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Optical properties of periodic nanorings with built-in V-shaped nanowedges (NRBV) are investigated theoretically. Tunable ultrahigh order Fano resonances are achieved and they are found to be sensitive to geometric parameters and surrounding dielectric environment of the planar nanostructure. High order Fano resonances can be suppressed or enhanced by adjusting the opening angle of the nanowedge, the size of the nanoring and the aspect ratio of the nanowedge. Moreover, manipulating the offset of the built-in nanowedge, or filling dielectrics asymmetrically can revive suppressed Fano resonances when the V-shaped nanowedge develops into a straight nanorod. Meanwhile, stronger plasmon resonances emerge alternately in the two parts of this planar nanostructure. This periodic plasmonic nanostructure produces ultrahigh order plasmon resonances and stronger electric field enhancement, which have great potential applications in multi-wavelength surface enhanced spectroscopy and biochemical sensing.
© 2015 Optical Society of America
1. Introduction
Noble metal nanostructures, which support surface plasmons (SPs), have the ability to manipulate light due to their unusual optical properties [1–3]. The optical properties of these metal nanostructures sensitively depend on their morphology and surrounding medium. The interaction between the incident light and coupled nanostructures produces hybridized collective plasmon modes, and Fano resonance (FR) can be achieved by the coherent interference of superradiant (bright) mode and subradiant (dark) mode [3–6]. Due to the interference between different plasmon modes of coupled nanostructures, some interesting phenomena can be observed, such as the generation of high-order magnetic modes and second harmonic [7–10]. Therefore, metal nanostructures have many important applications in various fields including surface-enhanced spectroscopy, photovoltaic devices, plasmonic holographic imaging, optical waveguiding, nanoantenna, and Fano interferometer [11–16].
In current work, a novel planar plasmonic nanostructure array is investigated. The unit of this periodic nanostructure consists of a nanoring and a built-in V-shaped nanowedge. Compared with the former relevant work [17–19], more interesting optical properties are represented by this structure. Firstly, in this symmetry-reduced nanostructure, ultrahigh order ring-wedge Fano resonances (FRs) (5-1, 6-2 and 7-2 modes) can be generated in the visible wavelength range when the wedge angle is properly designed. Secondly, some high order Fano resonances can be suppressed or enhanced by adjusting the structural parameters. The suppression of the FRs can reduce the cross-talk in spectroscopic measurement [17]. Thirdly, certain suppressed Fano resonances can be revived by manipulating the offset of the nanowedge or filling dielectrics. And an asymmetric distribution of the electric field appears in this planar nanostructure. Meanwhile, a electromagnetic theory based on Mexwell's equation is used to further understand the medium-induced Fano resonances. Compared with single FR, multiple FRs achieve resonant peaks at several spectral positions simultaneously. Therefore, such a planar nanostructure could be useful in multi-wavelength surface enhanced spectroscopy and biochemical sensing [20, 21].
2. Structure design and simulation method
Figure 1 illustrate the geometric structure of the silver NRBV studied in this work. The incident light propagates along the negative direction of z axis and the polarization is normal to the angular bisector of the wedge angle. In Fig. 1(a), the periodic length is a at both dimensions in x-y plane. The thickness of the metal layer is t and the width of the V-shaped wedge is d. The inner and outer radii of the NRBV is r and R, respectively. The opening angle of the V-shaped nanowedge is θ. Figure 1(b) displays the morphological evolution of the NRBV structure. When the wedge angle changes from 180° to 300°, discussions are neglected due to the geometrical transform symmetry. Comparing with a single nanoring, the geometric symmetry of NRBV is broken by adding the V-shaped nanowedge.
Fig. 1 (a) Scheme of the periodic silver NRBV. The incident light is supposed to propagate along the negative direction of z axis and the polarization is normal to the angular bisector of the wedge angle. (b) Schematics of the structural evolution of NRBV. (I)~(V): Manipulate the wedge angle from 60° to 180°. (VI): Adjust the location of the built-in straight nanorod at θ = 180°. (VII): Fill dielectrics asymmetrically into the nanostructure at θ = 180°.
