-1. The observed

reflection peaks indicate the SPhP modes. Generally, we observe that the wavevectors of SPhPs

increase continuously with the decrease of the GST thickness. In particular, the variation rate

(k/d) becomes significantly larger when the GST thickness is smaller than 5 nm.





Supplementary Figure S8. a, AFM topography image of the four GST domains shown in

main text Fig. 3. b and c are line profiles across one written and one erased domains (indicated

by dashed lines in a), respectively. They are averaged over 20 line scans. The written a-GST

domain is about 2 nm higher than the surrounding c-GST film. In the erased area, the thickness

difference is suppressed due to the re-crystallization. Film ablation at the domain boundary was

also observed, which can be avoided by adding a protection layer.





1127 cm-1 1132 cm-1 1140 cm-11136 cm-1

25 82 10 59 3.6 33.8 1.9 28 0.6 7

500 nm

1120 cm-1

Supplementary Figure S9. Additional spectroscopic imaging data of single a-GST/quartz

SPhP resonator discussed in main text Fig. 3. We revealed a clear transition of mode behaviors

in such SPhP resonator. However, we note these revealed patterns results from both the tip-

and boundary-launched SPhPs, which are not identical to the simulated data (without the tip

influence) shown in main text Fig. 4a.





Supplementary Figure S10. Inverse Resonators: c-GST spots in a-GST matrix. Additional experimental (a) and simulated (b) reflection spectra of GST/quartz SPhP resonators. In the experiment, the resonators are the c-GST spots switched by single (100 mW, 45 ns) laser pulses in a 30 nm a-GST film on quartz. Two dips are observed in the reflection spectra. The polarization-independent dip close to 1160 cm-1 is due to the intrinsic quartz phonon. The dip at around 1130 cm-1 is the SPhP resonance, showing polarization dependence: Its resonance position is red shifted when changing the polarization from the Elong direction (parallel to the major axis of the resonator) to the Eshort direction (parallel to the minor axis). This polarization dependence is also verified by the simulation shown in (b). As revealed by the simulated field distribution in (b), the resonator in this case is an analogy to a slot resonator. The SPhP field enhancement is mainly located at and outside the boundary of the resonator, which is in contrast to the a-GST SPhP resonator with the near-field enhancement mainly inside the resonator (see main text Fig. 4a).





Supplementary Figure S11. Simulated reflection spectra of the GST/SiC SPhP resonators for two polarizations. The resonator structures are the a-GST spots switched in a 30 nm c-GST film. The long axis of the resonators is 2 m long and the short axis is 1 m long. The periodicities on both x, y direction are 2.5 m. Due to the low damping of SiC, these structures can exhibit a stronger resonance (about 30% reflectivity variation) than the GST/quartz case.





Supplementary Figure S12. Effects of protection layer and increased resonator density. Additional experimental reflection spectra of GST/quartz SPhP resonators. The resonators are a-GST spots switched by single (300 mW, 12 ns) laser pulses in a 30 nm c-GST film. A 10 nm protection layer (ZnS:SiO2) is deposited on the top of the GST layer. The resonances are still present with added protection layer. Furthermore, resonators with two different periodicities (2.5 m and 5 m) are investigated. The array size of the reflection measurement is around 20 m 20 m. When increasing the resonator density, the resonance strength (change in reflectivity) in the reflection spectra is enhanced.

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Supplementary Figure S13. Additional experimental reflection spectra of c-GST stripes (brighter, about 20 m long) switched by single (100 mW, 45 ns) laser pulses in a 30-nm a-GST film on quartz. The inset is the optical microscope image of the switched grating structure. The periodicity is about 3 m. This grating-like structures show very clear SPhP resonance at around 1130 cm-1 for the (Eshort) polarization perpendicular to the grating. For the (Elong) polarization parallel to the structures, no SPhP resonance is observed. Therefore, this grating can be seen as a simple GST-SPhP metasurface structure that could be used for mid-IR nanophotonic applications.





Supplementary Figure S14. Additional experimental reflection spectra of the multiple-time reversible switching of the a-GST elliptical resonators in the 30 nm c-GST film, which are discussed in the main text Fig. 4. The switching times of these resonators without the protection layer are limited to 8. When adding a 10 nm ZnS:SiO2 protection layer, the resonators can be switched more than 40 times. a and b are for the two different polarizations.





Supplementary Figure S15. Examples of further improvements and application potential. a, High-resolution optical switching of the PCM can be achieved by coupling the writing/erasing pulses with the s-SNOM sharp tip. This technique can overcome the diffraction limit and achieve the switching spot size D down to 20 nm. b, Sketches (from top view) of two possible examples of the metasurface structures that can be created by our approach. The scattering amplitude and phase response of the antennas in the unit cell are varied by changing their orientation and/or their shape. c, A switchable GST/SiC/GST superlens. The SiC thickness is 400 nm. The thickness of each GST layer is 200 nm. False color plots are the optical transfer functions (transmission |T| as a function of ω and kx) of (left) the a-GST/SiC/a-GST and the (right) a-GST/SiC/a-GST configurations. At the so-called superlensing wavelength satisfying the condition of Re(εSiC)=Re(εGST), the superlens supports a transmission peak for high- kx components, enabling the reconstruction of a super-resolution image through the superlens. Therefore, it can be seen that by switching the GST structural phase, the superlensing wavelength of the GST/SiC superlens can be switched from ω= 860 cm-1 to ω = 822 cm-1

(indicated by dashed lines). This switchable superlens will have a broader imaging wavelength range compared to previously reported SiO2/SiC/ SiO2 superlens (main text, Ref. 10) with only a single superlensing wavelength.





