A sensitive 2D plasmon ruler based on Fano resonance

Abstract

In this paper, we designed a 2D distance and rotation angle plasmon ruler based on Fano resonance of a trimer nanostructure, which consists of a concentric square nanoring–disk and an outside nanorod (CSRDR). The Fano dip energy and depth are fairly sensitive to the nanometer-scale displacements and rotations, when the nanodisk moves in all direction and rotates around its center. When the symmetry of the nanoring is broken, we can identify the moving and rotating direction of the nanodisk more accurately. We use the CSRDR nanostructure which supports a narrow line-width as a 2D plasmon ruler, which can enhance the sensitivity of a plasmon ruler significantly.

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1. Introduction

Surface plasmons (SPs) have attracted much attention due to their ability to manipulate light at nanoscale and their extensive applications in chemical and biological sensing.^1,2 When two metallic nanoparticles are close to each other, their surface plasmon resonances (SPRs) spectra are significantly sensitive to the interparticle distance. This effect has been used to create plasmon rulers.^3,26–31 With a tiny change in separation distances of the particles, the plasmon resonance shift will exhibit a nonlinear trend, which can probe the nanoscale distances in antennas, photodetectors and biochemical sensing platforms.^4–7 In order to increase the sensitivity of the plasmon ruler, a nanostructure with a narrow resonance line-width and high tunability is essential.

Compared to the general plasmon resonance, Fano resonance can support an SPR with a narrow line-width, which causes the spectral shift to be more sensitive to the distance between nanostructures.⁸ So a nanostructure supported Fano resonance can serve as an outstanding plasmon ruler. Fano resonance in metal nanostructure originates from the interference between a dark SPR (subradiant mode) and a bright SPR (superadiant mode).^9,10 This has been observed in numerous plasmonic systems, such as heterogeneous dimer structures,^11–13 nanoring–disk cavities,^14–16 dolmen nanostructure, tetramer and heptamer Au nanosphere–sphere with different diameters.^17–21 Fano resonance makes a plasmon ruler more sensitive.^3,22,23 For example, Liu et al. designed a coupled plasmonic oligomer, whose scattering spectra can be used to retrieve three-dimensional configuration information of complex macromolecular and biological processes as well as their dynamic evolution.³ Shao et al. demonstrated that a nanorod–sphere structure that supported Fano resonance can be used to make a 2D plasmon ruler, which is more sensitive to the distance of the nanosphere and the nanorod.²² Liu and Yang et al. found that the plasmonic heptamer clusters comprising of split nanorings can form multiple Fano resonances and the modulation depth of each Fano resonance can be adjusted by modifying the geometry parameters.²³ However, the line-width and the tunability of the Fano resonance, which is excited by the nanostructure mentioned above cannot be controlled easily.

Herein, we demonstrate a sensitive and easily made 2D plasmon ruler based on a highly tunable plasmonic system, which consists of a concentric square nanoring–disk (CSRD) and an outside nanorod. This plasmonic system is abbreviated as CSRDR nanostructure. It can support a satisfactory Fano resonance with narrow line-width and obvious spectral contrast ratio. When the nanodisk in the nanoring moves toward different directions and rotates with different angles, the scattering spectra is certainly found to change, and its sensitivity also can be enhanced greatly.

2. Methods

The 2D plasmon ruler based on the CSRDR nanostructure is shown in Fig. 1, which consists of a concentric square nanoring–disk (CSRD) and an outside nanorod. To make the CSRDR nanostructure easy to fabricate in the experiment, we set all the dimension parameters to values greater than 10 nm. The length and the width of the nanorod are marked as a and b respectively. The side length of the nanoring and nanodisk are, respectively, marked as L₁ and L₂. The nanodisk is set within the nanoring coaxially, and the gap width between nanoring and nanodisk is marked as g. The distance between the nanorod and the nanoring is marked as d. The height of all these structures is set to 60 nm, and the wall width of the nanoring is set to 20 nm. The material of the CSRDR nanostructure is gold with the permeability μ = 1 and the complex permittivity is sourced from ref. 24. The CSRDR nanostructure is placed on a substrate with the refractive index of 1.5. As a plane wave polarized along the x direction irradiates down to the CSRDR nanostructures, a satisfying Fano resonance appears, which can be served as a 2D plasmon ruler.

