Unidirectional manipulation of surface plasmon polariton by dual-nanocavity in a T-shaped waveguide

Optics Communications 284 (2011) 795–798

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Optics Communications j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / o p t c o m

Unidirectional manipulation of surface plasmon polariton by dual-nanocavity in a T-shaped waveguide Yongkang Gong, Xueming Liu ⁎, Leiran Wang, Yani Zhang State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi'an 710119, China

a r t i c l e

i n f o

Article history: Received 18 June 2010 Received in revised form 30 July 2010 Accepted 28 September 2010 Keywords: Surface plasmon polaritons Integrated optics Waveguide

a b s t r a c t A structure of two dimensional T-shaped metal–insulator–metal waveguide with dual-nanocavity is proposed. The two nanocavities located at each side of the slit on the lower metallic surface, act as band rejection filters and are capable of stopping the surface plasmon polaritons (SPPs) at the resonant wavelengths. The Fabry–Perot interferometry theory and the Finite-Difference–Time–Domain method are utilized to investigate the proposed waveguide. The numerical results demonstrate the realization of miniaturized photonic devices for effectively switching the SPPs propagation between the left and right waveguides in one direction. © 2010 Elsevier B.V. All rights reserved.

1. Introduction The emerging field of surface plasmon polaritons (SPPs) is based on exploiting the coupling between light and collective electronic excitations within conducting materials [1]. The electromagnetic field associated with the SPPs is bounded along the interface and decreases exponentially in the direction perpendicular to the interface [2]. Therefore, SPPs are considered as one of the most promising ways for overcoming the diffraction limit and manipulating light at a subwavelength scale [3], which can find many applications such as sensing [4], extraordinary optical transmission [5], nanoscale waveguiding [6], and nanolithography [7]. In order to develop modern plasmonic technology, capabilities to excite and manipulate SPPs are the vital issues for applications. Since SPP modes have longer wave vectors than the light waves of the same energy, it cannot be excited by directly illuminating optical field on the flat metal surface. Aim to overcome the inherent momentum mismatch, different corrugated metallic systems can be utilized [8–13]. In most applications, since spatial symmetrical distribution of the nanostructures the excited SPPs propagate in both positive and negative directions, which may unfortunately play a limiting factor for building the efficient functionalized plasmonic circuits. Recently, investigations of unidirectional manipulation of SPPs have attracted a great attention. By introducing two different surface waveguides on opposite sides of the slit, a device capable of confining and guiding light at different incident wavelengths in different

⁎ Corresponding author. Tel.: + 862988881560; fax: + 862988887603. E-mail address: [email protected] (X. Liu). 0030-4018/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2010.09.074

directions is proposed [14]. Tejeira et al. had theoretically and experimentally demonstrated a unidirectional nanoslit coupler by placing nanogrooves on one side of the nanoslit to focus light on a chosen location [15]. Using gratings-based metallic structure, unidirectional control of SPPs has also been demonstrated [16,17]. In the above mentioned studies [14–17], structures are all based on forming asymmetric gratings to control SPPs, which need engraving multiple teeth on the metallic surface and thus increase the overall dimension of the integrated circuits. Quite recently, a compact structure with a thin silver layer perforated by two subwavelength slits is presented [18]. In this structure, by designing the specific effective index for each slit, the relative phase of plasmonics generated at the slit exit aperture can be tailored and SPP interference happens, thus the electromagnetic field intensity along one direction on the metal surface can be enhanced or suppressed. In the aforementioned publications [14–18], studies of SPP propagation are all focused on the interface of air and metal. Although the air–metal waveguide has relatively small loss and long propagation length, it suffers from poor ability of confining light into subwavelength scale, and is not suitable for the purpose of high integration. The metal–insulator–metal (MIM) waveguide has been shown efficient for subwavelength manipulation of light with an acceptable propagation length [19,20], and becomes increasingly popular. For example, SPP reflector has been realized by periodically introducing two effective index modulation in MIM waveguides [21,22], channel drop filters have been demonstrated in MIM-based ring resonators [23], all-optical switching has been realized in MIM waveguide both directly coupled and side-coupled to square and rectangular cavities based on the gain materials [24] and the absorption [25]. In this paper, a new kind of T-shaped MIM waveguide with dual-nanocavities drilled on the left and right branches is proposed. The Fabry–Perot interferometry theory and Finite-

