Terahertz-frequency dielectric anisotropy in three-dimensional polymethacrylates fabricated by stereolithography

The anisotropic optical dielectric functions of slanted columnar layers fabricated using polymethacrylate based stereolithography are reported for the terahertz-frequency domain using generalized spectroscopic ellipsometry. The slanted columnar layers are composed of spatially coherent columnar structures with a diameter of 100 µm and a length of 700 µm that are tilted by 45° with respect to the surface normal of the substrates. A simple biaxial (orthorhombic) layer homogenization approach is used to analyze the terahertz ellipsometric data obtained at three different sample azimuthal orientations. The permittivity along the major polarizability directions varies by almost 25%. Our results demonstrate that stereolithography allows tailoring of the polarizability and anisotropy of the host material, and provides a flexible alternative metamaterials fabrication method for the terahertz spectral range.

Anisotropic contrast optical microscope

An optical microscope is described that reveals contrast in the Mueller matrix images of a thin, transparent, or semi-transparent specimen located within an anisotropic object plane (anisotropic filter). The specimen changes the anisotropy of the filter and thereby produces contrast within the Mueller matrix images. Here we use an anisotropic filter composed of a semi-transparent, nanostructured thin film with sub-wavelength thickness placed within the object plane. The sample is illuminated as in common optical microscopy but the light is modulated in its polarization using combinations of linear polarizers and phase plate (compensator) to control and analyze the state of polarization. Direct generalized ellipsometry data analysis approaches permit extraction of fundamental Mueller matrix object plane images dispensing with the need of Fourier expansion methods. Generalized ellipsometry model approaches are used for quantitative image analyses. These images are obtained from sets of multiple images obtained under various polarizer, analyzer, and compensator settings. Up to 16 independent Mueller matrix images can be obtained, while our current setup is limited to 11 images normalized by the unpolarized intensity. We demonstrate the anisotropic contrast optical microscope by measuring lithographically defined micro-patterned anisotropic filters, and we quantify the adsorption of an organic self-assembled monolayer film onto the anisotropic filter. Comparison with an isotropic glass slide demonstrates the image enhancement obtained by our method over microscopy without the use of an anisotropic filter. In our current instrument, we estimate the limit of detection for organic volumetric mass within the object plane of ≈49 fg within ≈7 × 7 μm² object surface area. Compared to a quartz crystal microbalance with dissipation instrumentation, where contemporary limits require a total load of ≈500 pg for detection, the instrumentation demonstrated here improves sensitivity to a total mass required for detection by 4 orders of magnitude. We detail the design and operation principles of the anisotropic contrast optical microscope, and we present further applications to the detection of nanoparticles, to novel approaches for imaging chromatography and to new contrast modalities for observations on living cells.

Cavity-enhanced optical Hall effect in two-dimensional free charge carrier gases detected at terahertz frequencies

The effect of a tunable, externally coupled Fabry-Perot cavity to resonantly enhance the optical Hall effect signatures at terahertz frequencies produced by a traditional Drude-like two-dimensional electron gas is shown and discussed in this Letter. As a result, the detection of optical Hall effect signatures at conveniently obtainable magnetic fields, for example, by neodymium permanent magnets, is demonstrated. An AlInN/GaN-based high-electron mobility transistor structure grown on a sapphire substrate is used for the experiment. The optical Hall effect signatures and their dispersions, which are governed by the frequency and the reflectance minima and maxima of the externally coupled Fabry-Perot cavity, are presented and discussed. Tuning the externally coupled Fabry-Perot cavity strongly modifies the optical Hall effect signatures, which provides a new degree of freedom for optical Hall effect experiments in addition to frequency, angle of incidence, and magnetic field direction and strength.

