Thermo-optic-based phase-shifter power dither for silicon IQ optical modulator bias-control technology

Honggang Chen; Bo Zhang; Leilei Hu; Yong Luo; Yi Hu; Xi Xiao; Xuerui Liang; Feng Li; Linfei Gan

doi:10.1364/OE.27.021546

1. Introduction

Recently, advanced modulation formats and polarization multiplexing techniques have been widely applied in coherent optical communication systems; thus, increasing attention has been paid to the in-phase quadrature (IQ) optical modulator based on the dual-parallel Mach–Zehnder modulator (DP_MZ) structure as a key optical device in coherent optical communication systems. At present, DP_MZ IQ optical modulators based on lithium niobate (LiNbO₃) [1] or indium phosphide (InP) are typically used as the external modulation unit in the transceiver module of coherent optical communication systems. The LiNbO₃ modulator has the advantages of the linear electro-optic modulation effect and excellent optical performance; thus, it is employed in ultra-long distance transmission optical networks. Owing to the material property of LiNbO₃, this modulator cannot be applied to the integration of the transmitter and receiver coherent optical devices, limiting its applications in small-package coherent optical modules, such as CFP2-analogue and digital coherent optics modules. The InP modulator is conveniently integrated and has a high modulation efficiency; thus, it is extensively used in coherent optical modules. However, its complex technology and high cost present problems. With the rapid development of silicon-based photonics technology and the existing complementary metal–oxide semiconductor technology, silicon photonics technology is becoming a leading candidate for optical interconnect applications. Compared with the LiNbO₃ modulator, the silicon optical modulator has the advantages of a smaller size, higher electronic–photonic integration density, lower fabrication costs, etc.; therefore, the silicon IQ optical modulator (SIQOM) has attracted increasing attention for coherent optical modules. Nevertheless, all the IQ optical modulators in practice must solve the problem of the bias closed-loop control, because the temperature, mechanical vibration, and other external environmental changes lead to the drift of the optimum bias voltage, resulting in the deterioration of the constellation diagram in the optical transmitter system [2]. Therefore, to stabilize the optimum bias voltage of the IQ optical modulator, it is necessary to introduce automatic bias control (ABC) technology. Most of the published studies have focused on the LiNbO₃ modulator ABC, and several ABC approaches, such as optical-power monitoring [3–6], square-wave dither detection [7,8], frequency-spectra monitoring [9–13], and dither-correlation detection [11–14], have been reported. Optical-power monitoring methods are classified into two types. The first type — non-dither signal methods — implement ABC by monitoring the output optical power of the IQ modulator [3–5]. The second type applies the orthogonal sine and cosine dither to the bias signal of the IQ modulator and achieves ABC by monitoring the variation of the output optical power [6]. However, the optical-power monitoring methods are sensitive to noise and the input optical power; thus, the precision of bias voltage control is limited. In the square-wave dither detection method [7,8], the optimum bias voltages of the IQ modulator are locked by detecting the output optical jitter amplitude of the time-domain waveform; nevertheless, the jitter amplitude is too low to achieve precise bias locking. Although frequency-spectra monitoring—a high-precision locking method—is widely implemented for bias closed-loop control, the large amount of computing overhead due to the fast Fourier transform (FFT) operation reduces the control speed [9–12]. Another method of frequency-spectra detection involves coherent detection [13]. However, a local oscillation is provided by an input optical signal in this method, which increases the IQ modulator loss. In the dither-correlation detection method, two sine voltage dithers with different low frequencies are applied to the channels I and Q biases, and the optimum bias voltages of the IQ modulator are achieved by searching for the minimized correlation results between the output signal and the dither signal [14,15]. Compared with the aforementioned methods, this method has a higher speed and lower computational cost. However, all of the foregoing methods are applied to the LiNbO₃ modulator. The modulation characteristic of the silicon optical modulator is completely different from those of the LiNbO₃ modulator. The phase-modulation mechanism of the silicon optical modulator is divided into two parts: the constant-phase offset based on the thermo-optic effect of the silicon material, which determines the operation point of the modulating signal, and the radiofrequency (RF) modulation phase shifter based on the plasma-dispersion effect of the silicon material. Both of these effects are nonlinear electro-optic effects. Moreover, the channels I and Q biases of the SIQOM have a thermal crosstalk effect, which makes it impossible to achieve bias locking through a simple control mode. Therefore, none of the mathematical models or algorithms mentioned in the above references can be applied precisely to the ABC for SIQOM. To our knowledge, there has been little detailed theoretical analysis of the SIQOM ABC model and algorithm.

Herein, a novel ABC scheme is proposed that applies the power dither to the thermal-optic phase shifter by using the orthogonal cross-correlation integral algorithm, which cannot only eliminate the nonlinear effect of the silicon optical modulator but also improve the anti-noise ability to achieve high-precision closed-loop control for the SIQOM. The remainder of this paper is organized as follows. Section 2 introduces the transfer function between the output optical signal and the electric field of the SIQOM. The theoretical feasibility of the proposed ABC scheme is confirmed via simulation. Section 3 describes the implementation of the verification platform of ABC and measurements of the vector amplitude error (EVM) jitters caused by this scheme in 128-Gb/s dual-polarization quadrature phase-shift keying (DP-QPSK) and single-polarization 16-quadrature amplitude modulation (SP-16-QAM) formats. The conclusions are presented in Section 4.

2. Theoretical analysis

2.1. Model derivation

Figure 1 shows the DP_MZ structure of the SIQOM, which consists of three Mach–Zehnder interferometer (MZI) elements: the channel-I MZI, channel-Q MZI, and channel-P MZI. The channel-I and channel-Q MZIs, i.e., the inner MZIs, comprise the thermo-optic phase shifters and RF-modulation phase shifters that have a MZI structure driven by a single-drive push–pull traveling-wave electrode [16,17]. In contrast, the channel-P MZI, i.e., the outer MZI, is the thermo-optic phase shifter and is usually biased at the quadrature(quad) point such that the channel-I and channel-Q signals are orthogonal. The bias voltages of the three MZI elements should be set at the appropriate points to ensure that the transmitted optical signal is in the optimum modulation state. In the QPSK and 16-QAM modulation formats, the bias points of channels I and Q should be set at the null point, meanwhile the bias point of channel P should be set at the quad point. Meanwhile, a non-return-to-zero (NRZ) or four-level pulse-amplitude modulation (PAM-4) waveform is applied to the RF modulator arms of channels I and Q, which can produce a QAM or binary phase-shift keying (BPSK) signal, and then a QPSK or 16-QAM modulation signal is constructed by the above pair of orthogonal QAM or BPSK signals. Next, we deduce the transfer function of the output photoelectric field of the SIQOM; the effect of the thermal crosstalk between the thermo-optical phase shifters is ignored in the derivation. According to the foregoing model structure, the output optical field of the SIQOM, assuming the ideal DP_MZ model, can be expressed as [12]

E_{OUT_I/Q} = \frac{1}{2} [E_{IN_I/Q} exp (- j \frac{Δ ψ_{RF_I/Q}}{2})+ E_{IN_I/Q} exp (j \frac{Δ ψ_{RF_I/Q}}{2})exp (j Δ ψ_{DC_I/Q})],

E_{OUT} = \frac{1}{2} [E_{OUT_I} + E_{OUT_Q} exp (j Δ ψ_{DC_P})],

where

E_{OUT_I/Q}

is the channel-I/Q MZI output optical field vector,

E_{OUT}

is the output optical field of the silicon IQ modulator,

E_{IN_I/Q}

is the channel-I/Q MZI input optical field vector, and

Δ ψ_{DC}_{_I/Q/P}

is the phase shift induced by the thermo-optic phase shifter of the channel I/Q/P. A temperature increase(ΔT) of the thermo-optic phase shifter can be expressed as

