Frequency Domain Interferometry Research Articles

Single-shot observation of nonlinear pulse splitting in a Kerr medium.

We report single-shot, time-resolved observation of self-steepening and temporal splitting of near-infrared, 50 fs, micro-joule pulses propagating nonlinearly in flint (SF11) glass. A coherent, smooth-profiled, 60-nm-bandwidth probe pulse that propagated obliquely to the main pulse through the Kerr medium recorded a time sequence of longitudinal projections of the main pulse's induced refractive index profile in the form of a phase-shift "streak," in which frequency-domain interferometry recovered with ∼10 fs temporal resolution. A three-dimensional simulation based on a unidirectional pulse propagation equation reproduced observed pulse profiles.

Microwave Absolute Distance Measurement Method with Ten-Micron-Level Accuracy and Meter-Level Range Based on Frequency Domain Interferometry.

A microwave absolute distance measurement method with ten-micron-level accuracy and meter-level range based on frequency domain interferometry is proposed and experimentally demonstrated for the first time. Theoretical analysis indicates that an interference phenomenon occurs instantaneously in the frequency domain when combining two homologous broad-spectrum microwave beams with different paths, and the absolute value of the distance difference between the two paths is only inversely proportional to the period of frequency domain interference fringes. The proof-of-principle experiments were performed to prove that the proposed method can achieve absolute distance measurement in the X-band with standard deviations of 15 μm, 17 μm, and 26 μm and within ranges of 1.69 m, 2.69 m, and 3.75 m. Additionally, a displacement resolution of 100 microns was realized. The multi-target recognition performance was also verified in principle. Furthermore, at the expense of a slight decrease in ranging accuracy, a fast distance measurement with the single measurement time of 20 μs was achieved by using a digitizer combined with a Fourier transform analyzer. Compared with the current microwave precision ranging technologies, the proposed method not only has the advantages of high precision, large range, and rapid measurement capability, but the required components are also easily obtainable commercial devices. The proposed method also has better complex engineering applicability, because the ten-micron-level ranging accuracy is achievable only by using a simple Fourier transform without any phase estimation algorithm, which greatly reduces the requirement for signal-to-noise ratio.

High precision dynamic measurement method for axial clearance based on time division multiplexing with dispersive interferometry.

Rotor-stator axial clearance is a crucial design parameter affecting rotating machines' efficiency and safety. To accurately measure the dynamic axial clearance in high-speed machinery, a precise method based on time division multiplexing with frequency domain interferometry has been proposed. This method has proven robust and accurate through simulations and experiments. The inclusion of an optical switch enables the utilization of dispersive interferometry(DPI) and time division multiplexing for multiple channels of the light source. It achieves a static accuracy of 1.5 µm for a 15 mm range and a dynamic accuracy of 9 µm at 3000 rpm.

Frequency-domain interferometry for the determination of time delay between two extreme-ultraviolet wave packets generated by a tandem undulator

Synchrotron radiation, emitted by relativistic electrons traveling in a magnetic field, has poor temporal coherence. However, recent research has proved that time-domain interferometry experiments, which were thought to be enabled by only lasers of excellent temporal coherence, can be implemented with synchrotron radiation using a tandem undulator. The radiation generated by the tandem undulator comprises pairs of light wave packets, and the longitudinal coherence within a light wave packet pair is used to achieve time-domain interferometry. The time delay between two light wave packets, formed by a chicane for the electron trajectory, can be adjusted in the femtosecond range by a standard synchrotron technology. In this study, we show that frequency-domain spectra of the tandem undulator radiation exhibit fringe structures from which the time delay between a light wave packet pair can be determined with accuracy on the order of attoseconds. The feasibility and limitations of the frequency-domain interferometric determination of the time delay are examined.

