Demonstration of a Silicon Photonic Circuit for Half-Add Operations Using Cascaded Microring Resonators

We report a silicon photonic circuit that can perform half-add operations using cascaded microring resonators (MRRs). Electrical pulse sequences regarded as the operands are applied to the corresponding MRRs to achieve their dynamic modulations. The final operation results are directed to the corresponding outputs in the form of light. For proof of principle, the thermo-optic modulation scheme that needs simpler fabrication processes is employed to modulate MRRs. Finally, the circuit is fabricated on an 8-in silicon-on-insulator (SOI) substrate using complementary metal-oxide-semiconductor (CMOS) technology, and the half-add operations with the speed of 10 Kb/s are demonstrated successfully.

SECTION 1. Introduction

Silicon photonics is a popular research topic in the field of integrated optics whose purpose is to integrate various photonic devices on a tiny silicon wafer to achieve complex optical information processing using standard complementary-metal-oxide-semiconductor (CMOS) fabrication processing [1]–​[3]. Currently, silicon photonics has been greatly developed, and diversified photonic devices have been proposed and demonstrated such as routers [4] , lasers [5], modulators [6]–​[8], logic devices [9]–​[11], sensors [12], [13], multiplexers [14], microprocessors [15], etc, and silicon photonic devices are also very suitable for information processing due to its nature advantages such as high speed [16], [17], large capacity [18] , [19], low power [20], [21], etc. Therefore, silicon photonics is a promising solution to the problems of limited bandwidth [22], [23] , physical limited effect (quantum tunneling) and metal interconnect issue faced by silicon electronics [24], [25]. The microring resonator (MRR) is a fundamental building block for photonic devices [26], and it can be used to structure various photonic devices to achieve different optical information processing functions such as optical filtering [27], modulation [28] , [29], switching [30], [31], etc. One of the most important applications of MRR is that it can be designed to high compactness [32], low power [33], and high speed optical switch [34] , and the optical switch based on MRR is easily to realize on-chip large-scale integration and low fabrication cost [26], [35].

Directed logic proposed by Shamir and Hardy in 2007 is a novel logic scheme which employs optical switch network to perform Boolean logic operations [36], [37] . A continues monochromatic optical wave is coupled into the optical switch network, the operands are applied to the optical switch to control their working status [38], [39]. Therefore, the operand applied to the optical switches in the network can control the propagation direction of the light. In other word, the light signal directed to the output port of the network carries the information of the operand applied to the optical switch. Therefore, we can reasonably design the optical switch network to perform specific logic operation according to our specific requirements [40], and the final operation results are directed to the output port of the network in the form of light [41]. The optical half-adder plays a key role in the optical information processing and optical computing since the half-adder can be employed to structure full-adder through cascading some half-adders [42], [43]. As we know, all logic operations can be attributed to addition and multiplication operations. In other words, if we can achieve addition and multiplication operations, all other complex logic operations can be achieved. Therefore, the optical adder is an important building block for optical information system.

In this paper, we report a novel silicon photonic circuit which can performs half-addition using three cascaded MRRs. The Sum and Carry operation results of the addition could be obtained at its two output ports simultaneously. Compared with our previous works [44], the photonic circuit is simpler, and the multimode interference coupler (MMI) is eliminated in the circuit, which is very significant to improve the signal quality and reduce the insertion loss of the device. As a proof of principle, the thermo-optic modulation scheme is employed to achieve MRR's dynamic modulation, and the circuit is finally fabricated on silicon-on-Insulator (SOI) substrate using the CMOS technology. Finally, the half-add operation is demonstrated with the operation speed of 10 Kbps successfully.

SECTION 2. Architecture and Working Principle

The schematic of the half-add circuit is shown in Fig. 1. The proposed circuit consisting of only three cascaded MRRs connected by waveguides. Three ports of the circuit are defined as CW, S, and C on the basis of their functions. The port CW behaves as the input port of the half-adder. The ports S and C serve as the output of the sum bit and the carry bit of the circuit respectively. In the proposed circuit, MRR behaves as the 1 × 2 optical switch: When a high-level voltage is applied to MRR, it is on-resonance at the working wavelength of λw and the optical signal coupled into its input port is downloaded by the MRR subsequently directs to its drop port. When a low-level voltage is applied to MRR, it is off-resonance at the working wavelength of λw, and the optical signal coupled into its input port bypasses the MRR, thereafter directing to its through port. MRR₁'s working state is controlled by the working states of electrical pulse sequence (EPS) X, while MRR ₂ and MRR_2’ are working as a synchronous part since they are modulated by the working states of EPS Y.

Fig. 1.

Architecture of the proposed circuit. (CW: continuous-wave light. EPS: electrical pulse sequence. MRR: micro-ring resonator.)

