Introduction
Background
Ultrafast terahertz techniques
Terahertz generation
Broadband THz pulses can be generated by a biased photoconductive (PC) antenna excited with femtosecond optical pulses. The PC antenna is one of the most widely used components for THz generation and detection. A typical THz generation PC antenna structure. It is composed of two metal electrodes deposited on a semiconductor substrate [17,18].When generating THz radiation, a DC voltage is applied across the electrodes. The femtosecond optical pulses which have photon energy higher than the semiconductor energy band gap will radiate the area between the electrodes and generate photo-induced free carriers in the substrate. Sometimes, free carriers can also be formed using excitation pulses with photon energy lower than the semiconductor band gap, due to multi-photon absorption in the substrate. Once the free carriers are formed, they will be accelerated by the electric field between the electrodes, and a photocurrent J is produced. As the photocurrent varies with time, it radiates electromagnetic wave pulses with an electric field ETHz at the far field that can be expressed as [1]
The emitted THz electric field has a polarization parallel to the direction of the bias field, which can be flipped by switching the direction of the bias field. The power and bandwidth of the THz emission from PC antenna largely depend on the structure of the electrodes [19]. The output power of a PC emitter also depends on the bias voltage and the optical pump power. When the optical pump power is low and the bias field is weak, the THz radiation field amplitude increases linearly with these two parameters. However, increasing the bias voltage has a limitation because a high electric field may result in the breakdown of the substrate material.
In addition, the THz radiation output power will saturate as the optical pump power reaches a certain level, for the screening effect of the bias field by the photo-induced carriers.
Ever since the first introduction of THz generation by PC antenna in the 1980s [20], this technique has undergone dramatic developments, due to the soaring amount of research on the THz-time-domain-spectroscopy techniques. Up to now, the strongest broadband THz pulse energy emitted by PC antenna was reported to be 8.3 J with a peak electric field of 331 kV/cm, achieved with an encapsulated interdigitated ZnSe Large Aperture Photo-Conductive Antenna (LAPCA) [21].
Optical rectification (OR) is a second order nonlinear effect that is widely exploited for broadband THz pulse generation. Compared with PC antennae, OR crystals do not require application of high voltage on the material, making it one of the most efficient and convenient intense coherent broadband table-top THz sources [22].
In essence, OR is the generation of a quasi-DC polarization in a nonlinear material when it has been passed through by an intense optical beam, which results in a DC electric field proportional to the beam intensity. It can be understood as a second order phenomenon that is the reverse process of the electro-optic effect. If the light beam that induces OR is a pulse instead of a continuous wave, the electric field generated by OR will become a time varying function related with the pulse envelope, thus radiate electromagnetic waves. The far field radiation electric field should be proportional to the second derivative of OR induced time varying electric field.
(2)Here, is the time dependent optical beam intensity, is the second orderelectric polarization induced by OR, and is known as the second-order nonlinear optical susceptibility. When the optical pulse duration is in picosecond or sub-picosecond level, the radiation frequency is within THz range.
Due to the fact that the second order nonlinear susceptibility vanishesin the centrosymmetric medium [23], OR requires the material to have a noncentrosymmetric structure, such as the zinc-blended structure. The typical zinc-blended crystals that have been used in THz generations and detections include ZnTe, GaAs, GaP, etc.
Other than the susceptibility that is based on the crystal structure, the THz radiation efficiency, waveform and bandwidth depend on many factors, including laser beam properties, phase matching conditions, crystal thickness, orientation, absorption and dispersion, etc. In a nonlinear process such as optical rectification, one of the most crucial factors is the phase matching condition, which requires the energy and momentum conservation of the participating electromagnetic waves [24,25].
