Spiral Photonic Crystals Research Articles

Manipulating Orbital Angular Momentum Entanglement in Three-Dimensional Spiral Nonlinear Photonic Crystals

We propose and theoretically investigate two-photon orbital angular momentum (OAM) correlation through spontaneous parameter down-conversion (SPDC) processes in three-dimensional (3D) spiral nonlinear photonic crystals (NPCs). By properly designing the NPC structure, one can feasibly modulate the OAM-correlated photon pair, which provides a potential platform to realize high-dimensional entanglement for quantum information processing and quantum communications.

Broadband enhancement of Čerenkov second harmonic generation in a sunflower spiral nonlinear photonic crystal.

We present an experimental study on the Čerenkov second harmonic emission in a novel sunflower spiral array of ferroelectric domains in LiNbO3 crystal. The spiral patterns offer a diffusive, circularly symmetric distribution of reciprocal lattice vectors, thereby enabling enhanced emission of the Čerenkov beam in a broad spectral range. Instead of the traditional electric field poling, the sunflower spiral patterns are fabricated here by using our pioneering method of ferroelectric domain engineering with ultrafast light. This all-optical method gives access to high quality domain structures with short periods, which is beneficial for efficient Čerenkov harmonic generation.

Waveguide-mode polarization gaps in square spiral photonic crystals

We designed waveguide channels in two types of square spiral photonic crystals. Wide polarization gaps, in which only one circular polarization wave is allowed while the other counter-direction circular polarization wave is forbidden, can be opened up on the waveguide modes within the fundamental photonic band gap according to the calculation of band structures and transmission spectra. This phenomenon is ascribed to the chirality of the waveguide and is independent of the chirality of the background photonic crystal. Moreover, the transmission spectra show a good one-way property of the waveguide channels. The chiral quality factor demonstrates the handedness of the allowed and impeded chiral waveguide modes, and further proved the property of the waveguide-mode polarization gap. Such waveguides with waveguide-mode polarization gap are a good candidate for one-way waveguides with robust backscattering-immune transport.

Metallic Spiral Three-Dimensional Photonic Crystal with a Full Band Gap at Optical Communication Wavelengths

The optical properties of a gold spiral photonic crystal (PC) were studied numerically and a full 3-D band gap at near infrared wavelengths was found. This band gap, ranging from 1.2 to 1.8 m in wavelength, covers all the second and third telecom windows used in optical fiber communications. Chiral and other optical properties were also discussed. There is a very high absorption at the band gap edge due to the retarded speed of light and an abnormal high transmission outside the band gap contributed by surface plasmon polaritons. Both right circular polarized (RCP) and left circular polarized (LCP) light are studied and great diversities were found in certain regions of the spectrum. These optical properties maintain within large incident angles.

Square spiral photonic crystal with visible bandgap

Nanoimprint lithography was combined with glancing angle deposition (GLAD) of titanium dioxide to fabricate a square spiral columnar film with a bandgap in the visible spectral range. Nanoimprint stamps were fabricated with seed spacing ranging from 80 to 400 nm, and four periods of square spiral film were deposited on top of the 320 nm array of seeds. The ratio of lattice spacing, vertical pitch and spiral arm swing was chosen as a : P : A = 1 : 1.35 : 0.7 and the deposition angle was fixed at 86° to maximize the square spiral film’s bandgap. Reflectivity measurements show that the fabricated structure exhibit a pseudo-gap centered at around 600 nm wavelength, in good agreement with finite difference electromagnetic simulations. The absence of a full 3D bandgap is due the deviation of GLAD columns’ cross-section from the optimal one, which has to be highly elongated in the deposition plane. However, simulations show that a geometry close to the fabricated one will produce a full 3D bandgap, if the structure is inverted. The material refractive index in such an inverted photonic crystal can be as low as n = 2.15.