In the circuit, the high-level and low-level of the EPS applied to MRR represent logic 1 and 0 in electrical domain, and the high-level and low-level of the optical power at the output port are defined as logic 1 and 0 in optical domain. Monochromatic continuous-wave light with the working wavelength $\lambda _{{\rm{w}}}$ is coupled into the circuit through the CW port and then modulated by EPSs applied to MRRs. Finally, the operation results appear at the output ports of the circuit in the form of optical pulse. In order to clarify the principle of the circuit, the four working statuses are discussed in more detail as follows.

1. When X = Y = 0 (the voltage X applied to MRR₁ and the voltage Y applied to MRR₂ and MRR_2’ are both at low-level), all of the MRRs are at off-resonance at the working wavelength of $\lambda _{{\rm{w}}}$. The light signal coupled into the CW port of the circuit first bypasses MRR₁. Then, the optical signal bypasses MRR₂ and is finally directed to the terminal A. As a result, logical 0 is achieved at the output ports S and C with the working wavelength of $\lambda _{{\rm{w}}}\,(S\,= \,0,\,C\,= \,0)$.

2. When X = 0 and Y = 1 (the voltage X applied to MRR₁ is at the low-level and the voltage Y applied to MRR ₂ and MRR_2’ is at high level, respectively), the MRR₁ is at off-resonance. MRR₂ and MRR_2’ are both at on-resonance, since MRR₂ and MRR_2’ are working as a synchronous part. The light signal coupled into the CW port of the circuit firstly bypasses MRR₁ and is then downloaded by MRR₂, eventually directing to the S port, which means that logical 1 is achieved at the output port S, and logical 0 is achieved at the output port C with the working wavelength of $\lambda _{{\rm{w}}}\,(S\,= \,1,\,C\,= \,0)$.

3. When X = 1 and Y = 0 (the voltage X applied to MRR₁ is at high-level while the voltage Y applied to MRR ₂ and MRR_2’ is at low level, respectively), MRR₁ is at on-resonance, while MRR₂ and MRR_2’ are both at off-resonance. The light signal coupled into the CW port of the circuit firstly downloaded by MRR₁ and then bypasses MRR₂ and MRR_2’ successively and ultimately directed to the S port. Consequently, logical 1 is achieved at the output port S and logical 0 is achieved at the output port C with the working wavelength of $\lambda _{{\rm{w}}}\,(S\,= \,1,\,C\,= \,0)$.

4. When X = 1 and Y = 1(the voltages applied to MRR₁, MRR₂ and MRR_2’ are at high level), all the MRRs are at on-resonance with the working wavelength of $\lambda _{{\rm{w}}}$, the light signal coupled into the CW port of the circuit downloaded by MRR₁ and MRR _2’ successively, then directed to the port C. Therefore, logical 1 is achieved at the output port C, and logical 0 is achieved at the output port S with the working wavelength of $\lambda _{{\rm{w}}}\,(S\,= \,0,\,C\,= \,1)$.

In order to illuminate the principle of the proposed circuit clearly, the theoretical optical power levels at the output ports of the circuit with four working statuses are shown in the Table I, and from which we can see clearly that the circuit can perform the adding function of two binary numbers [45].

TABLE 1 Truth Table Achieved by the Proposed Circuit

SECTION 3. Design and Fabrication

The half-adder circuit is fabricated on an 8-inch SOI wafer with 220 nm top silicon layer and 2 μm buried SiO ₂ layer using the CMOS technology. The micrograph of the circuit is shown in Fig. 2(a). In order to reduce the scattering loss induced by the sidewalls of the waveguides and maintain single mode propagation, the rib waveguide with a slab thickness of 90 nm, width of 400 nm and height of 220 nm is employed to form the circuit. The radius of the MRRs are 10 μm, and the gap between the ring waveguide and straight is 350 nm. The titanium nitride (TiN) micro-heaters are fabricated on top of the MRRs. Aluminum wires are formed to connect the pads and the micro-heaters. Furthermore, with a view to enhance the coupling efficiency, spot size converters (see Fig. 2(b)) are designed on the terminals of the circuit [46].

Fig. 2.

(a) Micrograph of the circuit. (CW: continuous wave. EPS: electrical pulse sequence. MRR: micro-ring resonator.) (b) Spot size converters.

SECTION 4. Experimental Results and Discussion

Experimental tests of the circuit could be divided into static and dynamic response tests.

