1. Introduction

Extraordinary optical properties in the asymmetric structure have attracted a tremendous amount of attention in recent years [1–6]. The flexibility in the geometry of asymmetric structure has provides novel opportunities to manipulate an electromagnetic wave with artificial materials, leading to its novel optical properties and promising applications, such as biosensors [7], enhanced transmission [8], and absorber [9,10]. Recently, many groups have induces different designs of asymmetric structure to the sensing field. Accordingly, Sonnefraud et al demonstrated Fano-type resonances in the ring/disk cavity by introducing structural asymmetry to the system [11]. Later, Cetin et al further introduced a conducting metal layer to above asymmetric ring/disk nanocavity system to enhance Fano-type resonances in biosensing sensing application [12]. As we known, sensing platforms demand narrow resonances to accurately measure variations, which is essential for improving the sensing devices’ performance [13]. The appearance of Fano resonance due to structural asymmetry satisfies the requirement with narrow and sharp resonance. Meanwhile, in the other field, a bandpass filter has been designed based on the Fano-type resonance between metallic grating and thin dielectric layer with enhanced optical transmission [14]. To overcome the drawbacks of poor angular tolerance of the above filters, an asymmetric bi-atom pattern grating-dielectric structure was induced with a great increase of the angular tolerance [15]. In the previous works, a dual-wavelength filter was demonstrated based on symmetry-reduced double layer metallic gratings. The appearance of the two narrow-band resonance dips at the normal incidence is attributed to the structural symmetry breaking [16].

In this paper, based on the previous work about symmetry-reduced double layer metallic gratings, we further investigate the effect of this asymmetry induced by different thickness of the top and down layer metallic gratings on the optical properties of asymmetric double layer structure. We find that, one remarkable narrow-band transmission dip at normal incidence is generated in the structure when the thickness of the down layer metallic grating has certain fixed value. It is noticeable that FWHM of this dip in the designed asymmetric structure is more than two times narrower that of symmetry structure. It is more feasible and convenient to tune the position of transmission dip by only controlling the thickness of top layer metallic grating than by changing the period and width of the metal nanowires. However, the resonant dip is not adjusted by changing the grating thickness. It is observed that the transmission dip insensitive to lateral displacement between top and down layer metallic gratings, which provides less demanding for design of asymmetric structure. We also investigate the relationship between structure parameters of waveguide layer and the thickness of down layer metallic grating in order to guarantee the appearance of one dip in the designed structure. Finally, the fabrication tolerance of each design parameter and the effect of dielectric environmental changes in the both sides of structure on optical characteristics of structure are considered. The validity of these results is further verified by comparing results from different numerical methods.

2. Structure and the simulation method

Figure 1 illustrates the schematic of the designed wavelength filter, which include two sets of metallic gratings deposited on both sides of a waveguide layer with a refractive n = 2, respectively. As represented in Figs. 1(a) and 1(b), the asymmetric structure is achieved by two main parts: one corresponding to moving alternatively metal nanowires of the top layer metallic grating, the other corresponding to possessing different thickness of the top and down layer metallic gratings which is most important distinct from that in the previous report [16]. Cross-sectional views of symmetric and asymmetric double layer metallic gratings are shown in Fig. 1(b). The asymmetric structure is free-standing in the air (n_s = 1) and has dimensional parameters as follows: nanowire width (w), structure period (P), the thickness of top layer (t_m1) and down layer (t_m2) metallic gratings, waveguide layer thickness (t_d), and dielectric environment in the both sides of the structure (n_s). Compared to the symmetric structure, parameters L₁ and L₂ play an important role in the asymmetric structure. To investigate the extraordinary optical properties of the designed structure, we employ the commercial software Lumerical FDTD Solutions [17] for calculation. An incident light with its polarization along the x-axis is adopted. The frequency dispersion of the permittivity of bulk gold is expressed by the Drude-Lorentz model [18]. In our simulation, the detailed description about software’s settings is given in the previous report [16]. The parameters of the structure are given as follows: w = 100 nm, P = 1000 nm, t_m1 = 20 nm, t_m2 = 64 nm, t_d = 250 nm. The above parameters will keep constant unless noted in the following text.

 

Fig. 1 Structure schematic of guided mode resonance wavelength filter. (a) Three-dimensional diagram of the designed structure with two sets of metallic gratings deposited separately on both sides of a waveguide layer. (b) Cross-section of the symmetric and symmetry-reduced structures and their structure parameters.

