Microring assisted Mach–Zehnder interferometric structure based electro-optic adder for photonic integrated circuits

In this paper, a novel microring resonator (MRR)-assisted Mach-Zehnder interferometric (MZI) structure to operate as an electro-optic half adder utilizing the optical switching phenomenon of Si-MRR is proposed. The proposed device has two Si-MRRs with dual inputs, used in the tandem configuration in the lower and upper arms of an MZI structure. An externally controllable optical ‘π’ phase shifter is also incorporated in one of the arms of the MZI. The carrier-injected forward-biased PIN waveguide structure is incorporated into the ring resonator architecture to achieve the extinction ratio (ER) tunability. For the proposed electro-optic adder, −1.85 V and +2 V are considered as logic 0 and 1, respectively. One of the output terminals will emulate an optical AND gate providing the carry bit (CB), while the other output terminal will emulate an optical EX-OR gate offering the sum bit (SB). The proposed device was modeled and simulated using MATLAB. The simulation results estimate the simulated static ER of the SB and CB is 27.44 dB and 18.08 dB, respectively. To demonstrate the proposed device’s efficacy, two 10 Gb/s PRBS input streams at 1550 nm were used, and the time domain simulation results indicate a successful electro-optic half adder suitable for photonic integrated circuits (PICs).


Introduction
Optical communication has emerged as the backbone of ultra-high-speed communication and futuristic energy-efficient computing (Caulfield and Dolev 2010;Miller 2010).In the present scenario, high-speed computing requires multi-core CPUs to avoid the bandwidth constraint (Heirman et al. 2008;Lee et al. 2010).In contrast, all-optical signal processing can alleviate the bandwidth bottleneck by leveraging the inherent ultrahigh bandwidth of optical communications.Furthermore, it also eradicates the critical requirement of optical-to-electrical conversion (Thompson and Parthasarathy 2006).Thus all-optical signal processing offers energy-efficient high-speed computing (Li et al. 2017;Watanabe et al. 2008;Willner et al. 2008).Also, in recent times photonic interconnects has been replacing their electrical counterpart for both long and short-haul communications.Owing to its easy compatibility with mature CMOS technology, photonic integrated circuits (PICs) can potentially become the next-generation integrated circuits for exascale computing (Bogaerts et al. 2005).In this context, it is important to note that most of the fundamental blocks like phase-shifter, splitter/combiner, coupler, modulator, laser, photodetector, filter, etc. are already available in the standard SOI platforms (Baehr-Jones et al. 2005;Martínez et al. 2010).One can utilize these fundamental blocks to achieve complex optical signal processing in PICs.Among the various blocks, MRR and MZI (due to their various applications) are currently the subjects of intensive research.Similarly, various optical logic gates will also be required to achieve energy-efficient optical computing.Optical arithmetic and logical unit supporting instant optical arithmetic and logic functions can also be realized in the PICs.Additional operations like data transmission or code converters can also be easily incorporated into the same block (Saharia et al. 2021;Kumar et al. 2017;Stanley et al. 2016).
In PICs, all-optical logic operations had previously been reported by employing MZI, Distributed-Bragg gratings (Singh et al. 2014).Similarly, MRRs have also been utilized to form basic optical logic gates.Typically MRR based logic gates are more attractive as they support compact design and low power consumption (Biswas et al. 2021;Bogaerts et al. 2012;Law and Uddin 2020).Both device dimensions or switching threshold reductions had been achieved in such devices.The MRR can be classified into passive or active based on its underlying operating principles.Generally, passive and active MRRs are utilized in all-optical logic circuits (Hossain et al. 2022;Katti and Prince 2018) and electro-optic (E/O) logic circuits (Law et al. 2017;Qiu et al. 2014), respectively.The phase-shift keying (PSK) approach is generally utilized to achieve the E/O effect in MRRs (Padmaraju et al. 2011(Padmaraju et al. , 2012;;Dong et al. 2012).In such designs, higher switching contrast can be easily supported by altering the damping ratio of the MRR from underdamped to critically damped (Ibrahim et al. 2003).Si-MRR-based all-optical logic gates have been well discussed in Qiu et al. (2014), Dai et al. (2012), Rezaei and Zarifkar (2021), Pei-Li et al. (2006).