4.1. Static Response Test

In order to determine the working wavelength and the working voltages of the circuit, the static response spectra of the circuit should be measured first. As shown in Fig. 3, an optical spectrum analyzer (OSA), three tunable voltage sources (TVSs), and an amplified broadband spontaneous emission source (AES) are employed in the experiment scheme. A lensed fiber is used to couple the broadband wave light into the CW port of the circuit. And the output light of the circuit is directed into the OSA through another lensed fiber. Although the physical parameters of the circuit are designed to be identical, two tunable voltage sources should be applied to compensate the slight deviation caused by the limitation of fabrication accuracy. A redshift can be measured when the MRR is heated up by the tunable voltage source, arising from the effective refractive index of the ring increases [47]. Bias voltage of 0.86 V and 0.08 V are applied to the micro-heaters above MRR₁ and MRR_2’ respectively, in order to make MRRs have the same resonant wavelength of 1555.654 nm which is regarded as the initial state of the circuit. In principle, wavelength longer than 1555.654 nm could be chosen as the working wavelength. Wavelength of 1557.336 nm is chosen as the working wavelength as to achieve a large extinction ratio with low power consumption. The static response spectra of the circuit at the output port S are shown in Fig. 4(a)–(d), and the static response spectra at the output port C are shown in Fig. 4(e)–(h).

Fig. 3.

Experiment schematic for the device's static response. AES: amplified broadband emission source. TVS: tunable voltage source. DUT: device under test. OSA: optical spectral analyzer.

The static response spectra at the port S with no voltages applied to the MRRs is shown in Fig. 4(a). When the voltage applied to MRR₁ increases to 2.91 V, MRR₁‘s resonance wavelength is shifted to the working wavelength $\lambda _{{\rm{w}}}$, and the others still resonate at the initial state. Therefore, the static response spectra at the port S shows the drop filtering characteristics of MRR₁ and the through filtering characteristics of MRR_2’ and MRR₂ . And the response spectra at the output port S is shown in Fig. 4(b). When the voltages applied to MRR_2’ and MRR₂ are 2.12 V and 2.05 V, respectively, those two MRR's resonance wavelength will be shifted to the working wavelength $\lambda _{{\rm{w}}}$, while MRR₁ still resonate at the initial state. Hence the response spectra at the port S shows the through filtering characteristics of MRR₁ and the drop filtering characteristics of MRR₂, as shown in Fig. 4(c). When the voltages applied to MRR₁, MRR_2’ and MRR₂ are 2.91 V, 2.12 V and 2.05 V, respectively, their resonance wavelengths are shifted to the working wavelength $\lambda _{{\rm{w}}}$. The result is that there is a dip located at 1557.336 nm and the static response spectra at the port S is shown in Fig. 4(d).

Fig. 4.

Response spectra of the circuit at the Output port S (a)–(d) and C (e)–(h) with the applied voltages to MRR₁, MRR_2’ and MRR₂ being 0 V, 0 V, and 0 V [(a)–(e)], 2.91 V, 0 V, and 0 V. (b)–(f) 0 V, 2.12 V and 2.05 V [(c),(g)], 2.91 V, 2.12 V, and 2.05 V [(d)–(h)].

It is obviously that the insertion loss at the working wavelength $\lambda _{{\rm{w}}}$ is about −28.86 dB when X = 0 and Y = 0 (see Fig. 4(a)), while the insertion loss at the working wavelength $\lambda _{{\rm{w}}}$ is about −30.11 dB when X = 1 and Y = 1 (see Fig. 4(d)). Although the insertion levels are different at these two working statuses, both of them could be considered as the low level and the optical power at the port S is low (logical 0). On the other hand, the insertion loss at the working wavelength $\lambda _{{\rm{w}}}$ is about −13.77 dB when X = 1 and Y = 0 (see Fig. 4(b)), while the insertion loss at the working wavelength $\lambda _{{\rm{w}}}$ is about −11.44 dB when X = 0 and Y = 1 (see Fig. 4(c)). Both of them could be considered as the high level and the optical power at the port S is high (logical 1). The insertion losses get a slight deviation due to their different routing paths. Analogous to the concept of logic swing level in the electrical domain, the difference of insertion losses with the working wavelength $\lambda _{{\rm{w}}}$ between the high-level and low-level at the port S is equal to 15.09 dB.

The static response spectra at the port C show the drop filtering characteristics of MRR₁ and MRR_2’. Only when the voltages applied to MRR₁ and MRR_2’ are 2.91 V and 2.12 V, respectively, a peak appears at the working wavelength $\lambda _{{\rm{w}}}$. The insertion loss with the working wavelength $\lambda _{{\rm{w}}}$ is about −17.50 dB, and the optical power at the port C is high (logical 1), as shown in Fig. 4(h) . In other working statuses, the insertion losses at the working wavelength $\lambda _{{\rm{w}}}$ are −51.30 dB (see Fig. 4(e)), −43.89 dB (see Fig. 4 (f)), and −49.24 dB (see Fig. 4(g)), respectively. Although the optical power levels are different, all of them could be considered as the low level and the optical power at the port C is low (logical 0). The difference insertion losses with the working wavelength $\lambda _{{\rm{w}}}$ between the high-level and low-level at the port C is equal to 26.39 dB.