For OR THz generation process, it can be described as follows:
where and are the two frequency components that participate in the OR, and are their corresponding wave vectors. If we divide the first equation with the second one, we get where vG,O is the group velocity of the optical pulse, and vPh,THz is the phasevelocity of THz.When the optical pulse group velocity equals the phase velocity of THz wave, the phase matching condition of OR THz generation is satisfied. For THz generation ZnTe is one of the most popular crystals [26], because in this material the group velocity of femtosecond laser pulse around 800 nm (Ti:sapphire laser center wavelength) matches very well with phase velocity of THz wave.
ZnTe crystal’s electro-optic (EO) coefficient is relatively small compared with some other crystals, such as inorganic EO crystal LiNbO3 and organic crystal 4-N-methlystibazolium tosylate (DAST) [22]. THz generation from LiNbO3 based on the tilted pulse front techniques would be introduced in this section.
In 1971 Yang et al. first demonstrated the THz generation by OR with picosecond laser pulses, using LiNbO3 crystal as the excited material [27]. However, the conventional OR method of sending the pump beam at normal incidence to the crystal and generating THz radiation in the forward direction does not work efficiently with LiNbO3, due to the large mismatch between the optical group velocity and the THz phase velocity in the material. The optical group refractive index is nO = 2:3, and the THz refractive index is nT = 5:2 [17]. To conquer this mismatch, in 2002 Hebling et al. proposed the pulse front tilting technique [28], which later became a standard procedure for THz generation from LiNbO3 crystal.
In analogy to the Cherenkov radiation, in LiNbO3, a femtosecond laser beam with considerably smaller beam size than the THz wavelength can be seen as a point source moving faster than the THz radiation. If the optical beam size is not negligible compared to THz wavelength, when the pulse front is aligned with the Cherenkov cone, the optical pulse front will propagate with the THz radiation at the same speed. Therefore, the velocity matching is fulfilled. The Cherenkov cone anglecan be calculated using the optical group and THz phase refractive indices in LiNbO3 as follows:
The tilt of the optical pulse front can be achieved with a diffractive grating [29]. After the grating, an imaging system can be used to image the beam area on the grating onto the emitting surface of LiNbO3 crystal.
LiNbO3 based pulse front tilting setup is one of the most intense table-top ultrafast THz sources [30]. In 2011, Hirori et al. reported single cycle THz pulse with amplitude exceeding 1 MV/cm at room temperature [31]. Due to its strong THz radiation at low THz frequency, this technique was used to generate THz wave in the THz-radiation-enhanced-emission-of-fluorescence (THz-REEF) parts which will be discussed in this review.
Organic crystals have recently become a great interest for ultra intense THz pulse generation. In 1992, Zhang et al. first demonstrated the THz pulse generation from 4-N-methylstilbazolium tosylate (DAST) [32]. In 2011, a high quality THz beam generated from DAST with maximum electric field of 1.35 MV/cm was demonstrated [33]. However, although the THz spectrum extended up to 5 THz, a transverse optical (TO) phonon absorption of DAST can be clearly seen at 1.1 THz. To avoid this phonon absorption, other than cooling the crystal to suppress the vibration modes, alternative organic crystals such as 2- (3-(4-hydroxystyryl)- 5,5- dimethylcyclohex-2-enylidene) malononitrile (OH1) and 4-N,N-dimethylamino-4´-N´-methyl-stilbazolium 2,4,6-trimethylbenzenesulfonate (DSTMS) can be used. In 2015, Shalaby and Hauri generated an extremely bright THz bullet with peak field up to 83 MV/cm [34], which holds the current record of THz generation from an EO crystal. Meanwhile, the demanding conditions for growing good organic crystals in large dimension as well as the low damage threshold of organic crystals bring challenges to their wide use as THz sources.
Other than using solid materials, such as semiconductor crystals and photoconductive antenna, the ambient air can be ionized to the form of air-plasma by intense laser beams to generate broadband coherent THz radiations. THz generation through air-plasma can be conducted with many different methods. For example, THz radiation from single-color laser beam induced plasma was first reported by Hamster et al. [35]. Later, the generation efficiency was proved to be several orders of magnitudes higher if the plasma is induced by a mixture of two-color (fundamental and the second harmonic) femtosecond laser beams [36].The mechanism of such a strong THz generation efficiency have been explained by four-wave-mixing (FWM) model [37], and transient photocurrent model [38]. More details of THz generation from air-plasma will be reviewed in the next section.
