Abstract

In this report, we propose a large-area, scalable and reconfigurable single-shot optical fabrication method using phase-controlled interference lithography (PCIL) to realize submicrometer chiral woodpile photonic structures. This proposed technique involves a 3 + 3 double-cone geometry with beams originated from a computed phase mask displayed on a single spatial light modulator. Simulation studies show the filtering response of such structures for linearly polarized plane wave illumination, with structural features tunable through a single parameter of interference angle. Further, these single chiral woodpile structures show dual chirality on illumination with both right circularly and left circularly polarized light through simulation. Experimentally fabricated patterns on photoresist show resemblance to the desired chiral woodpile structures.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

With the advent of the field of nanophotonics, the 21st century has seen an exploration of different possibilities based on the light-matter interactions at the nanoscale and their applicability. Photonic crystals (PhCs) in particular, have the distinctive feature of controlling electromagnetic (EM) waves in three dimensions [1], where a periodic arrangement of high-indexed constituents restricts light propagation in different directions, thus opening up 3D-photonic band gaps. Among the different classes of photonic crystals proposed, 3D-woodpile structures [24] with periodic bars stacked orthogonally with respect to each layer result in strongest EM interactions, leading to fully potent photonic bandgaps [5]. Such structures on illumination with plane wave possess wide photonic bandgaps that can have possible applications as omnidirectional band-pass/rejection filters for telecommunication handling [4,6], imaging [7,8], high Q-microcavity based nanolasing [2], controlling of spontaneous emission [9] and so on. These 3D woodpile structures, however, start to possess an additional chiral nature when the alternate layers are stacked at non-orthogonal angles [10]. This opens up to a whole new property of polarization-dependent circular Bragg reflection [11,12] that produces differential transmission characteristics for left circularly polarized (LCP) and right circularly polarized (RCP) light i.e. circular dichroism. Chiral nanostructures such as nano-helices [1315] and gyroids [16,17] have mostly been appreciated for their applicability in achieving metamaterial characteristics of strong optical activity, circular dichroism, polarized antennas, etc. Similarly, ‘chiral-woodpile’ structures have shown promising circular dichroism [12], giant optical rotation [18], as well as circularly polarized thermal radiation emission [19] where the handedness has been attributed to the polarization-dependent frequency-gaps inherent in this layer-by-layer photonic crystal. Recent studies have shown that chiral woodpile structures fabricated out of semiconductors and possessing optical Weyl points [20] can act as planar waveguides for circularly polarized light at air-semiconductor interface leading to applications in spintronics and quantum information technology.

So far, such chiral woodpile structures have been fabricated mostly using different top-down techniques like e-beam lithography [21], direct laser writing [10], dip-in optical lithography [22] where precise structural features are obtained at the cost of limited small-area of fabrication. Recently reported micro-manipulation technique [23] has been adopted to create efficient 3D chiral photonic structures out of semiconductor [15] that still is limited by the final size of the patterned region. On contrary, interference lithography (IL) [24,25] promises a cheap, fast, large-area, and dynamic fabrication scheme through control over the polarization and phase of the individual interfering beams where desired interference pattern recorded on a photosensitive material can be transferred to suitable materials at later stages. By incorporating surface-plasmon resonance in such lithography techniques, nanofabrication beyond diffraction limit [26] has also been achieved. Although not reported for chiral woodpile, interference lithography has been applied towards the realization of woodpile [24] and diamond structures [25] through polarization manipulation of individual beams as well as phase manipulation [27]. To our knowledge, the closest resemblance towards chiral-woodpile through a simpler interference setup involves multiple-exposure for the fabrication of ‘woodpile-type’ photonic crystals [28] where a 1D phase mask with motorized translation and rotational stages are used to orient the interference pattern before each exposure. To avoid any motion-artefacts as well as complexities of tuning individual beams, a single-exposure, complexity-free interference method can be preferred towards the realization of these chiral woodpile structures. Hereby we propose a novel single-shot and easily reconfigurable interference technique using a spatial light modulator (SLM) to produce multiple phase-controlled beams that can be recorded in a 3 + 3 double-cone geometry. Unlike conventional umbrella geometry [27], this double-cone approach can effectively decrease the axial pitch in layered structures along with recording of multiple pitches within a certain photoresist thickness, and hence is feasible with applications in the visible and NIR wavelengths. Initial fabrication results of fewer layered patterns on photoresist confirms the experimental possibilities of the proposed method that can be further explored in the future with optimized design parameters and material transfer techniques.

2. Theory

Figure 1(a) represents the double-cone beam geometry for the interference of 3 + 3 coherent plane-wave beams. Pseudo-colors are given to each of the beams to identify the phase offsets introduced, with dots and crosses indicating their positions in the lower and upper cones respectively. Side by side, the projection of these beams on the X-Y plane is illustrated to provide an idea about the beam orientations with respect to the considered coordinate system. These beams are indexed by numbers m = 1,2,..,6 by taking into account of their corresponding phase offsets ${\psi _m} = ({2\pi /6} ){\ast }m$ which is actually required for the generation of the beams through a ‘phase-only’ SLM. Details of the beam generation technique are provided in the experimental section. Considering ${\vec{E}_m}$, ${\vec{k}_m}$, and ${\psi _m}$ as the electric field vector, propagation vector and phase offset of the mth beam taking part into the interference, the resultant chiral woodpile structure can be represented by the intensity distribution in Eq. (1)

 figure: Fig. 1.

Fig. 1. (a) Beam configuration in a 3 + 3 double-cone geometry for the realization of chiral woodpile structure using phase-controlled beams. XY projections of the beams show their orientation for defining the associated k vectors. (b, i) Actual chiral woodpile interference pattern produced in MATLAB. (ii) Chiral woodpile structure used for FDTD simulation.

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$$ \left.I(\vec{r})=\sum_{\mu=1}^{6}\left|\vec{E}_{\mu}\right|^{2}+\sum_{\mu=1}^{6} \sum_{\nu=1 \atop \mu \neq \nu}^{6} \vec{E}_{\mu} \cdot \vec{E}_{\nu}^{*} \exp \left[i (\vec{k}_{\mu}-\vec{k}_{\nu}\right) \cdot \vec{r}+i\left(\psi_{\mu}-\psi_{\nu}\right)\right]$$

where ${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over E} _m} = {E_m}\exp [i({\vec{k}_m} \cdot \vec{r}) + i{\psi _m}]$. The corresponding ${\vec{k}_m}$ vectors along with the associated ${\psi _m}$ are listed below in Eq. (2) with ${k_0}$= (2π/$\lambda $) and ${\; }\lambda $=405 nm as the operation wavelength used for the interference of these multiple beams. The choice of the wavelength is decided considering the availability of laser sources towards suitable polymerization of the photoresist material for experimental fabrication of these chiral woodpile photonic structures.

$$\left. \begin{array}{l} {\psi_1} = (2\pi /6)^\ast 1,\textrm{ }{{\vec{k}}_1} = {k_0}[\sin {\theta_{{\mathop{\rm int}} }}\cos (\frac{{4\pi }}{3}),\textrm{ }\sin {\theta_{{\mathop{\rm int}} }}\sin (\frac{{4\pi }}{3}), - \cos {\theta_{{\mathop{\rm int}} }}]\\ {\psi_2} = (2\pi /6)^\ast 2,\textrm{ }{{\vec{k}}_2} = {k_0}[\sin {\theta_{{\mathop{\rm int}} }}\cos (\frac{{4\pi }}{3}),\textrm{ }\sin {\theta_{{\mathop{\rm int}} }}\sin (\frac{{4\pi }}{3}),\textrm{ }\cos {\theta_{{\mathop{\rm int}} }}]\\ {\psi_3} = (2\pi /6)^\ast 3,\textrm{ }{{\vec{k}}_3} = {k_0}[\sin {\theta_{{\mathop{\rm int}} }}\cos (2\pi ),\textrm{ }\sin {\theta_{{\mathop{\rm int}} }}\sin (2\pi ), - \cos {\theta_{{\mathop{\rm int}} }}]\textrm{ }\\ {\psi_4} = (2\pi /6)^\ast 4\textrm{ }{{\vec{k}}_4} = {k_0}[\sin {\theta_{{\mathop{\rm int}} }}\cos (\frac{{2\pi }}{3}),\textrm{ }\sin {\theta_{{\mathop{\rm int}} }}\sin (\frac{{2\pi }}{3}),\textrm{ }\cos {\theta_{{\mathop{\rm int}} }}]\\ {\psi_5} = (2\pi /6)^\ast 5\textrm{ }{{\vec{k}}_5} = {k_0}[\sin {\theta_{{\mathop{\rm int}} }}\cos (\frac{{2\pi }}{3}),\textrm{ }\sin {\theta_{{\mathop{\rm int}} }}\sin (\frac{{2\pi }}{3}), - \cos {\theta_{{\mathop{\rm int}} }}]\\ {\psi_6} = (2\pi /6)^\ast 6,\textrm{ }{{\vec{k}}_6} = {k_0}[\sin {\theta_{{\mathop{\rm int}} }}\cos (2\pi ),\textrm{ }\sin {\theta_{{\mathop{\rm int}} }}\sin (2\pi ),\textrm{ }\cos {\theta_{{\mathop{\rm int}} }}] \end{array} \right\}$$
Since this corresponds to three-beam interference occurring from either (1,3,5) or (2,4,6) in each of the cones, the spatial periodicity of the resultant hexagonal structure is given by ${\Lambda _{sp}} = 2\lambda /({3{\; }\sin {\theta_{int}}} )$. ${\theta _{int}}$ is the interference angle made by each of these beams with respect to the normal to the recording plane and is just the single parameter needed to be tuned for obtaining different spatial features. The axial periodicity can be calculated by considering either of the three pairs of the beams (1,2), (3,6) or (5,4) where each of these pairs lie in the plane normal to the recording plane and hence is given by ${\Lambda _{ax}} = \lambda /({2{\; }\cos {\theta_{int}}} )$. Figure 1(b, i) shows the desired chiral woodpile interference pattern obtained via MATLAB [29] in terms of intensity distribution for ${\theta _{int}} = {40^\textrm{o}}$, $\lambda $ = 405 nm and the beam geometry as shown in Fig. 1(a). Y-X view shows the hexagonal lattice with spatial periodicity defined by the arms of the marked equilateral triangle. An equivalent CAD model showing an elliptic-cylindrical bar based chiral-woodpile structure is given in Fig. 1(b, ii) that is scripted in ‘Lumerical FDTD’, a commercial-grade 3D electromagnetic solver [30] for simulation purposes. We can define the periodicity of these bars in each layer by ‘a’ where a = ($\surd $3/2)*${\; }{\Lambda _{sp}}$ and the corresponding 3-layer pitch by ‘c’ where c = ${\Lambda _{ax}}$. Thus for a 50% duty cycle, the width (w) and thickness (t) of the cylindrical bars can be given by w=(a/2) and t=(c/3) as shown in Fig. 1(b, ii). We have obtained the simulated transmittance/reflectance characteristics of the proposed chiral structure by considering a unit cell with periodic boundary conditions in X, Y directions and perfectly matched layers in Z where periodicity along x = 2a and y = 2a/$\surd $3 are set in terms of the layer periodicity ‘a’. Plane-wave sources (Bloch/periodic-type) with unit amplitude and wavelength span of (400-2000) nm are used for obtaining filtering and circular dichroism in normal incidence whereas ‘Broadband Fixed Angle Source Technique’ (BFAST) type plane wave sources are considered for oblique incidence cases. 2D transmission and reflection monitor boxes kept normal to the substrate are set to linearly spaced frequency points corresponding to the wavelength span. For the dielectric properties of high-indexed materials like crystalline silicon (cSi) and gallium arsenide (GaAs), data from Palik [31] are used whereas for the photoresist, titanium dioxide (TiO2), and the glass substrate, the optical constants are adopted from [32]. The mesh size in the 3D FDTD region is set to auto-non uniform with a minimum mesh step of 0.25 nm. The equivalency of such a chiral woodpile structure using cylindrical bars in comparison to the MATLAB produced actual interference pattern has been cross-checked by exporting the pattern from MATLAB into Lumerical FDTD package as ‘stl’ file where both of these have shown identical transmission and reflection properties. However, in order to observe the effect of tuning the parameters like pitch and period, it is convenient to modify the ‘Lumerical’ scripted structure rather than importing from MATLAB while keeping the parameters exactly as expected from the interference formula.

3. Results and discussions

For studying the filtering response of these layered structures, we have operated our FDTD based simulations for structures with different periods, pitches and materials. Since both the spatial and axial periodicities are directly correlated by the interference angle (${\theta _{int}}$), we have directly characterized the filtering response as a function of this angle. It should be stated that all the results that have been described throughout this report are consistent with the actual nanometric feature sizes to be obtained by this PCIL method. Unlike the operational methods of ‘direct laser writing’ or ‘micro-manipulation technique’ where there is always flexibility in choosing the parameters ‘a’ and ‘c’, interference lithography techniques suffers through a constraint of limited combinations always resulting in ${\theta _{int}}$ dependent correlated parameters.

