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Abstract
In recent years, significant progress has been made in the fields of nonlinear and ultrafast optics, offering exciting opportunities for terahertz (THz) science and technology. In this study, we present a novel design of a SSBCD (Solid-State-Biased Coherent Detection) device for the coherent detection of ultra-broadband THz pulses. By increasing the number of cross-fingers, we have effectively enhanced the sensitivity of the SSBCD device. The design of stepped and circular structures has successfully expanded the detectable electric field directions while reducing the dependence on the incident field direction. As a result, we have achieved ultra-broadband detection with a high dynamic range and a wide detection angle. These research findings lay a critical foundation for the integration of solid-state ultra-broadband detection into compact and miniaturized terahertz systems.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In the past decades, there has been a growing interest in the research of the terahertz (THz) spectral range, which lies between the microwave and optical frequency ranges [1]. Terahertz waves have wide-ranging applications in various research fields such as fast imaging, spectroscopy, next-generation mobile communication, astronomy, and security screening [2–6]. Many of these applications involve the ability to generate and precisely reconstruct the temporal evolution of ultra-broadband THz pulses. The advantages of ultra-broadband terahertz pulses, which are electromagnetic waves covering a frequency range of 0.1-10 THz or even wider, have attracted significant attention compared to traditional THz systems. On one hand, a 10 THz wide radiation lasts only a few hundred femtoseconds (full width at half maximum), enabling high-resolution time-of-flight measurements for applications such as 3D THz imaging of multilayered structures or thickness evaluation of thin films [7]. On the other hand, many materials, including semiconductors, liquid crystals, chemicals like drugs and explosives, as well as biopolymers like proteins and DNA, exhibit specific rotational/vibrational modes above 2 THz [8–13]. Therefore, the capability of providing ultra-broadband detection is essential for their comprehensive investigation in a wider THz spectral window. In this context, efforts have been made to achieve efficient and cost-effective THz sources and detectors that can operate at room temperature. Currently, various terahertz time-domain spectroscopy (THz-TDS) systems have been developed, achieving bandwidths of up to 7 THz for spectral experiments [14–16]. The most common detection techniques in these systems rely on electro-optic sampling (EOS) in photoconductive antennas or second media (such as ZnTe and GaP crystals) [17]. However, neither of these methods easily enables coherent detection of ultra-broadband THz pulses (including phase and amplitude) without introducing unnecessary distortions. This is because they are inherently affected by drawbacks associated with long-lived free carriers and phonon resonances [14]. To overcome these issues, a class of gas-based detection techniques has been introduced, enabling spectral investigations up to or beyond 10 THz, assuming the employed ultrafast laser pulse duration is sufficiently short. Gases are continuously renewed, exhibit negligible dispersion, and lack phonon resonances due to their disordered structure. Among these techniques, notable ones include air-breakdown coherent detection, air-biased coherent detection (ABCD), optically biased coherent detection, and THz radiation-enhanced emission of fluorescence [18,19]. ABCD utilizes a detection technique based on the electric-field-induced second harmonic (EFISH) generation, where the optical local oscillator is obtained through an external bias electric field (Ebias), biasing the interaction between the THz and probe optical beams [20]. In this process, the strong electrostatic field breaks the symmetry of a centrosymmetric medium like air or silica, inducing electric-field-driven second-order nonlinearity. Similarly, a terahertz field can be regarded as static within the duration of an ultrafast optical probe pulse, resulting in its frequency doubling [20,21]. This nonlinear mixing leads to a total EFISH beam intensity containing a term directly proportional to the THz electric field. By modulating the bias electric field and performing heterodyne detection via a lock-in amplifier, it is possible to isolate and record this linear term, thus reconstructing both the amplitude and phase of the THz transient. The total intensity of the second harmonic (SH) beam is expressed as Eq. 1 [18]:
Currently, the SSBCD detection method is typically based on a single aperture or single fork-shaped structure, which still imposes significant limitations on the detection sensitivity and the ability to detect the polarization direction of the terahertz electric field. In this paper, we report three different SSBCD devices design structures and conduct simulation studies with varying parameters using three-dimensional electromagnetic field simulation software. These three structures address the limitations of conventional SSBCD devices in terms of detection sensitivity and the detection of the electric field polarization direction.
2. Device structure and layout design
Three different SSBCD devices with distinct designs are shown in Fig. 2. All three SSBCD devices consist of a 5-layer structure. The bottom layer is a 2mm-thick fused silica substrate, on which a Cr-Au-Cr trilayer patterned structure is deposited. The thicknesses of the layers are 30 nm, 100 nm, and 30 nm, respectively. Both Cr layers ensure proper adhesion of the dielectric material to the gold layer. Finally, a 1µm-thick SiN layer (not shown in Fig. 2.) is deposited on the patterned structure, completely filling the gap.
