Process parameter optimization for removable partial denture frameworks manufactured by selective laser melting.

STATEMENT OF PROBLEM: Selective laser melting (SLM), an additive manufacturing technology, is expected to replace the traditional lost-wax casting process used in producing removable partial denture (RPD) frameworks. However, studies comparing the accuracy of RPD frameworks and the effects of process parameters are lacking. PURPOSE: The purpose of this in vitro study was to optimize SLM process parameters and use a quantitative analysis method to improve the accuracy of 3D-printed RPD frameworks. MATERIAL AND METHODS: The orientation and support structure of Kennedy Class II RPDs were designed in various ways by using 2 different software programs, CAMbridge and Magics. The optimum melt-pool parameters, including laser power, scan speed, hatch distance, and layer thickness, were determined empirically before manufacturing 12 RPD frameworks with 4 different process designs by using SLM (n=3). The accuracy of the RPD frameworks was determined by 3D scanning and comparing the 3D scan data with the original standard tessellation language (STL) RPD design with the best-fit algorithm of the Geomagic software program. RESULTS: Optimum melt-pool parameters were found with the function of density, surface roughness, and productivity (P=180 W, v=1200 mm/s, h=60 µm, t=30 µm). RPD frameworks fabricated by the optimized process parameters (167 ±105 µm) showed significantly better (P<.05) mean ±standard deviation accuracy than the 3 other groups of RPD frameworks manufactured by using the nonoptimized process parameters (180 ±121 µm to 222 ±136 µm). The best accuracy was found with the transverse orientation and interconnected support structure. CONCLUSIONS: With the optimized design of process parameters, clinically acceptable RPD frameworks were produced. The accuracy of RPD frameworks fabricated by using SLM varied according to the design of the process parameters, indicating that SLM technology can replace the traditional lost-wax casting process.

Binary-lens-embedded photonic crystals.

A binary-lens-embedded photonic crystal (B-LEPC) was designed for operation at 1550 nm and fabricated by multiphoton lithography. The lens is binary in the sense that optical path difference is generated using unit cells having just two distinct fill factors. The unit cells have a "rod-in-wall" structure that exhibits three-dimensional self-collimation. Simulations show that self-collimation forces light to move through the device without diffracting or focusing, even as the wavefront is reshaped by the lensing region. Upon exiting the device, the curved wavefront causes the light to focus. The thickness of a B-LEPC was reduced threefold by wrapping phase in the style of a Fresnel lens. Embedding a faster-varying phase profile enables tighter focusing, and numerical aperture NA = 0.59 was demonstrated experimentally.

Cylindrical-lens-embedded photonic crystal based on self-collimation.

Photonic crystals can be engineered so that the flow of optical power and the phase of the field are independently controlled. The concept is demonstrated by creating a self-collimating lattice with an embedded cylindrical lens. The device is fabricated in a photopolymer by multi-photon lithography with the lattice spacing chosen for operation around the telecom wavelength of 1550 nm. The lattice is based on a low-symmetry rod-in-wall unit cell that strongly self-collimates light. The walls are varied in thickness to modulate the effective refractive index so light acquires a spatially quadratic phase profile as it propagates through the device. Although the phase of the field is altered, the light does not focus within the device because self-collimation forces power to flow parallel to the principal axes of the lattice. Upon exiting the device, ordinary propagation resumes in free space and the curved phase profile causes the light to focus. An analysis of the experimentally observed optical behavior shows that the device behaves like a thin lens, even though the device is considerably thick.

Wide-band self-collimation in a low-refractive-index hexagonal lattice.

Wide-angle, broadband self-collimation (SC) is demonstrated in a hexagonal photonic crystal (PhC) fabricated in a low-refractive-index photopolymer by multiphoton lithography. The PhC can be described as a hexagonal array of cylindrical air holes in a block of dielectric material having a low-refractive index. Optical characterization shows that the device strongly self-collimates light at near-infrared wavelengths that span 1360 to 1610 nm. SC forces light to flow along the extrusion direction of the lattice without diffractive spreading, even when light couples into the device at high oblique angles. Numerical simulations corroborate the experimental findings.