Terahertz detection
The electro-optic (EO) sampling technique measures the actual electric field of a THz pulse in time domain, sensing not only the amplitude, but also the phase information with high precision [17,39]. Taking advantage of second-order nonlinear optical process the Pockels effect in EO crystals, its mechanism can be seen as the reverse phenomenon of optical rectifications.
The Pockels effect indicates that a static external electric field can induce birefringence proportional to the field amplitude in a nonlinear material. Replacing the static electric field by a relatively slowly changing THz field, the THz field variation can be detected by measuring the birefringence it induces in an EO crystal. When without a THz field, the vertically polarized optical probe pulse will not undergo any polarization change after going through the EO crystal. After passing a quarter-wave-plate and a Wollaston prism, the optical pulse polarization will first become circular and then get separated to two orthogonal components. Eventually the two photo-diodes of the balanced photo-detector that detects the difference between the two “eyes” will see same intensity in both “eyes” and return zero. When with the existence of a THz field, the birefringence it induces in the EO crystal will change the polarization of the probe pulse, therefore result in an unbalanced value proportional to the induced birefringence at the detector. With ZnTe as the detector crystal, the polarizations of the probe pulse and the THz pulse are typically set to be parallel with its [10] to give an optimum measurement [17].
The phase retardation experienced by the probe beam in the EO crystal can be expressed as
where and are the refractive index along the two axises, nO is the refractive index at the optical frequency, L is the distance the probe beam goes through inside the crystal and r41 is the EO efficient. The intensities of the split probe beams at the balanced photo-detector are where I0 is the incident probe beam intensity. Take the approximation that , the signal measured by the balanced photo-detector will be directly proportional to the THz field amplitude:In reality, the temporal resolution or spectral bandwidth is limited by several factors, such as: the probe pulse duration, the dispersion of nonlinear susceptibility, the phase matching condition between the optical group velocity and the THz phase velocity, and the absorption of the crystal. For ZnTe, due to its TO phonon resonance at 5.3 THz, the detector response is negligible above 4 THz [17,39].
Terahertz time-domain techniques
As the base for THz time-domain techniques and a critical tool to study ultrafast phenomena, time-resolved pump-probe technique is taking advantage of the short and intense pulses of ultrafast lasers interacting with a material. The induced optical excitations can range from ionization, transient photo-current, birefringence to lattice vibrations, etc.
In a pump-probe set-up, the relative time delay between the pump pulse, which will create the transient excitations in the media, and the probe pulse, which is sent to probe the excitations, is fine controlled, mostly by a translational stage that changes the beam path of one of the beams. The temporal resolution of this technique is usually at the magnitude of femto-second, depending on the pump and probe pulse durations.
The basic methodology of THz time-domain spectroscopy (TDS) is similar to an ultra-fast pump-probe set-up [40,41]. The optical beam is split into the pump and probe beams, and the time delay is controlled by moving a translational stage. The pump beam is used to excite the THz emitter to generate THz beam. The THz beam is collected and focused onto the THz detector where the THz induced transient will be detected by the probe beam. The THz emitter and detector can be chosen among crystal, photo-conductive antenna and gas based methods, depending on the requirements of the measurements, such as THz intensity or detection bandwidth [17]. To induce spectroscopy on a sample, the TDS measurements will be made with and without the sample in the THz beam path, either in transmission mode or reflection mode. The difference between the two measurements gives not only the absorption but also the dispersion of the sample in THz frequencies by analyzing the Fourier transforms of the waveforms.
