Open Access
Add to BibSonomy
Abstract
In this paper, first, the optical two-circle switch (OTCS) and then, the XOR / XNOR and AND logic gates were designed, simulated, and optimized. The OTCS designed structure consisted of two rectangular waveguides and two optical circles between them. The light enters from one waveguide, and due to the coupling between the waveguide and the ring, it enters the circle in case of constructive interference, transmitted to the adjacent circle, and finally, transferred to another waveguide. If it is possible to change the properties of the circle in such a way that there is no constructive interference in it, the coupling of the light from the first waveguide to the circle will not occur, therefore the light will come out from the other side of the first waveguide. The continuity condition of electromagnetic fields at the boundary between rectangular and ring waveguides and the scattering condition has been used in all simulation boundaries to simulate this structure. By optimizing the size and type of material in the core and cladding the waveguides and circles, up to 90 percent of input waves were observed from the output of the second waveguide with the barium titanate core. This occurs as a result of coupling modes between waveguides and circles. In the second step, by applying transverse voltage and changing the refractive index, the conditions of constructive interference in the ring were eliminated, and the coupling between the rectangular waveguide and the circle did not occur. As a result, up to 85 percent of the light exited from the end of the first rectangular waveguide. This change of output power from the first to the second waveguide and vice versa can transform the designed structure into a two-state voltage-controlled optical switch; by putting two of these switches together in a row, optical logic gates of XOR / XNOR and AND are simulated and then optimized.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The science of optics has a wide range of scientific and technological applications, including the production of lasers, optical computing, multiplexers, demultiplexers, and switching and signal routing [1]. It is essential to know optical resonators and their combination can play an essential role in meeting these needs. Optical resonators are a set of waveguides that connect one output to one input with one or more circular waveguides, resulting in the transfer of information. In 1969, a general structure was designed for a planar optical filter waveguide consisting of silicon and germanium [2]. Due to the nature of the optical ring resonator, at specific wavelengths, a high- order optical filter can be created by serializing two optical circles, resulting in the possibility of making compounds of very small dimensions and low loss that are suitable for optical integrated circuits [3]. Because the coupling transmitted wavelengths can be easily changed by increasing or decreasing the radius of each circle, filters can be set to separate different frequencies [4]. Also, by changing the refractive index of the material using the electro-optic effect or magneto-optic effect, this process of frequency adjustment can be done in a controlled manner with voltage or electric or magnetic fields. [5,6]. To date, most of the structures introduced for optical switches have used Mach-Zehnder interferometers, which have been designed and implemented using a variety of optical logic gates such as OR XOR AND, for switching operations, but these structures have a relatively large size for application in optical integrated circuits [7] 8 [9]. Attempts to make optical switches using ring resonators have also led to the conclusion. The problem of them is that as the light output paths are not on the same side, the design of these structures is unsuitable for making optical logic gates [10,11]. In this research, first, a ring resonator was used to design an optical switch, which, despite its small size, performs the switching operation well. Then, using OTCS, two logic gates, XOR / XNOR and AND, were simulated. Due to their small size, all of these structures can have many applications in optical integrated circuits and will also be able to filter and separate a wide range of wavelengths.
2. Theoretical scheme
In electro-optical effect, by applying an external electric field in certain crystals, its refractive index changes, as a result, the direction of polarization of light passing through the material changes so the optical path for a specific polarization adjusts.
This effect has been observed in various materials such as lithium niobate, BaTiO3, and ammonium dihydrogen phosphate. The dependence of the refractive index on the electric field is expressed by the following:
The linear sentence is called the Pockels effect, and the square sentence is called the Kerr effect. In cases where the square effect is negligible, the refractive index tensor changes are given as follows:
where r is the electro-optical coefficient and E is the electric field vector [12].Figure 1 is a diagram of a double-ring resonator (serial double-ring) consisting of two rectangular waveguides and two circular waveguides and the transmitted and coupled fields. An optical double-ring resonator design consists of two rectangular waveguides and two circular waveguides and the transmitted and coupled fields are shown in Fig. 1 [13]. Two rectangular waveguides are used to transmit light from input to output, and the EM fields can be coupled with the fields inside the loops. When the path of light in the resonant ring is an integer multiple of the wavelength of light, light travels from a rectangular waveguide to a loop, otherwise light travels in a straight line. Therefore, by controlling the length of the optical path, the output power of the waveguides can be controlled. By applying a voltage to the metal gates around the waveguides and thus creating an electric field and due to the electro-optical effects, changing the refractive index of that material and, consequently, the light path in the rings; hence, the state of interference of the lights that pass through the circle changes, changing constructive interference to destructive interference and vice versa, which determines the entry or non-entry of light from the waveguide into the ring and the light output. This effect provides a set of features such as switching and routing [14].
