Intrinsic chirp analysis of a single dual-drive silicon PAM-4 optical modulator

Lingchen Zheng; Sizhu Shao; Jianfeng Ding; Lei Zhang; Xin Fu; Lin Yang

doi:10.1364/OE.26.032014

1. Introduction

The demand for high communication bandwidth and capacity is driving the development of new optical communication systems. Recently, many advanced optical modulation formats, such as binary-phase-shift-keying (BPSK) [1,2], quadrature-phase-shift-keying (QPSK) [3], quadrature-amplitude-modulation (QAM) [4,5] and pulse-amplitude-modulation (PAM) [6] are utilized to improve the spectral efficiency and increase the data rates. In short-reach applications, 4-level pulse-amplitude-modulation (PAM-4) is taken as an effective way to realize 400 Gbps Parallel Single Mode fiber 4-lane (PSM-4) systems as per recent IEEE taskforce discussions [7]. Compared with on-off-keying (OOK) modulation, PAM-4 modulation can double the overall bitrates using the same optical links [8,9]. Silicon photonics (SiP) is an emerging technology for short-reach interconnects in data centers and other computing system applications attribute to its compatibility with the existing complementary metal-oxide-semiconductor (CMOS) fabrication processes. A variety of reported SiP devices such as lasers, modulators, photodetectors and so on have shown the potential of SiP [10–19].

There are different methods of generating PAM-4 signals. One of the commonly used methods is to drive a single Mach-Zehnder modulator by a PAM-4 electrical signal or a pair of differential electrical PAM-4 signals [20,21]. A different approach to drive a dual-parallel Mach-Zehnder modulator by two binary electrical signals to generate PAM-4 optical signal is presented [22]. Yet another method is to apply two binary electrical signals to the two arms of a dual-drive Mach-Zehnder modulator (DD-MZM) [23]. DD-MZM method is of great interest as it utilizes a single MZM without the need of electrical PAM-4 driver signal which usually requires complex electrical circuits. There is one potential issue though. PAM-4 modulation generated using DD-MZM method is subject to inherent frequency chirp, which is different from the push-pull modulation with slightly negative frequency chirp [24]. To the best of our knowledge, the chirp characteristic with the silicon PAM-4 DD-MZM has not been investigated previously. And no corresponding chirp parameters have been quantified. It is well known that the modulation chirp affects the optical data transmission in fiber. Hence, it is important to analyze the inherent frequency chirp of the modulated PAM-4 signal generated using silicon MZ modulator.

In this paper, we analyze the intrinsic frequency chirp of the PAM-4 optical modulation using one silicon DD-MZM. The transmission intensity and output phase of a MZM modulator are effected by the plasma dispersion and propagation loss of silicon. We quantify the frequency chirp of PAM-4 modulations with different 3-dB quadrature points (Q_- and Q₊) set by thermal tuning. The simulation result indicates that the Q₊ modulator has mainly positive chirp while Q_- modulator has mainly negative chirp. In the experiment, we further measured the eye diagrams of the two types of the modulator at different modulation rates. The chirp parameters of different PAM levels’ switching are substantially different. In addition, the plasma dispersion and propagation loss of silicon will affect the value of chirp parameters. What is more, the BER’s of back to back and 2 km transmission of the PAM-4 optical signal were measured, which shows the impact of the modulator frequency chirp intuitively.

2. Analysis of the frequency chirp

2.1 Analytical model

The structure of a silicon Mach-Zehnder PAM-4 optical modulator is shown in Fig. 1(a). A continuous-wave light input to the modulator is first split into two ways by a 3-dB splitter. Two binary electrical signals (Signal₁ and Signal₂) are applied to the two arms of the symmetric Mach-Zehnder interferometer by a GSGSG (G: ground, S: signal) coplanar waveguide (CPW) electrode. The peak-to-peak voltage of the electrical signal Signal₁ is twice as large as the electrical signal Signal₂, which is the key to form two different phase shifts between the two arms of the modulator. And finally the light is combined by a 3-dB combiner and a PAM-4 optical signal is realized at the output of the modulator. In order to compensate the phase difference between the two arms of the modulator due to imperfect fabrication, a thermal-optic phase shifter is usually introduced to one arm of the modulator.

