Wide-range resistivity characterization of semiconductors with terahertz time-domain spectroscopy.

Resistivity is one of the most important characteristics in the semiconductor industry. The most common way to measure resistivity is the four-point probe method, which requires physical contact with the material under test. Terahertz time domain spectroscopy, a fast and non-destructive measurement method, is already well established in the characterization of dielectrics. In this work, we demonstrate the potential of two Drude model-based approaches to extract resistivity values from terahertz time-domain spectroscopy measurements of silicon in a wide range from about 10-3 Ωcm to 102 Ωcm. One method is an analytical approach and the other is an optimization approach. Four-point probe measurements are used as a reference. In addition, the spatial resistivity distribution is imaged by X-Y scanning of the samples to detect inhomogeneities in the doping distribution.

Coherent Off-Axis Terahertz Tomography with a Multi-Channel Array and f-theta Optics.

Terahertz tomography is a promising method among non-destructive inspection techniques to detect faults and defects in dielectric samples. Recently, image quality was improved significantly through the incorporation of a priori information and off-axis data. However, this improvement has come at the cost of increased measurement time. To aim toward industrial applications, it is therefore necessary to speed up the measurement by parallelizing the data acquisition employing multi-channel setups. In this work, we present two tomographic frequency-modulated continuous wave (FMCW) systems working at a bandwidth of 230-320 GHz, equipped with an eight-channel detector array, and we compare their imaging results with those of a single-pixel setup. While in the first system the additional channels are used exclusively to detect radiation refracted by the sample, the second system features an f-θ lens, focusing the beam at different positions on its flat focal plane, and thus utilizing the whole detector array directly. The usage of the f-θ lens in combination with a scanning mirror eliminates the necessity of the formerly used slow translation of a single-pixel transmitter. This opens up the potential for a significant increase in acquisition speed, in our case by a factor of four to five, respectively.

Mixing rule for calculating the effective refractive index beyond the limit of small particles.

Considering light transport in disordered media, the medium is often treated as an effective medium requiring accurate evaluation of an effective refractive index. Because of its simplicity, the Maxwell-Garnett (MG) mixing rule is widely used, although its restriction to particles much smaller than the wavelength is rarely satisfied. Using 3D finite-difference time-domain simulations, we show that the MG theory indeed fails for large particles. Systematic investigation of size effects reveals that the effective refractive index can be instead approximated by a quadratic polynomial whose coefficients are given by an empirical formula. Hence, a simple mixing rule is derived which clearly outperforms established mixing rules for composite media containing large particles, a common condition in natural disordered media.

Rapid-prototyping of microscopic thermal landscapes in Brillouin light scattering spectroscopy.

Since temperature and its spatial, and temporal variations affect a wide range of physical properties of material systems, they can be used to create reconfigurable spatial structures of various types in physical and biological objects. This paper presents an experimental optical setup for creating tunable two-dimensional temperature patterns on a micrometer scale. As an example of its practical application, we have produced temperature-induced magnetization landscapes in ferrimagnetic yttrium iron garnet films and investigated them using micro-focused Brillouin light scattering spectroscopy. It is shown that, due to the temperature dependence of the magnon spectrum, spatial temperature distributions can be visualized even for microscale thermal patterns.

Fiber-tip spintronic terahertz emitters.

Spintronic terahertz emitters promise terahertz sources with an unmatched broad frequency bandwidth that are easy to fabricate and operate, and therefore easy to scale at low cost. However, current experiments and proofs of concept rely on free-space ultrafast pump lasers and rather complex benchtop setups. This contrasts with the requirements of widespread industrial applications, where robust, compact, and safe designs are needed. To meet these requirements, we present a novel fiber-tip spintronic terahertz emitter solution that allows spintronic terahertz systems to be fully fiber-coupled. Using single-mode fiber waveguiding, the newly developed solution naturally leads to a simple and straightforward terahertz near-field imaging system with a 90%-10% knife-edge-response spatial resolution of 30 µm.

Electronic phase detection with a sub-10 fs timing jitter for terahertz time-domain spectroscopy systems.

