1.

Introduction

Spin-polarized terahertz waves with twisted electric- and magnetic-field directions and temporal evolution of the amplitudes have been widely utilized for non-thermal and selective excitation of electron spins, resulting in the discovery of the spin-galvanic effect,¹ the manipulation of terahertz nonlinear phenomena,² and optical spin injection in novel materials.^3–5 Recently, Mashkovich et al.⁶ found that linearly polarized terahertz waves can nonlinearly excite gigahertz spin waves in antiferromagnetic ${\mathrm{FeBO}}_3$ via terahertz field-induced inverse Cotton–Mouton effect. However, the inverse Faraday effect excited by circularly polarized terahertz waves has not yet been experimentally demonstrated, despite many theoretical predictions reported.⁷ Therefore, spin-polarized terahertz waves are essential for revealing electron spin-related linear and nonlinear ultrafast phenomena. In addition, spin-polarized terahertz waves naturally carrying chiral properties offer multifaceted spectroscopic capabilities for investigating low-energy macromolecular vibrations in biomaterials, understanding the mesoscale chiral architecture⁸ and confidential communication.^9,10 However, the proliferation of terahertz circular dichroism spectroscopy and other applications is impeded by the lack of generation and manipulation of chiral terahertz waves.

Conventional polarization shapers working in the terahertz electromagnetic frequency range are mainly segmental waveplates and metasurfaces,^11,12 both of which can be well applied for narrow bandwidth applications and low tolerance of flexible tunability. Various scalar manipulations of terahertz waves have been demonstrated in poled nonlinear optical crystals^13,14 or even in water¹⁵ and have synthesized different frequencies generated in spatially distributed sources.¹⁶ However, it would be much more elegant if polarization shaping functionality could be vectorized and integrated into the sources. Currently, there are already several such kinds of vector-manipulated polarized terahertz sources.^17–21 For example, femtosecond laser amplifier pumped air plasma, when intensively tuning the phase delay and the pump pulse polarization between two different pump pulse colors, can enable the opportunity to obtain arbitrarily shaped terahertz polarizations.¹⁷ Furthermore, terahertz polarization pulse shaping with arbitrary field control has also been demonstrated by optical rectification of a laser pulse whose instantaneous intensity and polarization state are flexibly controlled by an optical pulse shaper.¹⁸ Recently, elliptically and circularly polarized terahertz waves have been realized in W/CoFeB/Pt heterostructures through deliberately engineering the applied magnetic-field distribution and the cascade emission method, respectively.^19,20 In a NiO single crystal, double-pulse excitation has also been used to vectorially control magnetization by radiating spin-polarized terahertz waves,²¹ in which an electron spin-polarized wave (magnon oscillation) has been purposely vectorially controlled and manipulated. In addition, highly efficient chiral terahertz emission with elliptical polarization states has been obtained from the fascinating topological phase matter, bulk Weyl semimetal TaAs with reflection terahertz emission geometry.²² Inspired by these pioneering breakthroughs, the question of whether we can utilize the spin freedom of electrons to generate and manipulate spin-polarized terahertz waves has become very interesting.

Three-dimensional topological insulator ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ single crystals grown on ${\mathrm{Al}}_2{\mathrm{O}}_3$ substrates not only feature the spin-momentum–locked (topologically protected) surface states but also are adapted for various heterostructures with tunable quantum layers.²³ They are predicted to have the potential for achieving vectorial polarization shaping terahertz sources. The charge current and spin current inside topological insulators are simultaneously excited when being driven by femtosecond laser pulses.^24–28 However, topological insulator-based terahertz emission mechanisms are far more complicated when compared with conventional terahertz emitters. It is clarified that nonlinear effects play a predominant role in the ultrafast terahertz emission process.²⁹ Nonlinear effects include optical rectification, photogalvanic effect (PGE), and photon drag effect, among which PGE has a strong correlation to electron spin. Thus, there is the feasibility to generate a femtosecond laser helicity-dependent current component resulting in synthesizing chiral terahertz light.