Supplementary Note 1: Determination of SPhP wavelengths from the imaging data.

In Fig. 2 of the main text, the observed fringes result from the interference of three SPhP terms

(sketched in Supplementary Fig. S4a): boundary-launched SPhP fields Ep,b (see Supplementary

Fig. S3), tip-launched SPhP fields Ep,t and tip-launched and boundary-reflected SPhP fields

Ep,r. We assumed a launching-efficiency factor t for tip-launched SPhPs and a factor b for

boundary-launched SPhPs (t = b chosen in our cases). Then we expressed the tip-probed

fields in the a-GST/quartz part (x > 0) as (main text Refs. 2, 6),

a-GST 0 0

, , ,

2 [ cos[ ] ]p p

t background p t p r p b

i k x i k x k xbackground t i p t i i b

E E E E E

E E r E e E e

(N1.1)

where Ebackground is the background and Ei is the incident field. The reflection coefficient of the

SPhPs at the a-GST/c-GST boundary is rp = (np,a-GST np,c-GST )/(np,a-GST + np,c-GST). np is the

mode index of the SPhPs. εa-GST is permittivity of the a-GST. The incident angle θ of mid-IR

illumination is about 30 degree in our s-SNOM setup. φ0 is a phase difference between the tip-

and boundary-excited SPhPs (φ0 = /9 chosen in our fits).

The modeling results at two frequencies are shown in Supplementary Fig. S4b and c. Our model

agrees well with the experimental data and reveals that the measured fringe period almost

equals to the SPhP wavelength. Intuitively, this finding is different from the λp/2-model

(namely the measured fringe period equals to λp/2) used in previous studies (Ref. 2 in the main

text). However, our model is still consistent with theirs. In their studies the s-SNOM tip was

scanned directly on the surface of polar crystals or graphene. The strong tip-sample interaction

in a tiny nano-gap between the tip and the strong substrate results in that the strength factor of

boundary-launched SPhPs is much lower than that of the tip-launched SPhPs (namely b much

smaller than t). The term of boundary-launched SPhPs were neglected in their cases. In

contrast, in our case, the tip is away from the surface of the polar crystal (spaced by the high-

index GST layer), t becomes comparable to the b. Therefore, we should consider the term of

boundary-launched SPhPs in our model. In a recent literature (Ref. 17 in the main text) of

imaging graphene SPPs in an hBN/graphene/hBN heterostructure, the influence of boundary-

generated polaritons is also included due to the fact that a spacer between the s-SNOM tip and

the graphene is added by an hBN layer.





Supplementary Note 2: SPhP elliptical resonators.

The SPhP cavity resonances discussed in main text Fig.4 originate from the constructive

interferences of SPhPs launched and reflected at the a-GST/c-GST boundaries. Considering

the elliptical shape of the resonator, we transform the Cartesian coordinates (x, y, z) to the

elliptical cylindrical coordinates (ξ, η, z) with the relation of x = f coshξcosη, y = f sinhξsinη

and z = z. f is the focal length of the ellipse. The electrical field Ez in the resonator is thus given

as the product of the even and odd radial and angular Mathieu function as [Ref. 35 and S1, S2]

Even mode: ( , ) ( , )z m mE Je q Ce q , 0m (N2.1a)

Odd mode: ( , ) ( , )z m mE Jo q Se q , 1m (N2.1b)

Where Jem(ξ, q) and Jom(ξ, q) are the mth order even and order radial Mathieu functions of the

first kind. Cem(η, q) and Sem(η, q) are the mth order even and odd angular Mathieu functions.

q=f 2kp2/4 and kp is the SPhP wavevector. Considering the fact that the maximum near-field

enhancement is at the cavity edge, the cavity resonances are determined by the Neumann

boundary condition as [Ref. 35 and S1]

Even mode: ( , ) ( , ) 0m mJ e q Ce q (N2.2a)

Odd mode: ( , ) ( , ) 0m mJ o q Se q (N2.2b)

As a result, the cavity resonance modes are given by of the solutions of these equations, which

are the nth zero of the mth order Mathieu functions. As presented in Ref. 35 and S1, the even

modes indicate the resonance for the (Elong) polarization parallel to the long axis of the ellipse.

The odd modes correspond to the (Eshort) polarization parallel to the short axis. By comparing

our simulated field distribution (main text Fig. 4a) with the calculated modal distribution using

the Mathieu functions (see Ref. 35, S1 and S2), it is clear that for the Eshort direction in our

SPhP resonance is the fundamental (1,1) mode and for the Elong direction it is a higher order

(1,2) mode. The other even higher order modes cannot be excited in our cases because the

propagation length of the SPhPs is short. We also note that the modal behavior of our all-

dielectric, elliptical SPhP resonators is similar to the previous work of the metallic, circular

hole-cavity SPhP resonators though their geometrical shape is different from ours (main text

Ref. 8).





Supplementary Reference

S1. Wang F., Chakrabarty, A., Minkowski, F., Sun, K., & Wei, Q. H., “Polarization conversion

with elliptical patch nanoantennas”. Applied Physics Letters, 101, 0231010 (2012)

S2. Blanch G., “Mathieu Functions,” in Handbook of mathematical functions, Abramowitz M.,

Stegun I. A., ed. (Dover, New York, 1953).





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Reversible optical switching of highly confined phonon ...10.1038... · b) c-GST cases. Different GST thicknesses are investigated. The SiC dielectric function is modeled as a Lorentz