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Abstract
This study proposed what we believe to be a novel method for fabricating superconducting nanowire single-photon detectors (SNSPDs) with high efficiency, polarization insensitivity, and ultrafast response. To achieve these properties in niobium nitride (NbN) SNSPDs, the periodic four-split rings (PFSR) were positioned above the nanowires. This design uses the localized surface plasmon resonance to enhance the electric field around nanowires. For an incident light with a wavelength of 1550 nm, the PFSR-SNSPD structure achieved a polarization extinction ratio of 1.0064 and absorptions of 88.94% and 88.37% under TE and TM polarizations, respectively. The nanowire length was reduced by 85% using a meandering nanowire arrangement with a fill factor of 0.074.
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1. Introduction
Superconducting nanowire single-photon detectors (SNSPDs) exhibit high detection efficiency [1], low dark count rate [2], high resolution [3], and high-speed detection [4] in the near-infrared band. They are widely applicable in quantum information encryption [5], deep space communication [6], and laser radar [7]. However, the meandering nanowire structure limits the application of SNSPDs in quantum-key distribution [8], owing to the inherent absorption polarization sensitivity of these detectors. Using polarization-insensitive SNSPDs can eliminate polarization-related efficiency mismatches. Previous studies reduced the polarization sensitivity of nanowire absorption while maintaining high detection efficiency. The demand for polarization-insensitive SNSPDs with ultrafast response, large detection areas [9], and high detection efficiencies has increased owing to the development of quantum encryption [10,11].
Current research methods for reducing the SNSPD polarization sensitivity alter the shape or spatial distribution of nanowires. This involves using helical nanowire structures [12–14] to improve the device symmetry, designing planar orthogonal structures based on local and global self-similarities [13], and employing fractal structures or microstrip line structures [15–20]. Three-dimensional spatial distribution can be investigated using WSi orthogonal double-layer nanowires [21] to decrease the polarization sensitivity. However, this method requires high precision to maintain the smoothness between the upper and lower layers of nanowires. Another approach analyzes the classical electromagnetic field theory, revealing that the polarization sensitivity of nanowire absorption is caused by the low electric-field intensity regions near the boundaries of nanowires inside. The refractive indices become isotropic by filling the nanowires with high permittivity media [22], thereby enhancing the electric field around the nanowire and reducing its sensitivity to incident light with different polarizations. The aforementioned SNSPDs were designed to balance high system-detection efficiency and polarization-insensitive nanowire absorption. However, the filling factor in these designs affects the absorption efficiency, and there is a trade-off between reducing the filling factor and achieving high absorption efficiency. Fill factor is usually defined as a ratio of wire width to pitch. In conventional SNSPDs, the filling factor of the nanowires is 0.5. Recently, fractal structures have achieved a maximum system efficiency of 84% at a wavelength of 1550 nm with a nanowire filling factor of 0.33 and polarization sensitivity of 1.02. The performance of SNSPDs is enhanced by reducing the nanowire filling factor, which results in a lower kinetic inductance, shorter reset time, and faster response speed, expanding the applicability of polarization-insensitive SNSPDs. However, designing SNSPDs that can simultaneously achieve high detection efficiency, ultrafast response, and polarization insensitivity remains challenging.
Metallic four-splitting ring resonator (FSRR) metamaterial structures have attracted attention owing to their excellent characteristics. When excited by incident waves, the circular current distribution generates intense resonances in the gaps and inner surfaces of the metal rings. This phenomenon enhances the electric field intensity within the gaps and rings, concentrating the energy around the ring circumferences. This unique property forms the basis of this study. The simulations revealed that the electric field intensity around the nanowire increased by placing it in the near-field region of the split-ring resonator and aligning it along the gap direction. The energy concentrated around the nanowires was fully absorbed. The electric field intensity at the nanowire boundaries can be enhanced by adjusting the four gap angles and the inner and outer ring diameters. This optimization eliminates the polarization sensitivity of nanowire absorption, and the structure achieves a negligible nanowire filling factor.