In this work, we systematically studied terahertz emission from ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ nanofilms with various thicknesses grown on ${\mathrm{Al}}_2{\mathrm{O}}_3$ substrates excited by femtosecond laser pulses. Through elaborately controlling the pump laser pulse polarization, its incident angle, and the sample azimuthal angle, we not only successfully realized efficient linear polarization tunable terahertz radiation but also obtained high-quality chiral terahertz waves, as shown in Fig. 1(a). In addition, we also demonstrated arbitrary manipulation of the ellipticity and chirality of the emitted terahertz waves from topological insulators. Based on the radiated terahertz characteristics, which originated from the helicity-dependent photocurrent component featuring the spin selectivity in the surface state [Fig. 1(b)] and other components in the bulk state³⁰ [Fig. 1(c)], we provide a phenomenological PGE-based interpretation for the polarization tunable terahertz radiation mechanism. Such polarization-shaped topological insulator-based terahertz source can be used for terahertz circular dichroism spectroscopy, terahertz secure wireless communication, and electron spin correlated coherent excitation and manipulation investigations.

Fig. 1

Schematic diagram of the polarization tunable terahertz emission from ${\mathrm{Bi}}_2{\mathrm{Te}}_3$. (a) Femtosecond laser pulses, horizontal linear polarization (HLP), vertical linear polarization (VLP), left-handed circular polarization (LCP), and right-handed circular polarization (RCP), are incident onto the topological insulator ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ and produce polarization tunable terahertz waves. (b) Macroscopic helicity-dependent photocurrent and only unidirectional spin current can be generated. (c) Microscopic electronic transition under circularly polarized laser pulse illumination (Video 1, MP4, 15.5 MB [URL: https://doi.org/10.1117/1.AP.2.6.066003.1]).

2.

Linearly Polarized Terahertz Emission

2.1.

Experimental Results

In this experiment, we employed a commercial Ti:sapphire laser oscillator delivering nJ magnitude pulse energy with a central wavelength of 800 nm, a pulse duration of 100 fs, and a repetition rate of 80 MHz. The pump laser polarization was varied by inserting either a half-wave plate or a quarter-wave plate. The radiated terahertz polarization was probed by a polarization-resolved electro-optic sampling detection method. The topological insulator samples were grown by molecular beam epitaxy (MBE), and their lattice structures and the characterizations can be found in Supplementary Note 1 and Fig. S1 in the Supplementary Material.

First, we examined the sample azimuthal angle-dependent terahertz radiation polarization properties to unveil the radiation mechanism in topological insulators driven by femtosecond laser pulses. For the $p$-polarized pump laser at nearly normal incidence, as shown in Fig. 2(a), the radiated terahertz signal from 10-nm-thick ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ was $\sim 1/20$ compared with that from 1-mm-thick ZnTe (see Supplementary Note 2 and Fig. S2 in the Supplementary Material) and with $\sim 100$ dynamic range, which manifests its feasibility for terahertz spectroscopy. The radiated terahertz waves were always linearly polarized with a three-fold rotation angle depending on the sample azimuthal angle, as shown in Figs. 2(b) and 2(c). For the pump-fluence-dependence results [Fig. 2(d)], the terahertz signals of different thickness all exhibited a linear increasing tendency, indicating that the terahertz radiation mechanism under the linear-polarization laser pump was predominated by a second-order nonlinear effect.

Fig. 2

Linearly polarized terahertz emission and its shift current mechanism. (a) Schematic diagram of the experimental setup for linearly polarized terahertz emission. Linearly polarized laser pump passes through a half-wave plate of angle $\alpha$ and is incident onto the sample emitting linearly polarized terahertz wave. The incident angle of the pump laser, $\theta$; the azimuthal angle of the topological insulator, $\phi$. (b) Far-field polarization trajectories [$S_x(t)$, $S_y(t)$] of the radiated terahertz waves obtained experimentally from 10-nm-thick ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ when the pump laser polarization was nearly normal incidence while the sample azimuthal angle was varied. (c) The terahertz peak amplitude of $S_y(t)$ as a function of the azimuthal angle exhibits a 120-deg period. (d) Pump fluence dependence of terahertz peak amplitude from ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ with different thickness of 5, 8, and 10 nm. (e) Schematic of the shift current generated from the electron transfer along the Bi–Te bonds. (f) Parameters in the $y$ axis extracted through the symmetry analysis of surface state using Eq. (1). (g) $I_p$ denotes the laser intensity profile. Fitting the shape of the shift current (blue line) to the photocurrent in the material (green line).

3.

