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Abstract
Two-color femtosecond (fs) laser filamentation in the gas medium is an effective way to generate broadband and high intensity terahertz (THz) pulse. The interdigitated photoconductive antenna (iPCA) has the advantages of both broadband detection and high signal-to-noise ratio (SNR), which is a very effective way to detect the THz pulse produced by two-color fs laser filamentation. The THz signal from two-color fs laser filamentation is comprehensively characterized by the iPCA, which achieves high SNR, high sensitivity, and polarization detection. This work provides a new idea for high power broadband THz coherent detection.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Terahertz (THz) radiation has been becoming a research hot spot of the electromagnetic spectrum which is located between the microwave and the infrared range. Over the past 20 years, the global research and the development of THz science and technology have demonstrated its broad application prospects in the non-invasive imaging [1,2], the medical diagnosis [3], the military [4], the communications [5], the physics [6,7], and other fields [8]. Such applications increase the demand for the high efficient THz source and detection system. THz radiation can be generated through harmonic generation from the microwave source [9] or the nonlinear conversion from the optical source [10–12]. Currently, the most popular intense THz sources are based on the optical rectification in electro-optic crystals, and the two-color filamentation in gases and liquids. However, the optical damage threshold of the electro-optic crystals has limited the development of optical rectification in electro-optic crystals. The pulse duration of THz pulses generated by the optical rectification is only several picoseconds, and the corresponding spectrum is below 5 THz. Nevertheless, the optical damage threshold has no influence on gas or liquid media. Moreover, THz pulses generated by the two-color filamentation have a broadband spectrum. At the same time, the THz pulse can be modulated by adjusting the two-color fs laser filament length, gas pressure, driving laser energy, and phase shift between the fundamental laser and its second harmonic [13,14].
The detection measurement of the broadband THz radiation can be classified into two categories: the average power detection and the coherent detection. In this paper, the coherent detection is mainly explored by two kinds of photoconductive antennas. The most commonly used coherent detectors are photoconductive antenna [15], electro-optic sampling [16], autocorrelation, and air biased coherent detection [17]. The photoconductive antenna is convenient to process, and its structure can be customized according to different usage conditions to meet various detection requirements. For example, the butterfly antenna, and the single gap photoconductive antenna (sPCA) are used to detect narrowband THz signals, while the array antenna is used to detect broadband THz signals. The early array antennas just arranged the single-gap detection unit in a matrix to form an array structure. This simple arrangement only superimposes the signals of the single gap detection unit. It cannot effectively extend the electrode length, and some gaps cannot be excited by femtosecond laser, which cannot effectively generate photocarriers. For the high-power THz radiation from two-color fs laser filamentation, this low-efficiency arrangement makes the substrate material easily saturate, and cannot truly describe the electric field and the polarization information of the THz pulse.
THz radiation generated by two-color fs laser filamentation has a promising application prospect, as its bandwidth is up to 200 THz and has a high electric field up to 20 MV/cm [18,19]. Conventional photoconductive antennas are easy to saturate with the high THz power, and cannot fully describe the electric field information generated by two-color fs laser filamentation [20–22]. It has no ability to independently detect THz polarization, and can only characterize the electric field strength of THz signals. In comparison, the interdigitated photoconductive antenna (iPCA) holds much promise to simultaneously realize high power detection, large dynamic range response and broadband THz detection with high signal-to-noise ratio (SNR). In the iPCA structure, two finger-like electrodes are intertwined to form a large detection array, and the signals between the electrodes can be superimposed coherently. This structure combines the advantages of a large detection area and small electrode gaps. The larger detection area means that the probe laser power can be fully utilized. Under the condition of constant probe laser power, more photocarriers can be excited in a larger detection area, which can significantly improve the detection efficiency. In addition, the iPCA is quite sensitive to the THz signal whose polarization is perpendicular to the electrode array. It can independently complete the sensitive detection of THz polarization.