High‐Resolution Sporadic E Layer Observation Based on Ionosonde Using a Cross‐Spectrum Analysis Imaging Technique

AbstractThe appearance of the sporadic E (Es) layer is an occasional phenomenon in the ionosphere. Limited by range resolution, it is difficult to observe the fine structures and internal evolution processes using existing ionosonde detection techniques. In this study, by analyzing the cross‐spectrum of the echo and the modulation sequence of the transmitted signal, the coherence between frequency components in the signal bandwidth is utilized. Using the Capon spectrum estimation method in the range dimension, the range resolution and use efficiency of the ionosonde are improved. This method does not rely on the joint processing of multifrequency detection data, unlike the frequency domain interferometry technique, maintaining the resulting time resolution. Using this imaging method, observations of the Es layer show that multiple peaks within an intrinsic range bin (3.84 km) can be resolved at a range that is 10‐fold higher (384 m); the multilayer phenomenon inside the Es layer can be clearly imaged in a continuous echo. Semishading between the layers is present. In some cases, the mode of the echo traces can also be directly identified through high‐resolution imaging. Concurrently, observations show that dramatic short‐term evolution processes on the order of seconds inside the Es layer can be captured.

Improved Ionosonde Monitoring of the Sporadic E Layer Using the Frequency Domain Interferometry Technique

The sporadic E (Es) layer is a thin layer of ion plasma enhancement in the E-region ionosphere, typically at altitudes of 90–120 km with vertical and horizontal extent of several or several tens of kilometers. As the transition region between the lower and upper atmosphere, this layer is of critical importance for ionospheric studies. The most economical but effective method to observe this layer is using ionosonde, which, however, is incapable of capturing the finer structure or the internal inhomogeneity of the Es layer as the range resolution is on the order of kilometers. To overcome this limitation, we employ the frequency domain interferometry (FDI) technique, a technique that has been successfully applied to the analysis of some radar and sonar measurements. Here, we use the Es layer measurements near Wuhan, China (114°22′E, 30°30′N) on 8 June 2021 as examples to showcase the capability of this technique. Our results show that the spatial resolution of ionosonde imaging is remarkably increased: the complexity of the internal fine structure in the Es layer can be well observed in the FDI-processed ionograms, whereas the intrinsic range resolution is several kilometers. Moreover, by comparing the ionograms obtained with and without the FDI technique, it is found that the FDI-processed ionogram is particularly suitable for the observation of evolutional processes in the Es layer, as well as the identification of different types of Es layer. With this level of spatial resolution, ionosonde, in combination with the FDI technique, opens the possibility for more refined observations of the Es layer.

Extracting quantitative dielectric properties from pump-probe spectroscopy

Optical pump-probe spectroscopy is a powerful tool for the study of non-equilibrium electronic dynamics and finds wide applications across a range of fields, from physics and chemistry to material science and biology. However, a shortcoming of conventional pump-probe spectroscopy is that photoinduced changes in transmission, reflection and scattering can simultaneously contribute to the measured differential spectra, leading to ambiguities in assigning the origin of spectral signatures and ruling out quantitative interpretation of the spectra. Ideally, these methods would measure the underlying dielectric function (or the complex refractive index) which would then directly provide quantitative information on the transient excited state dynamics free of these ambiguities. Here we present and test a model independent route to transform differential transmission or reflection spectra, measured via conventional optical pump-probe spectroscopy, to changes in the quantitative transient dielectric function. We benchmark this method against changes in the real refractive index measured using time-resolved Frequency Domain Interferometry in prototypical inorganic and organic semiconductor films. Our methodology can be applied to existing and future pump-probe data sets, allowing for an unambiguous and quantitative characterisation of the transient photoexcited spectra of materials. This in turn will accelerate the adoption of pump-probe spectroscopy as a facile and robust materials characterisation and screening tool.

A high-performance ranging method with a long distance range and high accuracy

Distance measurement technology can greatly aid scientific research and engineering applications. The optical frequency-domain interferometry ranging method (OFDI-RM) has attracted a great deal of attention as it can achieve accuracy down to the micron and nanometer resolution. However, the main drawback of OFDI-RM is its short measuring range, which hinders its widespread use. In this paper, we present a high-performance OFDI-RM with a long distance range, high accuracy and high resolution. A high return-loss focus ranging probe is used to match the light intensity of reference and signal beams for acquiring high visibility interference fringes in the frequency domain at a distance of more than 100 mm. A novel signal processing method, which takes advantage of high-degree polynomial fitting and Hilbert transform (HT) to perfectly extract the harmonic component of the frequency-domain interference fringes, has also been demonstrated. The performance of OFDI-RM is verified by a linear motion measurement experiment. The measured range of OFDI-RM increased up to 170 mm, with an accuracy and resolution of up to 0.0040 mm–0.0005 mm/step, respectively.

