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Backward terahertz radiation from intense laser-solid interactions

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Abstract

We report a systematic study on backward terahertz (THz) radiation generation from laser-solid interactions by changing a variety of laser/plasma parameters. We demonstrate a high-energy (with an energy flux density reaching 80 μJ/sr), broadband (>10 THz) plasma-based radiation source. The radiation energy is mainly distributed either in the >10 THz or <3 THz regions. A radial surface current formed by the lateral transport of low-energy electrons (LEE) is believed to be responsible for the radiation in the high-THz region (>10 THz), while high-energy surface fast electrons (SFE) accelerated along the target surface mainly contribute to lower frequency (<3 THz) radiation. The unifying explanation could be applied to backward THz radiation generation from solid targets with presence of relative small preplasmas.

© 2016 Optical Society of America

1. Introduction

Terahertz (THz) wave generation from interactions between ultrashort laser pulses and plasmas has attracted considerable attention in recent years. THz radiation has been widely studied in laser-gas interactions [1–4 ]. On the other hand, both forward and backward THz radiation has been observed from laser-solid interactions at relativistic region [5–11 ]. Several generation mechanisms have been proposed accordingly [5–8,12,13 ]. Except for the “target normal sheath acceleration” (TNSA) and “ponderomotive” mechanisms [5,6 ], which are supposed more suitable for interpretations of forward-leading radiation, other controversies on backward THz radiation generation have persisted for decades [7,8,12,13 ]. The yield of backward THz radiation from solid targets is believed to be greatly affected by the density scale lengths of preplasmas [9]. With presence of very large preplasmas, where longitudinal plasma waves can be effectively excited, backward THz radiation could be generated through “Linear Mode Conversion (LMC)” [11,12 ]. Otherwise, electron currents near the front target surface would contribute to the long wavelength radiation.

Fast electrons are generally considered responsible for backward THz radiation generation from laser-solid interactions. Fast electron bunches are predicted to be able to emit coherent transition radiation (CTR) in THz frequency region when crossing the plasma-vacuum boundary of solid targets [13]. On the other hand, fast electron currents along the front target surface have been reported to be responsible for the generation of backward THz emission. Two related mechanisms have been proposed, which are named “antenna” and “surface fast electron (SFE)”, respectively [7,8 ]. The former attributed the observed radiation to a fast radial-current confined within the target surface, while the latter declared a directional SFE flow close to the surface [14]. Collisionless mechanisms for fast electron generation, such as resonance absorption, are found contributing to the SFE and THz emission generation [9,10 ].

By Kα imaging technique, lateral electron transport at the front target surface with high-intensity short-pulse lasers has been studied [15–17 ]. Evidence of surface transport of low-energy electrons (LEE) has been observed along with fast electrons. Unlike SFE emission close to the target surface [14], most of LEEs are confined in underdense preplasma due to the electrostatic field. For typical LEE (corresponding to <200 keV electron energy) transport of tens of micrometers [16], corresponding current lifetime would be sub-ps. Thus, in principle, the surface energy transport of LEE is also capable of producing radiation in terahertz region, though few related studies have been reported.

Nearly all previous experiments on backward THz radiation generation were conducted with a fixed incidence angle and with the THz radiation measured in the specular reflection direction [6–9,11 ]. In this paper, a more systematic study has been carried out by measuring backward THz radiation using a multichannel scheme, with a variety of laser and plasma parameters, including incident angles and plasma scale lengths, individually controlled. We demonstrate a broadband backward THz radiation source, which has two emission peaks in front of the target: the major one is along the target normal direction and dominated by higher frequency components (>10 THz), while the minor one is measured along the target surface direction and mainly made up of lower frequency components (<3 THz). By conducting two-dimensional particle-in-cell (2D-PIC) simulations, we found that two different types of surface current sources are responsible for the broadband THz radiation generation. The lateral transport of LEE in underdense plasma is considered as a radial current contributing to the higher frequency radiation above 10 THz; the drifting of a SFE beam along the target surface is believed to be responsible for THz emission with frequencies lower than 3 THz. By increasing the laser incident angle [14] and intensity [18,19 ], also with the preplasma scale length carefully controlled [9], SFE acceleration could be optimized and the backward THz radiation would be substantially red-shifted.

