Design and Analysis of A Complete Full AdderBased On Metal-Insulator-Metal (MIM) Waveguide-Based Plasmonic Wavesoraman yoose�  ( oraman.yoose�@gmail.com )

Universitat Politecnica de Catalunya https://orcid.org/0000-0002-1872-8054Angel Rodríguez 

Universitat Politecnica de Catalunya

Research

Keywords: Full adder, OR gate, Plasmonic waves, Resonance wavelength, MIM Waveguide

Posted Date: June 12th, 2020

DOI: https://doi.org/10.21203/rs.3.rs-34397/v1

License: This work is licensed under a Creative Commons Attribution 4.0 International License.  Read Full License

Design and Analysis of a Complete Full Adder Based on Metal-Insulator-

Metal (MIM) Waveguide-Based Plasmonic Waves

Oraman Yoosefi*1, Angel Rodríguez2

*1oraman.yoosefi@gmail.com ,

2angel.rodriguez@upc.edu

Department d’Enginyeria Electrònica, Universitat politècnica de Catalunya

C/Jordi Girona, 31, 08031, Barcelona, Spain.

Abstract

In this paper, metal-insulator-metal (MIM) plasmonic waveguide structures and a

rectangular cavity resonator at a central frequency of 1550 nm were used to propose a

complete full adder. Under this circumstances, the system has a fast function with slight

variations in real- time or near real-time manner, and this led to its minimum power

consumption, while serving in various situations. In this full adder, we benefited from the

property of combining resonant waves in the first and second modes, and we managed to

obtain a high transmission coefficient in states where the output must be active. This

complete full adder operates through designing 4-input AND, XOR, OR, and NOT logic

gates, resulting in the design of a complete full adder with low manufacturing complexity

and cost relative to ones designed through combining the conventional 2-input AND and

OR gates.

In comparison of three computational methods, finite‐difference time‐domain (FDTD) is a

simple and versatile method. This method directly discretizes the time‐domain partial

differential form of Maxwell's equations in various dimensions while using analytical

solution in the remaining direction and solving the 3D scattering problem. Therefore,

necessary simulations were conducted using FDTD software, and showed a good fit to the

results predicted through approximations intended for theoretical relations.

Keywords: Full adder, OR gate, Plasmonic waves, Resonance wavelength, MIM

Waveguide

1. Introduction

Control of light using light is the most fundamental topic in all-optical integrated circuits,

which have many applications in all-optical telecommunication networksb [6,7]. Extensive

research has been conducted on optical computing since the 1980s [8]. However, the

intensity of the research activities decreased due to some limitations of materials used in

the manufacture of optical chips that prevented the manufacture of small and inexpensive

optical chips for laboratory researches. The main reason for this is the problem of optical

diffraction in optical devices that could be overcomed using plasmonic waves [12,13].

With the advent of plasmonic structures as well as the approach of technology towards the

integrity of optoelectronic circuits, manufacturing problems and phenomena that helped

prevent further compression of the structure led to the study and use of plasmonic

structures and plasmonic waves. In very small sizes lower than the wavelengths, surface

plasmons provide a suitable basis for the realization and manufacture of all-optical devices

due to the increased intensity of concentrated optical fields. MIM waveguides are very

important structures in plasmonic devices due to guiding surface plasmons in the cross-

section of metal-dielectric structure [16, 18, 29, 30]. Because these waveguides not only

support the propagation of modes with very small wavelengths and high group velocities,

but also show their ability to guide the wave up to relatively long distances. Combination

of these waveguides with nano-resonators in various shapes, which are side-coupled to

them, creates a variety of new structures, which have many applications in all-optical

devices [1, 2]. The transmission medium in optical networks is the optical fiber; and the

wavelength band, which can be used to transmit information, is 1550 nm with minimal

losses in the third optical telecommunication window. Therefore, the full adder for a

wavelength of 1550 nm (C-Band: 1530-1565nm) will be designed [6, 31,32].

One of the major problems in the expansion of optical networks is the limitation of

diffraction in the limited size of optical devices due to the wavelength of light transmitted

by the network, which increases the sizes of optical devices relative to those of electronic

devices. The diffraction limit can be broken using plasmonics [7].

