We analyze the design of near infrared all-optical controllable and dynamically tunable multispectral Fano resonances based on subgroup decomposition of plasmonic resonances in hybrid nanoslits antenna plasmonic system. The theoretical investigation complemented with numerical simulations show that the Fano resonance lines shape can be tailored efficiently and continuously with the nanoslits geometry and the variation of the polarization states of the incident light. The subgroup decomposition of the spectral profile and the modification of plasmonic resonances lineshape that leads to the Fano-type profile of transmission is investigated and revealed. The separate contribution from individual spectral of single-slit array subgroup is attributed to the resulting overall multispectral Fano lineshape of the proposed T-shaped slits array at their corresponding spectral peaks zone. The polarization-selective tunability of the multispectral Fano resonances in the planar hybrid plasmonic system creates new avenues for designing multi-channel multi-wavelength tunable Fano effect.
© 2015 Optical Society of America
In the past decades, the Fano resonance in plasmonic nanostructures and metamaterials [1–4 ] have been realized and investigated vastly, which have generated a great deal of interest including switching , lasing, nonlinear and slow-light [6,7 ], particularly for applications such as refractive index sensing  for development of chemical or biological sensors that benefit from sharp spectral features and extreme field localization .
For complex plasmonic nanostructures, a rich resonance spectrum emerges, due to the coherent resonance arising from hybridization of plasmon modes. Meanwhile, symmetry-breaking of the nanostructures facilitates the multispectral Fano resonance with highly tunability [10–12 ]. Nevertheless, simpler geometry, less challenging fabrication of the system is in most strong desire. Recently, there have been fruitful experimental and theoretical researches demonstrating Fano resonance in various designed geometries using simple or complex nanostructures [13–19 ]. Plasmon resonances with Fano profile have also been observed in various metallic or dielectric nano-clusters exhibiting plasmonic hybridized modes, and remarkable efforts in theoretical and experimental works were reported [20–26 ]. Significant step forward was recently done by Ben Hopkins and associates, where the hybridization and combination of the nanoparticles oligomers and their collective behavior are comprehensively and instructively demonstrated. Thorough and robust approach for the physical mechanism and collective eigenmodes’ microscopic interaction of Fano and its applications can be found in the recent works by Ben Hopkins [22–24 ]. Meanwhile, it is noted that it lacks or does not have plenty of general method to control flexibly the Fano spectral profile featured by its linewidth, spectral contrast, and asymmetric factors, which is much desired for versatile and convenient manipulation and modification of the plasmonic response in nanostructures and plasmonic devices employing Fano resonance. Since the materials and geometry parameters of a plasmonic system are difficult to control at the nanoscale, due to the difficulty in tuning the dielectric constants or changing the geometry parameters after fabrication of the structure, more convenient and efficient approach enabling dynamically all-optical and large tunability is eagerly expected [25–31 ].
In this letter, we show that hybrid waveguide plasmon system with periodic metallic T-shaped nanoslits can exhibit multispectral sharp Fano resonance in optical frequencies as well as high spectral contrast with strong dispersive resonance and agile dynamic tunability by simply manipulating the incident light polarization state without the need to change the nanoslits geometry, or the structure parameters of the system. These Fano line-shapes clearly exhibit strong polarization dependence. The polarization-selective controllable multispectral Fano resonance is of practical significance for applications of sensitive bio-sensing, switching and optical signal processing. The geometry may be implemented within currently available lithographic techniques and integrated with other optical devices for polarization manipulation [32–35 ], detection, and sensing [8, 9, 36 ] at the nanoscale [2, 28 ].
2. Structures and method
The proposed system consists of metallic film with periodic subwavelength nanostructure on top of a high-index dielectric slab waveguide spacer layer with a lower dielectric index material as the substrate.
The scheme of the periodic array system with gold nanostructures thickness h, slab waveguide layer thickness T, and periodicity P is shown in Fig. 1(a) . The incident light with the electric field polarization along the x direction illuminates the system with an incident angle θ and angle of polarization α. A schematic of a T-shaped slot antenna is shown in Fig. 1(b). A T-shaped hole made of two orthogonal rectangle nanoslits is located in the gold film with a thickness of h = 50 nm. The arm lengths of the T-shaped slot antenna are labeled as L1, L2, whereas the arm width is w. The x and y axes lie along the directions of the antenna arms. The square period of the orthogonal nanoslits array is P.
