Open Access
Add to BibSonomy
Abstract
This work demonstrates the design of the digital half adder at the data rate of 1Mbit/s using micro-ring resonators (MRRs). In order to obtain the response of Sum and Carry ports, three micro-ring resonators are used, and a thermo-optic effect is achieved by placing micro heaters on top of each ring. All rings used in the design have identical parameters. Static and dynamic responses of the circuit are provided to show the ability of the device to work properly, and the obtained power level demonstrates that the circuit can transmit data at a specified speed without any additional active elements. The design achieved a compact size of about 658 × 486 µm2.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
High speed and compact size are factors that describe the future of technology. Digital integrated circuits in the processor play a crucial role in electronic device performance. One of the performance parameters to be considered in digital circuit design is the speed of the device. Photonic Integrated Circuit (PIC), which uses photons instead of electrons, is built on a thin substrate of semiconductor material. In PICs, the footprint area plays a vital role since a larger footprint increases the cost and the power consumption required for the PIC. So it requires circuit components to be as small as possible. This combination of light and the use of PIC technology provides a great solution to the constraints of the transmission data speed and compactness of the electronic counterparts [1]. In the case of digital circuits, it would be a considerable advantage to design PICs for digital photonic computing applications. Primarily, interferometers or resonators in the form of Mach-Zehnder interferometers (MZI) and micro-ring resonators (MRR) are used as basic units for designing digital circuits in PICs and implemented in silicon-on-insulator (SOI) substrate [2,3]. While both devices have the same benefits of low latency and low power consumption [4], micro-ring resonators (MRRs) have a higher sensitivity and compactness, which makes them more suitable for implementing optical logic gates and digital circuits [3].
Several investigations carried out for the demonstration of logic gates and digital circutis are mostly based on MRRs, MZI and multimode interference (MMI) coupler along with the ring resonators [5–8]. Authors in [8] provided detailed theoretical information of silicon MRR, while in [6] the researches actually fabricated the device that implements XOR and XNOR gates at 10 kbit/s and uses thermo-optic effect to tune the MRRs. The footprint of the device is 1000 × 500 $\mu {m^2}$. However, most of the devices which perform logic gates with the use of MRR represent active elements on their design which increases the working speed and also the price for fabrication [5,7].
In general, the resonance wavelength of the MRRs in logic gates and digital circuits can be tuned by adopting the method of electro-optic [9] and thermo-optic effects [10].
In [11], the authors employ two cascaded MRRs and an MMI coupler to design a half adder digital circuit. A thermo-optic effect is used in each ring resonator to compensate for fabrication errors and get the same resonance wavelength at the original state. The half adder achieves a speed of 100 Mbps. However, to simplify the circuit and reduce the insertion loss and crosstalk of the device, the authors eliminated the MMI coupler and added a third MRR in [12] and achieved a half-adder circuit that operates at the speed of 10 kbps.
The research works in [4,13] demonstrate logic units and digital circuits with the ring radius of r $= 10\mu $m. In [4], the researchers successfully demonstrated all basic logic gates at a high speed of 0.4 Mbps with each MRR having a ring radius of 10 $\mu $m using thermal tuning. Besides, in our previous work [14], a digital half adder was designed at the speeds of 100 to 1000 kbps, where the radius of each ring was also taken as 10 $\mu $m. However, da etailed performance analysis was not conducted. In this work, we demonstrate the design of a digital half adder with three MRRs where each has a smaller radius of 9 $\mu $m and the device works at a high speed of 1Mbit/s.