Fig. 1 (a) The structure of the silicon PAM-4 optical modulator, (b) the cross-section of the silicon MZM electro-optic phase shifter.

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Assuming the input electrical field (E₀) of the light is equally split into the two arms of the MZM without additional excess loss, after the electro-optic modulation and thermal phase tuning, the output filed can be expressed as follows:

E = \frac{E_{0}}{2} (A_{1} \cdot e^{j (φ_{1} + φ_{b i a s})} + A_{2} \cdot e^{j φ_{2}})

in which:

A_{1} = \sqrt{10^{- α (V_{1}) \cdot L / 10}}, A_{2} = \sqrt{10^{- α (V_{2}) \cdot L / 10}}

φ_{1} = n_{e f f} (V_{1}) \cdot L \cdot \frac{2 π}{λ}, φ_{2} = n_{e f f} (V_{2}) \cdot L \cdot \frac{2 π}{λ}

where

α (V)

and n_eff(V) are the propagation loss coefficient and effective refractive index of the doped silicon waveguide under a bias voltage of V, respectively; L is the length of the phase shifter;

φ_{bias}

is the phase shift induced by the thermal tuning;

λ

is the wavelength of the light in vacuum.

From Eq. (1), the instantaneous intensity I and phase $ϕ$ of the optical output signal can be further expressed as:

I = \frac{E_{0}^{2}}{4} [A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} \cos (φ_{1} + φ_{b i a s} - φ_{2})]

ϕ = \tan^{- 1} \frac{A_{1} \sin (φ_{1} + φ_{b i a s}) + A_{2} \sin φ_{2}}{A_{1} \cos (φ_{1} + φ_{b i a s}) + A_{2} \cos φ_{2}}

The modulation chirp parameter α of a modulator is defined as [25–27]:

α_{c h i r p} = 2 I \cdot (d ϕ / d t) / (d I / d t)

Combining Eqs. (4)-(6), the chirp parameter of the silicon MZM can be calculated.

2.2 Simulation and calculation of the frequency chirp

Figure 1(b) shows a cross-section view of the silicon MZM electro-optic phase shifter. A PN junction is embedded in the ridge waveguide of the silicon MZM. The ridge waveguide is 400 nm in width and 220 nm in height formed by silicon etch of 150 nm in depth. The concentrations of the p-doped region and the n-doped region are 1 × 10¹⁸/cm³ and 8 × 10¹⁷/cm³, respectively. Both the heavy p-doping and n-doping concentrations are 5.5 × 10²⁰/cm³. Using computer-aided design tool, the carrier distributions in the silicon electro-optical phase shifter under different bias voltages can be obtained. Using the formula created by Soref and Bennet [28], we then calculate the changes of the effective refractive index and propagation loss of the silicon electro-optic phase shifter under different bias voltages, as plotted in Figs. 2(a) and 2(b).

Fig. 2 Simulated (a) propagation loss versus bias voltage, (b) the effective refractive index versus bias voltage of the silicon electro-optic phase shifter.

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Figure 3(a) is the normalized transmission of the MZM, which shows the relationship between the output intensity I and the phase difference $φ$ between two arms of the modulator. There are two 3-dB quadrature points, Q_- and Q₊, that can be set using the thermal tuning. The modulator operating at point Q_- is called a Q_- modulator while the modulator operating at point Q₊ is called a Q₊ modulator. For the Q_- modulator, there are four intensity levels I_j (j = 0, 1, 2, 3) under four driving voltage states: ‘10’ (Bias₁ + V_pp1/2, Bias₂-V_pp2/2), ‘11’ (Bias₁ + V_pp1/2, Bias₂ + V_pp2/2), ‘00’ (Bias₁-V_pp1/2, Bias₂-V_pp2/2) and ‘01’ (Bias₁-V_pp1/2, Bias₂ + V_pp2/2). For the Q₊ modulator, there are also four intensity levels I_j (j = 0, 1, 2, 3) under four driving voltage states: ‘01’ (Bias₁-V_pp1/2, Bias₂ + V_pp2/2), ‘00’ (Bias₁-V_pp1/2, Bias₂-V_pp2/2), ‘11’ (Bias₁ + V_pp1/2, Bias₂ + V_pp2/2) and ‘10’ (Bias₁ + V_pp1/2, Bias₂-V_pp2/2). Bias_m is the DC bias voltage applied to arm_m and V_ppm is the peak-to-peak voltage of the electrical signal applied to arm_m (m = 1, 2), particularly V_pp1 = 2V_pp2.