Measurement of Film Structure Using Time-Frequency-Domain Fitting and White-Light Scanning Interferometry

A new technique is proposed for measuring film structure based on the combination of time- and frequency-domain fitting and white-light scanning interferometry. The approach requires only single scanning and employs a fitting method to obtain the film thickness and the upper surface height in the frequency and time domains, respectively. The cross-correlation function is applied to obtain the initial value of the upper surface height, thereby making the fitting process more accurate. Standard films (SiO2) with different thicknesses were measured to verify the accuracy and reliability of the proposed method, and the three-dimensional topographies of the upper and lower surfaces of the films were reconstructed.

Advanced and versatile interferometric technique for the characterization of photonic integrated devices.

Adaptable and complex optical characterization of photonic integrated devices, permitting to unearth possible design and fabrication errors in the different workflow steps are highly desired in the community. Here, we propose a technique capable of resolving full optical amplitude and phase response, in both frequency and time domains, of a photonic integrated device. It relies on optical frequency domain interferometry and makes use of a novel integrated architecture; a 3-way interferometer enabling single input and single output detection. We derive the test structure design rules and provide extensive experimental validation in silicon nitride and silicon on insulator technologies, by testing relevant devices such as arrayed waveguide grating, Mach-Zehnder interferometers, and ring resonators. Horizontal and vertical chip coupling, different external setup arrangements, and the optical dispersion de-embedding inherent to the technique are demonstrated. Finally, we discuss why this characterization approach might lay the groundwork of a standard testing tool for photonic integrated devices.

Sub-Picosecond Non-Equilibrium States in the Amorphous Phase of GeTe Phase-Change Material Thin Films.

The sub-picosecond response of amorphous germanium telluride thin film to a femtosecond laser excitation is investigated using frequency-domain interferometry and ab initio molecular dynamics. The time-resolved measurement of the surface dynamics reveals a shrinkage of the film with a dielectric properties' response faster than 300 fs. The systematic ab initio molecular dynamics simulations in non-equilibrium conditions allow the atomic configurations to be retrieved for ionic temperature from 300 to 1100 K and width of the electron distribution from 0.001 to 1.0 eV. Local order of the structures is characterized by in-depth analysis of the angle distribution, phonon modes, and pair distribution function, which evidence a transition toward a new amorphous electronic excited state close in bonding/structure to the liquid state. The results shed a new light on the optically highly excited states in chalcogenide materials involved in both important processes: phase-change materials in memory devices and ovonic threshold switching phenomenon induced by a staticfield.

Distributed X-Ray Dosimetry With Optical Fibers by Optical Frequency Domain Interferometry

This article reports on the first demonstration of in situ , real-time dosimetry realized with an enhanced backscattering optical fiber, and a high-resolution optical backscattering reflectometry measurement. This work is devised to overcome the current problems in monitoring radiotherapy treatments, in particular, the difficult evaluation of not only the actual X-ray dose that is accumulated on the target volume but also the distribution profile of the ionizing radiation beam. Overall, the research aims at developing a dose sensor with the most demanding features of small form factor, spatial profiling, and remote interrogation. The experiments have been conducted by evaluating the spatial profile of radiation-induced spectral shift of the Rayleigh backscattering along an optical fiber exposed to X-rays. The sensing element is a section of specialty optical fiber whose Rayleigh backscattering signature changes under ionizing radiation. The specialty fiber is designed to exhibit an enhanced backscattering, in order to overcome the poor sensitivity to radiation of standard optical fibers that are normally, used in telecommunications. The enhanced sensitivity is achieved by doping the core with either aluminum or magnesium nanoparticles, and two different fibers have been fabricated and tested. The experimental results show the capability of real time detection of the radiation profile from high-dose rates (700 Gy/min) to low-dose rates (2 Gy/min). Moreover, different sensing mechanisms and responses to high- and low-dose rates are evidenced. A comparison with a quasi-distributed sensing system based on an array of fiber Bragg gratings (FBGs) is discussed, highlighting the superior performance of the backscattering approach in terms of sensitivity and spatial resolution, whereas the array of FBGs exhibits an advantage in terms of sampling speed.