All eight static response spectra for the half-add circuit have been analyzed for logical combinations. Note that the bandwidth of the ring is about 0.16 nm, and the Q (quality factor) of the ring resonator is about 9733. Table II shows the measured insertion loss of the circuit at the output ports S and C with four working statuses, which is consistent with the theoretical values shown in Table I. Clearly, the static response spectra of the circuit indicate that the circuit can implement the half-add operations with high noise immunity due to their large logic swing.

TABLE 2 Experimental Insertion Loss, Optical Power Levels and Logical Value with Working Wavelength at the Out Ports of the Circuit

4.2. Dynamic Response Test

In the following, the dynamic response of the circuit is characterized by experiment. The experiment schematic for the device's dynamic response is shown in Fig. 5. A tunable laser (TL), two tunable voltage source (TVSs), two arbitrary function generators (AFGs), a two-channel oscilloscope (OSC), an erbium doped fiber amplifier (EDFA), and an optical filter and a photo-detector (PD) are employed to characterize the device's dynamic response.

Fig. 5.

Experiment schematic for the circuit's dynamic response. CTL: C-band tunable laser. PC: polarization controller. DUT: device under test. TVS: tunable voltage source. AFG: arbitrary function generator. EDFA: erbium doped fiber amplifier. PD: photo-detector. OSC: oscilloscope.

Firstly, a proper voltage supplied by the tunable voltage source is employed to MRR₁ and MRR_2’ to eliminate the fabrication errors, in order to guarantee the same resonant wavelength of MRRs at the original state [48], [49]. Monochromatic continuous-wave light generated by a C-band tunable laser with the wavelength $\lambda _{{\rm{w}}}$ of 1557.336 nm first directs into a polarization controller, and then, the light with TE polarization is coupled into the CW port of the circuit. The output optical signals at the two output ports of the device are fed into a high-speed photo-detector. And the electrical signals output from the detector are fed into an oscilloscope for waveform observation. Binary sequences Non-Return to Zero(NRZ) signals with the speed of 10 Kbps generated by the AFGs are applied to the Micro-heaters embedded around MRRs (The high-level is 2.05 V, and the low-level is 0 V). MRR₁'s working states is controlled by the working states of the electrical signal X. On the other hand, MRR₂ and MRR_2’ are working as a synchronous part, and the working states are controlled by the electrical signal Y. It is shown in Fig. 6 that the circuit can performs the half-add operation correctly by the speed of 10 kbps. In our experimental tests, the laser input power is about 15.4 mw. Besides, the coupling loss to the silicon photonics device is about 2.7 dB at each end face. And the power consumption is about 5mW for each MRR when the voltages applied to them are at the high level. It is easy to draw that the rise time (10%–90%), and the fall time (90%–10%) is about $44\;\mu s$ and $2\;\mu s$, respectively. In the design and testing process need to pay more attention to the following points:

1. In chip design, the rings should be as close as possible to prevent the limitation of fabrication accuracy of the deviation, and thermal crosstalk would exist when the rings are close enough. An ideal solution is fabricate some air trenches between the rings to block the spread of heat.

2. The limitation of fabrication accuracy of the deviation should be controlled to be as small as possible during the experimental test. A redshift can be measured when the MRR is heated up by the tunable voltage source, which derives from the effective refractive index of the ring increases. Therefore, the rings with shorter resonant wavelengths at the working wavelength needs to be compensated.

Fig. 6.

Signals applied to (a) MRR₁, (b) MRR₂, and MRR₂, (c) the SUM result at the S port, and (d) the Carry result at the C port.

Compared with [44], the structure becomes relatively simpler (the MMI is eliminated in the device, and there is no multi-coupling region in the device). What's more, the experimental results are much better than those demonstrated devices. In the dynamic response of previous demonstration, logical 1 is represented by two stages of optical power at the output port sum, and in this paper, logical 1 is represented by only one stage. In addition, output signal quality is improved significantly. As we known, other advanced modulation schemes such as electro-optic modulation scheme can also be employed to modulate MRR, which can achieve a higher modulation speed. In future, advanced modulation such as reversely biased PN junction through the plasma dispersion effect and highly accurate manufacturing technology can be exploited to improve the operation speed of the device [17], [50].

SECTION 5. Conclusion

In conclusion, we have reported a novel schematic which can perform the half-add operations based on cascaded MRRs. Compared to the previous structure, MMI and multi-coupling regions in a single MRR are eliminated in the proposed circuit, which are beneficial to reduce the insertion loss and crosstalk of the device. For proof of principle, a half-adder based on thermo-optic effect is fabricated. The device is demonstrated successfully at the speed of 10 kbps, and the signal quality is improved significantly.