An analytic model is proposed to study the linearity performance of the silicon Mach-Zehnder optical modulator. According to the simulation results, we optimize the width of the silicon rib waveguide and the location of the PN junction to improve the linearity performance. The fabricated silicon Mach-Zehnder optical modulator has a spurious free dynamic range of 113.3 dB.Hz2/3 and 88.9 dB.Hz1/2 for the third-order intermodulation distortion and the second-order harmonic distortion. We also demonstrate the optical four-level pulse-amplitude-modulation (PAM-4) signal generation through the device. The generated optical PAM-4 signal is characterized at the rates up to 35 Gbaud. The BERs of the optical PAM-4 signals can reach 5.2╳10−6 at 20 Gbaud and 6.6╳10−5 at 32 Gbaud, which are much lower than the threshold of hard decision forward error correction (3.8 ╳10−3).
© 2017 Optical Society of America
Many advanced modulation formats such as 4-level pulse-amplitude-modulation (PAM-4) [1, 2], binary-phase-shift-keying (BPSK) [3, 4], quadrature-phase-shift-keying (QPSK) [5, 6] and 16-quadrature-amplitude-modulation (16-QAM) [7, 8] are utilized to improve the data transmission capacity. PAM-4 is a modulation format using four amplitude levels in one symbol and thus its bit rate is twice as high as OOK at the same baud rate. Although the requirement for the optical signal-to-noise ratio of the PAM-4 modulation is much higher than that of the OOK modulation, this modulation format is still competitive for the next-generation short-reach optical communication. Up to now, the PAM-4 modulation format has been successfully conducted in the platforms like InP , LiNbO3  and silicon [11–13].
Silicon photonics is a promising platform for low-cost large-capacity data transmission. Lasers [14–16], modulators [17, 18], multiplexers/de-multiplexers [19, 20], routers [21, 22] and detectors [23–25] have been fabricated in this platform. Silicon optical modulators with a high linearity performance are very helpful not only to generate the optical PAM-4 signal but also to transmit the analog signal. Transmitting the analog signal is basic in the radar and 5G systems . In this paper, we propose an analytic model to study the differential linearity performance of the silicon Mach-Zehnder optical modulator. With the help of the model, we have optimized the device with a high linearity performance. The spurious free dynamic ranges (SFDRs) for the third-order intermodulation distortion (IMD3) and the second-order harmonic distortion (SHD) are 113.3 dB.Hz2/3 and 88.9 dB.Hz1/2. We also demonstrate the optical PAM-4 signal generation by the device.
2. Analytic model
PAM-4 modulation format is becoming more and more popular in short-reach optical communication, in which the intervals between the four amplitude levels are generally required to be equal for the applied electrical signal and the output optical signal. For the PAM-4 electro-optic modulator, this means that the output optical power is linearly dependent on the applied voltage. Several models have been created to analyze the distortion induced by the electrical structure, the interferometer and the free carrier dispersion [27–29]. In order to analyze the linearity performance related to the waveguide structure and the junction location, we develop an analytic model based on effective index method and abrupt PN junction model, with which we can quickly determine the optimization direction for various structural parameters.
Figures 1(a) and 1(b) show the schematics of the silicon Mach-Zehnder optical modulator and the cross section of the phase shifter. First of all, we get the TE polarization modal field distribution along the horizontal direction (x axis) for the silicon rib waveguide by the effective index method .
For the silicon Mach-Zehnder optical modulator, the output optical power is decided by the phase difference between its two arms, which is induced by the free carrier dispersion effect. As Fig. 1(b) shows, the change of the effective refractive index is caused by the variation of the carrier concentration within the PN junction, which can be calculated with the following expression :32] is used to calculate .
