SUPPLEMENTARY INFORMATION

Transcription

1 Supplementary Information S1. Galvo-dithered direct laser writing (GD-DLW) method In order to rectify the asymmetry of the fabrication voxel of the direct laser writing (DLW) method, we have developed the galvo-dithered DLW method (GD-DLW). Here we exploit GD-DLW to fabricate 3D networks with cubic symmetry that retain their symmetry during the fabrication process. The GD-DLW fabrication method shown in Supp. Figs. 1a and 1b uses a galvo-mirror and 4f imaging system to trace the focal spot in a circular motion within the focal plane. The dithering of the focal spot is achieved by using the galvo-mirrors to trace out a very small circular path in the focal plane, whose radius is comparable to the voxel resolution and at very high speeds compared to the speed of the translation stage during the DLW process. A frequency of 500 Hz was used, which is sufficiently fast for the translation stage speeds of 10 μm/s used here to fabricate the srs-networks. When the circular motion of the fabrication voxel is averaged over a period, it becomes wider in the directions of this dithering (i.e. ΔX GD > ΔX DLW ). Most importantly, the galvo-dithering causes the fabrication voxel to become shorter in the Z direction (i.e. ΔZ GD < ΔZ DLW ), improving the overall resolution of the 3D fabrication method. To approximate the effect of the galvo dithering on the fabrication voxel, Supp. Fig. 1c shows the fabrication voxel of the original and dithered DLW methods in blue and red, respectively. We have considered a focal spot with a 3D Gaussian distribution of full-width half maximum of 300 nm in the XY plane and 900 nm in the Z direction. The blue and red cross sections of the fabrication voxel are calculated based on a threshold value of 0.1 relative to the maximum intensity of the voxel with and without dithering, respectively. The dithered NATURE PHOTONICS 1

2 voxel (red) has been calculated by taking the average of 50 Gaussian focal spots that have been translated in a circular distribution. The dithered fabrication voxel is significantly more symmetric than the original voxel, albeit not perfectly spherical. The exact shape and size of the fabrication spot is dependent on the amplitude of the dithering used and the power of the laser used for the DLW (i.e. the threshold level). Supplementary Figure 1. The GD-DLW method used to correct the asymmetric fabrication voxel. a) Experimental schematic of the GD-DLW method. b) The circular translations of the focal spot in the XY plane. c) An illustration of the effect of the galvo dithering on the fabrication voxel. The voxel is widened in the XY direction and shortened in the Z direction, resulting in a more symmetric voxel shape. The width and height of the DLW (GD-DLW) fabrication voxel is labelled as ΔX DLW (ΔX GD ) and ΔZ DLW (ΔZ GD ), respectively. 2 NATURE PHOTONICS

3 SUPPLEMENTARY INFORMATION Note this is a very simplistic model of the effect of galvo-dithering that does not take into account the highly complex nonlinear photo-polymerisation process that includes thermal effects and diffusion. However, it provides a simple understanding of how galvodithering can improve the symmetry of the fabrication voxel. The following section provides evidence of the beneficial effects of the GD-DLW method compared the standard DLW method. S2. Fabrication of srs-networks via Galvo-Dithered DLW Supplementary Fig. 2 shows a scanning electron microscope (SEM) image of an array of srs-networks at different fabrication conditions. Each microstructure contains a rectangular 10x10x3 array of unit cells with unit cell size 1.2 μm. We have varied two parameters of the GD-DLW method. Vertically we vary the laser power (P) used to illuminate the sample and horizontally we vary the galvo-dithering amplitude (A) which is proportional to the voltage applied to the galvo mirrors. Importantly, the use of galvo-dithering clearly improves the mechanical integrity of the srs-network. Even the lowest laser power of 0.60 mw can lead to a mechanically stable structure for values of A > 2. This allows us to improve the fabrication resolution in the Z direction for two reasons. Firstly, a lower laser power can be used, closer to the polymerisation threshold due to the added mechanical stability of the structure. Secondly, the dithering causes the shortening of fabrication voxel height as seen in Supp. Fig. 1. Note that the most important resolution for the fabrication of 3D microstructures is the size of the longest axis of the fabrication voxel (i.e. the axial resolution). NATURE PHOTONICS 3