P = \frac{H}{τ} Δ T

[18], where P is the power of the heating electrode, H is the heat capacity and

τ

is the thermal time constant, meanwhile, the change in phase of the thermo-optic phase shifter can be expressed as

Δ ψ = \frac{2 π L}{λ} \frac{d n}{d T} Δ T

, where L is the length of the thermo-optic phase shifter, λ is the optical wavelength and

\frac{d n}{d T}

is the thermo-optic coefficient of silicon(1.87 × 10⁻⁴K⁻¹). so

Δ ψ = \frac{2 π L}{λ} \frac{d n}{d T} \frac{P τ}{H}

. From the above derivation one can argue that the phase shift of the thermo-optic phase shifter is proportional to the power of the heating electrode. Thus,

Δ ψ_{DC}_{_I/Q/P}

can be expressed as

Δ ψ_{D C_I / Q / P} = \frac{V_{I / Q / P_S E T}^{2} / R_{I / Q / P_S E T}}{V_{I / Q / P_π D C}^{2} / R_{I / Q / P_π D C}} π,

where

V_{I/Q/P_SET}

is the bias voltage of the channel-I/Q/P thermo-optic phase shifter,

R_{I/Q/P_SET}

is the resistance of the channel-I/Q/P thermo-optic phase shifter at the current bias voltage,

V_{I/Q/P_πDC}

is the half-wave voltage of the channel-I/Q/P thermo-optic phase shifter, and

R_{I/Q/P_πDC}

is the resistance of the channel-I/Q/P thermo-optic phase shifter at the half-wave voltage.

Δ ψ_{RF_I/Q}

is the phase shift of the channel I/Q induced by RF signals, and is determined by the driver mode of the silicon modulator. Three modulation mechanisms can be applied to the silicon modulator for RF modulation: carrier injection, accumulation, and depletion. The most commonly applied modulation mechanism in high-speed optical transfer is carrier depletion, as shown in Fig. 1. In the carrier-depletion silicon optical modulator, the depletion layer width of a PN is changed by the RF voltage signal, which causes a change in the free-carrier concentration inside the junction. This can achieve the refractive index modulation in the optical propagation region of the waveguide; thus, the phase of the optical field can be modulated. Hence,

Δ ψ_{R F_I / Q}

can be expressed as

Δ ψ_{R F_I / Q} = Δ ψ_{R F_I / Q_u p p e r} - Δ ψ_{R F_I / Q_l o w e r},

where

Δ ψ_{R F_I / Q_u p p e r}

and

Δ ψ_{R F_I / Q_l o w e r}

are the phase shifts of the channel I/Q induced by RF signals from the upper and lower arms, which can be expanded to a third-order polynomial with the channel-I/Q RF drive voltage (V_{I/Q_RFSET}), as follows [19]:

\begin{array}{l} Δ ψ_{NoneRF_I/Q_upper/lower} = φ_{RF_I/Q_1} + φ_{RF_I/Q_2} V_{P N} + φ_{RF_I/Q_3} V_{P N}^{2} + φ_{RF_I/Q_4} V_{P N}^{3}, \\ Δ ψ_{RF_I/Q_upper} = φ_{RF_I/Q_1} + φ_{RF_I/Q_2} (V_{P N} - \frac{1}{2} V_{I/Q_RFSET}) + φ_{RF_I/Q_3} (^{V_{P N} - \frac{1}{2} V_{I/Q_RFSET}) 2} + φ_{RF_I/Q_4} (^{V_{P N} - \frac{1}{2} V_{I/Q_RFSET}) 3} - Δ ψ_{NoneRF_I/Q_upper/lower}, \end{array}

Δ ψ_{RF_I/Q_lower} = φ_{RF_I/Q_1} + φ_{RF_I/Q_2} (V_{P N} + \frac{1}{2} V_{I/Q_RFSET}) + φ_{RF_I/Q_3} {(V_{P N} + \frac{1}{2} V_{I/Q_RFSET})}^{2} + φ_{RF_I/Q_4} {(V_{P N} + \frac{1}{2} V_{I/Q_RFSET})}^{3} - Δ ψ_{NoneRF_I/Q_upper/lower} .

Here,

Δ ψ_{NoneRF_I/Q_upper/lower}

are the initialization phase shifts of the channel-I/Q upper and lower arms without the RF signal, and

φ_{RF_I/Q_1,2,3,4}

represent the modulation coefficients of the channel-I/Q upper and lower arms. Hence,

Δ ψ_{R F_I / Q}

can be simplified as follows:

Δ ψ_{RF_I/Q} = (φ_{RF_I/Q_2} + 2 φ_{RF_I/Q_3} V_{P N} - 3 φ_{RF_I/Q_4} V_{P N}^{2}) V_{I/Q_RFSET} - \frac{1}{4} φ_{RF_I/Q_4} V_{I/Q_RFSET}^{3} .

For simplicity, assume that

Δ ψ_{RF_I/Q} = \frac{f (V_{I/Q_RFSET})}{f (V_{I/Q_πRF})} π

, where

V_{I/Q_πRF}

is the half-wave voltage of the channel-I/Q MZI RF element,

f (V_{I/Q_πRF})

is the phase shift induced by the MZI RF element when the RF signal amplitude of the channel I/Q is

V_{I/Q_πRF}

, and

f (V_{I/Q_RFSET})

is the phase shift induced by the RF signal of the channel I/Q, which is an odd function of V_{I/Q_RFSET}; thus the output optical field of the channel-I/Q MZI can be rewritten as

E_{OUT_I/Q} = E_{IN_I/Q} \frac{\exp [- j \frac{π f (V_{I/Q_RFSET})}{2 f (V_{I/Q_πRF})}] + \exp [j (\frac{π f (V_{I/Q_RFSET})}{2 f (V_{I/Q_πRF})} + π \frac{V_{I/Q_SET}^{2}}{V_{I/Q_πDC}^{2}})]}{2} .

By combining Eqs. (1) and (6), the output optical power of the SIQOM (

P_{OUT}

) can be expressed as

\frac{P_{OUT}}{P_{max}} = \frac{1}{8} {\begin{cases} 2 + \cos {π [\frac{V_{I_SET}^{2} / R_{I_SET}}{V_{I_πDC}^{2} / R_{I_πDC}} + \frac{f (V_{I_RFSET})}{f (V_{I_πRF})}]} + \cos {π [\frac{V_{Q_SET}^{2} / R_{Q_SET}}{V_{Q_πDC}^{2} / R_{Q_πDC}} + \frac{f (V_{Q_RFSET})}{f (V_{Q_πRF})}]} + \cos {π [\frac{V_{P_SET}^{2} / R_{P_SET}}{V_{P_πDC}^{2} / R_{P_πDC}} + \frac{f (V_{I_RFSET})}{2 f (V_{I_πRF})} - \frac{f (V_{Q_RFSET})}{2 f (V_{Q_πRF})}]} + \ \\ + \cos {π [\frac{V_{Q_SET}^{2} / R_{Q_SET}}{V_{Q_πDC}^{2} / R_{Q_πDC}} + \frac{V_{P_SET}^{2} / R_{P_SET}}{V_{P_πDC}^{2} / R_{P_πDC}} + \frac{f (V_{I_RFSET})}{2 f (V_{I_πRF})} + \frac{f (V_{Q_RFSET})}{2 f (V_{Q_πRF})}]} + \cos {π [\frac{V_{P_SET}^{2} / R_{P_SET}}{V_{P_πDC}^{2} / R_{P_πDC}} - \frac{V_{I_SET}^{2} / R_{I_SET}}{V_{I_πDC}^{2} / R_{I_πDC}} - \frac{f (V_{I_RFSET})}{2 f (V_{I_πRF})} - \frac{f (V_{Q_RFSET})}{2 f (V_{Q_πRF})}]} + \ \\ \cos {π [\frac{V_{Q_SET}^{2} / R_{Q_SET}}{V_{Q_πDC}^{2} / R_{Q_πDC}} - \frac{V_{I_SET}^{2} / R_{I_SET}}{V_{I_πDC}^{2} / R_{I_πDC}} + \frac{V_{P_SET}^{2} / R_{P_SET}}{V_{P_πDC}^{2} / R_{P_πDC}} - \frac{f (V_{I_RFSET})}{2 f (V_{I_πRF})} + \frac{f (V_{Q_RFSET})}{2 f (V_{Q_πRF})}]} \end{cases}} .

