Transformation Optics Technique Research Articles

Description of van der Waals Interactions Using Transformation Optics

Exact calculation of the van der Waals interaction between closely spaced plasmonic nanoparticles is challenging due to the strong concentration of the electromagnetic fields that takes place at the nanometric gap between them. The technique of transformation optics, capable of mapping a small volume into any desired length scale, enables us to shed physical insight into the intricate behavior of electromagnetic fields in extremely small gaps. Using this theoretical tool, we obtain universal analytical expressions for the van der Waals interactions between spherical nanoparticles made of realistic metals at arbitrary separation.

Rigorous analysis of axisymmetric transformation optics lenses embedded in layered media illuminated by obliquely incident plane waves

ABSTRACTA body of revolution, finite‐difference time‐domain (BOR‐FDTD) method is developed for rigorous analysis of axisymmetric transformation optics (TO) lens devices. For normal incidence, a one dimensional (1‐D) FDTD method based on the total‐field scattered‐field (TFSF) technique was proposed to model the propagation of a plane wave launched from the top of a layered medium in cylindrical coordinates. The 1‐D FDTD solutions were employed to efficiently inject normally incident plane waves into the BOR‐FDTD method. For oblique incidence, analytical formulations were derived and presented by expanding the plane wave into a series of cylindrical modes via Fourier series expansion of the ϕ‐dependent variables, which were then used to introduce obliquely incident plane waves into the TFSF formulas associated with the BOR‐FDTD method. These procedures allowed for accurate simulations of BOR TO lenses embedded in layered media illuminated by obliquely incident waves. The accuracy and efficiency of the proposed method were verified by comparing numerical results with either analytical solutions or a commercial software (COMSOL) package. Thereafter, the developed BOR‐FDTD code was utilized to study the imaging properties of (a) radial gradient‐index (GRIN) lenses with a parabolic index profile, (b) a flat TO GRIN lens, (c) a spherical Luneburg lens, and (d) a cylindrical TO Luneburg lens both in free space and on top of a substrate. Here the TO GRIN lenses were designed by using the quasi‐conformal transformation optics (QCTO) technique. It was found that the flat TO lens was able to provide identical focusing properties as a cemented doublet in both free space and over a dielectric substrate. Moreover, the numerical results demonstrated that the flattened TO Luneburg lens possessed the desired imaging properties under different illuminations for both polarizations.

Integrated photonic systems based on transformation optics enabled gradient index devices

Integrated photonics is expected to play an increasingly important role in optical communications, imaging, computing and sensing with the promise for significant reduction in the cost and weight of these systems. Future advancement of this technology is critically dependent on an ability to develop compact and reliable optical components and facilitate their integration on a common substrate. Here we reveal, with the utility of the emerging transformation optics technique, that functional components composed of planar gradient index materials can be designed and readily integrated into photonic circuits. The unprecedented design flexibility of transformation optics allows for the creation of a number of novel devices, such as a light source collimator, waveguide adapters and a waveguide crossing, which have broad applications in integrated photonic chips and are compatible with current fabrication technology. Using the finite-difference time-domain method, we perform full-wave numerical simulations to demonstrate their superior optical performance and efficient integration with other components in an on-chip photonic system. These components only require spatially-varying dielectric materials with no magnetic properties, facilitating low-loss, broadband operation in an integrated photonic environment.

Covariant description of transformation optics in nonlinear media

The technique of transformation optics (TO) is an elegant method for the design of electromagnetic media with tailored optical properties. In this paper, we focus on the formal structure of TO theory. By using a complete covariant formalism, we present a general transformation law that holds for arbitrary materials including bianisotropic, magneto-optical, nonlinear and moving media. Due to the principle of general covariance, the formalism is applicable to arbitrary space-time coordinate transformations and automatically accounts for magneto-electric coupling terms. The formalism is demonstrated for the calculation of the second harmonic wave generation in a twisted TO concentrator.

