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Abstract
Controlling the polarization state of an optical pulse within a short gating time facilitates ultrafast all-optical data processing and recording. Using the innovative all-optical modulation method such as the transient terahertz Kerr effect (TKE), the polarization state of the optical pulse can be switched within the gating time on the sub-picosecond scale. In this work, we use high-frequency single-cycle terahertz (THz) pulses to excite the Kerr effects of materials and explore the potential to shorten the gating time of the polarization modulator. A low-density polyethylene (LDPE) material with good Kerr-related properties is proposed to improve the performance of the TKE-based modulator and the obtained ultrafast gating time (FWHM) can reach 86 fs. Experimental evidence for the thickness dependence of the Kerr response demonstrates that the errors caused by optical transmission factors in the LDPE medium can be ignored, and thus the ultrafast gating modulation is mainly limited by the duration of probe pulse. Compared with common TKE-based materials, we believe that the low-cost LDPE is a good candidate to achieve high-power TKE-based ultrafast pulse switching.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The development of miniaturized ultrafast optical components is the core of the next-generation signal processing and communication technologies [1]. A key concept is the ultrafast control of the polarization states of optical pulses, which has been widely studied in the fields of optics, chemistry and biology [1–4]. The electronic modulators are based on the electro-optical Pockels effect, which causes a strong polarization rotation of optical pulse during the gate-switching process [5]. In general, the conventional devices are driven by high-voltage (KV/cm) electric gating pulse at GHz frequencies, which enables the gating time only in the nanosecond scale. In addition, the ultrafast laser polarization modulators can also be driven by an optical electric field. Traditional ultrafast laser pulses, such as the 800 nm pulses generated by the Ti: sapphire laser system, have been used to drive Kerr-based polarization rotation [6]. However, this type of near-infrared (NIR) laser has a large photon energy, and the polarization rotation often requires high-intensity laser driving, which makes it difficult to accurately control the gated waveform. Some materials with large Kerr coefficients (such as liquid CS2) [7] can reduce the requirement of high laser intensity. However, they are limited by the slow recovery time on the order of picoseconds, the toxicity and the complexity of liquid itself.
In recent years, researchers have found that terahertz (THz) electric field can be selected as the driving source in optical-controlled modulation [8,9]. Compared with the NIR pulse excitation, THz photon energies are only with several meV, which do not induce single or multi-photon absorption in the materials. The semiconductors with relatively small band gap, such as ZnTe, GaP, etc., are most common modulation materials that relies on the THz electric field-dependent Pockels effect [10]. Nonetheless, these materials have significant tail oscillations in their response signal. Moreover, intense THz excitation can cause extra significant nonlinear effects such as spectral distortion and absorption, thus it cannot obtain a high extinction ratio. Another method to achieve electro-optical modulation is based on THz induced nonlinear Kerr effect that is ubiquitous in all materials. Many insulators are good Kerr materials with large band gap and ignorable dispersion. However, strong polarization modulation based on terahertz Kerr effect (TKE) is rarely reported. This is because electro-optical modulation that relies on the Kerr effect are generally weak and achieving TKE-based polarization control usually requires an intense THz electric field. Until recently, Shalaby et al. found that diamond can be used as the modulation material to achieve ultrafast switching of optical pulses within ∼125 fs gating time (FWHM) under the intense single-cycle THz electric field excitation, and the temporal characteristic of Kerr response is completely controlled by the squared curve of the THz electric field strength [8]. This study leaves the possibility to further improve the performance of the TKE-based modulator. In addition, the application of ultrafast signal processing requires versatile nonlinear components. It is of great significance to develop and quantify different Kerr materials. Particularly, the low-density polyethylene (LDPE) is a good candidate for TKE-based polarization modulation, which has the advantages of large band gap, negligible dispersion, and high THz transmittance [11–13]. Meanwhile, the low-cost and mature manufacturing technique of LDPE makes it have promising application prospect.