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In addition, the designed structure can be fabricated by using modern nanostructure fabrication technology, such as electro-beam lithography (EBL), lift-off method and plasma-enhanced chemical vapour deposition (PECVD). The potential fabrication can be processed as follows: firstly, a 250 nm silicon nitride layer and alignment markers are deposited on the polished silicon substrate by using PECVD technology. On this layer, the top layer metallic grating of the designed structure is defined by EBL in a PMMA (poly(methyl-methacrylate)) resistant layer and then developed, following by gold deposition and lift-off; in the next step, the membrane is released with the wet etch of silicon substrate and the lower surface of silicon nitride is polished; on the lower surface of silicon nitride, the down layer metallic grating is fabricated by the same methods, just as it is in the top layer metallic grating. The upper and lower sides can be covered by the dielectric layer with different refractive index by using PECVD technology [19,20].

3. Results and discussion

To have a direct look at the effect of the thickness of metallic grating on the transmission dips, we quantitatively shows in Fig. 2 the relation between transmission dip position and two sets of metallic gratings thickness, respectively. As we previously reported and shown in Fig. 2(a), for asymmetry double layer metallic grating, there are two remarkable transmission dips (labeled A and B) at normal incidence. And there is no appearance of the transmission dip in the symmetry structure [red line of Fig. 2(a)]. However, further studies show that the thickness of the top layer and down layer metallic gratings has a different role in adjusting two transmission dips position. As shown in Fig. 2(b), the influence of the thickness of top layer metallic grating t_m1 on two transmission dips is shown. As grating thickness t_m1 increases, dips A and B have a red shift simultaneously. It is observed that the gap between dips A and B have remained about the same as grating thickness t_m1 changes from 20 nm to 100 nm. However, grating thickness t_m1 continues to increase from 100 nm, the gap between dips A and B is increasing. The main cause of this phenomenon observed is that when grating thickness t_m1 is less than 100 nm, the electromagnetic filed enhancement at the dips A and B is mainly confined inside the waveguide layer. As grating thickness t_m1 is larger than 100 nm, the magnetic field enhancement has a transfer from the waveguide layer to the slits of top layer metallic grating [16]. Figure 2(c) presents the dependence of dips A and B on the thickness of down layer metallic grating t_m2. It is interesting to see that the wavelength position of dip B keep constant with the change of grating thickness t_m2. And only dip A have an obvious redshift as grating thickness t_m2 increases. What calls for special attention is that when grating thickness t_m2 equals to 64 nm, the wavelength of dips A overlaps exactly with that of dip B, which generates that transmission dip can be transformed from two to only one dip even if the existence of symmetry breaking in double layer metallic grating. Compared to that of symmetric structure, the transmission dip of asymmetric structure has narrow full width at half maximum (FWHM), as shown clearly in Fig. 2(d). So, asymmetric structure is a good choice for the design of a wavelength filter.

 

Fig. 2 (a) The typical transmission spectra of the symmetric (red line) and symmetry-reduced (blue line) structures with t_m1 = t_m2 = 20 nm. The dependence of calculated two transmission dips on the thickness of metallic gratings for (b) top layer and (c) down layer. (d) The typical transmission spectra of three different structures with t_m1 = 20 nm and t_m2 = 64 nm.

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The validity of results from FDTD method is further confirmed by comparing the results with those obtained from the finite element method (FEM) [21]. As shown in Fig. 3(a), the results from FDTD method are almost in agreement with that of FEM. Moreover, we find that the transmission spectrum in Fig. 3(a) shows a striking characteristic of Fano-like resonance: a transmission dip close to a transmission peak. In order to verify the Fano-like resonance, we fit the transmission spectra to the analytical model of Fano-like resonance in Eq. (1) [22]

 

Fig. 3 The comparison of results for three kinds of computing methods. (a) FDTD simulation (blue solid line) and FEM simulation (red dashed line). (b) FDTD simulation (red solid line); fit with Eq. (1) (black dashed line) for the dip.

