arXiv subjects

Mathias Schubert

Publications and source records attributed to Mathias Schubert.

At least 19 recordsLinked to original sources

arXiv2025

Self-induced nonreciprocity from asymmetric photonic topological insulators

Photonic topological insulators and self-induced nonreciprocity based on nonlinear effects in asymmetric structures have garnered increased attention due to their potential applications in quantum information technologies and advanced photonic integrated circuits. In this study, we combine these two fields and present asymmetric photonic crystal designs based on all-dielectric checkerboard structures forming topological interfaces. The resulting topological photonic structures lead to the emergence of a narrowband leaky mode in their linear transmission response accompanied by an edge state with topological protection. The incorporation of the nonlinear optical Kerr effect in the system results to spectral tunability and transmission nonreciprocity in the induced topological edge states as the input beam intensity is increased due to the introduction of asymmetric defects along the interface. We envision that the findings presented in our work will lead to tunable photonic topological insulators with nonreciprocal response that promise to provide new avenues for the development of next-generation photonic devices and quantum optical technologies.

physics.optics↗

arXiv2025

Spectral tuning of hyperbolic shear polaritons in monoclinic gallium oxide via isotopic substitution

Hyperbolic phonon polaritons - hybridized modes arising from the ultrastrong coupling of infrared light to strongly anisotropic lattice vibrations in uniaxial or biaxial polar crystals - enable to confine light to the nanoscale with low losses and high directionality. In even lower symmetry materials, such as monoclinic $\beta$-Ga$_2$O$_3$ (bGO), hyperbolic shear polaritons (HShPs) further enhance the directionality. Yet, HShPs are intrinsically supported only within narrow frequency ranges defined by the phonon frequencies of the host material. Here, we report spectral tuning of HShPs in bGO by isotopic substitution. Employing near-field optical microscopy to image HShPs in $^{18}$O bGO films homo-epitaxially grown on a $^{16}$O bGO substrate, we demonstrate a spectral redshift of $\sim~40~$cm$^{-1}$ for the $^{18}$O bGO, compared to $^{16}$O bGO. The technique allows for direct observation and a model-free estimation of the spectral shift driven by isotopic substitution without the need for knowledge of the dielectric tensor. Complementary far-field measurements and ab initio calculations - in good agreement with the near-field data - confirm the effectiveness of this estimation. This multifaceted study demonstrates a significant isotopic substitution induced spectral tuning of HShPs into a previously inaccessible frequency range, creating new avenues for technological applications of such highly directional polaritons.

physics.optics↗

arXiv2025

Terahertz frequency-domain 4x4 Mueller matrix ellipsometer instrument designed for high-frequency magnetic resonance measurements

We report a Mueller matrix ellipsometer design using dual continuously rotating anisotropic meta wave plates which determines the full set of Mueller matrix elements in the terahertz spectral range. The instrument operates in the frequency domain and employs a frequency tunable, solid state synthesizer based, continuous wave terahertz source with sub-MHz bandwidth. The implemented source permits operation within 82-125 GHz and 170-250 GHz, without and with an additional frequency doubler, respectively. The terahertz transparent meta wave plates consist of 3D-printed polymer based columnar thin film structures with subwavelength dimensions. The rotating wave plates produce sufficient modulation of the Stokes vector components of transmitted terahertz light to use the wave plates in polarization state generator and polarization state detector devices. Fast terahertz light detection rate of a quasi optical solid state detector permits acquisition with few microsecond temporal resolution and electronic sweeping control of the source frequency. We develop a fast frequency sweeping scheme while continuously rotating the terahertz wave plates. Subsequent sorting of measured data permits measurements of Mueller matrix elements at hundreds of different wavelengths. The Mueller matrix elements are obtained by forward numerical reduction of the measured data using an algorithm developed by Ruder et al.[Opt. Lett. 45, 3541 (2020)]. The instrument is combined with a magnetocryostat capable of reaching magnetic field strengths at the sample position of -8 T...8 T and sample temperatures from 4 K...400 K. Hence, the instrument is suitable to measure the full Mueller matrix of samples with magnetic resonances as demonstrated recently by Rindert et al. [Phys. Rev. B 110, 054413 (2024)]. We discuss design, calibration, and example applications.