Terahertz air-photonics
Terahertz generation from air plasmas
Filamentation is the process by which a high-intensity beam self-focuses through nonlinear processes and collapses. This plasma channel stabilizes the beam at vary diameters (30 to 100) and maintains high intensities over ranges much longer than the Rayleigh length of a traditional, geometrically focused beam.
Intense broadband THz generation from ionized gas drew a great amount of attention ever since it was first demonstrated by Hamster et al. in 1993 [35]. In this work, strong femtosecond laser pulses were focused into a Helium gas target, generating strong emission of THz pulses with a conversion efficiency of less than 10−6. The mechanism behind the THz radiation is the Ponderomotive force at the focus of the laser beam. The Ponderomotive force is experienced by a charged particle in an inhomogeneous oscillating electro-magnetic field, pushing the particle toward the area of low optical intensity regardless of the sign of the charge [42]. However, since the ions are many orders of magnitude heavier compared to electrons, these forces generate a large density difference between ionic and electronic charges, and this charge separation results in a powerful electromagnetic transient [43].
The following relation between the emitted THz power from a one-color plasma and the excitation laser parameters was proposed by Hamster and coworkers in1994 [44]:
where W is the laser pulse energy, R0 is the 1/e2 radius of the laser beam at the focus, is laser wavelength and is the pulse duration. Therefore, this equation predicts a strong dependence of the THz power on the wavelength and the pulse duration of the excitation laser. In the presence of strong bias field, the generation efficiency can be improved to comparable to that of THz radiation from semiconductor surface [45].At the focus of the laser beam, the ionization front is moving in the wake of the laser pulse at light velocity, therefore generates THz radiation in a Cherenkov radiation cone shape in the forward direction (Fig. 1) [46].
The angular energy density distribution of the THz radiation can actually be expressed as [47]
where is the radiated THz frequency, is the emission angle, L is the longitudinallength of the plasma column, and c is the speed of light. As we can see, the THz radiation angular distribution has something to do with the plasma length. To explore the extreme case of THz radiation from “microplasma”, where the plasma length is at scale, Buccheri et al. demonstrated this fact with such a small length of plasma, the THz radiation cone angle opens up to about 80° [48].
All the THz generation schemes from gas plasma mentioned in last section use only one color laser pulses as the excitations. The mixing of laser pulses fundamental and their second harmonics (SH) to create the plasma has shown to provide enhancement of THz generation efficiency by several orders of magnitude [36].
Fig.2 Schematic demonstration of experimental setup for THz generation from two-color laser induced air plasma. An intense femto-second laser beam is focused by a lens to generate plasma in the air, -BBO is used to generate |
Figure 2 illustrates a basic experimental setup for the two color air plasma generation method. The SH of the laser pulse is usually generated by using a type-I -barium borate (BBO) crystal. The THz radiation intensity is maximized when the fundamental and SH polarizations are parallel, and is almost negligible when they are perpendicular [49–51]. THz radiation from two-color laser induced air plasma can be phenomenologically described as FWM process, which is a third order nonlinear optical process. The model can be expressed as
where ETHz,and are respectively the THz, the fundamental and the second harmonic (SH) electric field and is an effective third-order nonlinear susceptibility of the plasma filament. This relation has been experimentally confirmed by Xie et al. in 2006 [49]. We can see that above the ionization threshold, the generated THz field is proportional to intensity of the fundamental laser and is also proportional to the square root of the second harmonic laser. Other than the ambient air, noble gases can also be used in the two-color plasma THz generation scheme. The generation efficiencies from various noble gases highly depend on their ionization potentials [52]. The strongest THz emitter among them appeared to be Xenon.The generated THz field from two-color air plasma can be modified by changing the phase between the fundamental pulses and the SH pulses. In the FWM model, this can be expressed as