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To make a systematic discussion of the structure, we investigate the effect of various structure parameters on the transmission dip in the following. Figure 4(a) demonstrates the influence of grating thickness t_m1 on the transmission dip with grating thickness t_m2 = 64 nm. It is observed that there is only one transmission dip in the transmission spectrum of the designed structure and transmission dip position has a red shift monotonously as grating thickness t_m1 changes from 20 nm to 180 nm with keeping grating thickness t_m2 = 64 nm constant. This illustrates that whether there are two transmission dips or one transmission dips in the designed structure depends on the thickness of down layer metallic grating t_m2, which makes that the transmission dip can be adjusted by simply changing the thickness of top layer metallic grating t_m1. However, for the symmetric structure with P = 1000 nm, the thickness of the metallic grating hardly affect the position of dips [16]. It is more feasible and convenient to tune the position of transmission dip by controlling grating thickness t_m1 than by changing the period and width of the metal nanowires in the fabrication of some filters device. Moreover, Fig. 4(b) presents the dependence of calculated transmission spectra on structure period P with fixed duty cycle of metal nanowire w/P = 0.1 and grating thickness t_m1 = 20 nm and t_m2 = 64 nm. To our surprise, the change of structure period P doesn’t bring out the splitting of one transmission dip, and dip position is approximately linear to the structure period P. It demonstrates that the position of transmission dip can be easily tuned in a larger spectral region without modifying their spectral separation with the change of structure period.

 

Fig. 4 (a) The response of calculated transmission dip position on the top layer metallic grating with t_m2 = 64 nm. (b) The dependence of calculated transmission spectra on structure period with fixed t_m1 = 20 nm and t_m2 = 64 nm.

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In our research, the asymmetry of the designed structure mainly depends on parameters L₁ and L₂. As shown in Fig. 5, we further investigate the influence of different structure parameters L₁ and L₂ on the transmission dip with grating thickness t_m1 = 20 nm and t_m2 = 64 nm. Figure 5(a) demonstrates transmission spectra for different L₁ with fixed L₂ = 500 nm. From Fig. 1(b), we can observe that, when parameter L₁ varies from 0 nm to 100 nm, nanowire width w has a continuous increase from 100 nm to 200 nm in the top layer metallic grating, which cause that the position of dip have a red shift and the FWHM of dip increases. This phenomenon is attributed to the retardation effect and the radiation loss of metalmaterial due to the increase of metal nanowire width. As parameter L₁ changes from 150 nm to 480 nm, parameter L₁ have a minor effect on the position of dip, but the FWHM of dip decrease gradually. When parameter L₁ is close to 500 nm, corresponding to symmetric structure with P = 500 nm, transmission dip disappears due to guide mode resonance in the waveguide layer not excited. Calculated transmission spectra for different L₂ with fixed L₁ = 250 nm is plotted in Fig. 5(b). The most noticeable point is that when parameter L₁ is located in the range from 400 nm to 700 nm, the position and FWHM of dip is almost constant. So both the position and FWHM of dip have a little sensitivity on parameters L₁ and L₂, which makes the fabrication of a narrow-band wavelength filter based on asymmetric structure less demanding.

 

Fig. 5 Calculated transmission spectra for the designed structure at (a) different L₁ with fixed L₂ = 500 nm and different L₂ with fixed L₁ = 250 nm.

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To further investigate the mechanism of the generation of the single transmission dip, more analytical results are presented in Fig. 6. The normalized magnetic field distribution at wavelengths λ = 1279 nm corresponding to grating thickness t_m1 = 20 nm are shown in Fig. 6(a). It is observed that the standing wave is induced transversally in the thin waveguide layer. In other words, guide mode resonance is excited in waveguide layer in Fig. 6(a). Compared to that of dips A and B in Fig. 2(a) [16], a remarkable distinction is that magnetic field distribution for single transmission dip is a superposition of magnetic field distribution of dips A and B. This can be verified by that the maximum value of magnetic field in the waveguide layer has a P/8 shift to the left and is justly located in the middle between that of dips A and B. the above phenomenon means that two kinds of guide mode resonance can be excited simultaneously for wavelength λ = 1279 nm in the waveguide layer. As a comparison, Fig. 6(b) presents magnetic field distribution at wavelengths λ = 1394 nm with the thickness of top layer metallic grating t_m1 = 180 nm. It is noticed that guided mode in the waveguide layer is weaken as the thickness of top layer metallic grating increases. The enhanced magnetic field has a remarkable transfer from waveguide layer to metal slits. It means that magnetic dipole inside the metal slits is excited with the increase of grating thickness t_m1. As we previous reported, with the increase of grating thickness, angular tolerance of dip will be improved due to the excitation of magnetic dipole.

 

Fig. 6 Spatial distribution of magnetic field for the designed structure at (a) resonant wavelength λ = 1279 nm with the thickness of top layer metallic grating t_m1 = 20 nm and resonant wavelength λ = 1394 nm with the thickness of top layer metallic grating t_m1 = 180 nm. Spatial distribution of magnetic field at (c) λ = 1279 nm with t_m1 = 20 nm and (d) λ = 1394 nm with t_m1 = 180 nm.

