1. Introduction

Terahertz (1 THz = 10¹² Hz) technology has developed rapidly over the decades. Presently, it is employed in numerous fundamental research fields as well as in practical applications [1]. The discovery of coherent terahertz electromagnetic (EM) radiation emitted from stacks of intrinsic Josephson junctions (IJJs) in cuprate Bi₂Sr₂CaCu₂O_8+δ (Bi-2212) single crystals has revealed the possibility of using high-critical-temperature (high-${T_c}$) superconductors for compact and solid-state terahertz sources [2]. Recent reviews on this subject can be found in Refs. [3–5]. Nevertheless, continuous terahertz emission with a power output greater than 1 mW is yet to be realized.

Previous studies on Bi-2212 terahertz emitters have shown that the emission frequency of coherent terahertz EM radiation is determined purely by the Josephson relation [6] and internal cavity resonance [2,7–13]. Furthermore, the frequency is highly tunable by varying the bath temperature and bias voltage [14] as well as by scanning multiple current-voltage branches [15]. Tunable radiation is desired for applications in local oscillators employed in terahertz mixing. However, the emission intensity significantly reduces once the Josephson frequency deviates from the internal cavity condition. Notably, Bi-2212 sources entail this tradeoff problem; therefore, we previously proposed the integration of external resonators into Bi-2212 mesas [16]. External elements such as microstrip antennas are also expected to reduce impedance mismatch and facilitate highly efficient emissions at specific frequencies. Nevertheless, precise control of the emission characteristics by utilizing such external elements has not been explored so far.

In this study, we designed and characterized microstrip patch antennas aimed at controlling the emission characteristics of the IJJ terahertz source. In a pioneering study, passive terahertz responses were demonstrated using the IJJ stack embedded in bow-tie antennas [17]. We optimize the associated parameters using an EM simulator to make the microstrip patterns compatible with superconducting devices.

2. Experimental

Figure 1(a) depicts a schematic view of the Bi-2212 terahertz emitter designed in this study. The Bi-2212 single crystal was grown via the traveling solvent floating zone method. A piece of the crystal was annealed at 600 °C for 24 h in argon gas mixed with 0.1% oxygen to control the doping level. The crystal was then glued onto a sapphire substrate using a heat-conductive silver paste (Kaken Tech. Co., Ltd., TK paste CR-3520) and cleaved to expose a virgin surface. Immediately after, a 30-nm silver layer was evaporated onto the surface. Subsequently, a rectangular mesa (48 × 300 µm²) was milled from the crystal using UV lithography and argon ion milling techniques. A mesa thickness of 1.4 µm corresponds to $N = 910$ stacked IJJs.

 

Fig. 1. (a) Schematic view and (b) optical microscopy image of the Bi-2212 terahertz emitter with the DPA pattern.

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We designed a microstrip pattern based on a triangular antenna (hereinafter, we refer to it as a delta patch antenna (DPA)). The triangular antenna is categorized as a broadband monopole self-complementary antenna. The input impedance of monopole antennas is sufficiently low ($< 10\; \mathrm{\Omega }$) compared to that of dipole, bow-tie antennas; thus, we assume that the proposed pattern, shown in Fig. 1(a), is suitable for coupling DPAs with superconducting mesas with low characteristic impedance.

Four DPAs comprised of 100 nm thick silver layers were patterned onto a 600 nm silicon dioxide (SiO₂) layer using chemical vapor deposition. We refer to them as DPA-1, DPA-2, DPA-3, and DPA-4, as indicated in Fig. 1(a). The tip of each DPA is electrically connected to the top surface of the Bi-2212 mesa. Assuming that the fundamental internal cavity mode has antinodes of the electric field at the mesa edges, EM oscillations in DPA-1 (or DPA-3) may be opposite in phase to those in DPA-2 (or DPA-4). A DC bias electrode strip with a quarter-wavelength open stub (QWOS) was subsequently patterned using vacuum evaporation and lithography techniques. The length L of the QWOS [see Fig. 1(a)] coincides with the quarter wavelength $\; \lambda /4$. Figure 1(b) shows an optical microscopy image of an array of two Bi-2212 mesas. We fabricated four mesas A1–A4 on an identical crystal base to test the characteristic variation.

