High efficient unidirectional surface plasmon excitation utilizing coupling between metal-insulator-metal waveguide and metal-insulator interface

Optics Communications 389 (2017) 128–132

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Optics Communications journal homepage: www.elsevier.com/locate/optcom

High efficient unidirectional surface plasmon excitation utilizing coupling between metal-insulator-metal waveguide and metal-insulator interface☆

MARK

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Zhixiang Huang , Ke Xu, Deng Pan Key Laboratory of Intelligent Computing & Signal Processing, Ministry of Education, Anhui University, Hefei 230039, China

A R T I C L E I N F O

A BS T RAC T

Keywords: Waveguide Plasmon Optical integration

A new structure is proposed, which can realize parallel coupling between metal-insulator-metal (MIM) waveguide and plasmon on metal-insulator (MI) interface. An example for wavelength of 680 nm shows the coupling efficiency can be high as 82%, with short coupling length of 1.2 µm. By using MIM waveguide with proper length, a unidirectional plasmon generator is realized. The generator shows excitation efficiency as high as 78%, with high extinction ratio as 1:170. It also shows a good tolerance for the wavelength. The results are of vital importance for optical integration and unidirectional plasmon excitation.

1. Introduction SURFACE plasmon polaritons (SPPs) have received great attention in recent years for its potential application on integrated optical circuit, sensing and so on. Metal-insulator-metal (MIM) waveguide [1,2] and Metal-insulator (MI) interface [3] are two important nano-optical elements based on SPPs. To explore the full potential of SPP, it is necessary to control both its propagation direction and strength. The efficient unidirectional SPP source is also a common requirement for plasmonic integrations. The common way to realize unidirectional SPP excitation is applying an oblique incidence. Unidirectional SPP excitation can be achieved under normal incidence by breaking the symmetry of a single slit or grating [4,5]. Based on MIM waveguide, many optical elements have been proposed with normal incidence, including splitters [6], Mach–Zehnder interferometers [7], optical filters [8] and so on. The MI interface, is useful for detection and sensing [9]. MIM waveguide takes advantages in confining and guiding light. SPPs be excited in high efficiency as stated in [10,11]. MI interface is more preferable for sensing, for the field is exposed to the outer environment. But the usual method for excitation of plasmon on MI interface need large devices or gratings [12]. In this work, we study the coupling of MIM waveguide and MI interface. The result shows the coupling can be realized with high efficiency, if the structure parameter is properly designed to fulfill mode index match. An example structure for the coupling is shown. At wavelength of 680 nm, the coupling. efficiency is high as 82% and coupling length is short as 1.2 µm. Applying this kind of coupling, and using the MIM waveguide with

suitable length, a structure for unidirectional surface plasmon excitation is designed. The excitation efficiency can be much high as 78%, with extinction ratio of 1:170. These results are meaningful for the excitation of surface plasmon on single MI interface, or squeezing light into MIM waveguide, and arising new notion for optical integration. 2. Coupling characteristic of MIM/MI structure 2.1. Design of MIM/MI Structure Fig. 1(a) shows a composite structure, named MIM/MI structure, which includes an MIM region and an MI interface. Dielectric in the MIM region is set to be air. Generally, the permittivities of the metal and the dielectric above the MI interface are εM and εD . The width of air layer in MIM region is d, and the thickness of metal film between MIM region and MI interface is t. This structure can be roughly taken as a coupling structure for MIM waveguide and MI interface. In next section, based on this structure, coupling from independent MIM waveguide to MI interface will be shown. Now we illustrate how to choose the material and structural parameters to fulfill mode index match condition, by analyzing dispersion of individual MIM waveguide and MI interface. As we know, only if the two propagation modes have close propagation constant at a given frequency, can they show a strong coupling. The dispersion relations of plasmon on MI interface and even mode in MIM waveguide are shown in Fig. 1(b), following [12]:

β = k 0 εD εM /(εD + εM ) ( for MI interface)

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This work was supported in part by National Natural Science Foundation of China under Contract nos. 51277001 and 61471001. Corresponding author. E-mail address: [email protected] (Z. Huang).

http://dx.doi.org/10.1016/j.optcom.2016.12.001 Received 6 October 2016; Received in revised form 25 November 2016; Accepted 1 December 2016 0030-4018/ © 2016 Elsevier B.V. All rights reserved.