Chiral Terahertz Wave Emission and Manipulation

As shown in Fig. 3(a), when the left-handed circularly polarized (LCP) pump light was incident onto the sample at an incident angle around $+20\mathrm{deg}$, and, when we rotated the sample azimuthal angle, elliptically polarized terahertz waves were obtained and showed no significant change when scanning the azimuthal angle $\phi$ in Fig. 3(b). To produce circularly polarized terahertz pulses, simultaneously tuning the pump laser polarization and the sample azimuthal angle was necessary. The experimental results are shown in Fig. 3(c). When the sample azimuthal angle was fixed, we can also obtain elliptical terahertz beams with various ellipticities and principal axes. Within expectations, we can manipulate the chirality of the emitted terahertz waves via varying the incident laser helicity. It is obvious that the polarity of emitted terahertz signal along the $x$ direction reversed under illumination of the laser with different chirality [Fig. 3(d)] and sustained the sign along the $yz$ plane [Fig. 3(e)]. Therefore, the generation of pump laser helicity-dependent photocurrents with continuous tuning of the magnitude and polarity is the primary reason for the production of elliptically and circularly polarized terahertz pulses.

Fig. 3

Generation of elliptically and circularly polarized terahertz beams. (a) Experimental layout for circularly-polarized terahertz wave generation. Linearly polarized laser pump passes through a quarter-wave plate of angle, $\alpha$, producing elliptically or circularly polarized pump laser beams. The emitted terahertz wave polarization can be elliptical or circular. The incident angle of the pump laser, $\theta$; the azimuthal angle of the topological insulator, $\phi$. (b) Far-field detected elliptically polarized terahertz polarization trajectories when the pump laser polarization was fixed while rotating the sample azimuthal angles. (c) Production of circularly polarized terahertz waves when fixing the azimuthal angle while rotating the quarter-wave plate for the pump laser pulses. (d) Experimentally observed terahertz component $S_x(t)$ polarity reversal depends on the pump laser helicity. (e) Helicity-independent component $S_{yz}(t)$ from ${\mathrm{Bi}}_2{\mathrm{Te}}_3$. ${\delta }^{+}$ and ${\delta }^{-}$ mean left-handed and right-handed elliptically polarized terahertz, respectively.

To further investigate the helicity-dependent terahertz signal, a terahertz pulse with chirality was manipulated by rotating the quarter-wave plate with an angle $\alpha$ at a fixed incident angle around $+20\mathrm{deg}$. During the $\alpha$ scanning, the terahertz peak values clearly exhibited a 180-deg period [Fig. 4(a)], and the waveform shape along the $x$ axis was very similar to the result in Ref. 24 in the ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ thin film system. It illustrates the analogies among the family of topological insulators.

Fig. 4

Macroscopic analysis of PGE. (a) The terahertz peak amplitude of $S_x(t)$ and $S_{yz}(t)$, as a function of the quarter-wave plate angle, respectively. (b) and (c) The time-domain signals for the parameters $C(t)$, $L_1(t)$, $L_2(t)$, and $D(t)$ in the $x$ axis and $yz$ plane extracted using Eq. (3). (d) Spin-momentum-locked states selectively excited by spin-polarized pump laser form unidirectional spin currents. (e) and (f) The corresponding Fourier transformed spectra of the time-domain signals in (b) and (c).

Therefore, based on the geometric structure of the incident laser that was modulated via the quarter-wave plate (Supplementary Note 6 and Fig. S8 in the Supplementary Material), we can write the signal in the following form:^25,26,34

The coefficient $C(t)$ describes the helicity-dependent terahertz radiation that originates from CPGE. $L_1(t)$ denotes the coefficient induced by linearly polarized light, and LPGE may be responsible for it. For terahertz emission in 40-nm ${\mathrm{Sb}}_2{\mathrm{Te}}_3$, Yu et al.³⁴ attributed the origin of $L_2(t)$ to LPDE and experimentally verified that the trend of $L_2(t)+D(t)$ under the variation of the incidence angle $\theta$ was in accordance with the trend of pure LPDE for $p$-polarized laser excitation. However, as aforementioned, LPDE has already been eliminated, so it is not suitable for elucidating this phenomenon. In terms of $D(t)$, there is no uniform statement, and it is still subject to controversial debate. LPGE, drift current out of plane, or photo–Dember effect may be the candidates for this coefficient.

