Introduction
Generation of intense terahertz transients
Photoconductive antenna
Fig.1 Terahertz signals generated from annealed and unannealed LT-GaAs PCAs [22]. (a) Time-domain terahertz waveforms. (b) Fourier spectra of the waveforms. The Fourier spectra were both normalized by the peak values of the respective terahertz waveforms. A 700°C annealed PCA (bow-tie type) and an unannealed one were used in these measurements. Another unannealed PCA (bow-tie type) was used as a common detector |
Fig.3 (a) Schematic diagram and operating principle of a large-area plasmonic photoconductive emitter fabricated on a GaAs substrate [36]. (b) Power transmission of a TM-polarized optical beam incident on the GaAs substrate as a function of optical wavelength. The inset shows color plot of optical absorption in the GaAs substrate in response to a TM-polarized optical beam at 800 nm |
Fig.4 (a) Principle of a binary phase mask for single-cycle terahertz pulse generation from an interdigitated photoconductive antenna (PCA). (b) Terahertz pulse shape from an interdigitated GaAs antenna at a bias field of 1.2 kV/cm and a fluence of 14 mJ/cm2 with a standard shadow mask, a 510-mm-thick binary phase mask, and no mask (offset introduced for improved clarity). The inset shows the power spectra for a shadow mask and 510 mm glass phase mask [38] |
Optical rectification
crystal | effective nonlinear coefficient/(pm·V−1) | index of refraction | THz index of refraction | THz absorption coefficient/cm−1 |
---|---|---|---|---|
ZnTe | 68.5 | 2.85 (800 nm) | ~3.17 | 1.3 |
GaP | 24.8 | 3.67 (800 nm) | ~3.34 | 0.2 |
GaSe | 28.0 | 2.85 (800 nm) | ~3.72 | 0.5 |
GaAs | 65.6 | 3.61 (800 nm) | ~3.4 | 0.5 |
LiNbO3 | 168.0 | 2.25 (800 nm) | no~6.8, ne~4.98 | 18.2 |
LiTaO3 | 170.0 | 2.18 (800 nm) | no~6.5, ne~6.4 | 46.0 |
DAST | 615.0 | 2.25 (1550 nm) | ~2.4 | 41.5 |
Fig.7 (a) Schematic of a high energy terahertz source with tilted pulse wave front technique and electro-optic sampling (EOS) setup [50]. HWP: half-wave plate; LN: lithium niobate; OAP: 90° off-axis parabolic mirror; IS: integrating sphere; BPD: balanced photodiode. (b) Autocorrelation measurement of the pump laser pulse at its shortest duration of 30 fs. (c) Calculated chirped pulse duration as a function of the group velocity dispersion. (d) Input spectra for different group velocity dispersion measured before the laser beam enters the tilted pulse wave front setup. (e) Pump beam position relative to the edge of the LiNbO3 prism |
Fig.8 Terahertz generation with a DAST crystal [53]. (a) Schematic setup for terahertz generation and electro-optic detection. 50 fs probe pulses centered at 810 nm (inset) are used for sampling the terahertz pulse with a 95-mm-thick GaP crystal. QWP: quarter wave plate; WP: Wollaston prism; BPD: balanced photodiode detector. (b) Spectrum of pump pulse. (c) Measured autocorrelation signal of terahertz pulse |
Terahertz sources based on plasma
Novel approaches for intense terahertz generation
Fig.12 (a) Band structure of n-doped Bi2Se3 [75]. Surface electrons are directly excited by optical transitions from the conduction band (CB) to the second surface state (SS). Bulk electrons are directly excited by optical transitions from the valence band (VB) to the CB. (b) Schematic diagram of the experimental setup. WP: wave plate; WGP: wire grid polarizer |
Fig.13 Metallic spintronic terahertz emitter [78]. (a) Principle of operation. (b) Time-domain transient obtained from photoexcited Ta- and Ir- capped Co20Fe60B20 thin films (3-nm-thick) and detected by a 50-µm-thick GaP crystal. Inset: Terahertz signal amplitude as a function of incident pump power. (c) Fourier spectra of terahertz signal and the extracted transient terahertz electric-field incident on the electro-optic detector |
Fig.14 Experimental setup and results of a metasurface terahertz source [80]. (a) Schematic of terahertz generation and detection. The insert shows an electron micrograph of the SRR array. PM: parabolic mirror; WP: Wollaston prism. (b) Measured terahertz time-domain transient obtained by pumping the SRR electric-dipole resonance (red line) at 800 nm, magnetic-dipole resonance (black dots) at 1500 nm, and substrate only (green line) at 1500 nm, respectively. The inset shows the linear optical transmission including the electric (red curve) and magnetic (black curve) dipole resonances of the SRRs measured with the polarization of the incident light perpendicular and parallel to the gap of SRRs, respectively |
Tab.2 Comparison of terahertz generation techniques |
Ref. | peak electric field | Bandwidth/THz | advantage | disadvantage | |
---|---|---|---|---|---|
LAPCA [39] | few hundreds kV/cm | 20 | high stability | relatively low peak electric field | |
OR | DAST [38] | about 7 MV/cm | 0.3–20 | low dielectric constant | low damage threshold |
ZnTe [44] | about 70 kV/cm | 0.2–4 | better phase matching conditions | strong two-photon absorption | |
LiNbO3 [40] | up to 1.2 MV/cm | 0.1–2.5 | high damage threshold | low frequency | |
