A four-port plasmonic quasi-circulator based on metal-insulator-metal waveguides

Kunhua Wen; Lianshan Yan; Wei Pan; Bin Luo; Zhen Guo; Yinghui Guo

doi:10.1364/OE.20.028025

1. Introduction

Surface plasmon polaritons (SPPs) are electromagnetic waves propagating along the metal-dielectric interface with an exponentially decaying field in both sides [1]. SPPs have been considered as one of the most promising ways to overcome the classical diffraction limits of optical devices, therefore various plasmonic structures have been proposed and studied, such as particles [2,3], cavities [4–7], apertures [8,9], grooves [10–12], and so on. For all these spatially symmetric structures, subwavelength slits or gratings in a metal film are usually employed to reduce the momentum mismatch between the SPP modes and the p-polarized light at the same wavelength so that SPPs could propagate along both directions on the metal/insulator interface. To satisfy the demand of some special applications that utilize the direction of the excited SPP field, such as plasmonic antennas [13,14], C. Huang proposed a planar metal perforated by multiple slits with specified widths [15]. In addition, investigations about the directional propagation and focusing of SPPs using nano-scale waveguides have received considerable interests [16–19]. Optical circulators are well-known directional propagation devices in light transmission systems (e.g. optical fiber communication systems). With the development of “on-chip” photonic integration on micro- or nano-meter scale, it is highly desirable to design SPP devices with different functionalities, in particular, the plasmonic circulator is a challenging one to achieve.

In this paper, to the best of our knowledge, a four-port plasmonic circulator based on metal-insulator-metal (MIM) waveguides is proposed and investigated for the first time. The structure consists of four MIM bus waveguides, which are connected by two narrow slits respectively. As the scheme is designed without using nonreciprocity [20], the device is regarded as a “quasi” circulator. Such kind of optical circulator was also demonstrated by placing a multimode tapered bending waveguide made of passive materials in the rotational symmetry [21]. Compared with previous demonstrations, the key contribution of the proposed device is its capability of providing on-chip light transmission at nanometer scale. According to the SPPs interference effect at the exiting of the slits, the propagation direction of SPPs with the specific wavelength will follow the counter-clockwise rule. The transmittance for the appropriate output is as high as 0.63 while the absolute isolation in the other two output ports is more than 12dB. By changing the material in the slits to obtain better matched phase condition, the isolation can be improved to be higher than 20dB. Therefore the proposed structure may perform as a quasi-circulator. In addition, since the transmission peak is within a considerable bandwidth, the device could also be used for wavelength demultiplexing

2. Theory and analysis

The diagram of the proposed circulator is shown in Fig. 1(a) . The insulator in the MIM bus waveguides and the metal are assumed to be air and silver, respectively. Two parallel narrow slits (so-called inside and outside slits), which are used to connect two adjacent orthogonal bus waveguides, are firstly both considered to be filled with air. As well known, the transmission characteristics in the MIM waveguide are significantly affected by the effective refractive index $n_{e f f}$ because the real part $Re (n_{e f f})$ and the imaginary part $Im (n_{e f f})$ determine the optical phase retardation and the propagation loss coefficient for the plasmonic mode, respectively. Since the proposed structure is on a nanometer scale, $Im (n_{e f f})$ can be ignored and more attention is paid to $Re (n_{e f f})$ for obtaining the relative phase. The parameter $n_{e f f}$ can be obtained from the dispersion equation of the TM mode consisting of Ex, Ez, and Hy components in the waveguide given by [22,23]

\tan h (\frac{1}{2} k_{i} d) = - \frac{ε_{i} \sqrt{ε_{i} k_{m}^{2} - {(n_{e f f}^{} k_{m})}^{2}}}{ε_{m} \sqrt{ε_{m} k_{i}^{2} - {(n_{e f f}^{} k_{i})}^{2}}}

where

k_{i}

and

k_{m}

are the transverse propagation constants in the insulator and the metal, d is the width of the waveguide, and

ε_{i}

and

ε_{m}

are the dielectric constants of the insulator medium and the metal, respectively. Then

Re (n_{e f f})

can be derived by solving Eq. (1) and is shown in Fig. 1(b).

