Miniature resonator sensor based on a hybrid plasmonic nanoring

Xiaoming Ma; Xiaoming Ma; Shuzhen Fan; Shuzhen Fan; Shuzhen Fan; Heming Wei; Zhiyuan Zuo; Zhiyuan Zuo; Sridhar Krishnaswamy; Jiaxiong Fang; Jiaxiong Fang

doi:10.1364/OE.27.033051

1. Introduction

Optical microcavities are widely used for sensing applications in a variety of scientific disciplines ranging from fundamental science to engineering physics [1–3]. Among them, dielectric whispering-gallery mode (WGM) microcavity sensors based on microrings [4,5], microdisks [6–8], microspheres [9,10] and microtoroids [11] have attracted much attention due to their ultrahigh quality (Q) factors. However, there is a trade-off in confining the energy inside of the cavity body to obtain high Q-factor and the resulting sensitivity for optical resonator sensors. Specifically, the condition of energy confined in the cavity increases the Q-factor of the structure; but degrades the sensitivity and vice versa. Active research is ongoing to find the optimal geometry that attempts to maximize both factors [12]. In addition, the diffraction-limited size of these cavities, a cubic half-wavelength in material [13], restricts further miniaturization of photonic devices. In contrast to the dielectric cavities, plasmonic cavities are not limited by this and can in essence support a subwavelength mode volume [14]. However, they are inherently lossy. As such, hybrid plasmonic WGM resonators have been proposed as one of the most appealing candidates that could offer an effective solution to combine advantages of both devices. Sensors based on hybrid plasmonic WGM resonators not only possess high sensitivity, but also shrink the size of the device by orders of magnitude. Recently, people have developed various hybrid plasmonic microcavities for sensing applications, e.g. the hybrid plasmonic nanodisk [15], microring [16,17] and microtoroid [18], the hybrid plasmonic submicron-donut resonator [19] and plasmonic metamaterial arrays [20–23], etc. Currently, most researches in this field focus on silicon and silica, owing to the mature complementary-metal-oxide-semiconductor (CMOS) technology. However, these materials are not always the perfect choices under some severe conditions.

Diamond, known for its stable physical and chemical properties [24–26], including high thermal conductivity, biocompatibility, durability, chemical inertness, mechanical hardness, and a wide optical transparency window, from vacuum ultraviolet through the infrared, has attracted significant attention. Recently-developed methods of mass fabrication of inexpensive, high-purity diamond crystals have significantly promoted their use in a compact microcavity resonator [27,28]. Therefore, the hybrid plasmonic diamond WGM resonators, owing to combination of the exceptional sensitivity of the plasmonic WGM resonances to the ambient refractive index (ARI) changes and the robust physical properties of diamond, have great potential for sensing applications.

In this paper, we propose a compact hybrid plasmonic diamond nanoring (PDNR), including a layer of gold uniformly coated on the outer boundary. Simulation results reveal that this kind of diamond nanoring can exhibit high sensitivity of 339.8 nm/RIU, which is superior to many WGM-based microcavity resonator sensors [29]. The highest Q factor can reach ∼60,000 with this nanoring and the minimum detection limit is very low at 1.5 × 10⁻⁴ RIU. Here, the proposed PDNR has a compact structure. With the discussion of the resonant shifts and Q factors with the central holes of octagonal, dodecagonal, hexadecagonal and icosagonal prisms, respectively, it is shown that PDNR resonant sensor, when appropriately characterized upon fabrication, can function with high performance for highly sensitive ultracompact sensing applications.

