Shot noise reduced terahertz detection via spectrally postfiltered electro-optic sampling

Quantum-enhanced time-domain spectroscopy

The time-resolved detection of mid- to far-infrared electric fields absorbed and emitted by molecules is among the most sensitive spectroscopic approaches and has the potential to transform sensing in fields such as security screening, quality control, and medical diagnostics. However, the sensitivity of the standard detection approach, which relies on encoding the far-infrared electric field into amplitude modulation of a visible or near-infrared probe laser pulse, is limited by the shot noise of the latter. This constraint cannot be overcome without using a quantum resource. Here, we show that this constraint can be overcome using a two-mode squeezed state. Quantum-correlated ultrashort pulses, generated by parametric down-conversion, enhance the sensitivity of far-infrared detection beyond the classical limit, achieving a twofold reduction in measured noise. This advancement paves the way for further development of ultrafast quantum metrology, moving toward quantum-enhanced time-resolved electric field spectroscopy with sensitivities beyond the standard quantum limit.

Self-balanced and self-phase-corrected electro-optic sampling in a birefringent crystal

Mid-to-far-infrared (IR) spectral content is recorded using the novel self-balanced and self-phase-corrected electro-optical (EO) sampling arrangement. Self-balancing guarantees that the electric field emerging from the EO crystal yields a signal of zero via a Wollaston prism and balanced photodetector (i.e., without a wave plate following the EO crystal) in the absence of the electric field being sampled. Moreover, self-phase-correction ensures a nearly frequency-independent phase difference between the probe electric field pulse and the electric field pulse generated within the EO crystal via second-order nonlinear optical interactions. The self-balanced and self-phase corrected arrangement has the potential to yield enhancement of EO signals recorded using previously investigated birefringent crystals (implemented within traditional EO sampling geometries) and deliver optimum EO signal strengths when considering unexplored birefringent crystals.

Adaptable electro-optic detection of THz radiation using a laser-written bull's-eye antenna

We report a nonlinear terahertz (THz) detection device based on a metallic bull's-eye plasmonic antenna. The antenna, fabricated with femtosecond laser direct writing and deposited on a nonlinear gallium phosphide (GaP) crystal, focuses incoming THz waveforms within the sub-wavelength bull's eye region to locally enhance the THz field. Additionally, the plasmonic structure minimizes diffraction effects allowing a relatively long interaction length between the transmitted THz field and the co-propagating near-infrared gating pulse used in an electro-optic sampling configuration. We show an increased detection sensitivity over a large spectral range extending from 1.4 THz to 3.1 THz with a peak enhancement factor of 3.1 at 2.7 THz. We demonstrate that this plasmonic structure is especially effective in monitoring THz signals affected by beam wandering or varying spot sizes. Our concept can be adapted to any second-order nonlinear crystal to realize compact and sensitive THz detectors without the need for tight beam focusing or high-precision alignment. This work paves the way for future developments of compact and sensitive THz detectors, notably for applications in wireless communications.

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.

Zeptojoule detection of terahertz pulses by parametric frequency upconversion

We combine parametric frequency upconversion with the single-photon counting technology to achieve terahertz (THz) detection sensitivity down to the zeptojoule (zJ) pulse energy level. Our detection scheme employs a near-infrared ultrafast source, a GaP nonlinear crystal, optical filters, and a single-photon avalanche diode. This configuration is able to resolve 1.4 zJ (1.4 × 10-21 J) THz pulse energy, corresponding to 1.5 photons per pulse, when the signal is averaged within only 1 s (or 50,000 pulses). A single THz pulse can also be detected when its energy is above 1185 zJ. These numbers correspond to the noise-equivalent power and THz-to-NIR photon detection efficiency of 1.3 × 10-16 W/Hz1/2 and 5.8 × 10-2%, respectively. To test our scheme, we perform spectroscopy of the water vapor between 1 and 3.7 THz and obtain results that are in agreement with those acquired with a standard electro-optic sampling (EOS) method. Our technique provides a 0.2 THz spectral resolution offering a fast alternative to EOS THz detection for monitoring specific spectral components in spectroscopy, imaging, and communication applications.