physics.ins-det↗

arXiv2024

Origin of the Anisotropic Beer-Lambert Law from Dichroism and Birefringence in $\beta$-Ga$_2$O$_3$

The anisotropic optical absorption edge of $\beta$-Ga$_2$O$_3$ follows a modified Beer-Lambert law having two effective absorption coefficients. The absorption coefficient of linearly polarized light reduces to the least absorbing direction beyond a critical penetration depth, which itself depends on polarization and wavelength. To understand this behavior, a Stokes vector analysis is performed to track the polarization state as a function of depth. The weakening of the absorption coefficient is associated with a gradual shift of linear polarization to the least absorbing crystallographic direction in the plane, which is along the a-exciton within the (010) plane or along the b-exciton in the (001) plane. We show that strong linear dichroism near the optical absorption edge causes this shift in $\beta$-Ga$_2$O$_3$, which arises from the anisotropy and spectral splitting of the physical absorbers i.e., excitons. The linear polarization shift is accompanied by a variation in the ellipticity due to the birefringence of $\beta$-Ga$_2$O$_3$. Analysis of the phase relationship between the incoming electric field to that at a certain depth reveals the phase speed as an effective refractive index, which varies along different crystallographic directions. The critical penetration depth is shown to be correlated with the depth at which the ellipticity is maximal. Thus, the anisotropic Beer-Lambert law arises from the interplay of both the dichroic and birefringent properties of $\beta$-Ga$_2$O$_3$.

cond-mat.mtrl-sci↗

arXiv2024

The strain-stress relationships for coherent in-plane strain in heterostructures with monoclinic crystal systems: $\beta$-(Al$_x$Ga$_{1-x}$)$_2$O$_3$ on $(h0l)$ $\beta$-Ga$_2$O$_3$ as example

In this work we derive the state of strain or stress under symmetry conserving conditions in pseudomorphic lattices with monoclinic symmetry. We compare surface vectors across the template epitaxial layer interface and impose conditions of a stress free epitaxial layer. As a result, we demonstrate the existence, in theory, of exactly three possible unit cells which can establish onto a given template. We demonstrate this approach for a class of templates with $(h0l)$ planes and $\beta$-(Al$_x$Ga$_{1-x}$)$_2$O$_3$ on $(h0l)$ $\beta$-Ga$_2$O$_3$. We discuss the effects of composition $x$ and surface orientation onto the formation of three elastically stable unit cells, their strain and stress tensors, unit cell axes, unit cell volumes, lattice spacing, elastic potential energies, and stress free directions. The previous paradigm for epitaxial layer growth where the stress free direction is always perpendicular to the growing surface is not generally valid for low symmetry materials. In the example here, we find two possible competing domains with stress free direction oblique to the surface of the template for almost all planes $(h0l)$. We calculate the band-to-band transitions for $\beta$-(Al$_{0.1}$Ga$_{0.9}$)$_2$O$_3$ on $(h0l)$ $\beta$-Ga$_2$O$_3$ using the composition dependent deformation parameters and elastic coefficients reported prevoiously [Korlacki~\textit{et al.} Phys. Rev. Appl.~\textbf{18}, 064019 (2022)].

cond-mat.mtrl-sci↗

arXiv2024

The paramagnetic Lyddane-Sachs-Teller relation

In this letter, we derive an expression for magnetic dipole transitions that is analogous to the Lyddane-Sachs-Teller relation for dielectric polar lattice vibrations. We thereby define transverse and longitudinal optical frequencies at which paramagnetic resonance and antiresonance occurs, respectively. The relation found here thus permits non-invasive optical analysis of static magnetization properties in paramagnetic materials. Validated through terahertz electron paramagnetic resonance ellipsometry and superconducting quantum interference device measurements on Iron-doped Gallium Nitride, our findings show very good agreement between theory and experiment. We term the excitations associated with the paramagnetic transitions as paramagnetic polaritons which may find use in future photonic applications

cond-mat.mtrl-sci↗

arXiv2024

Plasmonic Nanocavity to Boost Single Photon Emission from Defects in Thin Hexagonal Boron Nitride