Fig. 3 (a) Transmission function of the MZM under four different driving conditions, (b) the frequency chirp between different PAM levels’ switching for the Q₊ and Q_- modulator.

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We analyze the frequency chirp parameters of the PAM-4 optical signal for the Q_- and Q₊ modulator, as depicted in Fig. 3(b). The value of chirp changes along with the switching between the two PAM levels. For example, when the PAM level switches from level ‘3′ to level ‘2’, for the Q_- modulator it would require the driving voltage to change from state ‘01’ to state ‘00’, while for the Q₊ modulator the driving voltage changes from state ‘10’ to state ‘11’. Correspondingly, the output instantaneous intensity and the output phase will also change, which results in the frequency chirp. For both the Q_- modulator and Q₊ modulator, there are twelve combinations of the two-level switching. However, the value of chirp parameter of the level switching from ‘3′ to ‘2’ is the same as the level switching from ‘2 to ‘3, which can be expressed as chirp_{’3′→’2’} = chirp_{’2’→’3′}. Therefore, there are total six chirp parameters for both of the Q_- modulator and Q₊ modulator. We conducted numerical simulation to calculate the chirp parameters of the PAM-4 modulation.

The driving voltages in the two arms of the modulator are given as two sinusoidal signals $V_{1} (t) = v_{b i a s 1} + v_{1} \sin (2 π f t)$ and $V_{2} (t) = v_{b i a s 2} + v_{2} \sin (2 π f t)$ for the chirp simulation. The DC bias voltages v_bias1 and v_bias2 are chosen to be 2 V, consistent with the follow-on experiments. When the driving voltage of the modulator changes from one state to the other, the intensity and phase of the output signal will change accordingly.

Figures 4(a)-4(f) and Figs. 5(a)-5(f) show the different transmission intensities and output phases of the Q_- and Q₊ modulator with 2 mm long phase shifters when the driving voltage state changes at 10 GHz modulation frequency for a working wavelength of 1550 nm. The phase shift φ_bias induced by the thermal tuning is set to make the modulator work on the quadrature point. In order to keep the PAM-4 modulator working in the linear region, the quadrature point is set approximately in the middle of PAM level ‘1’ and ‘2’. The driving voltages of the modulator are optimized to make the intervals of the PAM levels balanced. For the Q_- modulator, the phase shift φ_bias is 0.5115 $π$ .The driver voltage v₁ is 3.4, and v₂ is 1.709. The corresponding normalized intensities of four PAM levels ‘0’, ‘1’, ‘2’ and ‘3′ are 0.0410, 0.2062, 0.3713 and 0.5365, respectively. For the Q₊ modulator, the phase shift φ_bias is 1.5062 $π$ . The driving voltage parameters v₁ is 2.771, and v₂ is 1.7. The normalized intensities of four PAM levels ‘0’, ‘1’, ‘2’ and ‘3′ are 0.0592, 0.2166, 0.3740 and 0.5316, respectively.

Fig. 4 The transmission intensity and output phase variation versus time of Q_- modulator under the PAM levels’ switching from level (a) ‘3′ to ‘2’, (b) ‘3′ to ‘1’, (c) ‘3′ to ‘0’, (d) ‘2’ to ‘1’, (e) ‘2’ to ‘0’ and (f) ‘1’ to ‘0’.

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Fig. 5 The transmission intensity and output phase variation versus time of Q₊ modulator under the PAM levels’ switching from level (a) ‘3′ to ‘2’, (b) ‘3′ to ‘1’, (c) ‘3′ to ‘0’, (d) ‘2’ to ‘1’, (e) ‘2’ to ‘0’ and (f) ‘1’ to ‘0’.