Fig. 1 (a) Proposed scheme of the four-port circulator, (b) real part of the effective index, and (c) SPPs propagation direction.

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After transmitting through the bus waveguide, SPPs interference will occur at the exits of the slits which are at the end of the bus waveguide. In order to make sure that the SPPs propagation directions follow the counter-clockwise rule (i.e. Port1->Port4-> Port3-> Port2-> Port1, as shown in Fig. 1(c)), the phases at the exits of the inside and outside slits (i.e. $θ_{1}$ and $θ_{2}$ , respectively) along the bus waveguide should be satisfied as [18]

{\begin{cases} θ_{1} - θ_{2} = \frac{π}{2} \\ θ_{1} = \frac{2 π}{λ} (n_{b u s} L_{b u s} + n_{b u s} d_{s} + n_{i} L_{s l i t}) = \frac{2 m + 1}{2} π \\ θ_{2} = \frac{2 π}{λ} (n_{b u s} L_{b u s} + n_{o} L_{s l i t}) = m π \end{cases} \begin{matrix} m \end{matrix} = 1, 2, 3...

where

n_{b u s}

,

n_{i}

and

n_{o}

are the real parts of the effective indices for the bus waveguide, inside slit, and outside slit, and

L_{b u s}

and

L_{s l i t}

are the lengths of the bus waveguide and the slits, respectively. The center transmission wavelength can be easily obtained from Eq. (2), which is significantly determined by the length and the width (which affects the effective index). When the transmission wavelength is confirmed, a specific size of the structure is available. In addition, to forbid SPPs in the bus waveguide transmitting into the corresponding orthogonal slits, the phases at the entrances of the two slits should also be satisfied as

{\begin{cases} θ_{1}^{'} = \frac{2 π}{λ} n_{b u s} L_{1}^{} = m π \\ θ_{2}^{'} = \frac{2 π}{λ} n_{b u s} L_{2}^{} = \frac{2 m - 1}{2} π \end{cases} \begin{matrix} m \end{matrix} = 1, 2, 3...

where

L_{1}

and

L_{2}

are the distances from the input to the inside and outside silts, respectively. Here Port1 is specified as the input port and similar results would be obtained no matter which port is defined as the input port for this symmetrical structure. The electric fields at the exits of the slits can be expressed as [18,24]

{\begin{cases} E_{1}^{i n} = E_{2}^{o u t} + E_{4}^{o u t} \\ E_{2}^{o u t} = α_{2} E_{1}^{i n} (1 + β \exp (i (n_{i} L_{s l i t} + n_{b u s} d_{s} - n_{o} L_{s l i t}))) \\ E_{4}^{o u t} = α_{4} E_{1}^{i n} (1 + β \exp (i (n_{i} L_{s l i t} + n_{b u s} d_{s} - n_{o} L_{s l i t}))) \\ E_{3}^{o u t} = α_{3} E_{2}^{o u t} (1 + β \exp (i (n_{i} L_{s l i t} + n_{b u s} d_{s} - n_{o} L_{s l i t}))) \end{cases}

where

E_{1}^{i n}

is the electric field at the entrances of the slits along Port1,

E_{2}^{o u t}

,

E_{3}^{o u t}

and

E_{4}^{o u t}

are the electric fields at the exits of the slits leading to Port2 and Port 3, Port4,

α_{i, i = 2, 3,4}

is the corresponding SPPs transmission coefficient for the slits and satisfies the condition as

α_{4} > > α_{2} > α_{3}

, and

β

represents the contribution of the electromagnetic field from the partner slit. Therefore, the transmittance for Port4 is much larger than those for Port2 and Port3. Meanwhile, the isolation for Port3 is obviously larger than that for Port2 according to Eq. (4).