2. Micro-ring resonators
A micro-ring resonator is composed of a ring waveguide and one or two straight waveguides to allow coupling of light between them. In this work, an MRR with a ring and two waveguides is presented, and consequently, an add-drop ring resonator with four ports is utilized (Fig. 1). The field coupling coefficient, ${k_1}$, near the input of the ring shows the magnitude of the field from the waveguide that couples into the ring. When the light in the upper waveguide couples with the ring, it appears at the drop port as the fraction, ${k_2}$ (the field coupling coefficient between the ring and output), of the incoming field transferred to the ring and is linked to this port. For coupling to occur, the wavelength of the input light has to be an integer multiple of the round trip path. The mathematical expression of the resonance condition is shown below [15]:
where $\mathrm{\lambda }{{\; }_{res}}$ is the resonant wavelength, r is the ring radius, ${n_{eff}}$ is the effective refractive index of the waveguide, m is the mode number. Based on Eq. (1), when the wavelength of the input signal is different from the resonant wavelength, the signal goes to the through port of the device.As shown in Fig. 1, ${E_{in}}$ is taken as electric field at the input port and ${E_{drop}}$ as electric field at the drop port, whereas electric fields at the through and add ports are given as ${E_{through}}$ and ${E_{add}}$, respectively. Further, the fields at the points a,b,c,d are given as ${E_{ra}}$, $\; {E_{rb}}$, $\; {E_{rc}}$, $\; {E_{rd}}$, respectively, and their expressions are written as [16]:
So, if we take r as the radius, then the circumference of the ring is L=$2\pi r$. The intensity attenuation coefficient of the ring is $\alpha $, the intensity loss coefficient of the coupler is $\gamma $, the wave propagation constant is ${k_n}$, which is equal to ${k_n} = \left( {\frac{{2\pi }}{{\lambda \; }}} \right){n_{eff}}$.
The next equations represent electric fields at the through and drop ports:
Using the Eq. (2),(3),(4),(5) and replacing them in (6),(7), we can get the equations for electric fields at the through and drop ports:
Based on the works [17,18], the power transmission responses of the through and drop ports can be expressed as:
3. Device design and working principle
In this work, we propose the design of a digital half adder with three micro-ring repsonators. Figure 2 shows the circuit topology where each ring has a radius of 9 $\mu $m. It has been shown in practices, that the quality of the signal depends on the coupling gap and length [19]. In this work, the parameter of the gap distance between the rings and straight waveguides is set at 0.25 $\mu $m. In order to boost the coupling capability, the coupling length is set to 6.5 $\mu $m. The device structure includes bending waveguides with the radius of 9.25 $\mu $m. In comparison, in our previous works [4,14], the radius of the bent waveguide is set at 5 $\mu $m and the coupling length and gap are slightly less. In this work, the radius of the bent waveguide is increased in order to reduce the loss that occur due to the small bends in the previous works. After reducing the waveguide bend loss, the structure is further optimized for better performance by modifying the ring radius. We observed that when the ring radius is 9 $\mu $m which is 1 $\mu $m less than our previous works, the device provides the best output performance interms of the loss and the signal output. Hence, in this paper, the structure is made with the bent waveguide radius of 9.25 $\mu $m and ring radius of 9 $\mu $m for optimum performance at the output. In the proposed structure, the continuous wave (CW) light with the specific working wavelength ${\lambda _w}$ enters the first ring, MRR A, from the input port. Later it can be modulated through Electrical Pulse Sequence (EPS) applied to micro-heaters that are placed on top of each micro-ring resonators in order to make the rings on- and off-resonance. Then, depending on the resonance condition of the MRRs, light can travel through the circuit and exit it, resulting logical 0 or 1 at the output ports. The two rings which are labeled as MRR B in Fig. 2 perform the same operation and work together as B input of the half adder. They are modulated by the same EPS and work simultaneously.
As the working principle of the circuit is aimed to achieve the truth table of the half adder, as shown in Table 1, the workflow of the circuit is as follows:
Table 1. The truth table of a half adder
Case 1. If there is no voltage applied to the rings (EPS A = 0, EPS B= 0) then the incoming light is not coupled with MRR A and MRR B, as a result, logic 0 is observed at the outputs, Sum and Carry ports, S = 0, C = 0.
Case 2. When the voltage is applied only to MRR B and remaining MRR A at the low level (EPS A = 0, EPS B= 1) the CW light goes straight from the input port of MRR A and couples with MRR B, and exits through Sum port, as a result, S = 1 and C = 0.
Case 3. When the voltage is applied to MRR A and MRRs B are at low level (EPS A = 1, EPS B = 0), the entered light is downloaded with MRR A and then bypasses MRR B by going directly to the Sum port, which is meaning that S = 1, C = 0.
Case 4. Finally, when all rings are applied with voltage and they are at high level (EPS A = 1, EPS B = 1), the light couples with MRR A then with MRR B and exits through Carry port by giving logical 1 at that output, which means S = 0, C = 1.