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As shown in Figs. 4(a)-4(f), for the Q_- modulator, when the PAM level switches from level ‘3′ to ‘2’ and level ‘1’ to ‘0’, the output intensity reaches the maximum or minimum while the output phase reaches the maximum or minimum, synchronously. However, for the other four states of level-switching, the intensity reaches the minimum or maximum when the output phase reaches the maximum or minimum. The Q₊ modulator, on the other hand, has the opposite intensity and phase changing characteristics, as depicted in Figs. 5(a)-5(f).

From the frequency chirp definition, Eq. (6), the chirp parameter depends directly on the rate of change in intensity and output phase of the modulator. Using the intensity and output phase variation versus time, the chirp parameters of different PAM level’s switching for both the Q_- and Q₊ modulator can be calculated, as summarized in Table 1. When the PAM level changes from ‘2’ to ‘1’, the absolute value of the frequency chirp achieves the maximum value, resulted from the maximum output phase change and minimum intensity change. The Q_-modulator have four negative parameters and two positive parameters. On the contrary, the Q₊ modulator has four positive chirp parameters and two negative parameters. In other words, the Q_- PAM-4 modulator shows mostly negative chirp while the Q₊ PAM-4 modulator shows mostly positive chirp. Negative chirp can compensate the pulse broadening from the positive fiber dispersion, resulting in enhanced fiber bandwidth response. Positive chirp, on the other hand, increases the pulse broadening from the positive fiber dispersion, resulting in reduced fiber bandwidth.

Table 1. The chirp parameters of two-level switching for the Q_- and Q₊ modulator.

View Table

To analyze the relationship between the chirp parameters and the DC bias voltages of the modulator, the bias voltages v_bias1 and v_bias2 are synchronously changed from 0 V to 3 V. For both the Q_- and Q₊ modulator, the driving voltages and the phase shift φ_bias remain unchanged. As shown in Figs. 6(a) and 6(b), when the PAM level changes from ‘3′ to ‘2’ and ‘3′ to ‘1’, the chirp parameters are significantly changed with bias voltage variations for both two types of modulator. For the other four PAM level changes, the chirp parameters are slightly changed with bias voltage variations.

Fig. 6 The chirp parameters of the (a) Q_- modulator and (b) Q₊ modulator under different bias voltages (v_bias1 = v_bias2).

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3. Fabrication and experimental results

A top-view micrograph of a PAM-4 MZM device is shown in Fig. 7. It is fabricated on an 8-inch silicon-on-insulator (SOI) wafer with a 220-nm-thick top silicon layer and a 2-µm-thick buried dioxide layer at the Institute of Microelectronics (IME), Singapore. 248-nm deep ultraviolet photolithography and inductively coupled plasma etching are employed to form the silicon waveguide. A 1500-nm-thick silica layer is deposited on the silicon layer by plasma-enhanced chemical vapor deposition (PECVD) to minimize the optical absorption by metal and improve the thermal tuning efficiency. To compensate the possible phase difference between the two arms due to the imperfect fabrication, titanium nitride (TiN) heater is built on one arm of the device, with a length of 200 μm, a width of 2 μm and a thickness of 300 nm. The impedance of the CPW electrodes is designed to be 33 Ω with a thickness of 1 µm. To eliminate RF reflection, a 33-Ω terminator is integrated together with the device on-chip. The aluminum wires and pads are fabricated for connecting the microprobes and PN diodes.

Fig. 7 Experimental setup used to characterize the device (ASE: amplified spontaneous emission; LD: laser diode; PC: polarization controller; DUT: device under test; EDFA: erbium-doped fiber amplifier; OSA: optical spectrum analyzer; DCA: digital communication analyzer; LCA: lightwave component analyzer; PPG: pulse pattern generator; AMP: amplifier; PA: power attenuator; VOA: variable optical attenuator; RTO: real-time oscilloscope).

