Electro-optic Sampling Research Articles

Optical Time-Domain Quantum State Tomography on a Subcycle Scale

Following recent progress in the experimental application of electro-optic sampling to the detection of the quantum fluctuations of the electromagnetic-field ground state and ultrabroadband squeezed states on a subcycle scale, we propose an approach to elevate broadband electro-optic sampling from a spectroscopic method to a full quantum tomography scheme, able to reconstruct a free-space quantum state directly in the time domain. By combining two recently developed methods to theoretically describe quantum electro-optic sampling, we analytically relate the photon-count probability distribution of the electro-optic signal to a transformed phase-space quasiprobability distribution of the sampled quantum state as a function of the time delay between the sampled midinfrared pulsed state and an ultrabroadband near-infrared probe pulse. We catalog and analyze sources of noise and show that in quantum electro-optic sampling with an ultrabroadband probe pulse one can expect to observe thermalization due to entanglement breaking. Mitigation of the thermalization noise enables a tomographic reconstruction of broadband quantum states while granting access to its dynamics on a subcycle scale. Published by the American Physical Society 2024

Multi-cycle terahertz generation in lithium niobate wafer stacks via mid-infrared pumping.

Near-infrared laser-pumped optical rectification (OR) using quasi-phase matching (QPM) in lithium niobate (LN) is widely employed to generate multi-cycle terahertz (THz) pulses, which, however, suffer from low efficiency. Here, we demonstrate that mid-infrared pumping is an effective approach to increase the efficiency of multi-cycle THz generation. By using a 2.3-µm laser to pump a QPM macro-crystal composed of ten x-cut lithium niobate wafers, with their ferroelectric Z axis alternately rotated by π, a laser-to-THz conversion efficiency up to ∼0.4% has been achieved at room temperature, more than twice the efficiencies attained with near-infrared pumping. Electro-optic sampling reveals the generation of five-cycle THz pulses at 0.15 THz for 350-µm-thick wafers and 0.22 THz for 250-µm-thick wafers. Such mid-infrared laser-pumped OR in QPM wafer stacks provides an efficient, controllable, and scalable method for generating intense multi-cycle THz pulses suitable for diverse narrow-bandwidth applications.

Frequency-resolved measurement of two-color air plasma terahertz emission

We investigated the far-field terahertz beam profile generated from an air plasma induced by two-color femtosecond laser pulses. Under our experimental conditions (filament length shorter than the dephasing length between the two-color pulses), using electro-optic sampling in both ZnTe (0.2-2.2 THz) and GaP (0.4-6.8 THz) crystals, and ultra-broadband ABCD technique (1-17.5 THz), we determined that the THz beam exhibits a unimodal beam pattern below 4 THz and a conical one above 6 THz. This experimental finding is consistent with theoretical studies based on the unidirectional pulse propagation equation, which predict the transition of THz emission from a flat-top profile to a conical one due to the destructive interference of THz waves emitted from the plasma filament. Our results also underscore the importance of accounting for experimental artifacts, such as photo-excited losses in silicon resulting in on-axis THz absorption along with the influence of drilled mirrors, in characterizing the complex spatial and frequency-dependent behavior of two-color plasma-induced terahertz emission.

χ (2)-induced artifact overwhelming the third-order signal in 2D Raman-THz spectroscopy of non-centrosymmetric materials.

Through comprehensive data analysis, we demonstrate that a χ(2)-induced artifact, arising from imperfect balancing in the conventional electro-optic sampling detection scheme, contributes significantly to the measured signal in 2D Raman-THz spectroscopy of non-centrosymmetric materials. The artifact is a product of two 1D responses, overwhelming the desired 2D response. We confirm that by analyzing the 2D Raman-THz response of an x-cut beta barium borate crystal. We furthermore show that this artifact can be effectively suppressed by implementing a special detection scheme. We successfully isolate the desired third-order 2D Raman-THz response, revealing a distinct cross-peak feature, whose frequency position suggests the coupling between two crystal phonons.

FPGA-based measurements of the relative arrival time of a high-repetition rate, quasi-cw fourth generation light source.

In this paper, we demonstrate the successful implementation of reconfigurable field-programmable gate array technology into a pulse-resolved data acquisition system to achieve a femtosecond temporal resolution in ultrafast pump-probe experiments in real-time at large scale facilities. As proof of concept, electro-optic sampling of terahertz waveforms radiated by a superradiant emitter of a quasi-cw accelerator operating at a 50kHz repetition rate and probed by an external laser system is performed. Options for up-scaling the developed technique to a MHz range of repetition rates are discussed.

