SUPPLEMENTARY INFORMATION€¦ · (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

SUPPLEMENTARY INFORMATIONDOI: 10.1038/NPHOTON.2013.233

NATURE PHOTONICS | www.nature.com/naturephotonics 1

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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. ΔXGD > ΔXDLW). Most importantly, the galvo-dithering causes the fabrication

voxel to become shorter in the Z direction (i.e. ΔZGD < ΔZDLW), 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

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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. ΔXGD > ΔXDLW). Most importantly, the galvo-dithering causes the fabrication

voxel to become shorter in the Z direction (i.e. ΔZGD < ΔZDLW), 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

© 2013 Macmillan Publishers Limited. All rights reserved.

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SUPPLEMENTARY INFORMATION DOI: 10.1038/NPHOTON.2013.233

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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 ΔXDLW (ΔXGD) and ΔZDLW (ΔZGD), respectively.




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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 galvo-

dithering 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).




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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.




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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 ΔXDLW and ΔZDLW we have fitted a simulated image of the srs-

network shown in Supp. Fig. 3b. The estimated rod width and height are ΔXDLW = 205 ± 15

nm and ΔZDLW = 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).




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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 ΔXGD = 275 ± 15 nm and ΔZGD = 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 ΔXGD and ΔZGD for each structure. The results are summarised in Supp. Fig. 4. For

A = 3 we observe that ΔXGD is approximately equal to ΔZGD and for A > 3, ΔXGD > ΔZGD.

Supplementary Figure 4. The effect of the galvo-dithering amplitude (A) on the rod width

and height (ΔXGD and ΔZGD 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).




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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 silicon-

zirconium hybrid photoresist2. 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




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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 cm2) 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




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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 10-20 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 1770 77.1 10.9 88.0%

Chiral beamsplitting 1670 43.6 43.7 87.3

Reflection 1580 20.6 74.5 95.1

Higher order 1450 28.5 34.4 62.9

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




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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 srs-

network 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 srs-

network 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




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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




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reflection circular dichroism spectra in Supp. Figs. 8c and 8d are given by TLCP – TRCP and

RLCP – RRCP, 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




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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




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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, respectively1.

Supplementary Figure 10. Theoretically simulated band structure for the polymer srs-

network 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].




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S7. Polarisation analysis of the chiral beamsplitter

In this section we discuss the polarisation state of the exciting beam of the srs-

network 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 (anti-

clockwise) 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




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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 prisms3. 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 nano-

engineered 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 demonstrated3, 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 mid-

infrared wavelength regimes.




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Recent theoretical studies of prisms constructed from chiral metamaterials4,5 or

highly chiral homogeneous media6 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 metamaterials4,5. 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 impedance-

matching 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




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parameters to allow self-collimation and impedance matching as previously demonstrated for

2D linearly polarised PC beamsplitters7. 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 experimentally8 and

theoretically9 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, 103902 (2011). 2. Terzaki, K. et al. 3D conducting nanostructures fabricated using direct laser writing. Opt. Mater.

Express 1, 586–597 (2011). 3. Ghosh, A. & Fischer, P. Chiral molecules split light: Reflection and refraction in a chiral liquid.

Phys. Rev. Lett. 97, 173002 (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, 3203–3207 (2006). 5. Tamayama, Y., Nakanishi, T., Sugiyama, K. & Kitano, M. An invisible medium for circularly

polarized electromagnetic waves. Opt. Express 16, 20869–20875 (2008). 6. Mahmoud, S. F. & Tariq, S. Gaussian beam splitting by a chiral prism. J. Electromagnet. Wave 12,

73–83 (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, 587–589 (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, 355–357 (2003).


Documents

SUPPLEMENTARY INFORMATION€¦ · (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