Efficient and compact single photon emission platforms operating at room temperature with ultrafast speed and high brightness will be fundamental components of the emerging quantum communications and computing fields. However, so far, it is very challenging to design practical deterministic single photon emitters based on nanoscale solid-state materials that meet the fast emission rate and strong brightness demands. Here, a solution is provided to this longstanding problem by using metallic nanocavities integrated with hexagonal boron nitride (hBN) flakes with defects acting as nanoscale single photon emitters (SPEs) at room temperature. The presented hybrid nanophotonic structure creates a rapid speedup and large enhancement in single photon emission at room temperature. Hence, the nonclassical light emission performance is substantially improved compared to plain hBN flakes and hBN on gold-layered structures without nanocavity. Extensive theoretical calculations are also performed to accurately model the new hybrid nanophotonic system and prove that the incorporation of plasmonic nanocavity is key to efficient SPE performance. The proposed quantum nanocavity single photon source is expected to be an element of paramount importance to the envisioned room-temperature integrated quantum photonic networks.

physics.optics↗

arXiv2024

Bloch equations in Terahertz magnetic-resonance ellipsometry

A generalized approach derived from Blochs equation of motion of nuclear magnetic moments is presented to model the frequency, magnetic field, spin density, and temperature dependencies in the electromagnetic permeability tensor for materials with magnetic resonances. The resulting tensor model predicts characteristic polarization signatures which can be observed, for example, in fully polarization-resolved Mueller matrix element spectra measured across magnetic resonances as a function of frequency, magnetic field, magnetic moment density, and temperature. When augmented with thermodynamic considerations and suitable Hamiltonian description of the magnetic eigenvalue spectrum, important parameters such as zero-frequency magnetization, spectral amplitude distribution, relaxation time constants, and geometrical orientation parameters of the magnetic moment density can be obtained from comparing the generalized model approach to experimental data. We demonstrate our approach by comparing model calculations with full Mueller matrix element spectra measured at oblique angle of incidence in the terahertz spectral range, across electron spin resonance quintuplet transitions observed in wurtzite-structure GaN doped with iron. Measurements were performed by ellipsometry, using a superconducting cryostat magnet at magnetic fields of 7.23 T and at temperatures of 20 K and 30 K. We detail the occurrence of linear and circular birefringence and dichroism associated with each of the zero-field split spin transitions in the S = 5/2 defect system. We derive the spectral dependence of the magnetic susceptibility function and obtain the temperature and magnetic field dependence of the spin Hamiltonian. Our model correctly predicts the complexity of the polarization signatures observed in the 15 independent elements of the normalized Mueller matrix for both positive and negative magnetic fields.

cond-mat.mtrl-sci↗

arXiv2024

Effective uniaxial dielectric function tensor and optical phonons in ($\bar{2}01$)-plane oriented $\beta$-Ga$_2$O$_3$ films with equally-distributed six-fold rotation domains

Monoclinic $\beta$-Ga$_2$O$_3$ films grown on $c$-plane sapphire have been shown to exhibit six $(\bar{2}01)$-plane oriented domains, which are equally-spaced-by-rotation around the surface normal and equally-sized-by-volume that render the film optical response effectively uniaxial. We derive and discuss an optical model suitable for ellipsometry data analysis of such films. We model mid- and far-infrared ellipsometry data from undoped and electrically insulating films with an effective uniaxial dielectric tensor based on projections of all phonon modes within the rotation domains parallel and perpendicular to the sample normal, i.e., to the reciprocal lattice vector $\mathbf{g}_{\bar{2}01}$. Two effective response functions are described by model, and found sufficient to calculate ellipsometry data that best-match measured ellipsometry data from a representative film. We propose to render either effective dielectric functions, or inverse effective dielectric functions, each separately for electric field directions parallel and perpendicular to $\mathbf{g}_{\bar{2}01}$, by sums of Lorentz oscillators, which permit to determine either sets of transverse optical phonon mode parameters, or sets of longitudinal optical phonon mode parameters, respectively. Transverse optical modes common to both dielectric functions can be traced back to single crystal modes with $B_{\mathrm{u}}$ character, while modes with $A_{\mathrm{u}}$ character only appear within the dielectric function for polarization perpendicular to the sample surface. The thereby obtained parameter sets reveal all phonon modes anticipated from averaging over the six-fold rotation domains of single crystal $\beta$-Ga$_2$O$_3$, but with slightly shifted transverse optical, and completely different longitudinal optical phonon modes.