Fig. 2. Schematic diagrams of the three different SSBCD device structures. (a) Crossed-finger SSBCD device; (b) stepped SSBCD device; (c) circular SSBCD device.
In Fig. 2(a), we have optimized the structure based on [22]. By referring to the electrode structures on the left and right sides, we have designed a multi-forked electrode structure. This multi-forked electrode structure can effectively enhance the THz field intensity, resulting in a larger THz field compared to single-electrode or single-forked structures. It effectively increases the sensitivity of the SSBCD detector. Detailed simulation results comparing these structures will be discussed later. A drawback of traditional SSBCD devices is that the polarization direction of the THz field needs to be perpendicular to the gap direction of the device. Deviating from the exact perpendicular direction would affect the detection efficiency and prevent the device from achieving its highest sensitivity. Therefore, we have designed the stepped SSBCD device shown in Fig. 2(b). The gaps in this device are mutually perpendicular, which can effectively address the issue of THz field polarization direction to some extent. Building upon the design in Fig. 2(b), we have further developed the circular SSBCD device shown in Fig. 2(c). The circular device can better accommodate THz fields from different directions, eliminating the need to adjust the orientation of the SSBCD device specifically for coupling THz field direction and achieving excellent compatibility.
3. Simulation result
In this section, we employed the simulation software COMSOL Multiphysics, utilizing the Electromagnetic Wave Frequency Domain module within the software, to conduct simulated simulations for several different SSBCD devices.
We established a simulation model as schematically depicted in Fig. 3, where the origin is located at the center of the SSBCD device, with x representing the transverse axis and y indicating the propagation direction. As mentioned in [23], in our simulation model, we assumed that the SSBCD device is placed at the waist position of a collimated THz beam. This arrangement ensures that the plane of the designed slit coincides with the focus of the THz beam. Consequently, the THz beam has to traverse a 1-micrometer-thick SiN cover layer before reaching the metal contacts. Due to the subwavelength thickness of the cover layer, we disregarded the minimal deviation that the THz wave undergoes due to refraction at the air/SiN interface. The metal pads of the slit were modeled as a stack of metal sheets, as designed in Fig. 2, consisting of a 100-nm-thick aluminum layer sandwiched between two 30-nm-thick layers of chromium. The incident THz electric field follows the formula provided in [23]. We evaluated the complex, frequency-dependent dielectric parameters of the two metals throughout the entire THz range using the Drude model [24,25]. We conducted simulations in the 1-10 THz range, assessing the THz electric field at its focus, both in the presence of a single layer of SiN (background field) and when the metallic slit is included. The electric field is significantly confined within the metal slit, with this effect being more pronounced near the edges of the metal pads, as shown in Fig. 4 (right). We calculated the average value of the THz electric field within the slit by integrating along the x-axis coordinate (as depicted in Fig. 9), both with the presence of the slit and without (background field). The field enhancement (FE) can be quantified using Eq. 2 [23]:
where Egap represents the gap electric field intensity, and Ebackground represents the background electric field intensity.Fig. 3. Schematic diagram of the simulation model for ultra-wideband terahertz SSBCD device. (Top) Front view. (Bottom) Top view.
Fig. 4. (Left) Schematic diagram of the simulated structure of the crossed-finger SSBCD device. (Right) The distribution of the gap electric field in the crossed-finger SSBCD device at 1 THz.
First, we will provide a detailed overview of the simulation results for the SSBCD structure shown in Fig. 4 (left). Figure 4 (left) depicts a three-slit SSBCD device with a slit width (G) of 1 µm, finger width (W) of 60 µm, and gap width (L) of 100 µm between each pair of fingers. We conducted simulations for single-slit, double-slit, and three-slit SSBCD devices within the frequency range of 1 THz to 10 THz. Figure 4 (right) presents the electric field distribution of the 3-slit SSBCD device at 1 THz. The simulation results are presented in Fig. 5. In Fig. 5 (left), the blue dots, green pentagons, and red stars represent the gap terahertz electric fields for the single, double, and triple slit SSBCD devices, respectively, in the frequency range of 1 THz to 10 THz. The brown diamond represents the background electric field. From Fig. 5 (left), it can be observed that the terahertz electric field intensity increases with the number of slits. This is because the multi-slit structure can generate more surface-induced currents, leading to an overall enhancement of the induced electric field. Figure 5 (right) illustrates the simulated results of the field enhancement for the three different SSBCD devices. The results demonstrate that the field enhancement (FE) is superior in the triple-slit SSBCD device compared to the double-slit and single-slit SSBCD devices. We observe that in both double-finger and triple-finger SSBCD devices, field enhancement exhibits oscillatory behavior at specific frequencies. We speculate that this phenomenon is independent of gap width and may be attributed to the multi-finger structure, which might be creating a certain terahertz wave resonance effect, leading to oscillations at specific frequencies. We have observed that when a bias voltage is applied, although the bias electric field in the region between the two pairs of fingers is opposite to the bias electric field in the finger slits, this opposing effect may weaken the performance of the multi-slit structure. However, by appropriately increasing the distance between the two pairs of fingers, this weakening effect can be significantly reduced. Therefore, it is necessary to carefully design the distance between the finger pairs and the number of finger pairs to achieve an optimal balance.
