A low-loss metal-insulator-metal plasmonic bragg ... - OSA Publishing

A low-loss metal-insulator-metal plasmonic bragg reflector Amir Hosseini and Yehia Massoud Electrical and Computer Engineering Department, Rice University, Houston TX 77005 [email protected]

Abstract: In this paper, we present a low-loss plasmonic Bragg reflector structure with high light-confinement. We show that periodic changes in the dielectric materials of the metal-insulator-metal waveguides can be utilized to design efficient subwavelength Bragg reflectors and micro-cavities. FDTD simulation results of the designed Bragg reflector using realistic material parameters justify that the transfer matrix calculations are adequate for the design purposes. © 2006 Optical Society of America OCIS codes: (240.6680) Surface plasmons; (230.7390) Waveguides, planar

References and links 1. H. Reather, Suface Plasmons (Springer Tracts in Modern Physics, Springer Berlin, 1988). 2. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987). 3. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787-3790 (1996). 4. W. L. Barnes, A. Dereux, and T. Ebbesen, “Surface plasmon subwavelength optics,” Natrue 424, 824-830 (2003). 5. S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, “Waveguiding in surface plasmon polariton band gap structures,” Phys. Rev. Lett. 86, 3008-3011 (2001). 6. J. C. Weeber, Y. Lacroute, A. Dereux, E. Devaux, T. Ebbesen, C. Girard, M. U. Gonzalez, and A. L. Baudrion, “Near-field characterization of bragg mirrors engraved in surface plasmon waveguides,”Phys. Rev. B 70, 235406 (2004). 7. R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A 21, 2442-2446 (2004). 8. A. Degiron and D. R. Smith, “Numerical simulation of long-range plasmons,” Opt. Express 14, 1611-1625 (2006). 9. P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988). 10. B. Wang and G. P. Wang, “Plasmon bragg reflectors and nanocavities on flat metallic surfaces,” App. Phys. Lettersvol. 87, 013107 (2005). 11. J. A. Dionne, L. A. Sweatlock, and H. A. Atwater, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73, 035407 (2006). 12. G. Veronis and S. Fan, “Subwavelength plasmonic waveguide structures based on slots in thin metal films,” in proceedings of the SPIE 6123, (2006). 13. P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370-4379 (1972). 14. E. D. Palik, Handbook of Optical Constants and Solids (C Academic, Orlando, Fla, 1985). 15. R. Charbonneau, P. Berini, E. Berolo, and E. Lisicka-Shrzek, “Experimental observation of plasmon-polariton waves supported by a thin metal film of finite width,” Opt. Lett. 25, 844-846 (2000). 16. J. Q. Xi, M. Ojha, W. Cho, J. L. Plawsky, W. N. Gill, T. Gessmann, and EF. Schubert, “Omnidirectional reflector using nanoporous SiO2 as a low-refractive-index material,” Opt. Lett. 30, 1518-1520 (2005). 17. P. A. Hobson, S. Wedge, J. A. E. Wasey, I. Sage, and W. L. Barnes , “Surface plasmon mediated emission from organic light-emitting diodes,” Adv. Mater. 14, 1393-1396 (2005).

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Received 9 August 2006; revised 20 September 2006; accepted 21 September 2006

13 November 2006 / Vol. 14, No. 23 / OPTICS EXPRESS 11318

1.

Introduction

Optical devices, which are based on surface plasmon polaritons (SPPs), have recently been considered as solutions to overcome the diffraction in dielectric structures that limits the miniaturization of photonic devices. SPPs are electromagnetic modes coupled to the collective electron oscillations propagating along the interface between dielectric and metallic materials at the optical and near infra red frequency spectrum. In this frequency range, the metal exhibits a negative dielectric function. The electromagnetic field associated with SPPs is bounded along the interface and decreases exponentially in the direction perpendicular to the interface resulting in a subwavelength confinement of the electromagnetic mode [1]. Photonic crystals, periodic arrays of dielectric scatters in homogenous media, affect the properties of photons in the same way a semiconductor affects electrons. Therefore, photons can have band structures, forbidden frequency intervals, known as photonic band gaps (PBG), as well as localized defect states. PBGs and micro-cavities realized by intentionally introducing defects in the periodicity, have various applications, such as sharp bending of light and the control of spontaneous emission and zero-threshold lasing [2, 3]. Periodic gratings introduced on metallic surfaces can lead to photonic band gaps as SPPs propagate along the metallic surfaces. These structures have been used to build SPP mirrors and beam splitters [4, 5]. SPP-based Bragg reflectors (1D photonic crystals) have been previously fabricated by engraving slots into metal strips [6]. Since these corrugated metal strips are based on the insulator-metal-insulator (IMI) geometry, they did not provide the necessary confinement needed for subwavelength photonic devices [7]. This is due to the much longer penetration depth of SPP fields into the dielectric medium compared to that into the metallic medium at the metal-dielectric interface. In addition, the contrast between the effective indices of the alternating layers is small, resulting in small band gaps for the corrugated metal strips [8], as demonstrated by the equation of the first band gap (∆ωg ) in a 1D photonic crystal, ne f f ,2 − ne f f ,1 4 ∆ωg = ωc sin−1 , π ne f f ,2 + ne f f ,1