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Figure 7 shows the experimental setup for characterizing the transmission spectra, eye diagrams and BER performance of the modulator. The device is driven by two pseudo-random binary sequences (PRBS) with a length of 2¹⁵-1 generated by a multi-channel pulse pattern generator (SHF 12104A). The two PRBS sequences are amplified by a pair of 65 GHz electrical amplifiers and one of the binary electrical signals is attenuated by a 6-dB power attenuator. The peak-to-peak voltages of the two electrical signals are measured to be 3.4 V_pp and 1.7 V_pp, respectively. A DC bias voltage of 2 V is applied to the two arms of the modulator using bias tees. The resulted two electrical driving voltages are then applied to the modulator using a 67 GHz microprobe with GSGSG configuration. A fixed wavelength monochromatic light emitted from a tunable laser is coupled into the device with its polarization aligned with the TE mode of the silicon waveguide using a polarization controller. A heater is utilized to compensate the phase difference between the two arms of the modulator and bias the device at the quadrature point. The output light is amplified by an erbium-doped fiber amplifier (EDFA) and filter by a tunable optical filter with a passband of 1 nm before 0 km and 2 km transmission of G. 652 standard single-mode optical fiber (SSMF) with 17 ps/nm/km dispersion. A 65 GHz digital communication analyzer (Agilent 86100D) is used to obtain the eye diagrams.

Figure 8(a) is the electro-optic response of the modulator under a reverse bias voltage of 2.5 V. The electro-optic bandwidth of the modulator is 30.28 GHz. The optical spectra of the PAM-4 optical signal at the modulation rates of 25 Gbaud (50 Gbps) and 32 Gbaud (64 Gbps) for the Q_- and Q₊ modulator are presented in Figs. 8(b) and 8(c). The eye diagrams of the two bias types of the modulator at the modulation rates of 25 Gbaud and 32 Gbaud are shown in Figs. 9(a)-9(d) and Figs. 10(a)-10(d). The peak-to-peak voltages are adjusted to balance the intervals of the PAM levels. Figures 9(a)-9(c) show the eye diagrams of the Q₊ modulator and Q_- modulator at 25 Gbaud in back to back (B2B) transmission while Figs. 9(b)-9(d) are the corresponding transmission after 2 km of SSMF. The B2B eye diagrams show that the four levels of the modulated optical signals are clearly distinguishable with uniform intervals.

Fig. 8 (a) Measured frequency response of the modulator under a reverse bias voltage of 2.5 V, measured optical spectra of the PAM-4 optical signal at the modulation rates of (b) 25 Gbaud and (c) 32 Gbaud for the Q_- and Q₊ modulator.

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Fig. 9 The eye diagrams of the (a) Q₊ modulator in B2B transmission, (b) Q₊ modulator after 2 km of SSMF transmission, (c) Q_- modulator in B2B transmission, and (d) Q_- modulator after 2 km of SSMF transmission at the modulation rate of 25 Gbaud.

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Fig. 10 The eye diagrams of the (a) Q₊ modulator in B2B transmission, (b) Q₊ modulator after 2 km of SSMF transmission, (c) Q_- modulator in B2B transmission, and (d) Q_- modulator after 2 km of SSMF transmission at the modulation rate of 32 Gbaud.

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After 2 km of SSMF transmission, however, the eye diagram of the PAM-4 optical signal in Fig. 9(b) of the Q₊ modulator is degraded substantially because of the positive chirp as we discussed previously. In addition, the middle eye is visibly smaller than the other two eyes because of the negative chirp from switching PAM level ‘3′ to ‘2’ and ‘1’ to ‘0’ and the larger positive chirp switching from PAM level ‘2’ to ‘1’. The eye diagram in Fig. 9(d) of the Q_- modulator have a better performance attribute to its mainly negative chirp. The middle eye is visibly larger than the other two eyes because of the positive chirp from switching PAM level ‘3′ to ‘2’ and ‘1’ to ‘0’ and the larger negative chirp from switching PAM level ‘2’ to ‘1’.