Generation of 17-32 THz radiation from a CdSiP2 crystal

A phase-resolved electric field pulse is produced through the second-order nonlinear process of intra-pulse difference frequency generation (DFG) in a (110) CdSiP₂ chalcopyrite crystal. The generated electric field pulse exhibits a duration of several picoseconds and contains frequency components within the high-frequency terahertz regime of ∼17-32 THz. The intra-pulse DFG signal is shown to be influenced by single-phonon and two-phonon absorption, the nonlinear phase-matching criterion, and temporal spreading of the excitation electric field pulse. To date, this is the first investigation in which a CdSiP₂ chalcopyrite crystal is used to produce radiation within the aforementioned spectral range.

Mid-infrared cross-comb spectroscopy

Dual-comb spectroscopy has been proven beneficial in molecular characterization but remains challenging in the mid-infrared region due to difficulties in sources and efficient photodetection. Here we introduce cross-comb spectroscopy, in which a mid-infrared comb is upconverted via sum-frequency generation with a near-infrared comb of a shifted repetition rate and then interfered with a spectral extension of the near-infrared comb. We measure CO2 absorption around 4.25 µm with a 1-µm photodetector, exhibiting a 233-cm-1 instantaneous bandwidth, 28000 comb lines, a single-shot signal-to-noise ratio of 167 and a figure of merit of 2.4 × 106 Hz1/2. We show that cross-comb spectroscopy can have superior signal-to-noise ratio, sensitivity, dynamic range, and detection efficiency compared to other dual-comb-based methods and mitigate the limits of the excitation background and detector saturation. This approach offers an adaptable and powerful spectroscopic method outside the well-developed near-IR region and opens new avenues to high-performance frequency-comb-based sensing with wavelength flexibility.

Emission and sensing of high-frequency terahertz electric fields using a GaSe crystal

A GaSe crystal cut along the (001) crystallographic plane is investigated for the emission and detection of high-frequency (i.e. up to ∼20 THz) electric fields. To date, a comprehensive analysis on high-frequency difference frequency generation and electro-optic sensing in GaSe has not been performed and should consider aspects such as electric field polarization orientation, symmetries inherent to the crystal structure, and the various possible generation and detection phase-matching arrangements. Herein, terahertz radiation generation is investigated for various excitation electric field polarizations as the GaSe crystal is rotated in the (001) plane. Subsequently, the crystal is rotated out-of-plane to investigate the difference frequency generation and electro-optic sampling phase-matching conditions for various arrangements. The measured terahertz radiation spectra show peak generation at the frequencies of 10, 16, and 18 THz (dependent on the GaSe crystal orientation), in agreement with the frequencies exhibiting perfect phase-matching. GaSe has the potential to emerge as the primary crystal for the emission and detection of high-frequency electric fields, such that this comprehensive analysis is necessary for the widespread adoption and practical implementation of GaSe as a high-frequency source crystal.

Ultra-broadband all-optical sampling of optical waveforms

Optical-field sampling techniques provide direct access to the electric field of visible and near-infrared light. The existing methods achieve the necessary bandwidth using highly nonlinear light-matter interaction that involves ionization of atoms or generation of charge carriers in solids. We demonstrate an alternative, all-optical approach for measuring electric fields of broadband laser pulses, which offers an advantage in terms of sensitivity and signal-to-noise ratio and extends the detection bandwidth of optical methods to the petahertzdomain.

Electro-Optical Sampling of Single-Cycle THz Fields with Single-Photon Detectors

Electro-optical sampling of Terahertz fields with ultrashort pulsed probes is a well-established approach for directly measuring the electric field of THz radiation. This technique usually relies on balanced detection to record the optical phase shift brought by THz-induced birefringence. The sensitivity of electro-optical sampling is, therefore, limited by the shot noise of the probe pulse, and improvements could be achieved using quantum metrology approaches using, e.g., NOON states for Heisenberg-limited phase estimation. We report on our experiments on THz electro-optical sampling using single-photon detectors and a weak squeezed vacuum field as the optical probe. Our approach achieves field sensitivity limited by the probe state statistical properties using phase-locked single-photon detectors and paves the way for further studies targeting quantum-enhanced THz sensing.

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.

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.