The designed digital half adder using micro-ring resonators is expected to it’s the ability to perform addition of two bit binary numbers by achieving the output results shown in Table 1. Figure 3 shows an illustrative picture of the circuit with the micro-heaters on top of each ring resonator. There are two gold contacts on every heater which make the device two-terminal and they can be on and off depending on voltage variations. The device achieved a compact size of 658 × 486 $\mathrm{\mu }{\textrm{m}^2}$.
4. Results
4.1 Static response
The analysis of the circuit design shown in Fig. 2 for the half adder was carried out in Lumerical. In order to test the circuit performance with active elements, the optical network analyzer (ONA) is used. The ONA provides the light source and read the output data from the selected ports at the same time. As there is a necessity to have micro-heaters and supply MRRs with the voltage, DC sources are used to analyze the behavior of the device. Once the DC values are given, the circuit is able to evaluate the square differences of voltages as the tuning efficiency is specified with m/${V^2}$ in Lumerical Interconnect. So, EPS A is referred to as the DC sources that supply voltage to MRR A and EPS B is for MRR B.
The static response of Sum and Carry outputs are plotted in order to analyze their transmission. Their response spectrum is demonstrated in Fig. 4. It should be noted that the circuit is supplied with 2W power and the working wavelength is selected as 1557.55 nm.
Fig. 4. Static response spectra of the Sum output (a) and the Carry output (b) when MRR A and MRR B are {OFF:OFF (i), OFF:ON (ii), ON:OFF (iii), and ON:ON (iv)} conditions
The static response of the circuit when the CW light with the working wavelength is coupled into the input port, when there is no voltage applied to the heaters, is shown in Fig. 4(a)(i) and Fig. 4(b)(i).
Then, the voltage values of 1V are applied to MRRs B, keeping MRR A to resonate at its original point. From Fig. 4(a)(ii) and Fig. 4(b)(ii) it can be seen how the wavelength from the resonant point started moving closer to the working wavelength. Then the micro-heater supplies MRR A with voltage, while MRRs B are at off condition. This makes the CW light to be downloaded by MRR A and leaves straight through the upper waveguide of MRR B to the Sum port. The response spectrum is shown in Fig. 4(a)(iii), Fig. 4(b)(iii). It can be noticed from Fig. 4(b)(ii-iii) that the output results are a bit similar, since in both cases, the signal goes to the Sum port. The results from the last case when all MRRs are supplied with voltages are presented in Fig. 4(a)(iv) and Fig. 4(a)(iv). So the resonance wavelength of all micro-ring resonators is shifted to the working wavelength. The obtained results are Shown in Table 2.
Table 2. The obtained power level at the output of the half-adder
The response obtained from the Sum and Carry ports are given in Fig. 4. The static response given in Fig. 4(b)(ii) shows the output of the selected port when there is no voltage applied to the MRR A. This condition provides the smallest obtained power level (−3.8 dB). Meanwhile, when EPS A, B = 0 allows to obtain the greatest power level of −24.56 dB for this device with S = 1, C = 0 at the output. This can be seen in Fig. 4(a)(i). The device achieved an extinction ratio value of 8.46 dB at the Sum port and 9.25 dB at the Carry port.
4.2 Dynamic response
In the previous section, the behavior of each port under different states with respect to wavelength is analyzed. Since the working wavelength has been determined, this section examines the signal at the output ports with respect to the time response. In order to get the dynamic response, the CW laser with the wavelength of 1557.55 nm is connected to the input port. To conduct the dynamic response analysis, the pseudo-random bit sequence (PRBS) generator and a non-return-to-zero (NRZ) pulse generator are used to produce electrical signals, which are applied to the half adder. The signals applied to the device are 111000101 and 100100011. Their Sum and Carry outputs should be 011100110 and 100000001, respectively. Though the input signals are electrical, the output signals are displayed in optical domain using oscilloscopes. The results of the addition operation with the speed of 1Mbit/s are shown in Fig. 5.
Fig. 5. Output stream at (a) EPS A (b) EPS B (c) the Sum port (d) the Carry port with a bit rate of 1Mbit/s
The output of the Carry port in Fig. 5(d) shows that the power level of the output signal is twice less the optical power at the Sum port. When all rings are on resonance, light enters from MRR A and then couples with MRR B causing ‘1’ at the Carry port. But there are two rings which operate together as MRR B. So when both rings are at their resonant states, half of the light couples with the first MRR B and leaves through the Carry port while other half goes to the second MRR B. Another reason which can cause this different signal levels is that the design includes four bend waveguides which leads to losses such as mode mismatch and radiation [20].
