Electro-optic Sampling Research Articles

Complete positive operator-valued measure description of multichannel quantum electro-optic sampling with monochromatic field modes

We propose a multichannel version of quantum electro-optic sampling involving monochromatic field modes. It allows for multiple simultaneous measurements of arbitrarily many $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{X}$ and $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{Y}$ field quadratures for a single quantum-state copy, while independently tuning the interaction strengths at each channel. In contrast to standard electro-optic sampling, the sampled midinfrared (MIR) mode undergoes a nonlinear interaction with multiple near-infrared pump beams. We present a complete positive operator-valued measure description for quantum states in the MIR mode. The probability distribution of the electro-optic signal outcomes is shown to be related to an $s$-parametrized phase-space quasiprobability distribution of the indirectly measured MIR state, with the parameter $s$ depending solely on the quantities characterizing the nonlinear interaction. Furthermore, we show that the quasiprobability distributions for the sampled and postmeasurement states are related to each other through a renormalization and a change in the parametrization. This result is then used to demonstrate that two consecutive measurements of both $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{X}$ and $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{Y}$ quadratures can outperform eight-port homodyne detection.

The Coming Age of Pnictide and Chalcogenide Ternary Crystals in the Terahertz Frequency Regime

The last decade has witnessed explosive growth in terahertz radiation fields, ranging from fundamental research to applications. This progress has been marked by the introduction of various terahertz radiation sources and detectors. Here, we review the progress of nonlinear pnictide and chalcogenide ternary crystals for use in the terahertz frequency regime. At the center of this topical review are the various physical and optical properties of numerous emerging pnictide and chalcogenide nonlinear crystals, which are anchored to state-of-the-art coherent terahertz radiation sources based on optical rectification and difference frequency generation, as well as terahertz radiation phase-resolved detectors based on electro-optic sampling. This review aims to provide the foundation necessary to continue advancing pnictide and chalcogenide ternary crystals for the generation, detection, and manipulation of terahertz radiation.

Electro-optic sampling based characterization of broad-band high efficiency THz-FEL.

Extremely high beam-to-radiation energy conversion efficiencies can be obtained in a THz FEL using a strongly tapered helical undulator at the zero-slippage resonant condition, where a circular waveguide is used to match the radiation group velocity to the electron beam longitudinal velocity. In this paper we report on the first electro-optic sampling (EOS) based measurements of the broadband THz FEL radiation pulses emitted in this regime. The THz field waveforms are reconstructed in the spatial and temporal domains using multi-shot and single-shot EOS schemes respectively. The measurements are performed varying the input electron beam energy in the undulator providing insights on the complex dynamics in a waveguide FEL.

Ultrafast dynamics of coherent phonons and phonon-polaritons in lithium niobate crystals

This study investigates the ultrafast dynamics of coherent phonons and phonon-polaritons in lithium niobate (LiNbO3) crystals using reflective pump–probe spectroscopy with 25 fs time resolution. In addition to several coherent optical phonon modes, the electro-optic (EO) sampling measurements explored the coexistence of phonon-polariton E-modes near 3.8 and 14.9 THz, which agrees considerably with the theoretical phonon-polariton dispersion curves. We also discovered that a time lag ( 0.2 ps) between the coherent optical phonon and phonon-polariton originates from the coupling time for propagating phonon-polariton. Our findings provide a possible application of LiNbO3 for ultrafast EO phonon modulators with bandwidths greater than 10 THz.

Waveguide structure based electron acceleration using terahertz pulses.

We have developed a waveguide structure for electron acceleration using a few µJ energy THz pulse. The metallic device focuses the incoming linearly polarized nearly single-cycle THz pulse, hence increasing the peak electric field strength. We experimentally verified the gain and the temporal profile of the electric field in the structure using electro-optic sampling technique. The acceleration of the electron bunch from rest up to 8 keV was predicted using single-cycle THz pulses with µJ-energy level.

Frequency Alteration Built on an Electro-Optical Sampling SOA–MZI Using a Differential Modulation Schema

In this paper, we present a real and simulated study of a frequency up mixing employing an electro-optical sampling semiconductor optical amplifier Mach–Zehnder interferometer (SOA–MZI) along with the differential modulation schema. The sampling signal is generated by an optical pulse clock (OPC) at a frequency of fs= 19.5 GHz. The quadratic phase shift keying (QPSK) signal at an intermediate frequency (IF) fIF is shifted to high frequencies nfs ± fIF at the SOA–MZI output. Using a simulator entitled Virtual Photonics Inc. (VPI), we generate sampled QPSK signals and analyze their merits during conversion gains and error vector magnitudes (EVMs). We conducted simulations of mixing in the SOA–MZI operating in a high-frequency band up to 195.5 GHz. The positive conversion gain is accomplished over the mixing frequencies. The EVM is used to evaluate the performance of the electro-optical sampling up-convertor. The EVM reaches 14% at a data rate of 5 Gbit/s at 195.5 GHz. During the experimental work, the results obtained in simulations are set side by side with the factual ones in the frequency range up to 59 GHz. Thus, the comparison between them confirms that they have approximately the same performance.