2. Main diagnostics for experiments

The experiments were performed using an amplified Ti:sapphire laser system delivering ~100-fs, 800-nm pulses at a repetition rate of 10 Hz. Shot-by-shot waveforms of laser pulses were monitored by an 8-GHz bandwidth oscilloscope. The intensity contrast of amplified spontaneous emission (ASE) pedestal to the main pulse was measured to be ~10−8 by a third-order cross-correlator, which would create a small preplasma with the scale length less than a laser wavelength in front of the target [9]. A schematic of the experimental setup is shown in Fig. 1 , where p-polarized laser pulses were focused by an f/3 off-axis parabola onto a single-side polished copper target with 1-mm thickness. The focal spot contained 35% of the total energy within 5 μm full width at half maximum (FWHM), resulting in a typical intensity of 3.6 × 1018 W/cm2 for 200-mJ incident energy. The target was located on a motion control system of three dimensions translation (x-y-z in the laboratory frame) and could be rotated along z-axis to get different incidence angles, varying from 67.5°, 45°, to 22.5° in the experiments. For each laser shot, a fresh surface was provided.

 figure: Fig. 1

Fig. 1 Schematic of experimental setup. TL: TPX lens; TW: TPX window; QL: quartz lens; BS: 50/50 beamsplitter @ 800 nm; ZnTe: 1-mm thickness; Bulk medium: schott SF57HHT; HR-Si wafers were inserted before all three of the pyroelectric detectors to avoid visible light. The transmission curves of involved THz materials can be queried from Tydex®. (Inset) Definition of the target-binding frame X-Y-Z.

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Backward THz emission was collected by Polymethylpentene (TPX) lenses, directing out of the target chamber by TPX windows, and measured by pyroelectric detectors (SPI-A-62) using a three-channel scheme. The detectors have average voltage responsivity of 1.1 × 105 V/W between 1 and 3000 μm and were located at three fixed positions marked as P1 to P3 in Fig. 1. The detection directions were 45°, 90°, 135° with respect to the laser incidence axis (the upward direction within paper plane), corresponding collection angles were 0.022 sr, 0.022 sr and 0.046 sr from P1 to P3, respectively. The responsivities of the detectors have been calibrated using both 2.5-THz continuous-wave lasers (Edinburgh Instruments FIRL-100) and 0.8-μm picosecond lasers. The three detectors have been cross-calibrated. High resistivity silicon (HR-Si) wafers were inserted before the detectors to block any light with wavelength below 1.2 μm. The transmittance of the HR-Si wafer has been calibrated with a Fourier transform infrared (FTIR) spectrometer (Brukers Vertex 80V, range 1-200 μm). By combining the transmittance curve of the HR-Si wafers with the response curve of the pyroelectric detectors, we have obtained an overall detectable spectral range of 0.1-250 THz for the three-channel detection system [11]. Frequency spectrum of the scattered light was monitored by a fiber spectrometer (200-1100 nm) at a direction of 60° with respect to the laser incidence axis to provide additional information on laser-plasma interaction dynamics [20].

A target-binding frame X-Y-Z is defined as depicted in the inset of Fig. 1. Laser pulses are incident in the XY plane with an angle of incidence of θ. + X shows the normal direction of the rear target surface, while + Y shows the direction of projection of the reflected light along the target surface. We use a relative angle α' with respect to target normal direction to describe the three-channel THz-measurement system at different θ. If the observation direction is on the same side of laser incidence axis with respect to target normal direction, we haveα'<0; otherwise α'>0. The target surface direction can be expressed as α'=±90° (with the positive sign corresponding to + Y direction) accordingly.

Optional single-shot THz waveform measurements were based on a spectral encoding method [21]. A small leakage of light from the main laser pulse was broadened to ~2 ps by using optical glass (schott SF57HHT) with index of refraction dependent on the wavelength. The broadened pulse was further split by a 50/50 beamsplitter into two pulses: the reference and the probe; the spectrum of the latter was then modulated by a copropagating THz pulse in a 1-mm thick <110>-cut ZnTe crystal. The spectra with and without THz modulation were recorded into different channels of an imaging spectrometer; the measured differential spectral profile would give the temporal profile of the THz radiation. Discussions on possible distortions involved in the signal retrieving process could be found in [22]. The electro-optic measurement system has a high frequency cutoff at ~2.5 THz [23].