Accordingly, we extracted all coefficients along the $x$ axis and $yz$ plane (see Sec. 2). All data were offset to ensure great clarity, as shown in Figs. 4(b) and 4(c), which show the time-domain trace for every component. The main characteristics are summarized as follows. (i) In magnitude, along the $x$ axis, $C_x$, $L_{1x}$, and $D_x$ dominate the main components, while $L_{2x}$ is negligible. They are sorted from the largest to smallest $L_{1x}>D_x>C_x$. Along the $yz$ plane, $L_{2yz}$ and $D_{yz}$ dominate the main components, while $L_{1yz}$ and $C_{y\mathrm{z}}$ are negligible. In addition, $L_{2yz}$ and $D_{yz}$ have almost the same magnitude. (ii) $C_x$ shows similar characteristics to those for $L_{1x}$. In fast Fourier transformed spectra of $C_x$ and $L_{1x}$ [Figs. 4(e) and 4(f)], they both presented the same spectral shapes, strongly indicating that both $C_x$ and $L_{1x}$ shared the same physical origin and are consistent with previous observation.^{25,26,35–38} However, the $D_x$, $L_{2yz}$, and $D_{yz}$ terms also presented similar shapes in the frequency domain, and very few works pay attention to the underlying mechanism about these three terms. Ours is the first observation that all five terms resemble each other in nature, and we elucidate this phenomenon in a macroscopic phenomenological PGE-induced photocurrent framework.

Macroscopically, as a second-order nonlinear optical process, the PGE-induced photocurrent vanishes in the bulk region where inversion symmetry exists. Only on the surface where inversion symmetry is broken, the photocurrent induced by PGE can occur. Thus, taking the $C_{3v}$ symmetry into account, in our specific case in which the incident pulse shines on the $yz$ plane, the arbitary polarized laser pulse-induced photocurrent can be separated to CPGE- and LPGE-induced components (see the derivation in Supplementary Note 6 in the Supplementary Material):

The LPGE-induced photocurrent can be written in a compact way, $j_{\mathrm{LPGE}}=\left(\begin{array}{c}{j}_x\\ j_y\\ j_z\end{array}\right)$, and all components are written as

From the above four PGE-induced photocurrent equations, we can obtain four conclusions. (i) For the incident laser with arbitrary polarization and directions, in addition to the CPGE-induced term $j_{\mathrm{CPGE}}\propto \sin 2\alpha$, the LPGE-induced photocurrent can be written in a form of $j_{\mathrm{LPGE}}=j_{\mathrm{LPGE},1}\sin 4\alpha +j_{\mathrm{LPGE},2}\cos 4\alpha +j_{\mathrm{LPGE},3}$. The combination of these two photocurrents explains why we can write the emitted terahertz signals in a form of Eq. (3). (ii) We can readily find that when the incident laser pulse changes chirality from left-handed ($\alpha =\pi /4$) to right-handed ($\alpha =3\pi /4$), the CPGE-induced photocurrent will change signs. Furthermore, the CPGE-induced photocurrent only flows along the direction perpendicular to the incident plane, which is consistent with the results in Fig. 3(d). (iii) From these four equations, we can qualitatively analyze the magnitude relationship of the photocurrent components. As in the $x$ direction, from Eqs. (4) and (5), only CPGE-induced $C_x$ and LPGE-induced $L_{1x}$ components contribute to the photocurrent. Because the incident angle is relatively small, and $L_{1x}$ contains the $\cos \theta$ term, $L_{1x}$ should be significantly larger than $C_x$. And there is no $L_{2x}$ contribution in the $x$ direction. In the $yz$ plane, $C_{yz}$ and $L_{1yz}$ are both 0, and the magnitudes of $L_{2yz}$ and $D_{yz}$ are approximately identical. The magnitudes of these current components determined by the crystal symmetry in the $x$ axis and $yz$ plane are in good agreement with the relative magnitudes of the various components extracted in our experiments except for $D_x$. There is a relatively large $D_x$, observed in experiment, and the physical origin of this component may come from a dark current,³⁰ which needs further investigation. (iv) It is worth noting that the PGE theoretical framework illustrates that photocurrent components all originate from the same PGE mechanism, which is exactly the evidence reflected by their frequency spectral shapes. Therefore, we can conclude that the phenomenological PGE mechanism framework determined by the symmetry of the crystal surface is adequate for explaining most of the salient features of the resulting photocurrents.