cond-mat.mtrl-sci↗

arXiv2024

Controlling the broadband enhanced light chirality with L-shaped dielectric metamaterials

The inherently weak chiroptical responses of natural materials limit their usage for controlling and enhancing chiral light-matter interactions. Recently, several nanostructures with subwavelength scale dimensions were demonstrated, mainly due to the advent of nanofabrication technologies, as a potential alternative to efficiently enhance chirality. However, the intrinsic lossy nature of metals and inherent narrowband response of dielectric planar thin films or metasurface structures pose severe limitations toward the practical realization of broadband and tailorable chiral systems. Here, we tackle these problems by designing all-dielectric silicon-based L-shaped optical metamaterials based on tilted nanopillars that exhibit broadband and enhanced chiroptical response in transmission operation. We use an emerging bottom-up fabrication approach, named glancing angle deposition, to assemble these dielectric metamaterials on a wafer scale. The reported strong chirality and optical anisotropic properties are controllable in terms of both amplitude and operating frequency by simply varying the shape and dimensions of the nanopillars. The presented nanostructures can be used in a plethora of emerging nanophotonic applications, such as chiral sensors, polarization filters, and spin-locked nanowaveguides.

physics.optics↗

arXiv2023

Nanocolumnar Material Platforms:Universal structural parameters revealed from optical anisotropy

Nanostructures represent a frontier where meticulous attention to the control and assessment of structural dimensions becomes a linchpin for their seamless integration into diverse technological applications. By using integrative and comprehensive methodical series of studies, we investigate the evolution of the depolarization factors in the anisotropic Bruggeman effective medium approximation, that are extremely sensitive to the changes in critical dimensions of the nanostructure platforms. To this end, we fabricate spatially coherent highly-ordered slanted nanocolumns from zirconia, silicon, titanium, and permalloy on silicon substrates with varying column lengths using glancing angle deposition. In tandem, broad-spectral range Mueller matrix spectroscopic ellipsometry data, spanning from the near-infrared to the vacuum ultraviolet (0.72 eV to 6.5 eV), is analyzed with a best-match model approach based on the anisotropic Bruggeman effective medium theory. We thereby extracted the anisotropic optical properties including complex dielectric function, birefringence, and dichroism. Most notably, our research unveils a universal, material-independent inverse relationship between depolarization factors and column length. We envision that the presented universal relationship will permit accurate prediction of optical properties of nanocolumnar thin films improving their integration and optimization for optoelectronic and photonic device applications.

physics.optics↗

arXiv2023

Quantum Composites with the Functionality Defined by the Charge-Density-Wave Phase Transitions

We demonstrate a unique class of advanced materials - quantum composites based on polymers with fillers comprised of a van der Waals quantum material that reveals multiple charge-density-wave quantum condensate phases. Materials that exhibit quantum phenomena are typically crystalline, pure, and have few defects because disorder destroys the coherence of the electrons and phonons, leading to collapses of the quantum states. We succeeded in preserving the macroscopic charge-density-wave phases of filler particles after multiple composite processing steps. The prepared composites manifest strong charge-density-wave phenomena even above room temperature. The dielectric constant experiences more than two orders of magnitude enhancement while the material maintains its electrically insulating properties, opening a venue for advanced applications in energy storage and electronics. The results present a conceptually different approach for engineering the properties of materials, extending the application domain for van der Waals materials.

cond-mat.mtrl-sci↗

arXiv2022

Remote Surface Optical Phonon Scattering in Ferroelectric Ba$_{0.6}$Sr$_{0.4}$TiO$_{3}$ Gated Graphene