The detected electrical signal is measured by a real-time oscilloscope (Tektronix DPO75902SX) with a sampling rate of 200 GS/s. Off-line processing is utilized to calculate the bit error rate of the signal. Figures 11(a) and 11(b) show the BER performance of the Q_- and Q₊ modulator at different modulation rates. The two types of the modulator have almost the same B2B BER performance which are 6.0 × 10⁻⁵ (25 Gbaud) and 1.0 × 10⁻⁴ (32 Gbaud) with a received power of 2 dBm below the 7% overhead (OH) hard-decision forward error correction (HD-FEC) threshold 3.8 × 10⁻³. At the same received power level, the BER of the Q₊ modulator after 2 km SSMF transmission are 9.15 × 10⁻⁴ (25 Gbaud) and 1.19 × 10⁻³ (32 Gbaud). The BER of the Q_- modulator after 2 km SSMF transmission are 1.55 × 10⁻⁵ (25 Gbaud) and 1.86 × 10⁻⁵ (32 Gbaud).

Fig. 11 BERs performance of the Q_- and Q₊ modulator at the modulation rates of (a) 25 Gbaud and (b) 32 Gbaud.

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As evidenced by the measured results, the BER of the 2 km transmission is degraded. At the same received power level, the BER of the Q_- modulator after 2 km transmission is surprisingly lower than the B2B BER. The power penalties of the Q_- modulator are −1.01 dB and −1.66 dB at the modulation rates of 25 Gbaud and 32 Gbaud for 2 km transmission at the BER of 5.0 × 10⁻⁴. As we explained in the analysis previously, the reason for this negative power penalty behavior is because of the mainly negative chirp of the PAM-4 modulator. For the transmission distance of 2 km, the broadening of the pulse will be compensated by the effect of negative chirp [24,29]. Positive chirp, on the other hand, will result in higher BER because it induces intensity pulse broadening which results in inter-symbol interference.

4. Conclusion

In conclusion, we analyzed the intrinsic frequency chirp of PAM-4 optical signal generated by driving one silicon DD-MZM. With the analytical model, we quantified the chirp parameters of this PAM-4 generation numerically. We found that the modulator operating at different quadrature points (Q_- and Q₊) resulted in different frequency chirp parameters. We calculated the frequency chirp parameters of the Q_- and Q₊ modulator for different PAM level’s switching. The Q_- modulator has mainly negative chirp parameters while Q₊ modulator has mainly positive chirp parameters. Using a real fabricated DD-MZM device, the eye diagrams of PAM-4 modulation at different Baud rates of 25 Gbaud and 32 Gbaud were presented. Benefiting from its negative frequency chirp, the Q_- modulator has little of power penalty in transmission with the positive fiber dispersion. Thus the Q_- PAM-4 modulator is suitable for the short-distance transmission over standard single mode fiber with positive fiber dispersion such as in the 1550 nm wavelength range.

Funding

National Key R&D Program of China (2017YFA0206402); National Science Foundation for Distinguished Young Scholars (61825504); National Natural Science Foundation of China (NSFC) (61575187, 61535002, 61505198, 61704168).

References

1. K. Padmaraju, N. Ophir, Q. Xu, B. Schmidt, J. Shakya, S. Manipatruni, M. Lipson, and K. Bergman, “Error-free transmission of microring-modulated BPSK,” Opt. Express 20(8), 8681–8688 (2012). [CrossRef] [PubMed]

2. P. Dong, L. Chen, C. Xie, L. L. Buhl, and Y. K. Chen, “50-Gb/s silicon quadrature phase-shift keying modulator,” Opt. Express 20(19), 21181–21186 (2012). [CrossRef] [PubMed]

3. K. Xu, L.-G. Yang, J.-Y. Song, Y. M. Chen, Z. Z. Cheng, C.-W. Chow, C.-H. Yeh, and H. K. Tsang, “Compatibility of silicon Mach-Zehnder modulators for advanced modulation formats,” J. Lightwave Technol. 31(15), 2550–2554 (2013). [CrossRef]

4. D. Korn, R. Palmer, H. Yu, P. C. Schindler, L. Alloatti, M. Baier, R. Schmogrow, W. Bogaerts, S. K. Selvaraja, G. Lepage, M. Pantouvaki, J. M. D. Wouters, P. Verheyen, J. Van Campenhout, B. Chen, R. Baets, P. Absil, R. Dinu, C. Koos, W. Freude, and J. Leuthold, “Silicon-organic hybrid (SOH) IQ modulator using the linear electro-optic effect for transmitting 16QAM at 112 Gbit/s,” Opt. Express 21(11), 13219–13227 (2013). [CrossRef] [PubMed]