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Figures 6(c) and 6(d) depict the Poynting vector (S) distribution at different wavelengths λ = 1279 nm and λ = 1394 nm, corresponding to grating thickness t_m1 = 20 nm and t_m1 = 180 nm, respectively. Poynting vector (S) means that how the light propagates in the designed structure before it is absorbed, reflected and transmitted. The Poynting vector of the transmission dip of λ = 1244 nm [Fig. 6(c)] shows that the incident electromagnetic energy propagates along the waveguide layer with the surface of the metallic grating as upper and lower boundaries. Compared to that of Fig. 6(c), the Poynting vector at λ = 1394 nm with grating thickness t_m1 = 180 nm has a different distribution: the electromagnetic energy is mainly inside the narrow slits of the top layer metallic grating. Two stronger vortex flows are formed around the top layer metal nanowires. This reveals magnetic dipole inside the metal slits is excited with the increase of grating thickness t_m1. Furthermore, the formation of a vortex flow in the structure can also increase the time of light propagating in the structure and the dissipation losses of metal nanowires.

As illustrated in Fig. 7, we also investigate the influence of the incidence angle θ on the transmission dip. It is found that transmission dip is divided into two dip at non-zero incidence angle. As incidence angle θ increases, the gap between the two dips increases. And the two transmission dips can keep narrow bandwidth simultaneously in the angle range from 0° to 10°. It is worth noting that both transmission dips have a good linear approximation to incidence angle, as shown in Fig. 7(a). So single transmission dip is only achieved under the normal incidence.

 

Fig. 7 (a) Calculated transmission spectra for the designed structure at different incidence angle θ with fixed w = 100 nm, t_d = 250 nm, P = 1000 nm, t_m1 = 20 nm and t_m2 = 64 nm. (b) The linear approximations between the position of two transmission dips and incident angle.

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In addition, Fig. 8(a) shows the relationship between transmission dip and the lateral displacement ∆ (∆ refers to lateral displacement between top and down layer metallic gratings). It is interesting to notice that the position of transmission dip has weak dependence on lateral displacement ∆, and transmission dip has not be divided into two dip in the range from 0 nm to 1000 nm with fixed t_m1 = 20 nm and t_m2 = 64 nm. However, for some symmetric structure, the change of lateral displacement will induce the asymmetry of structure, which will increase some other peak as a by-product in the transmission spectrum. As we known, in the practical preparation of double layer metallic grating, it is extremely difficult to control the alignment of double metallic grating. This by-product induced by lateral displacement is some obstacle for the design of device. Here, the transmission dip insensitive to lateral displacement ∆ provides a simple way for design of asymmetric structure. Furthermore, Fig. 8(b) demonstrates the effect of the change of lateral displacement ∆ on the position of transmission dip for three sets of grating thickness t_m1 = 20 nm, t_m1 = 100 nm, and t_m1 = 180 nm. It is noticed that as grating thickness t_m1 increases, transmission dip for t_m1 = 100 nm and t_m1 = 180 nm still have not any split, but the fluctuation of transmission dip position increases. This fluctuation stems from the change of electron distribution in the nanowires of down layer metallic grating [16].

 

Fig. 8 (a) Calculated transmission spectra for different with fixed t_m1 = 20 nm and t_m2 = 64 nm. (b) The effect of the change of lateral displacement ∆ on the position of transmission dip for different thickness of top layer metallic grating.

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In order to ensure the appearance of single transmission dip in the asymmetric structure, the relationship between structure parameters of waveguide layer and the thickness of down layer metallic grating (t_m2) is explored in the following text. Figure 9(a) presents the relation between refractive index of waveguide layer (n) and grating thickness t_m2. It is interesting to see that there is a good linear approximation between refractive index and grating thickness t_m2 to keep the appearance of one dip in the designed structure. Meanwhile, resonant dip position also has a linear approximation on refractive index of waveguide layer (n), as shown in Fig. 9(b). According to above results, it demonstrates that transmission position can be easily adjusted in a large spectral region. Furthermore, Fig. 9(b) demonstrates that the relationship between the thickness of waveguide layer (t_d) and the thickness of down layer metallic grating (t_m2). As the thickness of waveguide layer increases, grating thickness t_m2 must have a corresponding increase to keep the appearance of single transmission dip. In Fig. 9(c), the relationship between the thickness of waveguide layer (t_d) and the thickness of down layer metallic grating (t_m2) satisfies secondary polynomial fit. It is notice that the dependence of resonant dip position on the thickness of waveguide layer also secondary polynomial fit. It is noteworthy that the above results are suitable for different thickness of top layer metallic grating.