Diffraction is a phenomenon, which occurs when a wave encounters an obstacle or a slit,

and which is defined as the bending of (electromagnetic) waves around the corners of an

obstacle or aperture and their propagation into the region of geometrical shadow of the

obstacle.

Using optical devices, like silicon photonic devices, it causes other problems such as cases

where the Pockels constant equals zero. Although effects such as the thermo-optic effect

and dispersion effect of free carriers have been dynamically employed to control the

optical properties of silicon, these technologies have adverse effects on velocity, losses,

and so on. It is very difficult to integrate high-speed optical devices using silicon

technology [28]. [Palik, 1977] Using plasmonic waveguides offers a new opportunity to

integrate electro-optic polymers in high-speed optical technology [8].

The term plasmonic has been explained based on the process of interactions between

electromagnetic waves and conduction electrons in metals with nanoscale dimensions. A

lot of plasmonic waveguides and optical equipment, based on the propagation of surface

plasmons, have been presented in recent studies [3,4,21]. All-optical logic gates with

plasmonic waveguide structures have been introduced and simulated in [3,21,23] using a

waveguide Y-branch splitter, but the theory of the problem has not been addressed in it,

and the optical power loss is very high in this structure as well. In an all-optical integrated

circuit, it is necessary to have several logic gates working in series, and if each gate causes

a lot of loss, the practical application will not be possible. In a recent work [4], a photonic

crystal waveguide and the nonlinear properties of optical materials have been used to

design all-optical logic gates. Although photonic crystal structures and non-linear light

have important applications, in comparison to plasmonic structures, they have major

disadvantages such as enlarged size of pieces and high power losses for logic gates.

Kaboli and Akhlaghi [5] have benefited from full absorption in periodic plasmonic

nanoparticles and the operation of pumping optical power to these nanoparticles to modify

the output, and to create an AND logic gate. Although their gate is a new design, it has a

very high manufacturing complexity for a simple logic gate, the size of the piece is large,

and the power consumption is high due to the permanent pumping of optical power.

In [6], the use of plasmonic waveguides and slot cavity resonators have been proposed

for basic logic gates, and has used transmission coefficients for the amplitude of waves in

waveguides.

Different sections of this paper are as follows: In Section 2, numerical methods and

Disadvantage of MPB software package already used are expressed. Section 3 will extend

the methodology. Section 4 discuses on the theoretical equations of plasmonic structures,

which theoretical equations related to plasmonic structures will be described and the basic

structure for designing the adder explained. Then, mathematical relations for the electric

permittivity coefficient in a plasmonic structure, as well as the wave equation will be

explained. Sections 5 and 6 present the results and discussion on OR logic gate and the

conclusion, respectively.

2. Numerical Methods

Computational Electromagnetics provide an in-depth introduction of the three main full-

wave numerical methods in computational electromagnetics (CEM); namely, the method

of moment (MoM), the finite element method (FEM), and the finite-difference time-

domain (FDTD) method.

One of the most popular computational methods for solving too large to handle problems

in finite element packages is FDTD (finite difference time domain), which gets around

having to invert a large linear system by instead mimicking Maxwell's Equations in the

time domain. By implementing a uniform mesh, the overhead associated with storing the

location of each point is eliminated (though there are conformal FDTD methods which try

to split the difference), allowing order-of-magnitude increases in the size of domains that

can be solved, compared to finite-element approaches. The cost for this is that FDTD

methods are far harder to use than finite-element approaches - the analysis of the data to

deconvolve behavior as a function of frequency can be nontrivial, and numerical stability is

not always assured. In general, it requires a couple of years of experience to get really

reliable results out of 3D FDTD methods, even with modern packages (Taflove and

Hagness, 2005; Sadiku, 2009; Sadiku, 2017).

Therefore, a full analysis is supposed to develop a quick and deep understanding of the

essentials of CEM and to solve real-life electromagnetic problems.

2.1 Frequency-Domain vs. Time-Domain

There are two common computational electromagnetic approaches to study the dielectric

structures: frequency-domain and time-domain. We feel that each one has not only its own

place in a researcher's toolbox but also its unique advantages and disadvantages. The MIT

Photonic Bands (MPB) package is frequency-domain. That is, it does a direct computation

of the eigenstates and eigenvalues of Maxwell's equations using a planewave basis. Each

field computed has a definite frequency. In contrast, time-domain techniques iterate

Maxwell's equations in time (Taflove and Hagness, 2005;Sadiku, 2017; Kang Ning et al.,

2017).