where denotes the phase difference betweenand . Due to the dispersion of the two colors in air, the phase shift between these two color beams varies as they propagate. Therefore, the phase can be easily controlled by shifting the-BBO longitudinally [50]. However, due to the laser intensity change toward the focus and the spatial limit between the focusing optic and the focus, simply shifting the -BBO cannot control the phase precisely or significantly enough for certain purposes, such as remote generation of THz [53]. In those cases, phase compensators including a pair of silica wedges were exploited in order to fine tune the phases and polarizations of the and beams [54]. Figure 3 lists two types of phase compensators, which respectively control the two color beams in one beam path or in two separate paths. With the help of phase compensator, the generated THz field strength as well as the pulse polarity can be modified explicitly [53]. Further examination on how the various pump pulse polarizations affect the THz generation field was also enabled due to the phase compensator technique [54].Although many experiments support the FWM model as the principle mechanism for THz generation from two-color laser induced air-plasma, the third order nonlinearity susceptibility of bound or free electrons is too small to explain the high intensity of THz radiation. Therefore, a transient photocurrent model was developed to explain coherent terahertz emission from air excited by a symmetry broken laser field composed of and laser pulses [38,55]. In this model, a nonvanishing transverse plasma current is produced when the bound electrons are stripped off the ions by an asymmetric laser field, e.g., a mixture of two-color laser field with a proper relative phase. This photocurrent transient, occurring on the timescale of the photoionization, can thus produce electromagnetic radiation at THz frequencies. The electron dynamics right after the ionization were treated classically by Kim et al. [38,55], whereas a full quantum mechanical simulation was reported by Karpowicz and Zhang [56].
Fig.3 (a) Inside the dashed line is the in-line PC (phase compensator). (b) Schematic illustration of the PC incorporated with a wedge pair: DM used to separate or recombine and beams; HWP used to control the polarization of the beam. DWP, dual-wavelength waveplate; BP, birefringent plate (α-BBO); QW, quartz wedges; Fs, femtosecond; HR, highly reflect; DM, dichroic mirror (Reprinted from Ref. [53] ©2011 IEEE) |
For elongated two-color filamentation, the THz radiation forms a cone shape due to off-axis phase matching [57]. The THz yield and angular distribution depend highly on the filament dimensions, and the dephasing length ld over which the THz radiation polarity remains the same. ld can be expressed as
where is the wavelength at, and are respectively the refractiveindex at frequency and . For filament with electron density of 1016 cm-3 inambientair, the dephasing length is about 22 mm.
Fig.4 Schematic of THz emission from a long, two-color laser-induced filament. The phase difference between 800 nm (dashed red curves) and 400 nm (solid blue curves) pulses along the filament results in a periodic oscillation of microscopic current amplitude and polarity. The resulting far-field THz radiation is determined by interference between the waves emitted from the local sources along the filament. P1, P2 and P3 are respectively the optical path along the different directions as shown in the figure, is the angle between P3 and P1 (Reprinted from Ref. [57]) |
For a filament comparable to or shorter than the dephasing length, THz waves generated along the filament have both positive polarity and negative polarity (As shown in Fig. 4) [57]. Those components interfere with each other constructively or destructively in the far field, depending on their path difference which is related to the radiation angle, forming a donut shape far field radiation profile. The angle of the THz radiation cone depends on the plasma length [58]. The longer the focal length of the focusing lens used for plasma generation is, the longer the plasma is, and the smaller the THz radiation cone is.
You et al. also found out that the generation yield increases almost linearly with the plasma filament length, so one can increase the THz generation by simply extending the plasma length [57]. Recently, different methods to tailor the filamentation toward more intense THz generation have been reported, including concatenating two plasmas into one [59].