 

Fig. 9 (a) In order to keep the appearance of one dip, the relationship between refractive index of waveguide layer (n) and the thickness of down layer metallic grating (t_m2). (b) The position of transmission dip on the dependence of refractive index of waveguide layer (n). (c) In order to keep the appearance of one dip, the relationship between the thickness of waveguide layer (t_d) and the thickness of down layer metallic grating (t_m2). (d) The position of transmission dip on the dependence of the thickness of waveguide layer (t_d).

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Moreover, the fabrication tolerance of each design parameter is presented as follows. The main design parameters of structure have period P, the thickness of top layer metallic grating t_m1, the thickness of down layer metallic grating t_m2, waveguide layer thickness t_d, and nanowire width w. The influence of period P and the thickness of top layer metallic grating t_m1 on the transmission dip are shown in Fig. 4(b) and Fig. 4(a), respectively. In the following, Fig. 10 presents that the influence of the thickness of down layer metallic grating t_m2, waveguide layer thickness t_d, and nanowire width w on transmission dip in the designed structure, respectively. As shown in Fig. 10(a), when the thickness of down layer metallic grating t_m2 ranges from 62.5 nm to 64 nm, there is a dip in the transmission spectrum. So, fabrication tolerance of thickness of down layer metallic grating t_m2 is small, around 62.5-64 nm. According to Fig. 10(b), the fabrication tolerance of waveguide layer thickness t_d is relative large, about 249.5-259 nm. It is about 10 nm for an error size of waveguide layer to keep a single transmission dip. Accordingly, fabrication tolerance of nanowire width w is also small, around 100-103.5 nm. Therefore, further investigation will focus on the device fabrication by controlling the tolerance of the design parameters.

 

Fig. 10 The effects of (a) the thickness of down layer metallic grating t_m2, (b) waveguide layer thickness t_d, and (c) nanowire width w on the transmission dip in the designed structure.

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Additionally, all above investigations is based on a free-standing structure in the air (n_s = 1), however, a practical structure design is located in dielectric environment. We find that transmission dip cannot be transformed from two to only one dip if upper side of the structure is covered by the air and lower side is supported by a dielectric substrate with a refractive index of n_s = 1.46 (data not shown here). In other words, the appearance of asymmetry between a dielectric substrate and air cladding makes single transmission dip disappear in the designed structure. It is impossible to design a single wavelength filter when the designed structure is located in the asymmetric environment (the upper side of structure is the air and the lower side is a dielectric substrate), however, it is possible when upper and down sides of the designed structure are located in the symmetric dielectric environment. As shown in red line of Fig. 11(a), when the designed structure is located in the symmetric environment of n_s = 1.46, there is a single transmission dip with narrower full width at half maximum. Figure 11(b) also illustrates that, there is a good linear approximation between refractive index of symmetric dielectric environment (n_s) and the thickness of down layer metallic grating (t_m2) to keep the appearance of one dip in the designed structure. All above results are suitable for applying the designed structure in different dielectric environment.

 

Fig. 11 (a) Calculated transmission spectra of the designed structure with upper and lower sides in air (blue solid line) and in a dielectric substrate with a refractive index of n_s = 1.46 (red solid line). (b) In order to keep the appearance of one dip, the relationship between the refractive index of a dielectric substrate (n_s) and the thickness of down layer metallic grating (t_m2).

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4. Conclusions

In summary, we have presented a novel metal-dielectric structure which can provide a narrow-band transmission dip in the transmission spectrum even if the existence of symmetry breaking. The appearance of single transmission dip mainly depends on the thickness of down layer metallic gating. However, the change of the thickness of top layer metallic grating only has an important role in the position of this single transmission dip. Compared to that of symmetric structure, FWHM of dip in the designed asymmetric structure is more than two times narrower. We find that the physical mechanism of the appearance of single transmission dip is that two kinds of guide mode resonance are excited simultaneously in the waveguide layer. Moreover, the position of transmission dip has weak dependence on lateral displacement between top and down layer metallic gratings, which makes the fabrication of device less demanding. Last but most important, the relationship between structure parameters of waveguide layer and the thickness of down layer metallic grating (t_m2) in order to guarantee the appearance of one dip in the designed structure. The fabrication tolerance of each design parameter and the effect of dielectric environmental changes in the both sides of structure on optical characteristics of structure are also considered. This study is valuable for developing subwavelength-based a wavelength narrow tunable filter, an important photonic component that has extensive application in integrated optoelectronics system.