Fano resonance of three-dimensional spiral photonic crystals: Paradoxical transmission and polarization gap

Extraordinary Fano resonance with right handedness is present in a right-handed polarization gap of compound spiral photonic crystals. The structure is composed of unit cells with double helices of π phase shift arranged in square lattice. Such a paradoxical phenomenon is derived from mode interferences between left-handed propagating modes along spiral axis and negative group velocity modes in extended Brillouin zone. By analyzing Fourier spectra and chirality of photonic eigenmodes, intrinsic mechanism is well understood by mode coupling theory.

Optimization of periodic column growth in glancing angle deposition for photonic crystalfabrication

We investigate the growth of periodically aligned silicon microstructures for the fabricationof square spiral photonic crystals using the glancing angle deposition phi-sweepprocess. We report the optimization of the phi-sweep offset angle for fabrication ofmicrostructures with more precise geometry. The effects of varying the sweep offset angle ofthe phi-sweep process are studied for films deposited onto a square lattice arrayof growth seeds. To represent one growth segment of the phi-sweep process, wefabricate 15 nm silicon thin films using several azimuthal substrate offsets from0° to45° at a vaporincidence angle of 85°. We also deposit silicon square spirals on square lattice arrayswith the phi-sweep method, using various sweep offset angles fromγ = 0° to45°. We find that usingan offset angle of γ = 26.5° optimizes the shadowing geometry, which minimizes anisotropic broadening,producing greater quality photonic crystal structures. From normalincidence reflection spectroscopy, a maximum full width at half-maximum of273 ± 3 nm and a relativepeak width (Δλ/λ) of16.1 ± 0.1% were found for asweep offset angle of γ = 26.5°.

Templating and Replication of Spiral Photonic Crystals for Silicon Photonics

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper describes femtosecond laser lithography of 3-D photonic crystal templates in commercial photoresist SU-8 and replication of these templates with silicon. Using this approach, silicon-based photonic crystals having 3-D square spiral architecture and exhibiting photonic stop gaps near the 2.5-<formula formulatype="inline"> <tex>$\mu$</tex></formula>m wavelength were fabricated. Possibilities to use a multiple-beam interference technique for two-photon absorption templating of photonic crystals are explored. </para>

Experimental realization of a well-controlled 3D silicon spiral photonic crystal

Three-dimensional (3D) Si spiral photonic crystals have been realized by oblique angle deposition with a new approach of substrate ‘swing’ rotation. We demonstrate that, by using swing rotation, the arms of the spirals can be grown with a uniform diameter. Without swing rotation the arms of the spirals may overgrow due to a ballistic ‘fan-out’ phenomenon. The fabricated 3D Si spiral photonic crystals have a [0 0 1]-diamond symmetry which has been shown previously to have a large photonic band gap. Our optical measurements of reflectance have suggested the existence of such a photonic band gap in our structures centred at a wavelength of 2 µm.

Polarization Stop Bands in Chiral Polymeric Three‐Dimensional Photonic Crystals

High-quality polymeric 3D spiral photonic crystals are fabricated via direct laser writing. Polarization stop bands for circularly polarized light are observed, leading to 5 % transmittance for the circular light polarization, which matches the handedness of the helix, and 95 % for the other polarization (see figure). The experimental results are in good agreement with theoretical calculations.