In this letter, an intense high-frequency single-cycle THz pump pulse (center frequency of 3.9 THz, bandwidth of 1-10 THz, and maximum THz electric field strength of 17.8 MV/cm) is used to excite the LDPE film to explore the potential to shorten the gating time of TKE-based modulator. LDPE can achieve an ultrafast gating time of 86 fs (FWHM) under high-frequency THz pulse excitation, which is faster than that of diamond under the same conditions. The optical properties of LDPE as modulation material under different driving frequencies and sample thicknesses were systematically investigated. The results demonstrate that LDPE can be adopted as an excellent modulator for THz-induced ultrafast polarization modulation compared to other common THz window materials.
2. Experimental results and theoretical analysis
The experimental setup is shown in Fig. 1(a). An organic 4-N, N-dimethylamino-4’-N’-methyl-stilbazoliumtosylate (DAST) crystal (Swiss Terahertz LLC) is excited by femtosecond laser pulses (0.4 mJ per pulse, repetition rate of 1 KHz, center wavelength of 1550 nm, pulse width of 50 fs) generated by an optical parametric amplifier (Light Conversion Topas OPA, Spectra Physics). To reach the diffraction limited focusing (using RIGI microbolometer camera, 17 µm pitch, Swiss Terahertz LLC) and allow for high field, we used the THz bullet lambda cubic wave front correction scheme [14]. The generated THz pump pulses are reflected by the off-axis parabolic mirrors and focused onto the sample surface. A set of low-pass filters (LPFs, QMC Instruments Ltd) with cut-off frequencies of 18 THz is used to filter out residual NIR and the THz energy is controlled by two THz polarizers (Tydex LLC). The vertically polarized THz pulse and 45° polarized 800 nm pulse are transmitted collinearly through the sample to induce electro-optical modulation. We perform two experimental protocols. In the case (I) (as shown in Fig. 1(a)), balanced differential photodiodes are used with a quarter waveplate and a Wollaston prism to detect the transient birefringence signal caused by the THz electric field. The time trajectory is recorded by scanning the delay between the pump and probe beams. Regarding the acquisition of the THz electric field waveform, we use electro-optical sampling with 100 µm GaP. Because the intense THz pulse saturates the GaP response, we use the THz Kerr signal of polycrystalline diamond to calibrate the THz electric field strength [11,15,16]. For an ultrabroadband THz pulse, it is additionally distorted by frequency-dependent phase matching, reflection, dispersive propagation, and absorption in the electro-optic detection crystal. Therefore, we use the full complex response function of GaP detector to reconstruct all the spectra presented in this work [17–21], and the obtained data are shown in Fig. 1(b) and Fig. 1(c). As a result, we obtain an intense (with peak electric field E=17.8 MV/cm) and ultrabroadband (over the range of 1-10 THz with a center frequency of 3.9 THz) THz pulse.
Fig. 1. (a) Diagram of the experimental system (LPF: low pass filter; TP: THz polarizer, L: lens, PM: parabolic mirror, P: polarizer, D: photodiode, WP: quarter waveplate, WS: Wollaston prism). About the sample: GaP is used in panel (I) to track the THz electric field waveform, LDPE and diamond are used in panel (II) to track the THz-induced Kerr effect. (b) Temporal profile and (c) the corresponding spectrum of the generated THz wave from DAST crystal.