Terahertz time-domain spectroscopy systems based on resonator-internal repetition-rate modulation, such as SLAPCOPS and ECOPS, rely on electronic phase detectors which are typically prone to exhibit both a non-negligible random and systematic timing error. This limits the quality of the recorded information significantly. Here, we present the results of our recent attempt to reduce these errors in our own electronic phase detection systems. A more than six-fold timing-jitter reduction from 59.0 fs to 8.6 fs led to a significant increase in both exploitable terahertz bandwidth and signal-to-noise ratio. Additionally, utilizing our interferometrically monitored delay line as a calibration standard, the systematic error could be removed almost entirely and thus, excellent resolution of spectral absorption lines be accomplished. These improvements increased the accuracy of our multi-layer thickness measurements based on electronic phase detection by more than a factor of five, pushing the overall performance well into the sub-µm regime.

Phase-quadrature quantum imaging with undetected photons.

Sensing with undetected photons allows access to spectral regions with simultaneous detection of photons of another region and is based on nonlinear interferometry. To obtain the full information of a sample, the corresponding interferogram has to be analyzed in terms of amplitude and phase, which has been realized so far by multiple measurements followed by phase variation. Here, we present a polarization-optics-based phase-quadrature implementation in a nonlinear interferometer for imaging with undetected photons in the infrared region. This allows us to obtain phase and visibility with a single image acquisition without the need of varying optical paths or phases, thus enabling the detection of dynamic processes. We demonstrate the usefulness of our method on a static phase mask opaque to the detected photons as well as on dynamic measurement tasks as the drying of an isopropanol film and the stretching of an adhesive tape.

Photonic quadrupole topological insulator using orbital-induced synthetic flux.

The rich physical properties of multiatomic crystals are determined, to a significant extent, by the underlying geometry and connectivity of atomic orbitals. The mixing of orbitals with distinct parity representations, such as s and p orbitals, has been shown to be useful for generating systems that require alternating phase patterns, as with the sign of couplings within a lattice. Here we show that by breaking the symmetries of such mixed-orbital lattices, it is possible to generate synthetic magnetic flux threading the lattice. We use this insight to experimentally demonstrate quadrupole topological insulators in two-dimensional photonic lattices, leveraging both s and p orbital-type modes. We confirm the nontrivial quadrupole topology by observing the presence of protected zero-dimensional states, which are spatially confined to the corners, and by confirming that these states sit at mid-gap. Our approach is also applicable to a broader range of time-reversal-invariant synthetic materials that do not allow for tailored connectivity, and in which synthetic fluxes are essential.

Phase-sensitive terahertz upconversion detection.

Nonlinear frequency conversion provides an elegant method to detect photons in a spectral range which differs from the pump wavelength, making it highly attractive for photons with inherently low energy. Aside from the intensity of the light, represented by the number of photons, their phase provides important information and enables a plethora of applications. We present a phase-sensitive measurement method in the terahertz spectral range by only detecting visible light. Using the optical interference of frequency-converted photons and leftover pump photons of the involved ultrashort pulses, fast determination of layer-thicknesses is demonstrated. The new method enables phase-resolved detection of terahertz pulses using standard sCMOS equipment while achieving sample measurement times of less than one second with a precision error of less than 0.6%.

Fiber-tip endoscope for optical and microwave control.

We present a robust, fiber-based endoscope with a silver direct-laser-written structure for radio frequency (RF) emission next to the optical fiber facet. Thereby, we are able to excite and probe a sample, such as nitrogen-vacancy (NV) centers in diamond, with RF and optical signals simultaneously and specifically measure the fluorescence of the sample fully through the fiber. At our targeted frequency range of around 2.9 GHz, the facet of the fiber core is in the near-field of the RF-guiding silver structure, which comes with the advantage of an optimal RF intensity decreasing rapidly with the distance. By creating a silver structure on the cladding of the optical fiber, we achieve the minimal possible distance between an optically excited and detected sample and an antenna structure without affecting the optical performance of the fiber. This allows us to realize a high RF amplitude at the sample's position when considering an endoscope solution with integrated optical and RF access. The capabilities of the endoscope are quantified by optically detected magnetic resonance (ODMR) measurements of an NV-doped microdiamond that we probe as a practical use case. We demonstrate a magnetic sensitivity of our device of 17.8 nT/Hz when measuring the ODMR exclusively through our fiber and compare the sensitivity to a measurement using a confocal microscope. Moreover, the application of our device is not limited to NV centers in diamonds. Similar endoscope-like devices combining optical excitation and detection with radio frequency or microwave antenna could be used as a powerful tool for measuring a variety of fluorescent particles that have so far only been investigated with bulky and large optical setups. Furthermore, our endoscope points toward precise distance measurements based on Rabi oscillations.

