1. INTRODUCTION

The frequency of terahertz (THz) waves spans two orders of magnitude, ranging from 0.1 to 10 THz, which has now been effectively supported by various techniques, such as the widely applied THz time-domain spectroscopy (TDS) systems [1,2]. Manipulating polarization in such a wide bandwidth is challenging but highly in demand, particularly for half-wave and quarter-wave conversions. For example, circularly polarized waves improve robustness against reflection loss for the next-generation wireless communications and sensing [3,4]. Further differentiating the left- and right-handedness enables the application of circular dichroism spectroscopy of chiral phonons in amino acids [5], helix structures in peptides [6], molecular enantiomers [7], and magneto-optical effects [8,9]. Half-wave conversion provides large-angle rotation, which is beneficial in investigating long-range biomolecular vibrations [10,11], ellipsometry, and cross-polarization imaging [12–14].

Existing technologies still fall short of the requirement for efficient and broadband polarization manipulation. The key challenge arises from the mesoscale wavelength of THz waves. The required long interaction distance limits the tunability and bandwidth due to the low efficiency, and large dispersion and absorption. A typical example is a liquid-crystal (LC) phase shifter. The LC thickness needs to be hundreds of times larger than that of optical devices in order to produce sufficient phase difference by the birefringence, severely limiting their tunability and transparency [15,16]. An artificial birefringent interface can be made extremely thin, but its bandwidth is relatively narrow and challenging to adjust [17,18]. Localized resonant metamaterials strongly confine the field and provide a high degree of freedom on the structural designs [19–22], yet they are naturally frequency-selective.

Fig. 1. Operation principle of the proposed PCMT device. (a) Structure and polarization modulation principle of the PCMT device. The composition of the liquid–crystal (LC) phase shifter is shown in the dashed gray box. (b) Phase difference between p- and s-reflections (?ps) caused by the mirror–TIR structure as a function of prism–mirror distance ? at 1, 2, and 3 THz, respectively. (c) In-plane birefringence Δ? of the LC as a function of applied voltage ?. (d) ?ps by the mirror–TIR structure, LC phase shifter, and the combined PCMT device at four combinations of ? and Δ?. Arrows and circles indicate the approximated polarization states by the combined PCMT device in 1.5–3.5, assuming a 45° linearly polarized incidence.

Some strategies have been proposed to extend the bandwidth. Tuning Fabry–Perot oscillations to create a constructively interfered region is an efficient solution pioneered by Grady et al. [23], followed by a couple of different structures [24–27]. This technique is basically only applicable for linear rotation, typically half-wave conversion, due to the ignorance of the phase. Phase compensation is another approach to cancel out dispersion, such as by tailoring the phase of two structures in the non-resonant region [28,29] or by superimposing two opposite phase slopes [30]. Nevertheless, the bandpass nature makes these improvements difficult to exceed a 1 THz bandwidth. Stacking multiple birefringent crystals, an idea originated by Destriau and Prouteau in 1949 [31], was realized in the THz band for quarter-wave conversion by Masson and Gallot using six quartz plates [32]. The inconvenience is that independent thickness and orientation are needed for each plate. Direct field shaping from the source may cover the entire bandwidth but cannot be integrated into other systems [33,34]. Total internal reflection (TIR) can also confine the field at the interface, thus reducing the interaction length. It has been utilized in devices in combination with anisotropic gratings [35,36] Brewster-critical modulation [37], wideband phase modulation [38], and dielectric-metallic phase jump [39]. However, active THz electro-optical materials, such as ion-gel gated graphene [39] and vanadium dioxide [36], are either bandwidth-limited due to the dispersion and absorption or slow in response.