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field decreases down to 1/e of its value on the MI interface. The quasieven mode have a relative wide mode distribution and the mode width is about 1 µm, while for the single MI structure, the mode width is 260 nm. As for quasi-odd mode, the field is greatly localized that the mode width is 120 nm. Denote the field of the two eigenmodes as Eo (x ) and Ee (x ). The total field of the composite waveguide can be expressed by a linear combination of the two eigenmodes [14]:

E (x, z ) = co Eo (x )⋅eiβo z + ce Ee ( y)⋅eiβe z

Fig. 1. (a) MIM/MI structure for coupling between MIM waveguides MI interface. (b) Dispersion relations for modes on independent MI interface, and for even modes in independent MIM structure, with d = 0.1λ . (λp = 2πc /ωp , c is the velocity of light in

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where βo and βe are the complex propagation constant of the two eigenmodes. The great discrepancies in the field distribution of the two modes lead to differences in their effective refractive index. The real parts of effective refractive index of the quasi-even and quasi-odd modes are ne=1.455 and no=1.733. The imaginary parts of effective refractive index correspond to the loss of the modes. The quasi-even mode with wide distribution, has a much low loss of −0.06 dB/μm. For quasi-odd mode, it has great localized field, which mean more power penetrating into metal, so that it suffer a much high loss of −0.75 dB/ μm. The coefficient is decided by the initial input field distribution. After the coupler is excited at z=0 from one port, most part of the field energy is transferred into the two eigenmodes and propagated. The coupling length LC is where the two eigenmodes have phase difference of π :

vacuum).

tanh( β 2 − k 02 ) = − β 2 − k 02 εM / εM β 2 − k 02 ( for MIM waveguide) (2) where βis the propagation constant, k0 is the wave vector in vacuum. Here, the permittivity of the metal is described by lossless Drude model: εM = 1−ωp 2 / ω 2 , where ωp is the bulk plasma frequency of the metal. The dispersion curve of even mode of the metal-air-metal waveguide lies below the dispersion of single metal-air interface without an intersection. For single MI interface, the wave vector increase monotonically with the frequency, and goes to infinite when the frequency approach the surface plasmon frequency:ωsp, D = ωp / 1 + εD . So, the phase match condition between the metal-air-metal waveguide and upper MI interface, can be fulfilled by increasing the permittivity of dielectric medium above. According to the discussion above, material and structural parameters are set as follow. The dielectric above MI interface is set to be silica, with the permittivity:εD = 2.1. Hereinafter, the metal is chosen as silver, with the permittivity interpolated from experimental data [13]. We pay attention to the wavelength of 680 nm, where εM = −21.52 + 0.418i . With these parameters, to fulfill the phase match condition, thickness of the air layer in the MIM waveguide d is set to be 37 nm. Another structural parameter t is not predominant to achieve efficient coupling, and mainly influence the coupling length. At first, t is set to be 25 nm, which is reasonable for field penetration. The effect of t on the coupling will be discussed later.

Lc = λ /[2⋅(ne − no )].

(4)

where λ is the wavelength in the vacuum. That gives LC of 1.22 µm for 680 nm. 2.3. Coupling Properties in MIM/MI Structure First, Fig. 3(a) shows an intuitive picture for the coupling. The field is excited in MIM part at z=0, with a mode distribution of the uncoupled MIM waveguide. After exciting at z=0, with z increasing, the energy is gradually coupled to the upper MI interface. At z=LC the energy in the MIM region reach the minimum and most are transferred to the upper MI interface. As z increases more, the energy above the MI interface again squeeze back into the MIM region. Fig. 3(b) shows the energy flow along z direction at different z position in the MIM region and above MI interface. The energy flow of the MIM port is measured, just taking into account the power in the air layer region. Considering the mode width of the two eigenmodes discuss in last section, we here define the energy flow within a wavelength above the MI interface as the energy flow of the MI port. At coupling length LC=1.22 µm from the input, 82% energy is coupled to the upper MI interface, and the ratio of the energy flow in two port here is 27:1. The attenuation of the total field is −0.61 dB/μm, lies between the attenuation of the two eigenmodes. It should be clarified that the radiation part by the exciting is small. We can see that in the propagation, the fields above the MI

2.2. Eigenmode of the MIM/MI Structure Fig. 2 shows the x direction electric field component of two eigenmodes supported by the MIM/MI structure, obtained by finite element method method. For one mode, the field in the MIM region is in phase with the field above the MI interface, while for the other one, the fields in the two regions are out of phase. Define the former as quasi-even mode, and the latter as quasi-odd mode. Since the size of the mode is mainly decided by the field above the MI interface, here the mode width of the two modes is defined as the distance over which the 129

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Fig. 5. Sketch map of unidirectional plasmon generator.

refractive index between quasi-even mode and quasi-odd mode reduces. Thus, according to Eq. (3), coupling length LC gets longer with the increasing of t. As show in Fig. 4(a), when the thickness t changes from 10 nm to 60 nm, the coupling length increases exponentially from 350 nm to 6.9 µm. Fig. 4(a) also shows the dependence of total loss on t. With increasing of t, more power penetrates into the metal, which leads to the increasing of total loss. Fig. 4(b) shows the ratio of energy coupled to the MI interface with input at coupling length. As t increases, both LC and total loss increase, so the total power decays to lower value at LC. Since at LC, most energy is coupled to the MI interface, the ratio of energy coupled to the MI interface also decrease.