4 Supplementary Figure 2. SEM image of srs-networks fabricated using GD-DLW in the IP-L photoresist demonstrating the beneficial effects of the galvo-dithering on the mechanical strength. For the lowest laser powers of P = 0.60 mw, when standard DLW is used (i.e. A = 0) the polymerisation is not strong enough to mechanically sustain the 3D microstructure, causing it to collapse and wash away during the rinsing procedure. As the power is increased to P = 0.70 mw polymerisation becomes stronger and the filling fraction of the polymer is increased, leading to improved mechanical stability. In order to determine if the cubic symmetry (manifested in the cross-sectional shape of the network rods) of the srs-network has been preserved during fabrication we have taken SEM images of the srs-network along [011] with and without galvo-dithering and compared these images with simulated structures as shown in Supp. Fig. 3. The srs-network has a unit cell size of 1.2 μm, is 10 unit cells wide and 3 unit cells tall and uses the silicon-zirconium hybrid photoresist. 4 NATURE PHOTONICS

5 SUPPLEMENTARY INFORMATION In Supp. Fig. 3a the srs-network has been fabricated with A = 0 (i.e. the standard DLW method) and the rods are clearly elongated in the vertical direction. In order to determine the values of ΔX DLW and ΔZ DLW we have fitted a simulated image of the srsnetwork shown in Supp. Fig. 3b. The estimated rod width and height are ΔX DLW = 205 ± 15 nm and ΔZ DLW = 480 ± 50 nm. Supplementary Figure 3. a) SEM image of a srs-network fabricated with the DLW method. b) A simulated image of the srs-network with rod width and height chosen to fit (a). c) SEM image of a srs-network fabricated with the GD-DLW method with A=2 demonstrating the improvement in the rod symmetry. d) A simulated image of the srs- network with rod width and height chosen to fit (c). NATURE PHOTONICS 5

6 When the GD-DLW method is used the rods become more symmetric as shown in Supp. Fig. 3c where the galvo-dithering amplitude is A = 2. The fitted simulated images of the srs-network in Supp. Fig. 3d have ΔX GD = 275 ± 15 nm and ΔZ GD = 400 ± 50 nm. This demonstrates that the GD-DLW method both widens the rod width (XY resolution) and reduces the rod height (Z resolution), as predicted in Supp. Fig. 1. In order to determine the dependence of the rod size and shape on the galvo-dithering amplitude we fabricated a series of srs-networks varying A from 0 to 4 and estimated the value of ΔX GD and ΔZ GD for each structure. The results are summarised in Supp. Fig. 4. For A = 3 we observe that ΔX GD is approximately equal to ΔZ GD and for A > 3, ΔX GD > ΔZ GD. Supplementary Figure 4. The effect of the galvo-dithering amplitude (A) on the rod width and height (ΔX GD and ΔZ GD respectively). It should be noted that for A 3 small dimples appear in the rods of the srs-networks due to lack of polymerisation in the centre of the dithering circle. This undesired feature could be avoided by modifying the galvo-dithering method to consider more complex dithering trajectories than the circular motions used here. However, we do not expect any significant effect on dielectric photonic crystals (PCs). 6 NATURE PHOTONICS