Fast optimal design of optical components using the cultural algorithm.

Design of the guided-mode resonance (GMR) grating filter, as one of the most important optical components, using the cultural algorithm (CA) is presented, for the first time. CA is an evolutionary algorithm (EA) which is easy-to-implement, flexible, inspired by the human cultural evolution, upon using the domain knowledge for reducing the search space as a metaheuristic optimization method. Reflection spectra of the designed GMR filter based on the CA is in good agreement with the previous simulation results. CA has both acceptable accuracy and enough high speed to optimize the complicated structures; therefore, a novel double-line asymmetrical transmitter (DLAT) is introduced and optimized as a complex grating-based optical component using the mentioned algorithm. The results show the transmittance at two different communication wavelengths (1.5039 and 1.6113 µm) using the combination of binary diffraction grating and customized photonic crystal (PhC) structure. Also, the DLAT shows the characteristics of a perfect transverse magnetic (TM) polarizer. Furthermore, we demonstrated the Talbot effect at the DLAT output which is so applicable in the optical usage, especially for the integrated optics.

Independent control of phase and power in spatially variant self-collimating photonic crystals.

Self-collimating photonic crystals are a promising technology to control waves in optical devices. A technique was recently developed that can bend, twist, and otherwise spatially vary a photonic crystal without deforming the unit cells, as this would weaken or destroy the optical properties. Applying this to self-collimating photonic crystals allows us to control multiple properties of light at the same time. A spatially variant self-collimating photonic crystal is shown that decouples the phase and power of the wave and controls them independently and at the same time within the same volume. This creates new physical mechanisms from which to design optical systems. Some possible applications include miniaturization of optical systems, integrated optics, beam steering, and imaging, among others.

Spatially variant periodic structures in electromagnetics.

Spatial transforms are a popular technique for designing periodic structures that are macroscopically inhomogeneous. The structures are often required to be anisotropic, provide a magnetic response, and to have extreme values for the constitutive parameters in Maxwell's equations. Metamaterials and photonic crystals are capable of providing these, although sometimes only approximately. The problem still remains about how to generate the geometry of the final lattice when it is functionally graded, or spatially varied. This paper describes a simple numerical technique to spatially vary any periodic structure while minimizing deformations to the unit cells that would weaken or destroy the electromagnetic properties. New developments in this algorithm are disclosed that increase efficiency, improve the quality of the lattices and provide the ability to design aplanatic metasurfaces. The ability to spatially vary a lattice in this manner enables new design paradigms that are not possible using spatial transforms, three of which are discussed here. First, spatially variant self-collimating photonic crystals are shown to flow unguided waves around very tight bends using ordinary materials with low refractive index. Second, multi-mode waveguides in spatially variant band gap materials are shown to guide waves around bends without mixing power between the modes. Third, spatially variant anisotropic materials are shown to sculpt the near-field around electric components. This can be used to improve electromagnetic compatibility between components in close proximity.

Tight control of light beams in photonic crystals with spatially-variant lattice orientation.

Spatially-variant photonic crystals (SVPCs), in which the orientation of the unit cell changes as a function of position, are shown to be capable of abruptly controlling light beams using just low index materials and can be made to have high polarization selectivity. Multi-photon direct laser writing in the photo-polymer SU-8 was used to fabricate three-dimensional SVPCs that direct the flow of light around a 90 degree bend. The lattice spacing and fill factor were maintained nearly constant throughout the structure. The SVPCs were characterized at a wavelength of 2.94 µm by scanning the faces with optical fibers and the results were compared to electromagnetic simulations. The lattices were shown to direct infrared light of one polarization through sharp bends while the other polarization propagated straight through the SVPC. This work introduces a new scheme for controlling light that should be useful for integrated photonics.

Optimization of planar self-collimating photonic crystals.