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Difference–Time–Domain (FDTD) method are employed to investigate the structure properties. Simulation results demonstrate that the proposed structure is compact and can effectively switch the SPPs propagation between the left and right waveguides in the desired direction. 2. Design and theory The proposed structure is simply composed with a T-shaped MIM waveguide as schematically depicted in Fig. 1. A nanoslit is fabricated at the center of the lower film, and two nanocavities with different widths or depths are engraved on each side of it. To investigate the optical properties of the proposed structure, the Finite-Difference– Time–Domain (FDTD) method with perfectly matched layer absorbing boundary condition is employed. In our simulations, the grid sizes in the X and the Y directions are both chosen to be 5 nm. For accurately matching the experimental optical constant of silver, the permittivity is characterized by the Lorentz–Drude model [26]: 5

εm = ε∞ − ∑

m=0

Gm Ω2m w2m −w2 + iwΓm

ð1Þ

where εm is the relative permittivity in the infinity frequency, Ωm is the plasma frequency, Gm is the oscillator strengths, ωm is the resonant frequency, Γm is the damping factor, and ω is the angular frequency of incident light, respectively. When TM polarized wave (the magnetic field is perpendicular to the x–y plane) impinges normally on the lower film, it readily flows to the upper film through the slit, and then splits and travels to the right and left waveguides simultaneously. When SPPs reach the nanocavities A and B, they are coupled into them and converted into two parts, the reflected wave and the transmitted wave. Therefore, A and B can act as resonance cavities [27,28], and standing waves are formed with some appropriate conditions in the nanocavities, i.e., Fabry–Perot (F– P) interferometers happen. The optical path difference of per roundtrip in our structure is 2neffd + D, so the phase delay for nanocavities A and B is Δφi = 2π(2neffi,di + D)/λi + Φi, and thereby the resonant conditions for them can be expressed as [29]: Δφi = ð2m + 1Þπ:

λ2 =


 2 2neff 2 d2 + D 2m + 1−Φ2 = π

:

ð4Þ

From above the equations, we can see that the resonant wavelength can be modulated by d and w (w determines the value of neff, which can be obtained from Eq. (5)). So by adjusting different structure parameters of nanocavities A and B, two different resonant wavelengths can be formed and guided in the left and right waveguides, respectively. This character enables us to manipulate and switch the SPPs in single direction. 3. Simulation and discussion A typical design example of the proposed structure is demonstrated in Fig. 2. The structure parameters are set to be: d1 = 120 nm, w1 = 150 nm, d2 = 160 nm, w2 = 100 nm, S = 200 nm, L = 600 nm, D = 60 nm. With these parameters the transmission spectra are calculated by the FDTD method and shown in Fig. 2(a). We can see that nanocavities A and B possess different resonant wavelengths of 604 nm and 891 nm with about zero transmissions, respectively. According to Eqs. (3) and (4), the resonant wavelengths are 670 nm and 907 nm for m = 1 assuming the phase shift is as small as zero. The time–average field distributions of the SPPs propagation are depicted in Fig. 2(b)–(d). From Fig. 2(a) we can seen that when the incident wavelength is 1200 nm the SPP transmissions from nanocavities A and B are large, so SPP can be guided both in the right and left waveguides as shown in Fig. 2(b). In Fig. 2(c), when the incident wavelength is at the resonate wavelength of 891 nm, SPPs are stopped by the nanocavity B and only guided to the left side of the waveguide. On the other hand, when the incident wavelength is at the resonate wavelength of 604 nm as shown in Fig. 2(d), almost no SPPs exist in the left-side waveguide, and the transmission of SPPs in the left direction is forbidden. The above results illustrate how the proposed

ð2Þ

Here, i = 1, 2, m is integer, D is the gap width. Φ1 and Φ2 are phase shift of a beam reflected on air–silver interfaces, neff1 and neff2 are effective refractive index for the gap plasmons in the gaps of widths w1 and w2, d1 and d2 are depth for cavity A and B, respectively. Therefore, the SPPs will be stopped and cannot be coupled out from the nanocavities A and B at the resonant wavelengths of

λ1 =


 2 2neff 1 d1 + D 2m + 1−Φ1 = π

;

ð3Þ

Silver Air Left Port

Right Port D

d1 A w 1

L

S

L

d2 w2 B

Y Z

X

Incident light

Fig. 1. Schematic diagram of the proposed structure to unidirectionally manipulate SPPs. All the structure parameter symbols are shown in the figure. In our designs, S and L are fixed to be 200 nm and 600 nm, respectively.

