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Abstract
We present a miniaturized single nanoparticle detector that utilizes an optical star polygon microcavity with a 3 µm-radius. The microcavity supports high-quality factor resonant modes, with light localized at the corners of the star-shaped polygon, where the air region is situated. When nanoparticles are positioned at the corners of the microcavity, the light-matter interactions are enhanced. Notably, increasing the number of particles has little effect on the quality factor of the cavity, making it ideal for the simultaneous detection of multiple targets. Our numerical simulations demonstrate the high precision detection of polystyrene nanoparticles with a radius of 3 nm using this method. Furthermore, the size and number of nanoparticles can be determined by utilizing the triangular corners of the cavity as rulers. These findings represent a significant advancement in miniaturized and multi-target simultaneous nanoparticle detection. The proposed detector is expected to have a wide range of applications in various fields, including biomedicine and environmental monitoring.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Nanoparticle detection is a crucial technology with numerous applications, including environmental monitoring, disease diagnosis, human health and homeland security [1–4]. Due to their small size and ultra-low polarizability, single nanoparticle detection remains a challenging task [2,4,5]. Recently, various optical microcavities have attracted significant attention for their ability to enhance the interaction between light and matter [6–16], making them suitable for nanoparticle detection and sizing applications [17–24]. The sensitivity and detection limit in nanoparticle detection are mainly determined by the properties of the cavity, and noise sources during measurements can limit them [4,25]. Recent advancements have focused on enhancing sensitivity by utilizing novel microcavity structures that reduce mode volumes, localize mode fields, or introduce optical gain [3,21,26–32]. Additionally, researchers have attempted to suppress experimental noise to improve spectral resolution [1,33–35], thereby reducing the detection limit.
Whispering gallery mode (WGM) microcavities have been increasingly investigated for their potential in nanoparticle detection, and various detection mechanisms based on WGMs have been proposed [1,5,35–38]. These mechanisms include mode shift [39,40], mode splitting [26,37], and mode broadening [2,41], which offer high sensitivity in the detection of single nanoparticles. Despite recent advances, conventional nanoparticle detectors face limitations in practicality and usefulness in various applications due to their bulky nature and difficulty in simultaneously detecting multiple targets. The challenge of detecting multiple targets using conventional nanoparticle detectors arises from the fact that the microcavity mode is altered upon the detection of the first particle, which leads to variations in the subsequent particles’ influence on the microcavity. Consequently, a complex detection signal is produced, making it challenging to distinguish and identify multiple particles.
To address these limitations, we propose a miniaturized single nanoparticle detector based on an optical star polygon microcavity. The proposed design utilizes a microcavity with a high-Q resonant mode that concentrates light around the corners of the star polygon, where the air region is located, allowing for enhanced light-matter interactions when nanoparticles are deposited on the corners of the microcavity. Importantly, the quality factor of the microcavity is hardly affected by the presence of multiple nanoparticles, making it advantageous for simultaneous detection of multiple targets.
In this work, we numerically demonstrate that the proposed design can detect polystyrene nanoparticles with radii as small as 3 nm. Furthermore, the microcavity can be used to detect the number of nanoparticles present and size them using the triangular corners as rulers. This combination of features makes our proposed design a promising candidate for the miniaturization and multi-target simultaneous detection of nanoparticles.
2. Structure model and simulation method
One of the most commonly used methods for detecting nanoparticles using optical microcavities is the mode shift induced by their presence. When the size of the nanoparticles is much smaller than the probe wavelength, the angular frequency shift can be calculated using first-order perturbation theory and represented by [39,40]:
According to Eq. (1), the mode shift can be enhanced by carefully designing the cavity mode field to interact strongly with the nanoparticles. A straightforward approach to improve mode shift is to position the nanoparticles in regions of high electric field amplitude, i.e. to increase $E_0(\vec {r}_p)$. Typically, nanoparticle detectors utilize the evanescent field of a cavity mode to interact with the nanoparticles. In order to enhance the interaction between the optical field and nanoparticles, it is necessary to localize the cavity mode field in the air region.