There are three independent antenna parameters: the patch width ${w_a}$, patch height ${h_a}$, and thickness of the dielectric layer ${t_a}$. To optimize them, we implemented an EM simulation using the Sonnet software. From the simulation results, we obtained ${w_a} = 103$ µm, ${h_a} = 90$ µm, and ${t_a} = 0.6$ µm for the fundamental resonant mode ${f_a} = 0.75$ THz. Here, the optimal value of ${w_a}$ is consistent with the equivalent half wavelength in the SiO₂ layer with a dielectric constant ${\varepsilon _a} = 3.9$. Note that terahertz time-domain spectroscopy showed that ${\varepsilon _a}$ of SiO₂ is nearly independent of temperature in a frequency range of 0.5-1.0 THz [18]. A bandwidth of 64.5 GHz and a quality factor of ∼12 can be tuned by changing ${h_a}$. The EM simulation is described in detail in the Appendix.

The sample was mounted on the cold finger of an optical cryostat equipped with a Gifford-McMahon cryocooler (Sumitomo Heavy Industries, Ltd., RDK-101D). The IJJ mesas are biased using a function generator. The current–voltage characteristics (IVCs) were monitored using standard electronic devices. The superconducting critical temperature ${T_c}$ of 84 K was obtained separately from the measurement of the temperature dependence of the c-axis resistance. We used a silicon-composite bolometer (Infrared Laboratories, Inc.) to measure the intensity of the terahertz emission outside of the cryostat. A lab-constructed Fourier transform interferometer system based on split mirrors [19] was used to measure the emission frequency. The spectral resolution was approximately 10 GHz for the present setup.

3. Results and discussion

In Fig. 2(a), we plot the bath temperature (${T_b}$) dependence of the returning IVCs for mesa A3. ${T_b}$ was scanned in the range of $10\; \textrm{K} < {T_b} < 70\; \textrm{K}$ at 5 K increments (the complete data are not shown here). The inset in Fig. 2(a) shows the overall IVCs at 10 K. The arrows in the inset indicate the I–V hysteresis typical of the underdamped IJJ. The stacked IJJs switch simultaneously from the zero-voltage state to the resistive state at a critical current ${I_c}$=13.0 mA with the appearance of irreversible I–V jumps. The color code used in Fig. 2(a) represents the bolometer output. The vertical arrows indicate the bias points with maximum emission intensities at each ${T_b}$.

 

Fig. 2. (a) ${T_b}$ dependence of the returning IVC curve for mesa A3. The inset shows the overall IVCs at ${T_b} = 10$ K. The color code represents the bolometer output. (b) ${T_b}$ dependence of the FFT spectra for A3 with a constant offset. The FFT spectra are obtained at the bias points with the maximum emission intensity (cf. arrows in (a)).

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We observed repeatable and stable emissions from all mesas, A1–A4, in a wide ${T_b}$ range. The maximum bolometer output of 2.8 mV obtained at ${T_b} = 30\; \textrm{K}$ corresponds to a power level of 20 nW, which is accurately calibrated using a calorimeter-style power meter (Virginia Diodes, Inc., PM4). By considering optical power losses caused by misalignment in the interferometer system, the observed emission power is comparable to that for conventional Bi-2212 terahertz emitters of the same device design [2,20]. This indicates that there is no significant power enhancement due to the presence of the DPAs. In fact, we obtained appreciable signals at any ${T_b}$ below ${T_c}$, although the intensity was so small that it was barely detectable because of the limited sensitivity of the bolometer, especially when ${T_b}$ was close to ${T_c}$. Such broad characteristics suggest that in contrast to the conventional bare mesa patterned solely on a flat Bi-2212 substrate, the proposed pattern with DPAs leads to broadband characteristics.