Fig. 1 Schematic diagram of the 2D plasmon ruler and definitions of the geometrical parameters. E – electric field; H – magnetic field; k – direction of light propagation.

The performance of the nanostructure has been calculated by solving two-dimensional Maxwell's equations using finite element method (Comsol Multiphysics). The scattering spectra are calculated by surface integration of the normalized electric field around a far-field transform boundary enclosing the CSRDR nanostructure. The absorption spectra are calculated by volume integration of the resistive heating in the CSRDR nanostructure. Besides, near-field information of this nanostructure can be directly observed from these simulations. Surface charge distribution is computed by Gauss's law, and the gradient operation is realized by implementing the up and down operators to the metal–dielectric interfaces.

3. Results and discussion

The narrow line-width of the Fano resonance plays a crucial role in obtaining a high sensitive plasmon ruler. The CSRDR nanostructure can support a Fano resonance at 0.83 eV, as shown in Fig. 2(b). Fig. 2(a)–(c) show the hybridization diagram of the CSRDR nanostructures. Fano resonances are formed by coupling the primitive plasmons of the nanorod and the CSRD. Fig. 2(a) shows the scattering and absorption spectra of the CSRD nanostructure. When the incident light irradiates vertically, only the bonding plasmon resonance can be excited (as shown by the red arrow in Fig. 2(a)). However, the quadrupolar resonance of the CSRD can be excited as the light irradiates horizontally (as shown by the blue arrow in Fig. 2(a)), which is a dark mode. The inset of Fig. 2(a) shows the charge distribution of the bonding plasmon resonance and quadrupolar resonance of the CSRD nanostructure. Fig. 2(c) shows the dipolar resonance of the individual nanorod, which can be strongly excited by the normally incident light. The combination of the dipole resonance of the outer nanorod and the bonding plasmon resonance of CSRD forms the broad bright mode (as shown by the green dashed curve in Fig. 2(a)). When it interacts with the narrow dark quadrupolar mode of the CSRD nanostructure, a Fano resonance occurs at 0.83 eV in the scattering spectra, as shown in Fig. 2(b). The charge distribution and electric field distribution at the Fano dips are shown in Fig. 2(d) and (e), respectively. The electric field located in the gap between nanoring and nanodisk can be enhanced 46.5 times. When the gap width g between the nanoring and nanodisk decreases, the line-width would become more narrow.²⁵ Thus, we can enhance the sensitivity of the nanoruler by tuning the gap width of the nanoring and nanodisk.

Fig. 2 Hybridization diagram of the CSRDR (a = 300 nm, b = 60 nm, L₁ = 300 nm, L₂ = 240 nm, d = 20 nm, g = 10 nm) for vertical (red solid curve) and parallel (black solid curve) incident light. The scattering (solid curve) and absorption (dashed curve) spectra are for the individual CSRD (a), the CSRDR (b), and the rod (c). The green dotted lines indicate the dipolar interactions. The blue lines indicate that the interaction between quadrupolar dark mode and the broader hybridized mode results in Fano resonances. The charge and electric field distributions at Fano dip are shown in (d) and (e), respectively.

