Phase and magnitude constrained metasurface holography at W-band frequencies.

Holographic optics are an essential tool for the control of light, generating highly complex and tailored light field distributions that can represent physical objects or abstract information. Conceptually, a hologram is a region of space in which an arbitrary phase shift and amplitude variation are added to an incident reference wave at every spatial location, such that the reference wave will produce a desired field distribution as it scatters from the medium. Practical holograms are composed of materials, however, which have limited properties that constrain the possible field distributions. Here, we show it is possible to produce a hologram with continuous phase distribution and a non-uniform amplitude variation at every point by leveraging resonant metamaterial elements and constraining the hologram's pixels to match the elements' resonant behavior. We demonstrate the viability of the resonant metamaterial approach with a single layer, co-polarized holographic metasurface that produces an image at millimeter wavelengths (92.5 GHz) despite the elements' limited phase range and coupled amplitude dependency.

Optical bistability with film-coupled metasurfaces.

Metasurfaces comprising arrays of film-coupled, nanopatch antennas are a promising platform for low-energy, all-optical switches. The large field enhancements that can be achieved in the dielectric spacer region between the nanopatch and the metallic substrate can substantially enhance optical nonlinear processes. Here we consider a dielectric material that exhibits an optical Kerr effect as the spacer layer and numerically calculate the optical bistability of a metasurface using the finite element method (FEM). We expect the proposed method to be highly accurate compared with other numerical approaches, such as those based on graphical post-processing techniques, because it self-consistently solves for both the spatial field distribution and the intensity-dependent refractive index distribution of the spacer layer. This method offers an alternative approach to finite-difference time-domain (FDTD) modeling. We use this numerical tool to design a metasurface optical switch and our optimized design exhibits exceptionally low switching intensity of 33 kW/cm2, corresponding to switching energy on the order of tens of attojoules per resonator, a value much smaller than those found for most devices reported in the literature. We propose our method as a tool for designing all-optical switches and modulators.

Clarifying the origin of third-harmonic generation from film-coupled nanostripes.

The resonance associated with plasmonic nanostructures strongly enhances local optical fields, and can thus dramatically enhance the nonlinear response of the composite structure. However, the origin of the nonlinear signal generated from hybrid nanostructures consisting of both metallic and dielectric components can be ambiguous when all constituents possess nonlinearities. In this paper, we introduce a method for specifically identifying the third harmonic generation (THG) originating from different nonlinear sources in a film-coupled nanostripe. The nanostripe consists of a metallic patch separated from a metallic film by a dielectric spacer. By considering the THG from each nonlinear source separately, we show that the near- and far-field behaviors of the THG generated within the various constituents of the nanostripe are distinguishable due to fundamental differences in the THG radiation properties. The THG signal from the metal is shown to be suppressed by the structure itself, while the THG signal from the spacer is enhanced by the gap plasmon modes supported by the structure. The total THG signal is found to be the sum of all nonlinear sources, with the far-field radiation pattern determined by the ratio between the third-order susceptibilities of the dielectric and the metal.

Design and fabrication of stress-compensated optical coatings: Fabry-Perot filters for astronomical applications.

The performance of optical coatings may be negatively affected by the deleterious effects of mechanical stress. In this work, we propose an optimization tool for the design of optical filters taking into account both the optical and mechanical properties of the substrate and of the individual deposited layers. The proposed method has been implemented as a supplemental module in the OpenFilters open source design software. It has been experimentally validated by fabricating multilayer stacks using e-beam evaporation, in combination with their mechanical stress assessment performed as a function of temperature. Two different stress-compensation strategies were evaluated: (a) design of two complementary coatings on either side of the substrate and (b) implementing the mechanical properties of the individual materials in the design of the optical coating on one side only. This approach has been tested by the manufacture of a Fabry-Perot etalon used in astronomy while using evaporated SiO2 and TiO2 films. We found that the substrate curvature can be decreased by 85% and 49% for the first and second strategies, respectively.