Self-collimation in photonic crystals has received a lot of attention in the literature, partly due to recent interest in silicon photonics, yet no performance metrics have been proposed. This paper proposes a figure of merit (FOM) for self-collimation and outlines a methodical approach for calculating it. Performance metrics include bandwidth, angular acceptance, strength, and an overall FOM. Two key contributions of this work include the performance metrics and identifying that the optimum frequency for self-collimation is not at the inflection point. The FOM is used to optimize a planar photonic crystal composed of a square array of cylinders. Conclusions are drawn about how the refractive indices and fill fraction of the lattice impact each of the performance metrics. The optimization is demonstrated by simulating two spatially variant self-collimating photonic crystals, where one has a high FOM and the other has a low FOM. This work gives optical designers tremendous insight into how to design and optimize robust self-collimating photonic crystals, which promises many applications in silicon photonics and integrated optics.

Fabrication of metal-oxide nano-hairs for effective index optical elements.

We present a method for fabricating high aspect ratio metal-oxide, sub-wavelength grating structures. These "nano-hair" structures are composed of alumina cylindrical pillars, partially embedded in a supporting fused silica substrate. The fabricated nano-hair structures demonstrate phase control of the transmitted beam while maintaining a peak transmitted power greater than 93% around a central wavelength of λ(o) = 1.55 µm. Based on this principle, discrete and continuous phase functions can be encoded by controlling the lithographic process.

Synthesis of spatially variant lattices.

It is often desired to functionally grade and/or spatially vary a periodic structure like a photonic crystal or metamaterial, yet no general method for doing this has been offered in the literature. A straightforward procedure is described here that allows many properties of the lattice to be spatially varied at the same time while producing a final lattice that is still smooth and continuous. Properties include unit cell orientation, lattice spacing, fill fraction, and more. This adds many degrees of freedom to a design such as spatially varying the orientation to exploit directional phenomena. The method is not a coordinate transformation technique so it can more easily produce complicated and arbitrary spatial variance. To demonstrate, the algorithm is used to synthesize a spatially variant self-collimating photonic crystal to flow a Gaussian beam around a 90° bend. The performance of the structure was confirmed through simulation and it showed virtually no scattering around the bend that would have arisen if the lattice had defects or discontinuities.

Fabrication of three-dimensional micro-photonic structures on the tip of optical fibers using SU-8.

A method is reported for fabricating truly three-dimensional micro-photonic structures directly onto the end face of an optical fiber using the cross-linkable resist SU-8. This epoxide-based material is well suited for micro-device fabrication because it is photo-processed as a solid and the cross-linked material is mechanically robust, chemically resistant, and optically transparent. Yet, procedures commonly used to process SU-8, particularly spin-coating, are impractical when the intended fabrication substrate is the end-face of an optical fiber. A melt-reflow process was developed to prepare optical fibers having SU-8 resin deposited at controlled thickness on the fiber end-face. Multi-photon direct laser writing was then used to fabricate various refractive lenses, a compound lens system, and a woodpile photonic crystal within the resin on the end-face of the optical fiber. Data are presented that show how the refractive lenses can be used to alter the output of the optical fiber. This work opens a new path to low-profile integrated photonic devices.

Two-dimensional guided mode resonance filters fabricated in a uniform low-index material system.

We demonstrate the fabrication, simulation, and experimental results of a buried, homogeneous narrowband spectral filter with a periodic, hexagonal unit cell of air pockets, encapsulated in a fused silica substrate. The leaky waveguide is formed by depositing SiO(x) on an etched fused silica grating via plasma-enhanced chemical vapor deposition. Design principles of guided mode resonance filters were utilized to achieve a resonance with 60% reflectivity at a wavelength of 1.741 µm. The device demonstrates resonance with FWHM of 6 nm.

Spatial and spectral beam shaping with space-variant guided mode resonance filters.

Novel all-dielectric beam shaping elements were developed based on guided mode resonance (GMR) filters. This was achieved by spatially varying the duty cycle of a hexagonal-cell GMR filter, to locally detune from the resonant condition, which resulted in modified wavelength dependent reflection and transmission profiles, across the device aperture. This paper presents the design, fabrication, and characterization of the device and compares simulations to experimental results.

Rigorous electromagnetic analysis of volumetrically complex media using the slice absorption method.