Invited article: An integrated mid-infrared, far-infrared, and terahertz optical Hall effect instrument

We report on the development of the first integrated mid-infrared, far-infrared, and terahertz optical Hall effect instrument, covering an ultra wide spectral range from 3 cm(-1) to 7000 cm(-1) (0.1-210 THz or 0.4-870 meV). The instrument comprises four sub-systems, where the magneto-cryostat-transfer sub-system enables the usage of the magneto-cryostat sub-system with the mid-infrared ellipsometer sub-system, and the far-infrared/terahertz ellipsometer sub-system. Both ellipsometer sub-systems can be used as variable angle-of-incidence spectroscopic ellipsometers in reflection or transmission mode, and are equipped with multiple light sources and detectors. The ellipsometer sub-systems are operated in polarizer-sample-rotating-analyzer configuration granting access to the upper left 3 × 3 block of the normalized 4 × 4 Mueller matrix. The closed cycle magneto-cryostat sub-system provides sample temperatures between room temperature and 1.4 K and magnetic fields up to 8 T, enabling the detection of transverse and longitudinal magnetic field-induced birefringence. We discuss theoretical background and practical realization of the integrated mid-infrared, far-infrared, and terahertz optical Hall effect instrument, as well as acquisition of optical Hall effect data and the corresponding model analysis procedures. Exemplarily, epitaxial graphene grown on 6H-SiC, a tellurium doped bulk GaAs sample and an AlGaN/GaN high electron mobility transistor structure are investigated. The selected experimental datasets display the full spectral, magnetic field and temperature range of the instrument and demonstrate data analysis strategies. Effects from free charge carriers in two dimensional confinement and in a volume material, as well as quantum mechanical effects (inter-Landau-level transitions) are observed and discussed exemplarily.

Polarization selection rules for inter-Landau-level transitions in epitaxial graphene revealed by the infrared optical Hall effect

We report on the polarization selection rules of inter-Landau-level transitions using reflection-type optical Hall effect measurements from 600 to 4000 cm(-1) on epitaxial graphene grown by thermal decomposition of silicon carbide. We observe symmetric and antisymmetric signatures in our data due to polarization preserving and polarization mixing inter-Landau-level transitions, respectively. From field-dependent measurements, we identify that transitions in coupled graphene monolayers are governed by polarization mixing selection rules, whereas transitions in decoupled graphene monolayers are governed by polarization preserving selection rules. The selection rules may find explanation by different coupling mechanisms of inter-Landau-level transitions with free charge carrier magneto-optic plasma oscillations.

Variable-wavelength frequency-domain terahertz ellipsometry

We report an experimental setup for wavelength-tunable frequency-domain ellipsometric measurements in the terahertz spectral range from 0.2 to 1.5 THz employing a desktop-based backward wave oscillator source. The instrument allows for variable angles of incidence between 30 degrees and 90 degrees and operates in a polarizer-sample-rotating analyzer scheme. The backward wave oscillator source has a tunable base frequency of 107-177 GHz and is augmented with a set of Schottky diode frequency multipliers in order to extend the spectral range to 1.5 THz. We use an odd-bounce image rotation system in combination with a wire grid polarizer to prepare the input polarization state. A highly phosphorous-doped Si substrate serves as a first sample model system. We show that the ellipsometric data obtained with our novel terahertz ellipsometer can be well described within the classical Drude model, which at the same time is in perfect agreement with midinfrared ellipsometry data obtained from the same sample for comparison. The analysis of the terahertz ellipsometric data of a low phosphorous-doped n-type Si substrate demonstrates that ellipsometry in the terahertz spectral range allows the determination of free charge-carrier properties for electron concentrations as low as 8x10(14) cm(-3).

Computation, visualization, and animation of infrared Mueller matrix elements by scattering from surfaces that are absorbing and randomly rough

Computation of Mueller matrix elements by infrared scattering from randomly rough two-dimensional surfaces and results of a method for graphic display of the data are presented. A full wave electromagnetic scattering model first generates raw data elements of the 4 × 4 Mueller matrix F(θ, nλ, kλ, σs(2), ?h(2)?) in beam backscattering angle (θ) ranging from normal to oblique incidence, in refractive index of the beam scatterer (nλ - ikλ) spanning the 9 ≤ λ ≤ 12.5 µm midinfrared band, and in mean-squared slope ((σS(2)) and mean-squared height (?h(2)?) of the scattering surface. These data are next compressed into a graphics format file occupying considerably less computer storage space and mapped into color images of the Mueller elements as viewed on a high-resolution graphics terminal. The diagonal and two off-diagonal elements are animated in the λ-θ plane according to varitions in σs(2) and ?h(2)?. Predicted elements for polarized IR beam energies on vibrational resonance of the surface molecules, and particularly the off-diagonal elements, show subtle properties of the scatterer as viewed in the animation sequences.