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Surface plasmon polaritons (SPPs) Bragg reflector with more excellent optical properties are investigated numerically. By introducing a finite array of periodic grooves on the two surfaces of metal-insulator-metal (MIM) waveguide, we fulfill the periodical changes of effective refractive index, which leads to the photonic band gap (PBG). And it has been further widened by inserting a dielectric material with higher refractive index in the waveguide with narrow slit width. Finite difference time domain (FDTD) simulation confirms the widened bandgap. In addition, a SPP nanocavity is introduced by breaking the periodicity of our proposed structure.
©2008 Optical Society of America
1. Introduction
Surface plasmon polaritons (SPPs) are the interaction between the surface charge oscillation and the electromagnetic field of the light, which are able to propagate along the metal surface with the amplitudes decaying into both sides. One of the most attractive aspects of SPPs is the way in which they help us concentrate and channel light using subwavelength structures. This could lead to miniaturized photonic circuits with length scales much smaller than those currently achieved[1]. Some novel photonic elements based on SPPs such as waveguide, lense, reflector and beam splitters have been theoretically proposed[2, 3, 4, 5, 6] and experimentally demonstrated[7, 8, 9, 10, 11]. Recently, it has been reported that a planar heterowaveguide constructed by alternately stacking two kinds of metal-insulator-metal (MIM) waveguides with the refractive index periodically modulated[12], improve the efficiency of energy transfer at the range of subwavelength because it provide spatial light confinement with lateral dimensions of less than of the free wavelength[13]. Later, this MIM heterowaveguide was extended to the quasi-periodic case and a double-band plasmon Bragg reflector was developed[14]. For this type of plasmonic Bragg reflector, one of the shortcoming is that the ohmic losses are significantly increased by introducing a lossy material such as aluminum in order to produce a refractive index contrast. To deal with this problem, a low-loss MIM plasmonic Bragg reflector has been proposed, which is constructed by periodic changes in the dielectric materials of the MIM waveguides [15].
Most recently, a modeling and design methodology based on characteristic impedance for plasmonic waveguide with MIM is proposed[16], where thick-modulated (ThM) and Index-Modulated (InM) Bragg reflector are studied, respectively. As is known, in some cases, wider bandgap is important for a photonic element. And the wider bandgap can not be realized only by changing the slit width (ThM) or dielectric (InM) in the waveguide. In the present work, we studied a wide bandgap Bragg reflector by modulating the MIM waveguide slit width and inserting dielectric materials with higher refractive index in the grating sections with narrow slit width. Both transfer matrix method (TMM) and FDTD simulation results show the bandgap is further widened. Moreover, the ohmic loss is reduced than the planar plasmonic Bragg reflector reported previously. In addition, the SPPs nanocavities are investigated in these configurations.
2. plasmonic Bragg reflector
We first consider a MIM waveguide, which is a planar metallic waveguide with two semi-infinite metal walls and the middle layer between the two walls is a dielectric film with width w, as shown in Fig. 1(a). When SPPs propagate in the MIM waveguides, the corresponding dispersion relation are determined by the following equation[17]
Fig. 1. (Coloron line) (a) Scheme of two MIM waveguides with slit widths wA,wB, respectively, produced by engraving two grooves on the surfaces of a single MIM waveguide. Here, dA and dB designate the waveguide thicknesses and the red section is metal. (b)–(c)Schematic of plasmonic Bragg reflector, alternately filled with air/air and SiO 2/air, respectively.
where
and
Here, βspp and neff designate the constant of propagation and effective refractive index for SPPs, and λ is the wavelength of incident light in free space, k 0 is the corresponding wave number, while εm and εd are the relative dielectric constant for the metal and dielectric materials between two metal walls, respectively.
