1. Introduction

With the improvement of integrated density on single chip and the shrinking of the transistor, the bandwidth limitations of silicon electronics and printed metallic track have approached [1–5]. Therefore, it is very difficult for silicon electronics to develop along with the speed of Moore’s law. Many researches have begun to ponder a novel scheme to resolve the challenges faced by silicon electronics. However, silicon photonics have achieved a great development in many fields in recent years, and various silicon-based optical devices have been demonstrated successfully such as electro-optic modulators [6–13], optical logics [14–16], optical buffers [17,18], optical analog-to-digital converters (ADCs) [19] etc. Therefore, silicon photonics is the most promising solution to replace silicon electronics to perform information processing and computing due to the inherent nature of optics such as parallelism, high bandwidth and high speed.

Generally, there are two feasible ways to make full use of the nature of optics to perform optical computing. One way is to achieve an optical transistor and then mimic the design of the electronic computer to design the optical computer to achieve optical computing. Perhaps this is the simplest way for the transition from electronic computer to optical computer. However, this is still a nice dream which has fascinated many researchers for many years, due to the inherent differences between the behaviors of electrons and photons. The other way is to break the traditional thinking trapped by the working principle of the traditional electronic computer, and invent a novel working scheme to perform optical computing. Directed logic scheme proposed by Hardy and Shamir in 2007 is very suitable for optical computing since it makes full use of the strengths of the electrons and photons while avoids their weaknesses [20].

Directed logic is a novel logical paradigm which employs an optical switching network to perform logical operation [20–23]. Electrical signals regarded as the operands of the operation control the state of each optical switch in the network and the operation results are output at the optical output ports in the form of light. The operation of each switch is independent from others and all switches perform their operations simultaneously, therefore, their switching delays do not accumulate—in contrast to electronic logic circuits wherein gate delays are cascaded, resulting in large latency [22]. Another important performance of directed logic is that both an operation and its complementary one can be achieved at the different output ports simultaneously such as one output port can obtain the OR result and another output port can obtain the NOR result [15], which means the power efficiency is higher than the traditional electronic logic which has two input signals and only one output signal. In a word, the directed logic has many potential advantages compared to the traditional electronic logic.

As the fundamental logical operations, the AND/NAND operations are same as the other fundamental logical operations which are very important for optical computing since more complex logical operations can be performed by properly cascading some fundamental logical operations. For proof of concept of directed logic, we have successfully demonstrated the directed AND/NAND operations with the operation speed of 10kbps through the silicon thermo-optic effect in our previous paper [15]. In this paper, we report an electro-optic directed logic circuit for AND/NAND operations with the operation speed of 100Mbps. PIN diodes are embedded around the MRRs in order to modulate the MRR-based optical switches through the plasma dispersion effect.

2. Device principle, design and fabrication

The proposed directed logic circuit composed of a pair of parallel MRRs is shown in Fig. 1(a) . The four ports of the circuit are denoted as Input, Through, Drop and Add which have been shown in Fig. 1(a). Monochromatic continuous optical wave with the working wavelength of λ_w is coupled into the device through the input port, and then modulated by two electrical pulse sequences applied to the MRRs through the plasma dispersion effect respectively. The high and low level of electrical pulses applied to the MRRs represent logical 1 and 0 in the electrical domain, the optical power output at the through and drop ports define logical output. Logical 1 is obtained in the optical domain when the optical power is at high level and logical 0 is obtained when the optical power is at low level. We define MRR is on-resonance at λ_w when the applied voltage is at low level, and MRR is off-resonance at λ_w when the applied voltage is at high level. Based on the above definitions, when the voltages applied to the MRRs are both at low level (X = 0, Y = 0), two MRRs are both on-resonance at λ_w and the light is directed to the drop port, and the optical power is at high level at the drop port and low level at the through port (Y₂ = 1, Y₁ = 0); when one of the voltages applied to MRR1 and MRR2 is at low (X = 0, Y = 1 or X = 1,Y = 0), only one of the MRRs is on-resonance at λ_w, and the light is downloaded by MRR1 or MRR2 and then directed to the drop port, therefore, the optical power is at high level at the drop port and low level at the through port (Y₂ = 1, Y₁ = 0); when the voltages applied to MRR1 and MRR2 are both at high level (X = 1, Y = 1), both MRR1 and MRR2 are off-resonance at λ_w, the light bypasses the two MRRs successively, and the light is directed to the through port at last, therefore, the optical power is at low level at the drop port and high level at the through port (Y₂ = 0, Y₁ = 1). Based on the above discussions for the four different working statuses, the truth table achieved by the proposed circuit can be summarized as the Table 1 . From Table 1, we can see the proposed directed logic circuit can perform AND and NAND operations at the through and drop ports simultaneously