3. Experimental results and discussions

We first investigated the frequency distribution of backward THz radiation by applying a set of low-pass band filters in front of the detectors, the cutoff frequency of which ranges from 0.3 to 10 THz. Table 1 shows the spectral distribution of THz radiation (as energy portions) in every frequency domain between 0.1 and 250 THz measured by three detectors at different angles of laser incidence. In each channel, THz signals were measured without and with particular low-pass filters for 10 laser shots to estimate the data fluctuation. The recorded signals have a maximum fluctuation of ± 15% for the input laser pulse energy of (180 ± 10) mJ. The radiation energies are retrieved from the detector signals by considering the product of detector spectral response curve and filter transmission curves [11].

Tables Icon

Table 1. Spectral distribution of THz radiation (energy in percentage) in every frequency domain between 0.1 and 250 THz.*

The filter-involved measurements show that the radiation which is confined in the vicinity of target normal direction (|α'|22.5°) is monopolized by higher frequency components. The radiation has more than 80% of the total energy distributed in the region above 10 THz, and about 10% energy distributed below 0.3 THz, while little energy is measured between 3 and 10 THz. On the other hand, radiation measured from a viewing angle of α'45° is found dominant by lower frequency components (<3 THz), which make up more than 80% of the total detected energy. Minor energy distribution in the frequency region of 3-10 THz indicates a less important role played by CTR for the observed backward THz radiation in our experiments, since the central frequency of CTR is predicted to be around 5 THz for a 100-fs incident pulse [13].

With a decrease of incidence angles θ in Table 1, the radiation measured at P1 and P3 show no obvious change in the frequency domain, while that measured at P2 is observed clearly red-shifted in spectrum. This indicates that the frequency distribution of backward THz radiation is closely related to the relative angle (between the observation direction and target surface) rather than to the angle of incidence. By using single-shot spectral encoding method, the Fourier-transformed spectrum of THz radiation at P3 was found to peak around 0.5 THz with a FWHM bandwidth of 0.7 THz [8], which is generally consistent with our filter measurement result given in Table 1. Since the single-shot electro-optic detection system based on a 1-mm-thick ZnTe-crystal will lose its precision beyond 2.5 THz, it is supposed not suitable to use the spectral encoding method to retrieve spectra of higher frequency dominated radiation.

In the second set of experiments, we investigated the angular distribution of backward THz radiation (|α'|90°) in the laser incidence plane for (180 ± 10) mJ incidence. The results are depicted in Fig. 2 , where each data point represents an average of 20-40 laser shots. The polar coordinates show the detector positions, i.e., the relative angles α' with respect to the target normal direction. Laser pulses are incident with varied angles onto the target which lies along the direction of α'=±90°. The colors of data points stand for different incidence angles θ: black, blue and red for 22.5°, 45°, and 67.5°, respectively. The symbols stand for different categories of radiation: the squares and triangles for higher (>10 THz) and lower (<3 THz) frequency radiation, respectively. For each incidence angle, data collections were repeated for two days to reduce possible errors coming from accidental changes of experimental conditions. There is an average fluctuation of THz signal of ± 20% in the measurement mainly due to the shot-to-shot laser fluctuation, which is not shown in Fig. 2. The losses of THz radiation energy when coupling and propagating are not taken into account.

 figure: Fig. 2

Fig. 2 Energy flux density of backward THz radiation measured by the three-channel scheme. P-polarized light of (180 ± 10) mJ per pulse is incident onto the target at different angles of incidence. The polar coordinates show the relative angles α' with respect to the target normal direction, while the colors of data point stand for different incidence angles θ. The units of angles θ and α’ are degrees. The squares and triangles stand for higher (>10 THz) and lower (<3 THz) frequencies, respectively. The average fluctuation of THz signals in the measurement is about ± 20%.

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From Fig. 2, we can see that the higher frequency radiation (>10 THz) measured in the vicinity of target normal direction (|α'|22.5°) is in most cases stronger than the lower frequency radiations (<3 THz). We observed a highest radiation energy flux density of >50 μJ/sr for an optical energy of (180 ± 10) mJ at 45° incidence. By comparing the data measured at α=67.5° for incidence angles of 22.5° and 67.5°, we found that a larger incidence angle is better for generating lower frequency radiation. On the other hand, a smaller incidence angle is better for generating higher frequency radiation, by comparing the data obtained at α=22.5° for θ=22.5°and 67.5°.