Generally, the half-adders (HAs) find wide applications in a processor's arithmetic and logical unit (ALU), calculations of checksums, generation of encrypted keys in secured networks, etc.Typically, an electronic HA contains AND and EX-OR logic gates, while its optical counterpart comprises of semiconductor optical amplifier (SOA) Dai et al. (2012).In such a design, two SOAs were employed to achieve an ER of 14 dB at 10 Gb/s.Such devices offer only a limited speed and ER due to the long response times and undesired spontaneous emission noises.Furthermore, such devices are also susceptible to the gain saturation effect of SOA (Rezaei and Zarifkar 2021).Another strategy makes use of an SOA-based four-wave mixing (FWM).The absence of patterning effect and usage of polarization-shift-keying (Pol-SK) offers ultrahigh-speed of operations (Pei- Li et al. 2006).Highly non-linear fiber (HNLF) is also used in some designs of optical HA.A versatile combinational logic module supporting simultaneous 1-bit comparison, 2-to-4 line decoding, and half-addition/subtraction operations was proposed in Kaur et al. (2022), Zahir et al. (2017), Singh et al. (2016).All of the aforementioned techniques differ from one another, considering several important device metrics like power consumption, optical integration, reliability, transient performances, and ease of fabrication (Wang et al. 2022).Recent efforts also explored the feasibility of graphene-based plasmonic waveguides and photonic crystals (PhCs) to alleviate the limits of different designs and perform all-optical signal processing at terabytes per second (Xu et al. 2021).Both plasmonic waveguide and PhC-based designs have their own merits (Rezaei and Zarifkar 2021) however, their limitations will support only limited functionalities in the designed optical logic devices.For example, once the PhC-based optical logic gates are designed and fabricated, they will manipulate only a narrowband of input optical signals.Complex doping techniques can be employed in the PhCs to overcome this issue, which will further degrade their performance metrics.Alternatively, 3D designs of such PhCs are extremely challenging.The E/O effect is a much more feasible solution to achieve highly energy-efficient, fast optical logic gates supporting extreme reliability and scalability (Ying et al. 2019).In this regard, MZIbased structures offer immense advantages to any PIC designer.Recently E/O HAs had been demonstrated in Kumar et al. (2014), Tian et al. (2014), Kumar (2016), Prajapat et al. (2020) while multiple MRR-based HAs were presented in Wu et al. (2016), Mohammadi et al. (2021), Alipbayeva et al. (2022).
This paper proposes an E/O HA utilizing two multiple-input active MRRs operating in carrier injection mode.Owing to the primary requirement of the over-coupling condition in the MRRs, a versatile design can be easily proposed based on the ring-assisted Mach-Zehnder interferometer or RAMZI.This leads the proposed design to support higher data rates with improved resilience.Furthermore, the nonlinear response originating from the free carrier plasma dispersion (FCD) effect in silicon can be easily tackled as the proposed structure is basically a RAMZI.However, cavity dynamics (including cavity photon lifetime) should be considered for efficient device design (Gutierrez et al. 2012;Pal andGupta 2020, 2019).We have proposed a new design and simulated the same to exhibit a first-ofits-kind E/O HA employing RAMZI structure.The performance of such a device is also supported by the simulation results, which include different input parameters of physical rationale.The proposed HA design has been subjected to an analysis strictly from a theoretical perspective.
The rest of the article is organized as follows: Sect. 2 begins with a brief description of the operation of an optical MRR.The configuration and use of the proposed design are demonstrated in Sect.3. Section 4 comprises the simulation results, including the estimation of different performance metrics indicating the correctness of the targeted logic gate operations.In Sect.5, a conclusion is made.