Arbitrary birefringent metamaterials for holographic optics at λ = 1.55 µm.

This paper presents an optical element capable of multiplexing two diffraction patterns for two orthogonal linear polarizations, based on the use of non-resonant metamaterial cross elements. The metamaterial cross elements provide unique building blocks for engineering arbitrary birefringence. As a proof-of-concept demonstration, we present the design and experimental characterization of a polarization multiplexed blazed diffraction grating and a polarization multiplexed computer-generated hologram, for the telecommunication wavelength of λ = 1.55 µm. A quantitative study of the polarization multiplexed grating reveals that this approach yields a very large polarization contrast ratio. The results show that metamaterials can form the basis for a versatile and compact platform useful in the design of multi-functional photonic devices.

Quantitative comparison of gradient index and refractive lenses.

We analyze the Seidel wavefront aberrations and spot sizes of gradient index (GRIN) singlet lenses with Δn≈1. We consider and compare curved and planar GRIN lenses with F-numbers of 5 and 1 against equivalent refractive lenses. We find that the planar GRIN lenses generally have larger spot sizes compared to their refractive lens equivalents at wide angles. This appears to be due to an inability to correct for coma by adjusting the refractive index gradient alone. We can correct for the coma by bending the GRIN lens. This results in a singlet lens with performance close to but not exceeding that of the equivalent refractive lens. We also examine the impact of anisotropy on the planar GRIN lenses. We find that fabricating the planar GRIN lenses from a uniaxial medium has the potential to improve the performance of the lenses.

Reconciliation of generalized refraction with diffraction theory.

When an electromagnetic wave is obliquely incident on the interface between two homogeneous media with different refractive indices, the requirement of phase continuity across the interface generally leads to a shift in the trajectory of the wave. When a linearly position-dependent phase shift is imposed at the interface, the resulting refraction may be described using a generalized version of Snell's law. In this Letter, we establish a formal equivalence between generalized refraction and blazed diffraction gratings, further discussing the relative merits of the two approaches.

Infrared metamaterial phase holograms.

As a result of advances in nanotechnology and the burgeoning capabilities for fabricating materials with controlled nanoscale geometries, the traditional notion of what constitutes an optical device continues to evolve. The fusion of maturing low-cost lithographic techniques with newer optical design strategies has enabled the introduction of artificially structured metamaterials in place of conventional materials for improving optical components as well as realizing new optical functionality. Here we demonstrate multilayer, lithographically patterned, subwavelength, metal elements, whose distribution forms a computer-generated phase hologram in the infrared region (10.6 µm). Metal inclusions exhibit extremely large scattering and can be implemented in metamaterials that exhibit a wide range of effective medium response, including anomalously large or negative refractive index; optical magnetism; and controlled anisotropy. This large palette of metamaterial responses can be leveraged to achieve greater control over the propagation of light, leading to more compact, efficient and versatile optical components.

Planar, flattened Luneburg lens at infrared wavelengths.

Employing artificially structured metamaterials provides a means of circumventing the limits of conventional optical materials. Here, we use transformation optics (TO) combined with nanolithography to produce a planar Luneburg lens with a flat focal surface that operates at telecommunication wavelengths. Whereas previous infrared TO devices have been transformations of free-space, here we implement a transformation of an existing optical element to create a new device with the same optical characteristics but a user-defined geometry.

Design and fabrication of a metamaterial gradient index diffraction grating at infrared wavelengths.

We demonstrate the design, fabrication and characterization of an artificially structured, gradient index metamaterial with a linear index variation of Δn ~ 3.0. The linear gradient profile is repeated periodically to form the equivalent of a blazed grating, with the gradient occurring across a spatial distance of 61 µm. The grating, which operates at a wavelength of 10.6 µm, is composed of non-resonant, progressively modified "I-beam" metamaterial elements and approximates a linear phase shift gradient using 61 distinguishable phase levels. The grating structure consists of four layers of lithographically patterned metallic I-beam elements separated by dielectric layers of SiO(2). The index gradient is confirmed by comparing the measured magnitudes of the -1, 0 and +1 diffracted orders to those obtained from full wave simulations incorporating all material properties of the metals and dielectrics of the structures. The large index gradient has the potential to enable compact infrared diffractive and gradient index optics, as well as more exotic transformation optical media.

