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.

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.

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.

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%.

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.

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.

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.

Terahertz cross-correlation spectroscopy driven by incoherent light from a superluminescent diode.

We present a novel terahertz spectroscopy principle by using incoherent light from a super luminescent diode for terahertz cross-correlation spectroscopy. The combless nature of this light source leads to a truly continuous terahertz spectrum. We demonstrate the possibility to influence the terahertz spectral bandwidth of the system by changing the bandwidth of different bandpass filters in the system. Depending on the employed bandpass filter we achieve peak dynamic ranges of 60 dB or a terahertz spectral width of about 1.7 THz. The applicability of the measurement system to spectroscopic terahertz measurement tasks is demonstrated.

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

We report on spontaneous parametric down-conversion (SPDC) in periodically poled lithium niobate (PPLN) using 660 nm pump wavelength and the type 0 phase-matching condition to the terahertz and even sub-terahertz frequency range. Detection of the frequency-shifted signal photons is achieved by using highly efficient and narrowband volume Bragg gratings and an uncooled sCMOS camera. The acquired frequency-angular spectrum shows backward and forward generation of terahertz and sub-terahertz photons by SPDC, as well as up-conversion and higher order quasi phase-matching (QPM). The frequency-angular spectrum is theoretically calculated using a Monte-Carlo integration scheme showing a high agreement with the measurement. This work is one important step toward quantum sensing and imaging in the terahertz and sub-terahertz frequency range.

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.

Single-laser, polarization-controlled optical sampling system.

Optical sampling systems traditionally require either one mode-locked laser with an external delay line or two mode-locked lasers with a controllable repetition rate difference. In this paper we present a novel polarization-multiplexed laser architecture combining the benefits of both approaches. The laser emits two mode-locked pulse trains sharing only one gain section without any external delay line. The colliding pulses in the laser have orthogonal polarization as well as opposite propagation directions to reduce coupling effects. With this, the two pulse trains can be freely phase controlled to conduct pump-probe measurements. To further analyze the timing stability of the system, we conducted a two-photon-absorption experiment, leading to a timing accuracy of 30 fs. Based on the novel laser architecture, we call this new approach single-laser polarization-controlled optical sampling, or SLAPCOPS.

Calibration sample for arbitrary metrological characteristics of optical topography measuring instruments.

Areal optical surface topography measurement is an emerging technology for industrial quality control. However, neither calibration procedures nor the utilization of material measures are standardized. State of the art is the calibration of a set of metrological characteristics with multiple calibration samples (material measures). Here, we propose a new calibration sample (artefact) capable of providing the entire set of relevant metrological characteristics within only one single sample. Our calibration artefact features multiple material measures and is manufactured with two-photon laser lithography (direct laser writing, DLW). This enables a holistic calibration of areal topography measuring instruments with only one series of measurements and without changing the sample.

Terahertz thickness determination with interferometric vibration correction for industrial applications.

In many industrial fields, like automotive and painting industry, the thickness of thin layers is a crucial parameter for quality control. Hence, the demand for thickness measurement techniques continuously grows. In particular, non-destructive and contact-free terahertz techniques access a wide range of thickness determination applications. However, terahertz time-domain spectroscopy based systems perform the measurement in a sampling manner, requiring fixed distances between measurement head and sample. In harsh industrial environments vibrations of sample and measurement head distort the time-base and decrease measurement accuracy. We present an interferometer-based vibration correction for terahertz time-domain measurements, able to reduce thickness distortion by one order of magnitude for vibrations with frequencies up to 100 Hz and amplitudes up to 100 µm. We further verify the experimental results by numerical calculations and find very good agreement.

Single-laser polarization-controlled optical sampling system for THz-TDS.

We demonstrate a polarization-multiplexed, single-laser system for terahertz (THz) time-domain spectroscopy without an external delay line. The fiber laser emits two pulse trains with independently adjustable repetition rates, utilizing only one laser-active section and one pump diode. With a standard fiber-coupled THz setup and a polarization-multiplexed optical amplifier, we are able to measure transients with a spectral bandwidth of 1.5 THz and a dynamic range of 50 dB in a measurement time of 1 s. Based on the novel laser architecture, we call this new approach single-laser polarization-controlled optical sampling, or SLAPCOPS.

Time-stretched real-time measurement technique for ultrafast absorption variations with TS/s sampling-rate.

We present a real-time measurement technique, based on time-stretching for measuring the temporal dynamic of ultrafast absorption variations with a sampling-rate of up to 1.1 TS/s. The single-shot captured data are stretched in a resonator-based time-stretch system with a variable stretch-factor of up to 13.8. The time-window of the time-stretch system for capturing the signal of interest is about 800 ps with an update-rate of 10 MHz. An adapted optical backpropagation algorithm is introduced for reconstructing the original unstretched event. As proof-of-principle the temporal characteristic of a picosecond semiconductor saturable absorber mirror is measured: The real-time results agree well with the results of a conventional pump-probe experiment. The time-stretch technique potentially allows to gain access to a large field of ultrafast absorption variations like semiconductor charge carrier dynamics, irreversible polymerization processes, and saturable absorber materials.

Interferometry-aided terahertz time-domain spectroscopy.

Terahertz time-domain spectroscopy as well as all optical pump-probe techniques with ultrashort pulses relies on the exact knowledge of an optical delay between related laser pulses. Classical realizations of the measurement principle vary the optical path length for one of the pulses by mechanical translation of optical components. Most commonly, only an indirect measurement of the translation is carried out, which introduces inaccuracies due to imprecise mechanics or harsh environment. We present a comprehensive study on the effect of delay inaccuracies on the quality of terahertz spectra acquired with time-domain spectroscopy systems and present an interferometric technique to directly acquire the optical delay simultaneously to the terahertz measurement data. This measurement principle enables high-precision terahertz spectroscopy even in harsh environment with non-systematic disruptions.