Terahertz detection by air-plasmas
As we have observed in the cases of EO sampling of THz waveform versus optical rectification THz generation, a reversed version of THz generation process can often be utilized to detect THz wave. Similarly, the two-color laser induced air plasma THz generation has a counter-part in detection as well. In the FWM model, if we replace the in the right hand side of Eq. (13), there will actually be a light generation that’s proportional to THz field:
where and ETHz are the electric field amplitudes of the , and THz waved respectively and is the third-order susceptibility of the gas. This third order nonlinear process was known as THz-field-induced-second-harmonic (TFISH) [63]. Since the second harmonic can only be directly detected by its optical intensity, without a local oscillator, the measured signal is proportional to the THz radiation intensity, i.e., . The phase information of the THz wave is lost in this measurement, therefore, it is incoherent detection.However, when a second harmonic local oscillator is introduced, its cross term with will be generated for coherent THz detection. The total second harmonic intensity can be expressed as
(17)The extraction of the cross term from the above equation is essential for coherent THz detection. In the original demonstration of broadband THz wave detection with laser-induced plasma in gaseous media by Dai et al. in 2006 [64], the cross term was extracted through making it dominant by a strong intensity. When , the term can be ignored, and the term is a DC term that can be filtered out through a lock-in amplifier or modulating the THz wave. However, since the local oscillator (400 nm) was contributed by the white light generation, this technique requires very high probe pulse energy. In the case of Ref. [65], when the probe pulse energy is higher than 440, the coherentdetection eventually dominates. At this point, the detection technique was named THz-air-breakdown-coherent-detection.
To reduce the probe pulse energy requirement and increase the signal noise-ratio of the air-based coherent THz detection, an external ac bias across the focal point of the probe beam was applied to provide a local oscillator for the second harmonic generation (Fig. 5) [66]. Using lock-in amplifier to lock onto the ac bias frequency would help successfully extract the coherent detection cross term in Eq. (17). With this technique, only 100 probe pulse energy was typically needed, and due to the heterodyne detection nature, the signal-noise-ratio was significantly improved. The air-based detection technique’s name was therefore switched to THz-air-biased-coherent-detection to accentuate the use of ac bias, but the acronym THz-ABCD still stands.
The detected second harmonic intensity is a function of normalized third order nonlinear susceptibility along with a quadratic fit [67]. C6H14 provides more than 243 times the sensitivity compared with N2 or air. Using gases with larger and higher probe pulse energy can help to optimizethe sensitivity of the air-plasma detector.
Due to the gaseous media used for detection, one of the most important features of THz-ABCD is that its detection bandwidth is only limited by the probe pulse duration [68,69]. With a sub-35femtosecond laser pulse, the THz-ABCD bandwidth can reach 30 THz [53].
Fig.5 (a) Basic concept of THz-ABCD: electrodes are placed at the geometric focus of collinearly focused THz and optical probe beams with a variable time delay. Second harmonic light is induced from the THz field and the local bias field Ebias. Modulating Ebias allows for heterodyne detection for enhanced sensitivity. (b) Measured second harmonic intensity vs third order nonlinear susceptibility . All are normalized with respect to nitrogen (Reprinted from Ref. [66] ©2011 IEEE) |
Terahertz remote sensing technology using terahertz air-photonics
Fig.6 Envisioned scheme for THz stand-off generation and detection. Two dual-color pulses are focused close to the target under investigation creating a plasma emitter and a plasma sensor. Inset shows an absorbance spectrum of 4A-DNT retrieved through THz-REEF (Reprinted from Ref. [71]) |
Ring-Airy beams
Airy beam family
Ring-Airy beams
Generation of ring-Airy beams
In the first demonstration of ring-Airy beam [85], the Fourier transform of the beam distribution was first encoded onto a phase filter and applied onto a phase only reflective SLM. The phase modulation capability of the device is up to so phase wrapping has to be used for any phase change higher than . Then the phase-modulated beam will be Fourier transformed by a lens. An opaque mask was used to block the unwanted zero-order. The schematic demonstration and the phase mask [87].
