## Abstract

Optical interferometric logic gates in metal slot waveguide network are designed and investigated by electromagnetic simulations. The designed logic gates can realize all fundamental logic operations. A single Y-shaped junction can work as logic gate for four logic functions: AND, NOT, OR and XOR. By cascading two Y-shaped junctions, NAND, NOR and XNOR can be realized. The working principle is analyzed in detail. In the simulations, these gates show large intensity contrast for the Boolean logic states of the output. These results can be useful for future integrated optical computing.

© 2013 OSA

## 1. Introduction

As is known, semiconductor-based electronic devices will reach their limit in near future. Photonic devices and circuits have been proposed to break this limitation, benefiting from the fast speed and low heat producing properties of photons [1]. The elementary units of electronic circuits are transistor based Boolean logic gates. In photonics circuits, logic functions can be realized by linear interferences [2–4] or by nonlinear optical processes [5,6]. For linear optical logic gates, the constructive or destructive interference of the input signals yields corresponding logic operation results, which show merits of good stability and extensibility.

The integration of the photonic devices is limited by diffraction of light. Surface plasmon polaritons (SPPs), which are localized surface electromagnetic waves at the interface of metal and dielectric, can be applied to overcome this limitation. Many kinds of plasmonic waveguides [7–10] and devices [11–16] have been proposed. We recently in experiment realized optical Boolean logic gates based on propagating plasmons on silver nanowires, and showed the integration potential by realizing NOR gate through cascading OR and NOT gates [15,16]. Compared with silver nanowires, the metal slot waveguides show good field confinement, and can be easily integrated to complex structures and networks. Therefore, slot-waveguide-based plasmonic devices have large potential to be employed for on-chip integration. Recently, optical logic gates in metal slot waveguides have been proposed [17]. However, the working principle of this kind logic gates has not yet been discussed in detail.

In this paper, we realize the whole set of fundamental logic gates using two kinds of structures formed by metal slot waveguides. A single Y-shaped waveguide structure can work as AND, OR, NOT and XOR logic gates. By using two cascaded Y-shaped structure, with one port for inputting control beam, NAND, NOR and XNOR can be realized. The working principle is discussed in detail and the working efficiency is verified by simulation. The metal slot waveguide based logic gates show small size and intensity contrast as high as 16dB. These gates are good candidates for constructing future optical computing chips.

## 2. Logic gates with two input ports

The proposed logic gates are composed by three metal slot waveguides with a Y-shape junction as shown in Fig. 1. The structure is fabricated in sliver film coated on SiO_{2} substrate. In the device, the two ports denoted by I_{1} and I_{2} are taken as channels for input signals. The remainder port denoted by O is used as the fan-out of the logic gate. The input and output are all encoded by their intensities. Two signals are transmitted to the junction from the input ports and then reach the output port. The amplitudes of transmitted powers for the two signals are E(I_{1}) and E(I_{2}). The constructive or destructive interference of E(I_{1}) and E(I_{2}), which is determined by the phases of the input signals, result in the output intensity I_{o}. By defining the value of the threshold intensity, the three port device can realize the logic operations of AND, OR, NOT and XOR gates.