Towards efficient structure prediction and pre-compensation in multi-photon lithography.

Microscale 3D printing technologies have been of increasing interest in industry and research for several years. Unfortunately, the fabricated structures always deviate from the respective expectations, often caused by the physico-chemical properties during and after the printing process. Here, we show first steps towards a simple, fast and easy to implement algorithm to predict the final structure topography for multi-photon lithography - also known as Direct Laser Writing (DLW). The three main steps of DLW, (i) exposure of a photo resin, (ii) cross-linking of the resin, and (iii) subsequent shrinkage are approximated by mathematical operations, showing promising results in coincidence with experimental observations. For example, the root-mean-square error (rmse) between the unmodified 3D print of a radial-symmetrically chirped topography and our predicted topography is only 0.46 µm, whereas the rmse between this 3D print and its target is 1.49 µm. Thus, our robust predictions can be used prior to the printing process to minimize undesired deviations between the target structure and the final 3D printed structure. Using a Downhill-Simplex algorithm for identifying the optimal prediction parameters, we were able to reduce the rmse from 4.04 µm to 0.33 µm by only two correction loops in our best-case scenario (rmse = 0.72 µm after one loop). Consequently, this approach can eliminate the need for many structural optimization loops to produce highly conformal and high quality micro structures in the future.

Spontaneous parametric down-conversion of photons at 660 nm to the terahertz and sub-terahertz frequency range: erratum.

In this erratum, we correct two typing errors from our previously published manuscript [Opt. Express27, 7458 (2019)10.1364/OE.27.007458]. In the original manuscript, the two errors were limited to the theoretical derivation and did not touch the numerical calculations such that the results and conclusions remain unchanged.

Observation of bound states in the continuum embedded in symmetry bandgaps.

In the past decade, symmetry-protected bound states in the continuum (BICs) have proven to be an important design principle for creating and enhancing devices reliant upon states with high-quality (Q) factors, such as sensors, lasers, and those for harmonic generation. However, as we show, current implementations of symmetry-protected BICs in photonic crystal slabs can only be found at the center of the Brillouin zone and below the Bragg diffraction limit, which fundamentally restricts their use to single-frequency applications. By microprinting a three-dimensional (3D) photonic crystal structure using two-photon polymerization, we demonstrate that this limitation can be overcome by altering the radiative environment surrounding the slab to be a 3D photonic crystal. This allows for the protection of a line of BICs by embedding it in a symmetry bandgap of the crystal. This concept substantially expands the design freedom available for developing next-generation devices with high-Q states.

Generalized laws of refraction and reflection at interfaces between different photonic artificial gauge fields.

Artificial gauge fields the control over the dynamics of uncharged particles by engineering the potential landscape such that the particles behave as if effective external fields are acting on them. Recent years have witnessed a growing interest in artificial gauge fields generated either by the geometry or by time-dependent modulation, as they have been enablers of topological phenomena and synthetic dimensions in many physical settings, e.g., photonics, cold atoms, and acoustic waves. Here, we formulate and experimentally demonstrate the generalized laws of refraction and reflection at an interface between two regions with different artificial gauge fields. We use the symmetries in the system to obtain the generalized Snell law for such a gauge interface and solve for reflection and transmission. We identify total internal reflection (TIR) and complete transmission and demonstrate the concept in experiments. In addition, we calculate the artificial magnetic flux at the interface of two regions with different artificial gauge fields and present a method to concatenate several gauge interfaces. As an example, we propose a scheme to make a gauge imaging system-a device that can reconstruct (image) the shape of an arbitrary wavepacket launched from a certain position to a predesigned location.

Terahertz detection by upconversion to the near-infrared using picosecond pulses.