When the metal nanostructures are placed closely, their plasmon resonance shows a distance-dependent characteristic.^26–31 In this article, we move the middle disk to create the distance-dependent characteristic, so the side length of the disk is decreased to 160 nm. In order to obtain a satisfactory Fano resonance by coupling the nanorod with the nanoring–disk mentioned above, the length of the nanorod is decreased to 260 nm. Fig. 3(a) shows the scattering spectra of the CSRDR as the nanodisk moving in lateral direction with different displacements S. When the disk moves to the left from 0 to −20 nm, the energy of the Fano dip red shifts from 1.12 to 1.07 eV, the depth of Fano dip increases first and then goes down to 0.56. Comparing with the 3D plasmon ruler and the Au nanorod–sphere nanoruler, the Fano resonance energy of the 3D plasmon ruler red shifts about 0.02 eV as the nanorod moves about 20 nm in the lateral direction. The resonance energy of the nanorod–sphere structure shifts about 0.016 eV as the nanosphere moves up approximately 20 nm. The sensitivity of the CSRDR nanostructure has a significant promotion. Oppositely, when the disk moves to the right from 0 to 20 nm, the Fano dip blue shifts from 1.12 to 1.147 eV, the depth of Fano dip decreases to 0.5, as shown in Fig. 3(b) and (c). Here, we define the depth of Fano dip as , where h₁ and h₂ are the peak values of the left and right peaks of Fano dip, respectively, and h₃ is the value of the Fano dip (as shown in Fig. 3(a)). So we can identify the lateral moving direction and the distance of the disk precisely by these changes in the scattering spectra.

Fig. 3 (a) The scattering spectra of the CSRDR nanostructure as the disk moves in lateral direction. The inset in (a) is the schematic diagram of the disk moving in CSRDR nanostructure. The energy and depth of Fano dip are shown in (b) and (c), respectively. The structural parameters are the same as that in Fig. 2. Besides the side length of the disk is decreased to 160 nm and the nanorod is decreased to 260 nm.

Fig. 4(a) shows the scattering spectra of the CSRDR with the movements H of the disk in vertical direction. When the disk moves down from 0 to −20 nm, the energy of the Fano dip red shifts from 1.12 to 1.095 eV, the depth of Fano dip decreases to 0.49. When the disk moves up from 0 to 20 nm, the energy of the Fano dip red shifts from 1.12 to 1.10 eV, the depth of Fano dip decreases from 0.56 to 0.48, as shown in Fig. 4(b) and (c). From the above, whether the disk moves in lateral direction or in vertical direction can be identified from Fig. 3 and 4. However, we cannot identify the moving distance and whether the disk moves up or down clearly in this CSRDR nanostructure.

Fig. 4 (a) The scattering spectra of the CSRDR nanostructure as the disk moves in vertical direction. The inset in (a) is the schematic diagram of the disk moving in CSRDR nanostructure. The energy and depth of Fano dip are shown in (b) and (c), respectively. The structural parameters are the same as that in Fig. 3.

We also calculated the scattering spectra of the CSRDR as the disk rotates around its center with different angles, as shown in Fig. 5(a). We studied only the anticlockwise rotation of the disk because of the symmetry of the CSRD nanostructure. When the disk rotates anticlockwise from 5 to 45 degrees, the Fano dip red shifts from 1.12 to 1.04 eV, as shown in Fig. 5(b). When the rotation angles are within 15 degrees, the Fano dip red shifts only from 1.12 to 1.098 eV, and the depth of the Fano dip decreases to approximately 0.108. However, when the disk rotates with an angle that is more than 15 degrees, the Fano dip apparently red shifts, and the depth of the Fano dip increases approximately 0.2. Although the resonance energy and the depth of the Fano dip of CSRDR are all remarkably sensitive to the rotation angle, the rotation direction still cannot be identified in the CSRD nanostructure.

Fig. 5 (a) The scattering spectra of the CSRDR nanostructure as the disk rotates with different angles. The inset in (a) is the schematic diagram of the disk moving in CSRDR nanostructure. The energy and depth of Fano dip are shown in (b) and (c), respectively. The structural parameters are the same as that in Fig. 3.