Inspired by the mesoscale characteristic of the TIR evanescent wave, micro-mechanical control offers a unique approach for efficiently manipulating the THz confined field, free from material dispersion and absorption. This concept can be achieved by finely tuning the mirror position on a micrometer scale to couple with the evanescent wave, and it has demonstrated its great phase-modulation potential in the millimeter-wave region [40]. In this work, we show that this scheme provides a large phase modulation range up to 289°, and its phase frequency dependence can be perfectly canceled out by a thin layer of LC. The integrated device, referred to as phase-compensated mirror-TIR (PCMT) device, supports the urgently required functions such as broadband half-wave and quarter-wave conversions, including left- and right-circular polarization switching. These functions achieve excellent average degrees of linear or circular polarization over 0.996 in 1.6–3.4 THz. Arbitrary polarization can be further realized by enabling the rotation of the incident polarization, with fractional bandwidths exceeding 90% for all cases. More importantly, the center frequency of the wide band can be freely tuned to adapt to the used equipment or experimental requirements. The exceptional performance and customizable bandwidth provide a universal solution for THz ultra-wideband polarization control, which can significantly advance the development of THz polarization-sensitive applications.

2. RESULTS

A. Principle

Figure 1(a) illustrates the composition and operational principle of the proposed PCMT device. It comprises a 120° isosceles triangular prism made of high-resistivity silicon (Si), a silver mirror, and LC phase shifter. The mirror is controlled by a motorized mechanical stage such that the prism–mirror distance ? can be varied. The schematic illustration within the dashed box shows the structure of the LC phase shifter in detail, comprising a LC layer sandwiched by two high-resistivity Si wafers with sulfonic azo dye (SD1) alignment layers. The LC phase shifter is physically insulated from the prism by an air gap. The polarization of the incident THz beam is linearly polarized at 45° relative to the plane of incidence. The incoming THz beam enters the Si prism at normal incidence and forms an incident angle of 30° at the prism–air–mirror interface, which leads to TIR when the prism–mirror distance ? is sufficiently large (critical angle of Si-air is ??=17°). When ? is smaller than the penetration depth, the mirror interacts with the evanescent wave, resulting in a mirror–TIR coupled reflection. In this configuration, the amplitudes of the p- and s-reflection coefficients are expected to be |??|=|??|=1 regardless of ? and frequency since both TIR and mirror reflection are zero-loss in theory. In contrast, the phase is not constant because the mirror–TIR coupling is dependent on both the polarization and the wavelength. Therefore, the phase difference between the p- and s-reflections (?ps=arg(??/??)) is a function of ? and frequency, which can be calculated by a tri-layer optical model. Details about the optical modeling can be found in Supplement 1. Figure 1(b) calculates ?ps as a function of ? at 1, 2, and 3 THz, respectively. A huge phase change over 280° can be achieved for all the three frequencies with a prism–mirror distance variation of less than 40 µm. This is because the evanescent wave confines the field on the order of ?/10, which is about a few tens of micrometers. This mesoscale distance enables a precise and efficient modulation of ? to vary the coupling between the TIR and the mirror reflection. ?ps approaches −180° at small ?, corresponding to pure mirror reflection (?=0), and it moves towards 109° at large ?, corresponding to pure TIR reflection (?=∞).

The coupled reflection further passes through the LC phase shifter. The LC layer has a thickness of µ?=210µm, and the LC molecules are initialized to the p-polarization direction by the SD1 alignment layers. Bias voltage ? applied on the electrodes will be homogeneously loaded onto the LC due to the orders-higher resistivity of the LC compared to that of the Si wafers, which tends to rotate the LC molecules towards the wavevector direction. Therefore, the in-plane birefringence Δ? between the p- and s-polarizations are maximum at zero bias and minimum at saturated bias. The in-plane birefringence Δ? varies with bias voltage ?, as illustrated in Fig. 1(c), which is expected to display an exponential-like behavior after the threshold voltage. Assuming that Δ? is frequency independent, ?ps produced by the LC can be expressed as ?ps=−?Δ??/?, which is negatively proportional to the frequency, and its slope can be adjusted by ?.