where

P_{max}

is the maximum output optical power when the bias points of the channel I/Q/P are set to the maximum point. As indicated by Eq. (7), the RF signal applied to the modulator changes the output optical power. Because ABC is usually achieved by a low-frequency photo-detector(PD) built-in the DP_MZ SIQOM and the modulation frequency of the optical signal is significantly larger than the bandwidth of the PD, the output photocurrent of the PD is proportional to the mean value of the time-varying optical power [12]. Additionally, the RF signals applied to channels I and Q usually are bipolar such that

〈 \sin [\frac{f (V_{I/Q_RFSET})}{f (V_{I/Q_πRF})} π] 〉 = 〈 \sin [\frac{f (V_{I/Q_RFSET})}{2 f (V_{I/Q_πRF})} π] 〉 = 0,

where <·> represents the time-varying integral function. Because the adjustment range of the bias voltage is small when ABC is implemented in the SIQOM, the variation in the heating electrode resistance caused by the bias voltage is also small; hence,

R_{I/Q/P_SET} \approx R_{I/Q/P_π,DC}

. Accordingly, the normalized output optical current of the PD can be simplified as

\frac{I_{OUT}}{I_{\max}} = \frac{1}{8} [\begin{array}{l} 2 + \cos (π \frac{V_{I_SET}^{2}}{V_{I_πDC}^{2}}) 〈 \cos [\frac{f (V_{I_RFSET})}{f (V_{I_πRF})} π] 〉 + \cos (π \frac{V_{Q_SET}^{2}}{V_{Q_πDC}^{2}}) 〈 \cos [\frac{f (V_{Q_RFSET})}{f (V_{Q_πRF})} π] 〉 + \ \\ {\cos (π \frac{V_{P_SET}^{2}}{V_{P_πDC}^{2}}) + \cos (π \frac{V_{P_SET}^{2}}{V_{P_πDC}^{2}} + π \frac{V_{Q_SET}^{2}}{V_{Q_πDC}^{2}}) + \cos (π \frac{V_{P_SET}^{2}}{V_{P_πDC}^{2}} - π \frac{V_{I_SET}^{2}}{V_{I_πDC}^{2}}) + \cos (π \frac{V_{P_SET}^{2}}{V_{P_πDC}^{2}} + π \frac{V_{Q_SET}^{2}}{V_{Q_πDC}^{2}} - π \frac{V_{I_SET}^{2}}{V_{I_πDC}^{2}})} 〈 \cos [\frac{f (V_{I_RFSET})}{2 f (V_{I_πRF})} π] 〉 〈 \cos [\frac{f (V_{Q_RFSET})}{2 f (V_{Q_πRF})} π] 〉 \end{array}] .

Equation (9) can be decomposed into three components (excluding the constant component). The factors of channels I, Q, and P are expressed as

\frac{I_{OUT_I}}{I_{\max}}

,

\frac{I_{OUT_Q}}{I_{\max}}

, and

\frac{I_{OUT_P}}{I_{\max}}

, respectively. Moreover, we can use the following equations for simplification:

\frac{I_{OUT}}{I_{\max}} = \frac{1}{4} + \frac{I_{OUT_I}}{I_{\max}} + \frac{I_{OUT_Q}}{I_{\max}} + \frac{I_{OUT_P}}{I_{\max}},

F_{I} (V_{I_RFSET}) = 〈 \cos [\frac{f (V_{I_RFSET})}{f (V_{I_πRF})} π] 〉,

F_{Q} (V_{Q_RFSET}) = 〈 \cos [\frac{f (V_{Q_RFSET})}{f (V_{Q_πRF})} π] 〉,

F_{P} (V_{I_RFSET}, V_{Q_RFSET}) = 〈 \cos [\frac{f (V_{I_RFSET})}{f (V_{I_πRF})} \frac{π}{2}] 〉 〈 \cos [\frac{f (V_{Q_RFSET})}{f (V_{Q_πRF})} \frac{π}{2}] 〉,

\frac{I_{OUT}}{I_{\max}} = \frac{1}{8} {\begin{cases} 2 + \cos (π \frac{V_{I_SET}^{2}}{V_{I_πDC}^{2}}) F_{I} (V_{I_RFSET}) + \cos (π \frac{V_{Q_SET}^{2}}{V_{Q_πDC}^{2}}) F_{Q} (V_{Q_RFSET}) + F_{P} (V_{I_RFSET}, V_{Q_RFSET}) \ \\ [\cos (π \frac{V_{P_SET}^{2}}{V_{P_πDC}^{2}}) + \cos (π \frac{V_{P_SET}^{2}}{V_{P_πDC}^{2}} + π \frac{V_{Q_SET}^{2}}{V_{Q_πDC}^{2}}) + \cos (π \frac{V_{P_SET}^{2}}{V_{P_πDC}^{2}} - π \frac{V_{I_SET}^{2}}{V_{I_πDC}^{2}}) + \cos (π \frac{V_{P_SET}^{2}}{V_{P_πDC}^{2}} + π \frac{V_{Q_SET}^{2}}{V_{Q_πDC}^{2}} - π \frac{V_{I_SET}^{2}}{V_{I_πDC}^{2}})] \end{cases}} .

The foregoing derivations are based on the ideal DP_MZ SIQOM; however, in practice, DP_MZ SIQOMs have finite extinction ratios (ERs) and chirp parameters of the channel-I/Q RF modulation signals (ɑ_I/Q), which are determined by the imbalanced plasma-dispersion effect of the channel-I/Q upper and lower arms. Accordingly, the ERs of the channel I/Q/P and ɑ_I/Q can be expressed as follows [20]:

E R_{m} = {(\frac{1 + G_{m}}{1- G_{m}})}^{2}, m \in {I, Q, P},

α_{m} = \frac{Δ ψ_{R F_m_upper} + Δ ψ_{R F_m_l o w e r}}{Δ ψ_{R F_m_u p p e r} - Δ ψ_{R F_m_l o w e r}}, m \in {I, Q},

where G_I/Q/P represent the electric-field split ratios of the channel-I/Q/P MZIs, which are determined by the asymmetry loss of the upper and lower arms of the MZIs. Therefore, Eqs. (1a)-(1b) and (11a)-(11b) can be rewritten as follows [12,20]:

Fig. 1 Model diagram of the DP_MZ SIQOM.