Numerical calculations are involved to investigate the optical properties of the periodic NRBV by using the 3D finite element method (FEM) [22], and COMSOL(4.4) Multiphysics software package is used as well. Here the scattering cross section is obtained by integrating the scattered power flux over an enclosed surface outside the NRBV and it is defined as:
where n is the norm vector pointing outwards from the enclosed surface, Ssc is the scattered intensity (Poynting) vector, and I0 is the incident intensity. The absorption cross section is determined by the integration of the Ohmic heating within the structure and it equals:where Q is the power loss density in the structure. The extinction cross section is the sum of the two others [23]:In order to describe the property of metallic silver, experimentally measured silver permittivity data (JC) is cited [24].3. Results and discussion
3.1 Optical properties of the periodic nanorings and V-shaped nanowedges
Here we fix the inner and outer radii of the nanoring (r = 80nm, R = 90nm), the arm length (L = 80nm) and the width (d = 20nm) of the V-shaped wedge, the thickness of matel layer (t = 30nm), and the periodic length (a = 300nm) of the nanostructure. For symmetric nanorings, shown in Fig. 2(a), only the dipolar mode (D mode) which centered at 1280nm can be excited by the normally incident light, while the multipolar mode of the symmetric rings can be excited only by an oblique incident light for the retardation effect [25]. For V-shaped nanowedges, shown in Fig. 2(b), both D modes and quadrupolar modes (Q modes) of FR can be excited. The insets represent the corresponding simulated electric field and charge density distribution of D mode (850nm) and Q mode (425nm) at θ = 120°, respectively. Compared with D modes, Q modes have higher energy and much lower extinction cross section. The increase of the wedge angle induces the effective dipole moment [26] of the V-shaped wedge increased, which results in the red-shift of D modes (from 820nm to 860nm).
Fig. 2 Extinction cross sections of periodic (a) nanorings and (b) V-shaped nanowedges (L = 80nm, t = 30nm, d = 20nm) at different wedge angle. The insets present the geometry, incident light condition, simulated electric field and charge density distributions of (a) nanorings and (b) V-shaped nanowedges. The arrows in red in Fig. 2(b) indicate the D mode (850nm) and Q mode (425nm) of FRs at θ = 120°. The colour bars represent the amplitude of |E/E0|, where E is the local electric field near the nanorings and nanowedges, and E0 is the background electric field. The positive and negative charge are represented by red and blue, respectively.
3.2 Generation and manipulation of higher order FRs by adding V-shaped wedges to nanoring array
As it is discussed above, only the dipolar mode of periodic nanorings can be excited by normally incident light. Adding V-shaped wedges to the nanoring array breaks the symmetry of the original nanostructure. This symmetry breaking allows the excitation of the multipolar modes (dark modes) of the nanoring, and the plasmon hybridization between bright modes and dark modes results in the formation of Fano resonances. In order to manipulate the high order ring-wedge Fano resonances, four different sets of geometric variables are controlled respectively. Firstly, high order Fano resonances can be suppressed or enhanced by adjusting the opening angle of the built-in nanowedge. The calculated extinction cross section of the periodic NRBV as a function of the wedge angle are shown in Fig. 3. The corresponding electric field and charge density distributions for different modes of FRs are compared in Fig. 4 as well. Here we define the dipolar mode as MN = 1, then the quadrupolar, octupolar, hexadedapolar and triakontadipolar modes are corresponding to MN = 2, MN = 3, MN = 4 and MN = 5, respectively. Thus the mode of ring-wedge Fano resonance can be defined. For example, the dipolar-dipolar mode of ring-wedge FR can be wrote as 1-1 mode.
Fig. 3 Extinction cross sections of periodic NRBV as a function of the wedge angle. The width of the V-shaped wedge d fixed at 20nm and the outer and inner radius of the nanoring (R and r) are fixed at 90nm and 80nm, respectively. Figure 3(a) is the close-up view of shadow zone of Fig. 3(b). The numbers ④, ⑤, ⑥ and ⑦ represent the 4-1, 5-1, 6-2 and 7-2 modes of ring-wedge FRs, respectively.
Fig. 4 The simulated (a) electric field and (b) charge density distributions of the NRBV at different wedge angle which changes from 60° to 180°. The colour bars represent the amplitude of |E/E0|, where E is the local electric field near the NRBV, and E0 is the background electric field. The positive and negative charge are represented by red and blue, respectively.