There is tremendous demand for numerical methods to perform rigorous analysis of devices that are both large scale and complex throughout their volume. This can arise when devices must be considered with realistic geometry or when they contain artificial materials such as photonic crystals, left-handed materials, nanoparticles, or other metamaterials. The slice absorption method (SAM) was developed to address this need. The method is fully numerical and able to break large problems down into small pieces, or slices, using matrix division or Gaussian elimination instead of eigensystem computations and scattering matrix manipulations. In these regards, the SAM is an attractive alternative to popular techniques like the finite-difference time domain method, rigorous coupled-wave analysis, and the transfer matrix method. To demonstrate the utility of the SAM and benchmark its accuracy, reflection was simulated for a photonic crystal fabricated in SU-8 by multiphoton direct laser writing. Realistic geometry was incorporated into the model by simulating the microfabrication process, which yielded simulation results that matched experimental measurements remarkably well.

Design and optimization of space-variant photonic crystal filters.

A space-variant photonic crystal filter is designed and optimized that may be placed over a detector array to perform filtering functions tuned for each pixel. The photonic crystal is formed by etching arrays of holes through a multilayer stack of alternating high and low refractive index materials. Position of a narrow transmission notch within a wide reflection band is varied across the device aperture by adjusting the diameter of the holes. Numerical simulations are used to design and optimize the geometry of the photonic crystal. As a result of physics inherent in the etching process, the diameter of the holes reduces with depth, producing a taper. Optical performance was found to be sensitive to the taper, but a method for compensation was developed where film thickness is varied through the device.

Spatially polarizing autocloned elements.

A space-variant polarization converting element is introduced that utilizes an autocloning effect to produce high aspect ratio from birefringent gratings. This method utilizes a multilayer deposition process on a template to convert a linearly polarized incident beam to an azimuthally polarized output at a wavelength of 1.55 microm with more than 90% efficiency.

Modeling fabrication to accurately place GMR resonances.

Numerical methods for simulating etching and deposition processes were combined with electromagnetic modeling to design guided-mode resonance (GMR) filters with accurately positioned resonances and study how fabrication affects their optical behavior. GMR filters are highly sensitive to structural deformations that arise during fabrication, making accurate placement of their resonances very difficult without active tuning while in operation. Inspired by how thin film resistors are trimmed during fabrication, the numerical tools were used to design a method for adjusting position of GMR resonances at the time of fabrication.

Design of generalized invisible scatterers.

A nonlinear signal processing method is applied to the design of strongly scattering objects to realize a defined angular response. Investigated as the complement of inverse scattering problems, k-space design methods are combined with cepstral filtering to obtain a permittivity distribution that scatters with the desired response. Starting with the rigorously computed angular spectrum of the scattering amplitude of an object of simple geometric shape, the corresponding k-space is modified to provide the desired scattering behavior. In order to account for strong scattering, cepstral filtering is applied to map the associated distribution of secondary sources to a unique permittivity distribution. The inversion process results in a structure that exhibits the desired properties and which can be interpreted as a perturbation of the initial structure. Simulation results are presented which illustrate the usefulness of this method. In particular, objects are modified to enhance forward scattering and suppress scattering in all other direction. Results are verified using a rigorous finite-difference frequency-domain scheme to simulate scattering. The method is demonstrated as a novel means for designing invisible objects that act as electromagnetic cloaks.

Fabrication and characterization of three-dimensional copper metallodielectric photonic crystals.

Three-dimensional metallodielectric photonic crystals were created by fabricating a micron-scale polymeric template using multiphoton direct laser writing (DLW) in SU-8 and conformally and selectively coating the template with copper (Cu) via nanoparticle-nucleated electroless metallization. This process deposits a uniform metal coating, even deep within a lattice, because it is not directional like sputter-coating or evaporative deposition. Infrared reflectance spectra show that upon metallization the optical behavior transitions fully from a dielectric photonic crystal to that of a metal photonic crystal (MPC). After depositing 50 nm of Cu, the MPCs exhibit a strong plasmonic stop band having reflectance greater than 80% across the measured part of the band and reaching as high as 95% at some wavelengths. Numerical simulations match remarkably well with the experimental data and predict all dominant features observed in the reflectance measurements, showing that the MPCs are structurally well formed. These data show that the Cu-based process can be used to create high performance MPCs and devices that are difficult or impossible to fabricate by other means.