7 SUPPLEMENTARY INFORMATION S3. Validity of the assumption T+R=1 In this section we provide an experimental investigation to the assumption in the main text that the scattering and absorption losses of the CBS are negligible. We have fabricated another CBS with same geometrical parameters as in the main text, using the siliconzirconium hybrid photoresist 2. However, this sample has been cleaved twice to form a sharp point that exposes both the input and exiting faces of the CBS. The cleaving was performed 50 μm from the structure to minimise distortions to the CBS. In Supp. Fig. 5 we provide SEM images of the CBS presented at different perspectives and zoom levels. Overall we observe good uniformity of the srs-network even after the double cleaving process. To estimate the amount of loss of the CBS, a germanium photo-detector is used to measure the light transmitting through and reflecting off the CBS. The detector was placed close to the structure (approximately 5 mm) to optimise the collection efficiency. These measurements were normalised to that of light directly incident to the detector without passing through the CBS. The experimentally measured values of T and R are summarised in Supp. Table 1. For this CBS the reflection band is at 1580 nm, the chiral beamsplitting band at 1670 nm and the transmission band at wavelengths larger than 1770 nm. Note that the red-shift in these wavelengths (compared to the CBS in the main text) is consistent with the increase in the refractive index of the silicon-zirconium hybrid photoresist (n=1.52) compared to the IP- L (1.48). At the wavelengths of interest between 1770 nm and 1580 nm the total light detected T+R varies between 87.3% and 95.1% illustrating the low loss of the CBS. These results further are a clear indicator that losses of the CBS are minimal and should not greatly affect the CBS characterisation presented in the main text via imaging. At the much shorter wavelength of 1450 nm where higher order bands are excited, the value of T+R is greatly NATURE PHOTONICS 7

8 decreased to 63.8%. Thus the operation at these shorter wavelengths should be avoided for this device. Supplementary Figure 5. SEM images of the CBS fabricated using GD-DLW and double cleaved to expose both input and exit faces. a) Angled front view showing the CBS sitting close to the cleaved substrate edges. b) Zoomed in view of (a). c) Zoomed in view of (b). d) Angled view of the edge between the input and top surfaces of the CBS. e) View of the CBS from above (i.e. along [001]). f) Zoomed in view of (e). The scale bars are 50 µm in (a), 20 µm in (b,e) and 2 μm in (c,d,f). It is important to note that due to the rapid diffraction of light exiting the CBS and finite detector area of the germanium (0.071 cm 2 ) a small fraction of the beam exiting the CBS was not collected. In addition, a fraction of the light is blocked by the substrate due to the finite height of the structure. Therefore, part of the loss of contributing to T+R < 1 is due to the experimental system and not the CBS itself. Due to the polarisation and wavelength 8 NATURE PHOTONICS

9 SUPPLEMENTARY INFORMATION dependence of the far-field diffraction effect, a direct spectral measurement of T and R is not comparable to the imaging characterisation method which measures the signal μm from the exiting surface of the CBS. Note that the values of T and R have been measured for several samples and found to vary slightly depending on the fabrication and cleaving quality. Wavelength region Wavelength (nm) T (%) R (%) T+R (%) Transmission % Chiral beamsplitting Reflection Higher order Supplementary Table 1. Experimentally measured values of T and R exiting the CBS for the structure shown in Supp. Fig. 5 at different wavelengths. The values of T+R range between 86.9% to 92.9% at the wavelengths of interest, illustrating the low loss of the CBS. S4. Numerical simulation of the chiral beamsplitter transmission and reflection In this section we present the numerical simulation of the CBS. In order to compare the transmission and reflection spectra measured by the imaging method, a numerical simulation was performed for the srs-network PC inclined at (110). The srs-network was excited by a circularly polarised plane wave along its [100] direction. An illustration of the numerical simulation conditions is shown in Supp. Fig. 6. The structure is infinitely periodic in two-dimensions with the input and exit boundaries of the srs-network both clipped with NATURE PHOTONICS 9