This study used a novel approach to eliminate the polarization sensitivity of SNSPDs and employed a negligible filling factor, resulting in the sparse arrangement of nanowires. In contrast to the methods that alter the nanowire shape or fill its surroundings with a medium, a metal FSRR metamaterial structure was placed above the nanowire. This structure enhanced the low electric field regions around the nanowire boundaries. The metal FSRR was integrated with the SNSPDs, resulting in a metal–insulator–metal nanocavity structure. The resonance peaks for TE and TM polarizations were shifted to 1550 nm by adjusting the inner and outer diameters, gap angles of the upper split-ring resonator, and overall device cavity length, resulting in the maximum polarization-insensitive absorption of the nanowire. The refractive index parameter of NbN was used as a representative nanowire material setting for simulation in this study. The simulation results show that the nanowire absorption efficiency for both polarizations at 1550 nm exceeded 88.37% and the measured polarization extinction ratio was 1.0064. Compared with the conventional design with a serpentine arrangement and filling factor of 0.5, the proposed approach achieved a negligible filling factor of 0.074, resulting in a response time 6.75 times faster than that of the conventional design. Therefore, SNSPDs exhibit high efficiency, ultrafast response, and polarization insensitivity.
2. Method
Figure 1(a) shows the diagram of the periodic four-split rings SNSPD (PFSR-SNSPD) unit. A plane wave with a central wavelength of 1550 nm was vertically incident along the z-axis. The entire structure unfolded with a unit-cell period of p = 1.35 µm, and the upper layer comprised a 95 nm-thick gold FSRR. Figure 1(b) shows the top view of unit cell, featuring the gold FSRR. The outer and inner radii were d1 = 430 nm and d2 = 250 nm, respectively. The gold FSRR comprises four parts, each corresponding to a central angle of 80.25°. The gaps parallel and perpendicular to the nanowire were measured as 14° and 5.5°, respectively. The bottom layer comprised a 100 nm-thick gold mirror that reflected the incident energy. A 630 nm-thick SiO2 cavity was formed between the upper gold FSRR and bottom gold mirror, and the meander nanowire was positioned within the cavity at a distance of 10 nm from the upper gold FSRR. The nanowire was 100 nm wide and 5 nm thick with a filling factor of 0.074. The refractive indices of SiO2, NbN nanowires, and gold at a wavelength of 1550 nm were 1.444, 5.23 + 5.82i, and 0.559 + 9.81i [23], respectively. The dispersion relation of the Lorenz–Drude model was used to calculate the gold constants at other frequencies [24]. The model was simulated using the time-domain finite-difference method.
Fig. 1. (a) Schematic of the PFSR-SNSPD unit. A plane wave is vertically incident on the device. The entire unit cell has a period of p, and the metal FSRR (shown in gold) is placed on top. (b) Detailed illustration of the gold FSRR, with each section spanning a central angle of 80.25°, θ1 = 5.5°, and θ2 = 14°. The outer and inner radii are denoted as d1 and d2, respectively. The nanowire (shown in gray) with a width w is located within the resonant cavity (indicated in blue) below the metal FSRR. The gold mirror is situated beneath the resonant cavity to serve as a reflector.
3. Results and analysis
When the light with a central wavelength of 1550 nm was vertically incident along the z-axis, the best results were obtained by optimizing the inner and outer radii of FSRR, horizontal and vertical gap angles, and device cavity length. Figure 2 shows the simulation results. The absorption peaks of nanowires coincided at 1550 nm and the absorption efficiencies were 88.94% and 88.37% for the TE and TM polarizations, respectively. The measured polarization extinction ratio was 1.0064. The results confirm the feasibility of using FSRR to enhance the electric field around nanowires and achieve high-efficiency polarization-insensitive absorption. The SNSPDs demonstrated a negligible filling factor of 0.074, therefore, SNSPDs have a low kinetic inductance that increases the response speed in nanowires. The optical losses within the system have also been analyzed. A proportion of these losses (approximately 5.96%) can be attributed to the gold split-ring resonator loss and reflection loss. The underlying gold reflector mirror comprised approximately 4.9% of the total losses. To sum up, the absorption rate of gold is much smaller than the NbN nanowires’, which is attributed to the fact that the imaginary part of the NbN dielectric constant is about 6 times of the gold's.