High-speed two-dimensional terahertz spectroscopy with echelon-based shot-to-shot balanced detection.

By using a reflective-echelon-based electro-optic sampling technique and a fast detector, we develop a two-dimensional terahertz (THz) spectrometer capable of shot-to-shot balanced readout of THz waveforms at a full 1-kHz repetition rate. To demonstrate the capabilities of this new detection scheme for high-throughput applications, we use gas-phase acetonitrile as a model system to acquire two-dimensional THz rotational spectra. The results show a two-order-of-magnitude speedup in the acquisition of multidimensional THz spectra when compared to conventional delay-scan methods while maintaining accurate retrieval of the nonlinear THz signal. Our report presents a feasible solution for bringing the technique of multidimensional THz spectroscopy into widespread practice.

Ultraefficient resistance switching between charge ordered phases in 1T-TaS2 with a single picosecond electrical pulse

Progress in high-performance computing demands significant advances in memory technology. Among novel memory technologies that promise efficient device operation on a sub-ns timescale, resistance switching between charge ordered phases of 1T-TaS2 has shown to be potentially useful for development of high-speed, energy efficient nonvolatile memory devices. Measurement of the electrical operation of such devices in the picosecond regime is technically challenging and hitherto still largely unexplored. Here, we use an optoelectronic “laboratory-on-a-chip” experiment for measurement of ultrafast memory switching, enabling accurate measurement of electrical switching parameters with 100 fs temporal resolution. Photoexcitation and electro-optic sampling on a (Cd,Mn)Te substrate are used to generate and, subsequently, measure electrical pulse propagation with intra-band excitation and sub-gap probing, respectively. We demonstrate high contrast nonvolatile resistance switching from high to low resistance states of a 1T-TaS2 device using single sub-2 ps electrical pulses. Using detailed modeling, we find that the switching energy density per unit area is exceptionally small, EA= 9.4 fJ/μm2. The speed and energy efficiency of an electronic “write” process place the 1T-TaS2 devices into a category of their own among new generation nonvolatile memory devices.

Detection of quantum-vacuum field correlations outside the light cone

According to quantum field theory, empty space—the ground state with all real excitations removed—is not empty, but filled with quantum-vacuum fluctuations. Their presence can manifest itself through phenomena such as the Casimir force, spontaneous emission, or dispersion forces. These fluctuating fields possess correlations between space-time points outside the light cone, i.e. points causally disconnected according to special relativity. As a consequence, two initially uncorrelated quantum objects in empty space which are located in causally disconnected space-time regions, and therefore unable to exchange information, can become correlated. Here, we have experimentally demonstrated the existence of correlations of the vacuum fields for non-causally connected space-time points by using electro-optic sampling. This result is obtained by detecting vacuum-induced correlations between two 195 fs laser pulses separated by a time of flight of 470 fs. This work marks a first step in analyzing the space-time structure of vacuum correlations in quantum field theory.

Electric-field-resolved near-infrared microscopy

Access to the complete spatiotemporal response of matter due to structured light requires field sampling techniques with sub-wavelength resolution in time and space. We demonstrate spatially resolved electro-optic sampling of near-infrared waveforms, providing a versatile platform for the direct measurement of electric field dynamics produced by photonic devices and sub-wavelength structures both in the far and near fields. This approach offers high-resolution, time- or frequency-resolved imaging by encoding a broadband signal into a narrowband blueshifted image, lifting the resolution limits imposed by both chromatic aberration and diffraction. Specifically, measuring the field of a near-infrared laser with a broadband sampling laser, we achieve 1.2 µm resolution in space and 2.2 fs resolution in time. This provides an essential diagnostic for complete spatiotemporal control of light with metasurface components, demonstrated via a metalens as well as a meta-axicon that forms broadband, ultrashort, truncated Bessel beams in the near infrared. Finally, we demonstrate the electric field dynamics of locally enhanced hot spots with sub-wavelength dimensions, recording the full temporal evolution of the electric field at each point in the image simultaneously. The imaging modality opens a path toward hyperspectral microscopy with simultaneous sub-wavelength resolution and wide-field imaging capability.