In Fig. 2(b), we plot the ${T_b}$ dependence of the fast Fourier transform (FFT) spectra for A3. These spectra were obtained at the bias points with the maximum emission intensities [see arrows in Fig. 2(a)]. The vertical arrows indicate the spectral peak frequency ${f_p}$. We observed continuously tunable emission over a wide range, 0.35 THz < ${f_p}$ < 0.85 THz, depending on the bias point and ${T_b}$. At any ${T_b}$, ${f_p}$ coincides with the Josephson frequency given by ${f_J} = ({2e/h} )V/N$ [6]. From these mesas, we do not observe any emissions in the high-bias regime where the local temperature rise is pronounced, owing to the substantial Joule heating [21–26].

The ${T_b}$ dependence of the peak frequencies ${f_p}$ and the FFT amplitude for all the data obtained from A1–A4 are plotted in Figs. 3(a) and 3(b), respectively. A profile measurement using an atomic force microscope reveals the homogeneous mesa geometry in A1–A4. Hence, we recognize that the characteristic variations among them can be explained by considering the non-uniform superconducting properties such as ${T_c}\; $ in the Bi-2212 base crystal. Nevertheless, for all mesas, ${f_p}$ plateaued when ${T_b}$ was below 40 K; however, it decreased monotonically as ${T_b}$ exceeded 40 K. Furthermore, the FFT amplitude shows a characteristic peak with two maximum values at 30 K and 65 K. The dashed wavy line in Fig. 3(b) delineates this peak structure. Note that we collected the radiation using a hemispherical silicon lens placed close to the sample; therefore, the FFT amplitude is assumed to be the total integrated emission power, which is consistent with the bolometer output [see the color code in Fig. 2(a)].

 

Fig. 3. ${T_b}$ dependence of (a) the peak frequencies ${f_p}$ and (b the FFT amplitude for A1-A4.

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Previous studies have shown that ${f_p}$ (${T_b}$) is a good measure of the boundary conditions at the top and bottom of the Bi-2212 mesa and its nonrectangular cross-sectional profile [14,27], where ${f_p}$ was found to decrease monotonically with increasing ${T_b}$ in the entire ${T_b}$ range. In contrast, the present ${f_p}$ plateau [Fig. 3(a)] and peak structure [Fig. 3(b)] provide a strong indication of the transition of the emission states with a boundary near 40 K. Hereinafter, we refer to these two states as the low-${T_b}$ state (indicated by a light blue background) and the high-${T_b}$ state (indicated by an orange background). Note that the effective local temperature of the biased mesa should be at least 5–10 K higher than ${T_b}$ in the low-bias region. This ambiguity in the thermal properties induces a systematic error in ${T_b}$, which can be removed entirely via direct thermal imaging [24,25,28].

We assume that the ${f_p}$ plateau behavior in the low-${T_b}$ state is inherently attributed to the modification of the geometrical resonance condition in the presence of DPAs. The dashed line in Fig. 3(a) represents ${f_a}$ = 0.75 THz. The observed value of ${f_p}$ at ${T_b}$ < 40 K is equal to ${f_a}$ within a constant deviation of approximately 8%. This difference can be explained by considering the error in the ${w_a}$ values employed in the simulation. Owing to the finite contact area at the top mesa surface, the actual patch width may be reduced by up to 10%, depending on the alignment accuracy in the lithography process. Since ${w_a}$ is associated with ${f_a}$, as mentioned above, a shorter patch width yields ${f_p}$ higher than that expected from the simulation. This quantitative estimation is in good agreement with our experimental results. Note that an internal cavity resonance frequency for a fundamental mode of 0.74 THz, which can be calculated from mesa width of 48 μm [2], is close to ${f_a}$. However, the peak structure seen in the overall ${T_b}$ range cannot be understood by considering the internal cavity resonance.

