Reconfigurable optically induced quasicrystallographic three-dimensional complex nonlinear photonic lattice structures

Holographic Fabrication of 3D Moiré Photonic Crystals Using Circularly Polarized Laser Beams and a Spatial Light Modulator

A moiré photonic crystal is an optical analog of twisted graphene. A 3D moiré photonic crystal is a new nano-/microstructure that is distinguished from bilayer twisted photonic crystals. Holographic fabrication of a 3D moiré photonic crystal is very difficult due to the coexistence of the bright and dark regions, where the exposure threshold is suitable for one region but not for the other. In this paper, we study the holographic fabrication of 3D moiré photonic crystals using an integrated system of a single reflective optical element (ROE) and a spatial light modulator (SLM) where nine beams (four inner beams + four outer beams + central beam) are overlapped. By modifying the phase and amplitude of the interfering beams, the interference patterns of 3D moiré photonic crystals are systemically simulated and compared with the holographic structures to gain a comprehensive understanding of SLM-based holographic fabrication. We report the holographic fabrication of phase and beam intensity ratio-dependent 3D moiré photonic crystals and their structural characterization. Superlattices modulated in the z-direction of 3D moiré photonic crystals have been discovered. This comprehensive study provides guidance for future pixel-by-pixel phase engineering in SLM for complex holographic structures.

Switchable optical ring lattice in free space

Optical lattices with spatially regular structures have recently attracted considerable attention across physics and optics communities. In particular, due to the increasing emergence of new structured light fields, diverse lattices with rich topology are being generated via multi-beam interference. Here, we report a specific ring lattice with radial lobe structures generated via superposition of two ring Airy vortex beams (RAVBs). We show that the lattice morphology evolves upon propagation in free space, switching from a bright-ring lattice to dark-ring lattice and even to fascinating multilayer texture. This underlying physical mechanism is related to the variation of the unique intermodal phase between the RAVBs as well as topological energy flow with symmetry breaking. Our finds provide an approach for engineering customized ring lattices to inspire a wide variety of new applications.

Generation of periodic and quasi-periodic two-dimensional non-diffractive beams with inhomogeneous polarization

In this work, two-dimensional periodic and quasi-periodic non-diffractive spatial inhomogeneous polarization optical fields are generated, numerically and experimentally, by the superposition of multiple plane waves with different polarizations. For the experimental implementation of the fields, synthetic phase holograms are employed in conjunction with half-wave and quarter-wave retarder films as polarization modulators. The obtained spatially inhomogeneous polarization optical fields show good quality and are in good agreement with numerical results. The proposed method is highly efficient for the generation of these types of optical fields.

Design approach for photonic quasicrystals to enable multiple nonlinear interactions

Photonic quasicrystals are poised to transform the field of nonlinear light-matter interactions due to their ability to support an unlimited number of combinations of wavevectors in their reciprocal lattices. Such greatly enhanced flexibility enabled by k-space engineering makes photonic quasicrystals a promising platform for novel approaches to multi-wavelength conversion, supercontinuum generation, and development of classical and quantum optical sources. Here, we develop a new design method for nonlinear photonic quasicrystals, consisting of a combination of one nonlinear material and one linear material that can simultaneously fulfill phase-matching conditions for a desired number of nonlinear optical interactions as long as the frequencies of the interacting waves are outside of the bandgaps of the quasicrystal structure. Our approach provides enhanced design flexibility, enabling new pathways to designing compact, integrated nonlinear photonic devices and systems on a chip.

Construction of photorefractive photonic quasicrystal microstructures by twisted square lattices

A convenient method to fabricate two-dimensional photonic quasicrystal microstructures was experimentally demonstrated by using a rotatable four-wedge prism. Two-dimensional eightfold symmetric quasicrystal microstructures are formed by two groups of twisted square lattices in a photorefractive crystal. The experimental devices of this method are simple and stable without complicated optical adjustment equipment. Optical-induced quasicrystal microstructures are analyzed and verified by magnified imaging and far-field diffraction pattern imaging. The method can be extended to fabricate more complex quasicrystal and moiré lattice microstructures. We numerically demonstrate that this method can be used to fabricate other complex photonic microstructures by using different multi-wedge prisms and adjusting the rotation angle properly.