2. Structure and basic theory

The cross section of the proposed PDNR is shown in Fig. 1, whose radius R and height h are 600 nm and 100 nm, respectively. A layer of gold with the width, w_Au, is uniformly coated on the boundary of the nanoring. The host material of the nanoring is pure silica, whose dispersion relationship can be calculated by the Sellmeier equation [30]. The dielectric constant of gold is determined by the Drude-Lorentz model [31], which is written as:

(1)$$ {\varepsilon _{Au}} = {\varepsilon _\infty } - \frac{{\omega _D^2}}{{\omega (\omega + j{\gamma _D})}} - \frac{{{\Delta }\varepsilon \cdot {\Omega }_L^2}}{{({\omega ^2} - {\Omega }_L^2) + j{{\Gamma }_L}\omega }}, $$

where ɛ_Au is the permittivity of the gold, ɛ_∞ is the permittivity at high frequency with a value of 5.9673, ω is the angular frequency expressed as ω = 2πc/λ, where c is the velocity of light in vacuum, ω_D is the plasmon frequency given by ω_D/2π = 2113.6 THz, γ_D is the damping frequency represented by γ_D/2π = 15.92 THz, and $\varDelta$ɛ is the weighting factor with a value of 1.09. Spectral width and oscillator strength of the Lorentz oscillators are expressed as $\varGamma$_L/ 2π = 104.86 THz and $\varOmega$_L/2π = 650.07 THz, respectively.

Fig. 1. (a) Schematic and (b) cross section view (purple rectangular in (a)) of the studied PDNR.

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From the point of view of wave optics, the resonance wavelength in the whispering gallery mode resonator can be written as [32]:

(2)$$ \lambda = \frac{{2\pi r{n_{eff}}}}{m},$$

where r is the radius of the nanoring, n_eff is the effective RI of the optical mode, and m is the azimuthal mode number, which is an integer representing the WGM angular momentum. Any wavelength that satisfies Eq. (2) can be regarded as the resonance wavelength of a WGM resonator. The resonance wavelength shifts accordingly as the n_eff changes. The evanescent field of the resonant light along the WGM resonator can reach several nanometers into the ambient medium (e.g., different liquids/chemicals) and effectively interact repeatedly with the analytes near the resonator’s surfaces.

The sensing mechanism of a resonator sensor involves measurement of the resonance shift which is induced by the interaction between the analyte and the mode field of the resonator. When the analyte is attached to the resonator’s surfaces, the n_eff of the resonator will increase. According to the first-order perturbation theory, the angular frequency shift ($\varDelta$ω) is given by [33]:

(3)$$ \frac{{{\Delta }\omega }}{\omega } \cong - \frac{{{\alpha _{ex}}{{\left| {E({r_d})} \right|}^2}}}{{2\int {\varepsilon (r){{\left| {E({r_d})} \right|}^2}d{V_m}} }},$$

where ω is the angular frequency, α_ex is the polarizability of the analyte, E(r_d) is the electric field amplitude at the position r_d, V_m is the volume of the WGM, and ɛ(r) and E(r) are the permittivity and the electric field amplitude of the resonator, respectively. It can be seen that the sensitivity is related to the electric field intensity. Accordingly, it is necessary to increase the proportion of the electromagnetic field in a resonator that interacts with the analytes to achieve higher sensitivity.

3. Simulation results

The Lumerical three-dimensional (3D) finite-difference-time-domain (FDTD) method is used to investigate the light guiding properties, and two-dimensional (2D) FDTD method is used for sensing performance of the proposed PDNR. Realistic material parameters are used, and the influence of the silica substrate is taken into account. The mesh size is set to 1 nm in the vicinity of the whole system. Regarding the FDTD box, the type of boundary conditions is the perfectly matched layer (PML) with a thickness of 1µm, defined on all surfaces of the computational domain, allowing to simulate an infinite domain while minimizing reflections. And two frequency-domain field profile (DFT) monitors, which are 2D Z-normal and 2D Y-normal, are setup with full apodization, respectively, to obtain the accurate intensity profiles of the electrical field in the structure.