The detection of terahertz photons by using silicon-based devices enabled by visible photons is one of the fundamental ideas of quantum optics. Here, we present a classical detection principle using optical upconversion of terahertz photons to the near-infrared spectral range in the picosecond pulse regime, which finally enables the detection with a conventional sCMOS camera. By superimposing terahertz and optical pump pulses in a periodically poled lithium-niobate crystal, terahertz photons at 0.87 THz are converted to optical photons with wavelengths close to the central pump wavelength of 776 nm. A tunable delay between the pulses helps overlap the pulses and enables time-of-flight measurements. Using a sCMOS camera, we achieve a dynamic range of 47.8 dB with a signal to noise ratio of 23.5 dB at a measurement time of one second, in our current setup.

Artificial gauge field switching using orbital angular momentum modes in optical waveguides.

The discovery of artificial gauge fields controlling the dynamics of uncharged particles that otherwise elude the influence of standard electromagnetic fields has revolutionised the field of quantum simulation. Hence, developing new techniques to induce these fields is essential to boost quantum simulation of photonic structures. Here, we experimentally demonstrate the generation of an artificial gauge field in a photonic lattice by modifying the topological charge of a light beam, overcoming the need to modify the geometry along the evolution or impose external fields. In particular, we show that an effective magnetic flux naturally appears when a light beam carrying orbital angular momentum is injected into a waveguide lattice with a diamond chain configuration. To demonstrate the existence of this flux, we measure an effect that derives solely from the presence of a magnetic flux, the Aharonov-Bohm caging effect, which is a localisation phenomenon of wavepackets due to destructive interference. Therefore, we prove the possibility of switching on and off artificial gauge fields just by changing the topological charge of the input state, paving the way to accessing different topological regimes in a single structure, which represents an important step forward for optical quantum simulation.

Terahertz quantum sensing.

Quantum sensing is highly attractive for accessing spectral regions in which the detection of photons is technically challenging: Sample information is gained in the spectral region of interest and transferred via biphoton correlations into another spectral range, for which highly sensitive detectors are available. This is especially beneficial for terahertz radiation, where no semiconductor detectors are available and coherent detection schemes or cryogenically cooled bolometers have to be used. Here, we report on the first demonstration of quantum sensing in the terahertz frequency range in which the terahertz photons interact with a sample in free space and information about the sample thickness is obtained by the detection of visible photons. As a first demonstration, we show layer thickness measurements with terahertz photons based on biphoton interference. As nondestructive layer thickness measurements are of high industrial relevance, our experiments might be seen as a first step toward industrial quantum sensing applications.

Observation of a Charge-2 Photonic Weyl Point in the Infrared.

Weyl points are robust point degeneracies in the band structure of a periodic material, which act as monopoles of Berry curvature. They have been at the forefront of research in three-dimensional topological materials as they are associated with novel behavior both in the bulk and on the surface. Here, we present the experimental observation of a charge-2 photonic Weyl point in a low-index-contrast photonic crystal fabricated by two-photon polymerization. The reflection spectrum obtained via Fourier-transform infrared spectroscopy closely matches simulations and shows two bands with quadratic dispersion around a point degeneracy.

Multilayer Thickness Measurements below the Rayleigh Limit Using FMCW Millimeter and Terahertz Waves.

We present thickness measurements with millimeter and terahertz waves using frequency-modulated continuous-wave (FMCW) sensors. In contrast to terahertz time-domain spectroscopy (TDS), our FMCW systems provide a higher penetration depth and measurement rates of several kilohertz at frequency modulation bandwidths of up to 175 GHz. In order to resolve thicknesses below the Rayleigh resolution limit given by the modulation bandwidth, we employed a model-based signal processing technique. Within this contribution, we analyzed the influence of multiple reflections adapting a modified transfer matrix method. Based on a brute force optimization, we processed the models and compared them with the measured signal in parallel on a graphics processing unit, which allows fast calculations in less than 1 s. TDS measurements were used for the validation of our results on industrial samples. Finally, we present results obtained with reduced frequency modulation bandwidths, opening the window to future miniaturization based on monolithic microwave integrated circuit (MMIC) radar units.