The energy distribution of higher frequency radiation is found to be non-symmetrical with respect to the target normal direction, but tends to be distributed more on the side of laser incidence (α'0). At 67.5° incidence, the radiation energy measured at α=22.5° (P2) is only ~1/6 of the value measured at α=22.5° (P1). By inserting a wire-grid polarizer, we investigated the polarization of the higher frequency radiation (>10 THz). Signal measured in the laser polarization (XY) plane is found to be twice as strong as that measured in the perpendicular (XZ) plane, which shows a much weaker polarization orientation of that measured at P3 [8]; the latter has a power extinction ratio (PER) of 10:1.

The normal-leading radiation could hardly be interpreted by any existing mechanisms for backward THz radiation generation, such as SFE, LMC, and CTR etc [8,12,13 ], by which little radiation power is predicted to be emitted along the target normal direction. On the contrary, the radiation pattern suggests that the higher frequency radiation (>10 THz) is possibly generated by slow moving electrons along the target surface. The energy distribution asymmetry with respect to the target normal direction indicates that the LEE transports is not parallel to the target surface, but tilt towards the direction of the laser electric field. This conjecture has been confirmed by our 2D-PIC simulations, which will be presented in Section 4.

Compared with the radiation with frequencies larger than 10 THz, the measured lower frequency radiation (<3 THz) has a weaker energy flux density in front of the target, typically 3-5 μJ/sr for (180 ± 10) mJ incidence with observation angles of 45°α'<90°. Previously we have attributed the radiation to surface acceleration of fast electrons [8]. For far-field detection of THz radiation, the SFE current could be treated as a point source mainly for two reasons. Firstly, the distance from the observation position to the current is much larger than the current size itself. Secondly, considering the long wavelengths of THz radiation, the phase differences of radiation generated by different electrons in the current could be ignored. Thus the angular distribution of far-field backward THz radiation generated by SFE could be written as [24],

sin2α(1βcosα)5,
where β=v/c is defined as the dimensionless average velocity of electrons in the current, α as the angle between the observation direction n and β. Equation (1) indicates that the peak of SFE-induced backward THz radiation would shift to the target surface with an increased electron kinetic energy.

Angular distribution of backward radiation between 0.3 and 3 THz at the incidence angle of 45° for (190 ± 10) mJ optical energy is depicted in Fig. 3(a) . We define a relative angle α with respect to the target surface direction + Y, with α+α'=90ο. Obvious enhancement in radiation energy is observed along + Y (α = 0) with an energy flux density up to 10 μJ/sr, while that measured at a direction of 45° away from + Y is only half of the value. Assuming the average drift velocity direction of SFE (see the solid-blue arrow in Fig. 3) is α and by substituting the experimental data into Eq. (1), we have,

sin2α(1βcosα)5=2sin2(45α)[1βcos(45α)]5.
By solving Eq. (2), we can estimate the SFE emission direction α corresponding to electron kinetic energies, as depicted in Fig. 3(b), from which an emission angle of 12° is derived for an electron temperature of 300 keV. Moreover, the SFE emission is mainly confined within an angle of 20° to the target surface. This is generally consistent with previous experimental observations of surface electron ejection [14,18,19 ]. On the other hand, the radiation measured along –Y direction (α=180°) has an energy flux density less than half that measured along + Y, which suggests that less SFE is emitted back to the laser incidence side (see the dash-blue arrow in Fig. 3). Polarization of THz radiation between 0.3 and 3 THz at each of the four observation directions in Fig. 3(a) is also examined. For p-polarized incidence, the radiation is found generally p-polarized (with PER value of ~10:1) in the laser incidence plane except for that measured along the target normal direction. The latter is found nearly unpolarized, and this is probably attributed to spontaneous black body emission which has a 4π emission pattern of one order weaker than the p-polarized emission.

 figure: Fig. 3

Fig. 3 (a) Energy flux densities of backward THz radiation in 0.3-3 THz region measured at an incidence angle of 45° for p-polarized light of (190 ± 10) mJ pulse energy. Each data point represents an average of ~20 laser shots. A mean fluctuation of ± 20% of the intensities of THz signals has been observed in the measurement. Red and blue arrows represent the direction of laser incidence and SFE emission, respectively. (b) The dependence of SFE beam emission direction α (with respect to the target surface + Y) on electron kinetic energies, calculated by Eq. (2).