The rigorous coupled wave analyses method is employed to model the optical properties of the structure . In the numerical modeling, the dielectric constants of Au is fitted by Drude-Lorentz model and the refractive index of the substrate and the waveguide layer are set as ns = 1.52 and nwg = 2.1, respectively.
3. Subgroup decomposition and polarization-selective properties of the plasmonic resonance in hybrid plasmonic system with T-shaped nanoslit antennas
The Fig. 2 shows the transmission spectra of the system at normal incidence for varied linear polarization angles. For TM polarization (transverse magnetic field, 0° polarization angle in this system), the transmission curves with two transmission peaks are clearly seen, exhibiting typical Fano asymmetric profile. For TE polarization (transverse electric field, 90° polarization angle) case, due to the excitation of different resonance modes in the two orthogonal nanoslits, the transmission spectra are deviated from that of TM polarization. For TM polarization, the narrow transmission peak centered at wavelength 992 nm is shown. Whereas, for TE polarization, a fully suppressed transmission dip with splitted new transmission peaks appear. This indicates that switchable optical transmission on-state and off-state can be realized by manipulating the polarization direction of the incident light. Introducing of the waveguide spacer layer can increase the freedom for tailoring the resonance response of the system, which leads to the variety of tunable multispectral planar plasmonic analogue of Fano resonances.
For increased polarization orientation angles, the first transmission peak at short wavelength zone exhibits only slightly weaken of transmission peak value featured with fixed center position. Meanwhile, for the second peak in the long wavelength zone, the resonance positions shifts toward to short wavelength zone. For varied incident light polarization direction, the first transmission peak appears at fixed central wavelength around 992 nm for TM polarization, and the peak value gradually decreases as the polarization angle increases from 0° to 90°. We note that this transmission intensity variation with unaltered peak position can be potentially used as a planar plasmonic attenuation-slice. The resonance transmission strength and the width of the Fano resonance is related to the polarization state of the incident light. This indicates the optically dynamic and continuously adjustable Fano resonance property of the system, the plasmonic response can be tuned with a fixed center position and the profile of the resonance is altered efficiently by polarization angles of incident light.
Furthermore, one can see that the second Fano resonance peak at longer wavelength zone shifts to short wavelength as the incident polarization angle increases. In traditional ways, the Fano resonance wavelength position is tuned by varying the geometrical parameters, however, efficient and convenient method to obtain Fano resonance intensity tuning without changing the position of resonance is desired. By introducing and adopting the asymmetric structure unit cell, the Fano resonance spectral position shifts is obtained simply by changing the angle of incident polarization.
To gain better view and insight to the nature, we have numerically calculated the field distribution on the upper surface of the metallic nanostructure for the Fano resonances peaks in the transmission spectrum for both TM and TE polarization. The distribution of magnetic field component Hz at the transmission peaks positions for both TM and TE polarization cases are shown in Figs. 3(a)-3(e) . The different features of the resonance property are obviously observed for each other. For TM polarization, the excited magnetic field distribution of its component Hz shows strong resonance localized in the slit perpendicular to the incident polarization; while for TE polarization, the resonance in the parallel and perpendicular slits both contribute to the resonance of its composited T-shaped structure. In addition, it is noted that the field distributions at resonance for the first transmission peak manifest itself with multiple resonance property (see Fig. 3(a), 3(c), and 3(d)), in contrast, the resonances at the second peak positions for TM at 1524 nm (see Fig. 3(b)) and TE at 1366 nm (see Fig. 3(e)) show typical dipolar resonance characters.
For further confirmation of the multi-resonant behavior and in order to gain insight understanding of the formation of multispectral Fano profile, the transmission responses of individual rectangular nano-aperture antenna are investigated. The individual orthogonal slits transmission are evaluated and the results shown in the Figs. 4(a) and 4(b) illustrate the Fano resonance transmission of the rectangular slit array for parallel and perpendicular incident light polarization, respectively.
From the results in Figs. 4(a) and 4(b), it is seen that, in TE polarization case, the overall spectra is attributed to the overlap of individual subgroup transmission at relevant resonance positions. The first and second transmission peaks below 1200 nm are mainly related to the transmission of slits array along Y-axis, and the third peak centered at 1366 nm is observed, which greatly arises from the transmission of subunit slits array along X-axis can find evidence from the transmission of the subunit slits array. Although the resonance intensity and positions show slight shifts and differences, the resonance profile of the whole spectra can be decoded into two individual contributions from its subgroup for different orientation of geometry and incident polarization. In TM polarization case, the whole spectral is dominated by the subgroup resonance contributes from the subunit with slits array perpendicular to the incident polarization [32, 33 ]. This result corroborates the observation in the overall spectra profile and the explanation of the overlapped spectral feature of its two subgroups for different polarization cases.