We report the effect of remote surface optical (RSO) phonon scattering on carrier mobility in monolayer graphene gated by ferroelectric oxide. We fabricate monolayer graphene transistors back-gated by epitaxial (001) Ba$_{0.6}$Sr$_{0.4}$TiO$_{3}$ films, with field effect mobility up to 23,000 cm$^{2}$V$^{-1}$s$^{-1}$ achieved. Switching the ferroelectric polarization induces nonvolatile modulation of resistance and quantum Hall effect in graphene at low temperatures. Ellipsometry spectroscopy studies reveal four pairs of optical phonon modes in Ba$_{0.6}$Sr$_{0.4}$TiO$_{3}$, from which we extract the RSO phonon frequencies. The temperature dependence of resistivity in graphene can be well accounted for by considering the scattering from the intrinsic longitudinal acoustic phonon and the RSO phonon, with the latter dominated by the mode at 35.8 meV. Our study reveals the room temperature mobility limit of ferroelectric-gated graphene transistors imposed by RSO phonon scattering.

cond-mat.mes-hall↗

arXiv2022

Strain and composition dependencies of the near bandgap optical transitions in monoclinic (Al$_x$Ga$_{1-x}$)$_2$O$_3$ alloys with coherent biaxial in-plane strain on (010) Ga$_2$O$_3$

The bowing of the energy of the three lowest band-to-band transitions in $\beta$-(Al$_{x}$Ga$_{1-x}$)$_2$O$_3$ alloys was resolved using a combined density functional theory (DFT) and generalized spectroscopic ellipsometry (GSE) approach. The DFT calculations of the electronic band structure of both, $\beta$-Ga$_2$O$_3$ and $\theta$-Al$_2$O$_3$, allow extracting of the linear portion of the energy shift in the alloys, and provide a method for quantifying the role of coherent strain present in the $\beta$-(Al$_{x}$Ga$_{1-x}$)$_2$O$_3$ thin films on (010) $\beta$-Ga$_2$O$_3$ substrates. The energies of band-to-band transitions were obtained using the spectroscopic ellipsometry eigenpolarization model approach [A. Mock et al., Phys. Rev. B 95, 165202 (2017)]. After subtracting the effects of strain which also induces additional bowing and after subtraction of the linear portion of the energy shift due to alloying, the bowing parameters associated with the three lowest band-to-band transitions in monoclinic $\beta$-(Al$_{x}$Ga$_{1-x}$)$_2$O$_3$ are found.

cond-mat.mtrl-sci↗

arXiv2022

Terahertz electron paramagnetic resonance generalized spectroscopic ellipsometry: The magnetic response of the nitrogen defect in 4H-SiC

We report on terahertz (THz) electron paramagnetic resonance generalized spectroscopic ellipsometry (THz-EPR-GSE). Measurements of the field and frequency dependencies of the magnetic response due to the spin transitions associated with the nitrogen defect in 4H-SiC are shown as an example. THz-EPR-GSE dispenses with the need of a cavity, permits independently scanning field and frequency parameters, and does not require field or frequency modulation. We investigate spin transitions of hexagonal ($h$) and cubic ($k$) coordinated nitrogen including coupling with its nuclear spin (I=1), and we propose a model approach for the magnetic susceptibility to account for the spin transitions. From the THz-EPR-GSE measurements we can fully determine the polarization properties of the spin transitions and we obtain $g$ and hyperfine splitting parameters using magnetic field and frequency dependent Lorentzian oscillator lineshape functions. We propose frequency-scanning THz-EPR-GSE as a new and versatile method to study properties of spins in solid state materials.

cond-mat.mtrl-sci↗

arXiv2021

Infrared dielectric functions and Brillouin zone center phonons of $\alpha$-Ga$_2$O$_3$ compared to $\alpha$-Al$_2$O$_3$

