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

The Role of Optical Phonon Confinement in the Infrared Dielectric Response of III-V Superlattices

Polar dielectrics are key materials of interest for infrared (IR) nanophotonic applications due to their ability to host phonon-polaritons that allow for low-loss, subdiffractional control of light. The properties of phonon-polaritons are limited by the characteristics of optical phonons, which are nominally fixed for most "bulk" materials. Superlattices composed of alternating atomically thin materials offer control over crystal anisotropy through changes in composition, optical phonon confinement, and the emergence of new modes. In particular, the modified optical phonons in superlattices offer the potential for so-called crystalline hybrids whose IR properties cannot be described as a simple mixture of the bulk constituents. To date, however, studies have primarily focused on identifying the presence of new or modified optical phonon modes rather than assessing their impact on the IR response. This study focuses on assessing the impact of confined optical phonon modes on the hybrid IR dielectric function in superlattices of GaSb and AlSb. Using a combination of first principles theory, Raman, FTIR, and spectroscopic ellipsometry, the hybrid dielectric function is found to track the confinement of optical phonons, leading to optical phonon spectral shifts of up to 20 cm-1 . These results provide an alternative pathway toward designer IR optical materials.

A 220 GHz-1.1 THz continuous frequency and polarization tunable quasi-optical electron paramagnetic resonance spectroscopic system

Here, we describe a custom-designed quasi-optical system continuously operating in the frequency range 220 GHz to 1.1 THz with a temperature range of 5-300 K and magnetic fields up to 9 T capable of polarization rotation in both transmitter and receiver arms at any given frequency within the range through a unique double Martin-Puplett interferometry approach. The system employs focusing lenses to amplify the microwave power at the sample position and recollimate the beam to the transmission branch. The cryostat and split coil magnets are furnished with five optical access ports from all three major directions to the sample sitting on a two-axes rotatable sample holder capable of performing arbitrary rotations with respect to the field direction, enabling broad accessibility to experimental geometries. Initial results from test measurements on antiferromagnetic MnF₂ single crystals are included to verify the operation of the system.

Terahertz optical Hall effect in p-type monolayer hexagonal boron nitride on fused silica substrate

We demonstrate for the first time, to the best of our knowledge, that the optical Hall effect (OHE) can be observed in p-type monolayer (ML) hexagonal boron nitride (hBN) on a fused silica substrate by applying linearly polarized terahertz (THz) irradiation. When ML hBN is placed on fused silica, in which the incident pulsed THz field can create local and transient electromagnetic dipoles, proximity-induced interactions can be presented. The Rashba spin-orbit coupling can be enhanced, and the in-plane spin component can be induced, along with the lifting of valley degeneracy. Thus, in the presence of linearly polarized THz radiation, the nonzero transverse optical conductivity (or Hall conductivity) can be observed. We measure the THz transmission through ML hBN/fused silica in the temperature range from 80 to 280 K by using THz time-domain spectroscopy in combination with an optical polarization examination. The Faraday ellipticity and rotation angle, together with the complex longitudinal and transverse conductivities, are obtained. The temperature dependence of these quantities is examined. The results obtained from this work indicate that ML hBN is a valleytronic material, and proximity-induced interactions can lead to the observation of OHE in the absence of an external magnetic field.

Tunable cavity-enhanced terahertz frequency-domain optical Hall effect

Presented here is the development and demonstration of a tunable cavity-enhanced terahertz (THz) frequency-domain optical Hall effect (OHE) technique. The cavity consists of at least one fixed and one tunable Fabry-Pérot resonator. The approach is suitable for the enhancement of the optical signatures produced by the OHE in semi-transparent conductive layer structures with plane parallel interfaces. Tuning one of the cavity parameters, such as the external cavity thickness, permits shifting of the frequencies of the constructive interference and provides substantial enhancement of the optical signatures produced by the OHE. A cavity-tuning optical stage and gas flow cell are used as examples of instruments that exploit tuning an external cavity to enhance polarization changes in a reflected THz beam. Permanent magnets are used to provide the necessary external magnetic field. Conveniently, the highly reflective surface of a permanent magnet can be used to create the tunable external cavity. The signal enhancement allows the extraction of the free charge carrier properties of thin films and can eliminate the need for expensive superconducting magnets. Furthermore, the thickness of the external cavity establishes an additional independent measurement condition, similar to, for example, the magnetic field strength, THz frequency, and angle of incidence. A high electron mobility transistor (HEMT) structure and epitaxial graphene are studied as examples. The tunable cavity-enhancement effect provides a maximum increase of more than one order of magnitude in the change of certain polarization components for both the HEMT structure and epitaxial graphene at particular frequencies and external cavity sizes.