10 inclination (110). Incident plane waves are angled 45 relative to the input surface (i.e. along [100]) to replicate the experimental excitation conditions. Supplementary Figure 6. A cross sectional illustration of the simulation setup for the srsnetwork clipped such that the input and output faces have inclination (110), the view is along [001]. Light is incident from the simulation input plane along the [100] direction as shown by the vertical blue arrow. Reflected light is measured at the simulation input plane. The srsnetwork has 4 periodic boundaries, two as shown in the illustration and two more out of and into the plane of the illustration. Transmission is measured at the simulation output plane. The simulation input and output planes are set a distance 3 μm away from the srs-network (110) surfaces. In Supp. Fig. 7 we show the numerically simulated transmission (solid lines) and reflection (dashed lines) spectra for RCP (red) and LCP (blue) incident light under the excitation conditions shown in Supp. Fig. 6. The structure has a thickness of 6 unit cells and a polymer filling fraction of 22%. We observe a good qualitative agreement with the 10 NATURE PHOTONICS

11 SUPPLEMENTARY INFORMATION experiment measurements even though the numerical simulation does not consider the prism shape of CBS and thus neglects the back surface inclination of (100). Therefore we expect the major contribution of the experimentally observed CBS phenomenon to be related to the coupling of circularly polarised light to the Bloch modes of the srs-network PC at the input surface of the CBS. Supplementary Figure 7. Numerically simulated transmission (solid lines) and reflection spectra (dashed lines) for a periodic srs-network that has been clipped such that the input and output planes of the PC have inclination (110). The structure is excited with RCP (red) and LCP (blue) light along [100] (i.e. at 45 to the input surface). The black arrow highlights the chiral beamsplitting wavelength region. S5. Numerical analysis of the excitation angle and voxel aspect ratio dependence Here we numerically investigate the dependence of the chiral beamsplitting phenomenon on the excitation angle of the incident light and the aspect ratio (i.e. symmetry) of the rods of the srs-network. In Supp. Fig. 8 we plot the numerically simulated spectra for light incident on an srs-network of unit cell size 1.2 μm clipped such that the input and exit surfaces are along (110) and with light incident at varying angles. The transmission and NATURE PHOTONICS 11

12 reflection circular dichroism spectra in Supp. Figs. 8c and 8d are given by T LCP T RCP and R LCP R RCP, respectively. Supplementary Figure 8. Numerically simulated transmission, reflection and circular dichroism spectra for varying angles of incidence. a) Transmission spectra. b) Reflection spectra. c) Transmission circular dichroism spectra. d) Reflection circular dichroism spectra. The simulation uses a polymer filling fraction of 32.4% and the aspect ratio of the rods was 1 (i.e. circular rods preserving cubic symmetry). The thickness of the structure was times the cubic lattice parameter a = 1.2 μm. As the incident angle is increased from 40 to 50 the spectra blue-shift and the circular dichroism increases. Further increasing of the angle beyond 50 (not shown here) leads to the excitation of higher order modes causing sharp resonances to form and thus should be avoided. The increase of the circular dichroism may be due to the refraction of the beam entering the 12 NATURE PHOTONICS

13 SUPPLEMENTARY INFORMATION crystal. By increasing the angle of incidence the refracted beam may propagate more along [100] in the PC. Supplementary Figure 9. Numerically simulated circular dichroism spectra for varying aspect ratio (elongation) of the polymer rods of the srs-network. a) Reflection circular dichroism spectra. b) Transmission circular dichroism spectra. To investigate the effect of the elongation of the rods and hence linear asymmetry on the chiral beamsplitting phenomenon we have performed numerical simulations for varying aspect ratio of the polymer rods. The srs-network has a filling fraction of 28% and unit cell size of 1.2 μm. In Supp. Fig. 9 we plot the circular dichroism spectra for the aspect ratio, varied from c = 1 (i.e. circular rods) to c = 2 (i.e. elliptical rods with height twice the width). As the aspect ratio is increased, the linear asymmetry of the structure increases causing a decrease in the circular dichroism for both the reflection and transmission spectra. This again emphasises the importance of maintaining the cubic symmetry of the srs-network during fabrication. S6. Bandstructure characterisation along [110] From the experimental images in the main text, it is clear that the incident beam refracts upon entering the CBS and excites Bloch modes propagating in the XY plane. The NATURE PHOTONICS 13