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E_{OUT_I/Q} = E_{IN_I/Q} \frac{\exp [- j \frac{π f (V_{I/Q_RFSET}) (1 + α_{I/Q})}{2 f (V_{I/Q_πRF})}] + G_{I/Q} \exp [j (\frac{π f (V_{I/Q_RFSET}) (1 - α_{I/Q})}{2 f (V_{I/Q_πRF})} + π \frac{V_{I/Q_SET}^{2}}{V_{I/Q_πDC}^{2}})]}{1 + G_{I/Q}},

E_{OUT} = \frac{1}{1 + G_{P}} [E_{OUT_I} + G_{P} E_{OUT_Q} exp (j π \frac{V_{P_SET}^{2}}{V_{P_πDC}^{2}})],

\frac{I_{OUT_I}}{I_{\max}} = \frac{1}{[{({1+G}_{P})}^{2} {({1+G}_{I})}^{2}]} [1 + G_{I}^{2} {+2G}_{I} \cos (π \frac{V_{I_SET}^{2}}{V_{I_πDC}^{2}}) F_{I} (V_{I_RFSET})],

\frac{I_{OUT_Q}}{I_{\max}} = \frac{G_{P}^{2}}{[{({1+G}_{P})}^{2} {({1+G}_{Q})}^{2}]} [1 + G_{Q}^{2} {+2G}_{Q} \cos (π \frac{V_{Q_SET}^{2}}{V_{Q_πDC}^{2}}) F_{Q} (V_{Q_RFSET})],

\frac{I_{OUT_P}}{I_{\max}} = \frac{2 G_{P}}{{({1+G}_{P})}^{2} ({1+G}_{I}) ({1+G}_{Q})} [\begin{array}{l} F_{P} (V_{I_RFSET} (1 + α_{I}), V_{Q_RFSET} (1 + α_{Q})) \cos (π \frac{V_{P_SET}^{2}}{V_{P_πDC}^{2}}) + \ \\ G_{I} F_{P} (V_{I_RFSET} (1 - α_{I}), V_{Q_RFSET} (1 + α_{Q})) \cos (π \frac{V_{P_SET}^{2}}{V_{P_πDC}^{2}} - π \frac{V_{I_SET}^{2}}{V_{I_πDC}^{2}}) + \ \\ G_{Q} F_{P} (V_{I_RFSET} (1 + α_{I}), V_{Q_RFSET} (1 - α_{Q})) \cos (π \frac{V_{P_SET}^{2}}{V_{P_πDC}^{2}} +π \frac{V_{Q_SET}^{2}}{V_{Q_πDC}^{2}}) + \ \\ G_{I} G_{Q} F_{P} (V_{I_RFSET} (1 - α_{I}), V_{Q_RFSET} (1 - α_{Q})) \cos (π \frac{V_{P_SET}^{2}}{V_{P_πDC}^{2}} + π \frac{V_{Q_SET}^{2}}{V_{Q_πDC}^{2}} - π \frac{V_{I_SET}^{2}}{V_{I_πDC}^{2}}) \end{array}] .

Because the RF signal is usually applied to the MZI in the push–pull mode, ɑ_I/Q ≈0 [21]. Equation (12b)-(12e) indicates that ɑ_I/Q does not affect the optimum point locking of the channel I/Q/P when we apply the low-frequency PD for the DP_MZ SIQOM ABC. Furthermore, the optimum bias voltages of the channel I/Q are dependent on ER_I/Q/P, and the optimum bias voltage of channel P is independent of ER_I/Q/P. For eliminating the bias offset errors of the channel I/Q induced by the ERs, the null/null/quad bias voltages of the non-ideal SIQOM channel I/Q/P are as follows:

V_{I_null} \approx \sqrt{2 k_{I} + 1 + \arcsin (\frac{G_{P} (1 + G_{I}) (〈 \cos [\frac{f (V_{Q_RFSET})}{f (V_{Q_πRF})} \frac{π}{2}] 〉 - G_{Q} 〈 \cos [\frac{f (V_{Q_RFSET})}{f (V_{Q_πRF})} \frac{π}{2}] 〉)}{(1 + G_{Q}) G_{I} 〈 \cos [\frac{f (V_{I_RFSET})}{f (V_{I_πRF})} \frac{π}{2}] 〉 π})} V_{I_πDC},

V_{Q_null} \approx \sqrt{2 k_{Q} + 1 + arc \sin (\frac{(1 + G_{Q}) (G_{I} 〈 \cos [\frac{f (V_{I_RFSET})}{f (V_{I_πRF})} \frac{π}{2}] 〉 - 〈 \cos [\frac{f (V_{I_RFSET})}{f (V_{I_πRF})} \frac{π}{2}] 〉)}{G_{P} G_{Q} (1 + G_{I}) 〈 \cos [\frac{f (V_{Q_RFSET})}{f (V_{Q_πRF})} \frac{π}{2}] 〉 π})} V_{Q_πDC},

V_{P_quad} = \sqrt{(k_{P} + \frac{1}{2})} V_{P_πDC},

where k_I, k_Q, and k_P are positive integers and V_{I_null}, V_{Q_null}, and V_{P_quad} are the optimum bias voltages of the channel-I, -Q, and -P MZIs, respectively, for the non-ideal SIQOM. Because G_I/Q/P ≈1 (and assuming

\cos [\frac{f (V_{I_RFSET})}{f (V_{I_πRF})} \frac{π}{2}] \approx \cos [\frac{f (V_{Q_RFSET})}{f (V_{Q_πRF})} \frac{π}{2}]

), Eq. (13a)-(13c) can be simplified as follows:

V_{I_null} \approx \sqrt{2 k_{I} + 1 + arc \sin (\frac{2 (1 - G_{Q})}{(G_{Q} + 1) π})} V_{I_πDC},

V_{Q_null} \approx \sqrt{2 k_{Q} + 1 + arc \sin (\frac{2 (G_{I} - 1)}{(G_{I} + 1) π})} V_{Q_πDC},

V_{P_quad} = \sqrt{(k_{P} + \frac{1}{2})} V_{P_πDC} .

In practical, the bias offset errors caused by the ERs of the inner MZIs of the channel I/Q can be calibrated via an initialization test. In the following simulation, we assume k_I/Q/P = 0 and G_I/Q = 1 for simplicity; thus, $V_{I/Q_null} = V_{I/Q_πDC}$ and $V_{P_quad} = \frac{\sqrt{2}}{2} V_{P_πDC}$ , and we could analyze the ideal DP_MZ SIQOM to substitute for the non-ideal DP_MZ SIQOM.

2.2. Simulation analysis of algorithm

The proposed ABC scheme can be implemented in two steps. First, the rough optimum bias voltages of channels I, Q, and P with no dither signal are identified. Second, the finely optimum bias voltages of channels I, Q, and P are determined and locked using the proposed scheme. In the initialization step, by scanning the bias voltages of channels I, Q, and P, and detecting the output optical power of the SIQOM synchronously, the rough optimum bias voltages are obtained. As indicated by Eq. (10), the output optical power is independent of the channel-P bias voltage if the channel-I MZI or the channel-Q MZI is biased at the null point. Thus, the rough optimum bias voltages of channels I and Q can be determined via the minimum ER method. To determine the rough optimum bias voltage of channel Q, the channel-I MZI is biased at the maximum point, and the channel-P bias voltages are scanned in a whole-wave period to obtain the ER at each bias voltage of channel Q, i.e., the ratio of the maximum output optical power to the minimum output optical power. Thus, we determine that the bias voltage corresponding to the minimum ER is the rough optimum bias voltage of channel Q. The rough optimum bias voltage of channel I can be determined in the same way as that of channel Q. To determine the rough optimum bias voltage of channel P, the channel-I and channel-Q MZIs are biased at the maximum point simultaneously, and the channel-P bias voltages are scanned in a whole-wave period. Then, the maximum and minimum output optical power corresponding to the bias voltage of channel P is recorded as V₁ and V₂, respectively. Hence, the rough optimum bias voltage of channel P is $\sqrt{(V_{1}^{2} + V_{2}^{2}) / 2}$ .

In the closed-loop control step, we recommend applying a sine power dither signal to the channel-I and channel-Q bias voltages of the SIQOM when channels I and Q are locked, respectively. The power dither signals can be expressed as

V_{I / Q_D ither} = \sqrt{V_{I/Q_SET}^{2} + P_{Dither} \sin (w_{I / Q} t)},

where P_Dither and w_I/Q are the amplitude and frequency of the power dither signal, respectively.

Because the lock method of the channel-Q bias voltage is the same as that of the channel-I bias voltage, we only present the bias voltage lock of channel I in the following analysis, for simplicity. Figure 2(a) shows the 1st harmonic component of the PD output signal as a function of the channel-I bias voltage with different channel-P bias voltages when a conventional sine voltage dither with a frequency of 210 Hz and an amplitude of 0.04 V_{I_πDC} is applied to channel I. Figure 2(b) shows the 1st harmonic component of the PD output signal as a function of the channel-I bias voltage with different channel-P bias voltages when a sine power dither with a frequency of 210 Hz and an amplitude equivalent to that of the sine voltage dither signal is applied to channel I. In the simulation diagram, $Δ V_{I / Q}$ and $Δ V_{P}$ can be expressed as follows:

Fig. 2 Simulated curves of the 1st harmonic component (210 Hz) versus the channel-I bias and channel-P bias when the (a) sine voltage dither and (b) sine power dither are applied to channel I.