Based on Eq. (10),(11),(12),(13), we plot the calculated transmission responses and compare them with the results from the simulation. The plots are shown in Fig. 6, where 6(a) is the Sum and 6(b) is the Carry. The calculation of the theoretical response of curves requires the use of coefficients of the optical powers $\; k_d^2\; \textrm{and}\; k_e^2$ which couple in and out from the waveguides. The width (FWHM) of the calculated curves (plots) for the drop and through ports, which are ∼1.4 nm and ∼1.1 nm, respectively, are in close agreement with the width of the simulated curves. Besides, the Sum port of the calculated response in Fig. 6(a) has some differences when compared with simulated output while the Carry port is fully matched with the theoretical response in Fig. 6(b). The reason for such discrepancies may be due to the losses experienced as light travels from one ring to another during simulation, which was not accounted for in the calculation part.
Fig. 6. The measured (orange dots) and simulation (blue line) responses of the Sum (a) and Carry ports (b)
The comparison is done by taking the data from the presented device that includes three ring-resonators. Nevertheless, the obtained performances of the micro-ring resonators satisfy the calculated results from the provided equations.
To further verify the performance of the design, the simulation of the time-dependent response of the device is done in order to obtain the rise and fall response of the system. Figure 7 is given to demonstrate the time which is needed to heat and cool the device. The shift in resonant wavelength is ∼1.5 nm and from Fig. 7 it can be seen that ∼1 $\mu $s is enough for the temperature to rise up to 335 K. And for cooling down the device and return to its initial condition (or to 300 K), ∼0.8 $\mu $s is needed.
Figure 8 illustrates how applied voltage heats the device by causing a change in the refractive index and leads to a phase shift in the micro-ring resonators.
Besides, the dynamic response of the device is also examined by applying 1Mbit/s square-wave electrical signals on the heaters (presented in Fig. 9 as orange lines). Then the waveform of the output light is measured by using an oscilloscope (presented in Fig. 9 as blue lines). Here the results also show that the heating time and cooling time for the presented device is 1 $\mu $s and 0.8 $\mu $s, respectively. For such measurements, it should be noted that the response time for thermal insulation devices are longer than for the thermal insulation free devices [21].
Fig. 9. Dynamic response of the device at 1Mbit/s, where orange lines correspond to the electrical input signal and the blue lines are optical output of the drop port
5. Conclusion
In summary, micro-ring resonators based digital half adder performance at a speed of 1Mbit/s is demonstrated in this paper. The design of the circuit employs thermo-optic effect to tune the MRRs by supplying voltage to each ring resonator. Comparing to our previous work, the obtained results show that the circuit can work with reduced radius at a higher speed. The static and dynamic responses are plotted and they show that the device can achieve good results without major losses. Additional simulations have been carried out to further analyze the performance of our device, where the rise and fall time of 1 $\mu $s and 0.8 $\mu $s, respectively, is achieved. For future work, the design of the circuit can be modified to improve the output power at the Sum and Carry gates. In that case, it would be desirable to optimize the device ring radius.
Funding
Nazarbayev University (NU) Faculty Development Competitive Research Grant (021220FD0451).
Disclosures
The authors declare no conflicts of interest.
Data Availability
No data were generated or analyzed in the presented research.
References
1. R. J. P. Menéndez, “Fiber-Optic Ring Resonator Interferometer,” Interferometry - Recent Developments and Contemporary Applications (2018), https://www.intechopen.com/chapters/64195.
2. W. Bogaerts and S. K. Selvaraja, “Silicon-on-insulator (SOI) technology for photonic integrated circuits (PICs),” in Silicon-On-Insulator (SOI) TechnologyWoodhead Publishing (2014), pp. 395–434.
3. A. Henriksson, L. Kasper, M. Jäger, P. Neubauer, and M. Birkholz, “An Approach to Ring Resonator Biosensing Assisted by Dielectrophoresis: Design, Simulation and Fabrication,” Micromachines 11(11), 954 (2020). [CrossRef]
4. D. Azhigulov, B. Nakarmi, and I. A. Ukaegbu, “High-speed thermally tuned electro-optical logic gates based on micro-ring resonators,” Opt. Quantum Electron. 52(9), 412 (2020). [CrossRef]
5. J. K. Rakshit, J. N. Roy, and T. Chattopadhyay, “All-optical XOR/XNOR logic gate using micro-ring resonators,” in 5th International Conference on Computers and Devices for Communication (IEEE, 2012), pp. 1–4.