Fast Acoustic Light Sculpting for On-Demand Maskless Lithography

Light interference is the primary enabler of a number of optical maskless techniques for the large-scale processing of materials at the nanoscale. However, methods controlling interference phenomena can be limited in speed, ease of implementation, or the selection of pattern designs. Here, an optofluidic system that employs acoustic standing waves in a liquid to produce complex interference patterns at sub-microsecond temporal resolution, faster than the pulse-to-pulse period of many commercial laser systems, is presented. By controlling the frequency of the acoustic waves and the motion of a translation stage, additive and subtractive direct-writing of tailored patterns over cm2 areas with sub-wavelength uniformity in periodicity and scalable spatial resolution, down to the nanometric range, are demonstrated. Such on-the-fly dynamic control of light enhances throughput and design flexibility of optical maskless lithography, helping to expand its application portfolio to areas as important as plasmonics, electronics, or metamaterials.

Distortion analysis of crystalline and locally quasicrystalline 2D photonic structures with grazing-incidence small-angle X-ray scattering

In this study, grazing-incidence small-angle X-ray scattering (GISAXS) is used to collect statistical information on dimensional parameters in an area of 20 × 15 mm on photonic structures produced by nanoimprint lithography. The photonic structures are composed of crystalline and locally quasicrystalline two-dimensional patterns with structure sizes between about 100 nm and 10 µm to enable broadband visible light absorption for use in solar-energy harvesting. These first GISAXS measurements on locally quasicrystalline samples demonstrate that GISAXS is capable of showing the locally quasicrystalline nature of the samples while at the same time revealing the long-range periodicity introduced by the lattice design. The scattering is described qualitatively in the framework of the distorted-wave Born approximation using a hierarchical model mirroring the sample design, which consists of a rectangular and locally quasicrystalline supercell that is repeated periodically to fill the whole surface. The nanoimprinted samples are compared with a sample manufactured using electron-beam lithography and the distortions of the periodic and locally quasiperiodic samples are quantified statistically. Owing to the high sensitivity of GISAXS to deviations from the perfect lattice, the misalignment of the crystallographic axes was measured with a resolution of 0.015°, showing distortions of up to ±0.15° in the investigated samples.

Holographic Fabrication and Optical Property of Graded Photonic Super-Crystals with a Rectangular Unit Super-Cell

Recently developed graded photonic super-crystals show an enhanced light absorption and light extraction efficiency if they are integrated with a solar cell and an organic light emitting device, respectively. In this paper, we present the holographic fabrication of a graded photonic super-crystal with a rectangular unit super-cell. The spatial light modulator-based pixel-by-pixel phase engineering of the incident laser beam provides a high resolution phase pattern for interference lithography. This also provides a flexible design for the graded photonic super-crystals with a different ratio of length over the width of the rectangular unit super-cell. The light extraction efficiency is simulated for the organic light emitting device, where the cathode is patterned with the graded photonic super-crystal. The high extraction efficiency is maintained for different exposure thresholds during the interference lithography. The desired polarization effects are observed for certain exposure thresholds. The extraction efficiency reaches as high as 75% in the glass substrate.