(1)

where ne f f ,1 and ne f f ,2 are the effective indices associated with the two alternately stacked waveguides, and ωc is the central frequency of in the gap [9]. As Shown in Equation 1, small contrast in the effective indices leads to narrow PBGs. SPP Bragg reflectors were also proposed based on the metal-insulator-metal (MIM) geometry, where different metallic materials are alternately stacked (heterowaveguides) [10]. MIM waveguides (Figure 1) can provide spatial light confinement with lateral dimensions of less than 10% of the free wavelength [11]. Also, they can exhibit zero propagation loss at bends and power splitters with dimensions much smaller than the wavelength of the optical mode [12]. Such MIM heterowaveguide can effectively confine the guided light. However, metallic materials with considerably different dielectric constants are needed in order to realize wide PBGs with high refection and low transmission for the frequencies inside the gaps. The dielectric constants of low loss metals (such as Ag, Au and Cu) are not different enough to produce an effective contrast [13]. This requires using a lossy metal such as aluminum together with a relatively low-loss metal such as silver. The utilization of a lossy material significantly increases the ohmic losses in an already lossy MIM type structure. In this paper, we present a new MIM-based low-loss Bragg reflector structure with high light confinement. We show that periodic changes in the dielectric materials of the MIM waveguides can be utilized to design effective filtering around the Bragg frequency. In order to avoid the approximation errors in the analysis, silver and aluminum are characterized by the optical constants from [13] and [14], respectively. The fundamental symmetric modes are considered #73928 - $15.00 USD

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because their field profiles are suitable for end-fire excitations [15] and also there are the dominant modes in terms of the lowest loss. 2.

MIM Bragg reflector

3.2 3 2.8

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Fig. 1. Variation of the ne f f values with wavelength for the fundamental TM mode in MIM waveguides, (a) Real[ne f f ], (b) Imag[ne f f ].

Assuming that all field components have the functional form of exp[i(β z − ω t)], the dispersion equation for the p-polarized symmetric mode in MIM structures can be written as −ikx1t εd kx2 + εm kx1 coth = 0, (2) 2 ω 2 2 kx1,2 = εd,m (3) − β 2, c where εd , εm and t are dielectric constants of dielectric, metallic materials and the dielectric thickness as shown in Figure 1(a), respectively [11]. The propagation constant (β ) is usually represented as a dimensionless effective index ne f f = β /k0 for the guided modes, where k0 is the free space wave-vector, and propagation is assumed to be in the z−direction. Figure 1 displays the variation of the ne f f values for the slab symmetric mode of MIM waveguides with silver or aluminum as the metal, and air or silicon dioxide (SiO2 , n = 1.46) as the dielectric. It is shown in Figure 1(a) that the real parts of the associated ne f f values for two MIM waveguides with the same metallic and different dielectric materials can exhibit better contrast compared to those of the waveguides with different metal and one dielectric. Therefore, when alternately stacked, the resulting frequency gap is wider if we change the dielectric instead of the metal. The propagation length of a propagating field inside a waveguide (L p = 1/Imag(β )) depends on the imaginary parts of the ne f f values shown in Figure 1(b). It can be seen that the propagation lengths in the MIM waveguides degrade about one order of magnitude when we replace silver with aluminum. In fact, aluminum is not suitable for waveguiding purposes because the imaginary part of the dielectric function is relatively large over the visible and infra red spectrum and it causes significant resistive heating [14, 7]. We can see that lower refractive index dielectric materials result in smaller Imag[ne f f ] values in plasmon slot waveguides. Therefore, it is necessary to use dielectric materials with low refractive index in order to reduce the loss for the passive device applications. Figure 2 compares the variation of the ne f f values for MIM waveguides with silver as the metal, and SiO2 or nanoporous SiO2 (PSiO2 , n = 1.23) as the dielectric for t = 30 nm. Nanoporous silicon oxide has been employed as a low-index material in microelectronic and #73928 - $15.00 USD

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−3

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Fig. 2. Variation of the ne f f values with wavelength for the fundamental TM mode in Ag − SiO2 and Ag − PSiO2 waveguides, t = 30 nm, (a) Real[ne f f ], (b) Imag[ne f f ].