2. System and experiment
As is shown in the Fig. 1, the broadband THz radiation is generated by two-color fs laser filamentation. During the experiment, the Ti:sapphire femtosecond laser amplifier (Legend, Coherent, Inc.) provide pulses with the center wavelength of 800 nm, the pulse width of 50 fs and the repetition rate of 500 Hz. The maximum output single pulse energy of Ti:sapphire femtosecond laser amplifier is 6mj. The fundamental laser pulse (horizontally polarized) propagated through the plano-convex lens (f = 300 mm) and then through a 100 $\mathrm {\mu }$m thick $\mathrm {\beta }$-BBO crystal to produce the two-color (800 nm and 400 nm) fs laser filament. Two 2 mm thick Teflon plates were placed behind the filament to block the femtosecond laser. The off-axis parabolic mirror (OAP) with 2 inches diameter and the 4 inches reflected focal length was used to collimate THz pulses. The collimated THz pulse is collected by another identical OAP and focused on the iPCA. The lock-in amplifier (Stanford Research Systems SR830) is used in our system to improve SNR.
Fig. 1. Schematics of the THz time-domain spectroscopy system based on two-color fs laser filamentation. In the illustration, the X, Y, and Z axis are the horizontal direction, the perpendicular direction, and the laser propagation direction, respectively.
Under the same experimental conditions, the Golay Cell was set at the same location of the iPCA to measure the THz power. The maximum THz electric field is 86 kV/cm (< 100 kV/cm) in the experiment. The nonlinear effect is negligible in the iPCA. When intense THz radiation interacts with iPCA, the nonlinear effect cannot be neglected. However, the measured THz electric field is always proportional to the THz electric field, even if there are nonlinear effects. We can still analyze the time and spectrum waveform detected by the iPCA with intense THz electric fields.
The model of the iPCA in the experiment is iPCA-21-05-300-800 from BATOP. The front side of the antenna is the hemispherical silicon lens for collecting the THz signals. The backside is the micro-lens array for focusing the probe laser. As it is shown in the Fig. 2(a), the micro-lens iPCA is mainly composed of four parts: the silicon lens, the interdigitated electrode, the low-temperature GaAs (LT-GaAs) substrate, and the micro-lens array. The material of the Silicon lens is high resistivity float zone silicon, in which the bottom surface radius is 6 mm and the cross-section height is 7.1 mm. The THz pulse passes through the silicon lens and is focused on the Lt-GaAs substrate. Figure 2(b) depicts the structure of interdigitated electrode array, which effective area is 300 $\mathrm{\mu}$m $\times$300 $\mathrm{\mu}$m. The single electrode’s width and gap distance of the iPCA are 8 $\mathrm {\mu }$m and 5 $\mathrm {\mu }$m, respectively. Figure 2(c) describes the structure of the micro-lens array which is installed on the interdigitated electrode array. The diameter of the single micro-lens is 27 $\mathrm {\mu }$m, and the distance between the adjacent micro-lens is 30 $\mathrm {\mu }$m. The focus of the micro-lens is arranged along the interdigitated electrode band gap position to improve the detection efficiency. The structure of the sPCA is shown in Fig. 2(d). The specific parameters of the two antennas are compared in Table 1. Although, the sPCA and iPCA have same gap distance, the larger band gap width determines that the iPCA can receive more THz signals. The smaller dipole length determines that the iPCA has more detection units within the fixed effective area. The above two points are the core advantages of the iPCA.
Fig. 2. (a) The schematic diagram shows the iPCA structure with the silicon lens and the micro-lens array. The interdigitated electrode array, the micro-lens array, and the sPCA structure are respectively shown in (b), (c), and (d). The bottom inserted pictures are the local enlargement of (b), (c), and (d).
Table 1. Structure parameters of sPCA and iPCA
3. Results and discussion
The THz time waveform of sPCA (bPCA-100-05-10-800-x from BATOP) and iPCA (iPCA-21-05-300-800 from BATOP) is shown in the Fig. 3. Under the same THz electric field (70 kV/cm), the THz time domain waveform peak-to-peak value detected by the iPCA is 6 times than the sPCA, which means the iPCA effectively improved the detection efficiency of THz signals.
Fig. 3. Under the same input THz intensity, The THz time domian waveform (a) and spectrum (b) are detected by the sPCA and the iPCA, respectively.