Fig. 5. (Left) The gap terahertz electric field intensity and background electric field intensity in the three SSBCD devices within the frequency range of 1 THz to 10 THz. (Right) The gap field enhancement in the three SSBCD devices within the frequency range of 1 THz to 10 THz.
We also studied the relationship between the field enhancement of the three-slit SSBCD device at 1 THz and the gap width and slit width respectively, as shown in Fig. 6. From Fig. 6 (left), it can be observed that as the gap width varies from 1 µm to 5 µm, the field enhancement decreases as the gap width increases. The fitted curve indicates that the field enhancement inversely changes with the square root of the gap width. This can be explained by two Sommerfeld half planes. For a Sommerfeld half plane, the electric field is proportional to the inverse square root of x, where x is the distance from the slit edge. Figure 6 (right) illustrates the variation in field enhancement as the gap width changes from 10 µm to 100 µm. As the gap width widens, the field enhancement becomes stronger. The fitted curve shows a logarithmic relationship between field enhancement and gap width. When the gap width is narrow, the reverse electric field within the gap significantly weakens the field enhancement within the slit. As the gap width increases, this field cancellation effect is greatly diminished.
Fig. 6. (Left) The relationships between different slit widths and field enhancement. (Right) The relationships between different gap widths and field enhancement
During the simulations, we observed the behavior of the guided terahertz waves as they interacted with the sub-wavelength metallic slits. This interaction generated a surface density of charge carriers. The rapid transient response of the charge carriers resulted in their accumulation along the edges of the metallic electrodes, thus enhancing the terahertz electric field within the slits. By analyzing the specific spectral response of these narrow slits, we can further improve the overall detection efficiency. These simulation results offer valuable insights into the behavior and performance of the structure in the terahertz frequency range. They contribute to a deeper understanding of the working principles and provide a basis for optimizing the design. Further research and analysis based on these results can lead to enhanced performance, increased sensitivity, and improved accuracy of SSBCD devices.
To address the limitation of the orthogonal alignment required between the incident electric field direction and the direction of the cross-fingers in the cross-finger structure, we have designed a stepped structure. The simulation structure of the stepped device is illustrated in Fig. 7, where the gap width G is 1 µm, the gap length L is 400 µm. The x-axis and y-axis dimension of the stepped SSBCD device is 2000 µm. As shown in Fig. 7, we have designed two mutually perpendicular gap structures. Compared to the structure in Fig. 4 (left), this design allows for the enhancement of terahertz electric fields from both horizontal and vertical directions simultaneously, eliminating the need to align the gap direction perpendicular to the incident terahertz field. The simulated results of the incident electric field and bias voltage distribution are presented in Fig. 8.
Fig. 8. (Left) The distribution of the gap electric field in the stepped SSBCD device at 1 THz. (Right) The distribution of the electric field in the stepped SSBCD device under bias voltage.
As shown in Fig. 7, we have designed another structure with mutually perpendicular gaps. This structure, compared to the one in Fig. 4 (left), can simultaneously enhance terahertz electric fields incident from both the horizontal and vertical directions, eliminating the need to intentionally adjust the gap direction to be perpendicular to the incident terahertz field. The simulated results of the incident electric field and bias voltage distribution are shown in Fig. 8. We used two terahertz waves with the same amplitude and perpendicular polarization to illuminate the detector. In Fig. 8 (left), the distribution of the gap electric field in the SSBCD device at 1 THz is shown. From Fig. 8 (left), it can be observed that the electric field is enhanced in both the vertical and parallel gaps.
Figure 9 displays the field distribution on the surface of the stepped SSBCD device at 1 THz. To better illustrate the gap field distribution, we have widened the gap width during plotting, making it appear that the gap width is not significantly different from the dimensions of the metallic electrodes between the gaps. In reality, the gap width should be proportionally much smaller compared to the metallic electrode dimensions than what is depicted in the figure. By separately calculating the field enhancement (FE) factor for each orthogonal electric field, it can be observed that the enhancement factors are similar. This indicates that when it is necessary to sequentially detect terahertz waves in two perpendicular directions, this device can be used without adjusting the orientation of the detector, simplifying the experimental steps. Figure 8 (right) shows the distribution of the electric field across the entire device when a bias voltage is applied, and the electric field is uniformly distributed within the gaps.