In the case (II) (as shown in Fig. 1(a)), we detect polarization rotation by placing a polarizer behind the sample. The polarizer is set to block NIR pulses without the presence of THz radiation. When the sample is excited by the THz electric field, the induced polarization rotation will turn on the pulse switch, and the transmitted NIR pulse is detected by the photodiode. Here, LDPE and diamond are used as pulse switch materials to explore their Kerr modulation performances under case (II) configuration. The resulting polarization modulation based on the phase shift $\Delta \varphi (t)$ between parallel and perpendicular to the THz polarization direction is detected through the sample thickness L along the propagation direction [22,23], which can be expressed as:
Here, we apply an intense high-frequency THz electric field (center frequency of 3.9 THz, bandwidth of 1-10 THz, maximum THz electric field strength of 17.8 MV/cm) to excite the electro-optical polarization modulation of LDPE film manufactured by the tape casting technique. This technique can provide LDPE films with the thickness ranging from 5-1000 µm, along with good uniformity and high light transmittance. In this work, the LDPE film used as the Kerr-based modulator has a diameter of 10 mm and a thickness of 300 µm, and shows isotropic characteristics without THz pulse excitation. Figure 2(a) shows the measured phase shift caused by the third-order nonlinear Kerr effect in LDPE with intense THz pump pulse excitation. The gating time can reach 86 fs (FWHM), indicating that LDPE can perform transient polarization rotation when used as a THz-induced Kerr-gated modulator. Figure 2(b) demonstrates the temporal characteristics of the phase shift in LDPE film excited by different THz electric field strengths and the inset shows the phase shift dependence on the THz electric field strength. The normalized temporal characteristics of Kerr response under different pumping THz electric fields are almost identical, which indicates that the artifact caused by high-field excitation can be ignored. We record the maximum values of Kerr responses under different THz electric fields and find the response scaling with the square of the THz electric field strength, indicating that the Kerr effect dominates during this process (as shown in the inset of Fig. 2(b)). For the 300 µm thick LDPE, a phase shift close to ∼150 mrad can be achieved under the THz electric field excitation with strength of ∼17.8 MV/cm. According to Malus law, a phase shift of ∼2.5 rad is required to achieve 90% extinction ratio in practical applications. Therefore, the realization of a high extinction ratio requires a thicker sample or a stronger THz wave excitation. Moreover, the Kerr response of LDPE does not instantaneously track the squared curve of the THz electric field strength. Compared to the squared curve of THz electric field strength, the gating time of LDPE is slightly broadened. This phenomenon is different from the study of Sajadi et al., in which the low-frequency THz pulses with ∼1 THz center frequency were used to excite some common THz window materials (diamond, LDPE, etc.) and the obtained Kerr-based temporal signal instantaneously follows the THz intensity [11].
Fig. 2. (a) Kerr response (red) of LDPE film excited by high-frequency THz pulse with 3.9 THz center frequency. The ultrafast gating time is 86 fs (FWHM). For comparison, the squared curve of the THz electric field strength measured by case (I) configuration is also shown (dashed line). (b) Kerr responses of LDPE excited by different THz electric field strengths, and the inset shows the Kerr response dependence of LDPE on THz electric field strength.
To further investigate the pumping frequency effect, we add a low-pass filter (LPF) of 3 THz cut-off frequency to limit the frequency component of THz electric field and the peak strength of the THz electric field decreases to ∼4.7 MV/cm. The inset of Fig. 3 shows the corresponding THz frequency-domain spectrum with the center frequency of 2.7 THz. In this condition, the Kerr response exhibits an expected slower gating time of ∼552 fs (FWHM) owing to the few-cycle low-frequency THz pulse excitation, and the measured temporal characteristics is well consistent with the THz intensity (∼E2(t)) curve instantaneously. This experimental result demonstrates that the polarization modulation of LDPE can be precisely controlled by the square of the low-frequency THz electric field.
Fig. 3. Kerr response (red) of LDPE film excited by low-frequency THz pulse with 2.7 THz center frequency. For comparison, the squared curve of the THz electric field strength is also shown (dashed blue line). Here, we consider the three peaks structure and draw an envelope to describe the gating time (dashed black line). The inset shows the corresponding frequency-domain spectrum of the pumping THz electric field.
