Characterization of the surface plasmon polariton band gap in an Ag/SiO2/Ag T-shaped periodical structure Cheng-Wen Cheng,1,2,3 Mohammed Nadhim Abbas,2,3,4 Min-Hsiung Shih,2* and YiaChung Chang2 1 Department of Physics, National Taiwan University, Taipei 10617, Taiwan Research Center for Applied Sciences, Academia Sinica, Taipei 11529, Taiwan 3 Taiwan International Graduate Program, Academia Sinica, Taipei 11529, Taiwan 4 Department of Engineering and System Science, National Tsing Hua University, Hsinchu 30013, Taiwan *
[email protected] 2
Abstract: In this study, the localized surface plasmon polariton (LSPP) band gap of an Ag/SiO2/Ag asymmetric T-shaped periodical structure is demonstrated and characterized. The Ag/SiO2/Ag asymmetric T-shaped periodical structure was designed and fabricated to exhibit the LSPP modes in an infrared wavelength regime, and its band gap can be manipulated through the structural geometry. The LSPP band gap was observed experimentally with the absorbance spectra and its angle dependence characterized with different incident angles. Such a T-shaped structure with a LSPP band gap can be widely exploited in various applications, such as emitters and sensors. ©2011 Optical Society of America OCIS codes: (160.5293) Photonic bandgap materials; (250.5403) Plamonics; (260.3060) Infrared.
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1. Introduction One method for controlling the numerous features of electromagnetic radiation, such as the propagation of light, the localization of light at defects, and the inhibition of radiation, using photonic band-gap structures has led to a number of interesting results [1–3]. The band gaps in photonic crystals depend on the periodic lattice arrangement of air holes/dielectric rods, the filling factor, and the dielectric contrast between the host and constituent object materials. Numerous possible applications of the photonic crystal band gap structures have been demonstrated [4–7]. Over the last two decades, plasmonics has emerged as a new research field in nanophotonics. Surface plasmon polaritons (SPPs) are electromagnetic waves coupled to the surface plasma oscillations of a metal surface. The coupling waves confined on the metal/dielectric interface will propagate with a strong field enhancement and an evanescent wave decay in the normal direction to the interface. Similar to the photonic crystal band-gap structures, surface plasmon polariton band gaps can occur with two-periodic metallic gratings. Surface plasmon polariton band gap structures have been theoretically and experimentally reported [8, 9]. The band gap feature is attractive for applications in SPP waveguides [10, 11], band gap cavities [12–14], surface plasmon lasers [15], and band gap-assisted sensors [16]. The resonant coupling of localized surface plasmon polaritons (LSPPs) confined at the interface between metallic and dielectric has also been reported [17]. The LSPPs have the advantages of a smaller optical mode volume and the ability to control the location of optical intensity. The special optical properties benefit numerous applications, such as sensors [18, 19], spasers [20] and thermal emitter devices [21, 22].
#154312 - $15.00 USD (C) 2011 OSA
Received 7 Sep 2011; revised 14 Oct 2011; accepted 14 Oct 2011; published 7 Nov 2011 21 November 2011 / Vol. 19, No. 24 / OPTICS EXPRESS 23699
In this study, we investigated the localized surface plasmon polariton band gap based on an Ag/SiO2/Ag asymmetric T-shaped structure both theoretically and experimentally. In a previous paper, we presented theoretical analysis of the photonic band structure of the asymmetric T-shaped structure [23], in which a structure gap is introduced in the middle of the post. In this paper, a structure gap is introduced between the Ag film and the T-shaped structure in order to reduce the fabrication steps. The band gap will appear with an index contrast modification without additional periodic grating. The phenomenon to control the surface plasmon polariton band gap was simulated by rigorous coupled-wave analysis (RCWA) [24–26] and directly observed using a Fourier transform infrared (FTIR) spectrometer. The T-shaped plasmonic periodical structure not only provides a new method for generating the band gap, but also provides a strategy to tune the LSPP band-gap with the geometry. 2. Design and simulation Figure 1 shows the proposed Ag/SiO2/Ag asymmetric T-shaped array with the geometric parameters as follows: Λg=1 µm, Wtop=550 nm, ttop=200 nm, Wpost=200 nm, tpost=0~320 nm, d=50 nm, Gt=320 to 0 nm, and tSiO2=320 nm.