Holographic fabrication of graded photonic super-quasi-crystals with multiple-level gradients

Photonic quasi-crystals and photonic crystals with certain degrees of disorder can have a broadband light-matter interaction. In this paper, we present the holographic fabrication of graded photonic super-quasi-crystals through pixel-by-pixel phase pattern engineering using a spatial light modulator. Using the same phase pattern arranged in a decagon, we have fabricated graded photonic super-quasi-crystals with five-fold symmetry and multiple levels of gradients and graded photonic super-crystals with rectangular unit super-cells, depending on the Fourier filter. Although a certain degree of disorder was incorporated in the quasi-crystals, we still observed the golden ratio in the diameters of the diffraction rings of the fabricated quasi-crystals, indicating five-fold symmetry. Using direct pixel-by-pixel phase engineering, the same laser projection system, consisting of an integrated spatial light modulator and a reflective optical element, can be used for the fabrication of graded photonic super-crystals with various symmetries. The multi-level gradient effects on the optical properties of an organic light-emitting diode were simulated. When the cathode of an organic light-emitting device is patterned in the graded photonic super-crystals, a light extraction efficiency up to 76% in the visible range can be achieved.

Deterministic composite nanophotonic lattices in large area for broadband applications

Exotic manipulation of the flow of photons in nanoengineered materials with an aperiodic distribution of nanostructures plays a key role in efficiency-enhanced broadband photonic and plasmonic technologies for spectrally tailorable integrated biosensing, nanostructured thin film solarcells, white light emitting diodes, novel plasmonic ensembles etc. Through a generic deterministic nanotechnological route here we show subwavelength-scale silicon (Si) nanostructures on nanoimprinted glass substrate in large area (4 cm²) with advanced functional features of aperiodic composite nanophotonic lattices. These nanophotonic aperiodic lattices have easily tailorable supercell tiles with well-defined and discrete lattice basis elements and they show rich Fourier spectra. The presented nanophotonic lattices are designed functionally akin to two-dimensional aperiodic composite lattices with unconventional flexibility- comprising periodic photonic crystals and/or in-plane photonic quasicrystals as pattern design subsystems. The fabricated composite lattice-structured Si nanostructures are comparatively analyzed with a range of nanophotonic structures with conventional lattice geometries of periodic, disordered random as well as in-plane quasicrystalline photonic lattices with comparable lattice parameters. As a proof of concept of compatibility with advanced bottom-up liquid phase crystallized (LPC) Si thin film fabrication, the experimental structural analysis is further extended to double-side-textured deterministic aperiodic lattice-structured 10 μm thick large area LPC Si film on nanoimprinted substrates.

Controlled soliton formation in tailored Bessel photonic lattices

Azimuthally modulated higher order rotationally symmetric Bessel-like optical patterns were generated by coherent superposition of two co-propagating Bessel beams - either in or out of phase. By changing the distance between the beam centers, a whole variety of transition states can be realized. As one prominent example, a 4-fold symmetry quadrupole-like photonic structure was optically inducted in an SBN crystal and nonlinear beam propagation in such a photonic wave-guiding structure is investigated in both self-focusing and self-defocusing regimes. The proposed device serves as an all-optical 2d 1 × 4 photonic interconnect.

Submicrometer photonic structure fabrication by phase spatial-light-modulator-based interference lithography

We present a large-area and single-step fabrication approach based on phase spatial light modulator (SLM)-assisted interference lithography for the realization of submicrometer photonic structures on photoresist. A multimirror beam steering unit is used to reflect the SLM-generated phase-engineered beams leading to a large angle between interfering beams while also preserving the large area of the interfering plane beams. Both translational and rotational periodic submicrometer structures are experimentally realized. This approach increases the flexibility of interference lithography to fabricate more complex submicrometer photonic structures and photonic metamaterial structures for future applications.

Holographic Fabrication of Designed Functional Defect Lines in Photonic Crystal Lattice Using a Spatial Light Modulator

We report the holographic fabrication of designed defect lines in photonic crystal lattices through phase engineering using a spatial light modulator (SLM). The diffracted beams from the SLM not only carry the defect's content but also the defect related phase-shifting information. The phase-shifting induced lattice shifting in photonic lattices around the defects in three-beam interference is less than the one produced by five-beam interference due to the alternating shifting in lattice in three beam interference. By designing the defect line at a 45 degree orientation and using three-beam interference, the defect orientation can be aligned with the background photonic lattice, and the shifting is only in one side of the defect line, in agreement with the theory. Finally, a new design for the integration of functional defect lines in a background phase pattern reduces the relative phase shift of the defect and utilizes the different diffraction efficiency between the defect line and background phase pattern. We demonstrate that the desired and functional defect lattice can be registered into the background lattice through the direct imaging of designed phase patterns.