 

Fig. 1 (a) Architecture and (b) micrograph of the device (CW: continuous wave, EPS: electrical pulse sequence, MRR: microring resonator)

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Table 1. The truth table achieved by the proposed circuit

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The device is fabricated on an eight inch silicon-on-insulator (SOI) wafer with a 220 nm top silicon layer and a 2 μm buried SiO₂ layer. The micrograph of the device is shown in Fig. 1(b). 248-nm deep ultraviolet photolithography is utilized to define the device patterns and inductively coupled plasma etching process is utilized to etch the top silicon layer. The rib waveguide with 400 nm in width, 220 nm in height and 70 nm in slab thickness is employed, which only supports the fundamental quasi-TE mode [15]. The radius of ring waveguides are both 10 μm, the gaps between the straight waveguides and the ring waveguides are 325 nm and the centre-to-centre distance between two MRRs is 4πR (R is the radius of ring waveguide). After the silicon waveguides are formed, the p- and n- doping regions with doped concentrations of 5.5x10²⁰ cm⁻³ are formed around two ring waveguides to form PIN diodes which are employed to modulate MRRs by the plasma dispersion effect. The edge to edge distance from the doped regions to the ring waveguides regarded as the intrinsic regions of the PIN diodes is about 500 nm. A 1500-nm-thick silica is deposited on the top silicon layer as the separate layer, and then two titanium nitride (TiN) microheaters with the thickness of 150 nm are fabricated on the top of MRRs in order to compensate the detuning resonances of the two MRRs which are mainly induced by the limited fabricating accuracy. Al trances are formed to connect the microheaters, PIN diodes and the pads at last. Note that the pads A and B which are mainly employed to change the optical path of two parallel straight waveguides and compensate the fabrication errors are useless in this working status.

3. Experimental results

3.1 Static response spectral

An amplified spontaneous emission source, three tunable voltage sources and an optical spectrum analyzer (OSA) are employed to characterize the static response spectra of the device. The broadband light is coupled into the input port of the device through a lensed fiber and the output light is fed into the OSA through another lensed fiber. Although two MRRs are designed to have the same physical parameters, the resonant wavelengths of two MRRs are slightly different due to the limited fabricating accuracy. In order to compensate the fabrication errors and let two MRRs have the same resonant wavelength at the initial state, one tunable voltage source with an appropriate voltage is applied to the microheater above MRR1 which has a shorter resonant wavelength. When MRR1 is heated up, the effective refractive index of ring waveguide increases, and the resonant wavelength of MRR1 shifts to the longer wavelength. The other two tunable voltage sources are applied to two MRRs through the PIN diodes in order to modulate two MRRs through the plasma dispersion effect.

The static response spectra of the device at the through port are shown in Figs. 2(a) -2(d). The MRR2’s resonant wavelength is 1544.06 nm which is longer than the MRR1’s. The wavelength of 1544.06 nm is chosen as the λ_w. At first, a bias voltage of 1.89 V is applied to the microheater above MRR1 in order to let two MRRs have the same resonant wavelength of 1544.06 nm which is regarded as the initial state of the device (Fig. 2(a)). When the voltages applied to MRRs through the PIN diodes are both 0 V (X = 0, Y = 0), the light is directed to the drop port and the optical power is at low level at λ_w at the through port (representing logical 0, Fig. 2 (a)). When the voltages applied to MRR1 and MRR2 through the PIN diodes are 0 and 1 V, respectively (X = 0, Y = 1), the MRR1’s resonant wavelength does not change, however, the MRR2’s resonant wavelength shifts from 1544.06 to 1542.99 nm since the free carriers are injected into MRR2 and the refractive index of MRR2 decreases, the light is downloaded by MRR1 and directed to the drop port, and the optical power is at low level at λ_w at the through port(representing logical 0, Fig. 2(b)). When the voltages applied to MRR1 and MRR2 through the PIN diodes are 1 and 0 V, respectively (X = 1, Y = 0), the MRR1’s resonant wavelength shifts from 1544.06 to 1542.88 nm and the MRR2’s resonant wavelength does not change, the light is downloaded by MRR2 and also directed to the drop port, and the optical power is at low level at λ_w at the through port (representing logical 0, Fig. 2(c)). When the voltages applied to MRR1and MRR2 through the PIN diodes are both 1 V (X = 1, Y = 1), the MRR1 and MRR2’s resonant wavelengths shift from 1544.06 to 1542.88 and 1542.99 nm, respectively, the light bypasses MRR1 and MRR2 successively and directed to the through port, and the optical power is at high level at λ_w at the through port (representing logical 1, Fig. 2(d)). Note that when the MRRs are modulated by the voltages through the plasma dispersion effect, the depths of the notches in the spectra decrease with the resonant wavelength shift from its original location to the shorter wavelength due to the increased optical absorption in microring by the electrons and holes (Figs. 2(b) and 2(c)) [7]. However, the deterioration of the depths of the notches does not affect the working of the device, since the working wavelength is chosen at the dip at the initial state and we do not care where the resonant wavelength shifts to when the voltage is applied to MRR. The static response spectra of the device at the drop port for the four different working statues are shown in Figs. 2(e)-2(h), which is corresponding to Figs. 2(a)-2(d) one by one. The only difference is that the resonant dip is employed to characterize the working statues of the device in the through port’s response spectra (Figs. 2(a)-2(d)), while the resonant peak is employed to characterize the working statues of the device in the drop port’s response spectra. Therefore, the discussions for all four different working statues for the through port are effective for the drop port. The total insertion is about 7.01 dB at the through port, which includes 0.1 dB propagation loss in the straight waveguide, 5.97 dB coupling loss and 0.94 dB bypass loss for two MRRs. Compared to the through port, the total insertion loss is lager at the drop port due to the drop loss of MRR (Fig. 2(f)).

