Transmission properties of metallic gratings coated symmetrically with a dielectric layer on both sides are studied theoretically. For subwavelength narrow slits, besides cavity resonances in slits and surface plasmon-polaritons, a new kind of mechanisms for enhanced transmission in coated metallic gratings, namely, guided resonances in the dielectric coating layers, is found. Transmission peaks mediated by guided resonances are found to be much sharper than those mediated by cavity or surface plasmon-polariton resonances.
© 2008 Optical Society of America
The experimental finding of extraordinary light transmission through optically thick metallic films perforated with periodic arrays of subwavelength holes  has sparked considerable interest. Enhanced light transmission through perforated subwavelength apertures is of great scientific values and can be exploited in different technological areas as well . For subwavelength hole arrays [3, 4, 5, 6, 7], it is generally believed that the excitations and coupling of surface plasmon-polaritons (SPPs), the collective electronic excitations at metallic surfaces , play an important role in enhanced transmission. In metallic gratings with subwavelength slits [9, 10, 11, 12], two mechanisms were revealed for enhanced transmission: cavity resonances in the slits and the excitations and coupling of SPPs.
In the present work, we study theoretically the transmission properties of metallic gratings coated symmetrically with a dielectric layer on both sides. For incident light with polarization parallel to the slit direction, besides cavity resonances in slits and the excitations and coupling of SPPs, another mechanism for enhanced transmission in coated metallic gratings, namely, guided resonances in the dielectric coating layers, is found. Interestingly, enhanced transmission mediated by guided resonances can also occur for subwavelength slits. Moreover, transmission peaks mediated by guided resonances are much sharper than those by cavity resonances or SPPs. These features would be exploited in the applications of photonic devices.
2. Results and discussions
The structure under study consists of a metallic grating coated symmetrically with a dielectric layer on both sides. The metallic grating has the following structural parameters: the grating thickness t, the grating period a, and the slit width w. For the coated metallic grating, it is assumed that the slits are filled with the same dielectric coating material. Without loss of generality, the dielectric layer is assumed to be characterized by a frequency-independent dielectric constant εd=2.25, while the metallic grating is made of Ag. The dielectric constant of Ag is described by the Drude model
where ωp is the plasma frequency and γ is the collision frequency, related to energy loss. The parameters used in the Drude model for Ag are ωp=1.37×1016 rad/s and γ=7.29×1013 rad/s, taken from Ref. . A plane-wave-based transfer matrix method [14, 15] is adopted to study the optical properties of the coated metallic grating. Within this method it is possible to calculate reflection, transmission, and absorption. In the present work, we only consider p-polarized incident light (with the magnetic field parallel to the slit direction).
Figure 1 shows the calculated transmission spectrum of a Ag grating coated symmetrically with a 600 nm dielectric layer under normal incidence. The structural parameters for the Ag grating are a=600 nm, w=15 nm, and t=300 nm. The transmission spectrum of the Ag grating immersed in a dielectric background with a dielectric constant of 2.25 is also given for comparison. For the Ag grating immersed in the dielectric background under normal incidence, there are basically three main transmission peaks in the displayed wavelength range, positioned at 552, 693, and 900 nm. By inspecting their magnetic field distribution patterns, it is found that the transmission peaks at 552 and 693 nm are due to the cavity resonances in the slits, while the transmission peak at 900 nm originates from the excitations of SPPs . When coated symmetrically with a dielectric layer on both sides, the transmission of the Ag grating is considerably modified. The three transmission peaks in the Ag grating immersed in the dielectric background still remain. The 552 nm transmission peak is nearly unaltered in wavelength, while the 693 and 900 nm transmission peaks shift their wavelengths to 691 and 884 nm, respectively. Interestingly, two sharp transmission peaks appear, one positioned at 625 nm and the other at 762 nm. Note that the corresponding wavelengths of the sharp transmission peaks are much larger than the slit width. Therefore, the observed enhanced transmission can be considered to be of subwavelength.
To explore the origin of the sharp transmission peaks, we show their corresponding magnetic field distributions in Fig. 2. It is obvious that for the two sharp transmission peaks at 625 and 762 nm their magnetic fields are sharply confined to the dielectric layers. They are no other than the guided resonances in the dielectric layers. Thus, the excitations of the guided resonances are responsible for the two sharp transmission peaks. From the field distributions, we can determine that the 552 and 691 nm transmission peaks are due to the cavity resonances in the slits. For the 884 nm transmission peak, the magnetic field is sharply confined to the interface between the Ag grating and the dielectric layer due to the excitations of SPPs. It can be seen from Fig. 1 that the half-width of the transmission peaks mediated by guided resonances is much smaller than those mediated by cavity resonances and SPPs. This can be understood by the fact that for guided resonances absorption by Ag is rather small since their magnetic fields are sharply confined to the dielectric layers. On the contrary, the magnetic fields of cavity resonances and SPPs are sharply confined either in the slits or at the grating surface, leading to a larger absorption.