The working principle for the logic operations is illustrated in Table 1. The input is expressed as {E(I_{1}),E(I_{2})}, using the amplitudes of transmitted powers. The input power at ports I_{1} and I_{2} is selected to be equal. For the inputs, “on” and “off” states correspond to “1” and “0”, respectively. For the output, the Boolean value is determined by the threshold intensity I_{t}. If the output intensity I_{o} is larger than the threshold I_{t}, the output value is “1”. If I_{o}<I_{t}, the output is “0”. For constructive interference, the complex amplitudes of the output for individual input E(I_{1}) and E(I_{2}) are set to be E. The output intensity I_{o} is |E|^{2} for inputs {E,0} and {0,E}, and 4|E|^{2} for input {E,E}. When choosing I_{t} below |E|^{2}, the output state is “1” for input {E,0}, {0,E} and {E,E}, realizing OR logic function. When I_{t} is chosen above |E|^{2} and below 4|E|^{2}, the output is “1” only for {E,E} input, corresponding to the AND logic operations. For destructive interference, the complex amplitudes of the output for individual input E(I_{1}) and E(I_{2}) are E or –E, respectively. Because of the symmetry of gate structure, complete destructive interference can be realized at port O, resulting in a large interference visibility. The output intensity I_{o} is |E|^{2} for inputs {E,0} and {0,-E}, and 0 for {E, -E}. Choosing I_{t} below |E|^{2} results in an XOR gate. If the signal at port I_{2} is used as control signal, for the input 0 and E at the I_{1} port, i.e. {0,-E} and {E, -E}, the output state is just opposite to the input state, which leads to the function of NOT gate.

To verify the functions of the logic gate, simulations based on finite element method are performed. In simulation, we pay attention to the wavelength of 632.8 nm, with the corresponding permittivity of silver −18.36 + 0.48i, interpolated from experimental data [18]. The permittivity value of SiO_{2} used here is 2.13. To obtain good confinement and acceptable loss, the thickness t and width of waveguide d is set to be: t = 100nm and d = 60nm. The corresponding fundamental mode distribution is shown in Fig. 2(a). As can be seen the electric field is mainly confined in the slot. At the wavelength, the slot waveguide also have a considerable propagation length of 5.33μm. Here, the propagation length is defined as the length over which the power in the direction of propagation decays to 1/e of its original value due to material losses. In the gate structure, the input light propagating to the output port O will suffer strong loss at the junction. To decrease the energy loss at the junction, small angle between the two input waveguide θ is preferred. But too small θ will decrease the separation between the two input waveguide w, leading to the cross talk. To determine the appropriate value of the separation w, coupling length of two parallel slot waveguides for different separations is calculated, as shown in Fig. 2(b). Here the coupling length is defined as the propagating distance over which the power coupled from one waveguide to the other reaches the maximum. After overall consideration, θ is chosen to be 30°, and w is 300 nm. In the simulations, all the bends in the structures are used as sharp corners. In practical experiment, these corners have round shapes, which is beneficial for decreasing the bending loss.

In the simulation, the power of signals on both input port I_{1} and I_{2} is I_{0}, but the initial phase differences Δφ of the two signals is adjustable. The Fig. 3(a) shows the output power, I_{o}(I_{1},I_{2}), for different Δφ. I_{o}(I_{1},I_{2}) shows an ideal interference of the two input light signals, which is well described by cosine function. The complete interference can be attributed to the single mode characteristic of the waveguide and the symmetry of the gate structure. The output powers for individual input I_{o}(I_{1}) and I_{o}(I_{2}) are shown as the blue line. Our designed logic functions can be realized at different values of Δφ by defining corresponding threshold intensity. For Δφ = π and threshold value of 0.2I_{0}, XOR or NOT operations can be realized. For Δφ = 2π and threshold value of 0.2I_{0}, the device functions as an OR gate. If the threshold is increased to I_{0}, the AND logic gate is realized. Figures 3(b)-3(d) show the field intensity distribution in the device for single input and both inputs with different Δφ. It is noteworthy that the intensity contrast for the output value “1” and “0” is high, for example, the intensity contrast is about 16dB for XOR, NOT and OR operations, and about 6dB for AND operations. It should also be noted that the choice of the threshold intensity and the phase difference can be quite flexible. For a given threshold intensity, these logic operations can be realized in a wide range of Δφ, which makes the devices have large tolerance.

