We present theoretical formulation and experimental demonstration of a novel technique for the fast compression-less terahertz imaging based on the broadband Fourier optics. The technique exploits k-vector/frequency duality in Fourier optics which allows using a single-pixel detector to perform angular scan along a circular path, while the broadband spectrum is used to scan along the radial dimension in Fourier domain. The proposed compression-less image reconstruction technique (hybrid inverse transform) requires only a small number of measurements that scales linearly with the image linear size, thus promising real-time acquisition of high-resolution THz images. Additionally, our imaging technique handles equally well and on the equal theoretical footing the amplitude contrast and the phase contrast images, which makes this technique useful for many practical applications. A detailed analysis of the novel technique advantages and limitations is presented, as well as its place among other existing THz imaging techniques is clearly identified
We present a detailed analysis and comparison of dielectric waveguides made of CdTe, GaP, GaAs and InP for modal phase matched optical difference frequency generation (DFG) in the terahertz domain. From the form of the DFG equations, we derived the definition of a very general figure of merit (FOM). In turn, this FOM enabled us to compare different configurations, by taking into account linear and nonlinear susceptibility dispersion, terahertz absorption, and a rigorous evaluation of the waveguide modes properties. The most efficient waveguides found with this procedure are predicted to approa…
We propose an all-optical Knife Edge characterization technique and we demonstrate its working principle by characterizing the sub-λ features of a spatially modulated Terahertz source directly on the nonlinear crystal employed for the Terahertz generation.
Using a 3D fully-vectorial nonlinear time-domain analysis we numerically investigate the generation of terahertz radiation by pumping a photonic crystal microcavity out of resonance. High quality factors and a quadratic susceptibility lead to few-cycle terahertz pulses via optical rectification. Material dispersion as well as linear and nonlinear anisotropy is fully accounted for.
We propose and experimentally prove efficient high-resolution electro-optic sampling measurement of broadband terahertz waveforms in a LiNbO$_3$ 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 LiNbO$_3$ 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 o…
High spectral purity frequency agile room temperature sources in the terahertz spectrum are foundational elements for imaging, sensing, metrology, and communications. Here we present a chip scale optical parametric oscillator based on an integrated nonlinear microresonator that provides broadly tunable single frequency and multi frequency oscillators in the terahertz regime. Through optical to terahertz down conversion using a plasmonic nanoantenna array, coherent terahertz radiation spanning 2.8 octaves is achieved from 330 GHz to 2.3 THz, with 20 GHz cavity mode limited frequency tuning step…
We introduce a general technique to generate compressed broadband terahertz pulses based on difference frequency generation of optical pump radiation using aperiodically poled structures. The pump pulse format and poling of the crystals conceived are such that the emergent terahertz pulse is compressed. The approach circumvents pump pulse distortions that result from non-collinear approaches and the need for external compression. It is particularly efficient for the generation of pulses of intermediate durations of few to tens of cycles. For instance, conversion efficiencies in the few percent…
In ultrabroadband terahertz electro-optic sampling, spectral filtering of the gate pulse can strongly reduce the quantum noise while the signal level is only weakly affected. The concept is tested for phase-matched electro-optic detection of field transients centered at 45 THz with 12-fs near-infrared gate pulses in AgGaS2. Our new approach increases the experimental signal-to-noise ratio by a factor of 3 compared to standard electro-optic sampling. Under certain conditions an improvement factor larger than 5 is predicted by our theoretical analysis.
We show that 3D Dirac semimetals are promising candidates for highly efficient optical-to-terahertz conversion due to their extreme optical nonlinearities. In particular, we predict that the conversion efficiency of Cd3As2 exceeds typical materials like LiNbo3 by >5000 times over nanoscale propagation distances. Our studies show that even when no restrictions are placed on propagation distance, Cd3As2 still outperforms LiNbo3 in efficiency by >10 times. Our results indicate that by tuning the Fermi energy, Pauli blocking can be leveraged to realize a step-like efficiency increase in the optica…
We use an open-aperture Z-scan technique to show how intense few-cycle terahertz pulses can experience a nonlinear bleaching of absorption in an n-doped semiconductor due to terahertz-electric-field-driven intervalley scattering of electrons in the conduction band. Coherent detection of the transmitted terahertz pulse waveform also allows the nonlinear conductivity dynamics to be followed with sub-picosecond time resolution. Both the Z-scan and time-domain results are found to be in agreement with our theoretical analysis.