First, we investigate the WGM mode distributions of the PDNR. The WGM profile of the resonant light for the bare diamond nanodisk without gold coated on the outer boundary is shown in Fig. 2(a), while Fig. 2(b) shows that of the PDNR possessing the same radius and height as the nanodisk. Their resonance wavelengths are 369 nm and 637 nm, respectively, which are consistent with Eq. (2). Comparing Fig. 2(a) with 2(b), it can be seen that the azimuthal mode number of the resonant light in the bare diamond nanodisk is much larger than that of PDNR. This has been theoretically proved by Wiersig in [34], and the reason is the hole in the center of the nanoring affects the light mode of the microcavity, and consequently reduces the azimuthal mode number significantly. As visualized in Fig. 2(c), the plasmonic effect due to the uniformly coated gold on the outer boundary of the PDNR makes the mode profile on the cross section move towards the outside, which is beneficial for the detection of ambient environment.

Fig. 2. WGM field distributions in (a) the bare diamond nanodisk and (b) the studied PDNR, respectively. (c) Cross-sectional field distribution of a fundamental WGM in the studied PDNR.

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The optimization process for determining the coating thickness w_Au is presented in Fig. 3. We numerically study the relationship between the resonance wavelength of the diamond nanodisk and the thickness of gold uniformly coated on the outer boundary to determine the optimum thickness. As shown in Fig. 3(a), all the resonance wavelengths redshift as ARI increases when w_Au =0, 10, 20, 30, 40 and 50 nm, respectively. When ARI increases above 1.35 for thicker plasmonic gold ring, the WGM mode is less confined in the nanodisk and very lossy. Under that condition, the fundamental resonant mode disappears. That is the reason for the cuts of the lowest curves in Figs. 3(a) and 4, when ARI values are over 1.35. Figure 3(b) shows the total net resonance shifts and the sensitivity for each specific w_Au. It can be clearly seen that the shift is greater, when w_Au is set at 20 nm, which implies that 20 nm is the optimized value for w_Au for sensing applications. The spectral response of the diamond plasmonic nanodisk is illustrated in Fig. 3(c). It shows that the resonance wavelength shifts of the fundamental mode for various ARI for w_Au=20 nm. When ARI changes from 1.0 to 1.5 (with a step of 0.1), the resonance wavelength redshifts across a wide range of 24.3 nm. From that figure, we can also see the redshift of the resonance wavelength and resonance width increases slightly with ARI. To determine the quality of resonance and achievable electromagnetic field enhancement near the metal, we introduce the dephasing time T₂, which is defined by considering the resonance narrowness as follows [35]:

(4)$${T_2} = 2\hbar /\Delta {\nu _{FWHM}} = 2\hbar \Delta {\lambda _{FWHM}}/c,$$

where ℏ is the Planck’s constant and c is the speed of the light in vacuum. For example, for ARI=1.3 the full width at half maximum of resonant peak (Δλ_FWHM) is as narrow as 0.06 nm. Accordingly, the dephasing time is estimated as 6.4×10⁻⁵ fs, representing the diamond plasmonic nanodisk has high quality of resonance. The little resonant peaks for the purple graph between 655 nm and 660 nm represent higher order modes other than the mode we focus on. Therefore, in the following simulation, the thickness of the gold layer of 20 nm has been chosen for PDNR.

Fig. 3. (a) Resonance wavelength versus ARI for different gold thickness w_Au. (b) Resonance shift and the sensitivity versus w_Au. (c) Intensity spectrum of the diamond plasmonic nanodisk for w_Au=20 nm when ARI changes from 1.0 to 1.5 obtained by 2D FDTD simulation. Inset: the zoom-in graph of the region highlighted by the purple rectangle.

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Figure 4 represents the effects of the central hole of the PDNR on the resonance wavelength. Comparing with the plasmonic diamond nanodisk PDNR with a central hole and the gold layer of 20 nm shows greater shift of resonance wavelengths with ARI, which means better refractive index response can be achieved with the central hole.

Fig. 4. Resonance wavelength versus ARI for the proposed PDNR and plasmonic diamond nanodisk with different w_Au. Inset: the schematic of the structure for different graphs.