Nevertheless, the fascination of a large-area patterning in a cost-efficient and time-saving method has led us towards the exploration of possibilities within this constraint that have been discussed through our simulation results. Experimentally, one can directly achieve such structures on negative photoresist where control over exposure dosage and development can lead to optimization of the fill-factor in each of the layers; our current study involves a 50% duty cycle as shown in Fig. 2(a). Table 1 displays the parameters used in our simulations throughout our study of these chiral woodpile structures that can be realized for different interference angles with $\lambda = 405$ nm. One can observe from the table that with the increase of interference angles in this ‘3 + 3 double cone PCIL’ approach, the spatial periodicity decreases with a simultaneous increase of the axial periodicity. Thus, although one can reach up to a spatial periodicity of ${\Lambda _{sp,min}} = 2\lambda /({3{\; sin\; }{{90}^o}} )\, = \,270{\; nm}$, the resultant interference pattern instead of chiral woodpile becomes 2D hexagonal pattern by losing its axial periodicity. A study regarding the dependence of ${\Lambda _{sp}}$ and ${\Lambda _{ax}}$ on ${\theta _{int}}$ showed that the minimum omnidirectional periodicity (${\Lambda _{sp}}$=${\Lambda _{ax}}$) to be achieved while realizing the desired structure is ∼337 nm when ${\theta _{int}}$ is kept ∼${53^o}$. This leads to bar width (w) ∼146 nm in each layer considering the 50% duty cycle that can be considered as the minimum size/ resolution of the proposed technique for the given laser wavelength.

 figure: Fig. 2.

Fig. 2. FDTD based comparison of plane-wave filtering response of the chiral woodpile layered structures fabricated with different interference angles. (i)-(iii) shows the effects of increment in the number of pitches from 3 to 9 for structures with materials like (a)photoresist, (b) titanium dioxide and (c) crystalline silicon.

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Tables Icon

Table 1. Parameters of chiral woodpile structure used in FDTD simulation

The study of the filtering response in the transmission scheme that can lead to the generation of a stopband starts with a 3 pitch structure (Fig. 2(a, i)) where variation in ${\theta _{int}}$ from ${10^\textrm{o}}$ to ${80^\textrm{o}}$ in steps of 10 degrees has led to red-shifting of the band position. This can be directly related to the fact that with increased angle of interference, there is an increase in the axial pitch. This increased pitch in the direction of light propagation causes the internal Bragg reflection for linearly polarized light resulting in the formation of standing waves for higher wavelengths [33]. Since the structures are also chiral in nature, thus apart from normal Bragg reflection, they support the circular Bragg phenomenon that reflects almost all of the incident co-handed circular-polarization state with an insignificant reflection of the cross-handed state for frequencies lying in the polarization-gap [11,19]. This control over the circularly polarized light for a chiral-woodpile structure is of general interest and is discussed in detail at a later section of the paper while currently focusing on the filtering effects of these layered-structures for linearly polarized lights. The filtering efficiency increases, as the pitch number increases from 3 to 6 and 9 as plotted in Figs. 2(a, ii) and 2(a, iii) respectively. On increasing the index contrast for the same axial pitch, the resonance conditions are brought into more prominence that can result in increased depth as well as the bandwidth of the transmittance dips. Thus by choosing high indexed TiO2 as a dielectric material, one can obtain efficient filtering even for a lesser number of pitches like the case shown in Fig. 2(b, i) where 3 pitches can produce better dips when compared to 3 pitched photoresist structures. With further increase of pitches to 6 and 9, a stopband filtering efficiency about (80-90) % has been obtained and its corresponding color representations are shown in Figs. 2(b, ii) and 2(b, iii) respectively. With the choice of further high indexed crystalline Silicon (cSi), we can obtain broader filtering bands for pitches 3, 6 and 9 as shown in Figs. 2(c, i)–2(c, iii). However, cSi is highly absorptive at visible wavelengths; hence the minima obtained for the range 400 nm-700 nm irrespective of the different interference angles and the number of pitches cannot be related to the filtering effect caused by the formation of photonic bandgap which has been cross-checked by recording the absorbance spectra. Thus one can conclude that with an increased number of pitches, one can design a stop-band filter with sharp edges. The choice of the filtering regime can be totally controlled by controlling the interference angle.

Next, we have also studied the omnidirectional filtering properties of the structures apart from the normal incidence response. We have considered a 9 pitched TiO2 structure with spatial and axial periodicities corresponding to interference angle of ${50^\textrm{o}}$ (close to ${53^\textrm{o}}$) that has shown a band-stop filtering effect for the range (800-1000) nm i.e. in the near infra-red (NIR) region. We have considered our simulation domain such that one of the layers of the bar is parallel to the y-axis. To study the effect of indenting the source from different directions let’s start with the plane of incidence parallel to the x-axis (Φ =${0^\textrm{o}}$) that can be also be rotated azimuthally to make parallel to y-axis (Φ = ${90^\textrm{o}}$). Also while a plane of incidence is considered, in-plane and out of plane polarization plane can have a different effect on the transmittance spectra. For normal plane wave incidence with a linearly polarized light along the x-axis as shown in Fig. 3(a, i), the azimuthal rotation actually implies the rotation of the polarization vector towards the y-axis, which is evident from Figs. 3(b, i) and 3(c, i) where the bandwidth remains constant, but the effective transmittance dip gets affected by the polarization orientation. With the plane of incidence fixed, as the angle of incidence is varied up to ${45^\textrm{o}}$, the position of the band shifts from (800-1000) nm to (700-900) nm thus effectively having a constant filtering band for the range (800-900) nm. This is implied for both of the planes of incidence with Φ = ${0^\textrm{o}}$ and Φ = ${90^\textrm{o}}$ for the in-plane polarization (Figs. 3(b, ii) and 3(b, iii)). Such a change in the bandgap position due to the change of angle of incidence has previously been explored for the FCC woodpile structure [34]. The effect of out of plane polarization for both of these planes is compared in Figs. 3(c, ii) and 3(c, iii) in contrast to the in-plane cases. Thus one can find that for polarization parallel to the y-axis i.e. along the direction in which one of the layers of rods is parallel, lesser transmittance dip arise than the case where the polarization is perpendicular to the rods of that same layer.

 figure: Fig. 3.

Fig. 3. (a) Schematic of beam orientation for omnidirectional filtering properties of the chiral woodpile structure studied with both (b) in-plane and (c) out of plane polarization. Different cases of (i) rotation of the plane of incidence for fixed normal incidence and (ii)-(iii) rotation of angle of incidence for fixed planes of incidence can give an idea about the omnidirectionality of the stop-band.

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So far we have described the filtering effect of the chiral woodpile structure in response to the incidence of a linearly polarized plane wave almost like an FCC woodpile structure. Chiral structures with specific handedness have the inherent property to respond selectively with respect to the handedness of the incident circularly polarized light. Thus a periodic structure with right-handedness along the axial direction will produce filtering response to right circularly polarized (RCP) light whereas will act as a transparent medium with an effective index for the other handedness, i.e. for the left circularly polarized (LCP) light. Such chiral structures have been of severe importance in designing efficient circular polarizers as well as other metamaterial effects on inclusion of metals [12,14]. Chiral woodpile structures, in particular, possess the unique property of having both the handedness [15,22] within the structure depending on the number of layers accounted into the repeating unit cell. Consider a structure with an initial layer parallel to the y-axis and circularly polarized light traveling through the structure towards z-direction. For a 6-layered system, as shown in Fig. 4(a), the tip of the electric vector starting from + ve y-direction can rotate by ${60^\textrm{o}}$ anticlockwise for each adjacent layer before coming to its initial position (red bar) on the 7th thus following the RCP convention. Figure 4(b) shows the 3 layered cases of the structure with the same orientation of bars where the tip of the electric vector can rotate by ${120^\textrm{o}}$, clockwise for each adjacent layer before coming to its initial position on the 4th following the LCP convention. Such chiral woodpile structures have been considered for fabrication using direct laser writing or micromanipulation techniques on different materials like photoresist [22], GaAs [20] and others for optimized parameters like period ‘a’ in each layer, axial pitch ‘c’ and bar width ‘w’. We have explored the possibilities of having such dual chirality with the constrained structural features that can be achieved through PCIL upon material transfer. Both the transmittance and reflectance of the chiral woodpile structures with 9 pitches and associated materials have been studied in accordance with the variation of ${\theta _{int}}$ for bar widths ‘w’ of 50% duty cycle.

 figure: Fig. 4.

Fig. 4. Schematic showing dual chirality in the chiral-woodpile structure. An RCP unit cell (a) can be considered consisting of 6 layers (a) whereas an LCP unit cell (b) constructed from only 3 layers.

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Figures 5(a) and 5(b) show the comparative analysis between structures with TiO2 and GaAs respectively. Since the RCP unit is composed of 6 layers in contrast to that of the LCP unit with 3 layers, the circular Bragg reflection for the RCP light is at higher wavelengths as compared to that of the LCP light. For simulation purposes, these RCP and LCP beams are composed with two plane waves having polarization orthogonal to each other with a phase offset of (+π/2) and (-π/2) respectively. With an increase in ${\theta _{int}}$ and correspondingly increase in axial pitch ‘c’, the polarization-dependent stopband is found to be red-shifted for both the RCP and LCP excitation. As seen in Figs. 5(a, i)–5(a, iii) for the case of TiO2 structures, the RCP light is reflected from around 906 nm, 1118 nm and 1638 nm for ${\theta _{int}}$ of ${50^\textrm{o}}$, ${\; }{60^\textrm{o}}$ and ${70^\textrm{o}}$ respectively whereas the LCP lights are found to be reflected around 530 nm, 600 nm and 847 nm corresponding to similar values of ${\theta _{int}}$. Thus, such structures are suitable for device applications in both visible and NIR region of the electromagnetic spectrum depending on the ${\theta _{int}}$ used in fabrication. For structures with GaAs as shown in Fig. 5(b), the reflected peaks of RCP light comes around 1250 nm, 1494 nm and 2000 nm for the ${\theta _{int}}$ values mentioned whereas the LCP reflected peaks appear at 827 nm, 908 nm, and 1208 nm thus having possible applications in the NIR range only. However, the reflection passbands/ transmission stop bands with GaAs are found to be wider than the structures with TiO2 for similar dimensions due to its higher refractive index. Unlike TiO2, GaAs is absorptive over (400-700) nm that can limit its applicability as a transmissive device in the visible range.

 figure: Fig. 5.

Fig. 5. Transmittance and reflectance from chiral woodpile structure on the incidence of circularly polarized light. The effects are studied on structures made out of two different materials, (a) Titanium dioxide and (b) Gallium arsenide. Structures fabricable with different interference angles (i-iii) are also studied to realize the possibility of tuning the range of circular dichroism.

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It is noteworthy to remark that such chiral woodpile structures as explored in [19] show enhanced absorption and hence thermal emission for circularly polarized light of particular handedness corresponding to the polarization gap. For example, RCP light for the range (800-1000) nm gets totally reflected in Fig. 5(a, i) thus allowing the LCP light to be transmitted through the structure for absorption, depending on the imaginary part of the dielectric constant (Im(ɛ)) of the PhC. Even PhCs with Im(ɛ) = 0 can show sharp absorbance around this polarization gap when placed on metallic films [19] due to excitation of the surface plasmons enabled by the Bragg scattering of the specific polarization that is only allowed to be transmitted through the structure up to the metal surface. Thus such chiral woodpile structures can be compared to tunable plasmonic nanostructures of a similar order of periodicities as reported in [35] for enhanced absorption in suitable material of interest over the entire NIR region tunable through the choice of ${\theta _{int}}$. Moreover, such structures when transferred to a silicon substrate can effectively reduce its inherent high-reflectivity through trapping of light within such a layered structure for application in anti-reflectivity [36] as well as in photodetector and photovoltaic devices [37] for enhanced absorption through scattering induced increased optical path lengths.

4. Experimental section

Although double-cone geometry has been proposed recently [38] for obtaining a double-helix structure, the sole purpose of this report is to introduce the use of a single SLM unlike the reported one where the use of two different SLMs with different phase masks has only been conceptualized. Figure 6(a) shows the actual experimental setup used with the involvement of a single phase only reflective SLM. The phase-mask addressed to the SLM has been derived by considering the phase of the resultant electric field produced by the interference of six-beams in an umbrella geometry [15] where the propagation vectors and phase offsets are given by:

$${\vec{k}_{m^{\prime}}} = {k_{eff}}[\sin {\theta _{diff}}\cos (\frac{{2\pi m^{\prime}}}{6}),\textrm{ }\sin {\theta _{diff}}\sin (\frac{{2\pi m^{\prime}}}{6}),\textrm{ }\cos {\theta _{diff}}]\textrm;\textrm{ }\textrm{ }{\psi _{m^{\prime}}} = (\frac{{2\pi m^{\prime}}}{6})\textrm{ }$$

 figure: Fig. 6.