BNA [56] | 10 MV/cm | 7 | highly nonlinear organic crystal | low damage threshold | |
air plasma [64] | several MV/cm | 0.1–75 | no concerns for damage with air | phase matching sensitivity | |
spintronic [80] | about 300 kV/cm | 0–4 | high potential | difficulty of artificial structure design and fabrication |
Detection of intense terahertz radiation
Detection by PCA
Detection by electro-optic sampling
Detection by air plasma
Applications of intense terahertz radiation
Applications of intense terahertz radiation in spectroscopy
Intense terahertz time-domain spectroscopy technique
Fig.15 Terahertz Z-scan experimental results for InGaAs [122]. (a) Z-scan normalized transmission of the total terahertz pulse energy measured with a pyroelectric detector after the sample (black curve: InGaAs epilayer on an InP substrate; red curve: InP substrate only). (b) Transmitted terahertz pulse electric field at different positions of the Z-scan. (c) Normalized transmission of the time integral of the modulus squared for the transmitted electric field as a function of z position along the scan. (d) Normalized electric field differential transmission as a function of time for different z positions along the scan. Note that the initial positive slope is related to the terahertz pulse duration and the population rate, while the negative slope is indicative of the carrier decay time |
Fig.16 Terahertz Z-scan experimental results for n-doped silicon [123]. (a) Experimental setup. The terahertz pulses are generated by tilted-pulse-front excitation in LiNbO3 and electro-optically detected by a ZnTe crystal. (b) Open-aperture Z-scan: change in transmitted terahertz amplitude through the doped silicon sample as a function of distance from the terahertz beam focus. Also, see Ref. [73] |
Fig.17 Terahertz Z-scan experimental results for graphene [132]. (a) Schematic of the experimental setup based on the titled-pulse-front technique and a LiNbO3 crystal. (b) Time-domain signal of terahertz pulses transmitted through the bare SiC substrate and the graphene sample for two terahertz electric-field strength levels, normalized to the response of the bare SiC (the inset shows a detail of the peaks of the three pulses), and (c) the transmission spectra for four different terahertz electric-field strength levels |
Optical-pump/intense-terahertz-probe technique
Fig.19 Calculated and experimental complex conductivity of pumped GaAs [133]. The experimental complex conductivity is extracted at a pump-probe delay time of 10 ps measured at low (a) and high (b) terahertz-probe fields. The solid blue lines in (a) and (b) are corresponding fits using the dynamic intervalley-electron-transfer model. The effect of neglecting intervalley scattering in the model is shown in (c) |
Fig.20 Intense terahertz-induced transmission enhancement in monolayer graphene [134]. (a) Time-domain signals of transmitted terahertz pulses without and with the pump beam probed by 9 kV/cm peak terahertz field. (b) Differential transmission DT/T0 of the peak terahertz field as a function of the pump-probe delay time, for various optical pump fluences. (c) Differential terahertz field DE/E0 of terahertz pulses at low (9 kV/cm) and high (63 kV/cm) terahertz peak electric fields. (d) Transient differential transmission DT/T0 of the terahertz peak field as a function of the pump-probe delay time at a fixed pump fluence of 137 mJ/cm2 while the terahertz field is varied from 9 to 63 kV/cm |
Terahertz-pump/terahertz-probe technique
Fig.21 Terahertz-pump/terahertz-probe time-resolved measurement of InSb [137]. Terahertz absorption data of the doped InSb sample at (a) 80 K and (b) 200 K. Terahertz absorption spectra at various pump intensities measured at a probe delay time of 35 ps at 80 K for (c) doped and (d) undoped InSb samples |
Fig.23 Terahertz-induced transparency of graphene [139]. (a) Transmission spectra of CVD graphene on fused silica at different fluences. The insets are the time-domain signals and spectra of the sample and bare substrate. The transmission increases with increasing terahertz field strength. (b) Terahertz power transmission integrated over the entire terahertz pulse as a function of the terahertz fluence |
Intense terahertz-pump/other radiation-probe technique
Fig.24 Terahertz derived transparency in graphene [140]. (a) Schematic of ITPOP experimental setup. An 800 nm laser pulse is frequency doubled using a β-barium borate crystal. (b) Time-domain signal of the incident terahertz electric field and its spectrum. (c) Terahertz-induced normalized differential optical density of graphene at 800 nm as a function of delay time |
Fig.25 Time-resolved ITPOP results [140]. Normalized differential optical density as a function of time delay with peak electric fields of (a) 170 kV/cm and (b) 300 kV/cm (experiment: circle, simulation: solid line). (c) and (d) Corresponding calculated carrier densities as a function of time delay. Dashed lines represent initial carrier density. (e) Terahertz-induced transparency of graphene as a function of a peak electric field (experiment: filled circle, simulation: solid and dashed lines). Experimental results follow a power law with an exponent of 2.5 (dotted line) |