The phase difference ?ps generated by the mirror–TIR structure is positively related to the frequency [Fig. 1(b)]. It can be reasonably expected that the combination with the LC phase shifter reduces the frequency dependence. Figure 1(d) show the ?ps by the mirror–TIR structure, LC phase shifter, and combined PCMT device at ?=1.7, 4.6, 12.3, and 25 µm, and Δ?=0.15, 0.15, 0.12, and 0.02, respectively. All mirror–TIR curves are positively frequency-dependent, while all LC curves are negatively proportional to the frequency. The four combinations of ? and Δ? are selected so that the negative slopes of the LC curves are about the additive inverses of the positive slopes of the mirror–TIR curves, resulting in combined ?ps around −180°, −90°, 0°, and 90° over a broad band (1.5–3.5 THz), respectively, as shown by the solid red curves. In other word, the LC phase shifter functions as an active phase compensator to adaptively eliminate the dispersion produced by the mirror–TIR structure, resulting in a nearly constant phase. As for the amplitude, we assume that the p- and s- transmission difference through the LC is ignorable with negligible frequency dependence. As a result, when the input beam is linearly polarized at 45° to the plane of incidence (LP45°), the above settings correspond to the four output polarization states shown in Fig. 1(d): linear polarization rotated by 90° (LP−45°), right-handed circular polarization (RHCP), unchanged polarization (LP45°), and left-handed circular polarization (LHCP), respectively, as indicated in Fig. 1(d). These examples demonstrate a novel polarization modulation mechanism by actively tuning the phase compensation between the mirror–TIR and the LC phase retardance, providing multiple polarization states in a broadband manner by simply varying ? and Δ?.

B. Mirror–TIR Modulation

The mirror–TIR structure and the LC phase shifter work individually in the proposed device. We first experimentally validated the phase control by the mirror–TIR structure (measurement details see Supplement 1). Figure 2(a) shows the measured ?ps (open circles) at different ? values, where the arrow indicates the sequence of increasing ? in 1.4–17.4 µm. The theoretical predictions, calculated at ? values that give the best fit to the experimental data, are shown by the solid curves and found to be highly coincident with the measured results. Positive frequency-dependence and large phase variation range are observed, agreeing well with the model. Figure 2(b) shows the amplitude ratios between ?? and ??. The ratio is neither dependent on ? nor frequency, as expected from the theory. All values closely approach unity, represented by the dashed gray line. The amplitude and phase together validate the good match between the experimental results and the theoretical model, showing a large dynamic range on the output phase. Figure 2(c) further shows the time-domain waveforms of the p- and s-electric fields, sharing the same color scheme as Fig. 2(a). ?? and ?? both display a nonlinear change, reflected by the deformed pulse shape. They also exhibit opposite time-shifting trends. These features well explain the origin of the frequency-dependent ?ps and the large variation range. The distance controlling accuracy was evaluated by comparing the set ? and the best fit from the model. Figure 2(d) shows the high degree agreement between them, with most measurements having difference less than 0.1 µm. Very small and large ? values have larger errors, which could be induced by the potential solid contact with the prism and the out-of-focus effect, respectively. Nevertheless, the observed accuracy is sufficient for a robust mechanical phase control by the mirror–TIR structure.

Fig. 2. Phase control by the mirror–TIR component. (a) Phase difference (?ps) and (b) amplitude ratio (|??/??|) between p- and s-reflections at 11 prism–mirror distance ?. Circles are the experimental results. Solid curves in (a) are the model fits and dashed gray line in (b) gives the theoretical unity ratio. (c) Evolution of the time-domain waveforms of ?? and ?? with increasing ? (offset for clarity). The same color scheme applies to (a–c), indicated by the arrows in (a) and (c). (d) Comparison of the set ? and the best fit for the 11 measurements.

Fig. 3. Characterization and active control of the liquid-crystal (LC) phase shifter. (a) Refractive indices ?, birefringence Δ?, and (b) absorption coefficients ? of the used LC NJU-LDn-4. (c) Time response of Δ? to the ON and OFF bias switch. The inset zooms in the rapid drop of Δ? after bias ON. (d) Hysteresis response of Δ? to bias voltage modulated by square waves with different duty cycles (?). Forward and backward correspond to increasing and decreasing ?, respectively. The inset shows the full 0–100% response.

C. LC Phase Compensation

The role of the LC phase shifter is to provide the required phase compensation. The maximum phase delay and its tunability should be evaluated. Dielectric characterization of the LC was first conducted without a bias (see Supplement 1). We used NJU-LDn-4 LC in our device, which works well at ambient temperature with a clearing point (Tc) of 157 °C and a melting point (Tm) below 0 °C [41]. The in-plane birefringent refractive indices ? and absorption coefficients ? are shown in Figs. 3(a) and 3(b), respectively. A large birefringence of Δ?≈0.3 are observed in 1–3 THz, which slightly decreases at lower frequencies. The achromatic Δ? assumed in the theoretical model matches well with the observation here. The large birefringence enables a small thickness of LC (210 µm) to provide sufficient phase compensation while maintaining a relatively fast switching speed. A maximum time delay of 0.21 ps can be achieved, which is sufficient to compensate the mirror–TIR phase dispersion. The small thickness also reduces the absorption. The electric-field attenuation is less than 20% by the LC across the entire bandwidth according to the measured ?? and ??.