Fig. 6. (a) Experimental setup towards the realization of a chiral woodpile structure involving a dual-cone geometry. The beams diffracted in umbrella geometry from the SLM (provided with computed phase-mask) are represented with pseudo colors; each color represents a particular phase associated with the individual beams. (b) A magnified version of arrangement to convert six diffracted beams into 3 + 3 dual cone geometry using mount 1 and mount 2. (c) Actual experimental counterpart of (b) with the irradiated plane of interference. (d) Interference angle in terms of distance along the Z-axis in dual cone geometry considering beams 1 and 2. (e) Pattern recording process in positive photoresist showing the complementary structure after development. (f) fabricated positive photoresist sample with complementary chiral structure showing different diffracted colors in different observing directions.

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Here m′=1 to 6 and ${k_{eff}}$=${k_0}$·u, for u = 6.4 µm which is the pixel size of the SLM. The interference is considered with λ=405 nm, for a mesh-grid with dimensions X = 1 to 1920, Y = 1 to 1080 with Z = 0 to cope up with the ‘Full HD’ resolution of the LCOS SLM (LETO, Holoeye, Germany) used. The effective area of the SLM is around 0.8cm x 1.2 cm over which the phase-mask can be displayed. This decides the cross-sectional area of the SLM-diffracted beams taking part in interference given that the incident collimated beam covers the entire SLM pixelated region. Thus, the maximum area of nano-patterning possible through this SLM based PCIL is around 1 cm2. The diffraction angle from the SLM (${\theta _{diff}}$) is kept ${0.65^\textrm{o}}$ in the construction of the phase-mask for our particular case. For the experiment, a 405 nm blue laser (BlueMode laser, TOPTICA Photonics, Germany) is spatially filtered and collimated using a microscope objective (20X), pin-hole (15 µm) and lens as shown in Fig. 6(a) and is allowed to be incident on the SLM at near-normal incidence. The 6 first-order beams diffracted from the SLM (shown via pseudo colors) are allowed to pass through a mask (DC blocker) while the higher orders along with the central zeroth order (DC component) are blocked. These six beams with the required phase offsets are arranged into a double-cone using two mounts. Beams 1, 3, and 5 are reflected from the mount 1 having 3 mirrors aligned in the path of these beams with a specific angle (${\theta _{tilt}}$) to produce ${\theta _{int}}$ at the plane of recording. The beams 2, 4, and 6 are allowed to pass the mount 1 and reach mount 2 in order to get them reflected into the same recording plane. To adjust the angles as well as to match with the required propagation vectors, mount 2 has been customized with six mirrors that have the capability of rotation about two axes to reflect each of the beams 2, 4, and 6 twice, as shown in the dual-cone geometry schematic enlarged in Fig. 6(b).

The part of the actual experimental setup involving both the customized mirrors mounts are shown in Fig. 6(c), where mount 1 is 3D printed out of PLA material with predesigned tilt angles to fit in three mirrors. Mount 2 is forged out of aluminum with the capability of producing customizable tilts along two axes. The recording plane is shown as the plane of interference where a photoresist coated sample can be placed to have the interference of 3 + 3 beams as per the prescribed double-cone. For a precise implementation of the desired incidence angle, Fig. 6(d) can be followed to tune the position of the mounts and the recording plane along the z-axis. Considering, z = 0 for z0, i.e. the position of the SLM, the mounts 1 and 2 can be positioned at a distance z1 and z3 respectively with the recording plane at z2. The radii of the mounts 1 and 2 are r1and r2 respectively, with

$$\left. \begin{array}{l} r1 = r2^{\ast} [{(\tan {\theta_{{\mathop{\rm int}} }} - \tan {\theta_{diff}})/(\tan {\theta_{{\mathop{\rm int}} }} + \tan {\theta_{diff}})} ]\\ z1 = [{r1/\tan {\theta_{diff}}} ]\\ z3 = [{r2/\tan {\theta_{diff}}} ]\\ z2 = z1 + [{r1/\tan {\theta_{{\mathop{\rm int}} }}} ]\end{array} \right\}\textrm{ }$$
In our case, r2 is fixed; r1, z1, z2, and z3 are calculated considering ${\theta _{diff}}$=${0.65^\textrm{o}}$ and ${\theta _{int}}$=${40^\textrm{o}}$ and accordingly, mount 1 is 3D-printed along with tilt angle given by ${\theta _{tilt}}$=0.5(${\theta _{int}}$-${\theta _{diff}}$). It should be noted that the beams 2, 4, and 6 suffer one extra reflection as compared to the beams 1, 3, and 5 which leads to an additional phase of π. However, this has been cross-checked with MATLAB simulation where the introduction of an additional π phase equally in these beams keeps the resultant intensity pattern intact in obtaining the chiral woodpile structure. An electronic shutter (Thorlabs) has been used to control the exposure dosage on the photoresist coated substrate. For the choice of photoresist, we have used AZ 1505 photoresist (Microchem) spin-coated at 4000 rpm using spin coater (Spin NXG, Apexequipments) to provide a rough thickness of around 0.5 µm. Figure 6(e) describes the common fabrication process of interference lithography where a positive photoresist coated substrate is exposed with the irradiance profile of the complex resultant wavefield of 3 + 3 phase-controlled beams. For such positive resist, a complementary form of the resultant intensity distribution is left on the substrate after the exposed region gets washed away during the development. This complementary structure can be hardened and used as a template to produce high-indexed chiral-woodpile photonic crystals through material infiltration at later stages. Figure 6(f) shows such positive photoresist template just after development (left) and later adhered to SEM-mount (right) for inspection, both producing strong diffracted colors at different angles.

The resultant patterns as shown via SEM images in Figs. 7(a) and 7(b) are the preliminary results as obtained from two different samples exposed for 10s and 15s along with a development time of 30 s using AZ 726 developer. For comparison and a better understanding of the resultant photoresist complementary structures that also show chiral nature, we have provided simulation images in the inset with a similar arrangement of rods for both of the Figs. 7(a) and 7(b). As seen, the top surface of both patterns has different orientations indicating the observation of two different layers of a single geometry. Since the 2D view of the pattern may somewhat be confusing, separate bars with pseudo colors have been provided along with the simulated plot to have a proper notion of different layers. Also the spatial periodicity ‘${\Lambda _{sp}}$’ and the periodicity in each layer ‘a’ of these structures produced with interference at ${40^\textrm{o}}$ is around 432 nm and 382 nm respectively as shown in Fig. 7(b) that matches well with the corresponding theoretical values of 420 nm and 364 nm. Figures 7(c) and 7(d) provide a top view and three-dimensional view over a large area which has only been efficiently possible through the use of interference lithography through convenient phase controlling of individual interfering beams. However, as one may observe, the contrast of the resultant pattern is somewhat low due to the finally available power from the laser source after successive spatial filtering, collimation, and SLM diffraction. Also, unlike other structures obtained through similar SLM based PCIL, there is no use of the relatively higher zeroth-order central beam that has resulted in obtaining low contrast structures. Thus, with the use of sufficiently higher laser power, one can achieve significantly improved patterns over a large area as compared to the ones obtained with direct laser writing.

 figure: Fig. 7.

Fig. 7. (a) A 2D SEM image of the fabricated complementary chiral woodpile on the positive photoresist AZ 1505. Inset shows a simulated structure identical to the fabricated sample in terms of the orientation of the rods with the top layer (blue) rotated at ${30^\textrm{o}}$ with respect to X-axis. (b) Similar structure with different photoresist thickness revealing the second layer(green) as top layer rotated at ${150^\textrm{o}}$ with respect to X-axis. Measured values disclose 2a = 763 nm and 3Λsp = 1295 nm. (c) & (d) 2D and 3D view of the samples over a large area showing the capability of PCIL.

Download Full Size | PPT Slide | PDF

 figure: Fig. 8.

Fig. 8. (a) Experimental setup to study filtering response of the fabricated structure using a broad white light source. (b)-(i)Transmittance of the fabricated complementary structure realized in positive photoresist (PPR). (ii) Simulated transmittance of a negative photoresist (NPR) structure (black curve) and its complementary structure out of positive photoresist (PPR) with 3 pitches. Inset in (b-ii) shows the two structures in NPR and PPR showing complementarity.

Download Full Size | PPT Slide | PDF

For the optical characterization of the fabricated photoresist complementary structure, a transmission geometry is experimentally arranged as shown in Fig. 8(a). An unpolarized white light source (Avalight-DH-S-BAL) is spatially filtered using a microscope objective (20X) and a pin-hole (0.1 mm) and collimated using a collimating lens (f = 50 mm) to produce a uniform plane-wave. Since the patterned regions are generally of dimensions 5 mm x 5 mm, an aperture is used to generate a characterizing light beam of 4 mm diameter to investigate within the region of interest. A linear polarizer is used to incident polarized light onto the fabricated structure that is placed normally with respect to the beam propagation direction using a sample-holder. The transmitted light through the sample is converged by a high NA lens and transferred to a spectrometer (AvaSpec-ULS3648TEC) through a multimode optical fiber cable. The recorded transmittance spectrum is displayed in Fig. 8(b, i), with a color plot showing maxima and minima in terms of dark and light tones just like the cases in Fig. 2. A similar substrate with a fine coating of positive photoresist was taken as a reference to record such transmittance data. The dips present in this transmittance data are due to the filtering response of this fabricated structure which is further analyzed with our simulation model in Fig. 8(b, ii). Initially in Fig. 2, we have shown simulated transmittance studies for low-indexed negative photoresist structures considering several pitches (3, 6 and 9). Here to cope-up with the fact of fewer pitches realized experimentally, we perform a transmittance test considering 3 pitches only for both the direct and the complementary structure to consider the effect of negative and positive photoresist (NPR and PPR) respectively. Whereas a prominent dip is expected for NPR (black curve), the PPR (red curve) exhibits similar transmittance dips (486 nm & 534 nm) in simulation as obtained experimentally (491 nm & 546 nm). An additional dip (611 nm) that is observed in the experimental transmittance data is not detected in the corresponding simulation results. The mismatch between the simulated and experimentally obtained spectra can be accounted for the difference in periodicities between the theoretical and experimentally obtained values as well as the deviation of the output structure contrast and layer numbers in comparison to the perfect case of simulations. A color plot for this simulated PPR case is also provided in Fig. 8(b, ii) whereas the same for the NPR case is already provided in Fig. 2(a, i). However, for better response, one either needs an increased number of PR layers or a higher index-contrast through material infiltration onto the positive resist template. Evaluation of circular dichroism property on such high-indexed or higher layered structures is appropriate which is currently beyond the scope of the experimental circumstances due to lack of multiple polarizing components and suitable material transfer processes.

5. Conclusion

Thus, in summary, we have shown the use of SLM based phase controlling in a novel 3 + 3 double-cone geometry for a convenient approach of fabricating chiral woodpile structures realized through the interference of multiple beams. The resultant structure with parameters based on calculations from this interference lithography technique has been exploited in full depth through FDTD based transmittance/ reflectance characterization along with its distinctive dual chirality. Hence, our proposed single-shot, scalable and reconfigurable approach of large-area pattern fabrication can have potential applications towards all-optical integrated photonic circuits acting as omnidirectional filters as well as circular polarizers upon suitable materialization. We do look in near-future for the association of high-indexed material, a proper experimental evaluation of the chiral polarizing properties and inclusion of a fill-factor dependent efficiency in our further studies of such PCIL fabricated chiral-woodpile structures. Moreover, the possibility of achieving sub-micron featured chiral structures paves the way toward exploring metamaterial aspects on the inclusion of metals in such future studies.

Funding

Department of Science and Technology, Ministry of Science and Technology Govt. of India (DST-INSPIRE fellowship); University Grants Commission Govt. of India (UGC fellowship).

Acknowledgment

We thank Central Research Facility (CRF), IIT Delhi, India for providing SEM facility.

Disclosures

The authors declare that there are no conflicts of interest related to this article.

References

1. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: Molding the flow of light - second edition (Princeton University, 2011).