The origin of the peaks in the whole spectra of the proposed system with T-shaped nano-holes can be explained by the clue and enlightenment from the decomposition of plasmonic resonances of the subcell with regular rectangular slits. The whole spectra resonance profile is related to the overlap of the resonance of the subcell rectangular slits array at different resonance positions. The results in Fig. 4 show the transmission spectra of the subcell and the proposed system, which presents intuitively understanding and tailoring of the overall spectra by the individual contributions from its subgroups at the relevant resonance positions. It is also noteworthy that polarization-selective window-mirror-like effect at around 992 nm for the system is also observed . The potential optical switch effect of the system centered at 992 nm can be simply controlled depending on the state of polarization of the incident light.
The total spectrum of the proposed T-shaped system can be regarded as the convolution of the two separate sub-spectra [19, 31 ]. The sketch of coupling and decomposing of the group and the subgroups are depicted in the Fig. 4(c). The observation of the subgroup resonance spectra position and strength confirms the very weak interaction between the two eigenstates of the two subgroups. It is also important to note that unlike systems with strong Fano interferences, for this case the subgroup interference is so weak that each subgroup is active at a particular frequency range where the other is inactive, leading in this way a final spectrum that is the exact convolution of the two sub-spectra [19, 31 ]. Such subgroups resonances are the real eigenstates of the subgroups whose interference gives rise to the overall resonance lineshape.
It can be seen clearly that these two different polarizations give the varied transmission spectral profile, where the transmission excited by the perpendicular polarized light dominates and contributes significantly to the whole spectral of the system with T-shaped nano-holes array . Meanwhile, it indicates that the geometric arm length L1 and L2 are related to the transmission value and peak positions particularly for perpendicular incident polarization. Therefore, the whole spectra for varied polarization can be tailored and manipulated. To verify this, we investigate the spectra evolution as a function of the arm length L1 of the nanoslits perpendicular to the polarization direction for TM polarization, and L2 for TE polarization. The results are plotted in Figs. 5(a) and 5(b) . For TM polarization, the resonance of the complex unit cell is dominated by the resonance excited in the nanoslit perpendicular to the polarization direction, where the plasmon resonance in the slit is dependent on the arm length of the nanoholes. The resonance position shows redshift as the arm length L1 increases. We can see that the transmission is enhanced for larger arm length, which shows monotonous change. It is noted that the resonance linewidth shows non-monotonous change. The first transmission peak is suppressed for increased arm length, whereas, the second transmission peak is broadened. The longer the perpendicular slit arm length the stronger of the second transmission peak, and the Fano lineshape is continuously modified as the geometry asymmetry is adjusted. The asymmetric shape of the transmission can be expressed by the Fano model as [1, 19 ]:
where q is an asymmetry factor, and are the central wavelength and width of the resonance, and A is a free parameter normalizing the transmission. The fitting parameters and the results are depicted in Fig. 6 . The Fitting parameters of the Fano-profile transmittance for both polarization cases are listed in the Table 1 .
Indicating from the decomposition and formation of the plasmonic resonances of the subcell and the overall multispectral Fano resonance, the subcell nanoslit resonance states for two horizontal and perpendicular polarized incidences can be regarded as two eigenstates. The hybridization and combination of these two eigenstates with two kinds of incident polarization excitation are attributed to the T-shaped holes transmission. Considering the positions of the peaks with respect to the resonance strength for different excitation polarization states, the variability and controllability of the Fano transmittance of the proposed T-shaped nanostructure can be obtained for varied incident polarization states. Afterwards, we test the special cases with the incident polarization state, where the left-handed circularly polarized (LCP) light and the right-handed circularly polarized (RCP) light are employed. The averaging-effect result of the resonance transmission for both peak positions and the peak values are observed, which can be understood by the linear superposition of the resonance eigenstates for directionally linear polarization. The transmission of the system for LCP and RCP incidence is shown in Fig. 7 .