LC molecules are susceptible to capacitor effect under long-term direct current voltage due to the charge accumulation, leading to hysteresis and reduced response speed. Alternating current voltage mitigates this issue, extending the lifespan of the LC molecules. We employed a 1 kHz square-wave signal to modulate the LC molecules. The threshold voltage is found to be ±5V, after which the birefringence Δ? decreases exponentially with the bias voltage. The LC response to the ±30V bias is shown in Fig. 3(c). The bias voltage aligns the LC molecules towards the out-of-plane direction and reduces Δ? to 0.015 in 5 s, as magnified in the inset of Fig. 3(c). When the bias was switched OFF, Δ? gradually increases, taking about 2 min to recover to over 90% of the maximum. Binary ON and OFF states cannot provide the required adaptive phase compensation. Fine-tuning the birefringence can be achieved by applying a smaller voltage, as illustrated in Fig. 1(c). However, this requires voltage-controlling precision on the order of 0.01 V. We adopted a different but equivalent scheme by varying the duty cycle (?) of an external modulating signal applied to the bias to enable a finer modulating step. In this scheme, the original 1kHz±30V bias was further modulated by an external 10 Hz square-wave signal with varying ? (at a step of 0.1%). Details can be found in Supplement 1. Δ? was characterized in a 0%–100% loop of increasing and decreasing ?, and the results are shown in Fig. 3(d) and its inset. Hysteresis effects are observed in the loop, which is a common behavior of LC due to the existence of the threshold voltage in the forward sweep (corresponding to ?=3%) [42]. The rapidly decreasing Δ? after the threshold is not ideal for a precise phase control. In contrast, the backward sweep allows a finer tuning of Δ?, and hence it was adopted in the following experiments. The comprehensive phase and amplitude response to ? as a function of frequency can be found in Supplement 1.

D. Achromatic Multifunctional Polarization Control

The mirror–TIR component and the LC phase shifter were integrated to control the polarization by tuning their phase compensation. We verified the conversions of the four polarization states predicted in Fig. 1(d). According to the prediction, ? was set at 1.7, 4.6, 12.3, and 25 µm, respectively. Duty cycle of the bias was adjusted to minimize the phase dispersion in real time, which was found to be ?=3.1%, 3.1%, 5%, and 80%, respectively. The corresponding Δ? determined from the measurements is 0.16, 0.16, 0.13, and 0.02 (See Supplement 1), respectively, highly approximating the theoretical values. The measured phase differences and amplitude ratios between the p- and s-reflections of the four settings are shown in Figs. 4(a) and 4(b), labeled as Pol. 1–4, respectively. ?ps of the four curves are essentially achromatic over the 1.6–3.4 THz band, highlighted by the white background. The values closely approximate −180°, −90°, 0°, and 90°, respectively. Meanwhile, the amplitude ratios are all close to unity, demonstrating that the LC device introduces a negligible birefringent transmission and amplitude dispersion.

Fig. 4. Multifunctional polarization control of the integrated device. (a) Phase differences (?ps) and (b) amplitude ratios (|??/??|) between p- and s-reflections at the optimized settings of the four polarization states. (c) Time evolution of the electric field corresponding to the four polarization states in 1.6–3.4 THz, stepped by 0.2 THz and represented by different colors indicated in the color bar. The arrows point to the rotational directions. DoLP and DoCP refer to the degree of linear/circular polarization, respectively.