We determine the anisotropic dielectric functions of rhombohedral $\alpha$-Ga$_2$O$_3$ by far-infrared and infrared generalized spectroscopic ellipsometry and derive all transverse optical and longitudinal optical phonon mode frequencies and broadening parameters. We also determine the high frequency and static dielectric constants. We perform density functional theory computations and determine the phonon dispersion for all branches in the Brillouin zone, and we derive all phonon mode parameters at the Brillouin zone center including Raman-active, infrared-active, and silent modes. Excellent agreement is obtained between our experimental and computation results as well as among all previously reported partial information from experiment and theory. We also compute the same information for $\alpha$-Al$_2$O$_3$, the binary parent compound for the emerging alloy of $\alpha$-(Al$_{x}$Ga$_{1-x}$)$_2$O$_3$, and use results from previous investigations [Schubert, Tiwald, and Herzinger, Phys. Rev. B 61, 8187 (2000)] to compare all properties among the two isostructural compounds. From both experimental and theoretical investigations we compute the frequency shifts of all modes between the two compounds. Additionally, we calculate overlap parameters between phonon mode eigenvectors and discuss the possible evolution of all phonon modes into the ternary alloy system and whether modes may form single mode or more complex mode behaviors.

cond-mat.mtrl-sci↗

arXiv2021

Optical phonon modes, static and high frequency dielectric constants, and effective electron mass parameter in cubic In$_2$O$_3$

A complete set of all optical phonon modes predicted by symmetry for bixbyite structure indium oxide is reported here from a combination of far-infrared and infrared spectroscopic ellipsometry, as well as first principle calculations. Dielectric function spectra measured on high quality, marginally electrically conductive melt grown single bulk crystals are obtained on a wavelength-by-wavelength (a.k.a. point-by-point) basis and by numerical reduction of a subtle free charge carrier Drude model contribution. A four-parameter semi-quantum model is applied to determine all sixteen pairs of infrared-active transverse and longitudinal optical phonon modes, including the high-frequency dielectric constant, $\varepsilon_{\infty}=4.05\pm 0.05$. The Lyddane-Sachs-Teller relation then gives access to the static dielectric constant, $\varepsilon_{\mathrm{DC}}=10.55\pm 0.07$. All experimental results are in excellent agreement with our density functional theory calculations and with previously reported values, where existent. We also perform optical Hall effect measurements and determine for the unintentionally doped $n$-type sample a free electron density of $n=(2.81 \pm 0.01)\times 10^{17}$~cm$^{-3}$, mobility of $\mu=(112 \pm 3)$~cm$^{2}$/(Vs), and an effective mass parameter of $(0.208\pm0.006)m_e$. Density and mobility parameters compare very well with results of electrical Hall effect measurements. Our effective mass parameter, which is measured independently of any other experimental technique, represents the bottom curvature of the $\Gamma$ point in In$_2$O$_3$ in agreement with previous extrapolations. We use terahertz spectroscopic ellipsometry to measure the quasi-static response of In$_2$O$_3$, and our model validates the static dielectric constant obtained from the Lyddane-Sachs-Teller relation.

cond-mat.mtrl-sci↗

arXiv2021

Broadband enhanced chirality with tunable response in hybrid plasmonic helical metamaterials

Designing broadband enhanced chirality is of strong interest to the emerging fields of chiral chemistry and sensing, or to control the spin orbital momentum of photons in recently introduced nanophotonic chiral quantum and classical optical applications. However, chiral light-matter interactions have an extremely weak nature, are difficult to be controlled and enhanced, and cannot be made tunable or broadband. In addition, planar ultrathin nanophotonic structures to achieve strong, broadband, and tunable chirality at the technologically important visible to ultraviolet spectrum still remain elusive. Here, we tackle these important problems by experimentally demonstrating and theoretically verifying spectrally tunable, extremely large, and broadband chiroptical response by nanohelical metamaterials. The reported new designs of all-dielectric and dielectric-metallic (hybrid) plasmonic metamaterials permit the largest and broadest ever measured chiral Kuhn dissymmetry factor achieved by a large-scale nanophotonic structure. In addition, the strong circular dichroism of the presented bottom-up fabricated optical metamaterials can be tuned by varying their dimensions and proportions between their dielectric and plasmonic helical subsections. The currently demonstrated ultrathin optical metamaterials are expected to provide a substantial boost to the developing field of chiroptics leading to significantly enhanced and broadband chiral light-matter interactions at the nanoscale.

physics.optics↗