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In experiments, the preplasma density scale lengths can be modulated by changing the intensity contrast ratio of laser pulses, and the measurement of harmonics generation is a powerful tool of laser-plasma interaction investigations [9]. For example, resonance absorption and two plasma decay (TPD) at the critical and quarter critical densities will lead to the generation of second and three-halves harmonic signals, respectively [25]. When the laser intensity contrast ratio was changed from 10−8 to 10−7 in our experiment, the scattered light spectrum collected by the fiber spectrometer at 22.5° incidence (15° anti-clockwise to the specularly reflection direction) was observed to change from second to three-halves harmonic dominate, which indicates a transition of principal absorption mechanisms from resonance absorption to TPD [9]. Meanwhile, the higher frequency (>10 THz) radiation signal measured at P1 was enhanced by 1.7 times. On the contrary, the yield of lower frequency radiation (<3 THz) measured at P3 was observed to be decreased when the frequency spectra of the reflected light had a similar change from second to three-halves harmonic dominant [9]. Thus we can conclude resonance absorption and TPD are two effective laser absorption mechanisms for backward THz radiation generation. With the transition from resonance absorption to TPD, the radiation spectrum would be blue-shifted.

4. Simulations

2D-PIC simulations have been carried out using the “KLAPS” codes [26]. The size of simulation is 440λ0 × 800λ0resolved by 8800 × 16000 grids with 16 particles per cell. The target is a plasma slab uniform along y-direction and located in the region from 400λ0 in x-direction with an exponential rise of L=(dlnn/dx)1 from 0.001ncto 5nc, where L is the plasma density scale length, nc the critical electron density and λ0the laser wavelength, respectively. L/λ0 is set to be 0.1 or 2 to represent small and large preplasma cases respectively. A p-polarized pulse with a sine-squared shape is incident from the left side of the simulation box and irradiated on the front target surface at the position (400, 0) with peak amplitude a 0, where a 0 a0 is related to the laser intensity by Iλ02=a02×1.37×1018 W/cm2 μm2. a 0 is set as 1 in the simulations unless specified otherwise. The laser pulse duration is set as 30τ0 and the waist6λ0, where τ0=λ0/c and c is the speed of light. The temporal resolution of the simulation is 0.025 laser cycle. Electrons emitted close to the target surface with an angle less than 20° are counted to study the properties of the SFE beam (Group I), while the energy and spatial distributions of electrons in the plasma slab of 0.001nc-0.01nc are studied to investigate the lateral electron transport along the target surface (Group II), as depicted in Fig. 4(a) . In following discussions, each direction in the laser incidence plane is defined by the direction of the electron momentum as tan−1 (py/px).

 figure: Fig. 4

Fig. 4 Schematics of the laser-target interaction geometry and of the two effective areas for electron counting are shown in (a). Time-dependent energy spectra of electrons emitted into vacuum within 20° to + y (I) and those laterally transported in underdense plasma along + y (II) are shown in (b) and (c), respectively. The laser pulse is incident at an angle of 60° with a small preplasma scale length of L/λ0 = 0.1.

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Energy spectra of the electrons emitted to vacuum with an angle α<20° (Group I) and those transported along + y (Group II) are recorded every 20 laser cycles, as shown in Figs. 4(b) and 4(c), respectively. The target with a small preplasma scale length of L/λ0 = 0.1 is illustrated at an angle of incidence of 60°. Three major differences between the two groups of surface electrons can be deduced from the simulations. Firstly, a substantial component of the surface electrons are in the form of lower energy electrons (Ek<200 keV), which are confined in the underdense preplasma – Fig. 4(c), while higher energy electrons are more likely to escape from the surface fields and to emit into vacuum – Fig. 4(b). Secondly, the lateral transport of surface electrons occurs immediately after the laser incidence, the energy spectrum of which tends to be stable after 80τ0 (~0.2 ps). On the contrary, no effective SFE emission has been observed before 80τ0. This indicates that a lateral energy transport is necessary before the fast electrons can be emitted into vacuum, which is consistent with previous simulation results [13]. Thirdly, Figs. 4(b) and 4(c) suggest typical current lifetimes of >320τ0(0.85 ps) and 80τ0(0.2 ps) for the two groups of surface electrons, respectively, corresponding to radiation frequencies of <1.2 THz and 5 THz. This suggests that lower energy electrons confined in the underdense preplasma are responsible for higher frequency radiation. By tracing the electron trajectory [27], we found that the electrons in SFE beam would be pulled in and out of the target by the effect of the surface fields, drifting along the target surface, while the THz radiation could possibly be generated. Figure 4(b) indicates that electrons with energies of Ek<200 keV are not related to the formation of the surface drifting current. Comparing the simulation results with our experimental observations, the SFE (Ek>200 keV) current lifetime given in Fig. 4(b) is deemed to fit our spectral measurements of the lower frequency radiation (<3 THz) properly. On the other hand, radiation measured above 10 THz (corresponding to a current lifetime of less than 0.1 ps) should be generated by LEEs with Ek<100 keV from Fig. 4(c). Electrons with energies in the region of 100–200 keV are also considered capable of producing radiation in an intermediate THz frequency, but the efficiency would be decreased rapidly with the reduction of the number of electrons. This may explain the measured energy gap in 3-10 THz region in the experiments.

