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Two-dimensional finite-difference time-domain (FDTD) method has been performed to numerically investigate the transmission through a one-dimension cupped surface metallic grating structure. The concept of coupling of optical modes in the notches and main slits, introduced by Crouse and Keshavareddy [1], is examined further in our work. Unexpected phenomenon is shown that even horizontal surface plasmons (HSPs) are inhibited, the transmission still can be enhanced or suppressed. And the periodicity of transmission depending on the phase change of the light striking on the grating surface is discovered. A hybrid optical mode combined by cavity mode and diffracted evanescent wave mode [2] is introduced to analyze the phenomenon.
©2006 Optical Society of America
1. Introduction
Since Ebbesen first reported the extraordinary optical transmission through a two-dimensional (2-D) hole array perforated on a metallic film in 1998 [3], optical properties of periodically subwavelength metallic structures have attracted a considerable interest during the past years [4–8]. As the simplified one-dimensional (1-D) version of the structure studied by Ebbesen’s group, a renewed attention also has been paid on analyzing the transmission properties of arrays of slits potential device applications [7–11]. The present common understanding of the mechanism responsible for this extraordinary enhanced transmission is the excitation of surface plasmon (SPs) at the interfaces of the structured film [3–7]. However, Cao and Lalanne [8] have argued that the resonant excitation of surface SPs suppresses the transmission in the 1-D gratings. While other viewpoints also exist which suggest that other factors, such as cavity mode (CM) or diffracted evanescent wave, may contribute more to enhanced transmission than SPs [2]. So recently there has been considerable disagreement in the roles of SPs and other factors in transmission and the physics behind this phenomenon remains in dispute [10–11]. More recently, Crouse and Keshavareddy [1] have examined several novel metallic grating structures with notches on surface which can inhibit HSPs. They come to the conclusion that in these structures, HSPs strongly inhibit transmission in most situations and only weakly enhance it in other situations, which contributs to new application in chemical and biological sensors etc.
In this paper, we numerically investigate the metallic grating structure with notches on front and back surface compared with Crouse and Keshavareddy’s result [1]. We mainly focus on the influence of the notches to the transmission and optical modes. The optical properties of this structure, involving the far-field transmission spectra, near-field electric field intensity and energy flow, are numerical discussed. We find that even if HSPs are inhibited in this structure, the transmission still can be enhanced or strongly suppressed.
2. Simulation method and model
The finite-difference time-domain (FDTD) method has been used in our work. The second-order Lorentz dispersion model [14] is used to simulate the metallic film, which has the frequency dependence of the permittivity. The second order Mur absorbing boundary conditions [13] are used in the left and right sides of gratings shown in Fig. 1. Furthermore, the others are confined with the periodic boundary conditions (PBC) [15].
Fig. 1. S1 is the classical lamellar grating profile. S2 has notches (gray part) in both front and back surfaces
The two grating structures examined are shown in Fig. 1. The left (denoted as S1) one is classical 1-D lamellar aluminum grating with narrow slits. The right one (denoted as S2) is the structure introduced in [1] which has notches in both front and back surfaces filled with nonmetallic substance. These two structures (S1 and S2) have the same grating period p=1500nm, the width of the slit w=300nm and the thickness h=1000nm. The width of notch in S2 is 1000nm and the depth d=300nm. The normal incident TM-polarized plane wave illuminates S1 and S2 from the left side. And the permittivity of aluminum is taken from values in [14]. In our analysis, the refractive index n of the nonmetallic substance in notches (S2) is main focus, and the range of wavelength we examined is 1450nm to 1650nm, including the HSPs excitation wavelength in S1 structure.
3. Simulation results and discussion
Above all, we consider the far-field optical responses to the structures. Figure 2(a) shows the zero-order transmission spectra of S1 and S2 with different refractive index n of substance in notches. A sharp peak with HSPs excitation can be observed in the spectrum of S1, but in S2 transmission can be enhanced or suppressed depending on the refractive index n. When n=1.3, the transmission is strongly enhanced due to the coupling between notches and main slits, which is similar to Crouse and Keshavareddy’s result. While Crouse and Keshavareddy only analyzed the structure where the notches enhance transmission, in our work we find that by studying a range of structure geometries that the notches can enhance or suppress transmission. For example, in S2 structure, the transmission is suppressed when n=3.2 shown in Fig. 2(a).