Steering Phased Array Antenna Beams to the Horizon Using a Buckyball NIM Lens

In this paper, we present the design, optimization, fabrication, and measurement of a negative index metamaterial (NIM) buckyball shell lens to steer phased array antenna (PAA) beams to the horizon. The conformal mapping technique of transformation optics is utilized in the design process to facilitate with lens fabrication. A new dual polarization unit cell is designed to avoid the issues associated with short cut wires, were a split ring resonator (SRR) and wire design to be used. The lens is measured using an actual PAA and it demonstrates to-the-horizon scanning as designed, although the material loss is high. An improved unit cell design is proposed to reduce several known loss mechanisms. A new lens design methodology using Bezier curves as seed surfaces is also described.

Broadband Wide Angle Lens Implemented with Dielectric Metamaterials

The Luneburg lens is a powerful imaging device, exhibiting aberration free focusing for parallel rays incident from any direction. However, its advantages are offset by a focal surface that is spherical and thus difficult to integrate with standard planar detector and emitter arrays. Using the recently developed technique of transformation optics, it is possible to transform the curved focal surface to a flat plane while maintaining the perfect focusing behavior of the Luneburg over a wide field of view. Here we apply these techniques to a lesser-known refractive Luneburg lens and implement the design with a metamaterial composed of a semi-crystalline distribution of holes drilled in a dielectric. In addition, we investigate the aberrations introduced by various approximations made in the implementation of the lens. The resulting design approach has improved mechanical strength with small aberrations and is ideally suited to implementation at infrared and visible wavelengths.

Multilayer <formula formulatype="inline"> <tex Notation="TeX">$W$</tex> </formula>-Band Artificial Dielectric on Liquid Crystal Polymer

We present an artificial dielectric material designed to operate at W-band millimeter-wave frequencies. The artificial dielectric exhibits a wide range of variation in its effective refractive index, making it suitable for use in planar gradient index (GRIN) microwave lenses and other quasi-optical devices. These devices include those designed using recently developed transformation optics techniques. Because the artificial materials are designed to be nonresonant, their effective refractive indices display very low dispersion with frequency; simulation and measurement results for a number of test samples are presented that confirm the expected broad bandwidth properties. A comparison between the expected and experimentally determined indices-of-refraction for these samples further reveals close, quantitative agreement.

Conformal mappings to achieve simple material parameters for transformation optics devices

The transformation optics technique for designing novel electromagnetic and optical devices offers great control over wave behavior, but is difficult to implement primarily due to limitations in current metamaterial design and fabrication techniques. This paper demonstrates that restricting the spatial transformation to a conformal mapping can lead to much simpler material parameters for more practical implementation. As an example, a flat cylindrical-to-plane-wave conversion lens is presented and its performance validated through numerical simulations. It is shown that the lens dimensions and embedded source location can be adjusted to produce one, two, or four highly directive planar beams. Two metamaterial designs for this lens that implement the required effective medium parameters are proposed and their behavior analyzed.

Transformation optical designs for wave collimators, flat lenses and right-angle bends

The transformation optics technique is applied to design three novel devices—a wave collimator, far-zone and near-zone focusing flat optical lenses and a right-angle bend for propagating beam fields. The structures presented in this paper are all two-dimensional (2D), however, the transformation optics design methodologies can be easily extended to develop 3D versions of these optical devices. The required values of the permittivity and the permeability tensors are derived for each of the three devices considered here. Furthermore, the functional performance of each device is verified using full-wave electromagnetic simulations. A wave collimator consists of a 2D rectangular cylinder where the fields (cylindrical waves) radiated by an embedded line source emerge normal to the top and bottom planar interfaces thereby producing highly directive collimated fields. Next, a far-zone focusing lens for a 2D line source is created by transforming the equi-amplitude equi-phase contour to a planar surface. It is also demonstrated that by aligning two far-zone focusing flat lenses in a back-to-back configuration, a near-zone focusing lens is obtained. Finally, a 2D square cylindrical volume is transformed into a cylinder with a fan-shaped cross section to design a right-angle bend device for propagating beam fields.

Polarization splitter and polarization rotator designs based on transformation optics

The transformation optics technique is employed in this paper to design two optical devices - a two-dimensional polarization splitter and a three-dimensional polarization rotator for propagating beams. The polarization splitter translates the TM- and the TE-polarized components of an incident beam in opposite directions (i.e., shifted up or shifted down). The polarization rotator rotates the polarization state of an incoming beam by an arbitrary angle. Both optical devices are reflectionless at the entry and exit interfaces. Design details and full-wave simulation results are provided.