Optical Bloch oscillations of an Airy beam in a photonic lattice with a linear transverse index gradient

We theoretically report the existence of optical Bloch oscillations (BO) of an Airy beam in a one-dimensional optically induced photonic lattice with a linear transverse index gradient. The Airy beam experiencing optical BO shows a more robust non-diffracting feature than its counterparts in free space or in a uniform photonic lattice. Interestingly, a periodical recurrence of Airy shape accompanied with constant alternation of its acceleration direction is also found during the BO. Furthermore, we demonstrate that the period and amplitude of BO of an Airy beam can be readily controlled over a wide range by varying the index gradient and/or the lattice period. Exploiting these features, we propose a scheme to rout an Airy beam to a predefined output channel without losing its characteristics by longitudinally modulating the transverse index gradient.

Generating a hexagonal lattice wave field with a gradient basis structure

We present a new, single-step approach for generating a hexagonal lattice wave field with a gradient local basis structure. We incorporate this by coherently superposing two (or more) hexagonal lattice wave fields, which differ in their basis structures. The basis of the resultant lattice wave field is highly dependent on the relative strengths of constituent wave fields, and a desired spatial modulation of basis structure is thus obtained by controlling the spatial modulation of relative strengths of constituent wave fields. The experimental realization of gradient lattice is achieved by using a phase-only spatial light modulator (SLM) in an optical 4f Fourier filter setup where the SLM is displayed with a numerically calculated gradient phase mask. The presented method is wavelength independent and is completely scalable, making it promising for microfabrication of corresponding structures.

Digitally tunable holographic lithography using a spatial light modulator as a programmable phase mask

In this paper, we study tunable holographic lithography using an electrically addressable spatial light modulator as a programmable phase mask. We control the phases of interfering beams diffracted from the phase pattern displayed in the spatial light modulator. We present a calculation method for the assignment of phases in the laser beams and validate the phases of the interfering beams in phase-sensitive, dual-lattice, and two-dimensional patterns formed by a rotationally non-symmetrical configuration. A good agreement has been observed between fabricated holographic structures and simulated interference patterns. The presented method can potentially help design a gradient phase mask for the fabrication of graded photonic crystals or metamaterials.

Tailored complex 3D vortex lattice structures by perturbed multiples of three-plane waves

As three-plane waves are the minimum number required for the formation of vortex-embedded lattice structures by plane wave interference, we present our experimental investigation on the formation of complex 3D photonic vortex lattice structures by a designed superposition of multiples of phase-engineered three-plane waves. The unfolding of the generated complex photonic lattice structures with higher order helical phase is realized by perturbing the superposition of a relatively phase-encoded, axially equidistant multiple of three noncoplanar plane waves. Through a programmable spatial light modulator assisted single step fabrication approach, the unfolded 3D vortex lattice structures are experimentally realized, well matched to our computer simulations. The formation of higher order intertwined helices embedded in these 3D spiraling vortex lattice structures by the superposition of the multiples of phase-engineered three-plane waves interference is also studied.