Angular distribution of electrons in vacuum (x<400) is investigated at T = 400τ 0 (~1 ps). In the simulations, L/λ0is set to be 0.1, since small preplasmas are better for the SFE emission [14]. Figure 5(a) shows the distribution of electrons with different kinetic energies for θ = 60° and a 0 = 1. The target lies along the direction of 0° ( + y) – 180°. We can see clearly that more energetic electrons tend to be emitted closer to the target surface. By changing the laser incident intensity, the SFE (Ek>200 keV) is found to be mainly emitted along + y direction with a 0<1, but is also observed along –y direction when a 0≥1. For a 0 = 1.3 (corresponding to an optical intensity of 200 mJ in our experiments), the angular distribution of fast electrons in vacuum with energies >200 keV is depicted in Fig. 5(b) for different incidence angles. The emission of SFE beam is found to be less effective with small incidence angles, which is consistent with our experimental measurements of radiation <3 THz in Fig. 2, as well as with previous experimental observations for SFE beams and THz radiation [10]. In the experiments, the actual incidence angle is always larger than the simulated angle because of plasma expansion, and thus may cause SFE acceleration even at small incidence angles.

 figure: Fig. 5

Fig. 5 Angular distribution of electrons in vacuum at T = 400τ 0, where angles are defined as tan−1 (py/px). Specifically, (a) for θ = 60°, a 0 = 1, (b) for electrons with energies >200 keV under different angles of incidence at a 0 = 1.3. Red arrows represent the direction of laser incidence.

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By changing the laser incidence angle θ and plasma scale length L, we investigate the optimal conditions for the lateral transport of surface electrons in underdense plasmas (Group II), the electron spectra of which after 80τ 0 (~0.2 ps) from laser incidence are depicted in Fig. 6(a) . The number of less energetic electrons (Ek<200 keV) confined in the plasma is found to be greatly enhanced by a larger preplasma scale length. On the other hand, the number of higher energy electrons (Ek>200 keV) in the underdense plasma drops sharply at a larger incidence angle, as more electrons escape from the surface fields and emit into vacuum. Similar conclusions have been made from Fig. 5(b). Small incidence angles are better for the lateral transport of surface electrons, which is consistent with our experimental observations for higher frequency radiation (>10 THz). By calculating the harmonics of ω 0 and ω 0/2 in the vacuum, where ω 0 is the angular frequency of the fundamental light, we found that the three-halves harmonic is enhanced at θ = 20° and L/λ0=2. This indicates that TPD is an important absorption mechanism to create effective lateral transport of surface electrons, which is also consistent with our experimental observations.

 figure: Fig. 6

Fig. 6 (a) Energy spectra of electrons in the underdense plasma over 2π integration at T = 80τ 0 for the incident angles θ = 20° and 60°, plasma scale length L/λ 0 = 0.1 and 2, respectively. (b) Time-dependent angular distribution of electrons in the underdense plasma for θ = 20° and L/λ 0 = 2. Angles are defined as tan−1(py/px). Red and blue arrows represent the direction of laser incidence and polarization, respectively.

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Time-dependent numbers of electrons moving in the underdense plasma along every single direction in the laser incidence plane are shown in Fig. 6(b) for θ = 20° and L/λ0 = 2, corresponding to the strongest lateral transport in Fig. 6(a). The target lies along the direction of 0°–180°. The electrons are found to be moving in a nearly circular velocity pattern with a favored direction of laser polarization, along which the electron count is about twice as large as the minimum. The lateral transport of surface electrons can be considered as a radial current, which will produce a radiation field polarized in every direction and has an orientation along the laser polarization. This is highly consistent with what we observed in the polarization measurements of high frequency radiation at P1, where the radiation shows a PER value of around 2. The electron transports would also result in an asymmetrical radiation pattern with respect to the target normal, just as what we observed in the experiments.