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Δ V_{I / Q} = V_{I / Q_S E T} - V_{I / Q_πDC},

Δ V_{P} = V_{P_S E T} - \frac{\sqrt{2}}{2} V_{P_πDC} .

As shown in the Figs. 2(a) and 2(b), if the conventional voltage-dither is applied to the channel I bias, the 1st harmonic component of the PD signal is not minimum when the channel I is biased at the optimum point; nevertheless, the optimum bias voltage of channel I can be obtained accurately by searching the minimum value of the PD signal 1st harmonic component when the sine power-dither method is used. This means that the power-dither method could eliminate the deviation between the null point and the optimum bias point compared with the conventional voltage-dither method. It is important to note that the bias voltage of channel I correspond to the minimum value of the 1st harmonic component gradually deviates from the optimum bias voltage if the bias error of channel P exceeds a certain threshold value. Fortunately, the aforementioned condition can be avoided by identifying the optimum bias voltage of channel P beforehand.

In this study, a pair of orthogonal reference functions with the same frequency as the power dither signal is constructed to stabilize the optimum bias voltage of channel I:

I_{R F E 1} = \sin (w_{I} (t + Δ t)),

I_{R E F 2} = \cos (w_{I} (t + Δ t)),

where

Δ t

is the delay of the PD output signal relative to the reference functions. We use the foregoing reference functions and the PD output signal to perform integral operations, and the results of the operations can be expressed as follows:

C_{I}_{_S I N} = \int_{0}^{T} (F_{I} (V_{I_R F S E T}) \cos (π \frac{{(\sqrt{V_{I_SET}^{2} + P_{D i t h e r} \sin (w_{I} t)})}^{2}}{V_{I_πDC}^{2}}) + {\begin{cases} \cos [π \frac{V_{P_SET}^{2}}{V_{P_πDC}^{2}} - π \frac{{(\sqrt{V_{I_SET}^{2} + P_{D i t h e r} \sin (w_{I} t)})}^{2}}{V_{I_πDC}^{2}}] + \ \\ \cos [π \frac{V_{P_SET}^{2}}{V_{P_πDC}^{2}} +π \frac{V_{Q_SET}^{2}}{V_{Q_πDC}^{2}} - π \frac{{(\sqrt{V_{I_SET}^{2} + P_{D i t h e r} \sin (w_{I} t)})}^{2}}{V_{I_πDC}^{2}}] \end{cases}} F_{P} (V_{I_RFSET}, V_{Q_RFSET})) I_{R E F 1} d t,

C_{I}_{_C O S} = \int_{0}^{T} (F_{I} (V_{I_R F S E T}) \cos (π \frac{{(\sqrt{V_{I_SET}^{2} + P_{D i t h e r} \sin (w_{I} t)})}^{2}}{V_{I_πDC}^{2}}) + {\begin{cases} \cos [π \frac{V_{P_SET}^{2}}{V_{P_πDC}^{2}} - π \frac{{(\sqrt{V_{I_SET}^{2} + P_{D i t h e r} \sin (w_{I} t)})}^{2}}{V_{I_πDC}^{2}}] + \ \\ \cos [π \frac{V_{P_SET}^{2}}{V_{P_πDC}^{2}} +π \frac{V_{Q_SET}^{2}}{V_{Q_πDC}^{2}} - π \frac{{(\sqrt{V_{I_SET}^{2} + P_{D i t h e r} \sin (w_{I} t)})}^{2}}{V_{I_πDC}^{2}}] \end{cases}} F_{P} (V_{I_RFSET}, V_{Q_RFSET})) I_{R E F 2} d t,

where T is the integral time of

C_{I}_{_S I N}

and

C_{I}_{_C O S}

. We find that

C_{I}_{_S I N} = 0

and

C_{I}_{_C O S} = 0

in Eq. (18a) and (18b) if V_{I_SET} = V_{I_πDC}; accordingly, the simulated curves of the in-phase integral error (

C_{I}_{_S I N}

) and quadrature integral error (

C_{I}_{_C O S}

) at different bias voltages of the channel I are obtained. The intersection point of these two curves is the optimum bias voltage of the channel I. Figure 3(a) shows the simulation results for the amplitude spectra of the PD output signal in cases where the deviation of the channel-I bias relative to the optimum point is –0.01 V_π, 0, and 0.01 V_π under different noise spectral densities (–20, –30, and –40 dBm/Hz). Figure 3(b) shows the simulation results for the in-phase integral error (

C_{I}_{_S I N}

) and quadrature integral error (

C_{I}_{_C O S}

) of the 1st harmonic component. The simulation parameters are as follows: P_Dither = 0.04 V_{I_πDC}, the frequency of the power dither signal is 210 Hz, the number of sampled data is 20480, and the sampling frequency is 215.04 KHz, which ensures that the reference values I_REF1 and I_REF2 are the same for each integral period. As shown in Figs. 3(a) and 3(b), the 1st harmonic component of the PD output signal is almost submerged in the noise spectra when the noise spectral density is –20 dBm/Hz; however, we could still confirm the intersection point of the

C_{I}_{_S I N}

and

C_{I}_{_C O S}

curves accurately, which is the optimum bias voltage according to the proposed orthogonal integral locking algorithm. Therefore, the proposed algorithm performs better than the FFT algorithm under conditions with a large amount of noise, and the operational complexity is lower than the FFT algorithm. Additionally, because the thermo-optic phase shifters of channel I and channel Q are close to each other in the silicon modulator chip, thermal crosstalk occurs between the two channels if the bias voltage of either channel changes. For eliminating the effect of thermal crosstalk between channels I and Q, the iterative locking method must be performed to ensure that both channels are at the null point. For example, if we set the bias voltage of channel I to the null point and adjust that of channel Q to the null point, we can judge whether the bias voltage of channel I is deviant, which confirms that the bias voltages of the channels are both at the null point. Figure 4(a) shows the simulation curves of the channel-I bias jitter caused by the power dither signal with different power dither amplitudes, as well as the maximum distinguishable noise spectral density of the PD output signal when the locked bias error of channel I is reduced to 0.01 V_{I_πDC} with different power dither amplitudes. The amplitude of the power dither signal is proportional to the phase jitter caused by the dither signal and the maximum distinguishable noise spectral density; thus, suppressing the noise power of the PD output signal can decrease the amplitude of the power dither signal in the ABC scheme, which reduces the optical signal–noise ratio penalty factor due to the ABC scheme. Figure 4(b) shows the simulation curves of

C_{I}_{_S I N}

and

C_{I}_{_C O S}

with RF signals of various amplitudes. The RF signal amplitude is inversely proportional to the slopes of

C_{I}_{_S I N}

and

C_{I}_{_C O S}

, and the slopes of

C_{I}_{_S I N}

and

C_{I}_{_C O S}

are reversed if the RF signal amplitude is

V_{I_πRF}

.

Fig. 3 (a) Simulated curves of the normalized amplitude spectra with different noise spectral densities after the sine power dither is applied to channel I. (b) Simulated curves of the channel-I in-phase integral error ( $C_{I_S I N}$ ) and quadrature integral error ( $C_{I_C O S}$ ) with different noise spectral densities after different voltages are applied to channel I.

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Fig. 4 (a) Simulated curves of the maximum noise power distinguished by the proposed ABC scheme with different power dither amplitudes applied to the channel I bias and the bias deviation degree relative to the optimum point with different power dither amplitudes applied to the channel-I bias. (b) Simulated curves of $C_{I}_{_S I N}$ and $C_{I}_{_C O S}$ with different RF signal amplitudes.