In the study of intense THz pulse-induced Kerr effect in a nonlinear medium, diamond has been used as a good modulation material to achieve ultrafast pulse switching with a gating time at the femtosecond time scale [8]. Here, we measure and compare the Kerr-based modulation performances of LDPE (300 µm thickness) and diamond (300 µm thickness) under the pumping THz pulses with 3.9 THz center frequency. The Kerr responses of these two materials have similar temporal characteristics, as shown in Fig. 4(a). The phase shift of diamond is about 1.18 times to that of LDPE, which is related to the relatively larger Kerr coefficient of diamond [11]. However, compared with the gating time of ∼102 fs (FWHM) in diamond (as shown in Fig. 4(a)), LDPE shows a competitive Kerr response speed with ultrafast gating time of 86 fs (FWHM) in this work. In addition, the corresponding normalized frequency-domain results are shown in Fig. 4(b). Compared with the pumping THz intensity curve, the high frequency components of the TKE responses for LDPE and diamond are suppressed. One reason is the influence of sampling error which is limited by the probe pulse width of 50 fs. In addition, the optical transmission factors cannot be ignored, which are the main reason for the slight discrepancy in frequency responses of diamond and LDPE.
Fig. 4. (a) Time-domain Kerr responses of diamond (blue) and LDPE (red) excited by THz wave under the same conditions. (b) The corresponding normalized frequency-domain results of diamond and LDPE film. The grey dotted line shows the fast Fourier transform (FFT) of the square of the THz electric field.
The optical transmission factors are closely related to the property and thickness of the medium, which are considered as the main influences to Kerr response in most materials. Specifically, the influences of optical transmission factors originate from a variety of optical mechanisms. Firstly, a good velocity matching between the THz pulse and the probe pulse in the medium is the premise of achieving polarization modulation at the sub-picosecond timescale [9,11]. Some common THz window materials, such as sapphire (velocity mismatching factor ${\beta _{A{l_2}{O_3}}} \approx 4.4ps/mm$) [24], silicon nitride (${\beta _{S{i_3}{N_4}}} \approx 2.5ps/mm$), magnesium oxide (${\beta _{MgO}} \approx 4.6ps/mm$) [11,25], etc., cannot satisfy the requirement of velocity matching between THz pulse and near-infrared pulse. As the thickness of the medium increases, the temporal characteristics of the Kerr response in these materials will show obvious delayed response and have a relaxation time of more than ∼1 ps [11]. Secondly, the modulation material needs to have a small dispersion factor in the THz range. Further shortening the gating time of the polarization modulation to the sub-picosecond scale requires a broadband THz electric field, which may cause other influences such as the self-steepness effect. In this condition, the refractive index depending on the frequency and intensity leads to the group velocity reduction of the THz main peak and thus the THz pulse is chirped in the medium. Thirdly, the Gouy phase shift of the THz pulse transmitted in the medium will also slightly distort the shape of the Kerr response.
LDPE has a much smaller velocity mismatching factor and chromatic dispersion factor (for 3.9 THz center frequency, ${\beta _{diamond}} \approx 0.21ps/mm,\textrm{ }$ $dn/d\lambda \approx \textrm{ - }1.54 \times {10^{ - 4}}/\mu m$ in diamond; and ${\beta _{LDPE}} \approx 0.02ps/mm,\textrm{ }$ $dn/d\lambda \approx \textrm{ - }0.2 \times {10^{ - 4}}/\mu m$ in LDPE) [12,26]. In addition, LDPE has a smaller refractive index and absorption coefficient than diamond (for 3.9 THz center frequency,${n_{diamond}} \approx 2.48,\textrm{ }$ ${\alpha _{diamond}} \approx 14.96/cm;\textrm{ }$ ${n_{LDPE}} \approx 1.52,\textrm{ }$ ${\alpha _{LDPE}} \approx 2.9/cm$) [12,26], and thus the effective medium length is smaller. Therefore, LDPE can be selected as an excellent polarization modulation material to achieve TKE-based ultrafast pulse switching.