In 2011, Chremmos et al. have proposed a method to create a family of abruptly auto-focusing beam [88], with the form of
where A is an envelope function such that the total energy is finite, is the phase of a sub-linear chirp, C>0 is a constant, 1<<2 is the index of the chirp. When = 3/2, the generated beam will auto-focus with a parabolic caustic.Therefore it is effectively equivalent to a ring-Airy beam.To realize this pre-engineered auto-focusing beam, the sinusoidal term can be expressed by the Euler’s formula:
where the first term denotes the outward wave and second the inward wave. Since we only care about the interference effect of the wave that will naturally come inward of the Airy primary ring structure, we can keep only the inward wave term, and reach to a math description that require only phase control:With such a method without Fourier transform, the loss due to the undesired zero order is reduced from ~90% for the Fourier transform approach to ~15% for the direct phase approach. The energy efficiency of the method allows the work in next section where high intensity beam is needed in order to generate plasma. Another advantage of the direct phase method would be the flexibility of changing the auto-focusing caustic by changing the index . For example, when = 3/2, the generated beam is equivalent to ring-Airy beam with a parabolic caustic; when = 1, the generated beam is equivalent to Bessel beam; when = 2, it is equivalent to a typical focusing scenario.
During the experiments of using a ring-Airy beam to generate two color laser induced plasma as THz source in 2015, the second harmonic generation (SHG) from the ring-Airy beam using β-BBO was observed to preserve the auto-focusing property and the focus will spatially overlap with the focus of the fundamental beam [89]. However, since the scope of the work mainly focused on THz generation from the plasma, the propagation property of the second harmonic (SH) beams was not explored with detail. In a recent report by Koulouklidis et al., it has been demonstrated both theoretically and experimentally the SHG from ring-Airy beams would preserve the phase distribution of the fundamental harmonic (FH) ring-Airy beam [90]. Therefore the SH will maintain the auto-focusing property with a focus position coincide with the FH beam focus [90].
Surprisingly, even after focusing with a lens the SH and FH still spatially overlap over an elongated focal volume. Both FH and SH show two foci as predicted by the case of all Janos waves [91]. However, the SH beam also shows one extra intense focus at the center, approximately at the focal point of the lens, due to the focusing of the pedestal term of the SH that does not have any autofocusing behavior.
The phenomena match very well with what have been observed during the work on THz generation from two-color ring-Airy beam induced plasma [89], as mentioned in the next section.
Fig.7 (a) Experimental set-up for observing the ring-Airy beam induced air plasma; (b) fluorescence false color images of ring-Airy beam plasmas (top 5) with pulse energy from 0.25 to 0.65 mJ, and Gaussian beam plasma (bottom) with pulse energy 0.65 mJ. The Gaussian plasma image intensity has been reduced 25 times to reach similar visibility of the ring-Airy beam plasmas |
Nonlinear propagation of ring-Airy beams in air
Terahertz generation from ring-Airy beam induced plasmas
Brief introduction
Experimental set-up
Fig.8 Experimental set-up. SLM: spatial light modulator, OD: opaque disk, on a transparent glass slide, L: lens, PM: parabolic mirror, M: mirror. Inset: Schematic comparison between the radial intensity distribution of the ring-Airy and the Gaussian beam; zoom-in on the beam area prior and post to the glass slide: case 1 is when using the Gaussian beam, the glass slide is shifted so the OD is removed from the beam path, case 2 is when using the ring-Airy beam, the OD is moved back into the center of the beam to block the unwanted part |
Terahertz radiation from two-color ring-Airy beam induced plasmas
Fig.10 THz emission peak amplitude versus the b-BBO distance from the focus. Blue dots: experimental data; blue solid curve: FWM model fitting result; black dashed curve: nonlinear fitting envelope taking into account the SHG efficiency change as the BBO is moving toward the focus; the insets show two sample THz waveforms having opposite polarities |