3. Structure of the optical two-circle switch
In previous works, the Mach-Zehnder interferometer has been used extensively to design various types of logic gates. In this study, we used an OTCS instead of the Mach-Zehnder interferometer. Figure 2 shows the geometry of OTCS, which has been simulated in 3D with Comsol software. This switch consists of 4 Ports and two circular waveguides in the middle of two rectangular waveguides. The OTCS structure has a silica clad and BaTiO3 as its core with a refractive index of 2.437. BaTiO3 exhibits electro-optic effects, and its Pockels coefficient is r42 = 820 pm/V, which is more than 20 times higher than LiNbO3 single crystals [15,16]. The wavelength used in the simulation is 1550 [nm], which is very useful in optical applications [17].
Scattering Boundary Condition is used for making boundaries transparent for scattered waves. In addition, we used another boundary condition to specify the tangential components of the electric field through simulation.
In Fig. 3 (a), in the absence of electric voltage and field (E = 0), the light goes to two optical rings after the constructor interference and finally to terminal number 4. According to Fig. 3, two conditions of an OTCS can be imagined. In Fig. 3 (a), by applying zero electrical fields to the core of circular waveguides, light travels from Port 1 to circular waveguides and Port 4 in case of constructive interference. This path of light is equivalent to a logical zero. Then in Fig. 3 (b), applying an electric voltage of 10.5 volts to the core of the structure made of BaTiO3, which is an electro-optic material, changes the refractive index of the material and thus changes the coupling coefficients; as a result, due to destructive interference, light does not enter into the rings and travels straight to Port 2. This case is equivalent to logic one.
Fig. 3. The electric field norm for: (a) 0 v applied electric field (b) 10.5 v applied electric field
Figures 4 a and b show the changes in the amount of conduction, reflection, and absorption between the waveguides in terms of the radius of the circles and the distance between the cores of the waveguides, respectively. The best distance between the cores of the waveguides is 0.37 micrometers, which demonstrates the least loss and the highest amount of transmittance to Port 4. When the radius of the circular waveguide is 6.2 μm, the transmittance rate reaches 90 percent, and the absorption is 5 percent.
Fig. 4. The transmittance and reflectance as a function of (a) the radius of circles (b) Distance between cores of waveguides
Figure 5 shows the transmission, reflection, and absorption diagrams in terms of applied voltage, in which the blue line represents the transmittance of light from Port 1 to 4. At the beginning of the simulation, when the applied voltage is zero, 90 percent of input light is transmitted to Port 4, and by applying 10.5 V voltage, its value reaches 10 percent. The green line indicates the transmittance of light from Port 1 to 2, which increases from 5 percent to 85 percent by applying 10.5 volts of electrical voltage. Reflection and absorption values are also small and negligible throughout the simulation.
In case the required dimensions for the shape are not fully observed in the construction processes of OTCS or other interactions or neglected boundary conditions flip the constructive and destructive interference, errors may be corrected by applying an additional offset electric voltage for each gate, which could be considered an advantage for the implementation of this design structure. nowadays, structures with smaller scale than our designed gates are being built in integrated optical circuits therefore, the possibility of error during the fabrication process is low.
Optimized values of parameters to achieve the best structure design are presented in Table 1:
Table 1. Design parameters.
Comparing an OTCS with the previous optical switches, which were based on the Mach_Zehnder interferometer, it can be seen that although the efficiency of OTCS is 90 percent for constructive interference and 85 percent for destructive interference, which is slightly lower than the previous switches with efficiencies of about 97 percent and 96 percent [18], the length of the designed structures have decreased from about 24 mm [19] or 33 mm [5,20] to about 30 micrometers. This has made the OTCS structure a helpful element in designing more complex optical integrated circuits and the construction of optical logic gates in the future. Other technologies such as photonic crystal with scale of about 6,7 um [21,22] and plasmonic with 500 and 1000 nm [23,24] have been used to make optical logic gates. Although their scale are smaller than OTCS logic gates, the manufacturing process is more difficult.