MRR and its operation as switch
As depicted in Fig. 1, the optical MRR consists of a ring and one or multiple bus waveguide(s), which are termed as all-pass or add-drop MRR, respectively (Hossain et al. 2022;Debbarma et al. 2021).The ring and bus waveguides are evanescently coupled, thereby allowing a small portion of the inward optical signal to be coupled inside the ring.The coupling coefficient ( ) of the MRR can be determined by the spacing (d) between the ring and bus waveguide (Bahadori et al. 2018) where is the operating wavelength and ' a E ',' E ','a o ', and ' o ' are the wavelength-depend- ant fitting parameters for even and odd modes, correspondingly.Owing to its selective resonance, typical applications of MRR include filtering, sensing, etc. Bogaerts et al. (2012).
Constructive interference occurs inside the MRR when the round-trip optical path length is equal or an integer multiple of the wavelength of the input optical signal (Bogaerts et al. 2012).Thus the transmission spectra at the through port will exhibit single or multiple troughs based on the operating wavelength.For a broadband input, MRR based on its radius and effective r.i.can selectively drop a narrow-band signal.Thus optical switching effect can be emulated using an add-drop MRR (Hossain et al. 2021).A small perturbation in r.i. of the MRR will detune the MRR, resulting in enhanced transmission at the through port.Removing the perturbation will force the MRR to tune back and thus reduce the transmission at the through port (Hossain et al. 2022).This gradual perturbation in the resonant wavelength can be employed to switch a specific wavelength optical signal.Assuming'E i1 ' and ' E i2 ' as the input and drop fields of the MRR, the output electric field at through and drop port are given by Hossain et al. (2021), Rakshit et al. (2012), ) , and ' k n ' is the propagation constant.Note that ' 1 ' and ' 2 are the field coupling coefficients between the input waveguides and the ring.The Eqs. ( 2) and (3) can be used to explain the switching mechanism of the (2) (3) 3 Proposed optical half adder

Device configurations
Refer to Fig. 3.The proposed design consists of an MZI structure.A couple of MRRs are placed parallel, while an optical phase shifter (PS) with 'π' phase shift is incorporated in the lower arm after MRR 2. Electrical input bits (input A and B) are provided into the proposed HA via MRR 1 and MRR 2, respectively.The radius (R) of both MRR 1 and MRR 2 was considered to be 7 µm.κ, group refractive index ( n g ), and carrier recombi- nation lifetime ( c ) of both MRR 1 and MRR 2 were assumed to be 0.05, 4.3 and 100 ps, respectively.The typical data rate for inputs A and B is 10 Gb/s.A continuous wave (CW) laser is provided at the input of the MZI structure.In the resonant or tuned condition, both MRRs will provide no output resulting in logic 0. Similarly, the out-of-resonant or detuned condition will provide strong output resulting in logic 1.To achieve the tuned and detuned condition in the proposed MRR at 1550 nm, bias voltages of −1.85 V, and +2 V were applied, respectively.We aim to design the crossing angle between two waveguides to closely approach 90 degrees (perpendicular).We have categorically chosen the different dimensions suitable for fabrication in the SOI platform (Bhowmik and Gupta 2016;Das et al. 2022).
Proper optimization of device dimensions and operating voltage significantly minimizes losses.Accurate biasing of the microring reduces losses arising from intraband absorption due to free carrier concentrations.Other losses encompass material, scattering, substrate coupling, and bus-to-ring coupling losses.To mitigate these, minimizing sidewall roughness through fabrication optimization and enhanced photoresist selection is suggested.Further loss reduction involves using Er: Al 2 O 3 as the upper cladding layer on standard Si/ SiO 2 rings, as detailed in Jarschel et al. (2018), requiring just one post-processing step.The final fabrication step typically involves creating the contact.Precise optimizations are necessary to prevent the RC cut-off frequency from the junction and parasitic capacitive effects.Contacts are often situated slightly away from the p-n junction (clearance region) to mitigate metal-induced losses in guided optical mode.Additionally, heavy doping is introduced through ion implantation in the slab waveguide to counter parasitic effects.Fabrication-wise, a thick SiO 2 layer (> 1 µm) is PECVD-deposited on the microring modulator.Contact windows are opened above P+ and N+ regions via etching.Electrodes are subsequently formed through a lift-off process.Further electrode fabrication details are comprehensively discussed in Dong et al. (2010).The Sum bit and Carry bit outputs of the device are referred as SB and CB, respectively.