14 two boundaries of the irreducible Brillouin-zone within that plane are the [100] direction and the [110] direction which is the inclination direction of the input surface of the CBS. In Supp. Fig. 10 we plot the bandstructure of the srs-network along [110]. The bandstructure for the srs-network along [110] shows that over the entire spectral range of interest, there are two almost degenerate Bloch modes that do not suggest circular dichroism (black colour of the bands). The dotted curve around 1.2 μm is a low coupling mode that does not significantly contribute to transmission and reflection properties. Note that the same geometrical parameters of the srs-network used in Fig. 2c of the main text has been used and the colour and size of the points of the bandstructure are given by the values of β and C, respectively 1. Supplementary Figure 10. Theoretically simulated band structure for the polymer srsnetwork with 35% filling fraction, for propagation along [110]. The colour and size of the points of the bandstructure are given by the values of β and C, respectively. The almost black colouring of the points over the entire spectral range suggests that the Bloch modes along [110] are not strongly circularly polarised. Hence, the circular dichroism along [110] would be expected to be much weaker than that in [100]. 14 NATURE PHOTONICS

15 SUPPLEMENTARY INFORMATION S7. Polarisation analysis of the chiral beamsplitter In this section we discuss the polarisation state of the exciting beam of the srsnetwork clipped along [110] discussed in Supp. Sec. 4. The s-parameters (magnitude and phase of the electric fields exiting the crystal relative to the incident electric field) of the numerical simulation in Supp. Fig. 7 were used to calculate the polarisation state of exiting light. In Supp. Fig. 11 we plot the polarisation ellipse for LCP (blue) and RCP (red) incident light at the chiral beamsplitting wavelength of 1618 nm. Supplementary Figure 11. Numerically calculated polarisation ellipse for light at the chiral beamsplitting wavelength shown in Supp. Fig. 7 for LCP (blue) and RCP (red) incident light. a) Transmitted light. b) Reflected light. RCP (LCP) light corresponds to clockwise (anticlockwise) rotation. For both the transmitted and reflected beams we observe that the incident circularly polarised light is converted to an elliptical polarisation with the same polarisation handedness (i.e. a RCP incident wave is converted to a right handed elliptical wave). The change in NATURE PHOTONICS 15

16 polarisation is caused by the finite polarisation conversion upon transmission and reflection of the photonic crystal. This effect has been observed in the reflection from chiral liquid crystal prisms 3. Further engineering of the PC internal symmetry could remove these undesired effects and will be the subject of future work. An ideal CBS device would have both a very high extinction ratio and in addition, maintain the polarisation state of the incident wave. Deeper theoretical investigation to the coupling of light into 3D chiral PCs could elucidate possibilities to maintain circular polarisation exiting the CBS and would be of great interest to developing higher performance devices. S8. Discussion Here we have presented the first experimental demonstration of a CBS from a nanoengineered chiral PC prism. Our design is based on the cubic chiral srs-network and has been fabricated to sufficient resolution, precision and symmetry using the novel GD-DLW method. Importantly, we have observed that the reflection and transmission from the (110) interface of the microscopic-sized prism can lead to significant circularly polarised beamsplitting. Whilst the splitting of light in chiral media such as liquid crystals has been experimentally demonstrated 3, the chirality of these homogeneous materials are much weaker than the chiral srs-network PC we have used here. Importantly, our chiral PC CBS is compact (less than 100 μm wide) compared to the centimetre scale of liquid crystal based beam splitting. Thus our compact CBS is a significant advancement towards the development of integrated photonic polarisation devices. The scalability of PCs also provides the ability for the CBS to be designed to operate at arbitrary wavelengths including visible and midinfrared wavelength regimes. 16 NATURE PHOTONICS