3. Simulation and discussion

In the following simulations, FDTD method is used to characterize the SPPs propagation under perfect-matching-layer (PML) absorbing boundary conditions. The mesh accuracy is set to be 5nm and the incident light is defined as a plane wave. Moreover, the tabulation of the optical constants of silver is the same as that used in [25]. During the simulation, the parameters are defined as: $L_{b u s} = 755 nm$ , $L_{s l i t} = 130 nm$ , $L_{1} = 560nm$ , $L_{2} = 480nm$ , $d_{bus} = 200nm$ , $d_{s l i t 1} = d_{s l i t 2} = 30 nm$ , and $d_{s} = 80 nm$ . The effective indices for the bus waveguide and the slits are $n_{b u s} = 1.188$ and $n_{o} = n_{i} = 1.874$ , respectively. Then, we can obtain the phase difference at the exits of slits along the input as $θ_{1} - θ_{2} = 0.434 π$ . Firstly, to investigate the directional transmission characteristics of the scheme with double silts, we also consider the cases with only inside slit, or only outside slit. By setting Port1 to be the entrance for SPPs, we can obtain the propagation direction through investigating the transmission spectra in the other output ports. As the structure is symmetrically distributed about the origin, the transmission direction for all the ports must satisfy one rule. The transmission spectra are shown in Fig. 2 . The transmittances in Fig. 2(a) are 0.06, 0.03, and 0.63 at the center wavelength 437.6nm for Port2, Port3, and Port4, respectively. Since the isolations for Port2 and Port3 to Port4 are achieved to be 12dB and 15dB, we consider there is only one valid output port (i.e. Port4 here). The results are also in highly accordance with the analysis in Eq. (4). Actually, to improve the SPPs isolations for the other outputs, the magnetic field distributions in the intersections between input bus waveguide and two orthogonal slits should satisfy the specific condition: $| H_{i n} (x, L_{1}) | ≅ | H_{o u t} (x, L_{2}) | ≅ 0$ .

Fig. 2 Transmission spectra of the propose schemes with (a) double silts, (b) only inside slit, and (c) only outside slit.

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Meanwhile, in Figs. 2(b) (with only inside slit) and 2(c) (with only outside slit), the transmittances at the same wavelength are all lower than 0.08 for all the outputs. It demonstrates that when the structure is with only one slit, SPPs at the specific wavelength cannot be transmitted through from any output ports. Therefore, it is believed that only the case of the scheme with double slits can satisfy the performance of the directional propagation. In addition, as there is only one transmission peak with 3-dB bandwidth of 13.3nm in Fig. 2(a), the scheme can also be regarded as a promising wavelength demultiplexing device.

To clearly show more details, four ports are respectively defined as an input port to find out the unique SPPs propagation characters in other ports, as shown in Fig. 3 . The electric field intensity distributions demonstrate that the SPPs transmission follows the counterclockwise direction, i.e. Port1 to Port4, Port2 to Port1, Port3 to Port2, and Port4 to Port3. In this case, according to the simulation results and the symmetrical character of the structure, we believe that no matter what input port is, the output port will only be the specific one in the counter clock-wise side.

Fig. 3 Electric field intensity distributions at the wavelength 437.6nm: (a) input: Port1, output: Port4, (b) input: Port2, output: Port1, (c) input: Port3, output: Port2, and (d) input: Port4, output: Port3.

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It should be noted that the value of $θ_{1} - θ_{2}$ is the main factor for the transmission and isolation of the device. Specifically, the transmissions for all the ports will increase slightly but the isolation level will become worse because of the phase deviation. Although the performance shown in Fig. 2 demonstrates that the device could tolerate slight phase error, the parameters should be optimized for better phase matching so as to obtain the best comprehensive performance. In Fig. 2, the device possesses a high transmission, but there is still a small amount of SPPs transmitting through the unexpected ports. The performances can be improved by changing air to be SiO₂ in the inside slits and adjusting the slits spacing to provide more accurate relative phase for Eq. (2). The real part of effective index for the inside slits is $n_{i} = 2 .29$ and the slits spacing is changed to be $d_{s} = 50 nm$ . The other simulation parameters are the same as those in Fig. 2(a). The corresponding phase condition is $θ_{1} - θ_{2} = 0.516 π$ . Simulation results are shown in Fig. 4 with Fig. 4(a) indicating that the largest transmittance reaches 0.48 in Port4 while those in Port2 and Port3 are lower than 0.01. Figure 4(b) is the corresponding electric field intensity distribution of the structure, and the propagation direction still remains the same. Here the optimized isolation and return loss are more than 20dB and 23 dB, respectively. It is difficult to accurately evaluate the insertion loss though by FDTD simulations [26]. For practical MIM waveguides [4–7,12,26], the incidence light could be send through a fiber and then evanescent coupled into silica submicrometre- or nanometre-diameter wires (SMNW) through a fiber tape. Since the diameters of the SMNW can be fabricated down to 50 nm [27], the sample can be excited by aligning the center of the SMNW with the bus waveguide directly or inserting a compact coupler [28] to improve the conversion efficiency. Therefore, it is possible to obtain the proposed device with reasonable insertion loss values.