When adjusting the wedge angle from 60° to 180°, ultrahigh order ring-wedge Fano resonances are achieved. The 7-2, 6-2 and 5-1 modes appear around 400nm in Fig. 3(b). Moreover, certain modes of ring-wedge FRs are suppressed at different wedge angles. The blanks in Fig. 4 clearly present the suppressed modes. For example, 2-1, 4-1 and 6-2 modes cannot be excited at θ = 180°, while only 1-1, 3-1, 5-1 and 7-2 modes are observed at 970nm, 600nm, 435nm and 410 nm, respectively. The ring-mode with an even order cannot be excited by the normal incidence plane wave. This is due to the symmetric geometry of the NRBV with x-polarized E at θ = 180°. These certain suppressed Fano resonances can reduce the cross-talk in spectroscopic measurement.
The built-in nanowedge divides the nanoring into two parts: an inferior partial ring and a complementary superior one. The partial ring which faces the wedge angle is called inferior partial ring and the remaining part is the superior one. In Fig. 3(a), an obvious blue-shift of extinction peaks appears for both 1-1 modes and 4-1 modes when increasing the wedge angle. For 1-1 modes, stronger plasmon resonance appears in the superior partial ring and the nanostructure can be regard as a dipole. When θ increases, the superior partial ring becomes smaller, which induces the shorter separation between equivalent positive and negative charges. The shorter charge separation results in the increased Coulombic restoring force and higher resonant energy [27, 28]. Due to the higher resonance energy, the incident light with shorter wavelength can be coupled to the nanostructure, and thus resulting in the blue-shift of the extinction peaks for 1-1 modes. As for 4-1 modes, stronger plasmon resonance appears in the inferior partial rings. According to charge distributions marked by the frames in Fig. 4(b), the inferior partial ring can be regard as a dipole at θ = 120° and it turns to be a quadrupole at θ = 150°. Compared with dipole's, the charge separation of the quadrupole is shorter, thus the incident light with shorter wavelength can be coupled to the nanostructure, which results in the blue-shifted extinction peaks of 4-1 modes.
While, the extinction peaks of 2-1 modes show an interesting movement. As it is shown in the second line in Fig. 4(a), stronger resonance appears in the superior partial ring when θ = 60° and θ = 90°, while it appears in the inferior one when θ = 120° and θ = 150°. According to the charge density distributions, the inferior and superior partial ring can be regard as a dipole and a quadrupole at 2-1 mode, respectively. With the increase of the wedge angle, the superior partial ring becomes smaller, while the inferior one becomes larger. The larger inferior partial ring indicates the reduced Coulombic restoring force, while the smaller superior partial ring means the increased one. The change from the increased Coulombic restoring force to the reduced one induces the firstly blue-shifted then red-shifted extinction peaks of 2-1 modes.
Secondly, certain high order Fano resonance can be revived by manipulating the geometrical dimension of the nanoring and nanowedge. As it is shown in Fig. 5(a) and 5(b), whenever increasing the inner and outer radii of the nanoring with the same width d, or enlarging the whole nanostructure with the fixed ratio r: d: Δ at 8:2:1, the suppressed 3-1 modes (indicated by the arrows in peach) are revived and the spectra of extinction cross sections are red-shifted. Both these two methods induce longer separation between equivalent positive and negative charges, thus resulting in the longer resonant wavelength. In Fig. 5(b), when increasing the inner and outer radius of the nanoring, the electric field intensity between the adjacent NRBVs is greatly enhanced and the Coulomb interaction between neighbor unit structures is attraction, which results in the formation of hot spots between nanostructures [29].
Fig. 5 (a) Extinction cross sections of the periodic NRBV as a function of the inner radius r at θ = 120°. The wall width Δ (Δ = R-r) is fixed at 10nm and the width of the nanowedge d is 20nm. (b) Extinction cross sections of the periodic NRBV as a function of the wall width Δ at θ = 120°. The ratio of r: d: Δ is fixed at 8:2:1. (c) The simulated electric field and charge density distributions of the NRBV at different modes with R = 130nm, r = 120nm and d = 20nm at θ = 120°. The revived 3-1 mode is marked by the frames.