The p-doping concentration of 1╳1018/cm3 and n-doping concentration of 8╳1017/cm3 are used in the waveguide region. We assume that the PN junction is abrupt so that the depletion region can be expressed as the following expression :
When the applied voltage is changed, the thickness of the depletion layer is changed due to the variation of the carrier concentration. The change of the effective refractive index is decided by the overlap of the changed depletion layer with the modal field distribution. Further, the output optical power is proportional to the change of the effective refractive index when the Mach-Zehnder optical modulator with the single-arm-driving scheme works at the quadrature point. So the linearity performance of the silicon Mach-Zehnder optical modulator with the single-arm-driving scheme is mainly decided by the overlap of the changed depletion layer with the modal field distribution.
With two time-dependent sine signals (f1 and f2) combined and applied to the phase shifter, we can work out the time-dependent change of the effective refractive index by Eqs. (1)-(4) as below:
By using the Fourier transformation of , we can get the SHD and IMD3 components as
Figure 2(a) shows the relationship between the propagation loss and the width of the silicon rib waveguide with 220 nm in height and 70 nm in slab thickness. Note that the sidewall roughness is supposed to be the same for all silicon rib waveguides, which is decided by the comparison between the calculated propagation loss and the measured one of the silicon rib waveguide with 400 nm in width. We scan the location of the PN junction in the range from x = −100 nm to x = 100 nm to get the maximum SFDR for each width of the silicon rib waveguide [Fig. 2(c)]. As shown in Fig. 2(b), the maximum SFDRs for the SHD and the IMD3 increase with a decrease in the width of the silicon rib waveguide. Clearly, there is a trade-off between the propagation loss and the linearity. In order to achieve high linearity without sacrificing the propagation loss, the width of the silicon rib waveguide is preferred to be 400 nm. Figure 2(c) shows the SFDRs for the SHD and the IMD3 for the silicon rib waveguide with 400 nm in width and different locations for the PN junction. There is a little mismatch between the optimum locations of the PN junctions for the maximum SFDR for the IMD3 and the maximum SFDR for the SHD. When the PN junction is located at 63 nm right to the center of the silicon rib waveguide, the SFDR for the IMD3 has the maximum value. When the PN junction is located at 91 nm right to the center of the silicon rib waveguide, the SFDR for the IMD3 has the maximum value. It is more difficult to eliminate the IMD3 component than to eliminate the SHD component with a filter as the IMD3 component is much more near to the carrier signals (f1 and f2) than the SHD component. So the PN junction is chosen to be located at 63 nm right to the center of the silicon rib waveguide. The calculated SFDRs for SHD and IMD3 are 90.7 dB.Hz1/2 and 112.3 dB.Hz2/3, respectively.
3. Device fabrication
The micrograph of the device is shown in Fig. 1(c). A symmetric Mach-Zehnder interferometer is adopted to obtain a large optical bandwidth. The device is fabricated on an 8-inch silicon-on-insulator wafer with a 220-nm-thick top silicon layer and a 2-μm-thick buried silicon dioxide layer at the Institute of Microelectronics, Singapore . 248-nm deep ultraviolet photolithography is used to define the pattern and inductively coupled plasma etching is utilized to form the silicon waveguides. A 200-μm-long inverse taper with a tip of 180 nm is utilized for coupling length into and out of the device. The p-doping (boron) concentration of 1╳1018/cm3 and n-doping (phosphor) concentration of 8╳1017/cm3 are used to form the PN junction in the waveguide region. The doping concentration is 5.5╳1020/cm3 for both the p-type and n-type heavily doped regions, which are 600 nm away from the side of the rib waveguide. After doping, the rapid thermal annealing process is followed. The device is annealed for 5 seconds at 1050 °C. After the PN junction is formed, a 1500 nm layer of silicon dioxide is deposited on the silicon layer to isolate the waveguide from a 150-nm-thick titanium nitride (TiN) layer which acts as the heater to tune the optical bias point and the termination resistor to avoid the microwave reflection. Another silicon dioxide layer of 300 nm thickness is deposited on the TiN layer. Aluminum wires are formed to connect the TiN heaters, termination resistor, the PN junctions and the electrical pads. At the end of signal and ground pads, termination resistors are used to eliminate the electrical signal reflection. The metal thickness is 1.5 μm. The width of the signal trace is 28 μm and the gap between the signal trace and the Ground is 5.5 μm. The electrode on the other arm is not connected to the PN junction. The unloaded electrode on the other arm is fabricated only to do the testing experiment of the electrode.