To understand the emission states in the presence of the DPAs more clearly, we measured the optical polarization for the emitted terahertz waves. We installed a wire grid polarizer (WGP) (Origin Ltd., MWG40-IIA) with an extinction ratio of up to 15 dB at 0.5–1.0 THz in the present system, by placing it between the cryostat and the bolometer. The rotation angle between the wire direction and the direction parallel to the mesa length (longer side) is defined as the WGP angle $\theta $. We monitored the bolometer output at a fixed bias point with the maximum emission intensity with respect to $\theta $ by rotating the WGP in a stepwise manner using a mounting stage.

Figure 4(a) shows a polar plot for the polarization characteristics for A3 at ${T_b}$ = 35 K. Here, the distance from the center to an open symbol indicates the bolometer output in a logarithmic scale, whereas the polar angle corresponds to $\theta $. The solid lines in Fig. 4(a) represent a sine-squared fitting given by ${y_0} + A{\sin ^2}\{{\pi ({\theta - {\theta_c}} )/B} \}$, where ${y_0}$, A, ${\theta _c}$, and B are the least-square fitting parameters. Thus, the axial ratio ${r_p}$ and the orientation angle $\psi $ ($- \frac{\pi }{2} \le \psi \le \frac{\pi }{2}$), which are basic parameters for describing the optical polarization, can be expressed in the following forms: ${r_p} = \sqrt {({{y_0} + A} )/{y_0}} $ and $\psi = \frac{B}{2} + {\theta _c}$. For instance, we obtain ${r_p} = 16.9$ and $\psi = 2.1$° from the experimental data shown in Fig. 4(a).

 

Fig. 4. (a) Polar plot for the polarization characteristics for A3 at ${T_b}$ = 35.0 K. The distance from the center to an open symbol indicates the bolometer output in a dB scale, whereas the polar angle corresponds to the WGP angle $\theta $. A solid line represents a sine squared fitting. (b) Polarization ellipse plotted using the experimentally obtained axial ratio ${r_p}$ and orientation angle $\psi $. (c) ${T_b}$ dependence of the normalized electric field amplitudes ${E_{0x}}$ and ${E_{0y}}$. The inset depicts the transition of the polarization anisotropy according to the ${T_b}$ change.

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Figure 4(b) shows a polarization ellipse plotted using the experimentally obtained values of ${r_p}$ and $\psi $. The electric $\; $ field vector at the detection plane is given by ${\boldsymbol {E}}(t )= {E_{0x}}exp [{i({\omega t + {\delta_x}} )} ]{\boldsymbol {i}} + {E_{0y}}exp [{i({\omega t + {\delta_y}} )} ]{\boldsymbol {j}}$, where the x and y axes are parallel to the mesa width and length, respectively, t represents time, ${E_{0x}}$ and ${E_{0y}}$ are the respective amplitudes, and ${\delta _x}$ and ${\delta _y}$ are the respective phase constants. A more detailed analysis of the full polarization parameters leads to a phase correlation between the synchronized mesa array [29].

In a pioneering study, the EM wave emitted from an elongated rectangular mesa was found to be polarized at a horizontal-to-vertical intensity ratio of ${E_{0x}}^2/{E_{0y}}^2\sim 3$ for mesas with $\ell /w\sim 3\textrm{ - }7$, where $\ell $ and w are the length and width of the mesa, respectively [2]. The anisotropic polarization ${E_{0x}} > {E_{0y}}$ arises from the predominance of the internal cavity mode excitation along the mesa width. In addition, the orientation angle $\psi $ is a good measure of the relative phase difference between EM oscillations along the x and y axes. For example, ${\delta _x} - {\delta _y} ={\pm} \pi /2$ gives $\psi = 0^\circ \; $ and ${\delta _x} - {\delta _y} = 0$ gives $\psi = 30^\circ $, when ${E_{0x}}^2/{E_{0y}}^2\sim 3$. However, in this study, we observed a linear polarization ${E_{0x}}^2/{E_{0y}}^2 > 250$ in the vicinity of $\psi \sim 0^\circ $. We attribute this remarkable polarization anisotropy to a mode-locking effect caused by the DPA pattern. Two pairs of the DPAs (DPA-1&2 and DPA-3&4) pump input EM energy into the internal cavity mode excitation along the mesa width, resulting in a linear polarization with ${E_{0x}} \gg {E_{0y}}$.