4. Design and simulation of logic gates
4.1 XOR / XNOR gate
XNOR / XOR logic gates can be created using two consecutive OTCS structures shown in Fig. 6. The control signals X and Y are the voltages applied at the second electrode of the first and second OTCS, respectively. In the specified arrangement of OTCSs, output ports 1 and 2 act as XNOR logic and XOR logic, respectively.
Fig. 6. represents the implementation of XOR and XNOR operation in Comsol. The following results are obtained from Fig. 6.
Fig. 7. Comsol result of the XOR and XNOR operation for the different combinations of the control signals.
Case 1: When X = 0 V (logic 0) and Y = 0 V (logic 0) (See Table 2)
When 0 voltage is applied to both electrodes, constructive interference occurs in both ring resonators, and light eventually exits from the XNOR gate output.
Case 2: When X = 0 V (logic 0) and Y = 10.5 V (logic 1)
Here, 0 voltage is applied to the first OTCS, and the constructive interference happens, and then 10.5 V voltage is applied to the second OTCS, and the light travels directly to the output of the XOR gate by making a destructive interference.
Case 3: When X = 10.5 V (logic 1) and Y = 0 V (logic 0)
In the beginning, when 0 V voltage is applied to the first OTCS, the wave goes straight. By applying a voltage to the second OTCS, when the destructive interference happens, the light goes to the output of the XOR gate.
Case 4: When X = 6.75 V (logic 1) and Y = 6.75 V (logic 1)
Voltage is applied to both OTCSs, so we have destructive interference in both cases, and the output light goes to the XNOR gate.
Table 2. Response obtained from the Fig. 7.
4.2 Implementation of AND gate
As Fig. 8 shows, this gate consists of two consecutive OTCSs, one of the output ports of the first OTCS is connected to the input port of the second OTCS, and the other output port of the OTCS is not connected to the input port of the second OTCS.
The simulation results of the AND gate are shown in Fig. 9; in only one case, the output of the AND gate is equal to one, and that is when 10.5 volts of the potential difference is applied to both OTCSs so that the constructive interference happens and the output of the AND gate is activated. In other cases, the output of the AND gate will be zero.
Result of simulation is shown in Table 3.
Table 3. Response obtained from the Fig. 9.
5. Conclusion
This paper designed, simulated, and optimized XOR / XNOR and AND logic gates using an optical two-circle switch (OTCS) resonator with acceptable results despite its small size. The designed structure of the switch had two rectangular waveguides and two optical loops, which changed the direction of output light from the end of the second rectangular waveguide to the end of the first rectangular waveguide when electrical voltage was applied to it. This occurs due to the shifting of constructive interference in the rings to destructive interference and the consequent uncoupling between the rectangular waveguide and the optical rings due to the electro-optic effect. This switch was used as a voltage-controlled two-state switch in optical integrated circuits to build XOR / XNOR and AND logic gates that met the expected value tables. Small size,lack of crosstalk, alignment of input and output, and the possibility of correcting construction problems with the help of offset voltage are the advantages of this design, making it potentially helpful designing in optical integrated circuits.
Disclosures
The authors declare no conflicts of interest.
Data availability
No data were generated or analyzed in the presented research
References
1. Y. Yadong, Responsive Photonic Nanostructures: Smart Nanoscale Optical Materials (RSC Cambridge, Berkeley, 2013).
2. E. Marcatili, “Bends in Optical Dielectric Guides,” Bell Syst. Tech. J. 48(7), 2103–2132 (1969). [CrossRef]
3. V. S. chenko II and A. B. Matsko, “Optical Resonators With Whispering-Gallery Modes-Part II Applications,” IEEE J. Sel. Top. Quantum Electron. 12(1), 15–32 (2006). [CrossRef]
4. W. J. Westerveld, S. M. Leinders, P. M. Muilwijk, J. Pozo, T. C. van den Dool, M. D. Verweij, and M. Yousefi, “Characterization of Integrated Optical Strain Sensors Based on Silicon Waveguides,” IEEE J. Sel. Top. Quantum Electron. 20(4), 101–110 (2014). [CrossRef]
5. R. Takei and T. Mizumoto, “Design and Simulation of Silicon Waveguide Optical Circulator Employing Nonreciprocal Phase Shift,” Jpn. J. Appl. Phys. 49(5), 052203 (2010). [CrossRef]
6. V. Sadasivan, “QCSE Tuned Embedded Ring Modulator,” J. Lightwave Technol. 32(1), 107–114 (2014). [CrossRef]
7. S. Kumar, A. Kumar, and S. K. Raghuwanshi, “Implementation of an Optical AND Gate using Mach-Zehnder Interferometers,” Opt. Modelling Des. 9131(3), 913120 (2014).