4. Characterization results and discussion
Figure 3 shows the experimental setup for characterizing the transmission spectra, linearity performance and eye diagrams of the device. An amplified spontaneous emission and an optical spectrum analyzer are used to characterize the transmission spectra of the device. A heater as shown in Fig. 1(a) is utilized to compensate the phase difference between the two arms of the silicon optical modulator due to the fabrication imperfections. As the brown line in Fig. 4(a) shows, the insertion loss of the device fluctuates from 9.6 dB to 10.3 dB in the wavelength range from 1525 nm to 1565 nm, which includes ~5.4 dB coupling loss between the device and the two lensed fibers, ~3.0 dB propagation loss of the phase shifter, 0.6 dB propagation loss of the splitter and combiner and 1.0 dB propagation loss of the waveguide. In order to achieve equal and maximum amplitude intervals of the optical PAM-4 signal, the silicon optical modulator should work in the linear region and its Vpp is chosen to be 5 V. The blue curve in Fig. 4(a) shows the transmission spectrum of the device optically biased at the quadrature point with the bias voltage of 2.5 V. The black, red, green and purple curves in Fig. 4(a) show the transmission spectra of the device with the driving voltages of 0 V, 1.66 V, 3.33 V and 5 V, corresponding to four amplitude levels of the optical PAM-4 signal. The four amplitude levels at the wavelength of 1545 nm are 10.7 dB, 12.1 dB, 14.4 dB and 18.9 dB, respectively and the normalized amplitude intervals are 0.24, 0.25 and 0.24 (normalized to the max transmission). The slight difference among the three amplitude intervals is caused by the transfer function of the Mach-Zehnder interferometer. Note that the power consumption for thermal tuning is the same for all five spectra with the driving voltages applied to the PN junctions, which is different from that for the maximum transmission spectra. The fluctuation of the transmission spectrum is mainly due to the dispersion effect of the M-Z interferometer, in which the phase difference between the two arms is a little different at different wavelengths. The modulation efficiency (Vπ⋅L) of the device is 1.68 V⋅cm. The dependence of the output optical power of the device biased at the quadrature point on the applied voltage is also measured [Fig. 4(b)], which is almost linear in the normalized optical power range from 0.15 to 0.85. The electro-optic response of the device under a reverse bias voltage of 2.5 V is measured and its corresponding 3 dB electo-optic bandwidth is 30.2 GHz [Fig. 4(c)]. The above two factors enable the equidistant optical PAM-4 modulation at the moderation rate up to 35 Gbaud.
For the SFDRs measurement, the light from a tunable laser is coupled into the device after its polarization is adjusted to be consistent with the TE mode of the silicon waveguide. Two tones generated by a microwave source are combined through an electrical combiner and applied to one arm of the device. After the erbium-doped fiber amplifier (EDFA: the noise figure is smaller than 6 dB and its output power can be tuned from 8 dBm to 33 dBm with the input power over −6 dBm) and the optical filter, the modulated light is fed to the photodetector (the bandwidth is 50 GHz, the input average power of PD is 11 dBm and the responsivity is 0.5 A/W) and transformed to an electrical signal. An electrical signal analyzer is used to study the frequency spectrum of the modulated light. The SFDRs for the SHD and the IMD3 of the device are measured with f1 = 2 GHz and f2 = 2.2 GHz, as shown in Fig. 4(b). The square dots show the powers of the 2-GHz component of the modulated light measured under different input electrical power, the triangle dots show the power of the 4-GHz SHD component and the circle dots show the power of the 1.8-GHz IMD3 component. By linearly fitting the experimental results, we achieve the SFDRs for the IMD3 and the SHD, which are 113.3 dB.Hz2/3 and 88.9 dB.Hz1/2 with the system noise floor being −165 dBm/Hz. The link parameters used in the calculation are the same with those in the experimental setup. The agreement between the calculated results and the measured results indicates the effectiveness of the proposed model in some sense. Compared with the device adopting the same driving scheme , our device shows an obvious improvement in linearity performance. Better results could be expected by adopting the push-pull driving scheme .