5. Conclusions

We have systematically studied the backward long-wavelength radiation generation from a solid target irradiated by intense femtosecond laser pulses. The strongest radiation is mainly emitted in the vicinity of the target normal direction and is dominated by middle-infrared (1–30 μm) components. A highest energy flux density measured in the target normal direction reaches 80 μJ/sr by 190 mJ optical energy at 45° incidence. In comparison, the far-infrared (100–3000 μm) radiation measured along the target surface is approximately 10 μJ/sr under similar experimental conditions. The spectral and spatial characteristics of the radiation are found to be strongly related to the electron currents established near the front target surface. SFE accelerated along the target surface and LEE transported in the underdense preplasmas are believed to be contributing to lower (<3 THz) and higher (>10 THz) frequency radiation, respectively. The emission of the higher and lower frequency radiation is concentrated in different spaces, providing an angular control scheme for purposeful frequency selection associated with applications. THz yield in 0.3–3 THz is expected to be optimized by increasing the SFE generation in the future.

Acknowledgments

This work is supported by the National Basic Research Program of China (Grant No. 2013CBA01501), the National Natural Science Foundation of China (Grant Nos. 11135012, 11105217, 11375262, 11520101003 and 11375261).

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Figures (6)

Fig. 1
Fig. 1 Schematic of experimental setup. TL: TPX lens; TW: TPX window; QL: quartz lens; BS: 50/50 beamsplitter @ 800 nm; ZnTe: 1-mm thickness; Bulk medium: schott SF57HHT; HR-Si wafers were inserted before all three of the pyroelectric detectors to avoid visible light. The transmission curves of involved THz materials can be queried from Tydex®. (Inset) Definition of the target-binding frame X-Y-Z.
Fig. 2
Fig. 2 Energy flux density of backward THz radiation measured by the three-channel scheme. P-polarized light of (180 ± 10) mJ per pulse is incident onto the target at different angles of incidence. The polar coordinates show the relative angles α ' with respect to the target normal direction, while the colors of data point stand for different incidence angles θ. The units of angles θ and α’ are degrees. The squares and triangles stand for higher (>10 THz) and lower (<3 THz) frequencies, respectively. The average fluctuation of THz signals in the measurement is about ± 20%.
Fig. 3
Fig. 3 (a) Energy flux densities of backward THz radiation in 0.3-3 THz region measured at an incidence angle of 45° for p-polarized light of (190 ± 10) mJ pulse energy. Each data point represents an average of ~20 laser shots. A mean fluctuation of ± 20% of the intensities of THz signals has been observed in the measurement. Red and blue arrows represent the direction of laser incidence and SFE emission, respectively. (b) The dependence of SFE beam emission direction α (with respect to the target surface + Y) on electron kinetic energies, calculated by Eq. (2).
Fig. 4
Fig. 4 Schematics of the laser-target interaction geometry and of the two effective areas for electron counting are shown in (a). Time-dependent energy spectra of electrons emitted into vacuum within 20° to + y (I) and those laterally transported in underdense plasma along + y (II) are shown in (b) and (c), respectively. The laser pulse is incident at an angle of 60° with a small preplasma scale length of L / λ 0 = 0.1.
Fig. 5
Fig. 5 Angular distribution of electrons in vacuum at T = 400τ 0, where angles are defined as tan−1 (py /px ). Specifically, (a) for θ = 60°, a 0 = 1, (b) for electrons with energies >200 keV under different angles of incidence at a 0 = 1.3. Red arrows represent the direction of laser incidence.
Fig. 6
Fig. 6 (a) Energy spectra of electrons in the underdense plasma over 2π integration at T = 80τ 0 for the incident angles θ = 20° and 60°, plasma scale length L/λ 0 = 0.1 and 2, respectively. (b) Time-dependent angular distribution of electrons in the underdense plasma for θ = 20° and L/λ 0 = 2. Angles are defined as tan−1(py/px ). Red and blue arrows represent the direction of laser incidence and polarization, respectively.

Tables (1)

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Table 1 Spectral distribution of THz radiation (energy in percentage) in every frequency domain between 0.1 and 250 THz.*

Equations (2)

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sin 2 α ( 1 β cos α ) 5 ,
sin 2 α ( 1 β cos α ) 5 = 2 sin 2 ( 45 α ) [ 1 β cos ( 45 α ) ] 5 .
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