Marco Rahm

Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations

The technique of applying form-invariant, spatial coordinate transformations of Maxwell’s equations can facilitate the design of structures with unique electromagnetic or optical functionality. Here, we illustrate the transformation-optical approach in the designs of a square electromagnetic cloak and an omni-directional electromagnetic field concentrator. The transformation equations are described and the functionality of the devices is numerically confirmed by two-dimensional finite element simulations. The two devices presented demonstrate that the transformation optic approach leads to the specification of complex, anisotropic and inhomogeneous materials with well directed and distinct electromagnetic behavior.

Transformation-optical design of adaptive beam bends and beam expanders

We describe the design of adaptive beam bends and beam splitters with arbitrary bend and split angles by use of finite embedded coordinate transformations. The devices do not exhibit reflection at the entrance or exit surfaces. It is shown that moderate and practically achievable values of the relative permittivity and permeability can be obtained for beam bends and splitters with both small and large bend radius. The devices are also discussed in the context of reconfigurable metamaterials, in which the bend and split angles can be dynamically tuned. The performance of adaptive beam bends and splitters is demonstrated in full wave simulations based on a finite-element method. Furthermore, the design of an adaptively adjustable transformation-optical beam expander/compressor is presented. It is observed that a pure transformation-optical design cannot result in a reflectionless beam expander/compressor.

Transformation-optical design of sharp waveguide bends and corners

Transformation optics is a recently appreciated approach for designing complex electromagnetic media. Here, we describe the extension of transformation optical techniques to include waveguide boundary conditions. We illustrate the use of finite embedded coordinate transformations to design a medium that can be incorporated into a waveguide bend or corner, rendering the structure reflectionless. The expected behavior of the waveguide bends is confirmed with numerical simulations.

Spectrally Wide-Band Terahertz Wave Modulator Based on Optically Tuned Graphene

New applications in the realms of terahertz (THz) technology require versatile adaptive optics and powerful modulation techniques. Semiconductors have proven to provide fast all-optical terahertz wave modulation over a wide frequency band. We show that the attenuation and modulation depth in optically driven silicon modulators can be significantly enhanced by deposition of graphene on silicon (GOS). We observed a wide-band tunability of the THz transmission in a frequency range from 0.2 to 2 THz and a maximum modulation depth of 99%. The maximum difference between the transmission through silicon and GOS is Δt = 0.18 at a low photodoping power of 40 mW. At higher modulation power, the enhancement decreased due to charge carrier saturation. We developed a semianalytical band structure model of the graphene-silicon interface to describe the observed attenuation and modulation depth in GOS.

Metamaterial-based gradient index lens with strong focusing in the THz frequency range

The development of innovative terahertz (THz) imaging systems has recently moved in the focus of scientific efforts due to the ability to screen substances through textiles or plastics. The invention of THz imaging systems with high spatial resolution is of increasing interest for applications in the realms of quality control, spectroscopy in dusty environment and security inspections. To realize compact THz imaging systems with high spatial resolution it is necessary to develop lenses of minimized thickness that still allow one to focus THz radiation to small spot diameters with low optical aberrations. In addition, it would be desirable if the lenses offered adaptive control of their optical properties to optimize the performance of the imaging systems in the context of different applications. Here we present the design, fabrication and the measurement of the optical properties of spectrally broadband metamaterial-based gradient index (GRIN) lenses that allow one to focus THz radiation to a spot diameter of approximately one wavelength. Due to the subwavelength thickness and the high focusing strength the presented GRIN lenses are an important step towards compact THz imaging systems with high spatial resolution. Furthermore, the results open the path to a new class of adaptive THz optics by extension of the concept to tunable metamaterials.

Polarization-independent active metamaterial for high-frequency terahertz modulation

We present a polarization-independent metamaterial design for the construction of electrically tunable terahertz (THz) devices. The implemented structure consists of an array of gold crosses fabricated on top of an n-doped gallium arsenide (GaAs) layer. Utilizing THz time-domain spectroscopy, we show that the electric resonance and thus the transmission properties of the cross structure can be tuned by an externally applied bias voltage. We further demonstrate the fast amplitude modulation of a propagating THz wave for modulation frequencies up to 100 kHz.