To further optimize the structure for detecting terahertz waves incident at arbitrary angles, we designed a circular SSBCD device, as shown in Fig. 10. The device has a gap width of G = 1 µm, an outer ring width of W = 600 µm, an inner ring width of H = 400 µm, and an outer radius of R = 1500 µm. The four square blocks on the upper side of Fig. 10 are electrodes used for applying bias voltage. Compared to the structure in Fig. 7, this design allows for the detection of terahertz waves that are nearly normal incident at various angles, eliminating the need for strict alignment between the device orientation and the electric field direction. The simulation results with applied terahertz incident field and bias voltage are shown in Fig. 11.
Fig. 11. (Left) The distribution of the gap electric field in the circular SSBCD device at 1 THz, the direction indicated by the arrows represents the polarization direction of the terahertz electric field. (Right) The distribution of the electric field in the circular SSBCD device under bias voltage.
Figure 11 (left) shows the distribution of the electric field in the device when a vertically polarized THz wave with a frequency of 1 THz is incident. The results indicate that the THz electric field can be effectively enhanced within the gaps of the circular SSBCD device. Figure 11 (right) shows the distribution of the electric field in the device when a bias voltage is applied. Although the direction of the electric field at the center of the device is opposite to the desired direction, the counteraction of the central electric field can be ignored due to the significantly larger distance between the inner two circular rings compared to the distance between the inner and outer rings.
To verify if the circular SSBCD device structure can detect terahertz waves with different polarization directions, we simulated the case of terahertz electric field incidence at various polarization angles (-45°to 45°). The results are shown in Fig. 12. In Fig. 12, the blue dots represent the electric field intensity in the gap, and the red pentagrams represent the field enhancement factor (FE). The 0° angle represents horizontal polarization. From the graph, it can be observed that the field enhancement factor (FE) slightly varies with the incident electric field angle. The FE coefficient is smallest at 0 degrees because the inner and outer circular rings in the center of the device are discontinuous, resulting in a partial loss of gap enhancement effect. Overall, the circular SSBCD device is capable of detecting incident electric fields at nearly any angle.
Fig. 12. The gap electric field intensity (in blue) and the terahertz field enhancement factor (in red) at different angles of incidence for 1THz terahertz waves.
4. Conclusion
In summary, we have demonstrated an integrated solid-state device, called SSBCD, for ultra-broadband coherent detection of THz pulses. The advantages of the SSBCD device include relatively high dynamic range, broad bandwidth, and significantly reduced probe energy and bias voltages compared to traditional ABCD methods. The SSBCD device can serve as an integrated sensor to fully characterize the spectral emission of different THz sources, overcoming the limitations of conventional band-limited THz detectors. We have designed and simulated multi-branch SSBCD devices, stepped SSBCD devices, and circular SSBCD devices. The multi-branch SSBCD device enhances the FE coefficient and improves detection sensitivity compared to traditional SSBCD devices. The stepped SSBCD device allows for simultaneous detection of electric fields in two orthogonal directions. The circular SSBCD device can detect electric fields incident from nearly any direction. This design addresses the challenge of matching the SSBCD device with the direction of the incident electric field and provides a reference for future designs of versatile and adaptable SSBCD devices. The fabrication feasibility for the three types of SSBCD devices is relatively high. However, they still encounter some challenges. The use of solid-state materials like silica or silicon nitride is well-established and feasible, as these materials are commonly used in microfabrication and semiconductor processes. The miniaturization of SSBCD devices is feasible due to the precision and capabilities of modern microfabrication techniques. However, there are also some challenges in Fabricating SSBCD devices. Achieving the necessary nanoscale dimensions and precise geometries for SSBCD components can be challenging, requiring advanced lithography and etching techniques. SSBCD devices may be sensitive to small variations in dimensions, which require careful quality control during fabrication. The dimensions of the electrodes and the SSBCD detector's central structure span a wide range, necessitating the use of several different thin-film fabrication techniques. This also introduces the possibility of some deviation between the actual manufactured size of the device and its intended design dimensions. Furthermore, SSBCD can be integrated with backend detectors, leading to more cost-effective THz devices and instruments in the future.
Funding
National Natural Science Foundation of China (12274424, 61988102); National Key Research and Development Program of China (2022YFA1203500); Science and Technology Planning Project of Guangdong Province (2019B090909011); Special Project for Research and Development in Key areas of Guangdong Province (2019B090917007); Guangzhou basic and applied basic research Project (2023A04J0017).
Acknowledgment
This work was financially supported by the National Natural Science Foundation of China (Grants No. 61988102, No. 12274424), the National Key Research and Development Program of China (2022YFA1203500), Key Research and Development Program of Guangdong Province (2019B090917007), Science and Technology Planning Project of Guangdong Province (2019B090909011), Guangzhou basic and applied basic research Project (No. 2023A04J0017).
Disclosures
The authors declare no conflicts of interest.
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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