Single-shot terahertz polarization detection based on terahertz time-domain spectroscopy

This paper presents a novel design for single-shot terahertz polarization detection based on terahertz time-domain spectroscopy (THz-TDS). Its validity has been confirmed by comparing its detection results with those of the THz common-path spectral interferometer through two separate measurements for the orthogonal components. Our results also show that its detection signal-to-noise ratios (SNRs) are obviously superior to those of the 45° optical bias THz-TDS by electro-optical sampling due to its operation on common-path spectral interference rather than the polarization-sensitive intensity modulation. The setup works without need of any optical scan, which does not only save time, but also efficiently avoids the disturbances from the fluctuations of the system and environment. Its single-shot mode allows it to work well for the applications with poor or no repeatability.

Contrast enhancement in near-infrared electro-optic imaging.

Access to subtle ultrafast effects of light-matter interaction often requires highly sensitive field detection schemes. Electro-optic sampling, being an exemplary technique in this regard, lacks high sensitivity in an imaging geometry. We demonstrate a straightforward method to significantly improve the contrast of electric field images in spatially resolved electro-optic sampling. A thin-film polarizer is shown to be an effective tool in enhancing the sensitivity of the electro-optic imaging system, enabling an adjustment of the spectral response. We show a further increase of the signal-to-noise ratio through the direct control of the carrier envelope phase of the imaged field.

Broadband terahertz time-domain polarimetry based on air plasma filament emissions and spinning electro-optic sampling in GaP.

We report on a time-domain polarimetry (TDP) system for generating and detecting broadband terahertz (THz) waves of different polarization angles. We generate THz waves from two-color laser filaments and determine their polarization states with a detection bandwidth of up to 8 THz using a spinning gallium phosphide crystal. The polarization of THz emission can be controlled by adjusting the position and tilt angle of the β-barium borate crystal. We characterize the precision of this system for polarimetric measurements at fixed time delay to be and for complete time-domain waveforms. We also demonstrate the feasibility of our TDP system by measuring broadband optical properties of anisotropic samples in both transmission and reflection geometries. The THz-TDP technique can be easily integrated in conventional THz time-domain spectroscopy setups using nonlinear crystal detectors.

Realizing a rapidly switched Unruh-DeWitt detector through electro-optic sampling of the electromagnetic vacuum

A new theoretical framework to describe the experimental advances in electro-optic detection of broadband quantum states, specifically the quantum vacuum, is devised. By making use of fundamental concepts from quantum field theory on spacetime metrics, the nonlinear interaction behind the electro-optic effect can be reformulated in terms of an Unruh-DeWitt detector coupled to a conjugate field during a very short time interval. When the coupling lasts for a time interval comparable to the oscillation periods of the detected field mode (i.e. the subcycle regime), virtual particles inhabiting the field vacuum are transferred to the detector in the form of real excitations. We demonstrate that this behavior can be rigorously translated to the scenario of electro-optic sampling of the quantum vacuum, in which the (spectrally filtered) probe works as an Unruh-DeWitt detector, with its interaction-generated photons arising from virtual particles inhabiting the electromagnetic vacuum. We discuss the specific working regime of such processes, and the consequences through characterization of the quantum light involved in the detection.

Electro-optic characterization of synthesized infrared-visible light fields

The measurement and control of light field oscillations enable the study of ultrafast phenomena on sub-cycle time scales. Electro-optic sampling (EOS) is a powerful field characterization approach, in terms of both sensitivity and dynamic range, but it has not reached beyond infrared frequencies. Here, we show the synthesis of a sub-cycle infrared-visible pulse and subsequent complete electric field characterization using EOS. The sampled bandwidth spans from 700 nm to 2700 nm (428 to 110 THz). Tailored electric-field waveforms are generated with a two-channel field synthesizer in the infrared-visible range, with a full-width at half-maximum duration as short as 3.8 fs at a central wavelength of 1.7 µm (176 THz). EOS detection of the complete bandwidth of these waveforms extends it into the visible spectral range. To demonstrate the power of our approach, we use the sub-cycle transients to inject carriers in a thin quartz sample for nonlinear photoconductive field sampling with sub-femtosecond resolution.

Electric-field-induced second harmonic generation in silicon dioxide.