2. A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5(2), 91–94 (2011). [CrossRef]  

3. K. Ishizaki, M. Koumura, K. Suzuki, K. Gondaira, and S. Noda, “Realization of three-dimensional guiding of photons in photonic crystals,” Nat. Photonics 7(2), 133–137 (2013). [CrossRef]  

4. M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3(7), 444–447 (2004). [CrossRef]  

5. L. A. Ibbotson, A. Demetriadou, S. Croxall, O. Hess, and J. J. Baumberg, “Optical nano-woodpiles: large-area metallic photonic crystals and metamaterials,” Sci. Rep. 5(1), 8313 (2015). [CrossRef]  

6. S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289(5479), 604–606 (2000). [CrossRef]  

7. H.-J. Choi, S. Choi, Y.-E. Yoo, E.-c. Jeon, Y. Yi, S. Park, D.-S. Choi, and H. Kim, “Transmission-type photonic crystal structures for color filters,” Opt. Express 21(15), 18317–18324 (2013). [CrossRef]  

8. L. Maigyte, V. Purlys, J. Trull, M. Peckus, C. Cojocaru, D. Gailevičius, M. Malinauskas, and K. Staliunas, “Flat lensing in the visible frequency range by woodpile photonic crystals,” Opt. Lett. 38(14), 2376–2378 (2013). [CrossRef]  

9. M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Simultaneous inhibition and redistribution of spontaneous light emission in photonic crystals,” Science 308(5726), 1296–1298 (2005). [CrossRef]  

10. M. Thiel, G. Von Freymann, and M. Wegener, “Layer-by-layer three-dimensional chiral photonic crystals,” Opt. Lett. 32(17), 2547–2549 (2007). [CrossRef]  

11. M. Faryad and A. Lakhtakia, “The circular Bragg phenomenon,” Adv. Opt. Photonics 6(2), 225–292 (2014). [CrossRef]  

12. S. Takahashi, T. Tajiri, Y. Ota, J. Tatebayashi, S. Iwamoto, and Y. Arakawa, “Circular dichroism in a three-dimensional semiconductor chiral photonic crystal,” Appl. Phys. Lett. 105(5), 051107 (2014). [CrossRef]  

13. J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009). [CrossRef]  

14. L. V. Poulikakos, P. Thureja, A. Stollmann, E. De Leo, and D. J. Norris, “Chiral light design and detection inspired by optical antenna theory,” Nano Lett. 18(8), 4633–4640 (2018). [CrossRef]  

15. S. Behera, S. Sarkar, and J. Joseph, “Fabrication of helical photonic structures with submicrometer axial and spatial periodicities following “inverted umbrella” geometry through phase-controlled interference lithography,” Opt. Lett. 43(1), 106–109 (2018). [CrossRef]  

16. J. A. Dolan, B. D. Wilts, S. Vijgnolini, J. J. Baumberg, U. Steiner, and T. D. Wilkinson, “Optical properties of gyroid structured materials: From photonic crystals to metamaterials,” Adv. Opt. Mater. 3(1), 12–32 (2015). [CrossRef]  

17. Z. Gan, M. D. Turner, and M. Gu, “Biomimetic gyroid nanostructures exceeding their natural origins,” Sci. Adv. 2(5), e1600084 (2016). [CrossRef]  

18. S. Takahashi, A. Tandaechanurat, R. Igusa, Y. Ota, J. Tatebayashi, S. Iwamoto, and Y. Arakawa, “Giant optical rotation in a three-dimensional semiconductor chiral photonic crystal,” Opt. Express 21(24), 29905–29913 (2013). [CrossRef]  

19. J. C. W. Lee and C. Chan, “Circularly polarized thermal radiation from layer-by-layer photonic crystal structures,” Appl. Phys. Lett. 90(5), 051912 (2007). [CrossRef]  

20. S. Takahashi, S. Oono, S. Iwamoto, Y. Hatsugai, and Y. Arakawa, “Circularly polarized topological edge states derived from optical Weyl points in semiconductor-based chiral woodpile photonic crystals,” J. Phys. Soc. Jpn. 87(12), 123401 (2018). [CrossRef]  

21. G. Subramania and S. Lin, “Fabrication of three-dimensional photonic crystal with alignment based on electron beam lithography,” Appl. Phys. Lett. 85(21), 5037–5039 (2004). [CrossRef]  

22. M. Thiel, J. Ott, A. Radke, J. Kaschke, and M. Wegener, “Dip-in depletion optical lithography of three-dimensional chiral polarizers,” Opt. Lett. 38(20), 4252–4255 (2013). [CrossRef]  

23. K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, K. Sakoda, N. Shinya, and Y. Aoyagi, “Microassembly of semiconductor three-dimensional photonic crystals,” Nat. Mater. 2(2), 117–121 (2003). [CrossRef]  

24. Y. K. Pang, J. C. W. Lee, C. T. Ho, and W. Y. Tam, “Realization of woodpile structure using optical interference holography,” Opt. Express 14(20), 9013 (2006). [CrossRef]  

25. W. Y. Tam, “Woodpile and diamond structures by optical interference holography,” J. Opt. A: Pure Appl. Opt. 9(11), 1076–1081 (2007). [CrossRef]  

26. X. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84(23), 4780–4782 (2004). [CrossRef]  

27. S. Behera and J. Joseph, “Design and fabrication of woodpile photonic structures through phase SLM-based interference lithography for omnidirectional optical filters,” Opt. Lett. 42(13), 2607–2610 (2017). [CrossRef]  

28. Y. Lin, D. Rivera, and K. Chen, “Woodpile-type photonic crystals with orthorhombic or tetragonal symmetry formed through phase mask techniques,” Opt. Express 14(2), 887–892 (2006). [CrossRef]  

29. MATLAB and Statistics Toolbox Release 2012b, The MathWorks, Inc., Natick, Massachusetts, United States.

30. “Lumerical inc. https://www.Lumerical.Com/products/.”

31. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985).

32. S. Sarkar, V. Gupta, M. Kumar, J. Schubert, P. T. Probst, J. Joseph, and T. A. König, “Hybridized Guided-Mode Resonances via Colloidal Plasmonic Self-Assembled Grating,” ACS Appl. Mater. Interfaces 11(14), 13752–13760 (2019). [CrossRef]  

33. M. Thiel, M. Decker, M. Deubel, M. Wegener, S. Linden, and G. von Freymann, “Polarization Stop Bands in Chiral Polymeric Three-Dimensional Photonic Crystals,” Adv. Mater. 19(2), 207–210 (2007). [CrossRef]  

34. L.-J. Chen, X.-Z. Dong, Y.-Y. Zhao, Y.-L. Zhang, J. Liu, M.-L. Zheng, X.-M. Duan, and Z.-S. Zhao, “Fabrication and optical transmission characteristics of polymers woodpile photonic crystal structures with different crystal planes,” AOPC 2015: Advances in Laser Technology and Applications, 967127 (2015).

35. Y. Chen, X. Li, X. Luo, S. A. Maier, and M. Hong, “Tunable near-infrared plasmonic perfect absorber based on phase-change materials,” Photonics Res. 3(3), 54–57 (2015). [CrossRef]  

36. J. Yang, F. Luo, T. S. Kao, X. Li, G. W. Ho, J. Teng, X. Luo, and M. Hong, “Design and fabrication of broadband ultralow reflectivity black Si surfaces by laser micro/nanoprocessing,” Light: Sci. Appl. 3(7), e185 (2014). [CrossRef]  

37. T. Yatsui, “Recent improvement of silicon absorption in opto-electric devices,” Opto-Electronic Advances 2(10), 19002301–19002308 (2019). [CrossRef]  

38. K. Samanta and J. Joseph, “Double-helix array structure using phase controlled interference of 6 + 6 beams,” Opt. Laser Eng. 113, 23–28 (2019). [CrossRef]  

References

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  • |
  • |

  1. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: Molding the flow of light - second edition (Princeton University, 2011).
  2. A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5(2), 91–94 (2011).
    [Crossref]
  3. K. Ishizaki, M. Koumura, K. Suzuki, K. Gondaira, and S. Noda, “Realization of three-dimensional guiding of photons in photonic crystals,” Nat. Photonics 7(2), 133–137 (2013).
    [Crossref]
  4. M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3(7), 444–447 (2004).
    [Crossref]
  5. L. A. Ibbotson, A. Demetriadou, S. Croxall, O. Hess, and J. J. Baumberg, “Optical nano-woodpiles: large-area metallic photonic crystals and metamaterials,” Sci. Rep. 5(1), 8313 (2015).
    [Crossref]
  6. S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289(5479), 604–606 (2000).
    [Crossref]
  7. H.-J. Choi, S. Choi, Y.-E. Yoo, E.-c. Jeon, Y. Yi, S. Park, D.-S. Choi, and H. Kim, “Transmission-type photonic crystal structures for color filters,” Opt. Express 21(15), 18317–18324 (2013).
    [Crossref]
  8. L. Maigyte, V. Purlys, J. Trull, M. Peckus, C. Cojocaru, D. Gailevičius, M. Malinauskas, and K. Staliunas, “Flat lensing in the visible frequency range by woodpile photonic crystals,” Opt. Lett. 38(14), 2376–2378 (2013).
    [Crossref]
  9. M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Simultaneous inhibition and redistribution of spontaneous light emission in photonic crystals,” Science 308(5726), 1296–1298 (2005).
    [Crossref]
  10. M. Thiel, G. Von Freymann, and M. Wegener, “Layer-by-layer three-dimensional chiral photonic crystals,” Opt. Lett. 32(17), 2547–2549 (2007).
    [Crossref]
  11. M. Faryad and A. Lakhtakia, “The circular Bragg phenomenon,” Adv. Opt. Photonics 6(2), 225–292 (2014).
    [Crossref]
  12. S. Takahashi, T. Tajiri, Y. Ota, J. Tatebayashi, S. Iwamoto, and Y. Arakawa, “Circular dichroism in a three-dimensional semiconductor chiral photonic crystal,” Appl. Phys. Lett. 105(5), 051107 (2014).
    [Crossref]
  13. J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
    [Crossref]
  14. L. V. Poulikakos, P. Thureja, A. Stollmann, E. De Leo, and D. J. Norris, “Chiral light design and detection inspired by optical antenna theory,” Nano Lett. 18(8), 4633–4640 (2018).
    [Crossref]
  15. S. Behera, S. Sarkar, and J. Joseph, “Fabrication of helical photonic structures with submicrometer axial and spatial periodicities following “inverted umbrella” geometry through phase-controlled interference lithography,” Opt. Lett. 43(1), 106–109 (2018).
    [Crossref]
  16. J. A. Dolan, B. D. Wilts, S. Vijgnolini, J. J. Baumberg, U. Steiner, and T. D. Wilkinson, “Optical properties of gyroid structured materials: From photonic crystals to metamaterials,” Adv. Opt. Mater. 3(1), 12–32 (2015).
    [Crossref]
  17. Z. Gan, M. D. Turner, and M. Gu, “Biomimetic gyroid nanostructures exceeding their natural origins,” Sci. Adv. 2(5), e1600084 (2016).
    [Crossref]
  18. S. Takahashi, A. Tandaechanurat, R. Igusa, Y. Ota, J. Tatebayashi, S. Iwamoto, and Y. Arakawa, “Giant optical rotation in a three-dimensional semiconductor chiral photonic crystal,” Opt. Express 21(24), 29905–29913 (2013).
    [Crossref]
  19. J. C. W. Lee and C. Chan, “Circularly polarized thermal radiation from layer-by-layer photonic crystal structures,” Appl. Phys. Lett. 90(5), 051912 (2007).
    [Crossref]
  20. S. Takahashi, S. Oono, S. Iwamoto, Y. Hatsugai, and Y. Arakawa, “Circularly polarized topological edge states derived from optical Weyl points in semiconductor-based chiral woodpile photonic crystals,” J. Phys. Soc. Jpn. 87(12), 123401 (2018).
    [Crossref]
  21. G. Subramania and S. Lin, “Fabrication of three-dimensional photonic crystal with alignment based on electron beam lithography,” Appl. Phys. Lett. 85(21), 5037–5039 (2004).
    [Crossref]
  22. M. Thiel, J. Ott, A. Radke, J. Kaschke, and M. Wegener, “Dip-in depletion optical lithography of three-dimensional chiral polarizers,” Opt. Lett. 38(20), 4252–4255 (2013).
    [Crossref]
  23. K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, K. Sakoda, N. Shinya, and Y. Aoyagi, “Microassembly of semiconductor three-dimensional photonic crystals,” Nat. Mater. 2(2), 117–121 (2003).
    [Crossref]
  24. Y. K. Pang, J. C. W. Lee, C. T. Ho, and W. Y. Tam, “Realization of woodpile structure using optical interference holography,” Opt. Express 14(20), 9013 (2006).
    [Crossref]
  25. W. Y. Tam, “Woodpile and diamond structures by optical interference holography,” J. Opt. A: Pure Appl. Opt. 9(11), 1076–1081 (2007).
    [Crossref]
  26. X. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84(23), 4780–4782 (2004).
    [Crossref]
  27. S. Behera and J. Joseph, “Design and fabrication of woodpile photonic structures through phase SLM-based interference lithography for omnidirectional optical filters,” Opt. Lett. 42(13), 2607–2610 (2017).
    [Crossref]
  28. Y. Lin, D. Rivera, and K. Chen, “Woodpile-type photonic crystals with orthorhombic or tetragonal symmetry formed through phase mask techniques,” Opt. Express 14(2), 887–892 (2006).
    [Crossref]
  29. MATLAB and Statistics Toolbox Release 2012b, The MathWorks, Inc., Natick, Massachusetts, United States.
  30. “Lumerical inc. https://www.Lumerical.Com/products/.”
  31. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985).
  32. S. Sarkar, V. Gupta, M. Kumar, J. Schubert, P. T. Probst, J. Joseph, and T. A. König, “Hybridized Guided-Mode Resonances via Colloidal Plasmonic Self-Assembled Grating,” ACS Appl. Mater. Interfaces 11(14), 13752–13760 (2019).
    [Crossref]
  33. M. Thiel, M. Decker, M. Deubel, M. Wegener, S. Linden, and G. von Freymann, “Polarization Stop Bands in Chiral Polymeric Three-Dimensional Photonic Crystals,” Adv. Mater. 19(2), 207–210 (2007).
    [Crossref]
  34. L.-J. Chen, X.-Z. Dong, Y.-Y. Zhao, Y.-L. Zhang, J. Liu, M.-L. Zheng, X.-M. Duan, and Z.-S. Zhao, “Fabrication and optical transmission characteristics of polymers woodpile photonic crystal structures with different crystal planes,” AOPC 2015: Advances in Laser Technology and Applications, 967127 (2015).
  35. Y. Chen, X. Li, X. Luo, S. A. Maier, and M. Hong, “Tunable near-infrared plasmonic perfect absorber based on phase-change materials,” Photonics Res. 3(3), 54–57 (2015).
    [Crossref]
  36. J. Yang, F. Luo, T. S. Kao, X. Li, G. W. Ho, J. Teng, X. Luo, and M. Hong, “Design and fabrication of broadband ultralow reflectivity black Si surfaces by laser micro/nanoprocessing,” Light: Sci. Appl. 3(7), e185 (2014).
    [Crossref]
  37. T. Yatsui, “Recent improvement of silicon absorption in opto-electric devices,” Opto-Electronic Advances 2(10), 19002301–19002308 (2019).
    [Crossref]
  38. K. Samanta and J. Joseph, “Double-helix array structure using phase controlled interference of 6 + 6 beams,” Opt. Laser Eng. 113, 23–28 (2019).
    [Crossref]