Enhanced intrapulse difference frequency generation in the mid-infrared by a spectrally dependent polarization state

We present a technique to optimize the intrapulse difference frequency generation efficiency for mid-infrared generation. The approach employs a multi-order wave plate that is designed to selectively rotate the polarization state of the incoming spectral components on the relevant orthogonal axes for subsequent nonlinear interaction. We demonstrate a significant increase of the mid-infrared average power generated, of a factor ≥2.5 compared with the conventional scheme, owing to an optimally distributed number of photons enrolled in the difference frequency generation process.

Ultra-rapid electro-optic sampling of octave-spanning mid-infrared waveforms

We demonstrate ultra-rapid electro-optic sampling (EOS) of octave-spanning mid-infrared pulses centered at 9 μm, implemented by mechanically scanning a mirror with a sonotrode resonating at 19 kHz (forward and backward acquisition at 38 kHz). The instrument records the infrared waveform with a spectral intensity dynamic range of 1.6 × 10⁵ for a single scan over a 1.6-ps delay range, acquired within 26 μs. The purely reflective nature of the delay scanning technique is compatible with broad optical bandwidths, short pulse durations (16 fs, centered at 1030 nm) and high average powers (Watt-level). Interferometric tracking of the sonotrode motion in combination with a predictor-corrector algorithm allows for delay-axis determination with down to single-digit attosecond precision. Ultra-rapid mid-infrared EOS will advance applications such as molecular fingerprinting of static samples as well as tracking of biological processes and chemical reactions and is likely to find new fields of application such as infrared-spectroscopic flow cytometry.

Few-cycle mid-infrared pulses from BaGa2GeSe6

BaGa₂GeSe₆ (BGGSe) is a newly developed nonlinear material that is attractive for ultrabroad frequency mixing and ultrashort pulse generation due to its comparably low dispersion and high damage threshold. A numerical study shows the material's capacity for octave-spanning mid-infrared pulse generation up to 18 µm. In a first experiment, we show that a long crystal length of 2.6 mm yields a pulse energy of 21 pJ at 100 MHz with a spectral bandwidth covering 5.8 to 8.5 µm. The electric field of the carrier-envelope-phase stable pulse is directly measured with electro-optical sampling and reveals a pulse duration of 91 fs, which corresponds to sub-four optical cycles, thus confirming some of the prospects of the material for ultrashort pulse generation and mid-infrared spectroscopy.

Multi-octave, CEP-stable source for high-energy field synthesis

The development of high-energy, high-power, multi-octave light transients is currently the subject of intense research driven by emerging applications in attosecond spectroscopy and coherent control. We report on a phase-stable, multi-octave source based on a Yb:YAG amplifier for light transient generation. We demonstrate the amplification of a two-octave spectrum to 25 μJ of energy in two broadband amplification channels and their temporal compression to 6 and 18 fs at 1 and 2 μm, respectively. In this scheme, due to the intrinsic temporal synchronization between the pump and seed pulses, the temporal jitter is restricted to long-term drift. We show that the intrinsic stability of the synthesizer allows subcycle detection of an electric field at 0.15 PHz. The complex electric field of the 0.15-PHz pulses and their free induction decay after interaction with water molecules are resolved by electro-optic sampling over 2 ps. The scheme is scalable in peak and average power.

Attosecond optoelectronic field measurement in solids

The sub-cycle interaction of light and matter is one of the key frontiers of inquiry made accessible by attosecond science. Here, we show that when light excites a pair of charge carriers inside of a solid, the transition probability is strongly localized to instants slightly after the extrema of the electric field. The extreme temporal localization is utilized in a simple electronic circuit to record the waveforms of infrared to ultraviolet light fields. This form of petahertz-bandwidth field metrology gives access to both the modulated transition probability and its temporal offset from the laser field, providing sub-fs temporal precision in reconstructing the sub-cycle electronic response of a solid state structure.

Characterization of light pulses is important in order to understand their interaction with matter. Here the authors demonstrate a nonlinear photoconductive sampling method to measure electric field wave-forms in the infrared, visible and ultraviolet spectral ranges.