A dielectric layer situated at a metallic surface can support guided modes for both s- and p-polarization . This kind of guided modes has many interesting features and can be exploited in integrated optics and sensor applications as well [17, 18, 19, 20]. It can be shown that the dispersion of the guided modes with p-polarization satisfies the following relation
where k 0=ω/c is the wave vector of incident light in vacuum, and k ‖ is the in-plane component of k 0.
For a flat metallic film coated with a dielectric layer on both sides, neither guided nor SPP modes can be directly excited by incident light since there exists a mismatch between the wave vector of incident light and that of guided or SPP modes. With the introduction of periodic slits, however, incident light will be scattered by the periodic slits. As a result, the wave vector of scattered light should be imposed additionally by the Bragg vectors resulting from the periodicity of the Ag grating. If the wave vector of guided or SPP modes matches that of scattered light, namely,
guided or SPP modes can be excited, where G=2π/a is the primitive reciprocal lattice vector and n is an integer. Thus, the scenario of enhanced transmission mediated by guided or SPP modes is as follows. Incident light is first scattered by the Ag grating, leading to the excitations of guided or SPP modes if the condition of Eq. (4) is satisfied. If the grating is not thick enough, the guided or SPP modes on both sides of the Ag grating can couple. Eventually, the coupled guided or SPP modes will be scattered out by the grating periodicity on the other side, reradiating into outgoing light.
Enhanced transmission can occur not only for normal incidence but also for oblique incidence. Transmission spectra of the coated Ag grating as a function of in-plane wave vector and frequency in the color scale form are plotted in Fig. 3. Folded dispersion for guided modes and SPPs of a 600 nm dielectric layer with a dielectric constant of 2.25 situated on a Ag surface in the first Brillouin zone of the grating periodicity is also given for comparison. Within the framework of the plane-wave-based transfer matrix method, we can also calculate the absorption spectra of the coated Ag grating. It is found that the transmission peaks coincide exactly with the absorption peaks. This result agrees with recent theoretical work for metallic gratings. Obviously, the transmission peaks exhibit a well-defined dispersion of modes of the structure. By comparing the dispersion defined by the transmission peaks with the folded dispersion of guided modes and SPP modes, we can also obtain information on the origin of these transmission peaks.
For p-polarized incident light, both guided and SPP modes can be excited. As a result, enhanced transmission mediated by guided and SPP modes can occur. It can be seen from Fig. 3 that some bands defined by the transmission peaks match closely with the folded dispersion of guided or SPP modes. This indicates that these bands originate from guided or SPP resonances. Discrepancy is found in the vicinity of the Brillouin zone center or boundary, which is expected owing to multiple Bragg scatterings. Besides bands originated from guided or SPP resonances, we also observe bands that do not match the folded dispersion of both guided and SPP modes. In the displayed wavelength range, there are three such bands. These bands are rather flat and discontinuous. By inspecting the magnetic field patterns, it is found that these bands stem from the cavity resonances in the slits . It is interesting to note that there are strong interactions between the guided, SPP, and cavity modes at their crossing points. The coupling between these modes is responsible for the discontinuity of the flat bands. For example, the bright band around 1020 nm is split into three parts due to the coupling between SPP and cavity modes around k ‖=0.25π/a and the coupling between guided and cavity modes around k ‖=0.7π/a. Similar coupling occurs for the cavity modes around 700 and 550 nm. We can also observe coupling between guided and SPP modes, e.g., around 830 nm, and coupling between different guided modes. In the strong coupling regions, transmission peaks are not pure guided, SPP, or cavity modes. Instead, they are the combination of guided, SPP, or cavity modes.
As shown above, guided resonances can render another interesting mechanism for enhanced transmission in coated metallic gratings with subwavelength slits. The introduction of the dielectric coating layers can offer a lot of degrees of freedom to tune the transmission, reflection, and absorption properties of metallic gratings, for example, by changing the thickness and dielectric constant of the dielectric coating layers. We can even introduce non-linear coating materials such that non-linearity related phenomena can be studied. It should be indicated that enhanced transmission mediated by guided resonances can be also expected for metallic films perforated with two-dimensional hole arrays since the physics mechanism is similar.
In summary, we show theoretically that guided resonances can give rise to sharp transmission peaks for metallic gratings coated with a dielectric layer on both sides. For subwavelength slits, besides cavity resonances in slits and SPPs, guided resonances in the dielectric layers render another mechanism for enhanced transmission. Transmission peaks mediated by guided resonances possess a much smaller half-width over those mediated by cavity and SPP resonances. These interesting features would be exploited in photonic applications.
This work was supported by the 973 Program (grant nos. 2007CB613200 and 2006CB921700) and NSFC (grant no. 10734010). Partial support from PCSIRT and Shanghai Science and Technology Commission is also acknowledged.
References and links
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