To acquire spin-polarized terahertz pulses with higher quality, we can also readily gain inspiration from the above framework. When the incident laser pulse is left-handed ($\alpha =\pi /4$), $j_{\mathrm{CPGE},x}=-2\gamma C^2\sin \theta$, $j_{\mathrm{LPGE},x}=0$, $j_{\mathrm{LPGE},yz}=f(\theta )$. When the incident laser pulse is right-handed ($\alpha =3\pi /4$), $j_{\mathrm{CPGE},x}=2\gamma C^2\sin \theta$, $j_{\mathrm{LPGE},x}=0$, $j_{\mathrm{LPGE},yz}=f(\theta )$. It indicates that when we change the chirality of the laser pulse, we can manipulate the polarity of the CPGE-induced photocurrent, keeping the orthogonal component invariant. Based on this statement, we can further analyze the manipulation of phase and amplitude for terahertz radiation. As for the phase between the $x$ axis and $yz$ plane, two different physical processes actually exist. The physical process in LPGE represents a shift current along the Bi–Te bond. As for the process in CPGE, the laser with certain chirality will selectively excite a certain spin alongside the direction of incidence due to the spin texture of the surface states [Fig. 4(d)]. Subsequently, the asymmetry distribution of spin would result in a photocurrent that is perpendicular to the direction of the spin because of the spin-momentum locking.²⁶ As long as a phase difference between CPGE- and LPGE-induced photocurrents exists, which has already been assured by the above two different physical processes, spin-polarized terahertz radiation is guaranteed. Regarding the amplitude, randomly choosing incident angle $\theta$ cannot warrant indentical amplitude along the $x$ axis and $yz$ plane. This explains why we cannot achieve optimal ellipticity when employing circularly polarized pulses. Therefore, to optimize the ellipticity, we can increase the incident angle and look forward to achieving higher ellipticity in a wider spectrum.

In short, we systematically analyzed the features of $L_1$, $L_2$, and $D$ via the symmetry on the surface of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ under a phenomenological PGE framework. We realized that the invariant $L_2$, $D$ components, and polarity-controllable $C$ component were all prerequisites for the spin-polarized terahertz emission. Furthermore, this framework can summarize most features of extracted components except for $D_x$ and gives hints for achieving optimal spin-polarized terahertz emission, which owns significant guidance.

Based on the above theoretical analysis, we summarize the terahertz emission experimental results in Fig. 5. From these results, we can see that, for a fixed laser incidence angle, linearly polarized pump light can only produce linearly polarized terahertz waves [Figs. 2 and 5(c)], circularly polarized light can produce chiral terahertz waves, and its chirality is consistent with that of the pump laser [Figs. 5(a) and 5(b)]. To make the terahertz generation and manipulation more advanced, we can successfully realize various complex terahertz wave polarization shaping in topological insulators.

Fig. 5

Arbitrary manipulation of various terahertz polarization states. Radiated terahertz chirality was consistent with that of the pump laser chirality. (a) LCP pump laser pulses can produce left-handed elliptically polarized terahertz waves and (b) right-handed elliptically polarized pump light can generate right-handed elliptically polarized terahertz beams. (c) Linearly polarized terahertz waves can be generated in ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ pumped by linearly polarized pump laser beams.

4.

Conclusion

We systematically studied terahertz emission from topological insulator ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ nanofilms driven by femtosecond laser oscillator pulses. Through experimentally investigating the sample thickness, azimuthal angle, and pump laser polarization-dependent terahertz radiation properties, we clarified that PGE played a predominant radiation mechanism in this light–matter ultrafast interaction process and produced efficient terahertz waves. Borrowing the spin-momentum–locked state-induced helicity-dependent spin-polarized current generation and combing it with the helicity-independent photocurrent, we not only realized circularly polarized terahertz beam generation but also demonstrated arbitrary manipulation of their polarization shaping in topological insulators via simultaneously adjusting the pump laser polarization states and sample azimuthal angles. Our method may have the feasibility to be extended to a variety of topological insulator materials and other related Dirac quantum materials. The topological insulator nanofilms can be grown with high quality and large size possible for high-field terahertz sources at transmission emission geometry, which may also provide very promising applications in fundamental nonlinear terahertz investigations and other real applications such as terahertz circular dichroism spectroscopy, polarization-based imaging, and terahertz secure communication.

5.

Appendix: Methods