By combining the phase and amplitude, we plot the time evolution of the electric field to intuitively display the polarization. The results in 1.6–3.4 THz are shown as different colors in Fig. 4(c) (at a step of 0.2 THz). Note that the light intensity (i.e., S0 of Stokes parameters) has been normalized to 1. The high degree overlap among all colors provides a straightforward proof of the achromatic performance. More importantly, the polarization states closely approximate the target output of LP−45°, RHCP, LP45°, and LHCP, respectively. This outcome is only possible when both the amplitude and phase have been precisely modulated to the target values. The averaged degrees of linear/circular polarization (DoLP/DoCP) were calculated and labeled in the figure. The absolute values ranging from 0.996 to 0.999 demonstrate the outstanding polarization accuracy. Note that the 1.6–3.4 THz bandwidth is selected as a common bandwidth for all the four states; individually each state has a broader range. The fractional bandwidth, calculated by dividing the absolute bandwidth (defined as ±10° phase error) by its center frequency, is 189%, 93%, 107%, and 94.8% for the four states, respectively. Finally, we highlight that Pol. 1 and Pol. 2 were achieved at the same ?, meaning that the active switching between the broadband half-wave and quarter-wave conversions can be realized by simply moving the mirror by 2.9 µm, taking only about 100 ms. These two important conversion functions over a wide bandwidth are realized in one device with a switching time less than a second.

E. Arbitrary Polarization at Customizable Center Frequency

The above examples demonstrate the active switching among four specific polarization states within a specific bandwidth. In fact, arbitrary and achromatic phase difference between −180° and 109° can be achieved at a customizable center frequency by specific combinations of ? and ?, equivalent to varying Stokes parameters S2 and S3. Under the setting of 45° linearly polarized input, the output p- and s-amplitudes are identical due to the unity reflectivity. This means Stokes parameter S1 is fixed at 0. By varying the linear polarization direction ?incid of the incidence (defined as the relative angle to p-polarization), we add one more degree of freedom to S1, and hence any polarization state on the Poincaré sphere can be realized by the proposed device (see Supplement 1). To show this, we randomly set three target polarization states with different center frequencies (?cent), as listed in Table 1. The polarization state is defined by the geometrical parameters of the ellipse, that is, the (?,?) coordinates, where ? represents the orientation angle and ? is the ellipticity angle, as illustrated in Fig. 5(b). We designed an algorithm to automatically convert (?,?) to the required ?ps and ?incid (see Supplement 1). The algorithm finds the optimized combination of ? and Δ? by maximizing the bandwidth around the target center frequency ?cent, where the bandwidth is defined as the range having phase error Δ? to the target phase smaller than the tolerance, defined as ±8° in the theoretical calculation to allow a small degree of experimental error (±10° considered as the practical bandwidth threshold). The optimized settings, together with the predicted bandwidth, are listed in Table 1. All the three target polarizations can be realized by two alternative settings of which ?ps differed by 180°, corresponding to positive and negative ?incid. Two settings are available when the two ?ps values are both within [−180°,109°]; otherwise, at least one solution will satisfy the requirement. However, the output bandwidth can differ significantly for the two settings, as can be seen from the predicted solid curves in Fig. 5(a). The difference comes from the different phase dispersion behavior at different ? values, which is obvious for polarizations 2 and 3.

Table 1. Randomly Assigned Target Polarization States and the Corresponding Optimized Settings and Performance Predicted by the Algorithm

Fig. 5. Conversions of arbitrary polarization states centered at customizable frequencies. (a) Phase differences (?ps) between p- and s-reflections for the three targeted polarization states, including six alternative settings. Symbols are the experimental results and solid curves are the theoretical predictions. Gray areas represent the range with ±10° to the target phase. (b–g) Time-evolution of the electric field for the six groups of settings. Colors represent different frequencies in units of THz. Dotted black curves indicate the targeted output. Arrows point to the rotational directions. The rectangle in (b) illustrates the definition of the (?,?) coordinates.