A phase-correction approach for enhancing mid-infrared electro-optic sampling in highly nonlinear and dispersive birefringent crystals

A phase-correction approach for enhancing mid-infrared electro-optic sampling in highly nonlinear and dispersive birefringent crystals

Sub-attosecond-precision optical-waveform stability measurements using electro-optic sampling

The generation of laser pulses with controlled optical waveforms, and their measurement, lie at the heart of both time-domain and frequency-domain precision metrology. Here, we obtain mid-infrared waves via intra-pulse difference-frequency generation (IPDFG) driven by 16-femtosecond near-infrared pulses, and characterise the jitter of sub-cycle fractions of these waves relative to the gate pulses using electro-optic sampling (EOS). We demonstrate sub-attosecond temporal jitter at individual zero-crossings and sub-0.1%-level relative amplitude fluctuations in the 10-kHz–0.625-MHz band. Chirping the nearly-octave-spanning mid-infrared pulses uncovers wavelength-dependent attosecond-scale waveform jitter. Our study validates EOS as a broadband (both in the radio-frequency and the optical domains), highly sensitive measurement technique for the jitter dynamics of optical waveforms. This sensitivity reveals outstanding stability of the waveforms obtained via IPDFG and EOS, directly benefiting precision measurements including linear and nonlinear (infrared) field-resolved spectroscopy. Furthermore, these results form the basis toward EOS-based active waveform stabilisation and sub-attosecond multi-oscillator synchronisation/delay tracking.

Modulation and real-time monitoring of the carrier-envelope phase of terahertz pulses based on shaping of near-infrared femtosecond pulses.

We propose a novel, to our knowledge, method for modulating and real-time monitoring of the carrier-envelope phase (CEP) of terahertz (THz) pulses. CEP is an essential parameter in the interaction of THz waves with matter due to the difference in temporal symmetry when the carrier is extended for several cycles. CEP can be continuously modulated at full range with high speed by oscillating the optical path length of the Michelson interferometer under 1 µm, as confirmed by electro-optic (EO) sampling. The proposed method can be combined with a data acquisition method that links the experimental parameters and measurements of individual high-repetition THz pulses to realize robust CEP modulation measurements. As the proposed CEP modulation and monitoring system does not require EO sampling but only extracts CEP dependence, the trend toward ultrafast physical property control and observation using THz pulses will spread to other fields.

Zeeman torque sampling of intense terahertz magnetic field in CoFe.

Free-space strong-field terahertz (THz) electromagnetic pulses have emerged as a potent tool for non-equilibrium quantum state control. However, these applications predominantly rely on electric field components, with limited utilization of magnetic field components. A traditional electro-optical sampling technique may encounter constraints due to the field strength saturation effect when detecting strong-field THz pulses. Here we have identified intense THz-induced Zeeman torque signals in CoFe and successfully detected the THz magnetic field components. Through variations in the type of ferromagnetic materials and the thickness of ferromagnetic films, we further refined the detection of THz magnetic field components. Our research revealed that a 15-nm CoFe thin film is more responsive in measuring magnetic field components.

Advanced Modeling of Electro‐Optic Sampling: Nonlinear Vectoral‐Field Solutions to Maxwell's Equations

AbstractA comprehensive modeling approach for elucidating the intricacies of electro‐optic (EO) sampling is presented, which fully encapsulates the EO sampling process by accounting for all linear and second‐order nonlinear optical effects. The developed approach implements a multi‐step procedure, involving a vectorial‐field modeling of the second‐order nonlinear interactions occurring within the EO crystal, followed by a theoretical evaluation of the subsequent optical EO sampling components. To assess the efficacy of the approach, it is used for the sampling of terahertz electric fields (<1–>60 THz) within the bulk crystals of ZnTe and LiNbO3, as well as a ZnTe‐based waveguide. Nonetheless, this versatile method enables the investigation of EO sampling within any crystal incorporated within any geometry. This model provides a powerful tool for the in‐depth exploration of EO sampling, paving the way for advancements in various applications.