5. X. Ruan, K. Li, D. J. Thomson, C. Lacava, F. Meng, I. Demirtzioglou, P. Petropoulos, Y. Zhu, G. T. Reed, and F. Zhang, “Experimental comparison of direct detection Nyquist SSB transmission based on silicon dual-drive and IQ Mach-Zehnder modulators with electrical packaging,” Opt. Express 25(16), 19332–19342 (2017). [CrossRef] [PubMed]

6. C. Xiong, D. M. Gill, J. E. Proesel, J. S. Orcutt, W. Haensch, and W. M. J. Green, “Monolithic 56 Gb/s silicon photonic pulse-amplitude modulation transmitter,” Optica 3(10), 1060–1065 (2016). [CrossRef]

7. IEEE, “200 Gb/s and 400 Gb/s ethernet task force,” IEEE P802.3bs 400GbE Task Force, 2017, available at http://www.ieee802.org/3/bs/index.html.

8. J. Wei, J. Ingham, D. Cunningham, R. Penty, and I. White, “Performance and power dissipation comparisons between 28 Gb/s NRZ, PAM, CAP and optical OFDM systems for data communication applications,” J. Lightwave Technol. 30(20), 3273–3280 (2012). [CrossRef]

9. M. Li, L. Wang, X. Li, X. Xiao, and S. Yu, “Silicon intensity Mach-Zehnder modulator for single lane 100 Gb/s applications,” Photon. Res. 6(2), 109–116 (2018). [CrossRef]

10. R. A. Soref, “The past, present and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006). [CrossRef]

11. B. Jalali, M. Paniccia, and G. Reed, “Silicon photonics,” IEEE Microw. Mag. 7(3), 58–68 (2006). [CrossRef]

12. H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, “An all-silicon Raman laser,” Nature 433(7023), 292–294 (2005). [CrossRef] [PubMed]

13. P. Dong, S. Liao, D. Feng, H. Liang, D. Zheng, R. Shafiiha, C.-C. Kung, W. Qian, G. Li, X. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Low Vpp, ultralow-energy, compact, high-speed silicon electro-optic modulator,” Opt. Express 17(25), 22484–22490 (2009). [CrossRef] [PubMed]

14. X. Xiao, H. Xu, X. Li, Z. Li, T. Chu, Y. Yu, and J. Yu, “High-speed, low-loss silicon Mach-Zehnder modulators with doping optimization,” Opt. Express 21(4), 4116–4125 (2013). [CrossRef] [PubMed]

15. R. Ding, Y. Liu, Y. Ma, Y. Yang, Q. Li, A. E.-J. Lim, G.-Q. Lo, K. Bergman, T. Baehr-Jones, and M. Hochberg, “High-speed silicon modulator with slow-wave electrodes and fully independent differential drive,” J. Lightwave Technol. 32(12), 2240–2247 (2014). [CrossRef]

16. E. Li, Q. Gao, R. T. Chen, and A. X. Wang, “Ultracompact silicon-conductive oxide nanocavity modulator with 0.02 lambda-cubic active volume,” Nano Lett. 18(2), 1075–1081 (2018). [CrossRef] [PubMed]

17. Y. Kang, H.-D. Liu, M. Morse, M. J. Paniccia, M. Zadka, S. Litski, G. Sarid, A. Pauchard, Y.-H. Kuo, H.-W. Chen, W. S. Zaoui, J. E. Bowers, A. Beling, D. C. McIntosh, X. Zheng, and J. C. Campbell, “Monolithic germanium/silicon avalanche photodiodes with 340 GHz gain–bandwidth product,” Nat. Photonics 3(1), 59–63 (2009). [CrossRef]

18. D. Gostimirovic and W. N. Ye, “Ultracompact CMOS-compatible optical logic using carrier depletion in microdisk resonators,” Sci. Rep. 7(1), 12603 (2017). [CrossRef] [PubMed]