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When the quad point voltage of channel P is locked, we recommend applying power dither signals with different frequencies to the bias voltages of channel I and channel Q simultaneously. Meanwhile, a pair of orthogonal reference functions whose frequency is the sum of the channel-I and channel-Q dither signals is constructed:

P_{R F E 1} = \sin (2 π (f_{I} + f_{Q}) (t + Δ t)),

P_{R F E 2} = \cos (2 π (f_{I} + f_{Q}) (t + Δ t)) .

Because the factors of channels I and Q are close to zero when the bias voltages of channels I and Q are at the null point, we use the orthogonal reference functions $P_{R F E 1}$ and $P_{R F E 2}$ with the output signal of the PD to perform the cross-correlation integral operations, which only need to consider the factor of channel P. The integral results can be expressed as follows:

C_{P_S I N} = \int_{0}^{T} F_{P} (V_{I_RFSET}, V_{Q_RFSET}) \cos [π \frac{{(\sqrt{V_{Q_S E T}^{2} + P_{D i t h e r} \sin (w_{Q} t)})}^{2}}{V_{Q_π D C}^{2}} + π \frac{V_{P_S E T}^{2}}{V_{P_π D C}^{2}} - π \frac{{(\sqrt{V_{I_S E T}^{2} + P_{D i t h e r} \sin (w_{I} t)})}^{2}}{V_{I_π D C}^{2}}] P_{R E F 1} d t,

C_{P_C O S} = \int_{0}^{T} F_{P} (V_{I_RFSET}, V_{Q_RFSET}) \cos [π \frac{{(\sqrt{V_{Q_S E T}^{2} + P_{D i t h e r} \sin (w_{Q} t)})}^{2}}{V_{Q_π D C}^{2}} + π \frac{V_{P_S E T}^{2}}{V_{P_π D C}^{2}} - π \frac{{(\sqrt{V_{I_S E T}^{2} + P_{D i t h e r} \sin (w_{I} t)})}^{2}}{V_{I_π D C}^{2}}] P_{R E F 2} d t .

Clearly, $C_{P}_{_S I N}$ and $C_{P}_{_C O S}$ are equal to zero if $V_{P_S E T} = \frac{\sqrt{2}}{2} V_{P_πDC}$ . Figure 4(a) presents simulation curves of the PD amplitude spectra value at 820 Hz versus the bias voltage of channel P under different channel-I and -Q bias voltages, where the bias voltages of channels I and Q apply the sine voltage dither with frequencies of 210 and 610 Hz, respectively, and an amplitude of 0.04 V_{I/Q_πDC}. As shown in Fig. 5(a), the PD amplitude spectra value at 820 Hz is related to the current bias voltage of channels I and Q when the bias voltage of channel P is at the optimum point. Figure 5(b) presents simulation curves of the PD amplitude spectra value at 820 Hz versus the bias voltage of channel P under different channel-I and -Q bias voltages. The bias voltages of channels I and Q apply the proposed sine power dither. As shown in Fig. 5(b), the PD amplitude spectra at the sum frequency vanishes when the bias voltage of channel P is optimum, which is independent of the channel-I and channel-Q current bias voltages.

Fig. 5 Simulated curves of the sum frequency harmonic component (820 Hz) with different channel-I, -Q, and -P biases when (a) the sine voltage dither is applied to channel I and (b) the sine power dither is applied to channel I.

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Because the amplitude spectra value at 820 Hz is significantly smaller than the 1st harmonic component when the bias voltages of channels I and Q are close to the optimum voltages, more sampled data is needed for locking the quad point voltage of the channel P compared with the channel I/Q. In our simulation, the sampling number is 204800 for channel-P bias locking, at which the noise spectral density is one tenth of the channel-I bias lock at the same noise power. Figure 6(a) shows the simulation results for the PD signal amplitude spectra with different noise spectral densities, i.e., –30, –40, and –50 dBm/Hz, when the bias voltage of channel P is higher than, lower than, and equal to the optimum bias voltage. Figure 6(b) shows the simulation results for the sum frequency component in-phase integral error $C_{P}_{_S I N}$ and quadrature integral error $C_{P}_{_C O S}$ . Clearly, the channel-P bias voltage corresponding to the intersection of the two curves is the optimum point, even if the sum frequency component is submerged in the noise spectra. Thus, it can be concluded that the anti-noise performance of the orthogonal locking algorithm is better than that of the FFT algorithm for channel-P bias locking. Figure 7(a) shows the simulation curves of the channel-I/Q bias jitter caused by the power dither signal with different power dither amplitudes, as well as the maximum distinguishable noise spectral density of the PD output signal when the locked bias error of channel P is reduced to 0.01 V_{P_πDC} with different power dither amplitudes. Figure 7(b) shows the simulation curves of $C_{P}_{_S I N}$ and $C_{P}_{_C O S}$ with different RF signal amplitudes. It is easily determined that the RF signal amplitude is inversely proportional to the slopes of $C_{P}_{_S I N}$ and $C_{P}_{_C O S}$ , as in the case of $C_{I}_{_S I N}$ and $C_{I}_{_C O S}$ ; however, the RF signal amplitude is proportional to the output optical power of the SIQOM and the modulation ER. Although increasing the RF signal amplitude improves the modulation performance of the SIQOM, the locking sensitivity of the channel-P bias voltage is decreased. Therefore, in practice, locking sensitivity for ABC is one of the considerations to determine the RF signal amplitude.

Fig. 6 (a)Simulated curves of the normalized amplitude spectra with different noise spectral densities after sine power dithers are applied to channels I and Q, (b) Simulated curves of the channel-P in-phase integral error ( $C_{P_S I N}$ ) and quadrature integral error ( $C_{P_C O S}$ ) with different noise spectral densities after different voltages are applied to channel P.

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Fig. 7 (a)Simulated curve of the maximum noise spectral density distinguished by the proposed ABC scheme with different power dither amplitudes applied to the channel-I and channel-Q biases simultaneously, and simulated curve of the bias deviation degree relative to the optimum point caused by the power dither signal. (b) Simulated curves of $C_{P}_{_S I N}$ and $C_{P}_{_C O S}$ with different RF signal amplitudes.

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3. Experimental setup and results

To evaluate the bias-point locking performance of the proposed ABC scheme, we constructed an experimental setup. As shown in Fig. 8, we used an integrable tunable laser assembly (ITLA) with a wavelength of 1550 nm as a light source. The output light was divided into two paths by a beam splitter (BS). One path was applied to the SIQOM as an input light source, and the other path, as a local light source, was provided to an integrated coherent receiver (ICR). The bias voltage and power dither signal of channels I and Q were supplied by a digital-to-analog converter (DAC) built into the ABC control unit. RF modulated signals for the SIQOM were applied by a quad-channel 32-Gb/s pulse-code generator (PPG, SHF12104A) that produced NRZ signals. Two NRZ signals were combined to produce a PAM-4 signal using twin DAC assemblies (SHF88041B). The signals were amplified by a high-speed driver (SHF 58214a) to apply RF pins in the SIQOM. The photocurrent of the PD built-in modulator was amplified by a transimpedance amplifier (TIA) in the ABC control unit, and the amplified signal was separated in two ways: sampling by an analog-to-digital converter (ADC) to implement ABC or sampling by an oscilloscope for data analysis. The modulated optical signal was amplified by erbium-doped fiber amplifiers (EDFAs) and converted into quad-channel RF signals by the ICR. The quad-channel RF signals were analyzed using a high-speed real-time oscilloscope (DPO73324DX) with a 33-GHz bandwidth.

Fig. 8 Experimental setup for implementing the ABC scheme in 128-Gb/s DP-QPSK and SP-16-QAM modulation.