Figs. 2(a) and (b) plot the complex effective refractive indices of SPPs in the MIM waveguide for variant wavelengths. Here, we take the metal as Ag, which is characterized by the optical constants from Ref. 17. Two insets shown in Fig. 2(a) and (b) display the dependence of neff on the slit width at λ=1.55µm. In fact, in the range of visible and near-infrared frequency, the dependence of neff on w are very similar. It is clear that the value of neff, both the real and imaginary parts, increase with the decrease of slit widths. For the character of the real part, it shows that two MIM waveguides with different slit widths lead to the contrast of effective refractive indices. Obviously, the contrast of neff can be fulfilled by symmetrically engraving two grooves on the two surfaces of a single MIM waveguide, which is shown in Fig. 1(a). In particular, if the grooves are arranged periodically along to the axis of the slit, i.e, the direction of SPPs propagation, as shown in Fig. 1(b) and (c), a periodic change of effective refractive indices can be produced. To compare with Ref. 15, we also give the variation of the neff with wavelength for planar MIM waveguide with SiO 2 and PSiO 2 alternately stacked in the slit (red lines). From Fig. 2(a), the contrast of effective refractive index for the studied Bragg reflector (between two thick, blue lines or between dash-dot and thin red line) is greater than the planar MIM structure with periodic dielectric. Moreover, the bandgap will be further widened by filling the dielectric with higher refractive index in the narrower slits (see Fig. 1(c)). This character means the plasmonic Bragg reflector in Fig. 1(c) will illustrate wider bandgap than that of Bragg reflector only with slit width or dielectric modulation. On the other hand, as shown in Fig. 2(b), the imaginary of MIM waveguide with wider slit (dash-dot blue line) always be smaller than the narrow one (solid blue line, dashed red line and solid red line), which implies the energy loss will be further reduced in this Bragg reflector, comparing with the planar plasmonic Bragg reflector.
Fig. 2. (Color on line) Variation of the real (a) and imaginary (b) parts of neff with wavelength for SPPs mode in the MIM waveguide. The two insets show the real and imaginary of neff as a function slit width. The thin solid, thin dash lines (red) and thick solid line (blue) correspond to the MIM waveguide with dielectric SiO 2 (εd=1.46), PSiO 2 (εd=1.23), air (εd=1.0), and the same slit width as Ref. 15, w=30nm. The thick dash-dot line presents MIM structure filled with air, w=100nm.
For the Bragg reflector shown in Fig. 1(a), the MIM waveguide with narrower slit designates the higher refractive index materials and the wider one (groove) corresponds to the low refractive index media, labeled as MIMA and MIMB in Fig. 1(a), respectively. In the case of slit width of wA=30nm and wB=100nm, dielectric constant εd=1, we can get the effective refractive indices of two sections as Re(neff,A)=1.575 and Re(neff,B)=1.20 at λ=1.55µm, respectively. According to Bragg condition dARe(neff,A)+dBRe(neff,B)=λb/2, where λb is the Bragg wavelength, we can realize Bragg scattering by choosing the corresponding thicknesses as dA=235nm and dB=315nm. For other slit widths, the thicknesses can be obtained by a similar way. Fig. 3(a) shows the transmission spectrum calculated by transfer matrix method for SPPs through the proposed plasmonic Bragg reflector (thick solid curves) and MIM structure with alternating stacking PSiO 2 and SiO 2 in the slit (thin solid black curve), consisting of 10 periods, which displays the incident plane wave is reflected at the λ=1.55µm and the corresponding bandgap occurs around this frequency. We can find that the proposed MIM waveguides with periodic grooves show wider bandgap than the MIM Bragg reflector in Ref. (15) with the same metal slit width, even the former structure is filled with air as structure in Fig. 1(b). If the SiO 2 and air are stacked alternately in the MIM waveguide as in Fig. 1(c), the larger contrast between the effective indices give rise to the wider bandgap (blue). It should be noted that the imaginary of neff has been considered in our TMM calculation, namely the propagation loss is calculated in the transmission spectra. From Fig. 3(a), the transmission of the plasmonic Bragg (thick red line and thick blue line) reflector are higher than the planar MIM Bragg reflector with periodical changes of dielectric, which is due to the smaller imaginary of neff caused by the grooves. The transmission spectrum shown in Fig. 3(a) also presents the minimum periodic number N required to realize a bandgap of minimum transmission decrease with the increase of badgap width. Therefore, the proposed wide bandgap plasmonic Bragg reflector can effectively improve the efficiency of energy transfer with less period number N.