In order to distinguish the movement along vertical and rotational direction, we break the symmetry of the CSRDR by means of making the nanoring to be a trapezoid-shaped nanoring, as shown in the inset of the Fig. 6(a). The length of upper line and lower line of the trapezoid in the nanoring are 260 and 220 nm, respectively. The other parameters of the CSRDR nanostructure in Fig. 6 are the same as in Fig. 3. We define anticlockwise direction as the positive direction and clockwise direction as the negative direction. Fig. 6(a) shows the scattering spectra of the CSRDR nanostructure as the disk rotates clockwise and anticlockwise with different angles. When the symmetry of the nanoring is broken, two Fano dips originating from two different modes of the CSRD structure and found to appear, as shown in Fig. 6(d) and (e). The second dip shown in Fig. 6(a) vanishes gradually as the disk rotates anticlockwise from 0 to 15 degrees, and we can identify the direction of rotation and the rotation angle through the energy shift of the two Fano dips. When the disk rotates clockwise from 0 to −15 degrees, the first Fano dip red shifts from 1.107 to 1.072 eV, and the second Fano dip blue shifts from 1.187 to 1.178 eV. The two Fano dips appear increasingly farther away from each other. However, when the disk rotates anticlockwise from 0 to 15 degrees, the first Fano dip blue shifts from 1.107 to 1.112 eV, and the second Fano dip red shifts from 1.187 to 1.167 eV. The two Fano dips approach each other gradually, as shown in Fig. 6(b) and (c). From this, we can judge the direction of the rotation and the rotation angles. In comparison with Fig. 5(a), the shifts of the Fano dips are more prominent in the asymmetric system.

Fig. 6 (a) Calculated scattering spectra of the asymmetric CSRDR structure as the disk rotates clockwise and anticlockwise. The inset in (a) is the schematic diagram of the disk rotation in CSRDR nanostructure. The energy change tendencies of I and II Fano dips are marked by black and magenta dot-line in (b) and (c), respectively. (d) and (e) show the surface charge distribution at Fano dips I and II, respectively, when the rotate angle of the disk is 0.

The direction of the disk moving along vertical direction can also be distinguished through this asymmetric CSRDR nanostructure, as shown in Fig. 7. Fig. 7(a) shows the scattering spectra of the asymmetric CSRDR with the movements H of the disk in vertical direction. As the disk moves up from 0 to 30 nm, the first Fano dip red shifts from 1.107 to 1.084 eV, and the second Fano dip shows significant shifts from 1.186 to 1.173 eV, as shown in Fig. 7(b). As the energy tendencies of the two dips are similar, we can judge whether the nanodisk moves up or down by the depth changes of the two Fano dips, as shown in Fig. 7(c). The depth of the first Fano dip decreases from 0.165 to 0.125, and the second Fano dip decreases from 0.095 to 0.037. When the disk moves down from 0 to −30 nm, the first Fano dip red shifts from 1.107 to 1.079 eV and while the second dip shifts from 1.186 to 1.154 eV, as shown in Fig. 7(b). The depth of the first Fano dip decreases from 0.165 to 0.147, while the second Fano dip decreases about 0.025, as shown in Fig. 7(c). Comparing these results to that of the symmetric CSRDR nanostructure, the changes in the spectra are more obvious. This allows us to make more accurate judgment on the moving direction of the disk. It is a potential application in the biological sensor, especially in molecule size detection.

Fig. 7 (a) Calculated scattering spectra of the asymmetric CSRDR structure as the disk moves in vertical direction. The inset in (a) is the schematic diagram of the disk moving in CSRDR nanostructure. The energy shifts and the depth of the two Fano dips are shown in (b) and (c), respectively. The energy and depth change tendencies of I and II Fano dips are marked by black and magenta dot-line, respectively.