Fig. 1. Schematic diagram of the T-shaped array structure
To understand the resonant behavior of the structure, its reflectance spectra and resonant mode profiles are calculated by RCWA simulation. Since there is no TE-polarized resonant response from the proposed structures in our designed photon energy region, we only present the case for TM-polarized incident light (with magnetic field parallel to the y-axis) in the simulation for different incident angles in the x-z plane, where the frequency-dependent complex dielectric constants of silver (Ag) and SiO2 are taken from Ref [27]. Figure 2(a) shows the calculated reflectance spectra of the Ag/SiO2/Ag multilayer structure (tpost = 0nm and Gt = 320nm) with the photon energy ranging from 0.5 eV to 1.2 eV, while the angle of incidence θi varies from 0° to 90°. The crossings are from the grating coupling at the SiO2/Ag interfaces and associated with the first Brillouin zone folding. The crossings all lies on the Bragg planes, and kx = m π/Λg where m is an integer. The slope of the dispersion indicates the group velocity (vg = ∂ ω/ ∂ kx) of the SPP propagation at the SiO2/Ag interface. Due to less interaction between the two branches, the crossing point is found to be 0.87 ev at normal incidence, showing no energy gap in the dispersion relation. To form an energy gap, additional periodic grating with a period of Λg/2 is commonly used [7–9]. The periodicityΛg/2 is designed to couple an energy gap region with photons inside the light line. However, this study found that without using extra periodic grating, an energy gap can be opened when tpost is introduced, as shown in Fig. 2(b). The slope of the bent dispersion curves provides the group velocity in the x-direction as a function of the resonance wavelength and incident angle. At small values of kx, we also found that a momentum band gap will occur in the first branch if the T-shaped structure becomes symmetric (d = 0 nm). The momentum gap is due to the non-coupling strength in the first branch and determined by the relative phase between the top grating strip and the post structure [8,23]. Regarding the |Hy|2 distributions at normal incidence for the two branches of the designed structures, Fig. 3(a) shows the freepropagation-like field distribution at the bottom SiO2/Ag interface along the x-direction in one
#154312 - $15.00 USD (C) 2011 OSA
Received 7 Sep 2011; revised 14 Oct 2011; accepted 14 Oct 2011; published 7 Nov 2011 21 November 2011 / Vol. 19, No. 24 / OPTICS EXPRESS 23700
pitch of the multilayer structure. Figures 3(b) and 3(c) are the field distributions for the two standing wave solutions at the first and second branches when the tpost = 170 nm. Most of the field intensity is concentrated in the corners between the post and the grating on the top layer for the first branch. Regarding the second branch, the intensity distribution reveals a periodicity equal to half the pitch period, with the strong field in the SiO2 spacer below the post.
Fig. 2. (a) Simulated reflectance spectra of the multilayer structure with design parameters of Λg = 1 µm, Wtop = 550 nm, ttop = 200 nm, Wpost = 200 nm, d = 0 nm, tpost = 0 nm, and Gt = 320 nm. (b) Stimulated reflectance spectra of the T-shaped structure when d = 50 nm, tpost = 170 nm, and Gt = 150 nm.
Fig. 3. |Hy|2 distribution at normal incidence in one period of (a) the Ag/SiO2/Ag multilayer structure at the crossing point 0.87 eV, and (b) the first and (c) second branches of the Tshaped structure when d = 50 nm, tpost = 170 nm, and Gt = 150 nm.
The mechanism of the dispersion-relation modification arises from the impedance mismatch [28] between the metal-metal and single metal regions of the T-shaped structure, where the impedances of the metal-metal regions strongly depend on the geometric parameters tpost and Wpost, and when the tSiO2 and Wtop are fixed. As the tpost increases, the band gap progressively opens and is linearly proportional to the post height (tpost) when 0 270 nm (Gt