We present a general analysis of the influence of nonlinear optical absorption on terahertz generation via optical difference frequency generation, when reaching for the quantum conversion efficiency limit. By casting the equations governing the process in a suitably normalized form, including either two-photon- or three-photon-absorption terms, we have been able to plot universal charts for phase matched optical-to-terahertz conversion for different values of the nonlinear absorption coefficients. We apply our analysis to some experiments reported to date, in order to understand to what exten…
With ever increasing availability of terahertz fields, it is important to find suitable detection techniques without compromising the measured dynamic range. Electro-optic terahertz sampling techniques, which are commonly used to detect terahertz fields, exhibit over-rotation at high fields that limit the detection accuracy. Here we discuss a method to correct for over-rotation that put no limits on measured terahertz field strengths, while preserving the low field sensitivity. We further evaluate the induced polarizations at high terahertz fields and show how over-rotation can be corrected by…
We explore the potential of 3D metal printing to realize complex conductive terahertz devices. Factors impacting performance such as printing resolution, surface roughness, oxidation, and material loss are investigated via analytical, numerical, and experimental approaches. The high degree of control offered by a 3D-printed topology is exploited to realize a zone plate operating at 530 GHz. Reflection efficiency at this frequency is found to be over 90%. The high-performance of this preliminary device suggest that 3D metal printing can play a strong role in guided-wave and general beam control…
We present a universal and rigorous approach to study difference frequency generation in the terahertz domain, keeping the number of degrees of freedom to a minimum, through the definition of a suitable figure of merit. The proposed method relies on suitably normalized charts, that enable to predict the optical-to-terahertz conversion efficiency of any system based on wave propagation in quadratic nonlinear materials. The predictions of our approach are found to be in good agreement with the best experimental results reported to date, enabling also to estimate the d22 nonlinear coefficient of …
Fibonacci or bifocal terahertz (THz) imaging is demonstrated experimentally employing silicon diffractive zone plate (SDZP) in a continuous wave mode. Images simultaneously recorded in two different planes are exhibited at 0.6 THz frequency with the spatial resolution of wavelength. Multi-focus imaging operation of the Fibonacci lens is compared with a performance of the conventional silicon phase zone plate. Spatial profiles and focal depth features are discussed varying the frequency from 0.3 THz to 0.6 THz. Good agreement between experimental results and simulation data is revealed.
An undoped double quantum well (DQW) was driven with a terahertz (THz) electric field of frequency ω_{THz} polarized in the growth direction, while simultaneously illuminated with a near-infrared (NIR) laser at frequency ω_{NIR}. The intensity of NIR upconverted sidebands ω_{sideband}=ω_{NIR} + ω_{THz} was maximized when a dc voltage applied in the growth direction tuned the excitonic states into resonance with both the THz and NIR fields. There was no detectable upconversion far from resonance. The results demonstrate the possibility of using gated DQW devices for all-optical wavelength shift…
We report an integrated all-optical radio frequency spectrum analyzer based on a ~ 4cm long doped silica glass waveguide, with a bandwidth greater than 2.5 THz. We use this device to characterize the intensity power spectrum of ultrahigh repetition rate mode-locked lasers at repetition rates up to 400 GHz, and observe dynamic noise related behavior not observable with other techniques.
We demonstrate a coherent imaging system based on a terahertz (THz) frequency quantum cascade laser (QCL) phase-locked to a near-infrared fs-laser comb. The phase locking enables coherent electro-optic sampling of the continuous-wave radiation emitted by the QCL through the generation of a heterodyne beat-note signal. We use this beat-note signal to demonstrate raster scan coherent imaging using a QCL emitting at 2.5 THz. At this frequency the detection noise floor of our system is of 3 pW/Hz and the long-term phase stability is <3 degrees/h, limited by the mechanical stability of the apparatu…
We investigate the spatially and temporally resolved four-wave mixing of terahertz fields and optical pulses in large band-gap dielectrics, such as diamond. We show that it is possible to perform beam profiling and space-time resolved mapping of terahertz fields with sub-wavelength THz resolution by encoding the spatial information into an optical signal, which can then be recorded by a standard CCD camera.