17 SUPPLEMENTARY INFORMATION Recent theoretical studies of prisms constructed from chiral metamaterials 4,5 or highly chiral homogeneous media 6 have also predicted circularly polarised beamsplitting. In contrast to such a CBS based on metallic metamaterials, our CBS is a simple dielectric PC at these wavelengths around 1.5 μm. The advantage of a PC based CBS is the significantly lower losses of dielectrics than metals and ease-of-fabrication (a metamaterials unit cell size should be much smaller than the operating wavelength). Intuitively, we expect that the extinction ratio could be improved through more advanced CBS designs with the addition of a second material (possibly a PC as well) on the opposite side of the incident surface. Analogous to the phase matching condition described in the theoretical investigations of beamsplitting with chiral metamaterials 4,5. If the wave-vector and impedance of this material is matched to that of the Bloch mode of the srs-network one could achieve perfect phase matching. This would remove the refraction of the beam entering the PC. Impedance matching may also play an important role in the control of the exiting polarisation state and thus further theoretical studies to the coupling of light to 3D chiral PCs such as the srs-network discussed here would be of great interest to developing high performance CBSs. It is also important to note that the input surface of the fabricated CBS presented here is not perfectly clipped at (110) as it consists of a discrete number of quarter unit cell fractions of the srs-network. A perfect (110) clipping would require physical cleaving of the srs-network. More advanced CBS designs that include a second homogeneous prism could be used to connect these boundaries to a solid homogeneous material such as an impedancematching material. This would avoid the mechanical distortion of the srs-network at the boundary and allow for a perfectly clipped (110) surface to be formed. Alternatively, a more complex architecture that includes a second photonic crystal with different geometrical NATURE PHOTONICS 17

18 parameters to allow self-collimation and impedance matching as previously demonstrated for 2D linearly polarised PC beamsplitters 7. Further theoretical investigations into the impedance and coupling of light between two 3D PCs would be of highly useful for designing high extinction ratio CBSs based on 3D chiral PCs. On a final note, circularly polarised beamsplitting has also been experimentally 8 and theoretically 9 investigated by using a combination of quarter-wave phase retardation with linearly polarised diffraction gratings and beamsplitters, respectively. These previous studies are based on completely different mechanisms to the CBS demonstrated here, which is built from on a chiral PC. References 1. Saba, M. et al. Circular dichroism in biological photonic crystals and cubic chiral nets. Phys. Rev. Lett. 106, (2011). 2. Terzaki, K. et al. 3D conducting nanostructures fabricated using direct laser writing. Opt. Mater. Express 1, (2011). 3. Ghosh, A. & Fischer, P. Chiral molecules split light: Reflection and refraction in a chiral liquid. Phys. Rev. Lett. 97, (2006). 4. Cheng, Q. & Cui, T. J. Reflection and refraction properties of plane waves on the interface of uniaxially anisotropic chiral media. J. Opt. Soc. Am. A 23, (2006). 5. Tamayama, Y., Nakanishi, T., Sugiyama, K. & Kitano, M. An invisible medium for circularly polarized electromagnetic waves. Opt. Express 16, (2008). 6. Mahmoud, S. F. & Tariq, S. Gaussian beam splitting by a chiral prism. J. Electromagnet. Wave 12, (1998). 7. Zabelin, V. et al. Self-collimating photonic crystal polarization beam splitter. Opt. Lett. 32, 530 (2007). 8. Davis, J. A., Adachi, J., Fernandez-Pousa, C. R. & Moreno, I. Polarization beam splitters using polarization diffraction gratings. Opt. Lett. 26, (2001). 9. Azzam, R. M. A. & De, A. Circular polarization beam splitter that uses frustrated total internal reflection by an embedded symmetric achiral multilayer coating. Opt. Lett. 28, (2003). 18 NATURE PHOTONICS