Circularly-polarized, semitransparent and double-sided holograms based on helical photonic structures

Recent advances in nanofabrication techniques are opening new frontiers in holographic devices, with the capability to integrate various optical functions in a single device. However, while most efficient holograms are achieved in reflection-mode configurations, they are in general opaque because of the reflective substrate that must be used, and therefore, have limited applicability. Here, we present a semi-transparent, reflective computer-generated hologram that is circularly-polarization dependent, and reconstructs different wavefronts when viewed from different sides. The integrated functionality is realized using a single thin-film of liquid crystal with a self-organized helical structure that Bragg reflects circularly-polarized light over a certain band of wavelengths. Asymmetry depending on the viewing side is achieved by exploiting the limited penetration depth of light in the helical structure as well as the nature of liquid crystals to conform to different orientational patterns imprinted on the two substrates sandwiching the material. Also, because the operation wavelength is determined by the reflection band position, pseudo-color holograms can be made by simply stacking layers with different designs. The unique characteristics of this hologram may find applications in polarization-encoded security holograms and see-through holographic signage where different information need to be displayed depending on the viewing direction.


Design and generation of the hologram pattern
The hologram pattern was generated by the Gerchberg-Saxton (G-S) algorithm according to the following procedure [18]. First, the target image was prepared in Fourier space (Fig. S1a) and rescaled to fit the projection area, which has an aspect ratio of 4:3; the actual number of pixels used was either 512 × 384 px or 1024 × 768 px, depending on the desired size of the hologram (the size of a pixel realized experimentally is approximately 2.6 × 2.6 µm 2 , yielding 1.35 × 1.01 mm 2 and 2.70 × 2.03 mm 2 as the hologram size). The source image was then inverse-Fourier-transformed to obtain a complex signal at the object plane, and its amplitude was replaced with a uniform signal before applying a Fourier transform to reproduce the image in the Fourier plane. The accuracy of image reproduction was improved by repetitively performing the procedure after replacing the amplitude of the image in the Fourier plane with the target image. The whole procedure was repeated until the zero mean normalized cross correlation (ZNCC) of the reproduced image to the original image was above 0.98. The final phase distribution and the reproduced image giving a ZNCC of 0.981 are shown in figs. S1b and S1c. In experiment in the manuscript, the phase distribution is converted to the helix phase distribution of ChLC by being multiplied by ±0.5 and rounded to have 60 levels with increment of 3 .

Reflection spectrum of the ChLC material
The ChLC material used to make the hologram was characterized in a standard sandwich cell with uniform planar alignment treatment. Two substrates coated with photoalignment agent were assembled into a 9 µm-thick sandwich cell and irradiated upon linearly polarized UV light (365 nm, 100 mW/cm 2 ) to induce uniform planar alignment. The reflectance spectrum was acquired with a spectrometer (PMA-11, Hamamatsu) coupled to a polarizing optical microscope (Nikon, Eclipse LV-POL 100) by a bundled fibre with diameter of 1 mm and an objective lens with 10× magnification. As shown in Fig. S2, the reflection band appeared between 634 and 724 nm. Using the Grandjean-Cano wedge method, the pitch was found to be approximately 420 nm. A similar value is also obtained from optical calculations, substituting refractive indices ne = 1.7688 and no = 1.5158 (measured at 589.3 nm, 20°C) from the datasheet of the host nematic LC into the equation for the reflection band, nopnep.

Effect of pitch distribution on the hologram quality
In the proposed hologram, the helix phase is varied through defining the orientational easy axis on a substrate. When the orientational easy axis of one substrate is varied with respect to the other while maintaining the cell-gap, the number of helix turns within the cell, and hence the helical pitch, changes.
The helical pitch for a cell with an arbitrary orientational easy axis, directed at angle  with respect to the counter-substrate is given by the following equation: where d is the cell gap and p0 is the pitch for parallel or antiparallel boundary condition ( = 0 or π).
Note that because of the head-tail symmetry, the pitch changes discontinuously at  = ±/2 so as to take a value that is close to the natural pitch, p, of the material, which is determined by the concentration of the chiral dopant. The largest pitch difference is obtained between regions with  = /2 and -/2 and is given by: (2) From Eq. 2, one finds that the pitch difference decreases with an increase in the cell-gap. By substituting the experimental condition d = 9 m and p0 = 420 nm for this study, p is calculated to be 9.8 nm (p0 ± 4.9 nm), agreeing satisfactorily with the experimental result in Fig. 2 in the manuscript.
The reflected light phase from a ChLC with varying helix pitch length and helix phase was calculated using Berreman's 4×4 matrix method [1]. In calculation a ChLC with the refractive indices ne = 1.7688 and no = 1.5158 were sandwiched between two glass substrates (n = 1.53) separated by a gap of 9 m.

Comparison of the transmittance spectrum of uniform planar and hologram ChLC devices
The transmittance of the ChLC cells were measured using the same setup as that for reflection measurements described in Section 2, but in transmission mode of the polarizing optical microscope. As shown in Fig. S4, the transmittance shows a decrease between approximately 630 and 720 nm, owing to the presence of the reflection band. The transmittance for both the planar and hologram samples are similar, indicating that the presence of the helix phase pattern has negligible effect on the transmittance of the sample. It is noted that the amplitude of the sidelobes (so-called Pendellӧsung oscillations) is smaller in the sample with the hologram pattern, as creating a phase distribution corresponds to making the reflection plane non-planar. where I0 is the incident light intensity at P1, I1 is the 0 th order intensity at P2, and I2 is the total light intensity at P2.

Comparison of double-sided and standard hologram devices
Here, the performance of the double-sided hologram device with asymmetric patterning (fabricated from a substrate with hologram pattern and the counter-substrate with uniform planar alignment) was compared with a standard device with symmetric patterning (same hologram pattern on both substrates).
The reflectance and transmittance spectra of the devices were first compared from microscopic spectroscopy, using the same setup as that described in Section 2. The reflectance and transmittance spectra shown in figs. S6 a,b show that the asymmetry in the pattern has a negligible effect on the optical quality of the sample. Figs. S7 a,b shows photos of illuminating the double-sided and standard hologram devices, using the same setup described in Fig. 3 of the manuscript. Unlike the double-sided device in which the image appears only from the side with the hologram pattern, the standard device generates an image from either side of the device. However, the image generated from the standard device becomes inverted on one side because the phase reverses sign as a result of creating the same pattern on both substrates [14].
Being able to suppress the appearance of such a conjugated image is an additional advantage of creating an asymmetric phase pattern. Moreover, the quality of the image from the two devices are 10 indistinguishable (compare Figs. S7 d,f), which again proves that effect of the pitch distribution on the hologram quality is insignificant.

Design of the pseudo-color, chiral binary hologram
The reflectance spectra of the six-layers were acquired using the same setup as that described in Section 2. As shown in fig. S8, three reflection bands appeared at approximate wavelength ranges of 450-470, 520-550, 620-660 nm. The sample was confirmed to reflect light at 455, 532, and 640 nm, which are the main emission wavelengths of the laser used to illuminate the sample.  is the reference wavelength (640 nm). Also, the optical phase was obtained by multiplying a factor of ±0.5 to the optical phase, since the relationship between the optical phase and helix phase reverses sign depending on the handedness of the helical structure [15]. Each layer was confirmed to operate as designed, as shown in Fig. 5b of the manuscript.