6. M. Geng, L. Jia, L. Zhang, L. Yang, P. Chen, T. Wang, and Y. Liu, “Four-channel reconfigurable optical add-drop multiplexer based on photonic wire waveguide,” Opt. Express 17(7), 5502–5516 (2009). [CrossRef]
7. G. K. Bharti and J. K. Rakshit, “All-optical logic AND/NAND gates using two symmetric micro ring resonators,” Proc. SPIE 11205, 2 (2019). [CrossRef]
8. W. Bogaerts, P. DeHeyn, T. VanVaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. VanThourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012). [CrossRef]
9. P. Bhardwaj, R. Ghosh, A. Das, and A. Dhawan, “Integrated electro-optic tunable power splitter based on microring resonators having interleaved PN junctions,” Proc. SPIE 113641, 56 (2020). [CrossRef]
10. S. De, R. Das, R. K. Varshney, and T. Schneider, “Design and Simulation of Thermo-Optic Phase Shifters With Low Thermal Crosstalk for Dense Photonic Integration,” IEEE Access 8, 141632–141640 (2020). [CrossRef]
11. Y. Tian, L. Zhang, J. Ding, and L. Yang, “Demonstration of electro-optic half-adder using silicon photonic integrated circuits,” Opt. Express 22(6), 6958–6965 (2014). [CrossRef]
12. X. Wu, L. Deng, Y. Meng, J. Yang, and Y. Tian, “Demonstration of a Silicon Photonic Circuit for Half-Add Operations Using Cascaded Microring Resonators,” IEEE Photonics J. 9, 1–9 (2017). [CrossRef]
13. Z. Yang, Y. Wang, C. Su, L. Shao, J.-J. He, and M. Li, “Thermo-Optical Tuning Cascaded Double Ring Sensor with Large Measurement Range,” Sensors 20(18), 5149 (2020). [CrossRef]
14. D. Beisenkhanov and I. Ukaegbu, “Silicon photonics based digital half-adder using micro-ring resonator structures,” Proc. SPIE 116910, 28 (2021). [CrossRef]
15. M. Margarat, B. Caroline, V. Nivedha, S. Sowmiya, and D. Purushothaman, “All Optical 3-Bit Octal to Binary Code Converter using Micro-Ring,” J. Phys.: Conf. Ser. 1717(1), 012059 (2021). [CrossRef]
16. J. Rakshit, T. Chattopadhyay, and J. Roy, “Design of ring resonator based all optical switch for logic and arithmetic operations – A theoretical study,” Optik 124(23), 6048–6057 (2013). [CrossRef]
17. S. Xiao, M. H. Khan, H. Shen, and M. Qi, “Modeling and measurement of losses in silicon-on-insulator resonators and bends,” Opt. Express 15(17), 10553–10561 (2007). [CrossRef]
18. P.-H. Wang, Y. Xuan, L. Fan, L. T. Varghese, J. Wang, Y. Liu, X. Xue, D. E. Leaird, M. Qi, and A. M. Weiner, “Drop-port study of microresonator frequency combs: power transfer, spectra and time-domain characterization,” Opt. Express 21(19), 22441–22452 (2013). [CrossRef]
19. M. Bahadoran, P. Yupapin, and I. S. Amiri, “Optimum light transmission via microring resonator under a lossy-coupler critical coupling condition,” Microw Opt Technol Lett 63(2), 653–661 (2021). [CrossRef]
20. L. Zhang, R. Ji, Y. Tian, L. Yang, P. Zhou, Y. Lu, W. Zhu, Y. Liu, L. Jia, Q. Fang, and M. Yu, “Simultaneous implementation of XOR and XNOR operations using a directed logic circuit based on two microring resonators,” Opt. Express 19(7), 6524–6540 (2011). [CrossRef]
21. D. Geuzebroek, E. Klein, H. Kelderman, and A. Driessen, “Wavelength tuning and switching of a thermo-optic micro ring resonator,” Proceedings of the 11th European Conference on Integrated Optics, 395–398 (2003).