The right angle in the CSRDR nanostructure in Fig. 1 is very difficult to fabricate in experiment. As the CSRDR nanostructure changes from a right angle to a filleted corner with the filleted radius of 8 nm, the Fano dip blue shifts slightly and the Fano line-width of the quadrupolar Fano resonance is changed a little, as shown in Fig. 8(a). When the disk moves left from 0 to −15 nm and moves right from 0 to 15 nm, the energy changes are found to be approximately 0.026 and 0.02 eV, respectively, as shown in Fig. 8(b). Comparing to the CSRDR nanostructure with the right angle, the energy was found to decrease from 0.01 to 0.0035 eV. When the disk rotates clockwise from 0 to 45 degrees, the energy of Fano dip with filleted corner shifts from 1.157 to 1.102 eV, as shown in Fig. 8(c). The sensitivity is also reduced compared with the CSRDR nanostructure with the right angle. However, the sensitivity is still higher than the nanorulers based on other nanostructures. When the asymmetric CSRDR nanostructure changes from a right angle to a filleted corner with the fillet radius of 8 nm, as shown in Fig. 8(d), the Fano dip blue shifts, but the Fano line-width is nearly unchanged. The energy of I and II Fano dips blue shifts from 1.1428 eV to 1.1443 eV and 1.2247 to 1.2265 eV, respectively, as the disk moves 20 nm in vertical direction. Comparing to the asymmetric nanostructure with right angle, the movement of the two Fano dips only decreases 0.003 eV and 0.004 eV, respectively. So the sensitivity remains almost unchanged.

Fig. 8 (a) Sketch and scattering spectra of the CSRDR with filleted corner, the structural parameters are the same as that in Fig. 2. The scattering spectra of the CSRDR nanostructure with filleted corner as the disk moves in lateral direction (b) and rotates with different angles (c). The scattering spectra of the asymmetric CSRDR nanostructure with filleted corner as the disk moves in vertical direction are shown in (d). The structural parameters in (b)–(d) are the same as that in Fig. 3.

The fabrication imperfections exist in fabrication of the CSRDR nanostructure. For example, the fabrication imperfection may be slightly asymmetric or the asymmetric CSRDR nanostructure edge appears in different directions. Fig. 9 shows the scattering spectra of the CSRDR nanostructure with slight asymmetry. When the respective lengths of upper line and lower line of the trapezoid in the nanoring are 260 and 240 nm, the two Fano dips are not as prominent as in Fig. 6(a). When the disk moves down from 10 to −10 nm, the energy of I and II Fano dips blue shifts only 0.003 and 0.004 eV, respectively, as shown in Fig. 9(a). When the disk rotates anticlockwise from 0 to 10 degrees, the I Fano dip disappears, and the energy of the II Fano dip blue shifts 0.005 eV. When the disk rotates clockwise from 0 to 10 degrees, the I Fano dip appears, and the energy of the II Fano dip red shifts 0.0018 eV, as shown in Fig. 9(b). Although we can distinguish the movement along the vertical and rotational directions, the sensitivity of the slightly asymmetric CSRDR nanostructure decreases. Then again, the fabrication imperfections appear in the other edges as shown in the insets of Fig. 10(a)–(c). The scattering spectra and the movement of Fano dips are all different. So we cannot identify the moving direction of the disk. Fabrication imperfections may help to distinguish the movement direction in the vertical and the rotation direction, but the results are not deterministic.

Fig. 9 Sketch and scattering spectra of the slightly asymmetric CSRDR nanostructure as the disk moves in vertical direction (a) and rotates clockwise and anticlockwise with different angles (b).

Fig. 10 Sketch and scattering spectra of the CSRDR with different asymmetric edges as the disk moves in vertical directions.

4. Conclusion

In this paper, a sensitive 2D plasmon ruler based on the CSRDR nanostructure on a substrate with the refractive index 1.5 was demonstrated theoretically. The CSRDR nanostructure can support a Fano resonance with a narrow line-width. The Fano dip shifts significantly and the depth of Fano dip also changes evidently, when the disk moves in all direction and rotates around its center. The energy and the depth of Fano dip can serve as a significant function of distance. According to these results, the CSRDR nanostructure has potential applications to enhance the sensitivity of sensors.

Acknowledgements

The authors are grateful for the financial support from the National Natural Science Foundation of China (11474187, 11504209, 11274204, 11404195) and Excellent Young Scholars Research Fund of Shandong Normal University.

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Footnote

† These authors contributed equally to this work.

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