The intense terahertz (THz) pulses facilitate the observation of various nonlinear optical effects and manipulation of material properties. In this work, we report a convenient approach that can produce strong broadband terahertz pulses with center frequency tunable between 2-4 THz. The coherent THz light source with pulse energy of 1.2 microjoule can be generated from a low-cost crystalline quartz pumped by an ultrashort tilted wave-front pulse. Thanks to the wide transparent spectral window and high damage threshold, our theoretical analysis and experiment show that the optical rectification…
We explore the dynamics of a system where input spectra in the optical domain with very disparate center frequencies are strongly coupled via highly phase-matched, cascaded second-order nonlinear processes driven by terahertz radiation. The only requirement is that one of the input spectra contain sufficient bandwidth to generate the phase-matched terahertz-frequency driver. The frequency separation between the input spectra can be more than ten times larger than the phase-matched terahertz frequency. A practical application of such a system where the cascading of a narrowband pump line center…
Single-shot recording of terahertz electric signals has recently become possible at high repetition rates, by using the photonic time-stretch electro-optic sampling (EOS) technique. However the moderate sensitivity of time-stretch EOS is still a strong limit for a range of applications. Here we present a variant enabling to increase the sensitivity of photonic time-stretch for free-propagating THz signals. A key point is to integrate the idea presented in Ref. [Ahmed et al., Rev. Sci. Instrum. 85, 013114 (2014)], for upgrading classical time-stretch systems. The method is tested using the high…
We report on an attempt to generate highly stable continuous terahertz (THz) wave by using optical frequency comb (OFC). About 10-nm wide OFC has been generated through a deep phase modulation of a 852 nm laser line in lithium niobate crystal cavity. The multiple optical modes (side bands) of the OFC, which are equally separated from each other by the modulation frequency (=6 GHz) are taken as the frequency reference. When another semiconductor laser is frequency locked, the stability of the difference frequency between the master laser and the second laser is improved on the same order of the…
Metallic structures with periodic array of slits are well-known to lead to extraordinary power transmission, when slits have dimensions much less than the wavelength of incident optical wave. Excellent power transmission originates from surface waves excited by incident transverse magnetic wave. Here we show that metallic structure with array of stepped-slits can transmit power of incident wave into the substrate at desired optical frequency entirely and simultaneously in terahertz frequency band by 70%, for In0.53Ga0.47As substrate. Transmitted power of the proposed structure is studied both …
We have performed ultrafast pump-probe experiments on a GaAs-AlAs microcavity with a resonance near 1300 nm in the "original" telecom band. We exploit the virtually instantaneous electronic Kerr effect to repeatedly and reproducibly switch a GaAs-AlAs planar microcavity. We achieve repetition times as fast as 300 fs, thereby breaking the THz modulation barrier. The rate of the switching in our experiments is only determined by optics and not by material related relaxation. Our results offer novel opportunities for fundamental studies of cavity-QED and optical information processing in sub-pico…
Using terahertz time domain spectroscopy we demonstrate tunable polarization rotation and circular dichroism in intrinsically nonchiral planar terahertz metamaterials without twofold rotational symmetry. The observed effect is due to extrinsic chirality arising from the mutual orientation of the metamaterial plane and the propagation direction of the incident terahertz wave.
Since its first demonstration in 1995, terahertz time-domain imaging has attracted an increasingly growing interest for its ability to reveal spectral fingerprints of materials, probe changes in refractive index and absorption, as well as detect the inner structure of complex objects via time-of-flight measurements. Practically, however, its widespread use has been hampered by the very long acquisition time typically required to spatially raster-scan the object and, for each spatial point, record the field in time via a delay line. Here, we address this fundamental bottleneck by implementing a…
The gain recovery time of a heterogeneous active region terahertz quantum cascade laser is studied by terahertz-pump,i terahertz-probe spectroscopy. The investigated active region, which is based on a bound-to-continuum optical transition with an optical phonon assisted extraction, exhibits a gain recovery time in the range of 34$\,$-$\,$50$\,$ps dependent on the operation condition of the laser. The recovery time gets shorter for stronger pumping of the laser while the recovery dynamics slows down with increasing operation temperature. These results indicate the important role of the intracav…
Transmission through a subwavelength terahertz fiber, which is positioned in parallel to a frequency selective surface, is studied using several finite element tools. Both the band diagram technique and the port-based scattering matrix technique are used to explain the nature of various resonances in the fiber transmission spectrum. First, we observe that spectral positions of most of the transmission peaks in the port-based simulation can be related to the positions of Van Hove singularities in the band diagram of a corresponding infinite periodic system. Moreover, spectral shape of most of t…