Fig. 4 Structure with air-outside and SiO2-inside slits: (a) transmission spectrum, and (b) electric field intensity distribution.

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Furthermore, according to Eqs. (2) and (3), we can adjust the transmission wavelength by changing the lengths of the bus waveguides and the slits. For instance, the parameters are defined as $L_{b u s} = 590nm$ , $L_{s l i t} = 120 nm$ , $L_{1} = 355nm$ , $L_{2} = 305nm$ , $d_{s} = 50 nm$ , while others keep no change. The inside and outside slits are filled with SiO₂ and air, respectively. The simulation results based on FDTD method are shown in Figs. 5 and 6 . Firstly, we define Port1 as the input, and the transmittances at the center wavelength 463.3nm are 0.03, 0.001, and 0.92 for Port2, Port3, and Port4. Obviously, the isolations for Port2 and Port3 to Port4 are about 15dB and 30dB, respectively. Compared to the results in Fig. 2(a), the variation range of center transmission wavelength is 25.7nm and the isolations are largely improved. Additionally, one should note that there is only one transmission peak in a large wavelength range for Port4, which is the same as that indicated in Fig. 2(a). This phenomenon further demonstrates that the device can also be used for wavelength demultiplexing. Moreover, the transmittance for Port4 in Fig. 5 is a little lager than that in Fig. 4(a) for the reason that the size of the structure becomes smaller in Fig. 5 and the transmission loss caused by ohmic heat will therefore be reduced. Figure 6 is the electric field intensity distribution for the cases of Port1-4 being an input port, respectively. The results clearly show that no matter what input port is, the output port must be the specific one in the corresponding counterclockwise direction. According to the simulations and analyses, the directional propagation performance of the proposed scheme is further investigated, and thus we consider that it can serve as a plasmonic circulator. Conventional optical circulators usually consist of various components, such as polarizer, faraday rotator, splitting mirror, combiners, and so on. Apparently several characteristics of the proposed circulator are not as good as commercial available circulators used for fiber applications. For example, the isolation of commercial ones is generally about 30~40dB (compared to the proposed one with isolation of 20dB). While our proposed device is targeting applications on the nanometer scale with a compact design for on-chip light manipulation, and its characteristics could be further improved.

Fig. 5 Transmission spectra for Port2, Port3 and Port4.

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Fig. 6 Electric field intensity distributions at the wavelength 463.3nm: (a) input: Port1, output: Port4, (b) input: Port2, output: Port1, (c) input: Port3, output: Port2, and (d) input: Port4, output: Port3.

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Conclusion

In conclusion, a four-port plasmonic circulator is proposed based on silver-air-silver structures. When the specific phase condition is satisfied at the exits of the slits, the SPPs propagation direction in the waveguide obeys the counter-clockwise rule, i.e. Port1 to Port4, Port2 to Port1, Port3 to Port2, and Port4 to Port3. The transmittance of the center wavelength of 437.6nm at the specified output port reaches 0.48 and the relative isolation in the other two output ports is more than 20dB. Therefore the structure can be regarded as a quasi plasmonic circulator. In addition, there is only one transmission peak within the long wavelength range, making the proposed scheme capable of wavelength demultiplexing. The center wavelength of the structure could be changed though adjusting the length of the waveguide.

Acknowledgments

The research is supported by the National Basic Research Program of China under Grant 2011CB301800, the Key Grant Project of Chinese Ministry of Education under Grant 313049, and the Funds for the Excellent Ph.D. Dissertation of Southwest Jiaotong University in 2011.

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A four-port plasmonic quasi-circulator based on metal-insulator-metal waveguides

Abstract

1. Introduction

2. Theory and analysis

3. Simulation and discussion

Conclusion

Acknowledgments

References and links

Cited By

Figures (6)

Equations (4)

Optics Express