Ion Beam Assisted Square Spiral Photonic Crystal Fabrication

AbstractPhotonic crystals currently hold exciting potential in waveguiding applications with the ability to greatly reduce waveguide bend radii, allowing for the realization of photonic networks with increased complexity and device density. Square spiral photonic crystals are comprised of periodic arrays of slanted cylindrical columns with periodic abrupt 90° changes in the column growth direction. The abrupt changes produce elbows which correspond to points in the three-dimensional diamond lattice, which are commonly referred to as diamond:n photonic crystal structures based on the nth nearest neighbor lattice point between column arms. The diamond:n structures are characterized by four parameters: column separation, spiral pitch, column diameter, and column growth angle. These structures have been shown theoretically to have a three-dimensional relative bandgap of approximately 15% for a direct silicon diamond:1 structure and approximately 24% for an inverse silicon diamond:5 structure with circular column cross sections. Silicon square spiral photonic crystals can be grown by a single-step thin film deposition process known as glancing angle deposition (GLAD), which utilizes rotation of lithographically patterned substrates and advanced control algorithms. While using GLAD to grow square spiral photonic crystals in a single-step process is desirable, it does have inherent limitations. Physical vapor deposited films deposited at oblique incidence angles form columns with angle ≤ 60° relative to the substrate normal. This deviates from the optimal diamond:1 and diamond:5 structures which require film growth angles of approximately 64° and 74°, respectively. Here we present SEM images of periodic silicon square spiral films grown with a vapor source incidence angle of 85° that indicate an average column tilt angle of 57˚ for films grown with the basic GLAD process and an average column tilt angle between 61˚ and 65˚ using an ion-assisted GLAD process. Photonic simulations indicating that square spiral films with complete three-dimensional photonic bandgaps are only achievable via ion-assisted GLAD are also presented.

Investigation of optical properties of circular spiral photonic crystals

The photonic bandgap of three-dimensional photonic crystals, formed by arranging circular spirals in face-centre-cubic lattice, was theoretically investigated. The structure was found to have a relative photonic bandgap of up to 25% in both direct and inversed configurations. The conditions under which the structure has a bandgap larger than 10% are described. Some considerations for optimizing such photonic crystal fabrication by two-photon polymerization are given. The theoretical results are implemented to fabricate polymeric structures that can be used as templates for photonic crystals with full photonic bandgap larger than 10% centered in the near-infrared region.

Three-dimensional circular spiral photonic crystal structures recorded by femtosecond pulses

Photonic crystal structures having three-dimensional (3D) circular spiral architecture have large theoretical photonic band-gap but cannot be implemented by most of the existing microfabrication techniques. We have successfully used a highly versatile 3D microstructuring technique called femtosecond laser microfabrication to prepare templates of the circular spiral photonic crystals in a commercially available photoresist SU-8. The structures fabricated have good structural quality, are highly periodic and exhibit spectral signatures of photonic bands dispersion in the short infrared wavelength region.

Three-dimensional horizontal circular spiral photonic crystals with stop gaps below 1μm

Three-dimensional photonic crystals with a circular spiral architecture were fabricated by direct laser writing (DLW) in a photoresist. DLW was performed with a laser beam having the direction of propagation and elongation of the ellipsoidal focal region perpendicular to the spirals’ orientation. This allowed the reduction of the turning period of the spirals while avoiding the overlap between their adjacent turns. Consequently, optical transmission and reflection spectra of the fabricated samples revealed multiple photonic stop gaps whose shortest wavelength was 0.88μm, the lowest observed so far in spiral structures. These results were qualitatively reproduced by finite-difference time-domain simulations. This fabrication scheme can be useful for DLW of structures where photonic stop gaps along particular directions, rather than complete photonic band gaps, are required.

Spiral three-dimensional photonic crystals for telecommunications spectral range

Three-dimensional photonic crystals consisting of periodic arrays of spiral columns were fabricated in a commercially available photoresist (SU-8) by a direct laser writing technique. Tailoring the pre- and post-processing conditions for the photoresist has enabled the recording of extended, self-supporting periodic structures with sub-diffraction resolution. Pronounced photonic stop gaps were observed at wavelengths between 1.5 and 1.8 μm, close to the telecommunications region. These structures can be used as accurate and robust templates for subsequent infiltration by materials with higher refractive index.

Morphology of periodic nanostructures for photonic crystals grown by glancing angle deposition

An enhancement of the glancing angle deposition (GLAD) technique called PhiSweep was used to grow slanted columns of silicon and titanium dioxide onto patterned substrates. The PhiSweep technique involves periodically rotating the substrate back and forth during the deposition process, which reduces column fanning caused by anisotropy in the shadowing conditions. The patterned substrates consisted of a tetragonal array of hillocks with 100, 200, and 300 nm periodicities and were fabricated using electron beam lithography. The PhiSweep method alters the tilt angle of the slanted columns compared with those grown using traditional GLAD. We present a derivation of the tilt angle of the slanted columns as a function of the parameters of the PhiSweep technique. The tilt angles of the silicon and titanium dioxide films were measured and agree with the predicted values. The films fabricated using the PhiSweep method are compared with similar films grown using traditional GLAD. The PhiSweep technique produced films with substantially less column fanning than those grown by traditional GLAD. This reduction in column fanning has extended the size range over which periodic GLAD structures, such as square spiral photonic crystals, can be grown.