Principle of operations
The operation of the proposed device will now be explained, considering the different resonance conditions of the MRRs.We assumed the input to MRR 1 and MRR 2 are considered to be input A and B, respectively.At first, assume both MRR 1 and MRR 2 are tuned (i.e.A = 0 , and B = 0 ).After equal splitting in both arms of the MZI, the input light passes through the waveguide and reaches MRRs.As both MRRs are tuned, no light reaches the MZI structure's end, resulting in zero SB.Next, consider MRR 1 and MRR 2 are tuned and detuned, respectively (i.e., A = 0 , and B = 1 ).In this case, some light will propagate through the lower arm of the MZI, and thereby SB becomes 1.In both cases, no light passes through the upper arm of the MZI.Thus, there is no possibility of achieving destructive interference at the output combiner of the MZI, and hence the CB will remain at 0. In the third case, assume MRR 1 and MRR 2 are detuned and tuned, respectively (i.e., A = 1 , and B = 0 ).The light will pass through the upper arm of the MZI, while light will not pass through the lower arm of the MZI.Thus the SB and CB output will become 1 and 0, respectively, in this case.Finally, consider the fourth case, where both MRR 1 and MRR 2 are detuned.In this condition, the light will pass on both the upper and lower arms of the MZI.However, due to the additional PS of π in the lower arm, there will be destructive interference at the end of the MZI, resulting in SB being 0 (Fu et al. 2013;Fujita et al. 2000).However, the CB will be 1 since both MRR 1 and MRR 2 are detuned.The proposed Half Adder based on the MRR shows that the carry output is independent of constructive and destructive interferences.Different tuning configurations of MRRs result in specific carry bit outputs, with detuned MRR 2 and MRR 1 leading to a carry bit of 1. Figure 4 illustrates the different operating scenarios of the proposed device schematically.In a bi-directional micro-ring resonator (MRR), simultaneous entry of optical signals from clockwise (CW) and anti-clockwise (CCW) directions leads to interference effects within the circular MRR section.The circulating CW and CCW waves interact constructively or destructively, depending on their phase alignment.Identical optical path lengths and in-phase waves result in significant constructive interference at resonant wavelengths, enhancing the optical signal within the MRR.However, due to the absence of a drop port in the proposed model, the intensified optical signal is absorbed by the ring itself during resonance.From the above discussion, it is clear that the proposed device structure supports the optical half-adder operation.Table 1 summarizes the different bias conditions required by the proposed structure to operate as an electro-optic half-adder suitable for PICs.

Simulation methodology and results
In this section, we discuss the simulation methodology utilized to achieve the time-domain results of the proposed structure.We assume that the MRRs and MZI are precisely fabricated using the standard CMOS fabrication techniques and are error-free.It is important to note that we have not categorically chosen any fabrication tolerances initially; however, the performance of the proposed structure is expected to achieve similar performance metrics even in the presence of fabrication tolerances.

Methodology
Considering the silicon MRRs are fabricated, we have modeled their resonance spectrum using an in-house code written in the MATLAB platform.The first step in simulating the MRR was to observe how the effective refractive index ( n eff ) varies with respect to an input electrical bit pattern.The carrier concentration in the active MRR significantly perturbs the n eff and loss coefficients ( eff ) of the MRR, and hence the optical length L opt = 2 n eff R of the MRR gets substantially influenced.Similarly, applying bias voltage ( V b ) across the MRR will alter the carrier concentration via the FCD effect.This change was considered in our simulation, and this change in the refractive index ( Δn ) at 1.55 μm was estimated using the relation mentioned in Brimont et al. (2008), where Δn e and Δn h represent the net change in electron and hole concentrations per cc.
Determining the proper range of V b for linear perturbation in Δn is essential for the lin- earized operation.Once the proper range of V b was determined, the proposed device was simulated utilizing an in-house code written in MATLAB platform obtained from the analytical formulation discussed in Sect. 2. For simulation, 1550 nm was assumed as the operating wavelength ensuring the entire C-band operation.refractive index due to weak charge carrier influence.Beyond 0.8 volts, precise tuning of the refractive index enables dynamic signal modulation in MRR, finding applications in optical switches and modulators.Figure 6a illustrates the relationship between the effective refractive index and the applied bias voltage.Thus, the two operating bias voltages are considered to be − 1.85 V and 2 V. Next, at these two voltages, the transmission spectrum of the MRRs was simulated to estimate the change in output optical power (see Fig. 6b).The power difference observed in the two output logic states, as shown in Fig 6b, is essential for distinguishing between the logical states of '1' and '0' at the outputs.The measured ER was 18 dB which is sufficient to consider the MRRs to be either in logic 0 or in logic 1 level based on the input V b .Also, the estimated 10-90% rise time ( t r ) and 90-10% fall time ( t f ) are 13.45 ps and 5.40 ps, respectively.Thus, the maximum data rate ( f max ) that the MRR can support is approximately 53 Gb/s.Next, the simulation of the proposed structure in the time domain was performed using the different input parameters obtained from the previous simulation results.We considered two uncorrelated 10 Gb/s PRBS patterns (bit 0 and bit 1 voltage levels are −1.85V and + 2 V, respectively) were provided to MRR 1 and MRR 2 through appropriate drive circuitry..While recognizing the potential exploration of different data rates in future studies, we are confident that the chosen rate of 10 Gb/s serves as a valuable starting point to effectively demonstrate the capabilities of our MRR-based E/O HA and their relevance in current communication scenarios.As per the simulation results incorporated in Fig. 7, the proposed structure clearly performs the error-free optical half-adder operation at 1550 nm.The Sum output produces optical low output when A = B = 0 or 1.Otherwise, it produces consistently high optical output.Similarly, the Carry bit produces high optical output only if A = B = 1 .The simulation also depicts a rational optical power difference between the optical logic 0 and 1 states, making it suitable for PICs.We have also estimated the other performance metrics like ER, contrast ratio (CR), amplitude modulation (AM), and relative eye-opening (REO) of the proposed HA from the simulation results and presented in Table 2.The simulation results estimate that ER of the Sum and Carry output is approximately 27.44 dB and 18.08 dB, respectively.The CR of both Sum and Carry output is > 25 dB while no AM was found in both outputs.