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Figure 9(a) shows the amplitude spectra measurement curves of the PD output signal at different channel-I bias voltages after the bias voltage of channel I was applied by the sine power dither with a frequency of 210 Hz and dither amplitude of $0 .04 V_{I_πDC}$ . Figure 9(b) shows the measurement curves of $C_{I}_{_S I N}$ and $C_{I}_{_C O S}$ after the application of different bias voltages to channel I. There were 10000 sampled data, and the sampling frequency was 210 kHz for locking the bias voltage of channel I. Additionally, it was necessary to ensure that the delay difference between the PD signal and the integral reference functions was constant in the measurement, for guaranteeing that the slopes of $C_{I}_{_S I N}$ and $C_{I}_{_C O S}$ remained unchanged. The slopes of $C_{I}_{_S I N}$ and $C_{I}_{_C O S}$ were constantly kept orthogonal by adjusting the delay difference in the initial test. The bias voltage corresponding to the intersection of $C_{I}_{_S I N}$ and $C_{I}_{_C O S}$ , which was the optimum bias voltage of channel I, is clearly shown in Fig. 9(b). The measured results agree well with the channel-I simulation results presented in Section 2.2.

Fig. 9 Measurements of (a) amplitude spectra versus the channel-I bias after the sine power dither was applied to channel I and (b) the channel-I in-phase integral error ( $C_{I_S I N}$ ) and quadrature integral error ( $C_{I_C O S}$ ).

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Figure 10(a) shows the amplitude spectra measurement curves of the PD output signal at different channel-P bias voltages after the bias voltage of sine power dithers was applied to channels I and Q with frequencies of 210 and 610 Hz, respectively, and a dither amplitude of $0 .04 V_{I_πDC}$ . Figure 10(b) shows the measurement curves of $C_{P}_{_S I N}$ and $C_{P}_{_C O S}$ after different bias voltages were applied to channel P. There were 100000 sampled data, and the sampling frequency was 820 kHz for locking the bias voltage of channel P. As shown in Fig. 10(b), the bias voltage corresponding to the intersection of $C_{P}_{_S I N}$ and $C_{P}_{_C O S}$ was the optimum bias voltage of channel P, in agreement with the channel-P simulation results presented in Section 2.2.

Fig. 10 Measurements of (a) the normalized amplitude spectra with different channel-P biases after channel I and channel Q applied the sine power dither and (b) the channel-P in-phase integral error ( $C_{P_S I N}$ ) and quadrature integral error ( $C_{P_C O S}$ ).

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Using the test platform, we evaluated the performance of the proposed ABC algorithm in the 128-Gb/s DP-QPSK and SP-16-QAM modulation formats. Figures 11(a)-11(h) show the constellation diagrams of the QPSK signal in eight different non-ideal states after the bias voltages of the channel I/Q/P deviated from the optimum voltage. Figure 11(i) shows the constellation diagram of the QPSK signal when ABC was on. The measurements indicate that the proposed ABC algorithm corrected the arbitrary bias drift relative to the optimum point of channels I, Q, and P.

Fig. 11 Constellation diagrams of the optical signal in QPSK modulation after the application of different bias voltages to channels I/Q/P. (a) Bias voltages of channels I, Q, and P were 0.95 V_π, 0.95 V_π, and 0.95 V_π/2, respectively; (b) bias voltages of channels I, Q, and P were 1.05 V_π, 0.95 V_π, and 0.95 V_π/2, respectively; (c) bias voltages of channels I, Q, and P were 0.95 V_π, 1.05 V_π, and 0.95 V_π/2, respectively; (d) bias voltages of channels I, Q, and P were 1.05 V_π, 1.05 V_π, and 0.95 V_π/2, respectively; (e) bias voltages of channels I, Q, and P were 0.95 V_π, 0.95 V_π, and 1.05 V_π/2, respectively; (f) bias voltages of channels I, Q, and P were 0.95 V_π, 0.95 V_π, and 1.05 V_π/2, respectively; (g) bias voltages of channels I, Q, and P were 1.05 V_π, 1.05 V_π, and 1.05 V_π/2, respectively; (h) bias voltages of channels I, Q, and P were 1.05 V_π, 0.95 V_π, and 1.05 V_π/2, respectively; (i) ABC was on.

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Figure 12 shows the curves of the EVM versus time in the QPSK and 16-QAM modulation formats when the ABC was on and off. The constellation diagram noticeably deteriorated, and the measured EVM increased. Nevertheless, the constellation diagram was stabilized under the optimum condition. The measured EVMs for the QPSK and 16-QAM modulation formats were less than 14% and 10%, respectively, when the ABC was on, and the EVM jitter caused by the proposed ABC scheme was <1% in our experiment.

Fig. 12 Measured EVM performance in (a) QPSK modulation and (b) 16-QAM modulation when the ABC was on and off.

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Figure 13(a) shows the EVM performance of 128 Gb/s optical DP-QPSK signal under a temperature-varying condition when ABC was on and off. In our experiment, the variation range of temperature was from 20 °C to 60 °C, and the increasing speed of temperature was set at 1 °C/min. It could be clearly observed that the constellation diagram of optical DP-QPSK signal became seriously degraded when ABC was off, however, the constellation diagram remained stable in the ABC-on case. The results show that the proposed ABC scheme provides a real time tracking ability in the temperature-varying condition. Moreover, we evaluated the performance of the proposed ABC against wavelength change, and the EVMs as a function of optical wavelength when ABC was on and off were shown in Fig. 13(b). We measured the wavelength spanning from 1531.12 nm to 1567.13 nm with an interval of 4 nm, and it could be clearly observed that there was an evidently degeneration of the EVM performance when ABC was off. The most likely reason is that the half-wave voltage of the thermo-optic phase shifter changes with wavelength, which leads to the current bias voltages of channels I, Q, and P deviate to the optimum bias points. However, the measured EVM performance maintained below 15% in the wavelength-varying condition when ABC was on, therefore, it can be concluded that the bias errors introduced by the optical wavelength change can be corrected by the proposed ABC. Furthermore, to investigate the optical signal-to-noise ratio(OSNR) penalty caused by the proposed ABC scheme, we measured the bit error ratio (BER) of both 128 Gb/s optical DP-QPSK signal and optical SP-16QAM signal versus OSNR when the proposed ABC scheme and the manual bias control method were implemented, which is shown in Fig. 13(c). The OSNR for the BER of 2 × 10⁻² is 12.37 dB and 12.21 dB under the proposed ABC and the manual bias control conditions respectively. The above result shows that the OSNR penalty induced by the ABC is 0.16 dB. Finally, the performances of the proposed ABC scheme are summarized in Table 1. Compared with other ABC schemes, the proposed ABC scheme and the dither-correlation scheme have a higher accuracy and lower complexity simultaneously. In addition, to achieve a same performance, the required dither amplitude for the proposed ABC scheme is lower than the dither-correlation scheme. This means that the phase jitter caused by the proposed ABC scheme is lower than the dither-detection scheme.

Fig. 13 Measured EVM performance versus temperature(a) and wavelength(b) when ABC was on and off, and the BER performance of 128 Gb/s optical DP-QPSK signal(c) when the proposed ABC and the manual control mode were applied respectively.

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Table 1. Comparison of the proposed ABC scheme and other ABC schemes

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4. Conclusions

A novel ABC scheme for the SIQOM was developed via theoretical derivation. This scheme applies two different sine power dithers to the thermo-optic phase shifter of channels I and Q to eliminate the deviation of the optimum point due to the nonlinear electro-optic effect of the silicon material. Cross-correlation integral operation between a pair of orthogonal reference functions and the PD output signal is implemented using the orthogonal integral lock algorithm to obtain two error amplitude curves. The cross-point corresponding to the bias voltage of these curves is identified as the optimum voltage, which is independent of the bias voltages of other channels. A theoretical simulation and experimental results not only verified the accuracy of the photoelectric model of the SIQOM but also confirmed that the proposed ABC scheme is independent of the modulation format. The performance of the ABC scheme was experimentally verified on a test platform using 128-Gb/s DP-QPSK and SP-16-QAM signals. The high-sensitivity, high-efficiency ABC scheme can be widely implemented in silicon optical coherent modules for medium-to-long-distance transmission and data-center interconnection applications.