2019 (3)

S. Sarkar, V. Gupta, M. Kumar, J. Schubert, P. T. Probst, J. Joseph, and T. A. König, “Hybridized Guided-Mode Resonances via Colloidal Plasmonic Self-Assembled Grating,” ACS Appl. Mater. Interfaces 11(14), 13752–13760 (2019).
[Crossref]

T. Yatsui, “Recent improvement of silicon absorption in opto-electric devices,” Opto-Electronic Advances 2(10), 19002301–19002308 (2019).
[Crossref]

K. Samanta and J. Joseph, “Double-helix array structure using phase controlled interference of 6 + 6 beams,” Opt. Laser Eng. 113, 23–28 (2019).
[Crossref]

2018 (3)

L. V. Poulikakos, P. Thureja, A. Stollmann, E. De Leo, and D. J. Norris, “Chiral light design and detection inspired by optical antenna theory,” Nano Lett. 18(8), 4633–4640 (2018).
[Crossref]

S. Behera, S. Sarkar, and J. Joseph, “Fabrication of helical photonic structures with submicrometer axial and spatial periodicities following “inverted umbrella” geometry through phase-controlled interference lithography,” Opt. Lett. 43(1), 106–109 (2018).
[Crossref]

S. Takahashi, S. Oono, S. Iwamoto, Y. Hatsugai, and Y. Arakawa, “Circularly polarized topological edge states derived from optical Weyl points in semiconductor-based chiral woodpile photonic crystals,” J. Phys. Soc. Jpn. 87(12), 123401 (2018).
[Crossref]

2017 (1)

2016 (1)

Z. Gan, M. D. Turner, and M. Gu, “Biomimetic gyroid nanostructures exceeding their natural origins,” Sci. Adv. 2(5), e1600084 (2016).
[Crossref]

2015 (3)

J. A. Dolan, B. D. Wilts, S. Vijgnolini, J. J. Baumberg, U. Steiner, and T. D. Wilkinson, “Optical properties of gyroid structured materials: From photonic crystals to metamaterials,” Adv. Opt. Mater. 3(1), 12–32 (2015).
[Crossref]

L. A. Ibbotson, A. Demetriadou, S. Croxall, O. Hess, and J. J. Baumberg, “Optical nano-woodpiles: large-area metallic photonic crystals and metamaterials,” Sci. Rep. 5(1), 8313 (2015).
[Crossref]

Y. Chen, X. Li, X. Luo, S. A. Maier, and M. Hong, “Tunable near-infrared plasmonic perfect absorber based on phase-change materials,” Photonics Res. 3(3), 54–57 (2015).
[Crossref]

2014 (3)

J. Yang, F. Luo, T. S. Kao, X. Li, G. W. Ho, J. Teng, X. Luo, and M. Hong, “Design and fabrication of broadband ultralow reflectivity black Si surfaces by laser micro/nanoprocessing,” Light: Sci. Appl. 3(7), e185 (2014).
[Crossref]

M. Faryad and A. Lakhtakia, “The circular Bragg phenomenon,” Adv. Opt. Photonics 6(2), 225–292 (2014).
[Crossref]

S. Takahashi, T. Tajiri, Y. Ota, J. Tatebayashi, S. Iwamoto, and Y. Arakawa, “Circular dichroism in a three-dimensional semiconductor chiral photonic crystal,” Appl. Phys. Lett. 105(5), 051107 (2014).
[Crossref]

2013 (5)

2011 (1)

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5(2), 91–94 (2011).
[Crossref]

2009 (1)

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref]

2007 (4)

J. C. W. Lee and C. Chan, “Circularly polarized thermal radiation from layer-by-layer photonic crystal structures,” Appl. Phys. Lett. 90(5), 051912 (2007).
[Crossref]

M. Thiel, G. Von Freymann, and M. Wegener, “Layer-by-layer three-dimensional chiral photonic crystals,” Opt. Lett. 32(17), 2547–2549 (2007).
[Crossref]

W. Y. Tam, “Woodpile and diamond structures by optical interference holography,” J. Opt. A: Pure Appl. Opt. 9(11), 1076–1081 (2007).
[Crossref]

M. Thiel, M. Decker, M. Deubel, M. Wegener, S. Linden, and G. von Freymann, “Polarization Stop Bands in Chiral Polymeric Three-Dimensional Photonic Crystals,” Adv. Mater. 19(2), 207–210 (2007).
[Crossref]

2006 (2)

Y. Lin, D. Rivera, and K. Chen, “Woodpile-type photonic crystals with orthorhombic or tetragonal symmetry formed through phase mask techniques,” Opt. Express 14(2), 887–892 (2006).
[Crossref]

Y. K. Pang, J. C. W. Lee, C. T. Ho, and W. Y. Tam, “Realization of woodpile structure using optical interference holography,” Opt. Express 14(20), 9013 (2006).
[Crossref]

2005 (1)

M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Simultaneous inhibition and redistribution of spontaneous light emission in photonic crystals,” Science 308(5726), 1296–1298 (2005).
[Crossref]

2004 (3)

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3(7), 444–447 (2004).
[Crossref]

G. Subramania and S. Lin, “Fabrication of three-dimensional photonic crystal with alignment based on electron beam lithography,” Appl. Phys. Lett. 85(21), 5037–5039 (2004).
[Crossref]

X. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84(23), 4780–4782 (2004).
[Crossref]

2003 (1)

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, K. Sakoda, N. Shinya, and Y. Aoyagi, “Microassembly of semiconductor three-dimensional photonic crystals,” Nat. Mater. 2(2), 117–121 (2003).
[Crossref]

2000 (1)

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289(5479), 604–606 (2000).
[Crossref]

Aoki, K.

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, K. Sakoda, N. Shinya, and Y. Aoyagi, “Microassembly of semiconductor three-dimensional photonic crystals,” Nat. Mater. 2(2), 117–121 (2003).
[Crossref]

Aoyagi, Y.

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, K. Sakoda, N. Shinya, and Y. Aoyagi, “Microassembly of semiconductor three-dimensional photonic crystals,” Nat. Mater. 2(2), 117–121 (2003).
[Crossref]

Arakawa, Y.

S. Takahashi, S. Oono, S. Iwamoto, Y. Hatsugai, and Y. Arakawa, “Circularly polarized topological edge states derived from optical Weyl points in semiconductor-based chiral woodpile photonic crystals,” J. Phys. Soc. Jpn. 87(12), 123401 (2018).
[Crossref]

S. Takahashi, T. Tajiri, Y. Ota, J. Tatebayashi, S. Iwamoto, and Y. Arakawa, “Circular dichroism in a three-dimensional semiconductor chiral photonic crystal,” Appl. Phys. Lett. 105(5), 051107 (2014).
[Crossref]

S. Takahashi, A. Tandaechanurat, R. Igusa, Y. Ota, J. Tatebayashi, S. Iwamoto, and Y. Arakawa, “Giant optical rotation in a three-dimensional semiconductor chiral photonic crystal,” Opt. Express 21(24), 29905–29913 (2013).
[Crossref]

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5(2), 91–94 (2011).
[Crossref]

Asano, T.

M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Simultaneous inhibition and redistribution of spontaneous light emission in photonic crystals,” Science 308(5726), 1296–1298 (2005).
[Crossref]

Baba, T.

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, K. Sakoda, N. Shinya, and Y. Aoyagi, “Microassembly of semiconductor three-dimensional photonic crystals,” Nat. Mater. 2(2), 117–121 (2003).
[Crossref]

Bade, K.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref]

Baumberg, J. J.

L. A. Ibbotson, A. Demetriadou, S. Croxall, O. Hess, and J. J. Baumberg, “Optical nano-woodpiles: large-area metallic photonic crystals and metamaterials,” Sci. Rep. 5(1), 8313 (2015).
[Crossref]

J. A. Dolan, B. D. Wilts, S. Vijgnolini, J. J. Baumberg, U. Steiner, and T. D. Wilkinson, “Optical properties of gyroid structured materials: From photonic crystals to metamaterials,” Adv. Opt. Mater. 3(1), 12–32 (2015).
[Crossref]

Behera, S.

Busch, K.

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3(7), 444–447 (2004).
[Crossref]

Chan, C.

J. C. W. Lee and C. Chan, “Circularly polarized thermal radiation from layer-by-layer photonic crystal structures,” Appl. Phys. Lett. 90(5), 051912 (2007).
[Crossref]

Chen, K.

Chen, L.-J.

L.-J. Chen, X.-Z. Dong, Y.-Y. Zhao, Y.-L. Zhang, J. Liu, M.-L. Zheng, X.-M. Duan, and Z.-S. Zhao, “Fabrication and optical transmission characteristics of polymers woodpile photonic crystal structures with different crystal planes,” AOPC 2015: Advances in Laser Technology and Applications, 967127 (2015).

Chen, Y.

Y. Chen, X. Li, X. Luo, S. A. Maier, and M. Hong, “Tunable near-infrared plasmonic perfect absorber based on phase-change materials,” Photonics Res. 3(3), 54–57 (2015).
[Crossref]

Choi, D.-S.

Choi, H.-J.

Choi, S.

Chutinan, A.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289(5479), 604–606 (2000).
[Crossref]

Cojocaru, C.

Croxall, S.

L. A. Ibbotson, A. Demetriadou, S. Croxall, O. Hess, and J. J. Baumberg, “Optical nano-woodpiles: large-area metallic photonic crystals and metamaterials,” Sci. Rep. 5(1), 8313 (2015).
[Crossref]

De Leo, E.

L. V. Poulikakos, P. Thureja, A. Stollmann, E. De Leo, and D. J. Norris, “Chiral light design and detection inspired by optical antenna theory,” Nano Lett. 18(8), 4633–4640 (2018).
[Crossref]

Decker, M.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref]

M. Thiel, M. Decker, M. Deubel, M. Wegener, S. Linden, and G. von Freymann, “Polarization Stop Bands in Chiral Polymeric Three-Dimensional Photonic Crystals,” Adv. Mater. 19(2), 207–210 (2007).
[Crossref]

Demetriadou, A.

L. A. Ibbotson, A. Demetriadou, S. Croxall, O. Hess, and J. J. Baumberg, “Optical nano-woodpiles: large-area metallic photonic crystals and metamaterials,” Sci. Rep. 5(1), 8313 (2015).
[Crossref]

Deubel, M.

M. Thiel, M. Decker, M. Deubel, M. Wegener, S. Linden, and G. von Freymann, “Polarization Stop Bands in Chiral Polymeric Three-Dimensional Photonic Crystals,” Adv. Mater. 19(2), 207–210 (2007).
[Crossref]

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3(7), 444–447 (2004).
[Crossref]

Dolan, J. A.

J. A. Dolan, B. D. Wilts, S. Vijgnolini, J. J. Baumberg, U. Steiner, and T. D. Wilkinson, “Optical properties of gyroid structured materials: From photonic crystals to metamaterials,” Adv. Opt. Mater. 3(1), 12–32 (2015).
[Crossref]

Dong, X.-Z.