A star-shaped microcavity, known as a star polygon microcavity, was first introduced as a means to improve the sensitivity of nanoparticle detection. The microcavity is fabricated by etching a silicon microdisk in the shape of a star polygon with equal length sides, as depicted in Fig. 1(a). The star polygon microcavity was designed with 44 vertices, achieving a balance between enhanced light-nanoparticle interactions and feasible fabrication. This configuration ensures sufficient light confinement and compatibility with microfabrication techniques. The star polygon cavity has an outer radius $r_{out}=3$ µm, an inner radius $r_{in}=2.4$ µm, and a thickness of 0.18 µm. Adjacent to the outer edge of the microcavity is a waveguide with a thickness of 0.18 µm and a width of 0.4 µm. The waveguide is used for efficiently directing light into and out of the microcavity. All optical responses of the structure are calculated using COMSOL software, where we performed 3D numerical simulations. The simulations allowed us to accurately capture the optical behavior of the star polygon microcavity, considering the full 3D geometry and its impact on the optical properties of the structure. To ensure that the mode shift was caused by the introduction of nanoparticles rather than the fluctuation of the mesh, we maintained a constant mesh before and after nanoparticle attachment.
Fig. 1. (a) Schematic diagram of the side-coupled optical star polygon microcavity to a waveguide. The input light enters from the right port of the waveguide and is detected at the left port. (b) Transmission spectrum of the coupled microcavity-waveguide system. The Lorentzian dip in the transmission corresponds to the resonant mode of the microcavity. (c) The normalized electric field intensity distribution of the resonant mode, with the inset showing a detailed view at the corner of the microcavity.
3. Results and discussion
Upon entering through the left port, light propagates through the waveguide and interacts with the microcavity before being detected at the right port. As shown in Fig. 1(b), a transmission spectrum is obtained, which displays a dip in the shape of a Lorentzian curve. The resonance wavelength, $\lambda _r$, is determined by locating the minimum of the transmission dip within its linewidth, $\delta \lambda _r$. In this study, the proposed star polygon microcavity demonstrates a resonant mode with a high quality factor of $9.07 \times 10^5$ at a specific wavelength of 1535.7073 nm. Figure 1(c) illustrates the electric field distribution of this resonant mode, revealing 44 antinodes that correspond to the 44 vertices of the star polygon. The highest electric field is localized at the triangular corners of the star polygon, located in the air region, resulting in enhanced light-matter interactions when particles are deposited at these regions.
The pronounced concentration of light in the star polygon microcavity is attributed to the self-similar electromagnetic boundary conditions that exist within the structure [42]. The dielectric discontinuities generated by the air wedges situated along the edges of the star polygon contribute to a significant heterogeneity in the dielectric material, leading to an increased electric energy density. This air wedge configuration is created through the iterative concatenation of slots and bridges, similar to the tip cavity discussed in reference [42], where the limiting case of multiple concatenations leads to the desired air wedge geometry. Consequently, the self-similar electromagnetic boundary conditions generate a strong electric field that is focused at the sharp edges of the air wedges.
The detection limit of a sensor is a critical parameter that characterizes its performance. In the case of the proposed star polygon microcavity, the detection limit is determined by both the resonance linewidth and the resonance shift. The quality factor, Q, defined as the ratio of the resonance wavelength to the linewidth $\delta \lambda _r$, is a key factor in determining the sensor’s performance. A higher Q value results in a narrower linewidth and better sensor sensitivity. The localized electric field at the corners of the star polygon microcavity enhances the light-matter interaction and can lead to a larger resonance shift. Therefore, the combination of the high Q and localized electric field in the air region of the star polygon cavity makes it a promising candidate for detecting very small nanoparticles.
The star polygon microcavity can be fabricated using advanced micro- and nanofabrication techniques. The fabrication process involved photolithography and mask preparation to define the microcavity structure. Electron beam lithography is employed to achieve subnanometer curvature radii at the corners. Laser ablation and surface treatment further refine the microcavity and optimized light confinement. Rigorous quality control and precise measurements ensure the reliability and reproducibility of the microcavity’s performance. As a result, the successful fabrication method can enable precise microcavity structures with subnanometer-level curvature radii and exceptional position precision, showcasing outstanding optical performance.