Applications of intense terahertz radiation to traditional nonlinear effects
High-order harmonic generation
Fig.26 Time-domain transients of pump terahertz and HHG [110]. (a) Waveform of the intense terahertz source (blue, solid curve) features a Gaussian envelope (black dashed curve) with an intensity full width at half-maximum of 109 fs. Inset: corresponding spectrum. (b) Electro-optic trace of the waveform generated by the intense terahertz pulse in a GaSe single crystal (220-μm-thick). The data are recorded by an AgGaS2 detector (100-μm-thick). Insets: corresponding amplitude spectrum and experimental geometry, indicating the incident angle of 70° |
Fig.27 Terahertz HHG waves in bulk GaSe [110]. (a) High-order harmonic (HH) intensity spectrum (solid line and shaded area) emitted from a GaSe single crystal. The blue dashed curve shows the computed HH intensity spectrum, obtained from a five-band model. (b) Dependence of the intensity I13 of the 13th harmonic on the incident terahertz amplitude Ea. Dashed line, scaling law of I13; dotted line, scaling law of I13. (c) Spectral interference between the frequency-doubled sixth harmonic and the 12th harmonic confirms the CEP stability of the HH radiation. (d) Model electronic band structure of GaSe between the G- and K-points, underlying the subsequent computations. Two conduction bands (CB1 and CB2) and three valence bands (VB1, VB2, and VB3) are considered. Coherent excitation of electrons (symbols), for example, from the second valence to the lowest conduction band, can proceed via interfering pathways with different scaling in powers of the terahertz field |
Fig.28 Experimental results and schematic diagram for explanation of HHG in graphene [111]. (a) Spectrum of the graphene sample (red line) and bare SiO2 substrate (blue line), the odd-order HHG waves are clearly observed. (b) Illustration of the mechanism of terahertz harmonic generation in graphene, based on calculations with the thermodynamic model of intraband nonlinear terahertz conductivity of graphene |
Saturation of absorption
Fig.29 Terahertz nonlinear absorption in graphene nanoribbons [113]. (a) False color scanning electron micrograph of fabricated graphene ribbons. (b) Cross sectional diagram of device. (c) Measured (blue) and best fit (green) linear transmission spectrum of device. (d) Sketch of the experimental setup for the pump-probe measurements |
Fig.30 Experimental results of nonlinear absorption in graphene nanoribbons [113]. (a) Measured relative change in transmission of the probe signal as a function of pump-probe time delay Dt for different pump fluences. The positive signal indicates a decrease in absorption that becomes stronger at higher pump fluences. (b) Calculated relative change in transmission based on a nonlinear thermal model for plasmonic absorption in graphene nanoribbons that includes supercollision cooling and longitudinal acoustic phonon scattering. (c) Comparison of normalized change in transmission for two different polarizations |
Four-wave mixing
Fig.31 Schematic representation of a non-collinear four-wave mixing experiment [117]. Two high-field terahertz pulses are focused into an InSb sample. The dashed lines illustrate the generated nonlinear signal. The pump-probe signals PP-BA (pump B/probe A) and PP-AB (pump A/probe B) propagate in the same direction as the probe pulses A and B, respectively. The coherent four-wave mixing signal depends on the relative phase of the interacting pulses and propagates in a different direction |
Fig.32 Experimental results of terahertz four-wave mixing [117]. (a) Transmitted terahertz signal through InSb as a function of the electro-optic sampling delay time t and relative pulse delay t. (b) Nonlinear four-wave mixing signal. (c) Two-dimensional Fourier spectrum of pump-probe and four-wave mixing contributions located at different points of the frequency plane. (d) and (e) Time-domain pump-probe signals PP-BA and PP-AB obtained by inverse Fourier transform of the signals at kA and kB, respectively. (f) Time-domain four-wave mixing signal obtained by inverse Fourier transform of the signal at 2kA− kB |
Application of intense terahertz magnetic field
Fig.33 Switching of coherent magnon [10]. (a) Schematic of terahertz-pump magneto optic-probe system. (b) Lattice geometry of NiO with the incident of terahertz magnetic field pulse. (c) Magnetic field of an incident single terahertz pulse B(t). (d) Induced Faraday rotation qF(t) as a function of pump-probe delay t. (e) Fourier amplitude spectrum of B and qF. (f) Double-pulse excitations with the second pulse in and (g) out of phase with the spin precession triggered by the first pulse. The red lines are the trace of the terahertz pulses, green lines are the experimental results for qF(t), and black lines are the simulation results |