2.2 Disadvantage of Frequency-Domain vs. Time-Domain

A traditional disadvantage of frequency-domain methods was that you had to compute all

of the lowest eigenstates, up to the desired one, even if you didn't care about the lower

ones. This was especially problematic in defect calculations, in which a large supercell was

used, because in that case the lower bands were "folded" many times in the Brillouin zone.

Thus, you often had to compute a large number of bands in order to get to the one you

wanted incurring large costs both in time and in storage(Taflove and Hagness, 2005;

Sadiku, 2009; Sadiku, 2017; Kang Ning et al., 2017).

2.3 MPB Software Package

MPB is a software package to compute definite-frequency eigenstates of Maxwell's

equations in periodic dielectric structures. It can compute optical dispersion relations and

eigenstates for structures such as strip waveguides and optical fibers. MPB is well suited

for the study of photonic crystals: periodic dielectric structures are exhibiting a band gap in

their optical modes and prohibiting propagation of light in that frequency range. High-

performance 3D/2D (FDTD) Maxwell's solver for design, analysis, and optimization of

nanophotonic devices and processes, which used in this work, is Version S2019A-R1

(8.21.1781) [26].

2.3.1 Disadvantage of MPB Software Package

The disadvantages of frequency-domain versus time-domain disappear to some degree in

MPB. However, the targeted eigensolver method used in MPB still has poor convergence,

so time-domain methods such as Meep still have an advantage here (Taflove and Hagness,

200; Kang Ning et al., 2017). FDTD can give almost arbitrarily accurate answers to the

macroscopic Maxwell's equations for any geometry. This could be further improved by

repeating many of the steps.

3. Methodology

In this paper, we will benefit from a plasmonic structure and a slot cavity resonator to

design a full adder. To this end, first OR and AND logic gates needed for the design of the

adder will be proposed. Then, necessary simulations will be conducted with the aid of

Lumerical's FDTD software. This is based on the finite element method. Numerical

simulation results will never give exactly the correct answer. Therefore, the steps should be

taken to reduce the error, for example via reducing the error often involves increased

simulation time and memory. In finite difference schemes (such as FDTD) is often

assumed that the error in a simulation result always diminishes with decreasing grid size.

4. Theoretical Equations of Plasmonic Structures

For the implementation of logic gates in this study, we benefit from a metal-insulator-metal

waveguide, where a nanoscale insulator is placed between two metal structures. When the

distance between the two metals is very short, the surface plasmons can be stimulated, and

the plasmonic waves, which propagate between the two metal surfaces, can be used as

messengers. As compared to Lorentz model, the FDTD approach can also account for a

large variety of materials such as Drude dispersion materials, perfect metal, second-order,

and third-order materials. As a result, this variety of materials can well support

multidimensional simulations.

In this study, we assume the insulator is air, and the metal is Drude model silver in which

the relative dielectric function for metals is expressed by Eq. (1) [9]. 𝜀𝑚(𝜔) = 𝜀∞ − 𝜔𝑝2𝜔(𝜔 + 𝑗𝛾) (1)

where, 𝜀∞ is the dielectric constant of the material at infinite frequency, 𝜔𝑝 shows the

plasma frequency, and 𝛾 denotes the angular frequency of damping. The complex-valued

dielectric function of evaporated and template stripped polycrystalline silver films (the

Complex permittivity of silver in terms of frequency) are determined from 0.05 eV (λ = 25 μm) to 4.14 eV (λ = 300 nm) with a statistical uncertainty of less than 1% [26]. As for

silver, these values are as follows: 𝜀∞ = 3.7, 𝜔𝑝 = 9.1 𝑒. 𝑉 , 𝑎𝑛𝑑 𝛾 = .018 𝑒. 𝑉 . Two waveguide modes (TM0 and TM1) for the electric field intensities are that propagate

Electromagnetic waves between two points. Under this condition, the system has a fast

function and minimizes power consumption.We assume the width of the waveguides to be

100 nm so that only the first and second modes (TM0, TM1) are stimulated and depending

on the application of equipment, the first or second mode is used. By solving the Maxwell

equations, we can reach the dispersion equation as shown in Equation (2). tanh (𝑘𝑑2 𝑤) = − 𝜀𝑑 𝑘𝑚𝜀𝑚𝑘𝑑 (2)

where, 𝜀𝑑 is the dielectric constant of the insulator (which is equal to one for air), 𝜀𝑚

illustrates the dielectric constant of the metal (silver), 𝑘𝑑 and 𝑘𝑚 are numbers for the

dielectric wave and the metal, respectively.