We numerically evaluated the performance of the star polygon cavity as a nanoparticle sensor by calculating the mode shift ($\triangle \lambda _r$) and linewidth of the microcavity mode after introducing nanoparticles. In experiments, a tapered fiber can be utilized to precisely transfer nanoparticles to specific positions at the corners of a star polygon microcavity [2]. The shift and linewidth of the microcavity mode were obtained from the transmission spectrum. We tested the cavity’s sensitivity by introducing polystyrene (PS) particles with a refractive index of 1.59 and radii ranging from 2 nm to 7 nm. Previous studies have established that the minimum detectable shift in resonance is typically a fraction of 1/50 to 1/100 of the reported mode linewidth, which can be as small as 6 fm and accurately measured [36,43]. Therefore, we used $\delta \lambda _r/50$ as the criterion for detectable mode shift.
Figure 2(a) illustrates the mode shift $\triangle \lambda _r$ and $\delta \lambda _r/50$ measurements of the microcavity upon the adsorption of individual PS particles with various radii. Our results indicate that for PS particles with a radius greater than or equal to 3 nm, $\triangle \lambda _r$ is larger than $\delta \lambda _r/50$, indicating that the nanoparticle can be detected from the transmission spectrum. We performed a second-order polynomial fitting to $\triangle \lambda _r$ and obtained a function that allows us to estimate the nanoparticle radius based on the mode shift. Additionally, we performed a first-order polynomial fitting to $\delta \lambda _r/50$, and the results suggest that $\delta \lambda _r/50$ remains relatively constant as the nanoparticle radius increases. This implies that the scattering of the nanoparticle does not significantly induce additional dissipation in this microcavity. As the linewidth remains relatively constant with the nanoparticle radius, the quality factor of the microcavity remains at a high level even after introducing the nanoparticle, which enhances the interaction between light and matter. Hence, the star polygon cavity can serve as a promising candidate for detecting nanoparticle size.
Fig. 2. (a) The mode shift $\triangle \lambda _r$ and 1/50 of the mode linewidth $\delta \lambda _r/50$ as a function of the radius of a single PS particle when the particle is localized at the corner of the star polygon cavity. (b) The normalized electric field of the resonant mode in the case of a single 3 nm-radius PS particle adsorbed on the corner of the cavity.
We note that in typical microcavities, the introduction of a nanoparticle can cause a reduction in the quality factor of the whispering gallery mode due to additional energy loss from the system. The scattering of light and absorption of energy from the cavity by the nanoparticle can result in an increase in the overall loss rate and a corresponding decrease in the quality factor. However, in the case of the star polygon cavity, a unique property is observed where the presence of a nanoparticle does not significantly affect the quality factor of the resonance mode. This phenomenon can be attributed to the cavity’s special geometry, which allows the light to be confined in multiple smaller sub-cavities that are isolated from each other. As a result, the scattering of light from the nanoparticle is limited to the sub-cavity where it is located (as shown in Fig. 2(b)), resulting in localized energy loss within this region. This effect is found to be responsible for maintaining the high quality factor of the microcavity even after introducing a nanoparticle.
The localized scattering of the nanoparticle is instrumental in preserving the high quality factor of the resonance mode, allowing the cavity to retain its high-quality factor even in the presence of the nanoparticle. This unique property renders the star polygon cavity an outstanding platform for investigating the characteristics of nanoparticles and their interaction with light, providing novel insights into the behavior of nanoscale systems in confined spaces.
We present the capability of our microcavity for simultaneous detection of multiple nanoparticles. The obtained results are depicted in Fig. 3, which displays the $\triangle \lambda _r$ and $\delta \lambda _r/50$ variations as a function of the number of particles. We applied a linear fit to both $\triangle \lambda _r$ and $\delta \lambda _r/50$ and observed excellent linearity. Specifically, Fig. 3(a) illustrates the $\triangle \lambda _r$ and $\delta \lambda _r/50$ for 3 nm-radius PS particles with different particle numbers. Our fitting results indicate that the linewidth remains constant as the number of particles increases. However, the shift increases linearly with the number of particles, enabling the simultaneous detection of multiple particles and estimation of the number of particles with the same radius.