Multibranch pulse synthesis and electro-optic detection of subcycle multi-terahertz electric fields

We present a robust, compact pulse synthesis scheme generating intense phase-locked subcycle multi-terahertz waveforms. The ultrabroadband laser fundamental is split into two parallel branches driving optical rectification in crystals of GaSe and LiGaS₂, each operated at the group velocity matching point. The coherent combination of the resulting pulses yields a continuous multi-terahertz spectrum covering 1.5 optical octaves. The corresponding 0.8-cycle electric field waveform is directly mapped out by electro-optic sampling, revealing peak fields of 15 kV/cm at a repetition rate of 0.4 MHz. The multiplexable and power scalable scheme opens the door to strong-field custom-tailored waveforms driving nonlinear optics and light wave electronics.

Octave-spanning single-cycle middle-infrared generation through optical parametric amplification in LiGaS2

We report the generation of extremely broadband and inherently phase-locked mid-infrared pulses covering the 5 to 11 µm region. The concept is based on two stages of optical parametric amplification starting from a 270-fs Yb:KGW laser source. A continuum seeded, second harmonic pumped pre-amplifier in β-BaB₂O₄ (BBO) produces tailored broadband near-infrared pulses that are subsequently mixed with the fundamental pump pulses in LiGaS₂ (LGS) for mid-infrared generation and amplification. The pulse bandwidth and chirp is managed entirely by selected optical filters and bulk material. We find an overall quantum efficiency of 1% and a mid-infrared spectrum smoothly covering 5-11 µm with a pulse energy of 220 nJ at 50 kHz repetition rate. Electro-optic sampling with 12-fs long white-light pulses directly from self-compression in a YAG crystal reveals near-single-cycle mid-infrared pulses (32 fs) with passively stable carrier-envelope phase. Such pulses will be ideal for producing attosecond electron pulses or for advancing molecular fingerprint spectroscopy.

Ultrabroadband etalon-free detection of infrared transients by van-der-Waals contacted sub-10-µm GaSe detectors

We demonstrate ultrabroadband electro-optic detection of multi-THz transients using mechanically exfoliated flakes of gallium selenide of a thickness of less than 10 µm, contacted to a diamond substrate by van-der-Waals bonding. While the low crystal thickness allows for extremely broadband phase matching, the excellent optical contact with the index-matched substrate suppresses multiple optical reflections. The high quality of our structure makes our scheme suitable for the undistorted and artifact-free observation of electromagnetic waveforms covering the entire THz spectral range up to the near-infrared regime without the need for correction for the electro-optic response function. With the current revolution of chemically inert quasi-two-dimensional layered materials, we anticipate that exfoliated van-der-Waals materials on index-matched substrates will open new flexible ways of ultrabroadband electro-optic detection at unprecedented frequencies.

Probing the interatomic potential of solids with strong-field nonlinear phononics

Nonlinear optical techniques at visible frequencies have long been applied to condensed matter spectroscopy. However, because many important excitations of solids are found at low energies, much can be gained from the extension of nonlinear optics to mid-infrared and terahertz frequencies. For example, the nonlinear excitation of lattice vibrations has enabled the dynamic control of material functions. So far it has only been possible to exploit second-order phonon nonlinearities at terahertz field strengths near one million volts per centimetre. Here we achieve an order-of-magnitude increase in field strength and explore higher-order phonon nonlinearities. We excite up to five harmonics of the A₁ (transverse optical) phonon mode in the ferroelectric material lithium niobate. By using ultrashort mid-infrared laser pulses to drive the atoms far from their equilibrium positions, and measuring the large-amplitude atomic trajectories, we can sample the interatomic potential of lithium niobate, providing a benchmark for ab initio calculations for the material. Tomography of the energy surface by high-order nonlinear phononics could benefit many aspects of materials research, including the study of classical and quantum phase transitions.

Phase-locked multi-terahertz electric fields exceeding 13 MV/cm at a 190 kHz repetition rate

We demonstrate a compact source of energetic and phase-locked multi-terahertz pulses at a repetition rate of 190 kHz. Difference frequency mixing of the fundamental output of an Yb:KGW amplifier with the idler of an optical parametric amplifier in GaSe and LiGaS₂ crystals yields a passively phase-locked train of waveforms tunable between 12 and 42 THz. The shortest multi-terahertz pulses contain 1.8 oscillation cycles within the intensity full width at half-maximum. Pulse energies of up to 0.16 μJ and peak electric fields of 13 MV/cm are achieved. Electro-optic sampling reveals a phase stability better than 0.1 π over multiple hours, combined with free carrier-envelope phase tunability. The scalable scheme opens the door to strong-field terahertz optics at unprecedented repetition rates.