Electric-field-induced second harmonic generation (EFISH) as a third order nonlinear process is of high practical interest for the realization of functional nonlinear structures. EFISH in materials with vanishing χ(2) and non-zero χ(3) offers huge potential, e.g., for background-free nonlinear electro-optical sampling. In this work, we have investigated SiO2 as a potential EFISH material for such applications using DC-electric fields. We were able to observe significant second harmonic generation (SHG) in comparison to the background SHG signal. The fundamental excitation at 800 nm results in a SHG signal at 400 nm for high applied DC electric fields, which is a clear indication for EFISH. Additionally, we were are able to precisely model the EFISH signal using time-domain simulations. This numerical approach will be of great importance for efficiency enhancement and prove as a valuable tool for future device design.

Noncollinear electro-optic sampling detection of terahertz pulses in a LiNbO3 crystal while avoiding the effect of intrinsic birefringence.

We propose and experimentally prove efficient high-resolution electro-optic sampling measurement of broadband terahertz waveforms in a LiNbO3 crystal in the configuration with the probe laser beam propagating along the optical axis of the crystal. This configuration allows one to avoid the detrimental effect of strong intrinsic birefringence of LiNbO3 without any additional optical elements. To achieve velocity matching of the terahertz wave and the probe beam, the terahertz wave is introduced into the crystal through a Si prism at the Cherenkov angle to the probe beam. The workability of the scheme at different wavelengths of the probe optical beam (800 and 1550 nm) is demonstrated.

Synchronization of an optical frequency comb and a microwave oscillator with 53 zs/Hz1/2 resolution and 10-20-level stability

Precise and stable synchronization between an optical frequency comb (femtosecond mode-locked laser oscillator or microresonator-based comb) and a microwave oscillator is important for various fields including telecommunication, radio astronomy, metrology, and ultrafast X-ray and electron science. Timing detection and synchronization using electro-optic sampling with an interferometer has been actively used for low-noise microwave generation, long-distance timing transfer, comb stabilization, time-of-flight sensing, and laser-microwave synchronization for ultrafast science facilities. Despite its outstanding performance, there has been a discrepancy in synchronization performance of more than 10 dB between the projected shot-noise-limited noise floor and the measured residual noise floor. In this work, we demonstrate the shot-noise-limited performance of an electro-optic timing detector-based comb-microwave synchronization, which enabled an unprecedented residual phase noise floor of − 174.5 dBc / Hz at 8 GHz carrier frequency (i.e., 53 zs / Hz 1 / 2 timing noise floor), integrated rms timing jitter of 88 as ( 1 Hz to 1 MHz ), rms timing drift of 319 as over 12 h, and frequency instability of 3.6 × 10 − 20 over 10,000 s averaging time. We identified that bandpass filtering of the microwave signal and optical pulse repetition-rate multiplication are critical for achieving this performance.

Phase Diversity Electro-optic Sampling: A new approach to single-shot terahertz waveform recording

Recording electric field evolution in single-shot with THz bandwidth is needed in science including spectroscopy, plasmas, biology, chemistry, Free-Electron Lasers, accelerators, and material inspection. However, the potential application range depends on the possibility to achieve sub-picosecond resolution over a long time window, which is a largely open problem for single-shot techniques. To solve this problem, we present a new conceptual approach for the so-called spectral decoding technique, where a chirped laser pulse interacts with a THz signal in a Pockels crystal, and is analyzed using a grating optical spectrum analyzer. By borrowing mathematical concepts from photonic time stretch theory and radio-frequency communication, we deduce a novel dual-output electro-optic sampling system, for which the input THz signal can be numerically retrieved—with unprecedented resolution—using the so-called phase diversity technique. We show numerically and experimentally that this approach enables the recording of THz waveforms in single-shot over much longer durations and/or higher bandwidth than previous spectral decoding techniques. We present and test the proposed DEOS (Diversity Electro-Optic Sampling) design for recording 1.5 THz bandwidth THz pulses, over 20 ps duration, in single-shot. Then we demonstrate the potential of DEOS in accelerator physics by recording, in two successive shots, the shape of 200 fs RMS relativistic electron bunches at European X-FEL, over 10 ps recording windows. The designs presented here can be used directly for accelerator diagnostics, characterization of THz sources, and single-shot Time-Domain Spectroscopy.

Probing the Purcell effect without radiative decay: lessons in the frequency and time domains

The effect of cavities or plates upon the electromagnetic quantum vacuum are considered in the context of electro-optic sampling (EOS), revealing how they can be directly studied. These modifications are at the heart of e.g. the Casimir force or the Purcell effect such that a link between EOS of the quantum vacuum and environment-induced vacuum effects is forged. Furthermore, we discuss the microscopic processes underlying EOS of quantum-vacuum fluctuations, leading to an interpretation of these experiments in terms of exchange of virtual photons. With this in mind it is shown how one can reveal the dynamics of vacuum fluctuations by resolving them in the frequency and time domains using EOS experiments.