Fig. 3. The mode shift $\triangle \lambda _r$ and 1/50 of the mode linewidth $\delta \lambda _r/50$ as a function of the number of 3 nm-radius PS particles (a), 7 nm-radius PS particles (b) and 7 nm-radius Si particles (c), when the particles are localized at the corner of the star polygon cavity.
The versatility of the microcavity for simultaneous detection of large-sized and high refractive index particles was further demonstrated by analyzing the resonance wavelength shift and linewidth as a function of the number of 7 nm-radius PS and silicon particles with the same radius. The results presented in Fig. 3 show that the linewidth remains constant regardless of the number of particles, including for large-sized and high refractive index particles. This observation confirms that the resonance wavelength shift maintains a linear relationship with the number of particles, which indicates the potential of the microcavity for detecting multiple particles simultaneously across a wide range of particle sizes and refractive index.
In the previous section, we demonstrated that the star polygon microcavity is an effective platform for detecting dielectric nanoparticles due to their scattering effect on light. Here, we further investigate its performance in detecting metallic nanoparticles, which have absorption properties. Figure 4(a) shows $\triangle \lambda _r$ and $\delta \lambda _r/50$ changes of the microcavity as a function of gold nanoparticle radius, ranging from 2 nm to 7 nm. It can be observed that the mode shift can be accurately fitted using a second-order polynomial as the gold nanoparticle radius changes. Additionally, the linewidth remains almost constant with increasing gold nanoparticle radius.
Fig. 4. (a) The mode shift $\triangle \lambda _r$ and $\delta \lambda _r/50$ of the microcavity mode as a function of gold nanoparticle radius from 2 nm to 7 nm. The mode shift can be accurately fitted by a second-order polynomial, while the linewidth remains almost unchanged. (b) $\triangle \lambda _r$ and $\delta \lambda _r/50$ as a function of the number of 3 nm gold particles. The mode shift shows a linear relationship with the number of gold particles, while the linewidth remains almost unchanged.
Figure 4(b) illustrates the dependence of $\triangle \lambda _r$ and $\delta \lambda _r/50$ on the number of 3 nm gold particles. The plot indicates that $\triangle \lambda _r$ exhibits a linear relationship with the number of gold particles, and the linewidth remains almost constant with increasing gold particle number. These findings suggest that the star polygon microcavity can effectively detect metallic nanoparticles based on the mode shift induced by the absorption effect.
Our results demonstrate that the star polygon microcavity is a versatile platform for detecting both dielectric and metallic nanoparticles with high sensitivity and accuracy. These findings have significant implications for applications in various fields, including biomedicine, environmental monitoring, and chemical sensing.
Practically, due to the limitations of micro- and nanofabrication techniques, it is difficult to fabricate perfectly sharp angles [44], so we must consider whether the star polygon cavity with rounded corners still has the good performance in detecting nanoparticles as discussed previously. We calculated the performance of nanoparticle detection for the cavity with different curvature radii at its corners. Figures 5(a)–5(c) show the mode shift of the microcavity as a function of the PS nanoparticle radius for the corner curvature radii of R = 1 nm, 2 nm, and 3 nm, respectively. The results show that, at different curvature radii, the mode shift can still be accurately fitted by a second-order polynomial as the gold nanoparticle radius changes. This indicates that the mode shift of this microcavity can be used to measure the size of nanoparticles.
Fig. 5. Upper panel: Mode shift $\triangle \lambda _r$ and $\delta \lambda _r/50$ of the microcavity as a function of PS particle radius with different curvature radii of the corners of the star polygon cavity, (a) R = 1nm, (b) R = 2nm, and (c) R = 3nm. Inset shows the field distribution of the resonant mode when a PS particle with a radius of 8nm is present in the microcavity, highlighting the structure of the corner with a curvature radius of R=3nm. Bottom panel: Mode shift $\triangle \lambda _r$ and $\delta \lambda _r/50$ of the microcavity as a function of the number of 3nm PS particles with different curvature radii of the corners of the star polygon cavity, (d) R = 1nm, (e) R = 2nm, and (f) R = 3nm.