For the optical PAM-4 signal generation, we measure the eye diagrams and BERs of the device at different baud rates. Two channels of pseudo-random binary sequence electrical signals with the length of 215-1 are combined through an electrical combiner to synthesize the electrical PAM-4 signal, one of which is attenuated to be half with a 6 dB power attenuator. Then the electrical PAM-4 signal is amplified to be 5 Vpp by an electrical amplifier and applied to the device. The amplified light by the EDFA is filtered by a tunable filer to reduce the noise floor. A digital communication analyzer is used for eye diagram observation.
To generate a good optical PAM-4 signal, we tune the heater and make the device work at the quadrature point, where the device has the best linearity performance. The electrical reverse bias is 2.5 V. Thus the amplitude levels of the electrical PAM-4 signal applied to the device is consistent with that in the static transmission spectra. Figure 5 shows the eye diagrams of the electrical PAM-4 signals and the generated optical PAM-4 signals at different baud rates at the wavelength of 1545 nm. The electrical PAM-4 signal is not so good at the higher baud rate which is mainly due to the limited bandwidth (30 GHz) of the electrical amplifiers. The linearity of the amplitude levels of the optical PAM-4 signal is good at 20 Gbaud and 25 Gbaud, which is consistent with the static measurement result in Fig. 4(a). However, the linearity performance becomes worse at the higher baud rates, which is mainly due to the deteriorated driving signal at higher baud rates and the limited electro-optic bandwidth of the device (30.2 GHz).
As the device is based on symmetric Mach-Zehnder interferometer, it can work in a wide wavelength range. Figure 6 shows the 32 Gbaud eye diagrams of the generated optical PAM-4 signals at the wavelengths of 1525 nm, 1535 nm, 1545 nm, 1555 nm and 1565 nm. Clear and open eye diagrams at different wavelengths indicate that the device is suitable for high-speed wavelength division multiplexing application.
To measure the BER of the generated optical PAM-4 signal, a receiver is used to convert the optical signal to an electrical one, which is further sampled by a real-time oscilloscope. An off-line digital signal processing program is adopted to calculate the BER. Figure 7 shows the BERs of the optical PAM-4 signals at 20 Gbaud, 25 Gbaud, 30 Gbaud and 32 Gbaud. The BERs of the optical PAM-4 signals can reach 5.2 × 10−6 at 20 Gbaud and 6.6 × 10−5 at 32 Gbaud, which are much lower than the threshold of hard decision forward error correction (3.8 × 10−3).
In conclusion, we propose an analytic model to study the linearity performance of the silicon Mach-Zehnder optical modulator. With the model, we have optimized the width of the silicon rib waveguide and the location of the PN junction. The SFDRs for the IMD3 and the SHD of the device are 113.3 dB.Hz2/3 and 88.9 dB.Hz1/2. We demonstrate the optical PAM-4 signal generation at the rates up to 35 Gbaud through the device. The generated optical PAM-4 signal at 32 Gbaud is characterized in the wavelength range of 1525-1565 nm.
Program 863 (2015AA015503, 2015AA017001); National Key R&D Program of China (2017YFA0206402, 2016YFB0402501); National Natural Science Foundation of China (NSFC) (61535002, 61505198, 61235001, 61575187, 61377067).
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