The Fano resonance generated in the microwave [25] and terahertz [26] frequency bands by the circular current distribution in metal split-ring resonators has attracted attention. This resonant optical field localization property has been used in the near-infrared [27] wavelength range to enhance the absorption efficiency of nanowires in SNSPDs. For the 1550 nm-wavelength vertically incident light, the metal FSRR exhibited strong resonances within the ring at the metal-dielectric boundaries and gaps. This is attributed to the localized surface plasmon resonance [28,29], as shown in Figs. 3(a) and 3(b). The top FSRR structure significantly enhanced the electric field around the nanowire under TE and TM polarizations. The electric field distribution in the z direction is given in Figs. 3(c) and 3(d). It can be seen that all the field energy is concentrated between the nanowires and the FSRR structure. Hence, polarization-insensitive absorption was achieved by the electric-field enhancement property of this structure, which elevated the low electric field boundary of nanowires. Notably, the highest electric field intensities in TE and TM polarizations were located in the y- and x-direction gaps, respectively. The two polarizations induce current inversion in FSRR owing to the proportionality between the electric field intensity and current density. For TE polarization, current inversions occurred in the left and right parts of the resonator, whereas for TM polarization, they occurred in the top and bottom parts. These inversions resulted in circular current distributions with equal amplitudes, forming a trapping mode. The gap was located at the standing wave node, exciting the standing wave resonance. The two resonant modes that were formed within the nanocavity strongly confined the energy within FSRR, resulting in high absorption efficiency of nanowires.
Fig. 3. Electric field distribution upper the surface of the nanowires (a) TE and (b) TM polarizations at the wavelength of 1550 nm. Electric field distribution in z direction below FSRR (c) TE and (d) TM polarizations at the wavelength of 1550 nm.
Based on the strong near-field enhancement at the gaps perpendicular to the incident polarizations in Figs. 3(a) and 3(b), the influence of varying the gap angles in the x- and y-directions on the absorption efficiency of nanowires under TE and TM polarizations was investigated. Figures 4(a), 4(b), and 4(c) show the wavelength-dependent absorption efficiency for different polarizations at the y-direction gap angles of 8°, 5.5°, and 4.5°, respectively. The absorption efficiency peak of the nanowires under TE polarization shifted toward longer wavelengths as the gap angle decreased. At the gap angle of 4.5° under TE polarization, the increased area of gold resulted in the decrease of the absorption efficiency. Contrastingly, the absorption efficiency was constant under TM polarization. Hence, this efficiency is sensitive to the y-direction gap angles under TE polarization. The absorption efficiency peak for TM polarization shifted toward longer wavelengths with decreasing gap angles, whereas the absorption curve remained unaffected for TE polarization. This corresponds to the sensitivity of absorption efficiency to the x-direction gap angles under TM polarization. For the y-direction gap angle θ1 at 5.5° and x-direction gap angle θ2 at 14°, both polarization-dependent absorption peaks were located at 1550 nm. This combination of FSRR gap angles resulted in nanowire absorption without polarization sensitivity. Furthermore, the variation in the gap angles along different directions shifted the peak positions of polarization-dependent absorption. This is consistent with the observations in Figs. 3(a) and 3(b), where different polarizations maximize the electric field at the gap position perpendicular to the incident light.
Fig. 4. Under TE and TM polarizations, the absorption efficiency of the nanowire varies with wavelength for different y-direction gap angles (θ1) (a) 8°, (b) 5.5°, and (c) 4.5° at a constant x-direction gap angle (θ2 = 14°), and different x-direction gap angles (θ2) (d) 16°, (e) 14°, and (f) 12° at a constant y-direction gap angle (θ1 = 5.5°).
Without altering the upper FSRR structure, the variation in cavity length influenced the absorption peak position of nanowires under different polarizations of incident light. The nanowire absorption efficiency was simulated for two different light polarizations at cavity lengths of 610, 630, and 650 nm. Figure 5 shows the nanowire absorption efficiency as a function of wavelength for TE and TM polarizations. For various cavity lengths, the peak absorption efficiency for both polarizations remains consistent and shifts toward longer wavelengths. Under TM polarization, the absorption efficiency exhibits an initial increase followed by a decrease, whereas under TE polarization, it gradually increases. At the cavity length of 630 nm, the nanowire exhibits peak absorption efficiency at 1550 nm for both polarizations. The absorption efficiencies were 88.94% and 88.37% for TE and TM polarizations, respectively, differing by only 0.57%. This confirms the polarization-insensitive absorption exhibited by the designed cavity length.
Fig. 5. Absorption efficiency curves of nanowires under TE and TM polarizations with cavity lengths of 590 nm, 630 nm, and 670 nm.