Methods for fast and accurate material properties estimate with terahertz time-domain spectroscopy in transmission and reflection with optically thick materials
Arising from modulation instability, Turing rolls in optical Kerr microresonators have been used in the generation of optical frequency combs and the synthesis of microwave and terahertz frequencies. In this work, by applying electro-optic modulation on terahertz-frequency Turing rolls, we implement electro-optic frequency division with a microcomb to synthesize variable low-noise microwave signals. We also actively stabilize the terahertz oscillations to a microwave reference via intracavity power modulation, obtaining fractional frequency instabilities that are better than those of the free-…
Carrier conversion from terahertz wave to dual-wavelength near-infrared light injection-locking to optical comb using asynchronous nonpolarimetric electro-optic downconversion with electro-optic polymer modulator
Platforms for all-optical computing possess photonic circuits made of silicon-based channels, metal wires or optical fibers, etc. However, such solid waveguides suffer from the lack of reversibility and reconfigurability if facing the next generation of light-guiding-light (LGL) computing scheme, which envisions circuitry-free and rapidly reconfigurable systems powered by dynamic interactions between light beams. Here, we proposed the ubiquitous air as a restorable LGL signal manipulation medium with transient air-plasma waveguide circuits. Briefly, by focusing femtosecond laser beams in the f…
The ability to engineer quantum-cascade-lasers (QCLs) with ultrabroad gain spectra and with a full compensation of the group velocity dispersion, at Terahertz (THz) frequencies, is a fundamental need for devising monolithic and miniaturized optical frequency-comb-synthesizers (FCS) in the far-infrared. In a THz QCL four-wave mixing, driven by the intrinsic third-order susceptibility of the intersubband gain medium, self-lock the optical modes in phase, allowing stable comb operation, albeit over a restricted dynamic range (~ 20% of the laser operational range). Here, we engineer miniaturized T…
Frequency conversion by means of Kerr-nonlinearity is one of the most common and exploited nonlinear optical processes in the UV, visible, IR and Mid-IR spectral regions. Here we show that wave mixing of an optical field and a Terahertz wave can be achieved in diamond, resulting in the frequency conversion of the THz radiation either by sum- or difference-frequency generation. In the latter case, we show that this process is phase-matched and most efficient in a counter-propagating geometry.
We present a method to measure quadratic Terahertz optical nonlinearities in Terahertz time-domain spectroscopy. We use a rotating linear polarizer (a polarizing chopper) to modulate the amplitude of the incident THz pulse train. We use a phase-sensitive lock-in detection at the fundamental and the second harmonic of the modulation frequency to separate the materials' responses that are linear and quadratic in Terahertz electric field. We demonstrate this method by measuring the quadratic Terahertz Kerr effect in the presence of the much stronger linear electro-optic effect in the (110) GaP cr…
We report the Terahertz optical properties of the Vanadium doped [100] \b{eta}-Ga2O3 using Terahertz Time-Domain Spectroscopy (THz-TDS). The V-doped \b{eta}-Ga2O3 crystal shows strong birefringence in the 0.2-2.4 THz range. Further, phase retardation by the V-doped \b{eta}-Ga2O3 has been measured over the whole THz range by Terahertz Time-Domain Polarimetry (THz-TDP). It is observed that the V-doped \b{eta}-Ga2O3 crystal behaves both as a quarter waveplate (QWP) at 0.38, 1.08, 1.71, 2.28 THz, and a half waveplate (HWP) at 0.74 and 1.94 THz, respectively.
By using two mutually phase-locked optical frequency combs with slightly different repetition rates, we demonstrate asynchronous optical-sampling terahertz time-domain spectroscopy (ASOPS THz-TDS) without using any trigger signals or optical delay lines. Due to a tight stabilization of the repetition frequencies, it was possible to accumulate the data over 48 minutes in a triggerless manner without signal degradation. The fractional frequency stability of the measured terahertz signal is evaluated to be $\sim$8.0$\times$10$^{- 17}$ after 730 s. The frequency accuracy of the obtained terahertz …
We report the development of new terahertz techniques for rapidly measuring the complex Faraday angle in systems with broken time-reversal symmetry using the cyclotron resonance of a GaAs two-dimensional electron gas in a magnetic field as a system for demonstration of performance. We have made polarization modulation, high sensitivity (< 1 mrad) narrow band rotation measurements with a CW optically pumped molecular gas laser, and by combining the distinct advantages of terahertz (THz) time domain spectroscopy and polarization modulation techniques, we have demonstrated rapid broadband rotatio…
We report on a giant Faraday effect in an electron plasma in n-InSb probed via polarization-resolved terahertz (THz) time-domain spectroscopy. Polarization rotation angles and ellipticities reach as large as π/2 and 1, respectively, over a wide frequency range (0.3-2.5 THz) at magnetic fields of a few Tesla. The experimental results together with theoretical simulations show its promising ability to construct broadband and tunable THz polarization optics, such as a circular polarizer, half-wave plate, and polarization modulators.