Refer to
The performance of the proposed HA was compared with some recently reported MRRbased optical HA in terms of the number of MRRs, radius of MRRs (R), ER, maximum  data-rate, and device structure and presented in Table 3.The comparison clearly indicates that the proposed structure offers both the highest ER and supports the maximum data rate which requires only two MRRs.However, in terms of device footprint, the proposed structure is slightly higher as it contains an MZI structure.

Conclusion
In this paper, we have proposed a novel electro-optic half-adder device.The proposed structure contains two Si-based MRRs loaded in an MZI and capable of operating in the C-band (1550 nm).Suitable device operation including the basics of the MRRs was explained.An in-house MATLAB code supporting the time-domain simulation was prepared in support of the theoretical analysis.Simulation results indicated that the utilized MRRs can be set in or taken out of the resonance by providing a bias voltage of +2 V and −1.85 V, respectively.Results indicate that two uncorrelated 10 Gb/s bit streams can be provided into two MRRs to achieve electro-optic HA operation.The estimated ER for Sum and Carry bit is approximately 27.44 dB, and 18.08 dB, respectively.However, the high thermal sensitivity of the MRR connected to the MZI structure poses a significant problem, and a thermal design should be considered during actual device fabrication.

Fig. 1
Fig. 1 Schematic of an optical MRR: (a) Ring structure with a single waveguide (all-pass configuration).(b) Ring structure with dual bus waveguides.(add-drop configuration)

Fig. 2
Fig. 2 Schematic representation of the MRR: (a) in resonant condition, (b) in out-of-resonant condition.Normalized transfer function versus operating wavelength (c) in resonant condition, and (d) out-of-resonant condition

Fig. 3
Fig. 3 Schematic diagram of the suggested E/O HA circuit based on mirroring resonator loaded on a MZI structure

Fig. 4
Fig. 4 Schematic presenting the different operating conditions of the proposed structure Fig. 5, which indicates the variation in total charge and Δn w.r.t V b ranging between −1.85 V to +2 V. Simulation results indicate a peak variation of − 0.06 in Δn can be achieved by altering the V b from +2 V to − 1.85.The silicon-based MRR experiences a change in the effective refractive index (RI) after reaching a voltage of 0.8 volts due to the electro-optic effect of silicon.Below 0.8 volts, the electric field has little impact on the (4) Δn = −8.8× 10 −22 Δn e − 8.5 × 10 −18 Δn 0.8 h

Fig. 5
Fig. 5 Time domain simulation of the MRR in the RAMZI: (a) pattern of V b versus time; (b) total charge versus time; (c) estimated Δn versus time

Fig. 7
Fig. 7 Time domain simulation results of the proposed structure offering HA operations: (a) Input A, (b) Input B, corresponding outputs of the structure: (c) SB, and (d) CB

Table 2
Different performance metrics of proposed E/O halfadder