Fig. 2. (a) Transmission at the left and right ports. Time–average field distributions of Real (Hz) at wavelengths of (b) 1200 nm, (c) 891 nm, and (d) 604 nm, respectively. The structure parameters for cavities A and B are d1 = 120 nm, w1 = 150 nm, d2 = 160 nm, w2 = 100 nm.

Y. Gong et al. / Optics Communications 284 (2011) 795–798

device manipulates nanoscale light in a desired direction in the integrated photonics. In our structure, the heights and lengths of the upper and lower metal films have no effects on the transmission spectrum. The reason why we set lengths of the upper and lower metallic films unequal as shown in Fig. 1, is that we just want to demonstrate that the proposed structure is flexible and can act as basic element which can find important potential application in integrated plasmonic systems [30]. As shown above, the wavelength satisfying the resonance conditions in Eqs. (3) and (4) can be stopped efficiently by the nanocavities, which enables us to have a unidirectional control of SPPs. So knowing the effects of structure parameters on the resonant wavelength is crucial. In our design, there are three parameters determining the resonant wavelength, i.e. the cavity depth d, cavity width w, and gap width D. Fig. 3 shows the transmission spectra of the SPPs for different w, D, and d. From Fig. 3(b) and (c), it can be clearly obtained that the resonant wavelength exhibits a red shift as D and d increase. This phenomenon can be physically explained by Eqs. (2) and (3): The resonant wavelength λ is proportional to D and d, so enlarging D and d will shift resonant wavelength to the longer wavelength. In Fig. 3(a), we fix d = 240 nm and D = 110 nm, and when increasing w from 40 nm to 60 nm, 80 nm, and 100 nm, the resonant wavelength is shifted from 1630 nm to 1531 nm, 1429 nm

797

and 1310 nm respectively. The effect of w on the resonant wavelength arises from the dispersion relation of SPPs in MIM waveguide [31] qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  −ε2 n2eff −ε1 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : tanh neff −ε2 wπ = λ = ε1 n2eff −ε2

ð5Þ

Here, ε1 and ε2 are permittivity for silver and air, respectively. According to the above equation, increasing w will decrease the effective index neff [31], so the resonant wavelength exhibits blue shift as shown in Fig. 3(a). An interesting issue should be also noted that with the same varying step of 20 nm for parameters d and D, the resonant wavelength shifts faster when adjusting d than D as shown in Fig. 3(b) to (c). This is because in Eqs. (3) and (4) the coefficient for d is 2 but for D is 1, so d has a relatively larger effect on the resonant wavelength. Knowing how d, w, and D influence the transmission properties, we can easily tune the resonant wavelength by choosing the appropriate structure parameters. 4. Conclusion In conclusion, a novel plasmonic device for unidirectional excitation and control of SPPs is proposed. This waveguide consists of two metal films with a T-shaped structure. A subwavelength slit is fabricated at the center of lower film, and two nanocavities are engraved on each side of the metallic surface. When the plasmonic wave transmits through the slit, it splits and travels to the right and left nanocavities simultaneously. Whether the SPPs are coupled out or stopped by the two nanocavities are determined by the resonant wavelengths. The two nanocavities having different depths or widths can support two different resonant wavelengths. This personality enables us to switch the SPPs propagation in single direction. Based on and the F–P interferometry theory and the FDTD simulations, the influences of the cavity depth d, cavity width w, and gap width D on the transmission properties are numerically investigated and analyzed. It is found that the resonant wavelength exhibits a red shift as D and d increase, and a blue shift as w increases. In our studies, the nanocavities A and B are filled with air. Our structure can be improved in the future and is more flexible by filling them with nonlinear medium such as Kerr material, since the resonant wavelength can be easily tuned by the incident optical intensities in this case [24,25,32]. The proposed structure may have potential applications such as in planar nanophotonic circuits and on-chip optical interconnects. Acknowledgments This work was supported by the “Hundreds of Talents Programs” of the Chinese Academy of Sciences and by the National Natural Science Foundation of China under Grant 10874239 and 10604066. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]

Fig. 3. Dependence of the nanocavity transmission on structure parameter (a) w when d = 240 nm, D = 110 nm, (b) d when w = 40 nm, D = 110 nm, (c) D when w = 40 nm, d = 240 nm, respectively.

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