Nonlinear parameter retrieval from three- and four-wave mixing in metamaterials.

We present a generalized nonlinear susceptibility retrieval method for metamaterials based on transfer matrices and valid in the nondepleted pump approximation. We construct a general formalism to describe the transfer matrix method for nonlinear media and apply it to the processes of three- and four-wave mixing. The accuracy of this approach is verified via finite element simulations. The method is then reversed to give a set of equations for retrieving the nonlinear susceptibility. Finally, we apply the proposed retrieval operation to a three-wave mixing transmission experiment performed on a varactor loaded split ring resonator metamaterial sample and find quantitative agreement with an analytical effective medium theory model.

Step method: a new synthesis method for the design of optical filters with intermediate refractive indices.

We propose a new synthesis method for the design of multilayer optical filters with intermediate refractive indices, the step method. This method consists in adding infinitesimally small index steps in the index profile at optimal positions and then reoptimizing the thickness and the refractive index of the layers. Application of the method to the design of an antireflective coating, a low-pass edge filter, and an immersed polarizing beam splitter shows that it provides interesting solutions, even in the absence of a proper starting design. The formalism developed for the method also serves to demonstrate that the optimal filter consists of either homogeneous layers that maximize the effective refractive index contrast, or of graded-index layers.

Optical filters with prescribed optical thickness and refined refractive indices.

We propose to refine the refractive index of the layers composing optical filters while keeping their optical thicknesses constant. Using this technique, one can optimize filters made of quarter-wave layers using conventional optimization techniques, while preserving the possibility to use turning-point monitoring during their fabrication. Application of this method to the design of a dual narrowband filter and a tilted edge filter demonstrates its effectiveness.

OpenFilters: open-source software for the design, optimization, and synthesis of optical filters.

The design of optical filters relies on powerful computer-assisted methods. Many of these methods are provided by commercial programs, but, in order to adapt and improve them, or to develop new methods, one needs to create his own software. To help people interested in such a process, we decided to release our in-house software, called OpenFilters, under the GNU General Public License, an open-source license. It is programmed in Python and C++, and the graphical user interface is implemented with wxPython. It allows creation of multilayer and graded-index filters and calculation of reflection, transmission, absorption, phase, group delay, group delay dispersion, color, ellipsometric variables, admittance diagram, circle diagram, electric field distribution, and generation of reflection, transmission, and ellipsometric monitoring curves. It also provides the refinement, needle, step, and Fourier transform methods.

Dispersion implementation in optical filter design by the Fourier transform method using correction factors.

The Fourier transform method to design graded-index optical filters, that relates the desired reflection spectrum and the index profile through the use of a Q function, has two important drawbacks: (1) It relies on approximate Q functions, and (2) it does not account for the dispersion of the index of refraction. The former is usually addressed by an iterative correction process. We propose to address the latter by scaling the wavelength in the Fourier transform by the optical thickness of the filter and to multiply the Q function by a wavelength-dependent correction factor. We demonstrate the high effectiveness of this approach by the performance of optical filters designed with such correction factors using the optical properties of SiO2/TiO2 mixtures.

Design and plasma deposition of dispersion-corrected multiband rugate filters.

Inverse Fourier transform method has been commonly used for designing complex inhomogeneous optical coatings. Since it assumes dispersion-free optical constants, introducing real optical materials induces shifts in the position of reflectance bands in multiband inhomogeneous minus (rugate) filters. We propose a simple method for considering optical dispersion in the synthesis of multiband rugate filter designs. Model filters designed with this method were fabricated on glass and polycarbonate substrates by plasma-enhanced chemical vapor deposition of silicon oxynitrides and SiO2/TiO2 mixtures with precisely controlled composition gradients.