Mueller matrix ellipsometer using dual continuously rotating anisotropic mirrors

We demonstrate calibration and operation of a single wavelength (660 nm) Mueller matrix ellipsometer in normal transmission configuration using dual continuously rotating anisotropic mirrors. The mirrors contain highly spatially coherent nanostructure slanted columnar titanium thin films deposited onto optically thick gold layers on glass substrates. Upon rotation around the mirror normal axis, sufficient modulation of the Stokes parameters of light reflected at oblique angle of incidence is achieved. Thereby, the mirrors can be used as a polarization state generator and polarization state analyzer in a generalized ellipsometry instrument. A Fourier expansion approach is found sufficient to render and calibrate the effects of the mirror rotations onto the polarized light train within the ellipsometer. The Mueller matrix elements of a set of anisotropic samples consisting of a linear polarizer and a linear retarder are measured and compared with model data, and very good agreement is observed.

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.

Electromagnon excitation in cupric oxide measured by Fabry-Pérot enhanced terahertz Mueller matrix ellipsometry

Here we present the use of Fabry-Pérot enhanced terahertz (THz) Mueller matrix ellipsometry to measure an electromagnon excitation in monoclinic cupric oxide (CuO). As a magnetically induced ferroelectric multiferroic, CuO exhibits coupling between electric and magnetic order. This gives rise to special quasiparticle excitations at THz frequencies called electromagnons. In order to measure the electromagnons in CuO, we exploit single-crystal CuO as a THz Fabry-Pérot cavity to resonantly enhance the excitation’s signature. This enhancement technique enables the complex index of refraction to be extracted. We observe a peak in the absorption coefficient near 0.705 THz and 215 K, which corresponds to the electromagnon excitation. This absorption peak is observed along only one major polarizability axis in the monoclinic a–c plane. We show the excitation can be represented using the Lorentz oscillator model, and discuss how these Lorentz parameters evolve with temperature. Our findings are in excellent agreement with previous characterizations by THz time-domain spectroscopy (THz-TDS), which demonstrates the validity of this enhancement technique.

In-situ terahertz optical Hall effect measurements of ambient effects on free charge carrier properties of epitaxial graphene

Unraveling the doping-related charge carrier scattering mechanisms in two-dimensional materials such as graphene is vital for limiting parasitic electrical conductivity losses in future electronic applications. While electric field doping is well understood, assessment of mobility and density as a function of chemical doping remained a challenge thus far. In this work, we investigate the effects of cyclically exposing epitaxial graphene to controlled inert gases and ambient humidity conditions, while measuring the Lorentz force-induced birefringence in graphene at Terahertz frequencies in magnetic fields. This technique, previously identified as the optical analogue of the electrical Hall effect, permits here measurement of charge carrier type, density, and mobility in epitaxial graphene on silicon-face silicon carbide. We observe a distinct, nearly linear relationship between mobility and electron charge density, similar to field-effect induced changes measured in electrical Hall bar devices previously. The observed doping process is completely reversible and independent of the type of inert gas exposure.

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.

Optical Hall effect-model description: tutorial

The optical Hall effect is a physical phenomenon that describes the occurrence of magnetic-field-induced dielectric displacement at optical wavelengths, transverse and longitudinal to the incident electric field, and analogous to the static electrical Hall effect. The electrical Hall effect and certain cases of the optical Hall effect observations can be explained by extensions of the classic Drude model for the transport of electrons in metals. The optical Hall effect is most useful for characterization of electrical properties in semiconductors. Among many advantages, while the optical Hall effect dispenses with the need of electrical contacts, electrical material properties such as effective mass and mobility parameters, including their anisotropy as well as carrier type and density, can be determined from the optical Hall effect. Measurement of the optical Hall effect can be performed within the concept of generalized ellipsometry at an oblique angle of incidence. In this paper, we review and discuss physical model equations, which can be used to calculate the optical Hall effect in single- and multiple-layered structures of semiconductor materials. We define the optical Hall effect dielectric function tensor, demonstrate diagonalization approaches, and show requirements for the optical Hall effect tensor from energy conservation. We discuss both continuum and quantum approaches, and we provide a brief description of the generalized ellipsometry concept, the Mueller matrix calculus, and a 4×4 matrix algebra to calculate data accessible by experiment. In a follow-up paper, we will discuss strategies and approaches for experimental data acquisition and analysis.

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.

Magneto-optical Kramers-Kronig analysis

We describe a simple magneto-optical experiment and introduce a magneto-optical Kramers-Kronig analysis (MOKKA) that together allow extracting the complex dielectric function for left- and right-handed circular polarizations in a broad range of frequencies without actually generating circularly polarized light. The experiment consists of measuring reflectivity and Kerr rotation, or alternatively transmission and Faraday rotation, at normal incidence using only standard broadband polarizers without retarders or quarter-wave plates. In a common case, where the magneto-optical rotation is small (below ∼0.2 rad), a fast measurement protocol can be realized, where the polarizers are fixed at 45(∘) with respect to each other. Apart from the time-effectiveness, the advantage of this protocol is that it can be implemented at ultra-high magnetic fields and in other situations, where an in-situ polarizer rotation is difficult. Overall, the proposed technique can be regarded as a magneto-optical generalization of the conventional Kramers-Kronig analysis of reflectivity on bulk samples and the Kramers-Kronig constrained variational analysis of more complex types of spectral data. We demonstrate the application of this method to the textbook semimetals bismuth and graphite and also use it to obtain handedness-resolved magneto-absorption spectra of graphene on SiC.