Experimental verification was conducted by setting the device according to suggested optimized parameters. The measured ?ps are shown as symbols in Fig. 5(a). All the six groups coincide well with the theoretical predictions. A small degree of discrepancy is reasonable considering the Δ? dispersion and the experimental errors. Most values are found within ±10° error relative to the target phase (i.e., within the gray areas), hence the predicted bandwidths are mostly satisfied. The actual polarization state should further consider the amplitude ratios (see the Supplement 1). We combined the ratio and the phase to plot the time-evolution of the electric fields in Figs. 5(b)–5(g). Again, the high degree of overlapping of the curves in different colors demonstrates the achromatic performance. Furthermore, they all coincide well with the target polarization represented by the dotted black curves, indicating that both the amplitude and phase have been accurately modulated. It should be noted that apart from group 2-2, all the other groups are precisely centered at the target ?cent. Group 2-2 is an exception because the algorithm finds an extremely large bandwidth of 0.1–6.3 THz. In the measurement, this is limited by the system upper bandwidth at around 3.5 THz. Note that because ?ps is −180° in this setting, arbitrary linear polarization oriented at any direction can be achieved in such a wide bandwidth by varying ?incid. Therefore, implementing the proposed device has an ignorable influence on the original system bandwidth and polarization. These examples demonstrate the high degree of accuracy of the model prediction and the impressive ability of arbitrary polarization control using a single device. In Supplement 1, we provide more examples to show the excellent scalability for center frequencies from 0.6–10 THz, covering the entire THz bandwidth.

3. DISCUSSION

Modulation speed and insertion loss are two important evaluation parameters for a functional device. The switching time between states mainly depends on the LC, specifically the variation range and direction of Δ?. The mechanical movement can be done within 1s, and hence it is ignorable. According to Fig. 3(c), the maximum time cost by the LC is about 2 min, corresponding to increasing Δ? from the minimum to the maximum. Because most polarization states work with a small Δ? at which region has a relatively high variation speed according to Fig. 3(c), most modulation can be done in a few tens of seconds. The device insertion loss mainly comes from the reflection loss at the interfaces between air, Si, and LC, as well as the propagation loss within the Si and the LC (major). Considering the largest LC index mismatch (??=1.5) and absorption (??), the maximum reflection loss and absorption loss are 7.6 and 2.4 dB, respectively, according to Fresnel’s reflection formulas and Beer–Lambert’s Law. Note that the reflection from the Si–air–mirror structure causes a negligible loss of 2% even considering the limited conductivity of metal (∼4×107S/m). Therefore, the maximum loss of the entire device is about 10 dB. This loss can be reduced to 6.9 dB by fabricating the LC shifter onto the prism exit surface, which avoids the reflection loss at the Si–air–Si interfaces.

The proposed device still has much untapped potential. One particularly meaningful direction is to integrate it with THz emitters to develop compact and multi-polarization sources, thanks to its achromatic and customizable bandwidth features. It is especially efficient for multi-contact photoconductive antennas, which can emit quasi-linear THz waves along different directions by the orthogonal units [43]. The linear output can be switched into handedness-selective circular or other polarizations by the PCMT device, and the original imperfect linearity caused by the cross talk [44] can be adaptively optimized by finely tuning the phase difference. Such an integration also prevents the reflection loss by providing a matching refractive index to the Si prism. This design can also be implemented with spintronic emitters of which polarization can be simply rotated by the magnetic field [45]. The exceptional bandwidth tunability can efficiently support the ultra-broadband feature of spintronic sources. In addition, we can further enhance the compactness by integrating LC phase shifter with the Si prism as mentioned above. The mirror control can be accomplished by a piezo stage to provide a more compact, precise, and faster modulation.

4. CONCLUSION

We have comprehensively investigated the proposed PCMT device, demonstrating its remarkable polarization control ability. The low interaction efficiency issue in conventional THz devices is overcome by utilizing the mesoscale characteristic of the THz–TIR evanescent field. Specially, this is achieved by mechanically modulating its coupling to the zero-loss and achromatic mirror reflection. Phase compensation provided by the LC adaptively eliminates the frequency dependence while maintaining a wide phase modulation range. The integrated device can be actively switched between some of the urgently required functions, including the half-wave conversion and chirality-dependent quarter-wave conversion. All these functions are realized in the overlapping broad bandwidth of 1.6–3.4 THz with an excellent degree of accuracy. By enabling the selection of the incident polarization orientation, an arbitrary polarization state at a customizable center frequency can be realized, with optimized parameters and expected performance accurately suggested by the developed algorithm. Therefore, the device possesses the capability to be widely adapted to various THz systems due to its broadband tunability, multifunctional regulation, and high accuracy, opening the door for a wide range of THz applications that require broadband polarization control.