Since the polarization states of the incident light is tightly related to the Fano transmission features, which indicates that the Fano resonance profile can be tuned by two incident beams, one with a linear polarized light and the other as a modulation beam with varied polarization direction, and electric field amplitude. By controlling properties of incident light beams, the Fano resonance spectrum including the resonance peak positions, resonance intensity, and peak numbers can be efficiently and agilely manipulated. This sheds light on way of dynamically tuning Fano resonance with polarization modulation incident wave.
4. Tunability and dispersion manipulation of the Fano resonance transmission
To understand the underlying physic, we investigate the light-matter interaction process in the system, which is intuitive and essential for manipulating and designing of the multiple Fano resonance. Figure 8 demonstrates the calculated transmission spectra for varied array periodicity p = px = py. The dispersion of the SPP (Surface Plasmon Polaritons) and Wood Anomalies (WA) are calculated and superimposed.
For an optically opaque metal film, only one SPP mode exists at the interface, e.g. the single-interface SPP. To understand the underlying physics and the cause of the transmission spectra feature, we investigate the dispersion curve of the system. The periodic structure of the square lattice nanoslits array enables light to be coupled to SPP through the grating momentum and obeys the conservation of momentum. The excitation condition of the (i, j)th-order SPP-Bloch wave mode is:
where is the momentum of free space light, and are the permittivity of metal and dielectric, respectively. and are the reciprocal lattice unit vectors in two periodic directions with . This is valid only for slightly modulated metal surfaces and ignores the coupling of SPP on the upper and lower interfaces of the thin metal film and can be used as a reference to help identify the SPP modes.
In addition, the condition for Wood anomaly, which is associated with light diffracted parallel to the surface, is written as:
Figure 8 shows the calculated transmission spectra of the system, where the calculated dispersion curves of SPP and WA are superposed. To make clear the appearance of the period-resolved spectra’s evolution, the condition for the cutoff of the (i, j)th diffraction order, where the optical anomalies corresponding to different interfaces occurs, is investigated. The WA appears in the transmission spectra of the system, where abrupt turning or suppression of the transmission happens.
The black and white dashed lines in Fig. 8(a) are the dispersion curves of SPP and WA Bloch waves of various orders, calculated with Eqs. (2) and T(3), respectively. The texts “air” and “sub” indicate the modes on the upper (air-gold) and substrate (gold-glass) interfaces, respectively. We can see clearly the signatures of all WA in the TM and TE cases (see Figs. 8(a) and 8(b)), where the spectra features can be figured out explicitly. The SPP Bloch wave dispersion curves always show a bit of red-shifted with respect to the corresponding WA due to its slightly higher effective index value. It is noted that the substrate and the metallic film are separated with a spacer layer in the proposed hybrid plasmonic system, therefore, the calculated dispersion illustrates guide to the eye and indicates that for short wavelength zone the dispersion of SPP-Bloch wave originates from the metallic and substrate is dominating. This is helpful for understanding the response zone and multiple resonance mechanism of the system, which implies the tunability and evolution of the overall spectra. For increased array period, the resonance of the first Fano transmission peak shifts to longer wavelengths.
The dispersion of the whole spectra can be engineered and the polarization-selective property of the multi-spectral Fano resonance is exhibited in a broadband zone. The active control of the wavelength-selective switchable multispectral Fano resonance can be feasibly manipulated by tailoring the geometry of the system and by conveniently adjusting the angle of incidence polarization.
In summary, the optical properties of hybrid waveguide-plasmon system supporting polarization-selective dynamically tunable multispectral Fano resonances have been investigated with numerical simulations and compared to the verification of theoretical analysis. Dynamic tunable multispectral Fano resonance at optical frequencies with flexible control over the Fano profile characterized by its resonance peak positions and spectral contrast is achieved through polarization-dependent response of the system. Dynamic and switchable Fano spectral profile can be efficiently tuned by external light polarization, which shed light on novel pathway for flexibly shaping and manipulating the plasmonic Fano resonance. The polarization-tunable multispectral Fano resonance could have far-reaching consequence for efficient plasmon functional tunable devices. The wavelength-tunability of the resonance and the transmission attenuation for the first resonance peak is enchanting, which provides the potential possibility for multifunctional nanophotonics devices design and application.
This work was supported by the Fundamental Research Funds for the Central Universities (Grant NO. XJS14068, NO. JB150514). The authors acknowledge financial support from the National High Technology Research and Development Program of China (863 Program) (Grant NO. 2014AA8098089D).
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