If we assume the complex propagation constant in the plasmonic waveguide to be β, we

can achieve Equations (3) and (4) by writing electrical and magnetic fields inside the

insulator and the metal , using boundary conditions. 𝑘𝑑 = √(𝛽2 − 𝜀𝑑𝑘02) (3) 𝑘𝑚 = √(𝛽2 − 𝜀𝑚𝑘02) (4)

Through the simultaneous solution of Equations (2), (3) and (4), we can obtain the

propagation constant in the waveguide (β). Take Figure 1, which has been used as a basis for this study, and which consists of an MIM

waveguide and a rectangular slot with a length of Ls. After the stimulation of the MIM

waveguide, if the resonance conditions are met in the rectangular slot, the plasmonic waves

will form inside the rectangular slot in a static form and in the form of sequential

reciprocating motions. Resonance occurs when the phase shift caused by the sequential

reciprocations in the slot (in addition to phase differences that occur when colliding with

the end of each side of the slot) is equal to an integer multiple of 𝜋; that is, relation ∆𝜑 = 𝛽𝑚𝐿𝑠 + 𝜑𝑟 = 𝑚𝜋 is true. Note that 𝜑𝑟 is ignored due to its negligible value. If we

assume the refractive index inside the plasmonic waveguides and the resonance slot to be 𝑛𝑒𝑓𝑓, where 𝑘0 = 2𝜋𝜆 is the wave number in the vacuum, we will obtain the Equation (5) as

follows: 𝑛𝑒𝑓𝑓 = 𝛽𝑘0. 𝛽𝑚𝐿𝑠 = 𝑚𝜋 ⟹ 𝑛𝑒𝑓𝑓 . 2𝜋𝜆𝑚 . 𝐿𝑠 = 𝑚𝜋 ⟹ 𝜆𝑚 = 2𝐿𝑠.𝑛𝑒𝑓𝑓𝑚 (5)

If the input port in Figure 1 is stimulated by an electromagnetic wave at optical

frequencies, resonant static electric and magnetic fields in a rectangular slot can be

obtained by solving the Maxwell equations. The intensity of the magnetic fields in this

resonatory nano-slot for the m-th mode is obtained through Equation (6). 𝐻𝑚(𝑥, 𝑡) = 2𝐻0 cos(𝛽𝑚𝑥 − 𝛽𝑚.𝐿𝑠2 )𝜎 [𝑒𝑗(32𝛽𝑚.𝐿𝑚−𝛽𝑚.∆𝐿) + 𝑒𝑗(𝛽𝑚.∆𝐿−12𝛽𝑚.𝐿𝑚)] (6)

where, ∆𝐿 is the distance from the input port to the middle of the rectangular nano-slot, and

since waveguides usually reach the edge of the nano-slot, ∆𝐿 = 𝐿𝑆2 is usually true (of

course, it can be less than this value too, and will not cause any problems). Given that we

assumed the width of the waveguides to be very small, only the first and second modes are

stimulated in the nano-slot. For instance, the magnetic field intensity equation for the first

mode is as shown in Equation (7). 𝑚 = 1 ⟹ 𝐻𝑚(𝑥, 𝑡) = 2𝐻0. sin(𝛽1. 𝑥)𝜎 [− sin(𝛽1. ∆𝐿)𝑒−𝑗(𝜔1.𝑡)] (7)

From Equation (7), we derived the necessary idea to design the AND, OR, and XOR gates,

which are necessary bases for the adder because if we assume two input waveguides,

whose distances to the middle of the nano-resonator are asymmetric to each other; that is,

for one of them, the distance is ∆𝐿1, and for the other ∆𝐿2 = −∆𝐿1, then the two resonated

magnetic fields in the rectangular slot will neutralize each other, and the field inside the

rectangular slot will become zero. In addition, by increasing the number of waveguides,

and adjusting their distances to each other, the desired output parameters can be obtained.