Fig. 3. (Color on line)(a) Transmission spectrum of Bragg reflector consisting of 10 periods. The thin (black) line represent the MIM Bragg reflector with periodic changes of dielectric in the slit, width w=30nm. The thick red and blue solid lines stand for the structure shown in Fig. 1(b) and (c), respectively. The slit widths are wA=30nm,wB=100nm, respectively. (b) Bandgap as a function of slit width difference h=wB-wA, filled with dielectric in the narrow MIM waveguides (εd=2.5). The inset shows bandgap as a function of dielectric constants with h=70nm.(c)–(d) The field distribution of |Hz|2 in the reflector (Fig. 1(b)) at λ=1µm and λ=1.55µm, respectively. (e)–(f) |Hz|2 distribution for the cases shown in Fig. 1(b) and (c) at λ=1.3µm, respectively. The white thin lines give the profile of the reflector.
To fully understand how the filled dielectric and the groove depth influence the bandgap width, we demonstrates the badgap as a function of the groove depth h or the dielectric constants εd, as depicted in Fig. 3(b). Here, we calculated the bandgap according to Eq. (1) in Ref. 15. Both the larger groove depth h and the higher dielectric constants of the dielectric materials in the narrow slits lead to the wider bandgap, where we assume the grooves are filled with air. Clearly, beyond a certain groove depth, the width for bandgap increase slowly with the increase of groove depth. This is because the coupling of SPP mode become weaker as the groove depth grows. We also use the FDTD method[19, 20] to verify the bandgap and its variation with the dielectric materials. Fig. 3(c) and (d) show the incident plane wave propagate through the structure shown in Fig. 1(b) at λ=1µm and λ=1.5µm, which are outside and inside of the badgap, respectively. According to the transmission spectra shown in Fig. 3(a), we simulated the field distribution at the same wavelength λ=1.3µm, which is inside the bandgap for the case of Fig. 1(c) and outside of the bandgap for the case shown in Fig. 1(b). From Fig. 3(f), the incident radiation can not pass the structure as Fig. 1(c), indicating its bandgap has been further widened. The FDTD results agree well with our calculation by the transfer matrix method.
In order to investigate the properties of photonic microcavities for the proposed wide bandgap plasmonic Bragg reflector, we change the MIM thickness dA in the center of this periodic structure. Fig. 4(a) indicates the transmission spectrum when dA layer is repeated between the 10th and 11th layer in the cases of air/air(red), PSiO 2/air (black) and SiO 2/air (blue) stacked alternately in the slits and grooves, respectively. One can find the wider badgap, namely the larger contrast of neff, the poorer transmission for the defect mode, resulting from the weaker coupling between the adjacent SPPs modes. Also, the FDTD simulated results are demonstrated in Fig. 4(b) and (c), corresponding to the case of air/air and SiO 2/air filled in the proposed MIM waveguide, respectively. We notice the transmission for the larger effective refractive indices difference is weaker than that smaller one. And the field intensity is localized mainly near the defect waveguide.
Fig. 4. (Color on line)(a)Transmission of nanocavity with different dielectric/air alternately filled in the slits and grooves. The thick solid(blue), thin solid(black) and thick solid lines (red) correspond to the dielectric constants as εd=1.46,εd=1.23,εd=1.0, respectively. (b)–(c) The field distribution of |Hz|2 for defect mode at λ=1.55µm, filled with air/air, SiO 2/air, respectively.
3. Conclusion
In summary, we have investigated a type of wider bandgap plasmonic Bragg reflector constructed with MIM structure symmetrically engraved periodic grooves on two surfaces. We present that the bandgap width could be further widened by filling with higher refractive index dielectric materials in the narrow slit of the proposed structure. And the efficiency of energy transport also has been improved in this wide bandgap plasmonic Bragg reflector. Additionally, the transmission properties of nanocavities are investigated when one of waveguide thickness is changed in this periodic structure. FDTD simulation verify the widened bandgap as well as the resonance of localized SPPs mode. This plasmonic Bragg reflectors and nanocavities are expected to have application in SPP-based devices such as distributed Bragg SPP emitter, filters and other nanophotonic devices, especially for the demand of broad badgap elements.
Acknowledgements
The authors would acknowledge financial support from the Major Research plan of the National Natural Science Foundation of China (Grant No. 90606001), the National Nature Science Foundation of China (Grant Nos. 10674045 and 60538010) and the Natural Science Foundation of Hunan Province, China (Grant No. 07JJ3114).
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