Polarization gaps in spiral photonic crystals

We studied the optical properties of a dielectric photonic crystal structure with spirals arranged in a hexagonal lattice. The dielectric constant of the material was 9 and the filling ratio was 15.2%. We found that this kind of structure exhibits a significant polarization gap in the light that was incident along the axis of the spirals. The eigenmodes inside the polarization gap were predominantly right-hand (left-hand) polarized depending on the whether if the spirals are left-handed (right-handed). We calculated the transmission spectrum of a slab of such a structure and it matches well with the analysis of the eigenmodes.

Advanced techniques for the fabrication of square spiral photonic crystals by glancing angle deposition

Using the glancing angle deposition thin film fabrication technique, it is possible to create tailored, three-dimensional periodic square spiral photonic crystals that exhibit a band of forbidden electromagnetic frequencies related to the dimensions of the nanostructures. Typically, when fabricating square spirals by traditional means, several problems arise due to nonuniform shadowing that results in column broadening and the loss of required periodicity for thicker crystals. Through the use of complex substrate motion that imposes greater restrictions on growth and shadowing, many of these problems have been overcome, in particular through the implementation of two new algorithms: the slow corner and the variable angle post methods. These motion algorithms have been implemented in conjunction with square spiral photonic crystal fabrication to provide more uniform spiral structures along with more stringent periodicity across the crystal that will allow for photonic band gap structures with more ideal characteristics.

Optical properties of a three-dimensional silicon square spiral photonic crystal

We report the fabrication and optical characterization of a tetragonal square spiral photonic crystal with a three-dimensional relative band gap of approximately 10% using the glancing angle deposition (GLAD) technique. This thin film structure is produced in a one-step process that is highly versatile as a wide range of crystal structures can be created simply through the variation of deposition parameters. Measurements indicate upper and lower frequency band edges at vacuum wavelengths of 2.50 and 2.75 μm, in the infrared region of the spectrum.

Square spiral photonic crystals: robust architecture for microfabrication of materials with large three-dimensional photonic band gaps.

We provide a blueprint for microfabricating photonic crystals with very large and robust three-dimensional photonic band gaps (PBG's). These crystals are based on interleaving polygonal spiral posts and can be efficiently manufactured on a large scale in a one-step process using the recently introduced technique of glancing angle deposition. We classify various families of spiral photonic crystals based on (i) the parent three-dimensional (3D) point lattice to which they are most closely related, (ii) the crystallographic axis of the parent lattice around which the spiral posts wind, and (iii) the set of points of the parent lattice which the spiral arms connect or nearly connect. We obtain optimal geometries for the spiral photonic crystals by detailed mapping of the size and location of the PBG within a multidimensional parameter space which characterizes the shape of each spiral post. For the optimum PBG, the spiral arms and elbows may deviate significantly from the points of the original point lattice. The largest 3D PBG's are obtained for square spiral posts that wind around the [001] axis of diamond (or face centered cubic) lattice and in which the spiral arm segments approximately connect either the fifth or first nearest-neighbor points of the parent lattice. In the case of silicon posts (with a dielectric constant of 11.9) in an air background, whose arm segments nearly connect fifth nearest-neighbor point of the diamond lattice, the full PBG can be as large as 16% of the gap center frequency. For the corresponding air posts in a silicon background, the maximum PBG is 24% of the gap center frequency. We compute both the total electromagnetic density of states and the electromagnetic field distributions near the PBG. It is suggested the PBG in an optimized structure is highly tolerant to various forms of disorder that may arise during the manufacturing process.