5.Input OR Gate

There were two main reasons for choosing a resonance structure in this paper. The first and

the most important reason is that there is a high rate of leakage from one input to other

inputs in structures, where the input and output plasmonic waveguides are physically

connected to each other. This causes a lot of errors especially when there are a large

number of inputs, thus making it practically impossible to design a structure with a large

number of inputs in a package. On the other hand, as suggested in this paper, as resonance

enclosures are used, the inputs will be practically isolated from each other, and only a

slight leakage due to resonance may occur between the inputs, which will not cause many

errors in response to the output, and which will be negligible. The second reason is the

possibility of using a large number of inputs in a resonance structure. In this section of our

paper, the experiences of Mohsen Olyaee et al.’s (2019) paper on the structure of the OR gate are used. In study of these researches, with increasing number of inputs, it will not be

geometrically and physically possible to design and connect the waveguides. Even if this

can be done for a small number of inputs, the surface of the design piece will become very

large, but in the resonance design, a larger number of inputs can be designed on a piece

with a smaller surface.

5.1 Simulation structures and method

The structure and dimensions of a 4-input OR logic gate are illustrated in Figure 1. We

assume the threshold of the optical electric field amplitude in the waveguides equal to 0.4.

If the field amplitude is greater than 0.4, it will be assumed as a logical one, and if the field

amplitude is less than 0.4, it will be assumed as a logical zero.

We have four input ports. We consider the intensity of light (the intensity of the

electromagnetic wave), i.e. the square of the amplitude, as the inputs, and the intensity of

light in the output as the gate output. In OR gate , to set a measurement criterion for the

field amplitude, we set the threshold value (E) to 0.4.

Figure 1. The structure and dimensions of a 4-input OR logic gate

5.2 discussion and results

First, we obtain resonance wavelengths for the structure. The following graph is obtained

for the transmission coefficient of the structure. If the transmission coefficient is greater

than one, this is because when Lumerical software deals with several inputs, it will be

somewhat problematic in terms of defining the transmission coefficient, but this curve is

sufficient for our work, and determines the the optimal operating wavelength.

Figure 2. The resonance wavelengths for the structure

Considering the Figure 2, a wavelength of 1490 nm will be suitable for the gate’s operation. Of course, we have resonance in a wavelength of 780 nm too, but since the

telecommunication windows are within 1470-1550 nm, we consider the main wavelength

at 1490 nm.

In fact, the resonance wavelength is obtained from a Equation (8), which λ depends on the

length of the rectangle (l) in the cavity. 𝜆 = (𝑘)Π𝑙 , k = 1, 2, … (8)

where 780 nm is synonymous with the first resonance, and 1490 nm is synonymous with

the second resonance.

In State 1 (wavelength of 780 nm), we assume that all four inputs are active (we assume

the electric field amplitude of the input electromagnetic wave at each of the four inputs as

being equal to the normalized one). In this state, the amplitude of the optical electric field

at the output is about 1.5 units as shown in Figure 3-b, and since it is greater than 1.3 units,

it will be considered equal to a logical one as being expected too. The electric fields in the

structure of the OR gate are illustrated in Figure 3-c, and we can see that the circuit has

operated correctly.

The structure of the OR gate is illustrated in Figure 3(a). In electromagnetic waves,

the amplitude is the maximum field strength of the electric and magnetic fields. We

assume the threshold of the optical electric field amplitude in the waveguides equal to 1.3

units. If the field amplitude is greater than 1.3, it will be assumed as a logical one, and if

the field amplitude is less than 1.3, it will be assumed as a logical zero. In this state, the

amplitude of the electric field intensity at the output port equals 1.3 units as shown in the

Figure 3.

Figure 3. The structure of the designed 4-input OR gate: (a) The state where all four input

ports are stimulated;(b) The electric field amplitude at a wavelength of 1490 nm at the

output port; (c) Shows the fields in the gate structure at a wavelength of 1490 nm.