Modified snapshot spectroscopic ellipsometry based on optical frequency-domain interferometry

We propose a modified snapshot spectroscopic ellipsometry based on optical frequency-domain interferometry. The proposed system employs only one high-order retarder and a Wollaston prism to analyze the changed state of polarization of the reflected light and can provide the maximum channel bandwidth of the channeled spectroscopic ellipsometry. The spectroscopic ellipsometric parameters of isotropic samples can be accurately measured in a measurement speed of 40 ms without mechanical or active modulation devices. The feasibility of the proposed spectroscopic ellipsometry is demonstrated by experiments.

Performance limits of astronomical arrayed waveguide gratings on a silica platform

We present a numerical and experimental study of the impact of phase errors on the performance of large, high-resolution arrayed waveguide gratings (AWG) for applications in astronomy. We use a scalar diffraction model to study the transmission spectrum of an AWG under random variations of the optical waveguide lengths. We simulate phase error correction by numerically trimming the lengths of the optical waveguides to the nearest integer multiple of the central wavelength. The optical length error distribution of a custom-fabricated silica AWG is measured using frequency-domain interferometry and Monte-Carlo fitting of interferogram intensities. In the end, we give an estimate for the phase-error limited size of a waveguide array manufactured using state-of-the-art technology. We show that post-processing eliminates phase errors as a performance limiting factor for astronomical spectroscopy in the H-band.

Iterative Frequency-Domain Interferometry Technology for Ultrafast Phase Measurement

This paper presents an original design of the single-shot iterative frequency-domain interferometry (IFDI) technology to measure the ultrafast phase. Unlike frequency domain holography (FDH), in which the reference pulse interferes with the phase-modulated probe pulse, in IFDI two linearly chirped probe pulses co-propagate and are both phasemodulated by the measured ultrafast phase, and then the phase can be reconstructed with the iterative algorithm. Compared with two types of FDH, the IFDI technology has better accuracy and stability.

Single-shot measurement of the free-space time domain terahertz (THz) waveforms by iterative frequency-domain interferometry technology

In this paper, a design of single-shot iterative frequency-domain interferometry (IFDI) technology is presented to measure ultrafast phase. Compared with frequency domain holography (FDH), IFDI technology has better accuracy and stability in some situations. Besides, combined with electro-optic sampling, comparative experiments on the free-space time domain terahertz waveforms measurement using FDH, IFDI, and femtosecond pump-probe technology are conducted, and the results confirm the feasibility and accuracy of the IFDI.

(Invited) Plasma Processing with Feedback Control of Wafer Temperature By Non-Contact Temperature Measurement System