Funding

National Key Research and Development Project of China (2018YFB2201102).

References

1. T. Fujita, T. Kawanishi, T. Sakamoto, K. Higuma, S. Mori, J. Ichikawa, T. Miyazaki, and M. Izutsu, “80 Gb/s Optical Quadrature P Shift Keying Modulation Using an Integrated LiNbO3 Modulator,” in Conference on Lasers & Electro-optics(CLEO 2006), paper CFP4.

2. J. P. Salvestrini, L. Guilbert, M. Fontana, M. Abarkan, and S. J. J. L. T. Gille, “Analysis and Control of the DC Drift in LiNbO3-Based Mach–Zehnder Modulators,” J. Lightwave Technol. 29(10), 1522–1534 (2011). [CrossRef]

3. K. Sekine, C. Hasegawa, N. Kikuchi, and S. Sasaki, “A Novel Bias Control Technique for MZ Modulator with Monitoring Power of Backward Light for Advanced Modulation Formats,” in Optical Fiber Communication and the National Fiber Optic Engineers Conference 2007 (Optical Society of America, 2007), paper OTuH5. [CrossRef]

4. M.-H. Kim, B.-M. Yu, and W.-Y. Choi, “A Mach-Zehnder Modulator Bias Controller Based on OMA and Average Power Monitoring,” IEEE opticals Technology Letters 29(23), 2043–2046 (2017). [CrossRef]

5. P. S. Cho, J. B. Khurgin, and I. Shpantzer, “Closed-Loop Bias Control of Optical Quadrature Modulator,” IEEE opticals Technology Letters 18(21), 2209–2211 (2006). [CrossRef]

6. H. Kawakami, T. Kobayashi, M. Yoshida, T. Kataoka, and Y. Miyamoto, “Auto bias control and bias hold circuit for IQ-modulator in flexible optical QAM transmitter with Nyquist filtering,” Opt. Express 22(23), 28163–28168 (2014). [CrossRef] [PubMed]

7. T. Yoshida, T. Sugihara, K. Uto, H. Bessho, K. Sawada, K. Ishida, K. Shimizu, and T. Mizuochi, “A study on automatic bias control for arbitrary optical signal generation by dual-parallel Mach-Zehnder modulator,” in 36th European Conference and Exhibition on Optical Communication, (2010), pp. 1–3. [CrossRef]

8. H. S. Chung, S. H. Chang, J. H. Lee, and K. Kim, “Field trial of automatic bias control scheme for optical IQ modulator and demodulator with directly detected 112 Gb/s DQPSK Signal,” Opt. Express 21(21), 24962–24968 (2013). [CrossRef] [PubMed]

9. T. Gui, C. Li, Q. Yang, X. Xiao, L. Meng, C. Li, X. Yi, C. Jin, and Z. Li, “Auto bias control technique for optical OFDM transmitter with bias dithering,” Opt. Express 21(5), 5833–5841 (2013). [CrossRef] [PubMed]

10. L. L. Wang and T. Kowalcyzk, “A Versatile Bias Control Technique for Any-Point lock in Lithium Niobate Mach–Zehnder Modulators,” J. Lightwave Technol. 28(11), 1703–1706 (2010). [CrossRef]

11. H. Kawakami, E. Yoshida, and Y. Miyamoto, “Auto Bias Control Technique Based on Asymmetric Bias Dithering for Optical QPSK Modulation,” J. Lightwave Technol. 30(7), 962–968 (2012). [CrossRef]

12. M. Sotoodeh, Y. Beaulieu, J. Harley, and D. L. McGhan, “Modulator Bias and Optical Power Control of Optical Complex E-Field Modulators,” J. Lightwave Technol. 29(15), 2235–2248 (2011). [CrossRef]

13. X. Zhu, Z. Zheng, C. Zhang, L. Zhu, Z. Tao, and Z. Chen, “Coherent Detection-Based Automatic Bias Control of Mach–Zehnder Modulators for Various Modulation Formats,” J. Lightwave Technol. 32(14), 2502–2509 (2014). [CrossRef]

14. X. Li, L. Deng, X. Chen, M. Cheng, S. Fu, M. Tang, and D. Liu, “Modulation-format-free and automatic bias control for optical IQ modulators based on dither-correlation detection,” Opt. Express 25(8), 9333–9345 (2017). [CrossRef] [PubMed]

15. X. Li, L. Deng, X. Chen, H. Song, Y. Liu, M. Cheng, S. Fu, M. Tang, M. Zhang, and D. Liu, “Arbitrary Bias Point Control Technique for Optical IQ Modulator Based on Dither-Correlation Detection,” J. Lightwave Technol. 36(18), 3824–3836 (2018). [CrossRef]

16. 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 opticals Technology Letters 24(11), 936–938 (2012). [CrossRef]

17. J. Wang, L. Zhou, H. Zhu, R. Yang, Y. Zhou, L. Liu, T. Wang, and J. J. P. R. Chen, “Silicon high-speed binary phase-shift keying modulator with a single-drive push–pull high-speed traveling wave electrode,” Photon. Res. 3(3), 58–62 (2015). [CrossRef]

18. N. C. Harris, Y. Ma, J. Mower, T. Baehr-Jones, D. Englund, M. Hochberg, and C. Galland, “Efficient, compact and low loss thermo-optic phase shifter in silicon,” Opt. Express 22(9), 10487–10493 (2014). [CrossRef] [PubMed]

19. Y. Zhou, L. Zhou, F. Su, X. Li, and J. Chen, “Linearity Measurement and Pulse Amplitude Modulation in a Silicon Single-Drive Push–Pull Mach–Zehnder Modulator,” J. Lightwave Technol. 34(14), 3323–3329 (2016). [CrossRef]

20. A. Napoli, M. M. Mezghanni, S. Calabro, R. Palmer, and B. J. J. L. T. Spinnler, “Digital Pre-Distortion Techniques for Finite Extinction Ratio IQ-Mach-Zehnder Modulators,” J. Lightwave Technol. 6(1), 1–8 (2017).

21. Y. Wei, Y. Zhao, J. Yang, M. Wang, and X. J. J. L. T. Jiang, “Chirp Characteristics of Silicon Mach–Zehnder Modulator Under Small-Signal Modulation,” J. Lightwave Technol. 29(7), 1011–1017 (2011). [CrossRef]

ABC scheme type	Lock accuracy	Complexity	OSNR penalty(dB)	Dither amplitude	Modulation format	Ref.
Optical power monitor(LiNbO₃)	low	low	0.5	none	43-Gbit/s RZ-DQPSK	[3]
Synchronization detection(LiNbO₃)	medium	medium	0.3	10%V_π	16,32,64QAM(21 Gbaud)	[6]
Square-wave dither detection(LiNbO₃)	medium	low	<0.5	5%V_π	112Gbit/s DC-DQPSK	[8]
FFT(LiNbO₃)	medium	high	0.2	10%V_π	12.5 Gbit/s QPSK-OFDM,	[9]
Dither-correlation(LiNbO₃)	high	medium	<0.2	6.6%V_π	17.9 Gbit/s 16QAM-OFDM	[14], [15]
Cross-correlation integral and power-dither(silicon)	high	medium	<0.2	4%V_π	128 Gbit/s DP-QPSK/SP-16-QAM	This work

Thermo-optic-based phase-shifter power dither for silicon IQ optical modulator bias-control technology

Abstract

1. Introduction

2. Theoretical analysis

2.1. Model derivation

2.2. Simulation analysis of algorithm

3. Experimental setup and results

4. Conclusions

Funding

References

Cited By

Figures (13)

Tables (1)

Equations (40)

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