19. X. Zheng, S. Lin, Y. Luo, J. Yao, G. Li, S. S. Djordjevic, J.-H. Lee, H. D. Thacker, I. Shubin, K. Raj, J. E. Cunningham, and A. V. Krishnamoorthy, “Efficient WDM laser sources towards Terabyte/s silicon photonic interconnects,” J. Lightwave Technol. 31(24), 4142–4154 (2013). [CrossRef]

20. C. Chen, X. Tang, and Z. Zhang, “Transmission of 56-Gb/s PAM-4 over 26-km single mode fiber using maximum likelihood sequence estimation,” in Optical Fiber Communication Conference (2015), paper Th4A.5. [CrossRef]

21. C. Tseng, J. Yeh, P. Chen, W. Chung, T. Yeh, K. Feng, M. Wu, and M. Lee, “A dual-drive PAM-4 Si Mach–Zehnder modulator for 50 Gb/s data transmission at 1550 nm wavelength,” in Conference on Lasers and Electro-Optics (2017), paper SM2O.7.

22. A. Samani, V. Veerasubramanian, E. El-Fiky, D. Patel, and D. V. Plant, “A silicon photonic PAM-4 modulator based on dual-parallel Mach-Zehnder interferometers,” IEEE Photonics J. 8(1), 1–10 (2016). [CrossRef]

23. B. Moeneclaey, G. Kanakis, J. Verbrugghe, N. Iliadis, W. Soenen, D. Kalavrouziotis, C. Spatharakis, S. Dris, X. Yin, P. Bakopoulos, E. Mentovich, H. Avramopoulos, and J. Bauwelinck, “A 64 Gb/s PAM-4 linear optical receiver,” in Optical Fiber Communication Conference (2015), paper M3C.5. [CrossRef]

24. L. Chen, P. Dong, and Y. K. Chen, “Chirp and dispersion tolerance of a single-drive push–pull silicon modulator at 28 Gb/s,” IEEE Photonics Technol. Lett. 24(11), 936–938 (2012). [CrossRef]

25. F. Koyama and K. Iga, “Frequency chirping in external modulators,” J. Lightwave Technol. 6(1), 87–93 (1988). [CrossRef]

26. Y. Wei, Y. Zhao, J. Yang, M. Wang, and X. Jiang, “Chirp characteristics of silicon Mach–Zehnder modulator under small-signal modulation,” J. Lightwave Technol. 29(7), 1011–1017 (2011). [CrossRef]

27. H. Kim and A. H. Gnauck, “Chirp characteristics of dual-drive Mach-Zehnder modulator with a finite DC extinction ratio,” IEEE Photonics Technol. Lett. 14(3), 298–300 (2002). [CrossRef]

28. R. Soref and B. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987). [CrossRef]

29. H. Yi, Q. Long, W. Tan, L. Li, X. Wang, and Z. Zhou, “Demonstration of low power penalty of silicon Mach-Zehnder modulator in long-haul transmission,” Opt. Express 20(25), 27562–27568 (2012). [CrossRef] [PubMed]

PAM Level	Driving State Q_-	Driving State Q₊	Chirp Q_-	Chirp Q₊
‘3′ →‘2’	‘01’ →‘00’	‘10’ →‘11’	2.1045	−2.2075
‘3′ →‘1’	‘01’→‘11’	‘10’ →‘00’	−2.0628	1.4778
‘3′ →‘0’	‘01’ →‘10’	‘10’ →‘01’	−0.6332	0.1878
‘2’ →‘1’	‘00’ →‘11’	‘11’ →‘00’	−3.7908	3.4485
‘2’ →‘0’	‘00’ →‘10’	‘11’ →‘01’	−0.8905	0.6438
‘1’ →‘0’	‘11’ →‘10’	‘00’ →‘01’	0.3671	−0.6773

Intrinsic chirp analysis of a single dual-drive silicon PAM-4 optical modulator

Abstract

1. Introduction

2. Analysis of the frequency chirp

2.1 Analytical model

2.2 Simulation and calculation of the frequency chirp

3. Fabrication and experimental results

4. Conclusion

Funding

References

Cited By

Figures (11)

Tables (1)

Equations (6)

Optics Express