L.-J. Chen, X.-Z. Dong, Y.-Y. Zhao, Y.-L. Zhang, J. Liu, M.-L. Zheng, X.-M. Duan, and Z.-S. Zhao, “Fabrication and optical transmission characteristics of polymers woodpile photonic crystal structures with different crystal planes,” AOPC 2015: Advances in Laser Technology and Applications, 967127 (2015).

Duan, X.-M.

L.-J. Chen, X.-Z. Dong, Y.-Y. Zhao, Y.-L. Zhang, J. Liu, M.-L. Zheng, X.-M. Duan, and Z.-S. Zhao, “Fabrication and optical transmission characteristics of polymers woodpile photonic crystal structures with different crystal planes,” AOPC 2015: Advances in Laser Technology and Applications, 967127 (2015).

Faryad, M.

M. Faryad and A. Lakhtakia, “The circular Bragg phenomenon,” Adv. Opt. Photonics 6(2), 225–292 (2014).
[Crossref]

Fujita, M.

M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Simultaneous inhibition and redistribution of spontaneous light emission in photonic crystals,” Science 308(5726), 1296–1298 (2005).
[Crossref]

Gailevicius, D.

Gan, Z.

Z. Gan, M. D. Turner, and M. Gu, “Biomimetic gyroid nanostructures exceeding their natural origins,” Sci. Adv. 2(5), e1600084 (2016).
[Crossref]

Gansel, J. K.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref]

Gondaira, K.

K. Ishizaki, M. Koumura, K. Suzuki, K. Gondaira, and S. Noda, “Realization of three-dimensional guiding of photons in photonic crystals,” Nat. Photonics 7(2), 133–137 (2013).
[Crossref]

Gu, M.

Z. Gan, M. D. Turner, and M. Gu, “Biomimetic gyroid nanostructures exceeding their natural origins,” Sci. Adv. 2(5), e1600084 (2016).
[Crossref]

Guimard, D.

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5(2), 91–94 (2011).
[Crossref]

Gupta, V.

S. Sarkar, V. Gupta, M. Kumar, J. Schubert, P. T. Probst, J. Joseph, and T. A. König, “Hybridized Guided-Mode Resonances via Colloidal Plasmonic Self-Assembled Grating,” ACS Appl. Mater. Interfaces 11(14), 13752–13760 (2019).
[Crossref]

Hatsugai, Y.

S. Takahashi, S. Oono, S. Iwamoto, Y. Hatsugai, and Y. Arakawa, “Circularly polarized topological edge states derived from optical Weyl points in semiconductor-based chiral woodpile photonic crystals,” J. Phys. Soc. Jpn. 87(12), 123401 (2018).
[Crossref]

Hess, O.

L. A. Ibbotson, A. Demetriadou, S. Croxall, O. Hess, and J. J. Baumberg, “Optical nano-woodpiles: large-area metallic photonic crystals and metamaterials,” Sci. Rep. 5(1), 8313 (2015).
[Crossref]

Hirayama, H.

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, K. Sakoda, N. Shinya, and Y. Aoyagi, “Microassembly of semiconductor three-dimensional photonic crystals,” Nat. Mater. 2(2), 117–121 (2003).
[Crossref]

Ho, C. T.

Y. K. Pang, J. C. W. Lee, C. T. Ho, and W. Y. Tam, “Realization of woodpile structure using optical interference holography,” Opt. Express 14(20), 9013 (2006).
[Crossref]

Ho, G. W.

J. Yang, F. Luo, T. S. Kao, X. Li, G. W. Ho, J. Teng, X. Luo, and M. Hong, “Design and fabrication of broadband ultralow reflectivity black Si surfaces by laser micro/nanoprocessing,” Light: Sci. Appl. 3(7), e185 (2014).
[Crossref]

Hong, M.

Y. Chen, X. Li, X. Luo, S. A. Maier, and M. Hong, “Tunable near-infrared plasmonic perfect absorber based on phase-change materials,” Photonics Res. 3(3), 54–57 (2015).
[Crossref]

J. Yang, F. Luo, T. S. Kao, X. Li, G. W. Ho, J. Teng, X. Luo, and M. Hong, “Design and fabrication of broadband ultralow reflectivity black Si surfaces by laser micro/nanoprocessing,” Light: Sci. Appl. 3(7), e185 (2014).
[Crossref]

Ibbotson, L. A.

L. A. Ibbotson, A. Demetriadou, S. Croxall, O. Hess, and J. J. Baumberg, “Optical nano-woodpiles: large-area metallic photonic crystals and metamaterials,” Sci. Rep. 5(1), 8313 (2015).
[Crossref]

Igusa, R.

Inoshita, K.

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, K. Sakoda, N. Shinya, and Y. Aoyagi, “Microassembly of semiconductor three-dimensional photonic crystals,” Nat. Mater. 2(2), 117–121 (2003).
[Crossref]

Ishida, S.

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5(2), 91–94 (2011).
[Crossref]

Ishihara, T.

X. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84(23), 4780–4782 (2004).
[Crossref]

Ishizaki, K.

K. Ishizaki, M. Koumura, K. Suzuki, K. Gondaira, and S. Noda, “Realization of three-dimensional guiding of photons in photonic crystals,” Nat. Photonics 7(2), 133–137 (2013).
[Crossref]

Iwamoto, S.

S. Takahashi, S. Oono, S. Iwamoto, Y. Hatsugai, and Y. Arakawa, “Circularly polarized topological edge states derived from optical Weyl points in semiconductor-based chiral woodpile photonic crystals,” J. Phys. Soc. Jpn. 87(12), 123401 (2018).
[Crossref]

S. Takahashi, T. Tajiri, Y. Ota, J. Tatebayashi, S. Iwamoto, and Y. Arakawa, “Circular dichroism in a three-dimensional semiconductor chiral photonic crystal,” Appl. Phys. Lett. 105(5), 051107 (2014).
[Crossref]

S. Takahashi, A. Tandaechanurat, R. Igusa, Y. Ota, J. Tatebayashi, S. Iwamoto, and Y. Arakawa, “Giant optical rotation in a three-dimensional semiconductor chiral photonic crystal,” Opt. Express 21(24), 29905–29913 (2013).
[Crossref]

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5(2), 91–94 (2011).
[Crossref]

Jeon, E.-c.

Joannopoulos, J. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: Molding the flow of light - second edition (Princeton University, 2011).

Johnson, S. G.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: Molding the flow of light - second edition (Princeton University, 2011).

Joseph, J.

S. Sarkar, V. Gupta, M. Kumar, J. Schubert, P. T. Probst, J. Joseph, and T. A. König, “Hybridized Guided-Mode Resonances via Colloidal Plasmonic Self-Assembled Grating,” ACS Appl. Mater. Interfaces 11(14), 13752–13760 (2019).
[Crossref]

K. Samanta and J. Joseph, “Double-helix array structure using phase controlled interference of 6 + 6 beams,” Opt. Laser Eng. 113, 23–28 (2019).
[Crossref]

S. Behera, S. Sarkar, and J. Joseph, “Fabrication of helical photonic structures with submicrometer axial and spatial periodicities following “inverted umbrella” geometry through phase-controlled interference lithography,” Opt. Lett. 43(1), 106–109 (2018).
[Crossref]

S. Behera and J. Joseph, “Design and fabrication of woodpile photonic structures through phase SLM-based interference lithography for omnidirectional optical filters,” Opt. Lett. 42(13), 2607–2610 (2017).
[Crossref]

Kao, T. S.

J. Yang, F. Luo, T. S. Kao, X. Li, G. W. Ho, J. Teng, X. Luo, and M. Hong, “Design and fabrication of broadband ultralow reflectivity black Si surfaces by laser micro/nanoprocessing,” Light: Sci. Appl. 3(7), e185 (2014).
[Crossref]

Kaschke, J.

Kim, H.

König, T. A.

S. Sarkar, V. Gupta, M. Kumar, J. Schubert, P. T. Probst, J. Joseph, and T. A. König, “Hybridized Guided-Mode Resonances via Colloidal Plasmonic Self-Assembled Grating,” ACS Appl. Mater. Interfaces 11(14), 13752–13760 (2019).
[Crossref]

Koumura, M.

K. Ishizaki, M. Koumura, K. Suzuki, K. Gondaira, and S. Noda, “Realization of three-dimensional guiding of photons in photonic crystals,” Nat. Photonics 7(2), 133–137 (2013).
[Crossref]

Kumar, M.

S. Sarkar, V. Gupta, M. Kumar, J. Schubert, P. T. Probst, J. Joseph, and T. A. König, “Hybridized Guided-Mode Resonances via Colloidal Plasmonic Self-Assembled Grating,” ACS Appl. Mater. Interfaces 11(14), 13752–13760 (2019).
[Crossref]

Lakhtakia, A.

M. Faryad and A. Lakhtakia, “The circular Bragg phenomenon,” Adv. Opt. Photonics 6(2), 225–292 (2014).
[Crossref]

Lee, J. C. W.

J. C. W. Lee and C. Chan, “Circularly polarized thermal radiation from layer-by-layer photonic crystal structures,” Appl. Phys. Lett. 90(5), 051912 (2007).
[Crossref]

Y. K. Pang, J. C. W. Lee, C. T. Ho, and W. Y. Tam, “Realization of woodpile structure using optical interference holography,” Opt. Express 14(20), 9013 (2006).
[Crossref]

Li, X.

Y. Chen, X. Li, X. Luo, S. A. Maier, and M. Hong, “Tunable near-infrared plasmonic perfect absorber based on phase-change materials,” Photonics Res. 3(3), 54–57 (2015).
[Crossref]

J. Yang, F. Luo, T. S. Kao, X. Li, G. W. Ho, J. Teng, X. Luo, and M. Hong, “Design and fabrication of broadband ultralow reflectivity black Si surfaces by laser micro/nanoprocessing,” Light: Sci. Appl. 3(7), e185 (2014).
[Crossref]

Lin, S.

G. Subramania and S. Lin, “Fabrication of three-dimensional photonic crystal with alignment based on electron beam lithography,” Appl. Phys. Lett. 85(21), 5037–5039 (2004).
[Crossref]

Lin, Y.

Linden, S.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref]

M. Thiel, M. Decker, M. Deubel, M. Wegener, S. Linden, and G. von Freymann, “Polarization Stop Bands in Chiral Polymeric Three-Dimensional Photonic Crystals,” Adv. Mater. 19(2), 207–210 (2007).
[Crossref]

Liu, J.

L.-J. Chen, X.-Z. Dong, Y.-Y. Zhao, Y.-L. Zhang, J. Liu, M.-L. Zheng, X.-M. Duan, and Z.-S. Zhao, “Fabrication and optical transmission characteristics of polymers woodpile photonic crystal structures with different crystal planes,” AOPC 2015: Advances in Laser Technology and Applications, 967127 (2015).

Luo, F.

J. Yang, F. Luo, T. S. Kao, X. Li, G. W. Ho, J. Teng, X. Luo, and M. Hong, “Design and fabrication of broadband ultralow reflectivity black Si surfaces by laser micro/nanoprocessing,” Light: Sci. Appl. 3(7), e185 (2014).
[Crossref]

Luo, X.

Y. Chen, X. Li, X. Luo, S. A. Maier, and M. Hong, “Tunable near-infrared plasmonic perfect absorber based on phase-change materials,” Photonics Res. 3(3), 54–57 (2015).
[Crossref]

J. Yang, F. Luo, T. S. Kao, X. Li, G. W. Ho, J. Teng, X. Luo, and M. Hong, “Design and fabrication of broadband ultralow reflectivity black Si surfaces by laser micro/nanoprocessing,” Light: Sci. Appl. 3(7), e185 (2014).
[Crossref]

X. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84(23), 4780–4782 (2004).
[Crossref]

Maier, S. A.

Y. Chen, X. Li, X. Luo, S. A. Maier, and M. Hong, “Tunable near-infrared plasmonic perfect absorber based on phase-change materials,” Photonics Res. 3(3), 54–57 (2015).
[Crossref]

Maigyte, L.

Malinauskas, M.

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: Molding the flow of light - second edition (Princeton University, 2011).

Miyazaki, H. T.

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, K. Sakoda, N. Shinya, and Y. Aoyagi, “Microassembly of semiconductor three-dimensional photonic crystals,” Nat. Mater. 2(2), 117–121 (2003).
[Crossref]

Noda, S.

K. Ishizaki, M. Koumura, K. Suzuki, K. Gondaira, and S. Noda, “Realization of three-dimensional guiding of photons in photonic crystals,” Nat. Photonics 7(2), 133–137 (2013).
[Crossref]

M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Simultaneous inhibition and redistribution of spontaneous light emission in photonic crystals,” Science 308(5726), 1296–1298 (2005).
[Crossref]

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289(5479), 604–606 (2000).
[Crossref]

Nomura, M.