Furthermore, we measure the modulation performances of LDPE films with different thicknesses under the same THz electric field excitation with 3.9 THz center frequency (as show in Fig. 5). The temporal characteristics remain almost the same when adjusting the thickness of LDPE film, revealing that the distortion caused by the optical transmission factors is negligible. Therefore, the slightly broadened Kerr response of LDPE relative to the squared curve of THz electric field strength is mainly caused by the sampling error. In addition, we theoretically simulate the thickness dependent phase shift in LDPE by considering the absorption coefficient of $a \approx 2.9/cm$ for 3.9 THz center frequency [12], as shown by the yellow line in the inset of Fig. 5. Compared with the linear fitting (red curve in the inset of Fig. 5), the slight reduction of the phase shift in the fitting curve is mainly due to the attenuation of the THz wave energy transmitting through the LDPE material.
Fig. 5. Kerr responses of LDPE films with different thicknesses excited by THz wave under the same conditions, and the inset shows the Kerr response dependence on the thickness of LDPE film.
In addition to the response speed, the switching contrast is also an important factor to evaluate the pulse modulator performance. Compared with absorption-based modulation, polarization modulation has the advantage of higher switching contrast since it is easier to achieve extremely high extinction ratio [27,28]. The currently common THz window materials with a large band gap, such as LDPE (∼8 eV) [29], diamond (∼5.5 eV) [8], silicon nitride (>2 eV) [30], sapphire (∼6.7 eV) [31], etc., will not cause saturation distortion due to single or multi-photon absorption in the materials when driven by an intense THz electric field (∼MV/cm). For sufficiently intense THz pumping electric field, these materials can theoretically achieve up to 90% complete polarization extinction. A recent example is that a diamond with 500 µm thickness can achieve an extinction ratio of 90% when driven by an intense THz electric field with 55 MV/cm strength [8]. In our present work, the 600 µm thick LDPE with 17.8 MV/cm electric field excitation has a phase shift of 286 mrad, as shown in Fig. 5. Based on Malus law, a 90% extinction ratio requires a phase shift of at least ∼2.5 rad. It can be predicted that the 600 µm thick LDPE film, can achieve 90% extinction ratio when driven by the THz electric field strength of ∼52.7 MV/cm. Moreover, the experimental results of LDPE thickness dependence showed the negligible errors caused by optical transmission factors, indicating that it still has the potential to use a longer medium length to reduce the THz electric field strength requirement. However, since thick samples are difficult to fabricate, the alternative solution will be using the multistage modulation scheme where a series of small modulators are utilized. This solution may imply some losses due to the reflections, but such losses are not significant because of the low refractive index of LDPE. Therefore, we believe that the low-cost LDPE can be a good candidate for the new generation polarization modulator.
3. Conclusion
In conclusion, we investigate the ultrafast electro-optical polarization modulation driven by high-frequency THz pulse based on LDPE material. LDPE has the advantages of large band gap, small velocity mismatching factor between the THz pulse and the probe pulse, high transmittance and small chromatic dispersion in the THz region, which can effectively reduce the influence to Kerr response caused by optical transmission factors. A phase shift of ∼286 mrad with an ultrafast gating time of 86 fs (FWHM) is achieved in our experimental condition. We believe that LDPE still has high potential to achieve complete polarization extinction by enhancing the THz electric field strength or increase the medium length. The low-cost LDPE holds great potential to become a superior material for high-power TKE-based modulator in terms of the excellent properties of band gap, velocity matching, chromatic dispersion and gating time.
Funding
National Natural Science Foundation of China (61935001, 61905271, 12074272); Natural Science Foundation of Beijing Municipality (JQ18015); Guangdong Basic and Applied Basic Research Foundation (2020A1515011083); Beijing Advanced Innovation Center for Imaging Technology.
Disclosures
The authors declare no conflicts of interest.
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