8. A. H. Alizadeh and A. Rashidi, “Implementation of optical OR and NOR gates using Mach-Zehnder interferometers,” J. Phys. Commun. 4(8), 085014 (2020). [CrossRef]
9. S. Kumar, S. K. Raghuwanshi, and A. Kumar, “Implementation of optical switches using Mach–Zehnder interferometer,” Opt. Eng. 52(9), 097106 (2013). [CrossRef]
10. S. J. Emelett and R. A. Soref, “Synthesis of dual-microring-resonator crossconnect,” Opt. Express 13(12), 4439–4456 (2005). [CrossRef]
11. X. Yan, C. Ma, C. Zheng, and D. Zhang, “Multi-channel switch array on the base of triple series-coupled,” Opt. Laser Technol. 53, 9–16 (2013). [CrossRef]
12. P. Castera, A. M. Gutierrez, D. Tulli, S. Cueff, R. Orobtchouk, R. P. Romeo, G. Saint-Girons, and P. Sanchis, “Electro-Optical Modulation Based on Pockels Effect in BaTiO3 With a Multi-Domain Structure,” IEEE Photonics Technol. Lett. 28(9), 990–993 (2016). [CrossRef]
13. D. G. Rabus, “Ring Resonators: Theory and Modeling,” in Integrated Ring Resonators, Springer, Berlin, 2007, pp. 3–40.
14. J. Kedia and N. Gupta, “An FDTD analysis of serially coupled double ring resonator for DWDM,” Optik 126(24), 5641–5644 (2015). [CrossRef]
15. Y. Avrahami, BaTiO3 based materials for Piezoelectric and Electro-Optic Applications, Doctoral dissertation, Massachusetts Institute of Technology, 2003.
16. R. L. Holman, L. M. Althouse Johnson, and D. P. Skinner, “THE DESIRABILITY OF ELECTROOPTIC FERROELECTRIC MATERIALS FOR GUIDED-WAVE OPTICS,” in Sixth IEEE International Symposium on Applications of Ferroelectrics, Bethlehem, PA, USA, 1986.
17. J. Piprek, “Electroabsorption Modulator,” in Semiconductor Optoelectronic Devices, Academic Press, California, 2003, pp. 213–225.
18. N. A. Mohammed, H. S. Abo Elnasr, and M. H. Aly, “Performance Evaluation and Enhancement of 2×2 Ti: LiNbO3 Mach Zehnder Interferometer Switch at 1.3 µm and 1.55 µm,” The Open Elect. & Elect. Eng. J. 6(1), 36–49 (2012). [CrossRef]
19. M. Zhang, K. Chen, W. Jin, and K. S. Chiang, “Electro-optic mode switch based on lithium-niobate Mach–Zehnder interferometer,” Appl. Opt. 55(16), 4418–4422 (2016). [CrossRef]
20. C. Taraphdar, T. Chattopadhyay, and J. Nath Roy, “Mach–Zehnder interferometer-based all-optical reversible logic gate,” Opt. Laser Technol. 42(2), 249–259 (2010). [CrossRef]
21. R. H. Yuan, C. Wang, and Z. Y. Li, “Design of on-chip optical logic gates in 2D silicon photonic crystal slab,” Opt. Rev. 27(3), 277–282 (2020). [CrossRef]
22. D. Rao, S. Swarnakar, and S. Kumar, “Performance analysis of all-optical NAND, NOR, and XNOR logic gates using photonic crystal waveguide for optical computing applications,” Opt. Eng. 59(5), 057101 (2020). [CrossRef]
23. M. Moradi, M. Danaie, and A. Orouji, “Design of all-optical XOR and XNOR logic gates based on Fano resonance in plasmonic ring resonators,” Opt. Quantum Electron. 51, 154 (2019). [CrossRef]
24. T. Sadeghi, S. Golmohammadi, A. Farmani, and H. Baghban, “Improving the performance of nanostructure multifunctional graphene plasmonic logic gates utilizing coupled-mode theory,” Appl. Phys. 125, 189 (2019). [CrossRef]