In Fig. 4(c), we plot the ${T_b}$ dependence of the normalized electric field amplitudes ${E_{0x}}$ and ${E_{0y}}$. Particularly, ${E_{0x}}$ reaches a peak at ${T_b}$ = 30 K, whereas ${E_{0y}}$ is almost zero over a wide range of ${T_b}$. The bolometer output and the FFT amplitude shown in Figs. 2(a) and 3(b), respectively, are consistent with the total intensity given by $P = {E_{0x}}^2 + {E_{0y}}^2$. Hence, the polarization analysis reveals that the internal cavity resonance along the width direction parallel to the $x$-axis dominates the integrated emission power. Unfortunately, it was impossible to measure the polarization characteristics for the high-${T_b}$ emission for the following reason. High-${T_b}$ emission inevitably occurs at an unstable and irreversible retrapping bias point [see arrows in Fig. 2(a)]. Therefore, when we rotate the WGP using a stepping motor to measure the polarization, the unstable bias state may unexpectedly switch to another state in the inner IVC branches due to either electrical or optical noises, resulting in the loss of the emission signal.

There remains another open question regarding the ${T_b}$ dependence of the emission intensity. The superfluid density and amplitude of the AC Josephson supercurrent should be increased with decreasing ${T_b}$. However, Fig. 4(c) reveals that the emission intensity decreases slightly at ${T_b}$ < 20 K, despite a systematic increase in the critical current density for A1–A4 (not shown here). In some extreme cases [14,20,30,31], the emission does not occur at ${T_b}$ below a certain value, even though the bias conditions are fully satisfied for matching the Josephson relation with the internal cavity resonance condition. Figure 4(c) shows that the far-field polarization ellipse becomes isotropic with decreasing ${T_b}$, as illustrated by the insets, leading to a reduction in the total intensity P. According to the patch antenna theory, the minimum anisotropy should be determined by an inverse mesa aspect ratio given by ${E_{0x}}/{E_{0y}} \ge \ell /w$ [29]. We expect that further investigations on the ${T_b}$ dependence of the optical polarization will significantly aid our understanding of the ${T_b}$ dependence of the emission intensity.

We now discuss the emission characteristics in the high-${T_b}$ state. Figure 3(b) shows that the intensity reaches a second maximum value at ${T_b}$ = 65 K. Note that the peak frequency ${f_p}$ = 0.42 THz is exactly one-half of that obtained from the low-${T_b}$ emissions. Since the effective wavelength of 170 µm does not coincide with any of the geometrical parameters such as w and ${w_a}$, the observed peak behavior is apparently inconsistent with the internal cavity mode. The emission modes for equilateral triangular Bi-2212 mesas were calculated in the literature [32] to analyze experimental results obtained using isosceles triangular mesas [33].

We attribute the enhancement of the emission intensity at 65 K to the excitation of the monopole resonance mode of the composite DPA patterns for the following reason. In the general antenna theory, a pair of identical monopole antennas connected via a common ground can work as a single dipole antenna. For instance, two triangular patch antennas (monopole antennas) facing each other can function as a single bow-tie antenna (dipole antenna) when they are electrically connected through their tips. Hence, when two opposite DPAs (e.g., DPA-1 and DPA-2) are connected to each other through the IJJ mesa with a small characteristic impedance, the resonance frequency for a fundamental monopole mode in a combined system is ${f_a}/2$. Further experimental studies on emission characteristics, such as the emission directivity and/or polarization analysis, would provide new insights into the accurate identification of the excited resonance mode.