## 3. Logic gates with three input ports

For logic gates NOR, NAND and NXOR, the output is “1” when both input ports are empty, so additional input of the logic gate is needed to work as control signal. From another point of view, these logic functions are composite operations of the former functions, and their gates can be realized by cascading NOT gate and OR, AND, XOR, respectively [16]. The sketched structure of the logic gate with three input ports is shown in Fig. 4. In the structure, two input ports, I_{1} and I_{2}, are connected to a Y-shape junction G_{1}, which can independently operate as a logic gate. The output of G_{1} and another input port C are connected, forming a second independent gate, named G_{2}. The output port of G_{2} is denoted as port O. In this design, the output of the first operation in G_{1} is used as the input signal of G_{2}. Thus cascaded logic gates can be realized in such structure. The ports I_{1} and I_{2} are used for input signals, while the port C is used for control signal. Port O is the fan-out of the whole structure. All the parameters are denoted similar as in last section. The complex amplitude of light in port O transmitted from port C is denoted as E(C). For further extension of the device to realize more complex functions, the geometries of the basic gates, for instance G_{1} and G_{2}, are exactly the same.

The working principle of the gate is analyzed as shown in Table 2. For operations OR and AND, the two input signals from port I_{1} and I_{2} are in phase (Fig. 3(a) and Table 1). An out-phase control signal from port C can inverse the output of G_{1}. Here the second gate G_{2} operates as a NOT gate. As shown in Table 2, when E(C) is twice as E(I_{1}) and E(I_{2}) (E(I_{1}) = E(I_{2}) = E), with a phase difference of π, NOR and NAND operations can be obtained. For a threshold value I_{t} above |E|^{2} and below 4|E|^{2}, the output correspond to NOR logic operation. For a threshold value I_{t} below |E|^{2}, the logic function of the whole structure is NAND. The cascade approach for constructing NOR and NAND is not applicable for XNOR. For XOR operation, the output for input patterns {E,0} and {0,-E} are out phase. An additional control signal will lead to different output result for the two input patterns. However, the XNOR operation can still be realized in the structure with three input ports. Table 2 shows that, when E(I_{1}) = E(I_{2}) = E and the control signal is out-phase with E(C) = -E, the outputs correspond to XNOR operation for a threshold value below |E|^{2}.

Electromagnetic calculations were performed to quantitatively investigate the outputs of the device. For ports I_{1} and I_{2}, their equal distance to port O produces no additional phase difference. So the two input signals are set to be with equal phase at the two ports. By setting the input power at port I_{1}, I_{2} and C equal to I_{0}, the output intensity at port O is calculated for varying phase difference between the control signal and the input signals, as shown in Fig. 5(a). The minimum of the output power, corresponding to destructive interference at port O, occurs at Δφ = 1.1π, which is determined by the difference of the distances travelled by the control signal and the input signals. This phase difference is fixed for latter simulations. Figure 5(b) shows the variation of the output power at port O for different inputs when the power of control signal I_{C} is increased. The red crosses mark the corresponding area and power threshold for the three logic functions. As an example of the three logic functions, the distribution of field intensity for operating XNOR gate is shown in Fig. 6, with the power of control beam I_{C} to be 0.58I_{0}. This XNOR logic gate shows a high intensity contrast of the output states “1” and “0” as about 16dB.

## 4. Conclusion

In this paper, we realize the whole set of fundamental logic operations in devices formed by metal slot waveguides. We show a single Y-shaped waveguide junction can work as AND, OR, NOT and XOR logic gates. By using two cascaded Y-shaped junction, with one port for control signal, NAND, NOR and XNOR gates can be realized. The working principle is discussed in detail and the working efficiency is verified by electromagnetic simulations. The metal slot waveguide based logic gates show small sizes and high intensity contrasts for the output states “1” and “0”. Assembles of these gates can realize more complicated functions and construct future optical computing chip.

## Acknowledgments

This work was supported by MOST Grants (No. 2009CB930700), NSFC Grants (Nos. 11004237, 11134013, 11227407) and “Knowledge Innovation Project” (KJCX2-EW-W04) of CAS.

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