Thirdly, high order Fano resonances can be manipulated by controlling the width of the nanowedge. Due to the width-mismatching between d and Δ (Δ = R-r), the suppression of mode occurs. As it is shown in Fig. 6, increasing the width d of the V-shaped nanowedge when fixing the outer and inner radius of the nanoring makes the corresponding extinction peaks blue-shifted at θ = 120°. In addition, the original 7-2 mode of FRs is suppressed when the d is fixed at 10nm. The change of the aspect ratio of a nanorod could affect properties of the plasmon resonance [30]. Fixing the inner radius r of the nanoring means keeping the arm length of the V-shaped nanowedge unchanged, and the increased wedge width makes the aspect ratio (AR = r:d) of the nanowedge reduced, thus resulting in the blue-shifted spectra of the extinction cross sections.
Fig. 6 (a) Extinction cross sections of the periodic NRBV as a function of the width d at θ = 120°. The inner and outer radii of the ring are fixed at 80nm and 90nm, respectively. (b) The simulated electric field and charge density distributions of the NRBV at different modes with R = 90nm, r = 80nm and d = 10nm at θ = 120°.
3.3 Reviving and manipulation of suppressed higher order FRs by adjusting the V-shaped wedge and asymmetrically filling dielectrics
As it is discussed above, due to the symmetric geometry of the NRBV with x-polarized E at θ = 180°, the ring-mode with an even order cannot be excited by the normal incidence plane wave. When θ = 180°, the built-in V-shaped nanowedge develops into a straight nanorod and it divides the nanoring into two identical semi-hole-rings: part A and part B (shown by the inset in Fig. 7(b) and Fig. 8(a)). Firstly, it is found that the suppressed modes of FRs can be revived by moving the built-in straight nanorod upward (or downward). The symmetry of the nanostructure is broken when adjusting the location of the straight nanorod and it results in an additional interesting phenomenon of the plasmon resonance.
Fig. 7 (a) Extinction cross sections of the periodic NRBV at θ = 180° when moving the straight nanorod upward 10nm, 20nm, 30nm, and 40nm, respectively. Here R = 90nm, r = 80nm and d = 20nm. Numbers 1~7 represent the 1-1 (980nm), 2-1 (750nm), 3-1 (610nm), B-bright 4-1 (520nm), A-bright 4-1 (490nm), B-bright 5-1 (450nm) and A-bright 6-2 (430nm) modes, respectively. (b) The simulated electric field and charge density distributions of corresponding modes marked by the same numbers in Fig. 7(a).
Fig. 8 (a) Extinction cross sections of the periodic NRBV at θ = 180° when filling the part B with different dielectrics with refractive index of n = 1.00, 1.33, 1.45 and 1.56, respectively. Here R = 90nm, r = 80nm and d = 20nm. Numbers 1~6 represent the 1-1 (990nm), 2-1 (790nm), 3-1 (630nm), A-bright 4-1 (510nm), B-bright 5-1 (470nm), and A-bright 6-2 (440nm) modes, respectively. (b) The simulated electric field and charge density distributions of corresponding modes marked by the same numbers in Fig. 8(a). (c)~(d) The energy shifts (dots in color) of the resonances as a function of the refractive index. The inset shows the FOM of the corresponding mode.
In Fig. 7(a), compared with the former spectrum of the extinction cross section (dashed line in black), the suppressed 2-1, 4-1 and 6-2 modes can be excited under the same incident field condition when increasing the offset δl of the nanowedge. It is interesting to find that the same order mode of FR can split into two modes: a A-bright mode (high energy) and a B-bright mode (low energy). For example, the A-bright 4-1 mode and B-bright 4-1 mode locate at 490nm and 520nm, respectively. According to Fig. 7(b), stronger plasmon resonances emerge alternately in the two parts of this planar nanostructure. Numbers 1~7 represent the electric field and charge intensity distributions of 1-1 (980nm), 2-1 (750nm), 3-1 (610nm), B-bright 4-1 (520nm), A-bright 4-1 (490nm), B-bright 5-1 (450nm) and A-bright 6-2 (430nm) modes, respectively.
As we have discussed above, the incident light with shorter (or longer) wavelength can be coupled to the nanostructure when the effective distance between equivalent positive and negative equivalent charges becomes shorter (or longer). The shorter (longer) effective distance results in the blue-shift (or red-shift) of the extinction spectra. For 5-1 mode, the direction of movements for extinction peaks changes when increasing δl from 20nm to 30nm, which can be illustrated by the mode switch from B-bright 5-1 mode (low energy) to A-bright 5-1 mode (high energy).