photonic applications [16]. In order to produce a practical Bragg reflector design, we propose to use PSiO2 instead of air as a low refractive index material in MIM waveguides. As depicted in Figures 1(a) and 2(a), the real parts of the ne f f values are always greater for the waveguides with higher index dielectric materials at frequencies less than the surface plasmon frequency (ωsp ), which is the frequency where Real(εm ) = −Real(εd ). In the cases of the Ag − PSiO2 and Ag − SiO2 waveguides, the surface plasmon wavelengths (λsp = 2π /ωsp ) are 346 nm and 356 nm, respectively [13]. In addition, the ne f f curves become almost horizontal lines at wavelengths longer than about λ = 1 µ m for MIM waveguides with silver. Figure 2(a) indicates that we can use alternately stacked Ag − SiO2 and Ag − PSiO2 to realize Bragg reflectors since the associated ne f f curves are well separated. For the Bragg reflector shown in Figure 3(c), alternately stacking Ag − PSiO2 and Ag − SiO2 waveguides, gives rise to an effective index modulation. For these waveguides with t = 30 nm, ne f f ,1 = 1.878 + 0.008i and ne f f ,2 = 2.241 + 0.009i at λ = 1.55 µ m, respectively. According to the Bragg condition [d1 Real(ne f f ,1 )+d2 Real(ne f f ,2 ) = nλb /2], we can realize Bragg scattering around λ = 1.55 µ m, by choosing d1 = 200 nm and d2 = 180 nm. The transmission spectrum of SPPs propagation through this structure can be calculated by the standard transfer matrix method. As shown in Figure 3, there is PBG around λ = 1.55 nm when a finite number of the periods of the alternating layers (N) is considered. For the plasmonic reflector, as the imaginary parts of the ne f f values of MIM structures increase rapidly with the frequency near ωsp as shown in Figure 2(b), the transmission drops for the wavelengths smaller than about λ = 1 µ m. It should be noted that the propagation loss is automatically considered in the results form the transfer matrix method calculations. For example for N = 15, at λ = 1.55 µ m and λ = 1 µ m, the output power is about 3 dB and 2.2 dB less than the input, respectively. Theoretically Bragg scattering occurs for any number of periods. However, in the cases of the alternating Ag − PSiO2 and Ag − SiO2 waveguides of dielectric thickness t = 30nm, we found that the minimum N required to realize transmission less than 1% in the gap, is N = 15. As shown in Figure 3(a), the increase of the number of periods give rise to higher losses. By introducing a defect in the periodicity, micro-cavities can be formed which trap the incident radiation for applications such as ultra low-threshold lasers and light-emitting diodes [17]. Figure 3(b) shows the transmission spectrum when the 8th period is replaced with a single Ag − PSiO2 waveguide of 30 nm thickness and 390 nm length. We can define the cavity quality factor as Q = λ0 /∆λ where λ0 and ∆λ are the central resonance wavelength and the full width at half maximum of the SPP defect mode, respectively. This quantity describes the ratio of the

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90

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Fig. 3. Transmission spectrum, (a) Bragg reflector structures consisting of 9 and 29 periods, (b) Bragg reflector and microcavity structures of 15 periods, (c) schematic of Bragg reflector consisting of alternately stacked MIM waveguides with different dielectric materials.

energy stored in the cavity at resonance to the energy escaping from the cavity per cycle of oscillation. The quality factor for the cavity in Figure 3(b) is found to be about 145. We verify the results form the transfer matrix calculations for the Bragg reflector using the finite-difference time-domain (FDTD) method with the perfectly matched layer (PML) as the boundary condition. The structure in Figure 4(a) is simulated choosing the grid sizes in the x and y directions to be 5 nm × 2.5 nm by a 2D FDTD solver. This structure is excited by a dipole source located in the middle of the feeding waveguide (Ag − PSiO2 , t = 30 nm). The field profiles, |Hx |2 , associated with the SPP propagation through this reflector are displayed in Figure 4. Figure 4(c) shows that the incident radiation is reflected at the λ = 1.55 µ m, while it propagates through the structure at λ = 1 µ m and λ = 1.9 µ m that are outside the frequency gap [Figures 4(b) and 4(d)]. The transmitted power is in good agreement with the spectrum shown in Figure 3(b). Simulation results for the microcavity described in the previous section is shown in Figure 5. As depicted in this figure, the incident radiation couples into the microcavity structure (390 nm long Ag − PSiO2 waveguide). 3.

Conclusion

We presented a new SPP based low-loss Bragg reflector structure with high light-confinement. We showed that alternately changing of the dielectric materials of the MIM waveguides can be utilized to design effective subwavelength Bragg reflectors and micro-cavities. FDTD simulation results with realistic material parameters were presented which revealed that the transfer matrix approach utilizing the effective indices associated with subwavelength waveguides, is adequate for the design purposes. The reflectors and micro-cavities are expected to have applications in highly integrated photonic circuits and SPP-based devices.

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b)

x(µm)

c)

x(µm)

d)

x(µm)

a)

z(µm)

Fig. 4. Field profile [|Hx |2 ] in the Bragg reflector at different wavelengths, (a) simulated structure, (b) λ = 1.9 µ m, (c) λ = 1.55 µ m, (d) λ = 1 µ m.

b)

x(µm)

a)

z(µm)

Fig. 5. FDTD simulation of the micro-cavity structure, (a) micro-cavity schematic, (b) field profile [|Hx |2 ] at λ = 1.55 µ m

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