The iPCA is composed of 30 $\times$30 detection units, and each unit is equivalent to one sPCA. The type, size, and carrier migration rate of each unit are exactly the same, so the photocurrent generated by the carrier migration in each unit can be superimposed coherently.
After excitation by the probe laser, photocarriers are accelerated by the THz field and move directionally to the antenna electrode. The photocurrent intensity between the two antenna electrodes is proportional to the THz electric field intensity. In the Hertzian dipole approximation, the photocurrent is proportional to the time derivation of the THz electric field intensity:
THz signal detected by the iPCA is proportional to the averaged photocurrent $\bar {J}$ divided by the duty ratio of the probe laser pulse, which is approximated with the ratio of the lifetime of the photocarriers $\tau _{c}$ and the interval of the probe laser pulses $T_{\textrm {probe}}$ [20]. Therefore:
Taking the mobility $\mu$, the averaged probed laser power $P_{\textrm {probe}}$, the bias voltage $V$, and the antenna gap $D$ in the Eq. (2), the THz electric field can be calculated in Eq. (3):
From Eq. (3), the detection efficiency is inversely proportional to the antenna gap $D$. Under the tight focus condition, it is beneficial to improve detection efficiency by using a smaller antenna band gap. However, the detection efficiency would be saturated at the higher probe laser power. The overmuch photocarriers cause the screening effect, which limits the photocarriers to flow to the electrode. The correspondence between the iPCA band gap and the probe laser power should be optimized. For the iPCA, a square-shaped antenna gap is ($D {\times } D$), so the probe intensity on the antenna gap is $F=n P_{\textrm {probe}} / D^{2}$, where $n$ is the iPCA constant. The detection THz field is proportional to the antenna gap square. Therefore, the detected THz electric field can be shown as:
From the Eq. (4), the probe laser intensity should match to the gap $D$ to enhance the detected THz signal as much as possible [20].
In conventional interdigitated electrodes, the bias electric field direction is rotated 180$^{\circ }$ between adjacent gaps. The opposite acceleration of carriers results in the destructive interference net current. The micro-lens array structure ensures that the photocarriers move along the same direction, leading to the constructive interference net current. The micro-lens array structure also greatly increases the utilization rate of laser energy to excite more photocarriers.
A X-Y-Z coordinates based on the polarization direction of the pump laser. During measurements, the electrode is placed along the X-direction and Y-direction by rotating the iPCA.
As it is shown in Fig. 4(a), the iPCA can only respond to the THz polarization perpendicular to the interdigitated electrode, so it can realize the measurement of the THz polarization and can be used as the polarization-sensitive THz detector. The interdigitated electrode structure is similar to the THz polarizer and can be regarded as closely arranged wire grids. The polarization extinction ratio (PER) is used to analyze the polarization sensitivity of the iPCA. The PER is generally defined as:
According to the data in Fig. 4(a), the PER as a function of the THz frequenciey is shown in Fig. 4(c). The PER is above 10 dB from 0 $\sim$ 7 THz. The maximum PER is 52 dB at 0.57THz. The ratio of the maximum value $E_{\max }$ to the mean square error $\sigma _{\textrm {noise}}$ of the noise $N_{\textrm {noise}}$ of the system is defined as the signal-to-noise ratio (SNR) of the system:
In the Fig. 5, The SNR of the iPCA system is about 3 $\times 10^{3}$. The main performance parameters of the sPCA and the iPCA are compared as shown in the Table 2.
Fig. 4. (a) The polarization response of iPCA with the $\textrm {E}_{ \textrm {X}}$ and the $\textrm {E}_{ \textrm {Y}}$ input electric field.(b) The corresponding spectrum of $\textrm {E}_{ \textrm {X}}$ and $\textrm {E}_{ \textrm {Y}}$ (c) The polarization extinction ratio as a function of THz frequency.
Fig. 5. The THz time-domain waveform (black line) and the background noise (red line) detected by the iPCA.