Fig. 3. (a) Field pattern of Hy in the coupling between MIM waveguide and MI interface. (b)Power flow (normalized to the input) of the MIM and MI port along the propagation direction.

interface have a wide distribution, which should not be taken as radiation field for its equiphase surface is vertical to the MI interface. This wide field distribution related to the slow field decaying above MI interface in the even mode in Fig. 2. Fig. 4 shows the dependence of coupling on the thickness of silver film t. As t increases, it becomes more difficult for energy of light to tunnel through the film, and the modes of the structure approach the uncoupled modes of the two ports. So the discrepancy of effective

3. Application of directional coupling for unidirectional plasmon excitation In the discussion above, the length of MIM waveguide is infinite. When the length of MIM waveguide is suitable, such as equal to the coupling length LC, we can realize unidirectional plasmon generator. Unidirectional plasmon generator is sort of important plasmon source, which are needed in many applications [15,16]. The proposed unidirectional plasmon generator is shown in Fig. 5. The structure is a MIM/MI structure, with the field in the coupler excited by a 90°bending MIM waveguide. Most of the structural and material parameters are equal to the MIM/MI structure discussed in last section, shown in Fig. 5. Since many works have been devoted to enhance the excitation efficiency of MIM waveguide [10,11], here we only pay attention to the coupling efficiency from MIM waveguide to MI interface. So light of 680 nm is incident within the MIM waveguide with the mode distribution. Then it is transferred into the coupling region and coupled to the upper MI interface. The length of the coupling region L is set equal to the coupling length for 680 nm: L=LC=1.22 µm and the widths of different section are optimized using a genetic global optimization algorithm [10]. So at the end of the coupling region, the energy in the MIM region reaches its minimum. In this way, the energy can be farthest coupled from MIM to the MI interface. Fig. 6(a) shows the field distribution of Hy in the structure at 680 nm. As we designed, the light is coupled to the upper MI interface unidirecionally and efficiently. Fig. 6(b) describes the spectrum response of the unidirectional excitation structure. For wavelength of 680 nm, the efficient of energy coupling from MIM waveguide to the MI interface is high as 72%, and the extinction ratio (define as power propagated along the MI interface to the left and to the right) is about 1:60. It can be seen that the excitation performance are weakly depended on the wavelength, so the structure have a good tolerance. From about 550–700 nm, the excitation efficiency is all above 70%, and even reaches 78% at 620 nm, with the extinction ratio of 1:170. In Fig. 6(b), the most optimum wavelength is not 680 nm, for the loss is not lowest at this wavelength. Apart from the material loss, the energy losses in this structure mainly include two parts. First is the bending loss at the corner. This includes the light reflected and scattered by the corner. The scattering may lead to energy propagate on the left MIM and MI interface which also go against the extinction

Fig. 4. Dependence of coupling on t. (a) coupling length and total loss for variant t. (b) Ratio of energy coupled to the MI interface with input at first coupling length for variant t.

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Ratio of coupling efficiency

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Fig. 7. (a) Hy distribution for the coupling of plasmon from MI interface to MIM waveguide at 680 nm; (b) Solid line and dash line show the coupling efficiency of plasmon from right and left on the MI interface into the MIM waveguide. Dash line shows the ratio of the efficiency.

ratio of the plasmon excitation. Second is the loss at the end of the coupling region, including the reflection and the mode mismatch of the super mode and single MI interface mode. Losses for 620 nm are lower than that for 680 nm, result in the performance is preferable at 620 nm. Otherwise, a round corner can be introduced to reduce the reflection and scattering, consequently further improve coupling efficiency and the extinction ratio. In addition, since there is no nonreciprocal material, the coupling efficiency from MIM waveguide to MI interface must be equal to that from MI interface to MIM waveguide. From this point of view, this structure is also a high efficient optical component for squeezing light into MIM waveguide from MI interface. As show in Fig. 7, the coupling from right on the MI interface also exhibit high coupling efficiency, and the coupling efficiency from left on the MI interface to the MIM waveguide is low as about 0.1% around 620 nm. The spectrum in Fig. 7(b) in not exactly the same as that in Fig. 6(b), for the power flow taken into consideration is different in the two situations. Thus unidirectional excitation of MIM waveguide may also be achieved by this structure.

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4. Conclusion In conclusion, we have proposed that the MI interface and MIM waveguide, which can couple with each other when their mode index matches. We show a simple structure for the coupling. At 680 nm, the coupling efficiency can be higher than 82% and the coupling length is short as 1.2 µm. By using MIM waveguide with suitable length, we can realize unidirectional surface plasmon generator. The generator shows excitation efficiency as high as 78%, and unidirectional extinction ratio of 1:170, which can be further improved. It also shows a good tolerance for the wavelength. Our result is meaningful for the excitation of surface plasmon as plasmon source and instructive for the optical 131

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surface plasmons with subwavelength slits, Appl. Phys. Lett. 92 (10) (2008) 101501.

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