Polarized light waves are light waves in which the vibrations occur in a single plane and

Metallic surfaces reflect light with a variety of vibrational directions. A plane wave's

electric and magnetic field vectors are in directions perpendicular to the direction of wave

propagation. The field oscillates in the x-y plane, along the page, with the wave

propagating in the z direction, which is perpendicular to the page.

Due to the symmetry of the shape in State 2, we assume that it is sufficient to arbitrarily

activate one of the inputs with an amplitude of 1 while inactivating the other or setting it to

zero. The field amplitude equals 0.65 in this state. Figure 3(a) shows the shape of the

inputs and outputs, and Figure 3(b) shows the amplitude of the electric field at the output,

which is about 1.1 units, and which represents a logical one because it is larger than the

threshold. The electric fields in the structure of the OR gate are illustrated in Figure 3(c),

and we can see that the circuit has operated correctly. In this state, due to the resonance of

the field caused by the rectangular resonator, the waveguide side has inclined towards

orange, which represents a field resonating into the waveguide.

Figure 4. The structure of the designed 4-input OR gate: (a) The stimulation state where

Input-1 = 0, Input-2 = 1, Input-3 = 0, and Input-4 = 1; (b) The electric field amplitude at a

wavelength of 1490 nm at the output port; (c) Shows the fields in the gate structure at a

wavelength of 1490 nm.

In the other states, where the two opposite inputs are stimulated, and the two other ones are

off, the conditions are like those in the previous state. Hence, to avoid repetition, we avoid

describing these states.

In State 3, we assume that two of the neighboring inputs are stimulated with a

normalization power of 1, and the two others are inactive. As for this state, Figure 5(a)

shows the shape of the inputs and outputs, and Figure 5(b) shows the amplitude of the

electric field at the output, which is about 0.7 units, and which represents a logical one

because it is larger than the threshold. The electric fields in the structure of the OR gate are

illustrated in Figure 5(c), and we can see that the circuit has operated correctly. In this

state, due to the resonance of the field caused by the rectangular resonator, the side of the

Input-1 and Input-2 waveguides has inclined towards yellow, which represents a field

resonating into these two waveguides.

Figure 5. The structure of the designed 4-input OR gate: (a) The stimulation state where

Input-1 = 1, Input-2 = 1, Input-3 = 0, and Input-0 = 0; (b) The electric field amplitude at a

wavelength of 1490 nm at the output port; (c) Shows the fields in the gate structure at a

wavelength of 1490 nm.

In State 4, we assume that only one of the inputs is active, and the rest are inactive. Since

the structure is symmetric, there is no difference in which input you choose as the active

input. In this state, we consider the structure of the logic gate as shown in Figure 6(a). The

electric field at the output is shown in Figure 6(b), and Figure 6(c) shows the size of the

fields in the gate structure using colored markers.

Figure 6. The structure of the designed 4-input OR gate: (a) The stimulation state where

Input-1 = 1, Input-2 = 0, Input-3 = 0, and Input-0 = 0; (b) The electric field amplitude at a

wavelength of 1490 nm at the output port; (c) Shows the fields in the gate structure at a

wavelength of 1490 nm.

In the final state, where all four input ports are zero, logically, none of the fields get into

the output port. Therefore, the amplitude of the electric field at the output port is zero,

which represents the correct function of the proposed 4-input OR logic gate. Table 1 shows

the electric field amplitudes at the inputs and outputs of the proposed logic gate as well as

the correct functioning states of the logic gate. The remaining combinations of the four

inputs are not shown in Table 1 due to their structural symmetry.

Table (1): Electric field amplitudes at the inputs and outputs of the proposed logic gate

Elec

Amplitude

Elec

Amplitude

Elec

Amplitude

Elec

Amplitude

Elec

Amplitude

No.

0 1 1 0 1 Input-1

0 0 1 1 1 Input-2

0 0 0 0 1 Input-3

0 0 0 1 1 Input-4

0 1.4 2.3 0.65 1.3 Output

Elec

Amplitude

0 1 1 1 1 Output

6. Conclusion

With the aid of the logic gates designed, we managed to design a half adder circuit with a

simple structure through propagation of plasmonic waves at an optical frequency and

window of 1550 nm. In Section 2, we used a 4-input OR gate to design and simulate a full

adder circuit, which used plasmonic waves to transmit signals. The 4-input gates, presented

in this study for the first time, have a simple structure, and are manufactured at a low cost.