Metamaterial near-field sensor for deep-subwavelength thickness measurements and sensitive refractometry in the terahertz frequency range

We present a metamaterial-based terahertz (THz) sensor for thickness measurements of subwavelength-thin materials and refractometry of liquids and liquid mixtures. The sensor operates in reflection geometry and exploits the frequency shift of a sharp Fano resonance minimum in the presence of dielectric materials. We obtained a minimum thickness resolution of 12.5 nm (1/16 000 times the wavelength of the THz radiation) and a refractive index sensitivity of 0.43 THz per refractive index unit. We support the experimental results by an analytical model that describes the dependence of the resonance frequency on the sample material thickness and the refractive index.

Highly Selective Terahertz Bandpass Filters Based on Trapped Mode Excitation

We present two types of metamaterial-based spectral bandpass filters for the terahertz (THz) frequency range. The metamaterials are specifically designed to operate for waves at normal incidence and to be independent of the field polarization. The functional structures are embedded in films of benzocyclobutene (BCB) resulting in large-area, free-standing and flexible membranes with low intrinsic loss. The proposed filters are investigated by THz time-domain spectroscopy and show a pronounced transmission peak with over 80% amplitude transmission in the passband and a transmission rejection down to the noise level in the stopbands. The measurements are supported by numerical simulations which evidence that the high transmission response is related to the excitation of trapped modes.

Strongly birefringent metamaterials as negative index terahertz wave plates

We report an alternative approach for the design and fabrication of thin wave plates with high transmission in the terahertz regime. The wave plates are based on strongly birefringent cut-wire-pair metamaterials that exhibit refractive indices of opposite signs for orthogonal polarization components of an incident wave. As examples, we fabricated and investigated a quarter- and a half-wave plate with high intensity transmittance. The wave plates displayed a maximum figure of merit (FOM) of 23 at a frequency around 1.3 THz where the refractive index was n′=−1.7. This corresponds to one of the highest FOMs reported at terahertz frequencies.We report a new approach for the design and fabrication of thin wave plates with high transmission in the terahertz (THz) regime. The wave plates are based on strongly birefringent cut-wire pair metamaterials that exhibit refractive indices of opposite signs for two orthogonal polarization components of an incident wave. As specific examples, we fabricated and investigated a quarterand a half-wave plate that revealed a peak intensity transmittance of 74% and 58% at 1.34 THz and 1.3 THz, respectively. Furthermore, the half wave plate displayed a maximum figure of merit (FOM) of 23 at 1.3 THz where the refractive index was −1.7. This corresponds to one of the highest FOMs reported at THz frequencies so far. The presented results evidence that negative index materials enter an application stage in terms of optical components for the THz technology.

Material parameters and vector scaling in transformation acoustics

The degree to which the coordinate transformation concept first demonstrated for electromagnetic waves can be applied to other classes of waves remains an open question. In this work, we thoroughly examine the coordinate transformation invariance of acoustic waves. We employ a purely physical argument to show how the acoustic velocity vector must transform differently than the E and H fields in Maxwells equations, which explains why acoustic coordinate transformation invariance was not found in some previous analyses. A first principles analysis of the acoustic equations under arbitrary coordinate transformations confirms that the divergence operator is preserved only if velocity transforms in this physically correct way. This analysis also yields closed-form expressions for the bulk modulus and mass density tensor of the material required to realize an arbitrary coordinate transformation on the acoustic fields, which we show are equivalent to forms presented elsewhere. We demonstrate the computation of these material parameters in two specific cases and show that the change in velocity and pressure gradient vectors under a nonorthogonal coordinate transformation is precisely how these vectors must change from purely physical arguments. This analysis confirms that all of the electromagnetic devices and materials that have been conceived using the coordinate transformation approach are also in principle realizable for acoustic