Generalized 4 ×\times 4 Matrix Formalism for Light Propagation in Anisotropic Stratified Media: Study of Surface Phonon Polaritons in Polar Dielectric Heterostructures

We present a generalized 4 $\times$ 4 matrix formalism for the description of light propagation in birefringent stratified media. In contrast to previous work, our algorithm is capable of treating arbitrarily anisotropic or isotropic, absorbing or non-absorbing materials and is free of discontinous solutions. We calculate the reflection and transmission coefficients and derive equations for the electric field distribution for any number of layers. The algorithm is easily comprehensible and can be straight forwardly implemented in a computer program. To demonstrate the capabilities of the approach, we calculate the reflectivities, electric field distributions, and dispersion curves for surface phonon polaritons excited in the Otto geometry for selected model systems, where we observe several distinct phenomena ranging from critical coupling to mode splitting, and surface phonon polaritons in hyperbolic media

Femtosecond electrons probing currents and atomic structure in nanomaterials

The investigation of ultrafast electronic and structural dynamics in low-dimensional systems like nanowires and two-dimensional materials requires femtosecond probes providing high spatial resolution and strong interaction with small volume samples. Low-energy electrons exhibit large scattering cross sections and high sensitivity to electric fields, but their pronounced dispersion during propagation in vacuum so far prevented their use as femtosecond probe pulses in time-resolved experiments. Employing a laser-triggered point-like source of either divergent or collimated electron wave packets, we developed a hybrid approach for femtosecond point projection microscopy and femtosecond low-energy electron diffraction. We investigate ultrafast electric currents in nanowires with sub-100 femtosecond temporal and few 10 nm spatial resolutions and demonstrate the potential of our approach for studying structural dynamics in crystalline single-layer materials.Comment: 18 pages, 4 figures, includes 8 pages supplementary informatio

Low-temperature infrared dielectric function of hyperbolic α\alpha-quartz

We report the infrared dielectric properties of $\alpha$-quartz in the temperature range from $1.5\ \mathrm{K}$ to $200\ \mathrm{K}$. Using an infrared free-electron laser, far-infrared reflectivity spectra of a single crystal $y$-cut were acquired along both principal axes, under two different incidence angles, in S- and P-polarization. These experimental data have been fitted globally for each temperature with a multioscillator model, allowing to extract frequencies and damping rates of the ordinary and extraordinary, transverse and longitudinal optic phonon modes, and hence the temperature-dependent dispersion of the infrared dielectric function. The results are in line with previous high-temperature studies, allowing for a parametrized description of all temperature-dependent phonon parameters and the resulting dielectric function from $1.5\ \mathrm{K}$ up to the $\alpha$-$\beta$-phase transition temperature, $T_C = 846\ \mathrm{K}$. Using these data, we predict remarkably high quality factors for polaritons in $\alpha$-quartz's hyperbolic spectral region at low temperatures

Terahertz sum-frequency excitation of a Raman-active phonon

In stimulated Raman scattering, two incident optical waves induce a force oscillating at the difference of the two light frequencies. This process has enabled important applications such as the excitation and coherent control of phonons and magnons by femtosecond laser pulses. Here, we experimentally and theoretically demonstrate the so far neglected up-conversion counterpart of this process: THz sum-frequency excitation of a Raman-active phonon mode, which is tantamount to two-photon absorption by an optical transition between two adjacent vibrational levels. Coherent control of an optical lattice vibration of diamond is achieved by an intense terahertz pulse whose spectrum is centered at half the phonon frequency of 40 THz. Remarkably, the carrier-envelope phase of the driving pulse is directly imprinted on the lattice vibration. New prospects in infrared spectroscopy, light storage schemes and lattice trajectory control in the electronic ground state emerge

Second-harmonic phonon spectroscopy of α\alpha-quartz

We demonstrate midinfrared second-harmonic generation as a highly sensitive phonon spectroscopy technique that we exemplify using $\alpha$-quartz (SiO$_2$) as a model system. A midinfrared free-electron laser provides direct access to optical phonon resonances ranging from $350\ \mathrm{cm}^{-1}$ to $1400\ \mathrm{cm}^{-1}$. While the extremely wide tunability and high peak fields of an free-electron laser promote nonlinear spectroscopic studies---complemented by simultaneous linear reflectivity measurements---azimuthal scans reveal crystallographic symmetry information of the sample. Additionally, temperature-dependent measurements show how damping rates increase, phonon modes shift spectrally and in certain cases disappear completely when approaching$T_c=846\ \mathrm{K}$where quartz undergoes a structural phase transition from trigonal$\alpha$-quartz to hexagonal$\beta$-quartz, demonstrating the technique's potential for studies of phase transitions

Second Harmonic Generation from Critically Coupled Surface Phonon Polaritons

Mid-infrared nanophotonics can be realized using sub-diffractional light localization and field enhancement with surface phonon polaritons in polar dielectric materials. We experimentally demonstrate second harmonic generation due to the optical field enhancement from critically coupled surface phonon polaritons at the 6H-SiC-air interface, employing an infrared free-electron laser for intense, tunable, and narrowband mid-infrared excitation. Critical coupling to the surface polaritons is achieved using a prism in the Otto geometry with adjustable width of the air gap, providing full control over the excitation conditions along the polariton dispersion. The calculated reflectivity and second harmonic spectra reproduce the full experimental data set with high accuracy, allowing for a quantification of the optical field enhancement. We also reveal the mechanism for low out-coupling efficiency of the second harmonic light in the Otto geometry. Perspectives on surface phonon polariton-based nonlinear sensing and nonlinear waveguide coupling are discussed

Second Harmonic Generation from Phononic Epsilon-Near-Zero Berreman Modes in Ultrathin Polar Crystal Films

Immense optical field enhancement was predicted to occur for the Berreman mode in ultrathin films at frequencies in the vicinity of epsilon near zero (ENZ). Here, we report the first experimental proof of this prediction in the mid-infrared by probing the resonantly enhanced second harmonic generation (SHG) at the longitudinal optic phonon frequency from a deeply subwavelength-thin aluminum nitride (AlN) film. Employing a transfer matrix formalism, we show that the field enhancement is completely localized inside the AlN layer, revealing that the observed SHG signal of the Berreman mode is solely generated in the AlN film. Our results demonstrate that ENZ Berreman modes in intrinsically low-loss polar dielectric crystals constitute a promising platform for nonlinear nanophotonic applications

Layer-Resolved Resonance Intensity of Evanescent Polariton Modes in Anisotropic Multilayers

Phonon polariton modes in layered anisotropic heterostructures are a key building block for modern nanophotonic technologies. The light-matter interaction for evanescent excitation of such a multilayer system can be theoretically described by a transfer matrix formalism. This method allows to compute the imaginary part of the p-polarized reflection coefficient Im$(r_{pp})$, which is typically used to analyze the polariton dispersion of the multilayer structure, but lacks the possibility to access the layer-resolved polaritonic response. We present an approach to compute the layer-resolved polariton resonance intensity in aribtrarily anisotropic layered heterostructures, based on calculating the Poynting vector extracted from a transfer matrix formalism. Our approach is independent of the experimental excitation conditions, and fulfills an empirical conservation law. As a test ground, we study two state-of-the-art nanophotonic multilayer systems, covering strong coupling and tunable hyperbolic surface phonon polaritons in twisted \MoO~double layers. Providing a new level of insight into the polaritonic response, our method holds great potential for understanding, optimizing and predicting new forms of polariton heterostructures in the future.Comment: 7 pages, 2 figure