This proposed design functions much better in comparison to similar designs in credible

studies conducted on logic gates designed using plasmonic waves. For instance, the logic

gates designed in [10] using plasmonic waves have thresholds variable relative to the phase

of the input wave, and are very vague, which makes the output separation very difficult.

Whereas, in the proposed designs in this study, the threshold limit is clearly defined, and

the outputs are clearly defined as logical 0 and 1 relative to this threshold, which is a very

important advantage in the proposed design. Using a rectangular resonator and plasmonic

waves, a filter with a central wavelength of 1550 nm has been designed in [11], which has

high electromagnetic wave losses due to a failure to adjust the dimensions and correctly

optimize the width of the resonatory slot and the distance of the waveguides to the

resonator's center. Under this circumstance, in the proposed design the system has a fast

function with slight variations in real- time or near real-time manner, and this led to its

minimum power consumption, while serving in various situations. Additionally, the use of

optical devices, like silicon photonic devices, causes other problems, for example, cases

where the Pockels constant equals zero. Although the thermo-optic effect and dispersion

effect of free carriers have been dynamically employed to control the optical properties of

silicon, these technologies have adverse effects on velocity, losses, costs, and so on.

However, by optimizing the dimensions of the structure, we managed to reduce the losses,

and achieve a transmission coefficient of about 0.62, thus reducing the losses down to 25%

less than the design in [12].

Furthermore, in our idea, given that the number of input ports varies in different states, the

transmission coefficient of the amplitude cannot, in practice, show the changes in the

output. Under this condition, a wave radiates to one of the inputs and the transmission

coefficient at the output equals to the ratio of the output wave amplitude to the input wave

amplitude. In other words, when light is radiated to both input ports, the transmission

coefficient at the output is equaled to the ratio of the output wave amplitude to the sum of

the amplitudes of both waves at the two inputs.

Although the previous researches’ designed gates are new and high-efficiency in terms of

some characteristics, they also have a very high manufacturing complexity for a simple

logic gate, for example, the piece size is large and the power consumption is high due to

the permanent pumping of optical power. Therefore, all the calculations for the design of

the structure will face difficulties. For this, the intensity of the wave amplitude at the

output port as well as a plasmonic structure accompanied by a slot cavity resonator to

design a full adder should be considered. After proposing the OR and AND logic gates for

the design of the full adder, necessary simulations are conducted with the aid of

Lumerical's FDTD software.

Recommendations

FDTD software is a powerful tool for various physics and engineering applications.

One of its disadvantage is that it may provide an accuracy with slightly more fault than

other software in simulating large-scale electrical properties.

Acknowledgements

None. No funding to declare.

6. References

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Figures

Figure 1

The structure and dimensions of a 4-input OR logic gate

Figure 2

The resonance wavelengths for the structure

Figure 3

The structure of the designed 4-input OR gate: (a) The state where all four input ports are stimulated;(b)The electric �eld amplitude at a wavelength of 1490 nm at the output port; (c) Shows the �elds in the gatestructure at a wavelength of 1490 nm.

Figure 4

The structure of the designed 4-input OR gate: (a) The stimulation state where Input-1 = 0, Input-2 = 1,Input-3 = 0, and Input-4 = 1; (b) The electric �eld amplitude at a wavelength of 1490 nm at the output port;(c) Shows the �elds in the gate structure at a wavelength of 1490 nm.

Figure 5

The structure of the designed 4-input OR gate: (a) The stimulation state where Input-1 = 1, Input-2 = 1,Input-3 = 0, and Input-0 = 0; (b) The electric �eld amplitude at a wavelength of 1490 nm at the output port;(c) Shows the �elds in the gate structure at a wavelength of 1490 nm.

Figure 6

The structure of the designed 4-input OR gate: (a) The stimulation state where Input-1 = 1, Input-2 = 0,Input-3 = 0, and Input-0 = 0; (b) The electric �eld amplitude at a wavelength of 1490 nm at the output port;(c) Shows the �elds in the gate structure at a wavelength of 1490 nm.

Supplementary Files

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