Exploiting aperiodic designs in nanophotonic devices

In this work we consider the role of aperiodic order-order without periodicity-in the design of different optical devices in one, two and three dimensions. To this end, we will first study devices based on aperiodic multilayered structures. In many instances the recourse to Fibonacci, Thue-Morse or fractal arrangements of layers results in improved optical properties compared with their periodic counterparts. On this basis, the possibility of constructing optical devices based on a modular design of the multilayered structure, where periodic and quasiperiodic subunits are properly mixed, is analyzed, illustrating how this additional degree of freedom enhances the optical performance in some specific applications. This line of thought can be naturally extended to aperiodic arrangements of optical elements, such as nanospheres or dielectric rods in the plane, as well as to three-dimensional photonic quasicrystals based on polymer materials. In this way, plentiful possibilities for new tailored materials naturally appear, generally following suitable optimization algorithms. Then, we present a detailed discussion on the physical properties supporting the preferential use of aperiodic devices in a number of optical applications, opening new avenues for technological innovation. Finally we suggest some related emerging topics that deserve some attention in the years to come.

Sculptured 3D twister superlattices embedded with tunable vortex spirals

We present diverse reconfigurable complex 3D twister vortex superlattice structures in a large area embedded with tunable vortex spirals as well as dark rings, threaded by vortex helices. We demonstrate these tunable complex chiral vortex superlattices by the superposition of relatively phase engineered plane waves. The generated complex 3D twister lattice vortex structures are computationally as well as experimentally analyzed using various tools to verify the presence of phase singularities. Our observation indicates the application-specific flexibility of our approach to tailor the transverse superlattice spatial irradiance profile of these longitudinally whirling vortex-cluster units and dark rings.

Efficient generation of periodic and quasi-periodic non-diffractive optical fields with phase holograms

The superposition of multiple plane waves with appropriate propagation vectors generates a periodic or quasi-periodic non-diffractive optical field. We show that the Fourier spectrum of the phase modulation of this field is formed by two disjoint parts, one of which is proportional to the Fourier spectrum of the field itself. Based on this result we prove that the non-diffractive field can be generated, with remarkable high accuracy and efficiency, in a Fourier domain spatial filtering setup, using a synthetic phase hologram whose transmittance is the phase modulation of the field. In a couple of cases this result is presented analytically, and in other cases the proof is computational and experimental.

Systematic approach to complex periodic vortex and helix lattices

We present a general comprehensive framework for the description of symmetries of complex light fields, facilitating the construction of sophisticated periodic structures carrying phase dislocations. In particular, we demonstrate the derivation of all three fundamental two-dimensional vortex lattices based on vortices of triangular, quadratic, and hexagonal shape, respectively. We show that these patterns represent the foundation of complex three-dimensional lattices with outstanding helical intensity distributions which suggest valuable applications in holographic lithography. This systematic approach is substantiated by a comparative study of corresponding numerically calculated and experimentally realized complex intensity and phase distributions.

Tunable complex photonic chiral lattices by reconfigurable optical phase engineering

We present a novel single-step fabrication approach, based on optical phase engineering, for tunable complex photonic chiral lattices of diverse geometries in a large area. By means of engineered reconfigurable phase patterns, we computationally simulate as well as experimentally investigate these complex structures. We show the generation of both periodic right- and left-handed chiral structures as well as photonic transversely quasi-crystallographic chiral structures. These complex chiral lattices are also demonstrated in a photorefractive material, and the lattice formation is analyzed by plane-wave-guided imaging as well as diffraction pattern imaging. Furthermore, complex photonic chiral structures with engineered tunable relative phase shifts between adjacent spiral units realizable in a single step are explored and analyzed.

Mathieu beams as versatile light moulds for 3D micro particle assemblies

We present tailoring of three dimensional light fields which act as light moulds for elaborate particle micro structures of variable shapes. Stereo microscopy is used for visualization of the 3D particle assemblies. The powerful method is demonstrated for the class of propagation invariant beams, where we introduce the use of Mathieu beams as light moulds with non-rotationally-symmetric structure. They offer multifarious field distributions and facilitate the creation of versatile particle structures. This general technique may find its application in micro fluidics, chemistry, biology, and medicine, to create highly efficient mixing tools, for hierarchical supramolecular organization or in 3D tissue engineering.