Fig. 2. (a).The zero-order transmission spectra of S1, S2 with n=1.3, 2.5 and 3.2. (b).The transmission spectrum at λ=1500nm versus refractive index n in S2. (c) The transmission spectra of S1, S2 with n=2.5, 5, 7.5.
Furthermore, for observing the influence of the notches clearly, we change the value of refractive index n continuously. Figure 2(b) shows the transmission spectrum at λ=1500nm versus refractive index n in S2, which exhibits the periodicity of transmission variety obviously. We think that this periodical variety is due to the phase change of the light striking on the grating surface. In our analysis, the phase change of the light striking on the grating surface is different between S1 and S2 for the notches. If refractive index n of the notches changes, the optical path difference between S1 and S2 changes subsequently as well as the phase difference. The formula of the phase difference between S1 and S2 is knd nd . d is the depth of notch and n is the refractive index of substance in notch. λ is the wavelength of incident light which is set to λ=p=1500nm for convenience. We can see the period Pn of refractive index variety is about 2.5 in Fig. 2(b), so the period of phase difference is equal to . Hence, we think the phase change of the light striking on the grating surface is a key factor to transmission, which is in essence a parameter describing the coupling of optical modes in the notches and main slits. If the phase difference equals to multiple of 2π, the transmission keeps the value still.
In order to check our conjecture above, the optical properties of S2 with different refractive index have been compared with that of S1. The transmission spectra of S1 and S2 with n=2.5, 5, 7.5 (withΔϕ=2π,4π,6π) are shown in Fig. 2(c), in which the positions and shapes of peaks at Δϕ=2π,4π,6π all approach to the one in S1 with HSPs. The near-field images are also depicted in Fig. 3(a), which shows the near-field time-average distribution of |E|2 at the peaks of transmission spectra of S1 and S2 with n=2.5. For the situations of n=2.5, 5 and 7.5 are similar, we only choose n=2.5 for example. In common understanding, HSPs can be excited in S1 and cause electronic field localization only on metallic surface. The same situation should not appear in S2 because nonmetallic notches inhibit HSPs. However, we find the similar electronic field distribution in Fig. 3(a) on nonmetallic surface in S2 as HSPs in S1, with the phase difference Δϕ=2mπ (m=1, 2, 3…). Localized electric field in the slits (cavity mode) in Fig. 3(a) can be observed both in S1 and S2. Figure 3(b) shows the pointing vector distribution at the peaks of transmission of S1 and S2 with n=2.5. The situations of energy flow are also similar according to the pointing vector distribution. Two vortexes formed by energy flow above the surface can be observed which fits to the result reported before [1, 9]. Nonmetallic notches seem to have no effect on energy flow.
Fig. 3. (a)The electric field time-average distribution of |E|2 at the peaks of transmission spectra of S1 and S2 with n=2.5.(b)The pointing vector distribution at the peaks of transmission spectra of S1 and S2 with n=2.5.
Then a question appears: what is the reason to cause the similar optical properties including transmission and electronic field distribution in S2 as HSPs? We introduce the diffracted evanescent wave model [2] to analyze the question, which has reported that composite diffra-cted evanescent wave (CDEW) can enhance transmission on nonmetallic surface like HSPs. According to the paper [2], the CDEW model is in essence a Wood’s anomaly model which incorporates both the minima as Rayleigh anomalies and the maxima as Fano resonances. However, the CDEW model goes beyond the phenomenological approach and offers a concrete and quantitative description of the transmission of hole arrays, of which the principles are amply supported by experimental data. Although HSPs are inhibited in S2, the CDEW exists and influences the transmission and electronic field distribution. According to the transmission function in [2],
T H(λ) is relation to the cavity mode in the slits of grating, A 1(λ) and A 2(λ) are the front-surface and back-surface modulation functions of CDEW respective. In structure S2,
n 0 is the effective index of refraction on the surface of S1, and Δϕ is the phase difference between S1 and S2. If the phase difference fits the condition Δϕ=2mπ (m=1, 2, 3…), the values of A 1(λ) and A 2(λ) have no change, so the transmissions keeps the value, which fits the result above well. Therefore, we can explain the unexpected phenomenon in S2 using a CDEW/CM hybrid optical mode, and consider the phase change on surface of grating is a key factor to influence the hybrid mode periodically. In order to investigate the influence of the phase change to the CDEW/CM hybrid mode in great detail, we discuss other two representative situations hereinafter.