Secondly, the plasmon resonance is strongly influenced by the dielectric refractive index n of the surrounding medium [17, 31–34]. Only filling different dielectrics in part B (shown by the inset in Fig. 8(a)) breaks the symmetry between two parts (part A and B) of the nanostructure, and thus reviving the suppressed FRs (2-1, A-bright 4-1, and A-bright 6-2 modes). According to Fig. 8(b), a similar A-bright or B-bright plasmon resonance phenomenon is observed clearly in 4~6. In order to evaluate the refractive index sensitivity of the nanostructure, figure of merit (FOM) [35] is introduced, which is defined as:
Where Δω is the energy shift, Δn is the variation of the refractive index, and fwhm is the full wave at half maximum. According to Figs. 8(c) and 8(d), Δω increases with the increasing value of the refractive index. The insets show that high order modes of the plasmon resonances are sensitive to the changes of the refractive index, while 1-1 mode shows relative low refractive index sensitivity because of its large fwhm. Moreover, the filled dielectrics induce the increase of the effective refractive index of the whole nanostructure, which results in a red shift to the extinction spectra [36].To further understand this medium-induced Fano resonances, an electromagnetic theory based on Mexwell's equation is introduced [37, 38]. The radiative (bright mode) dipole resonance strength follows a symmetric Lorentzian line shape as a function of the frequency ω:
Where A is the maximum amplitude of the resonance, ωs and Ws are the resonance frequency and spectral width, respectively. Meanwhile, the spectrum with the Fano-like asymmetric line shape caused by the interference of the bright and dark modes can be regarded as:Where i represents different interference modes (i = 1,2,3,4…), ωi and Wi are the corresponding central spectral position and width, respectively. qi is the asymmetry parameter, and bi is the modulation damping parameter originating from intrinsic losses. The resonance strength of the entire system can be regard as the product of the symmetric Lorentzian line shape modulated by different Fano-like asymmetric line shapes as follows:Where i = 1,2,3,4…, and m represents the total number of the interference modes.Due to the relatively low resonance strength of the high order Fano resonances (4-1, 5-1 and 6-1 modes) when filling different dielectric materials in part B, only the 1-1, 2-1 and 3-1 modes are fitted, which means m = 2 in Eq. (7). When m = 2, Eq. (7) develops into:
According to Eq. (8), we fit the numerical simulated reflection spectra in Fig. 9.Fig. 9 The numerical simulated (solid line in black) and fitted (short dash line in red) reflectance of the periodic NRBV at (a) n = 1.00, (b) n = 1.33, (3) n = 1.45, and (d) n = 1.56, respectively. The inset show the characteristic parameters q1, q2, b1 and b2 obtained by Eq. (6).
4. Concluding remarks
A novel planar NRBV array has been designed and its optical properties has been investigated theoretically. Ultrahigh order ring-wedge FRs (5-1, 6-1 and 7-2 modes of FRs) are generated in the visible wavelength range when the V-shaped wedge angle locates in the certain range. Such FRs are sensitive to the geometric parameters of the nanostructure and the dielectric property of the environment. Certain high order Fano resonances are suppressed or enhanced by adjusting the opening angle of the nanowedge, the size of the nanoring and the aspect ratio of the nanowedge. The suppressed Fano resonances are revived by manipulating the offset of the V-shaped nanowedge or asymmetrically filling dielectrics. Stronger plasmon resonance emerges alternately in the two parts of the planar nanostructure when the V-shaped nanowedge develops into a straight nanorod. This study suggests that the NRBV can provide a promising method of manipulating the Fano resonance signals and producing strong electric field enhancements, which could be utilized in the biosensing, enhancing Raman scattering and light trapping in solar cells. It is also expected that the NRBV might have potential platforms for sub-wavelength optics and other relevant frontier research field.
Acknowledgments
This work is supported by the National Science Foundation of China (Grant No. 11174190 and 11304247), the Natural Science Foundation of Shaanxi Educational Committee (No.2013JK0627) and the Natural Science Basis Research Plan in Shaanxi Province of China (Program No.2013JM1008).
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