Propagation of broadband mid-infrared optical pulses in atmosphere

We study and describe the reshaping of ultrashort and broadband mid-IR optical pulses in an ambient atmosphere. While all pulse propagation undergoes dispersion and absorption, which causes pulse reshaping, the effects are strongly pronounced for broadband radiation in the mid-IR due to the orders of magnitude greater oscillator strengths of molecular constituents of our atmosphere. A noticeable macroscopic impact is a transition of the measured autocorrelation function from squared hyperbolic secant to Lorentzian, which we fully explain based on pulse propagation, including molecular free induction decay. Electro-optical sampling directly reveals the light wave response to atmospheric molecular free induction decay, and a Kramers–Kronig-based propagation model thoroughly explains the observation. The findings are essential for applications in sensing, standoff detection, high-energy pulse propagation, and energy delivery.

Excitation-dependent features and artifacts in 2-D terahertz spectroscopy.

Recently, two-dimensional terahertz spectroscopy (2DTS) has attracted increasing attention for studying complex solids. A number of recent studies have applied 2DTS either with long pulses or away from any material resonances, situations that yield unconventional 2DTS spectra that are often difficult to interpret. Here, we clarify the generic origins of observed spectral features by examining 2DTS spectra of ZnTe, a model system with a featureless optical susceptibility at low terahertz frequencies. These results also reveal possible artifacts that may arise from electro-optic sampling in collinear 2DTS experiments, including the observation of spurious rectified or second harmonic signals.

Spatiotemporal walk-off and improved focusing of plasma THz sources.

High-field THz sources with peak field strengths exceeding MV/cm are essential for nonlinear THz spectroscopy and coherent control of matter on ultrafast time scales. Two-color femtosecond laser plasma sources employing long filamentation have been reported as providing single-cycle, >MV/cm fields, with multi-decade spanning bandwidth and polarization control, making them promising sources for such experiments. In this work, we report the observation of spatiotemporal spreading of the THz pulse when standard off-axis parabolic mirrors are used for collection and focusing of long filament plasma-based THz pulses. This produces a flying focus for THz light, with the axial focal region propagating at a velocity of 1/3 the speed of light. The THz emission is then subsequently spread over a temporal width of ∼10 ps, approximately 100 times the THz pulse duration detected by electro-optic sampling at any single point along the focus. The consequences of this non-ideal focusing are a potential and drastic overestimation of the peak THz electric field based on energy measurements, as well as significant phase noise arising from beam pointing fluctuations. We show that this spatiotemporal spreading can be minimized using a simple axicon lens that perfectly collimates the extended filament source, resulting in improved spatial and temporal focusing of the THz pulse.

An optical fiber integrated device for nonlinear generation of femtosecond mid-infrared pulses

Compact and broadband mid-infrared (MIR) sources are in high demand because of a wide range of potential applications such as molecular sensing in the fingerprint region. The generation of coherent MIR radiation at arbitrary frequencies typically requires nonlinear mixing between at least two input waves, which is often cumbersome to implement. We present an integrated and, therefore, adjustment-free solution combining few-femtosecond pulse compression in a germanosilicate optical fiber and optical rectification. To this end, a 16-μm-thin GaSe crystal is directly mounted on the end facet of a highly nonlinear fiber assembly exploiting a focused ion beam. With input pulses of a minute energy of 5 nJ and a duration of 120 fs at the telecom wavelength of 1.55 μm, we directly obtain ultrabroadband and phase-stable output transients. Electro-optic sampling in free space reveals single-cycle pulses with spectral components covering the entire MIR from 10 to 120 THz.

Dual-oscillator infrared electro-optic sampling with attosecond precision

Electro-optic sampling of infrared electric fields has set sensitivity and dynamic-range records in broadband molecular vibrational spectroscopy. Yet, in these works, the 1-second-scale single-trace acquisition time leads to intra-scan noise accumulation and restricts the throughput in measurements of multiple samples and of dynamic processes. We present a dual-laser-oscillator approach capturing 2800 mid-infrared waveforms per second by scanning the relative delay between the sampled waveform and the gate pulses using a modulated repetition-frequency lock. The new technique of electro-optic delay tracking (EODT) provides delay calibration with down to few-attosecond precision and provides a general route to high-precision dual-oscillator spectroscopy with picosecond delay ranges. Our work has immediate applications in, e.g., precision electric-field metrology and high-speed biosensing.

Increasing terahertz spintronic emission with planar antennas

Spintronic THz emitters, consisting of Ta/Co/Pt trilayers patterned into lateral-sized rectangles in the 10 μm range, have been integrated in planar electromagnetic antennas of various types (dipole, bow-tie, and spiral). The antenna dimensions and shapes have been optimized with the help of electromagnetic simulations so as to maximize antenna efficiency in both narrow-band and broadband geometries at/around 1 THz. The THz emission has been studied using a pump–probe free space electro-optic sampling setup, both for single-emitter geometry and for arrays of emitters. The results show an increase in the detected THz signal for all antenna geometries, with enhancement ratios in the range of three to fifteen, depending on the antenna type and frequency range, together with changes in the emission bandwidth consistent with simulated characteristics.