 

Fig. 2 Response spectra of the device at the through port (a-d) and the drop port (e-h)with the applied voltages to the PIN diodes around MRR1 and MRR2 being 0 and 0 V ((a),(e)), 1 and 0 V ((b),(f)), 0 and 1 V((c),(g)), and both 1 V ((d),(h)).

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3.2 Dynamic operation results

The dynamic response of the device is shown in Fig. 3 . A tunable laser, a tunable voltage source, two pulse pattern generators (PPG) and a four-channel oscilloscope are employed to characterize the dynamic response of the device. At first, the voltage of 1.89 V is applied to the microheater above the MRR1 in order to let two MRRs have the same resonant wavelength. After that, monochromatic light with the λ_w of 1544.06 nm from a tunable laser is coupled into a polarization rotator and then the light with TE polarization is coupled into the input port of the device. Two binary sequences non-return-to-zero signals at 100 Mbps with appropriate amplitudes and offsets generated by the PPGs are applied to the MRRs, respectively. The output light signal is fed into a high-speed detector, and the electrical signals generated by the PPGs and the electrical signal converted by the detector are fed into a four-channel oscilloscope for waveform observation. From Fig. 3, we can see the AND and NAND operations can be carried out correctly by the device at the through and the drop ports simultaneously. Some small sharp peaks and dips which are corresponding one by one can be found in Figs. 3(c) and 3(d), it is mainly because the transition of two different working states. For example, the logical 0 is from the combination of the off-resonance MRR1 and the on-resonance MRR2 (X = 0, Y = 1) while the other logical 0 is from the combination of the on-resonance MRR1 and the off-resonance MRR2 (X = 1, Y = 0), it must undergo the middle state of the on-resonance MRR1 and the on-resonance MRR2 (X = 1, Y = 1) (which means the MRR1’s resonance shifts from the working wavelength to the shorter wavelength, and the MRR2’s resonance does not shift from the shorter wavelength to the working wavelength at this time) when the working state transmit from the off-resonance MRR1 and the on-resonance MRR2 (X = 0, Y = 1) to the on-resonance MRR1 and the off-resonance MRR2 (X = 1, Y = 0). Therefore, we can see a sharp peak between two continuous logical 0 (Fig. 3(c)). Similar phenomenon can be found in our previous work [15].

 

Fig. 3 Signals applied to (a) MRR1 and (b) MRR2, (c) the AND result at the through port and (d) the NAND result at the drop port.

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4. Conclusion

We report an electro-optic directed logic circuit which can implement the AND/NAND operations at the through and drop ports simultaneously. PIN diodes embedded around the MRRs are employed to modulate MRRs through the carrier-injection modulation scheme. The AND/NAND operations with the operation speed of 100Mbps are demonstrated successfully. Although the operation speed is not very high, it proof that the plasma dispersion effect can be used to modulate MRRs to achieve logical operation, which is very important for us to optimize the design of the PIN diodes or employ other advanced modulation schemes such as the carrier-depletion modulation and the electric field effects to achieve the faster operation speed [24–26]. The demonstration of electro-optic directed logic opens up the opportunities for the application of directed logic in optical computing field.