Fig.11 Emitted THz wave peak amplitude as a function of total pump pulse energy (800 and 400 nm). Red dots: experimental data from ring-Airy beam; red dashed line: fitting of the ring-Airy data with the FWM model. The error bars are the measurements standard deviation of each point |
Comparison between ring-Airy beams and Gaussian beams
Fig.12 (a) Fluorescence image comparison between an ring-Airy beam plasma and a Gaussian plasma (intensity reduced by 20 times), both generated with pump pulse energy 0.5 mJ; (b) measured THz waveforms and (c) their corresponding normalized spectra generated by the two plasmas in (a) |
Numerical simulation
Interference model of terahertz generation from two-color plasmas
Simulation results
Fig.15 (a) Normalized simulations of THz radiation spectrums without and (b) with the 3-mm-thick ZnTe detection bandwidth limitation; the inset in (a) is the enlarged version of the blue area (0−4 THz). Red solid curves: emission from ring-Airy plasma; black dashed curves: emission from Gaussian plasma |
Section summary
Terahertz-radiation-enhanced-emission-of-fluorescence of air-plasma in co-propagation geometry
Fig.16 Spectrum of air interacting with a 220 fs laser pulse. The lines marked by 1 are assigned to the first negative band system of and those marked by 2 are assigned to the second positive band systemof respectively. In the transitions (v–v′), v and v′ denote the vibrational levels of upper and lower electronic states, respectively (Reprinted from Ref. [105]) |
Fig.17 (a) Schematics of the interaction between the THz wave and laser induced plasma. (b) Measured fluorescence spectra versus THz field as td = −1 ps. Major fluorescence lines are labeled. (c) Measured quadratic THz field dependence of 357 nm fluorescence emission line as td = −1 ps. Inset: Theisotropic emission pattern of THz-REEF (Reprinted from Ref. [60]) |
One-color scheme
Two-color scheme
Fig.20 Terahertz wave assisted electron impact ionization of high-lying states in plasma. (a) High-lying states can be ionized by a series of collisions with energetic electrons; (b) interaction between the terahertz pulse and the asymmetric photoelectron velocity distributions generated by two-color field ionization (Reprinted from Ref. [61]) |
Terahertz remote detection at 30 m
Terahertz-radiation-enhanced-emission-of-fluorescence of air-plasma in counter-propagation geometry
Terahertz-REEF of elongated plasmas in counter-propagation geometry
Fig.24 Depiction of the co-propagation and counter-propagation interaction geometries. (a) and (c) are showing the plasma fluorescence intensity enhancement as a function of in (a) co-propagating and (c) counter-propagating geometriesmeasured by PMT. Both curves are normalized to 1. (b) In co-propagating geometry the THz (blue) and the NIR (red) pulses travel in the same direction. (d) In counter-propagating geometry the THz and NIR pulses travel in opposite directions. is the time delay between the two pulses. The special cases of = t1, t2 in co-propagation or in counter-propagation are respectively denoted in (a,b) and (c,d) |
Terahertz-REEF of micro-plasmas in counter-propagation geometry
Fig.26 (a) Time-resolved counter-propagation THz-REEF intensity for 2 inch EFL lens case (solid red) and its derivative (solid black). The black dots represent the data sampling rate used for the derivative in order to reduce the noise of the result. The curves are offset for clarity. (b) Derivative of REEF signal curve (solid black) is compared to the square of the experimental THz waveform measured with electro-optic sampling (solid blue) |
Fig.28 Micro-plasma fluorescence emission spectra with different values of plasma excitation laser pulse energy. Red is when no THz pulse is applied and blue is when a THz pulse with peak field of 90 kV/cm is applied. The microplasmas are obtained with a 1 inch EFL plano-convex lens |
Two-color terahertz-REEF in counter-propagation
Terahertz-REEF in counter-propagation for plasma diagnosis
Fig.30 Experimental (solid line) and numerical fitted (dashed line) time resolved counter-propagation THz-REEF intensity for the following focusing conditions: (a) 2 inch EFL lens; (c) 1 inch EFL lens; in (b), (d), the solid shaded areas represent the integration of the plasma fluorescence intensity along the radial dimension as measured with the iCCD camera, and the dashed lines are the numerically evaluated plasma effective electron densities producing the dashed curves plotted in (a) and (c) |