Noncollinear electro-optic detection of terahertz waves: Advantages and limitations

Electro-optic sampling of terahertz waves by noncollinearly propagating femtosecond laser pulses in electro-optic crystals can provide high efficiency and high spectral resolution of terahertz detection with various types of crystals and laser wavelengths, unlike the conventional collinear scheme. We develop an analytical theory of noncollinear electro-optic sampling detection technique that describes the modulation of the probe laser beam polarization as a result of nonlinear interaction between the optical and terahertz fields. The theory accounts for finite widths of the terahertz and probe beams. It is found that noncollinear scheme operates as a low-pass terahertz filter with the frequency cut-off determined by the width of the probe beam and the crossing angle of the terahertz and probe beams. We apply the theory to two practical situations: sampling of terahertz waves by fiber laser pulses (1.55 μm wavelength) in a GaAs crystal and sampling by Ti:sapphire laser pulses (800 nm wavelength) in a LiNbO3 crystal.

Electro-optic 3D snapshot of a laser wakefield accelerated kilo-ampere electron bunch

Laser wakefield acceleration, as an advanced accelerator concept, has attracted great attentions for its ultrahigh acceleration gradient and the capability to produce high brightness electron bunches. The three-dimensional (3D) density serves as an evaluation metric for the particle bunch quality and is intrinsically related to the applications of an accelerator. Despite its significance, this parameter has not been experimentally measured in the investigation of laser wakefield acceleration. We report on an electro-optic 3D snapshot of a laser wakefield electron bunch at a position outside the plasma. The 3D shape of the electron bunch was detected by simultaneously performing optical transition radiation imaging and electro-optic sampling. Detailed 3D structures to a few micrometer levels were reconstructed using a genetic algorithm. The electron bunch possessed a transverse size of less than 30 micrometers. The current profile shows a multi-peak structure. The main peak had a duration of < 10 fs and a peak current > 1 kA. The maximum electron 3D number density was ~ 9 × 1021 m -3. This research demonstrates a feasible way of 3D density monitoring on femtosecond kilo-ampere electron bunches, at any position of a beam transport line for relevant applications.

Third order nonlinear correlation of the electromagnetic vacuum at near-infrared frequencies

In recent years, electro-optic sampling, which is based on Pockel’s effect between an electromagnetic mode and a copropagating, phase-matched ultrashort probe, has been largely used for the investigation of broadband quantum states of light, especially in the mid-infrared and terahertz frequency range. The use of two mutually delayed femtosecond pulses at near-infrared frequencies allows the measurement of quantum electromagnetic radiation in different space-time points. Their correlation allows therefore direct access to the spectral content of a broadband quantum state at terahertz frequencies after Fourier transformation. In this work, we will prove experimentally and theoretically that when using strongly focused coherent ultrashort probes, the electro-optic sampling technique can be affected by the presence of a third-order nonlinear mixing of the probes’ electric field at near-infrared frequencies. Moreover, we will show that these third-order nonlinear phenomena can also influence correlation measurements of the quantum electromagnetic radiation. We will prove that the four-wave mixing of the coherent probes’ electric field with their own electromagnetic vacuum at near-infrared frequencies results in the generation of a higher-order nonlinear correlation term. The latter will be characterized experimentally, proving its local nature requiring the physical overlap of the two probes. The parameters regime where higher order nonlinear correlation results predominant with respect to electro-optic correlation of terahertz radiation is provided.

DC electrical conductivity measurements of warm dense matter using ultrafast THz radiation

We describe measurements of the DC electrical conductivity of warm dense matter using ultrafast terahertz (THz) pulses. THz fields are sufficiently slowly varying that they behave like DC fields on the timescale of electron–electron and electron–ion interactions and hence probe DC-like responses. Using a novel single-shot electro-optic sampling technique, the electrical conductivity of the laser-generated warm dense matter was determined with &amp;lt;1 ps temporal resolution. We present the details of the single-shot THz detection methodology as well as considerations for warm dense matter experiments. We, then, provide proof-of-concept studies on aluminum driven to the warm dense matter regime through isochoric heating and shock compression. Our results indicate a decrease in the conductivity when driven to warm dense matter conditions and provide a platform for future warm dense matter studies.