4. Conclusions

In summary, we have proposed a planar patterned array of triangular microstrip patch antennas to control the basic characteristics of a superconducting terahertz emitter. Optimum design parameters were obtained using an EM simulation. We observed repeatable and stable emissions from all IJJ mesas over a wide ${T_b}$ range, although the enhancement of the integrated power that we expected initially was not observed using the present patterns. Nonetheless, we observed an intriguing plateau behavior and characteristic peak structure in the temperature dependence of the spectral characteristics. The occurrence of the plateau indicates a modification of the resonance condition owing to the presence of the DPAs near the emitting IJJ mesa. A remarkably high anisotropic polarization at an axial ratio of 16.9 indicates a mode-locking effect. The findings have significant implications in the construction of compactly assembled, monolithic, and broadly tunable superconducting terahertz sources, capable of emitting terahertz radiation with controlled characteristics.

Appendix: Simulation

We implemented an EM simulation using the Sonnet software to design a microstrip pattern of planar patch antennas compatible with the superconducting Bi-2212 terahertz emitter. Detailed specifications of the software are available at https://www.sonnetsoftware.com. Sonnet uses the method of moments applied directly to Maxwell’s equations to analyze high-frequency planar circuits. The proposed design is comprised of four DPAs made out of a silver layer deposited on top of a SiO₂ dielectric base layer. The fabrication process is described in the main text.

Here, we discuss three independent size parameters: the patch width ${w_a}$, patch height ${h_a}$, and thickness of the SiO₂ layer ${t_a}$. Refer to Fig. 1(a) in the main text for the geometry. According to antenna theory, the resonance frequency ${f_a}$ is determined primarily by ${w_a}$, whereas ${h_a}$ affects the resonance bandwidth. We adjusted these parameters to fit the fundamental resonant frequency ${f_a} = 0.75$ THz, which is the optimal value for the frequency band of the Schottky barrier diode detector used in the sub-terahertz heterodyne mixing experiment (not implemented in this study).

Figures 5(a) and 5(b) show the simulation results for the scattering parameter ${S_{11}}$ and input impedance ${Z_{\textrm{in}}} = R + jX$, respectively, for a single DPA with ${w_a} = 103$ µm, ${h_a} = 90$ µm, and ${t_a} = 0.6$ µm. R and X denote resistance (left axis) and reactance (right axis), respectively. The emergence of a sharp drop in S₁₁ and a characteristic peak at R at ${f_a}$ indicate the minimum return loss owing to the excitation of the dipole resonance (cf. $X = 0$ Ω). We found that the EM energy is transferred from the Bi-2212 mesa, which acts as an oscillation source, to the DPA due to impedance matching. The obtained ${w_a}$ reasonably coincides with the equivalent half wavelength of the EM standing wave in the SiO₂ layer with a dielectric constant of ${\varepsilon _a} = 3.9$. In addition, the simulated bandwidth of 64.5 GHz corresponds to a quality factor of approximately 12. The inset of Fig. 5(a) depicts the geometry of the optimized DPA with a color code indicating a snapshot of the calculated amplitude of the surface electric current density $|{{J_{xy}}} |$ at an arbitrary scale. Note that the linear enhancement of $|{{J_{xy}}} |$ at two boundary edges of the DPA arises from the skin effect of the high-frequency electrical currents.

 

Fig. 5. Simulation results for (a) scattering parameter ${S_{11}}$ and (b) input impedance ${Z_{in}}$ for the DPA pattern with ${w_a} = 103$ µm, ${h_a} = 90$ µm, and ${t_a} = 0.6$ µm. The inset of (a) depicts the geometry of the optimized DPA pattern with a color code indicating a snapshot of the calculated amplitude of the surface electric current density $|{{J_{xy}}} |$.

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Funding

Japan Society for the Promotion of Science (19H02540); Office of Science (DEAC02- 06CH11357).

Acknowledgments

The Bi-2212 single crystal was provided by T. Yamamoto at the University of Tsukuba. The authors thank V. K. Vlasko-Vlasov, A. E. Koshelev, and N. Fujita for the valuable discussions. Sample characterization was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering

Disclosures

The authors declare no conflicts of interest.

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