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5(2), 91–94 (2011).
[Crossref]

Norris, D. J.

L. V. Poulikakos, P. Thureja, A. Stollmann, E. De Leo, and D. J. Norris, “Chiral light design and detection inspired by optical antenna theory,” Nano Lett. 18(8), 4633–4640 (2018).
[Crossref]

Oono, S.

S. Takahashi, S. Oono, S. Iwamoto, Y. Hatsugai, and Y. Arakawa, “Circularly polarized topological edge states derived from optical Weyl points in semiconductor-based chiral woodpile photonic crystals,” J. Phys. Soc. Jpn. 87(12), 123401 (2018).
[Crossref]

Ota, Y.

S. Takahashi, T. Tajiri, Y. Ota, J. Tatebayashi, S. Iwamoto, and Y. Arakawa, “Circular dichroism in a three-dimensional semiconductor chiral photonic crystal,” Appl. Phys. Lett. 105(5), 051107 (2014).
[Crossref]

S. Takahashi, A. Tandaechanurat, R. Igusa, Y. Ota, J. Tatebayashi, S. Iwamoto, and Y. Arakawa, “Giant optical rotation in a three-dimensional semiconductor chiral photonic crystal,” Opt. Express 21(24), 29905–29913 (2013).
[Crossref]

Ott, J.

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985).

Pang, Y. K.

Y. K. Pang, J. C. W. Lee, C. T. Ho, and W. Y. Tam, “Realization of woodpile structure using optical interference holography,” Opt. Express 14(20), 9013 (2006).
[Crossref]

Park, S.

Peckus, M.

Pereira, S.

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3(7), 444–447 (2004).
[Crossref]

Poulikakos, L. V.

L. V. Poulikakos, P. Thureja, A. Stollmann, E. De Leo, and D. J. Norris, “Chiral light design and detection inspired by optical antenna theory,” Nano Lett. 18(8), 4633–4640 (2018).
[Crossref]

Probst, P. T.

S. Sarkar, V. Gupta, M. Kumar, J. Schubert, P. T. Probst, J. Joseph, and T. A. König, “Hybridized Guided-Mode Resonances via Colloidal Plasmonic Self-Assembled Grating,” ACS Appl. Mater. Interfaces 11(14), 13752–13760 (2019).
[Crossref]

Purlys, V.

Radke, A.

Rill, M. S.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref]

Rivera, D.

Saile, V.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref]

Sakoda, K.

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, K. Sakoda, N. Shinya, and Y. Aoyagi, “Microassembly of semiconductor three-dimensional photonic crystals,” Nat. Mater. 2(2), 117–121 (2003).
[Crossref]

Samanta, K.

K. Samanta and J. Joseph, “Double-helix array structure using phase controlled interference of 6 + 6 beams,” Opt. Laser Eng. 113, 23–28 (2019).
[Crossref]

Sarkar, S.

S. Sarkar, V. Gupta, M. Kumar, J. Schubert, P. T. Probst, J. Joseph, and T. A. König, “Hybridized Guided-Mode Resonances via Colloidal Plasmonic Self-Assembled Grating,” ACS Appl. Mater. Interfaces 11(14), 13752–13760 (2019).
[Crossref]

S. Behera, S. Sarkar, and J. Joseph, “Fabrication of helical photonic structures with submicrometer axial and spatial periodicities following “inverted umbrella” geometry through phase-controlled interference lithography,” Opt. Lett. 43(1), 106–109 (2018).
[Crossref]

Schubert, J.

S. Sarkar, V. Gupta, M. Kumar, J. Schubert, P. T. Probst, J. Joseph, and T. A. König, “Hybridized Guided-Mode Resonances via Colloidal Plasmonic Self-Assembled Grating,” ACS Appl. Mater. Interfaces 11(14), 13752–13760 (2019).
[Crossref]

Shinya, N.

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, K. Sakoda, N. Shinya, and Y. Aoyagi, “Microassembly of semiconductor three-dimensional photonic crystals,” Nat. Mater. 2(2), 117–121 (2003).
[Crossref]

Soukoulis, C. M.

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3(7), 444–447 (2004).
[Crossref]

Staliunas, K.

Steiner, U.

J. A. Dolan, B. D. Wilts, S. Vijgnolini, J. J. Baumberg, U. Steiner, and T. D. Wilkinson, “Optical properties of gyroid structured materials: From photonic crystals to metamaterials,” Adv. Opt. Mater. 3(1), 12–32 (2015).
[Crossref]

Stollmann, A.

L. V. Poulikakos, P. Thureja, A. Stollmann, E. De Leo, and D. J. Norris, “Chiral light design and detection inspired by optical antenna theory,” Nano Lett. 18(8), 4633–4640 (2018).
[Crossref]

Subramania, G.

G. Subramania and S. Lin, “Fabrication of three-dimensional photonic crystal with alignment based on electron beam lithography,” Appl. Phys. Lett. 85(21), 5037–5039 (2004).
[Crossref]

Suzuki, K.

K. Ishizaki, M. Koumura, K. Suzuki, K. Gondaira, and S. Noda, “Realization of three-dimensional guiding of photons in photonic crystals,” Nat. Photonics 7(2), 133–137 (2013).
[Crossref]

Tajiri, T.

S. Takahashi, T. Tajiri, Y. Ota, J. Tatebayashi, S. Iwamoto, and Y. Arakawa, “Circular dichroism in a three-dimensional semiconductor chiral photonic crystal,” Appl. Phys. Lett. 105(5), 051107 (2014).
[Crossref]

Takahashi, S.

S. Takahashi, S. Oono, S. Iwamoto, Y. Hatsugai, and Y. Arakawa, “Circularly polarized topological edge states derived from optical Weyl points in semiconductor-based chiral woodpile photonic crystals,” J. Phys. Soc. Jpn. 87(12), 123401 (2018).
[Crossref]

S. Takahashi, T. Tajiri, Y. Ota, J. Tatebayashi, S. Iwamoto, and Y. Arakawa, “Circular dichroism in a three-dimensional semiconductor chiral photonic crystal,” Appl. Phys. Lett. 105(5), 051107 (2014).
[Crossref]

S. Takahashi, A. Tandaechanurat, R. Igusa, Y. Ota, J. Tatebayashi, S. Iwamoto, and Y. Arakawa, “Giant optical rotation in a three-dimensional semiconductor chiral photonic crystal,” Opt. Express 21(24), 29905–29913 (2013).
[Crossref]

M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Simultaneous inhibition and redistribution of spontaneous light emission in photonic crystals,” Science 308(5726), 1296–1298 (2005).
[Crossref]

Tam, W. Y.

W. Y. Tam, “Woodpile and diamond structures by optical interference holography,” J. Opt. A: Pure Appl. Opt. 9(11), 1076–1081 (2007).
[Crossref]

Y. K. Pang, J. C. W. Lee, C. T. Ho, and W. Y. Tam, “Realization of woodpile structure using optical interference holography,” Opt. Express 14(20), 9013 (2006).
[Crossref]

Tanaka, Y.

M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Simultaneous inhibition and redistribution of spontaneous light emission in photonic crystals,” Science 308(5726), 1296–1298 (2005).
[Crossref]

Tandaechanurat, A.

S. Takahashi, A. Tandaechanurat, R. Igusa, Y. Ota, J. Tatebayashi, S. Iwamoto, and Y. Arakawa, “Giant optical rotation in a three-dimensional semiconductor chiral photonic crystal,” Opt. Express 21(24), 29905–29913 (2013).
[Crossref]

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5(2), 91–94 (2011).
[Crossref]

Tatebayashi, J.

S. Takahashi, T. Tajiri, Y. Ota, J. Tatebayashi, S. Iwamoto, and Y. Arakawa, “Circular dichroism in a three-dimensional semiconductor chiral photonic crystal,” Appl. Phys. Lett. 105(5), 051107 (2014).
[Crossref]

S. Takahashi, A. Tandaechanurat, R. Igusa, Y. Ota, J. Tatebayashi, S. Iwamoto, and Y. Arakawa, “Giant optical rotation in a three-dimensional semiconductor chiral photonic crystal,” Opt. Express 21(24), 29905–29913 (2013).
[Crossref]

Teng, J.

J. Yang, F. Luo, T. S. Kao, X. Li, G. W. Ho, J. Teng, X. Luo, and M. Hong, “Design and fabrication of broadband ultralow reflectivity black Si surfaces by laser micro/nanoprocessing,” Light: Sci. Appl. 3(7), e185 (2014).
[Crossref]

Thiel, M.

M. Thiel, J. Ott, A. Radke, J. Kaschke, and M. Wegener, “Dip-in depletion optical lithography of three-dimensional chiral polarizers,” Opt. Lett. 38(20), 4252–4255 (2013).
[Crossref]

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref]

M. Thiel, G. Von Freymann, and M. Wegener, “Layer-by-layer three-dimensional chiral photonic crystals,” Opt. Lett. 32(17), 2547–2549 (2007).
[Crossref]

M. Thiel, M. Decker, M. Deubel, M. Wegener, S. Linden, and G. von Freymann, “Polarization Stop Bands in Chiral Polymeric Three-Dimensional Photonic Crystals,” Adv. Mater. 19(2), 207–210 (2007).
[Crossref]

Thureja, P.

L. V. Poulikakos, P. Thureja, A. Stollmann, E. De Leo, and D. J. Norris, “Chiral light design and detection inspired by optical antenna theory,” Nano Lett. 18(8), 4633–4640 (2018).
[Crossref]

Tomoda, K.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289(5479), 604–606 (2000).
[Crossref]

Trull, J.

Turner, M. D.

Z. Gan, M. D. Turner, and M. Gu, “Biomimetic gyroid nanostructures exceeding their natural origins,” Sci. Adv. 2(5), e1600084 (2016).
[Crossref]

Vijgnolini, S.

J. A. Dolan, B. D. Wilts, S. Vijgnolini, J. J. Baumberg, U. Steiner, and T. D. Wilkinson, “Optical properties of gyroid structured materials: From photonic crystals to metamaterials,” Adv. Opt. Mater. 3(1), 12–32 (2015).
[Crossref]

von Freymann, G.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref]

M. Thiel, G. Von Freymann, and M. Wegener, “Layer-by-layer three-dimensional chiral photonic crystals,” Opt. Lett. 32(17), 2547–2549 (2007).
[Crossref]

M. Thiel, M. Decker, M. Deubel, M. Wegener, S. Linden, and G. von Freymann, “Polarization Stop Bands in Chiral Polymeric Three-Dimensional Photonic Crystals,” Adv. Mater. 19(2), 207–210 (2007).
[Crossref]

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3(7), 444–447 (2004).
[Crossref]

Wegener, M.

M. Thiel, J. Ott, A. Radke, J. Kaschke, and M. Wegener, “Dip-in depletion optical lithography of three-dimensional chiral polarizers,” Opt. Lett. 38(20), 4252–4255 (2013).
[Crossref]

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref]

M. Thiel, G. Von Freymann, and M. Wegener, “Layer-by-layer three-dimensional chiral photonic crystals,” Opt. Lett. 32(17), 2547–2549 (2007).
[Crossref]

M. Thiel, M. Decker, M. Deubel, M. Wegener, S. Linden, and G. von Freymann, “Polarization Stop Bands in Chiral Polymeric Three-Dimensional Photonic Crystals,” Adv. Mater. 19(2), 207–210 (2007).
[Crossref]

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3(7), 444–447 (2004).
[Crossref]

Wilkinson, T. D.

J. A. Dolan, B. D. Wilts, S. Vijgnolini, J. J. Baumberg, U. Steiner, and T. D. Wilkinson, “Optical properties of gyroid structured materials: From photonic crystals to metamaterials,” Adv. Opt. Mater. 3(1), 12–32 (2015).
[Crossref]

Wilts, B. D.

J. A. Dolan, B. D. Wilts, S. Vijgnolini, J. J. Baumberg, U. Steiner, and T. D. Wilkinson, “Optical properties of gyroid structured materials: From photonic crystals to metamaterials,” Adv. Opt. Mater. 3(1), 12–32 (2015).
[Crossref]

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: Molding the flow of light - second edition (Princeton University, 2011).

Yamamoto, N.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289(5479), 604–606 (2000).
[Crossref]

Yang, J.

J. Yang, F. Luo, T. S. Kao, X. Li, G. W. Ho, J. Teng, X. Luo, and M. Hong, “Design and fabrication of broadband ultralow reflectivity black Si surfaces by laser micro/nanoprocessing,” Light: Sci. Appl. 3(7), e185 (2014).
[Crossref]

Yatsui, T.

T. Yatsui, “Recent improvement of silicon absorption in opto-electric devices,” Opto-Electronic Advances 2(10), 19002301–19002308 (2019).
[Crossref]

Yi, Y.

Yoo, Y.-E.

Zhang, Y.-L.