Figures 6(a) and 6(b) show the effect of different nanowire widths on the absorption efficiency and absorption peak under TE and TM polarizations, respectively. The influence of size variations during nanowire fabrication on the polarization sensitivity of nanowire absorption efficiency was studied. In the aforementioned cavity, simulation calculations were performed for the NbN nanowires with widths of 90, 100, and 110 nm under TE and TM polarizations. The absorption efficiency increased with increasing nanowire width under the two polarizations. However, the difference in the sensitivity of nanowire absorption efficiency varied the width, which was more pronounced under TM polarization. The can be explained as follows: As the upper FSRR configuration remained unchanged, the electric field at the nanowire boundary increased with the increasing width of nanowire owing to its expanded boundary. As shown in Fig. 3(b), the electric field around FSRR decays from the slit toward the surroundings under TM polarization. Increasing the nanowire width implies placing the nanowire in a stronger electric field, which is advantageous for TM polarization. However, the variation in electric field intensity at the nanowire boundary caused by the widening of nanowire was relatively small under TE polarization. A 100 nm-wide nanowire was selected based on its high absorption efficiency with polarization insensitivity and low nanowire filling factor. The device performance was minimally affected by minor fabrication errors.
Fig. 6. Absorption efficiency of nanowires with widths of 90 nm, 100 nm, and 110 nm as a function of wavelength under (a) TE and (b) TM polarizations
4. Discussion
SNSPDs exhibit exceptional detection efficiency, minimal dark counts, and rapid detection speeds. These characteristics are associated with the following key metrics: absorption efficiency, dark count rate, kinetic inductance, and effective detection area. SNSPDs face new challenges owing to the development of fields, such as quantum communication. These challenges go beyond the previous focus on improving single-performance characteristics, such as high detection efficiency or large detection area. Conversely, a growing need has been observed to simultaneously address multiple features, including rapid detection, multi-wavelength capability, and polarization insensitivity. This broader set of characteristics may expand the applicability of SNSPDs. For instance, achieving high efficiency and polarization insensitivity in devices relies on auxiliary cavity structures. Accelerating the response times by reducing the nanowire fill factor may improve device efficiency and increase sensitivity. Therefore, the development of novel research methods and device structures is essential.
The proposed PFSR-SNSPD simultaneously achieves the following three crucial features: high detection efficiency, ultrafast response speed, and polarization insensitivity. Compared to conventional meander nanowire designs, the response speed of efficient and polarization-insensitive SNSPDs was enhanced by a factor of 6.75. Hence, SNSPDs can reduce error rates and enhance the detection speed when applied to a quantum key distribution.
The expansion of polarization-insensitive SNSPDs with ultrafast response speed has a key limitation of further reducing the nanowire fill factor. This reduction necessitates an increase in the size of the upper split-ring resonator and underlying gold reflector mirror, thereby increasing the metallic losses. The proposed SNSPD structure exhibited an ultrafast response speed while maintaining a high detection efficiency without polarization sensitivity, signifying its potential in quantum key distribution.
5. Conclusion
We designed a novel SNSPD structure with high detection efficiency and speed, which simultaneously exhibits polarization insensitivity within the wavelength of 1550 nm. The split rings, which were configured into a mutually orthogonal four-aperture structure, enhanced the near-field at their apertures for various incident polarization states. This generated a significant field intensity distribution within the dielectric region of the ring. The NbN nanowires were strategically placed along one pair of apertures, resulting in nanowires with nearly consistent absorption efficiency when subjected to incident light of any polarization.
By combining this structure with a resonant cavity, absorption efficiencies of 88.94% and 88.37% were achieved at a wavelength of 1550 nm for parallel and perpendicular polarizations, respectively. Consequently, a polarization extinction ratio of 1.0064 was obtained. Owing to the light-field localization properties of FSRR over various periodicities, a negligible filling factor of 0.074 was achieved. By reducing the filling factor while maintaining a constant nanowire width, the nanowire length was decreased by 85.2% compared to the traditional nanowire lengths. This resulted in faster detection rates for practical applications. Therefore, integrating the PFSR structure into SNSPDs is a novel approach to realize high-efficiency and high-speed detectors that are insensitive to polarization.
Funding
the Innovation Program for Quantum Science and Technology (2021ZD0303401); Quantum Science Strategic Project of Guangdong Province (GDZX2306004); Basic and Applied Basic Research Foundation of Guangdong Province (2022A1515140139); National Natural Science Foundation of China (61801183, 62375089).
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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