Table 2. Performance comparison between sPCA and iPCA
In order to explore the effect of the probe laser polarization on the detection performance by the iPCA, the probe laser polarization direction is continuously controlled by rotating the Zero-Order half-wave plate. The relationship between the THz signal and the polarization is shown in Fig. 6, where the $\mathrm {\theta }$ is the angle between the polarization and the antenna electrode. Photocarriers dynamics in the iPCA is influenced by THz electric field and probe laser electric field. The transient current J(t):
Fig. 6. The probe laser polarization as function as the peak-to-peak value of THz field measured by iPCA.
As it is shown in Fig. 7(a), when the probe laser polarization is parallel to the electrode, the THz signal detected by the iPCA reaches its maximum. While the minimum THz signal is detected at the $\theta$ = 90$^{\circ }$. The minimum is about 60 % of the maximum. The detected THz signal intensity drops monotonously from the $\theta$ = 0$^{\circ }$ to 90$^{\circ }$. The probe laser polarization only affects the detected intensity of the THz signal, and it has little effect on the spectrum width of the THz field as is shown in the Fig. 7(b).
Fig. 7. The response of the iPCA to the polarization of the probe laser. (a) THz time waveform was detected by the iPCA with various probe laser polarization directions. (b) THz power spectrum by the Fourier transform of (a).
The reasons for the physical phenomena are that the iPCA has a similar structure to the THz wire grid. The iPCA is consist of a row of parallel electrodes. When the THz polarization is parallel to the electrodes, the THz signal would cause free electrons to oscillate along its length. This interaction leads to the re-radiation and dissipation of THz energy through joule heating. The re-radiated wave in the forward direction acts to cancel the transmitted wave, and in the reverse direction appears as reflected radiation. In this way, the parallel polarization component of the THz signal is stripped out of the transmitted radiation and appears as a reflected wave.
In Fig. 8(a), four groups of THz intensity are detected by the iPCA. The THz electric field intensity can be modulated by changing the number of Teflon plates. The iPCA shows excellent properties that distinguish four different THz intensities accurately and clearly. As the black curve shown in Fig. 8, the THz signal detected by the iPCA gradually enhances with the increase of the probe laser power until 8 mW. When the probe laser power is beyond 8 mW, the probed THz signal tends to saturation.
Fig. 8. (a) The THz peak-to-peak value as a function of the probe laser power with the different THz electric field intensity. (b) The variation curve of the THz field with the pump laser power at 15 mW probe power.
The probe laser cannot produce enough photocarriers excited by the low probe laser intensity. Essentially, the detected THz signal originates from the bias signal generated by the accumulation of photocarriers. Because the photocarriers in the antenna electrodes would be depleted, the bias signal cannot always keep increasing with the probe power. This is another manifestation of saturation that the depletion of the electrostatic energy stored in the antenna gap. The dynamic balance between the bias and the THz induces the screening effect. The relationship between the THz signal and the pump laser power with the 15 mW probe laser power is shown in Fig. 8(b). The pump laser energy corresponding to the black curve, red curve, blue curve and green curve are 2.88 mJ, 1.86 mJ, 1.40 mJ, and 1.08 mJ, respectively. Our results imply that an intense pump laser can efficiently enhance the THz signal from two-color fs laser filament. The iPCA can accurately describe the relative relationship between the different THz electric fields.
4. Conclusion
The iPCA is selected to exhaustive study as detection method of THz radiation from two-color fs laser filamentation. The experimental results show that the iPCA has obvious advantages in both intensity and polarization detection compared with the sPCA. The maximum detection intensity of the iPCA is 6 times than the sPCA. As the geometry of the iPCA is similar to the THz wire grid, so it has the sensitive response to the THz polarization. The PER is reaches up to 52 dB at 0.57 THz. The system is ideal for studying the nonlinear properties of samples in the THz band. To this end, the iPCA is the stable and efficient scheme for intensity and polarization detection of THz radiation, which paves the way for THz time-domain spectroscopy on high power THz detection.
Funding
National Natural Science Foundation of China (12061131010, 12074198); Russian Science Foundation (21-49-00023); Natural Science Foundation of Tianjin City (20JCYBJCO1040).
Acknowledgments
The authors would like to thank the funding support from National Natural Science Foundation of China (12061131010, 12074198), Russian Science Foundation (21-49-00023), Natural Science Foundation of Tianjin municipality (20JCYBJCO1040).
Disclosures
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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