We report on the computational development of novel architectures of low impedance broadband antennas, for efficient detection of Terahertz (THz) frequency beams. The conceived Split Ring Resonator Resonance Assisted (SRR RA) antennas are based on both a capacitive and inductive scheme, exploiting a 200 Ohm and 400 Ohm impedance, respectively. Moreover, the impedance is tunable by varying the coupling parameters in the exploited geometry, allowing for better matching with the detector circuit for maximum power extraction. Our simulation results have been obtained by assuming a 1.5 THz operatio…
We report an experimental demonstration of thermal tuning of resonance frequency in a planar terahertz metamaterial consisting of a gold split-ring resonator array fabricated on a bulk single crystal strontium titanate (SrTiO3) substrate. Cooling the metamaterial starting from 409 K down to 150 K causes about 50% shift in resonance frequency as compare to its room temperature resonance, and there is very little variation in resonance strength. The resonance shift is due to the temperature-dependent refractive index (or the dielectric constant) of the strontium titanate. The experiment opens up…
The resonant acousto-optic effect is studied both analytically and numerically in the terahertz range where the transverse-optical (TO) phonons play the role of a mediator which strongly couples the ultrasound and light fields. A propagating acoustic wave interacts with the TO phonons via anharmonic channels and opens band gaps in the TO-phonon polariton energy dispersion that results in pronounced Bragg scattering and reflection of the incoming light. The separation in frequency of different Bragg replicas, which is at the heart of acousto-optics, allows us to study the resonant acousto-optic…
It was demonstrated that optical modulation together with simultaneous terahertz (THz) imaging application enables an increase in contrast by an order of magnitude illustrating hence the technique as convenient contactless tool for characterization of graphene deposited on high-resistivity silicon substrates. It was shown that the single- and double-layer graphene can be discriminated and characterized via variation of THz image contrast using a discrete frequency in a continuous wave mode. Modulation depth of 45 % has been reached, the contrast variation from 0.16 up to 0.23 is exposed under …
As we read this text, our eyes dynamically adjust the focal length to keep the line image in focus on the retina. Similarly, in many optics applications the focal length must be dynamically tunable. In the quest for compactness and tunability, flat lenses based on metasurfaces were introduced. However, their dynamic tunability is still limited because their functionality mostly relies upon fixed geometry. In contrast, we put forward an original concept of a tunable Optical Magnetic Lens (OML) that focuses photon beams using a subwavelength-thin layer of a magneto-optical material in a non-unif…
THz spectroscopy is an emerging tool for detection of microorganisms and harmful compounds in the food industry, the study of proteins in biomedicine and the development of electron-beam X-ray sources for molecular imaging and lithography. Recording of THz electric field evolution in single-shot is crucially needed in terahertz spectroscopy of irreversible processes in such applications as well as for data communication in the THz portion of the spectrum where there is an abundance of untapped bandwidth. However, achieving sub-picosecond resolution over a long time window has been an open prob…
Presented here is the development and demonstration of a tunable cavity-enhanced terahertz frequency-domain optical Hall effect technique. The cavity consists of at least one fixed and one tunable Fabry-Pérot resonator. The approach is suitable for enhancement of the optical signatures produced by the optical Hall effect in semi-transparent conductive layer structures with plane parallel interfaces. The physical principle is the constructive interference of electric field components that undergo multiple optical Hall effect induced polarization rotations upon multiple light passages through th…
Recent advances in deep learning have been providing non-intuitive solutions to various inverse problems in optics. At the intersection of machine learning and optics, diffractive networks merge wave-optics with deep learning to design task-specific elements to all-optically perform various tasks such as object classification and machine vision. Here, we present a diffractive network, which is used to shape an arbitrary broadband pulse into a desired optical waveform, forming a compact pulse engineering system. We experimentally demonstrate the synthesis of square pulses with different tempora…
Terahertz (THz) near-field imaging is a flourishing discipline [1], with applications from fundamental studies of beam propagation [2,3] to the characterisation of metameterials [4,5] and waveguides [6,7]. Beating the diffraction limit typically involves rastering structures or detectors with length scale shorter than the radiation wavelength; in the THz domain this has been achieved using a number of techniques including scattering tips [8,9] and apertures [10]. Alternatively, mapping THz fields onto an optical wavelength and imaging the visible light removes the requirement for scanning a lo…
We present a modified $8f$ geometry for time domain terahertz (THz) spectroscopy (TDTS) experiments. We show, through simulations and data, that a simple rearranging of the off-axis parabolic mirrors, which are typically used to focus and direct THz radiation in TDTS experiments, results in a nearly 40% reduction in the THz focal spot diameter. This effect stems from significant reduction of the principle optical aberrations which are enhanced in the conventional $8f$ geometry but partially compensated in the modified $8f$ experimental setup. We compare data from our home-built TDTS spectromet…