L.-J. Chen, X.-Z. Dong, Y.-Y. Zhao, Y.-L. Zhang, J. Liu, M.-L. Zheng, X.-M. Duan, and Z.-S. Zhao, “Fabrication and optical transmission characteristics of polymers woodpile photonic crystal structures with different crystal planes,” AOPC 2015: Advances in Laser Technology and Applications, 967127 (2015).

Zhao, Y.-Y.

L.-J. Chen, X.-Z. Dong, Y.-Y. Zhao, Y.-L. Zhang, J. Liu, M.-L. Zheng, X.-M. Duan, and Z.-S. Zhao, “Fabrication and optical transmission characteristics of polymers woodpile photonic crystal structures with different crystal planes,” AOPC 2015: Advances in Laser Technology and Applications, 967127 (2015).

Zhao, Z.-S.

L.-J. Chen, X.-Z. Dong, Y.-Y. Zhao, Y.-L. Zhang, J. Liu, M.-L. Zheng, X.-M. Duan, and Z.-S. Zhao, “Fabrication and optical transmission characteristics of polymers woodpile photonic crystal structures with different crystal planes,” AOPC 2015: Advances in Laser Technology and Applications, 967127 (2015).

Zheng, M.-L.

L.-J. Chen, X.-Z. Dong, Y.-Y. Zhao, Y.-L. Zhang, J. Liu, M.-L. Zheng, X.-M. Duan, and Z.-S. Zhao, “Fabrication and optical transmission characteristics of polymers woodpile photonic crystal structures with different crystal planes,” AOPC 2015: Advances in Laser Technology and Applications, 967127 (2015).

ACS Appl. Mater. Interfaces (1)

S. Sarkar, V. Gupta, M. Kumar, J. Schubert, P. T. Probst, J. Joseph, and T. A. König, “Hybridized Guided-Mode Resonances via Colloidal Plasmonic Self-Assembled Grating,” ACS Appl. Mater. Interfaces 11(14), 13752–13760 (2019).
[Crossref]

Adv. Mater. (1)

M. Thiel, M. Decker, M. Deubel, M. Wegener, S. Linden, and G. von Freymann, “Polarization Stop Bands in Chiral Polymeric Three-Dimensional Photonic Crystals,” Adv. Mater. 19(2), 207–210 (2007).
[Crossref]

Adv. Opt. Mater. (1)

J. A. Dolan, B. D. Wilts, S. Vijgnolini, J. J. Baumberg, U. Steiner, and T. D. Wilkinson, “Optical properties of gyroid structured materials: From photonic crystals to metamaterials,” Adv. Opt. Mater. 3(1), 12–32 (2015).
[Crossref]

Adv. Opt. Photonics (1)

M. Faryad and A. Lakhtakia, “The circular Bragg phenomenon,” Adv. Opt. Photonics 6(2), 225–292 (2014).
[Crossref]

Appl. Phys. Lett. (4)

S. Takahashi, T. Tajiri, Y. Ota, J. Tatebayashi, S. Iwamoto, and Y. Arakawa, “Circular dichroism in a three-dimensional semiconductor chiral photonic crystal,” Appl. Phys. Lett. 105(5), 051107 (2014).
[Crossref]

J. C. W. Lee and C. Chan, “Circularly polarized thermal radiation from layer-by-layer photonic crystal structures,” Appl. Phys. Lett. 90(5), 051912 (2007).
[Crossref]

G. Subramania and S. Lin, “Fabrication of three-dimensional photonic crystal with alignment based on electron beam lithography,” Appl. Phys. Lett. 85(21), 5037–5039 (2004).
[Crossref]

X. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84(23), 4780–4782 (2004).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

W. Y. Tam, “Woodpile and diamond structures by optical interference holography,” J. Opt. A: Pure Appl. Opt. 9(11), 1076–1081 (2007).
[Crossref]

J. Phys. Soc. Jpn. (1)

S. Takahashi, S. Oono, S. Iwamoto, Y. Hatsugai, and Y. Arakawa, “Circularly polarized topological edge states derived from optical Weyl points in semiconductor-based chiral woodpile photonic crystals,” J. Phys. Soc. Jpn. 87(12), 123401 (2018).
[Crossref]

Light: Sci. Appl. (1)

J. Yang, F. Luo, T. S. Kao, X. Li, G. W. Ho, J. Teng, X. Luo, and M. Hong, “Design and fabrication of broadband ultralow reflectivity black Si surfaces by laser micro/nanoprocessing,” Light: Sci. Appl. 3(7), e185 (2014).
[Crossref]

Nano Lett. (1)

L. V. Poulikakos, P. Thureja, A. Stollmann, E. De Leo, and D. J. Norris, “Chiral light design and detection inspired by optical antenna theory,” Nano Lett. 18(8), 4633–4640 (2018).
[Crossref]

Nat. Mater. (2)

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3(7), 444–447 (2004).
[Crossref]

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, K. Sakoda, N. Shinya, and Y. Aoyagi, “Microassembly of semiconductor three-dimensional photonic crystals,” Nat. Mater. 2(2), 117–121 (2003).
[Crossref]

Nat. Photonics (2)

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5(2), 91–94 (2011).
[Crossref]

K. Ishizaki, M. Koumura, K. Suzuki, K. Gondaira, and S. Noda, “Realization of three-dimensional guiding of photons in photonic crystals,” Nat. Photonics 7(2), 133–137 (2013).
[Crossref]

Opt. Express (4)

Opt. Laser Eng. (1)

K. Samanta and J. Joseph, “Double-helix array structure using phase controlled interference of 6 + 6 beams,” Opt. Laser Eng. 113, 23–28 (2019).
[Crossref]

Opt. Lett. (5)

Opto-Electronic Advances (1)

T. Yatsui, “Recent improvement of silicon absorption in opto-electric devices,” Opto-Electronic Advances 2(10), 19002301–19002308 (2019).
[Crossref]

Photonics Res. (1)

Y. Chen, X. Li, X. Luo, S. A. Maier, and M. Hong, “Tunable near-infrared plasmonic perfect absorber based on phase-change materials,” Photonics Res. 3(3), 54–57 (2015).
[Crossref]

Sci. Adv. (1)

Z. Gan, M. D. Turner, and M. Gu, “Biomimetic gyroid nanostructures exceeding their natural origins,” Sci. Adv. 2(5), e1600084 (2016).
[Crossref]

Sci. Rep. (1)

L. A. Ibbotson, A. Demetriadou, S. Croxall, O. Hess, and J. J. Baumberg, “Optical nano-woodpiles: large-area metallic photonic crystals and metamaterials,” Sci. Rep. 5(1), 8313 (2015).
[Crossref]

Science (3)

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289(5479), 604–606 (2000).
[Crossref]

M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Simultaneous inhibition and redistribution of spontaneous light emission in photonic crystals,” Science 308(5726), 1296–1298 (2005).
[Crossref]

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref]

Other (5)

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: Molding the flow of light - second edition (Princeton University, 2011).

L.-J. Chen, X.-Z. Dong, Y.-Y. Zhao, Y.-L. Zhang, J. Liu, M.-L. Zheng, X.-M. Duan, and Z.-S. Zhao, “Fabrication and optical transmission characteristics of polymers woodpile photonic crystal structures with different crystal planes,” AOPC 2015: Advances in Laser Technology and Applications, 967127 (2015).

MATLAB and Statistics Toolbox Release 2012b, The MathWorks, Inc., Natick, Massachusetts, United States.

“Lumerical inc. https://www.Lumerical.Com/products/.”

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985).

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Figures (8)

Fig. 1.
Fig. 1. (a) Beam configuration in a 3 + 3 double-cone geometry for the realization of chiral woodpile structure using phase-controlled beams. XY projections of the beams show their orientation for defining the associated k vectors. (b, i) Actual chiral woodpile interference pattern produced in MATLAB. (ii) Chiral woodpile structure used for FDTD simulation.
Fig. 2.
Fig. 2. FDTD based comparison of plane-wave filtering response of the chiral woodpile layered structures fabricated with different interference angles. (i)-(iii) shows the effects of increment in the number of pitches from 3 to 9 for structures with materials like (a)photoresist, (b) titanium dioxide and (c) crystalline silicon.
Fig. 3.
Fig. 3. (a) Schematic of beam orientation for omnidirectional filtering properties of the chiral woodpile structure studied with both (b) in-plane and (c) out of plane polarization. Different cases of (i) rotation of the plane of incidence for fixed normal incidence and (ii)-(iii) rotation of angle of incidence for fixed planes of incidence can give an idea about the omnidirectionality of the stop-band.
Fig. 4.
Fig. 4. Schematic showing dual chirality in the chiral-woodpile structure. An RCP unit cell (a) can be considered consisting of 6 layers (a) whereas an LCP unit cell (b) constructed from only 3 layers.
Fig. 5.
Fig. 5. Transmittance and reflectance from chiral woodpile structure on the incidence of circularly polarized light. The effects are studied on structures made out of two different materials, (a) Titanium dioxide and (b) Gallium arsenide. Structures fabricable with different interference angles (i-iii) are also studied to realize the possibility of tuning the range of circular dichroism.
Fig. 6.
Fig. 6. (a) Experimental setup towards the realization of a chiral woodpile structure involving a dual-cone geometry. The beams diffracted in umbrella geometry from the SLM (provided with computed phase-mask) are represented with pseudo colors; each color represents a particular phase associated with the individual beams. (b) A magnified version of arrangement to convert six diffracted beams into 3 + 3 dual cone geometry using mount 1 and mount 2. (c) Actual experimental counterpart of (b) with the irradiated plane of interference. (d) Interference angle in terms of distance along the Z-axis in dual cone geometry considering beams 1 and 2. (e) Pattern recording process in positive photoresist showing the complementary structure after development. (f) fabricated positive photoresist sample with complementary chiral structure showing different diffracted colors in different observing directions.
Fig. 7.
Fig. 7. (a) A 2D SEM image of the fabricated complementary chiral woodpile on the positive photoresist AZ 1505. Inset shows a simulated structure identical to the fabricated sample in terms of the orientation of the rods with the top layer (blue) rotated at ${30^\textrm{o}}$ with respect to X-axis. (b) Similar structure with different photoresist thickness revealing the second layer(green) as top layer rotated at ${150^\textrm{o}}$ with respect to X-axis. Measured values disclose 2a = 763 nm and 3Λsp = 1295 nm. (c) & (d) 2D and 3D view of the samples over a large area showing the capability of PCIL.
Fig. 8.
Fig. 8. (a) Experimental setup to study filtering response of the fabricated structure using a broad white light source. (b)-(i)Transmittance of the fabricated complementary structure realized in positive photoresist (PPR). (ii) Simulated transmittance of a negative photoresist (NPR) structure (black curve) and its complementary structure out of positive photoresist (PPR) with 3 pitches. Inset in (b-ii) shows the two structures in NPR and PPR showing complementarity.

Tables (1)

Tables Icon

Table 1. Parameters of chiral woodpile structure used in FDTD simulation

Equations (4)

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I ( r ) = μ = 1 6 | E μ | 2 + μ = 1 6 ν = 1 μ ν 6 E μ E ν exp [ i ( k μ k ν ) r + i ( ψ μ ψ ν ) ]
ψ 1 = ( 2 π / 6 ) 1 ,   k 1 = k 0 [ sin θ int cos ( 4 π 3 ) ,   sin θ int sin ( 4 π 3 ) , cos θ int ] ψ 2 = ( 2 π / 6 ) 2 ,   k 2 = k 0 [ sin θ int cos ( 4 π 3 ) ,   sin θ int sin ( 4 π 3 ) ,   cos θ int ] ψ 3 = ( 2 π / 6 ) 3 ,   k 3 = k 0 [ sin θ int cos ( 2 π ) ,   sin θ int sin ( 2 π ) , cos θ int ]   ψ 4 = ( 2 π / 6 ) 4   k 4 = k 0 [ sin θ int cos ( 2 π 3 ) ,   sin θ int sin ( 2 π 3 ) ,   cos θ int ] ψ 5 = ( 2 π / 6 ) 5   k 5 = k 0 [ sin θ int cos ( 2 π 3 ) ,   sin θ int sin ( 2 π 3 ) , cos θ int ] ψ 6 = ( 2 π / 6 ) 6 ,   k 6 = k 0 [ sin θ int cos ( 2 π ) ,   sin θ int sin ( 2 π ) ,   cos θ int ] }
k m = k e f f [ sin θ d i f f cos ( 2 π m 6 ) ,   sin θ d i f f sin ( 2 π m 6 ) ,   cos θ d i f f ] ;     ψ m = ( 2 π m 6 )  
r 1 = r 2 [ ( tan θ int tan θ d i f f ) / ( tan θ int + tan θ d i f f ) ] z 1 = [ r 1 / tan θ d i f f ] z 3 = [ r 2 / tan θ d i f f ] z 2 = z 1 + [ r 1 / tan θ int ] }  

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