Fig. 4. (a) The near-field electric field time-average distribution of |E|2 with n=3.2 and λ=1550nm. (b) The pointing vector distribution with n=3.2 and λ=1550nm.
When we set , the transmissions get the minimal values according to numerical study. We take n=3.2(Δϕ=2.5π) for example. The transmission spectrum is shown in Fig. 2(a). In fact, we find in numerical that if the phase change increases continuously, the transmission peak red-shifts and reduces to zero, then new peak appears and red-shifts again. In the spectrum of n=3.2 in Fig. 2(a), the transmission is just at the situation that last peak is reducing to zero while the new one is appearing freshly. So the transmissions are minimized. The images of near-field electronic field and energy flow with n=3.2 at λ=1550nm are shown in Fig. 4. In Fig. 4(a) the localized electronic field on surface is weak and cavity mode nearly disappears in slits of gratings. And in Fig. 4(b) most energy flows in the notches not in the slits. Hence, in this situation, we consider that CDEW and CM are both strongly inhibited which minimizes the transmission and localized electric field.
Fig. 5. (a) The near-field electric field time-average distribution of |E|2 with n=1.3 and λ=1550nm. (b) The pointing vector distribution with n=1.3 and λ=1550nm.
When we set Δϕ=(2m-1)π (m=1, 2, 3…), the transmissions obtain the maximal values. We take n=1.3(Δϕ=π) for example. Higher and broader peaks are shown in transmission spectrum of n=1.3 in Fig. 2(a). The near-field images about electronic field and energy flow with n=1.3 at λ=1550nm are shown in Fig. 5. Localized electric field on the surface is inhibited in Fig. 5(a) and only appears in the slit of grating. In Fig. 5(b) most energy flows in the slit and transmits, only a little flows in notches and reflects. This situation fits to the result in [1] which also shows higher and broader transmission peak and similar pointing vector distribution. So we conclude that in this situation, CDEW is inhibited but CM is strong enhanced, and transmission is maximized by CM mode.
Since the grating structures S1 and S2 are all composed of aluminum which has a high absorption and may lead to suppression in transmission, we also examine the same structures composed of gold to checkout our result. The transmission spectra of S1 and S2 composed of gold are shown in Fig. 6, which is similar to Fig. 2(a). When n=3.2 in golden S2 structure, the transmission is still inhibited in Fig. 6. Although aluminum has been changed to gold in the grating structures, the same enhanced and suppressed situations still appear which prove that the absorption of aluminum seems to have no effect on the phase relations above.
4. Summary
In this paper, we investigate further about the concept of coupling between optical modes in the notches and main groove introduced by Crouse and Keshavareddy [1] and analyze the phenomenon that transmission can be enhanced or suppressed when HSPs are inhibited. Through discussing with the CDEW model [2], we consider that transmission is controlled by a CDEW/CM hybrid optical mode, and the phase change of light striking on surface of grating is a key factor to this hybrid mode. By controlling the phase change, CDEW and CM component can be inhibited or enhanced respectively to influence the optical properties, including the transmission and near-field electronic field and energy flow. We have mainly focused on three representative situations to describe the properties of CDEW/CM mode, involving the maximal, minimal and similar transmission situations to classical metallic grating, which may lead to much new application in different fields. For example, the maximal transmission is useful to chemical and biological sensors, and the similar surface localized electric field as HSPs can be used in near-field detector etc. We hope that our works are helpful for understanding the essence of extraordinary transmission for grating structures, and contribute to more application.
Acknowledgments
This work is supported by National Natural Science Foundation of China under Grant No 90206002, 10474093, and the Special Funds for Major State Basic Research Programme of China under Grant No. 2005CCA04200.
References and links
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