Figures 5(d)–5(f) show the variation of the mode shift as the number of 3 nm PS nanoparticles increases for the corner curvature radii of R = 1 nm, 2 nm, and 3 nm, respectively. It can be seen that, at different curvature radii, the mode shift is linearly proportional to the number of nanoparticles. However, as the curvature radius of the corner increases, the slope of the linear fit decreases, indicating that the sharper the corner, the better the localization of light, and the greater the interaction between light and matter, resulting in a larger mode shift for nanoparticle detection. In the previous calculations, the mode linewidth almost did not change with the increase of nanoparticle radius or number.
In practical microcavity fabrication, achieving uniformity in the vertex positions and the corner curvature radii of the star polygon cavity is challenging. We performed tolerance analysis to assess the performance of the microcavity as a detector when considering imperfections introduced during micro-nano fabrication. In our calculations, we considered deviations in both the vertex positions and curvature radii. The curvature radii of the corners were randomly set in the range [1 nm, 3 nm]. The deviation for the vertex positions was set to random values within the interval [$-\sigma$, $\sigma$].
We calculated the variation in the microcavity’s quality factor and its detect limit for PS particles as $\sigma$ increased, as shown in Fig. 6(a). As $\sigma$ increased, the microcavity’s quality factor decreased, and the minimum detectable radius of PS particles also increased. However, the microcavity’s ability to localize the optical field at the corners remained, enhancing the interaction between nanoparticles and the optical field. This ensured that the microcavity maintained excellent sensitivity as a detector. Even when $\sigma$ was as large as 10 nm, the microcavity could still detect PS particles with a radius as small as 11 nm.
Fig. 6. (a) Impact of tolerance analysis on microcavity performance. The plot shows the variation in the microcavity’s Q and its minimum detectable PS (polystyrene) particle radius as the vertex position deviation $\sigma$ increases, the curvature radii of the corners were randomly set in the range [1 nm, 3 nm]. (b) Multi-target detection in the microcavity. The plot illustrates $\triangle \lambda _r$ and $\delta \lambda _r/50$ variation as the number of 11 nm radius PS particles increases.
To validate the microcavity’s capability for simultaneous multi-particle detection, we set the curvature radii of the cavity’s corners as random numbers within the range of [1 nm, 3 nm], and the vertex position deviation $\sigma$ was set at 10 nm. We conducted calculations to analyze the variation in mode shift and linewidth as we increased the number of 11 nm radius PS particles within the microcavity, the results are shown in Fig. 6(b). Similar to our previous analysis, we performed first-order polynomial fitting on $\triangle \lambda _r$ and $\delta \lambda _r/50$. We observed that $\delta \lambda _r/50$ remained relatively constant with an increasing number of particles. The mode shift exhibited a linear relationship with the number of particles, and any minor deviations can be negligible compared to the overall shift.
These results demonstrate the microcavity’s robustness in detecting multiple particles simultaneously, with minimal impact on the mode properties as more particles are introduced. With current micro-nano fabrication techniques, it is possible to sharpen the corners to a curvature radius of subnanometer scale [42,45]. Furthermore, advancements in nanofabrication technologies enable us to achieve position precision at the subnanometer level [46]. These results demonstrate that this microcavity can be used for simultaneous detection of multiple nanoparticles and measurement of nanoparticle size, which is feasible in experiments.
4. Conclusions
In summary, we have presented a novel miniaturized optical star polygon microcavity, which allows for the simultaneous multi-target detection and sizing of single nanoparticles with remarkable sensitivity and accuracy. The distinctive features of the star polygon cavity make it an excellent alternative to conventional whispering gallery mode cavities, particularly in its ability to sustain a high quality factor even in the presence of multiple nanoparticles. Our numerical results demonstrate that the microcavity can detect and size nanoparticles of varying sizes and refractive indices, suggesting its potential applications in diverse fields such as biological sensing, environmental monitoring, and chemical analysis. The proposed microcavity represents a promising solution for high-throughput and label-free detection of single nanoparticles, and is expected to stimulate further research in the field of nanophotonics and optical sensing.
Funding
National Natural Science Foundation of China (12274192, 62075194, U21A6006); Natural Science Foundation of Shandong Province (ZR2022MA080).
Acknowledgments
This work was supported by the National Supercomputer Center in Guangzhou.
Disclosures
The authors declare no conflicts of interests.
Data availability
Data that support the findings of this study are available from the corresponding author upon reasonable request.
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