Terahertz Light-Matter Interaction beyond Unity Coupling Strength

Achieving control over light-matter interaction in custom-tailored nanostructures is at the core of modern quantum electrodynamics. In strongly and ultrastrongly coupled systems, the excitation is repeatedly exchanged between a resonator and an electronic transition at a rate known as the vacuum Rabi frequency Ω_R. For Ω_R approaching the resonance frequency ω_c, novel quantum phenomena including squeezed states, Dicke superradiant phase transitions, the collapse of the Purcell effect, and a population of the ground state with virtual photon pairs are predicted. Yet, the experimental realization of optical systems with Ω_R/ω_c ≥ 1 has remained elusive. Here, we introduce a paradigm change in the design of light-matter coupling by treating the electronic and the photonic components of the system as an entity instead of optimizing them separately. Using the electronic excitation to not only boost the electronic polarization but furthermore tailor the shape of the vacuum mode, we push Ω_R/ω_c of cyclotron resonances ultrastrongly coupled to metamaterials far beyond unity. As one prominent illustration of the unfolding possibilities, we calculate a ground state population of 0.37 virtual photons for our best structure with Ω_R/ω_c = 1.43 and suggest a realistic experimental scenario for measuring vacuum radiation by cutting-edge terahertz quantum detection.

Rydberg-atom based radio-frequency electrometry using frequency modulation spectroscopy in room temperature vapor cells

Rydberg atom-based electrometry enables traceable electric field measurements with high sensitivity over a large frequency range, from gigahertz to terahertz. Such measurements are particularly useful for the calibration of radio frequency and terahertz devices, as well as other applications like near field imaging of electric fields. We utilize frequency modulated spectroscopy with active control of residual amplitude modulation to improve the signal to noise ratio of the optical readout of Rydberg atom-based radio frequency electrometry. Matched filtering of the signal is also implemented. Although we have reached similarly, high sensitivity with other read-out methods, frequency modulated spectroscopy is advantageous because it is well-suited for building a compact, portable sensor. In the current experiment, ∼3 µV cm^-1 Hz^-1/2 sensitivity is achieved and is found to be photon shot noise limited.

Improving time and space resolution in electro-optic sampling for near-field terahertz imaging

In this Letter, we present a significant improvement to time and space resolutions in electro-optic sampling (EO) for two-dimensional terahertz (THz) near-field imaging. Using a THz microscope, we readapt a recent EO sampling scheme based on optical probe spectrum filtering. Combined with an ultra-thin EO crystal, we achieve record broadband video-rate THz near-field imaging. Particularly, this new scheme improves the THz bandwidth, the imaging contrast, and the spatial resolution. To validate our method, we show THz near-field images ranging from 100 GHz to 4 THz with a spatial resolution up to λ/600 at 100 GHz. This demonstration positively affects the detection of intense THz pulses derived from the tilted-pulse-front excitation of lithium niobate and will accelerate our understanding of the interaction processes between electromagnetic waves and the conducting electrons of metallic interfaces.

Low-cost and broadband terahertz antireflection coatings based on DMSO-doped PEDOT/PSS

We report the potential application of 6% dimethylsulfoxide (DMSO)-doped poly (3, 4-ethylenedioxythiophene)/poly (4-styrenesulfonate) (PEDOT/PSS) as a low cost and broadband terahertz (THz) antireflection coating based on the impedance matching effect. The reflected pulses from the quartz and silicon substrates are observed to change with the thickness of the PEDOT/PSS layer. Theoretical analysis based on an equivalent transmission line circuit model and FDTD computational simulations have been used to understand the experimental results. Excellent impedance matching is achieved by a ∼39-nm-thick 6% DMSO-doped PEDOT/PSS layer on quartz, and a ∼101-nm-thick 6% DMSO-doped PEDOT/PSS layer on silicon due to the almost-frequency-independent conductivity of the thin film between 0.3 and 2.5 THz. In the critical conditions, the normalized main pulse transmission remains as high as 74% and 64%, for the quartz and silicon substrates, respectively, significantly higher than the existing state of the art THz antireflection coatings.