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For sensing applications of PDNR, the optimization process for the central hole size which relates to w_D also needs to be assessed. Considering the trade-off between Q factor and the sensitivity, we should analyze the relationship of Q factor and S with w_D. The Q factor, widely used to characterize a WGM resonance, is defined as [36]:

(5)$$Q = {\lambda _{res}}\tau = \frac{{{\lambda _{res}}}}{{\triangle {\lambda _{FWHM}}}},$$

where τ is the cavity ring down lifetime, i.e. the time required for the field intensity to decay by a factor of e, λ_res is the resonance wavelength. 1/Q=1/Q_rad+1/Q_abs is a measure of the loss in the WGM. Q_abs and Q_rad are respectively induced by metal absorption loss and radiation loss. The diamond absorption loss, which is much smaller than the metal absorption loss, is not considered in our simulation. Moreover, scattering losses due to the surface roughness, which can be controlled to a minimum in the experiment, are omitted. Here we utilize a PML to calculate the total Q, which provides an ideal theoretical value.

For sensing applications, the sensitivity S describes the smallest ARI value that can be reliably measured by an analytical procedure, which can be defined as:

(6)$$ S = d\lambda /dn.$$

Figure 5 depicts the Q factors and the sensitivity for PDNR versus w_D when ARI changes between 1.0 and 1.5. The Q factor increases significantly as w_D increases from 0.2R to 0.5R. However, the Q factor does not change dramatically as w_D increases further. For a constant w_D, the calculated results show that a higher Q factor is associated with a smaller ARI. As shown in Fig. 5, we find that for the ARI values between 1.0 and 1.3, a larger Q factor is associated with a larger w_D. This is because there is stronger confinement for a plasmonic diamond nanoring with a larger w_D value. In addition, it is seen that a Q factor as high as ∼60,000 can be achieved when the ambient environment is air. However, when ARI is 1.4 or 1.5, which is comparable with the refractive index of the host material silica around the resonance wavelength of the PDNR, it can be seen from the Figs. 5(b) and 5(c), the WGM field profile moves away from the plasmonic layer and the lower part of it merges into the host material silica due to the evanescent field between their interfaces. Therefore, the confinement of the WGM field comes from the joint function of the diamond and the silica. When w_D is as small as 0.2R, the confinement from the diamond still dominates. But with further increase of w_D, the confinement is slightly decreased. This is why the Q factor for w_D=0.2R is shown to be higher than the Q factor for w_D=0.3R when ARI is larger than 1.3. It also shows the trend for the sensitivity with increasing w_D, and higher sensitivity (∼339.8 nm∕RIU) is obtained when w_D=0.2R_D. The opposite trend for the sensitivity and Q factor is also observed from this figure, which reinforces the point that the there is a trade-off between both. With the increase of w_D, the sensitivity is decreased while the Q factor is increased. When w_D is between 0.2R and 0.3R, the Q factor of PDNR is lower than the Q factor when w_D is larger, which means less photons are confined within the cavity. Under this condition, the interaction between the light and the ambient environment is stronger through the evanescent wave, which eventually causes a higher sensitivity. Therefore, we can choose a trade-off value around 0.3R. For sensing applications of PDNR, the preferred value of w_D is determined.

Another important parameter for sensing applications is the detection limit (DL), which refers to the minimal RI that can be detected. DL can be defined as:

(7)$$ DL = \frac{{{\lambda _{res}}}}{{QS}},$$

where λ_res is the resonance wavelength. Figure 6 shows the trend for DL with increasing w_D, and higher sensitivity (∼339.8 nm∕RIU) is obtained when w_D=0.2R_D. If w_D continues to decrease, there would be no WGM formed in the PDNR. As given in the discussion of Figs. 4 and 5, and according to Eq. (7), the lowest detection limit for the proposed PDNR is 1.5 × 10⁻⁴ RIU when w_D=0.3R_D, 6 times lower than that of the diamond nanodisk (9.4 × 10⁻⁴ RIU). Consequently, as mentioned above, w_D around 0.3R_D is also preferred for low DL.