Plasma processes such as deposition and etching, trimming, are required for nanoscale devices which are Fin-field effect transistors (FETs), nanowires, and others 3D devices. Control plasma processes according to the plasma internal parameters, which define the process characteristics directly, are effective because the parameters can vary over process time even if external parameters are fixed. Significant one of the parameters is the wafer temperature for the precise etching process because the etched profile is sensitive to the temperature [1]. Additionally, Increasing the wafer temperature by heat flux from a plasma are considerable to be one of the most important disturbances in the etching process because the recombination coefficients and sticking probability of active species on the surface depend significantly on surface temperature. The temperature monitoring system with high precision had been required to develop the process characteristics. Many methods of measuring substrate temperatures during plasma processes were proposed. However, there remain difficulties such as their poor tolerance to mechanical disturbances, resulting in limited resolution and temperature ranges when monitoring silicon wafers. We developed a real-time wafer temperature measurement system by an autocorrelation-type frequency-domain low-coherence interferometry (ACT-FD-LCI) system [2-4]. Since the wafer temperature is rapidly increased by energetic ion bombardments and radiative heat-fluxes from the plasma during processes, the surface reaction mechanism also varies with process time. To suppress the temperature variation during processes, a feedback control system of the wafer temperature was constructed. Controlling the plasma excitation and switching the biasing power “ON” and “OFF” enabled the actual temperature to be maintained within a range of ±1.2 °C from the set temperature.[5,6] This system revealed that the profile evolutions of anisotropic organic pattern etching by a H2/N2 plasma were temporally separated into vertical and lateral directions. Subsequently, trimming process of etched organic were performed without supplying bias power, while the substrate temperature was precisely controlled within ±0.7 °C of a set temperature due to lower heat flux from the plasma. The free-standing feature of organic material, with a width narrower than 12 nm, was fabricated in a self-limiting manner. [7] We expect that this self-limiting process could be applied to various advanced processes. References; [1] H. Yamamoto, H. Kuroda, M. Ito, T. Ohta. Hori, Jpn J Appl Phys, 51, 016202 (2012). [2] T. Tsutsumi, T. Ohta, K. Ishikawa, K. Takeda, H. Kondo, M. Sekine, M. Hori, M. Ito, Appl. Phys. Lett., 103, 182102 (2013). [3] T. Tsutsumi, T. Ohta, K. Ishikawa, K. Takeda, H. Kondo, M. Sekine, M. Hori, M. Ito, Jpn J Appl. Phys., 54, 01AB03 (2015). [4] T. Tsutsumi, T. Ohta, K. Ishikawa, K. Takeda, H. Kondo, M. Sekine, M. Hori, M. Ito, Appl. Opt., 54, 7088 (2015). [5] T. Tsutsumi, Y. Fukunaga, K. Ishikawa, K. Takeda, H. Kondo, T. Ohta, M. Ito, M. Sekine, M. Hori, IEEE Trans. Semicond. Manufact., 28, 515 (2015). [6] Y. Fukunaga, T. Tsutsumi, K. Takeda, H. Kondo, K. Ishikawa, M. Sekine, M. Hori, Jpn. J. Appl. Phys. 56, 076202 (2017). [7] Y. Fukunaga, T. Tsutsumi, H. Kondo, K. Ishikawa, M. Sekine, M. Hori, Jpn. J. Appl. Phys. 58, 020906 (2019).

Large Axial Range Frequency-Domain Optical Low Coherence Interferometry

In this letter, we propose a new experimental setup to extend the measurement range of frequency-domain low coherence interferometry (FD-LCI) from 3 mm to 2 cm. The FD-LCI can be extended to the technique of frequency domain optical coherence tomography by performing additional lateral scanning. This new and simple arrangement just attaches an extra interferometer before the spectrometer in a typical FD-LCI setup. With this configuration, it is possible to overcome the limitation of the dynamic range of the conventional technique. This allows us to measure the optical path difference of the sample of interest, which is outside the detection range of the spectrometer, using an extra interferometer as a tuner system. In addition, this tuning allows significant minimization of the effects produced by the fall-off. The accuracy of the new system is obtained by adding the FD-LCI and the tuning micrometric translator accuracies. In our experimental setup, this value is 20 $\mu \text{m}$ .

Refractive index measurement of compressed nitrogen using an infrared frequency-domain interferometer

Frequency-domain interferometry is used to obtain the refractive index of compressed nitrogen in the vicinity of 1550 nm as the pressure of nitrogen increases from 0 to 40 MPa at room temperature. By referring to the equation of state of nitrogen, the relation between the refractive index and the nitrogen density is obtained and the electric polarizability of a nitrogen molecule is thereby determined to be (1.82 ± 0.15) × 10−30 m−3 according to the Lorentz-Lorentz relation.

In Vivo Sarcomere Length Measurement in Whole Muscles during Passive Stretch and Twitch Contractions

Muscle force is dictated by micrometer-scale contractile machines called sarcomeres. Whole-muscle force drops from peak force production to zero with just a few micrometers of sarcomere length change. No current technology is able to capture adequate dynamic sarcomere data in vivo, and thus we lack fundamental data needed to understand human movement and movement disorders. Methods such as diffraction, endoscopy, and optical coherence tomography have been applied to muscle but are prohibitively invasive, sensitive to motion artifact, and/or imprecise. Here, we report dynamic sarcomere length measurement in vivo using a combination of our recently validated resonant reflection spectroscopy method combined with optical frequency domain interferometry. Using a 250-μm-wide fiber optic probe, we captured nanometer sarcomere length changes from thousands of sarcomeres on the sub-millisecond timescale during whole-muscle stretch and twitch contraction. We believe that this demonstrates the first large-scale sensing of sarcomere dynamics in vivo, which is a necessary first step to understand movement disorders and to create patient-specific surgical interventions and rehabilitation.