Fig. 5. (a) Q factors and the sensitivity versus width of diamond nanoring w_D. Inset: the schematic of the PDNR. (b) The intensity spectrum at the resonance wavelength and the cross-sectional field intensity when ARI=1.3, 1.4 and 1.5 highlighted by the left brown dotted rectangle in (a) for w_D =0.2R and (c) right brown dotted rectangle in (a) for w_D =0.3R.

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It is known that the boundaries of the diamond nanoring may not be perfectly round, due to the limitation of fabrication technology and the anisotropy of the diamond single crystal. It is therefore useful to investigate the effects of the imperfection of the boundaries on the characteristics of the PDNR. Regarding the outer boundary, it is easier to obtain high quality surfaces because of the coating process of gold. However, etching the inner boundary smoothly would be a great challenge. Hence, the central holes of octagonal, dodecagonal, hexadecagonal and icosagonal prisms are utilized to illustrate the imperfection of the inner boundary of the PDNR, as shown in Fig. 7. The behavior of the resonance wavelengths and Q factors of the PDNR with different holes is illustrated in Figs. 8(a) and 9, respectively. Figure 8(b) shows the total net resonance shifts for the ones with the central holes of 8-gonal, 12-gonal, 16-gonal and 20-gonal prisms, individually. One sees that for the same hole, when ARI increases, the trend for resonance wavelengths is opposite to that for the Q factors. Following this trend, we can anticipate that the sensitivity will be improved as the inner boundary gets closer to a perfectly circle, while the Q factor will significantly increase. As shown in Figs. 8 and 9, even though the resonance wavelength shifts with the geometric shapes of the inner boundary, we can still obtain decent sensitivity and Q factor. This suggests that our miniature resonator sensor has good potential for highly sensitive ultracompact sensing applications, but one which might require characterization of the resonance wavelength as this may be subject to deviation due to manufacturing tolerances.

Fig. 6. Detection limits versus w_D.

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Fig. 7. Schemes of the proposed PDNR with central holes of octagonal, dodecagonal, hexadecagonal and icosagonal prisms.

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Fig. 8. (a) Resonance wavelengths versus ARI and (b) resonance shifts for the proposed PDNR versus holes of octagonal, dodecagonal, hexadecagonal and icosagonal prisms.

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Fig. 9. Q factors for the proposed PDNR with holes of octagonal, dodecagonal, hexadecagonal and icosagonal prisms versus ARI.

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4. Conclusion

In conclusion, a hybrid PDNR consisting of a layer of gold uniformly coated on the outer boundary of a diamond nanoring is described and investigated theoretically for possible applications in sensing. By using the Lumerical FDTD method, it is revealed that this kind of PDNR achieves a high sensitivity of 339.8 nm/RIU. The highest Q factor can reach ∼60,000 with this nanoring, however the sensitivity will decrease. Considering this trade-off, the primary parameters of the resonator sensor are determined, and the minimum detection limit is as low as 1.5 × 10⁻⁴ RIU. Besides, through the research on the resonance shifts and Q factors for PDNR with central holes of octagonal, dodecagonal, hexadecagonal and icosagonal prisms, respectively, it is shown that our miniature resonator sensor, when appropriately characterized upon fabrication, can function with high performance for highly sensitive ultracompact sensing applications.

Funding

Natural Science Foundation of Shandong Province (Grant ZR2017MF038); Fundamental Research Fund of Shandong University (Grant 2016TB004); National Natural Science Foundation of China (Grant 51702186); Overseas Exchange program of Shandong University; Key R&D Project of Shandong Province (Grant 2018GGX101033); National Key R&D Program of China (2016YFB0401802); Young Scholars Program of Shandong University.

Disclosures

The authors declare no conflicts of interest.

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Miniature resonator sensor based on a hybrid plasmonic nanoring

Abstract

1. Introduction

2. Structure and basic theory

3. Simulation results

4. Conclusion

Funding

Disclosures

References

Cited By

Figures (9)

Equations (7)

Optics Express