Self-referenced electro-optic response measurement of dual-parallel Mach-Zehnder modulators employing single-tone level control and low-frequency bias swing

Ying Xu; Mengke Wang; Yutong He; Chaoyu Gu; Zhiyao Zhang; Yali Zhang; Shangjian Zhang; Yong Liu

doi:10.1364/OE.454101

1. Introduction

Thanks to the unique structure of two parallel sub-MZMs nested on two arms of a parent-MZM, dual-parallel Mach-Zehnder modulators (DPMZM) can achieve various advanced modulation formats including single sideband (SSB), double sideband (DSB), carrier-suppression single sideband (CS-SSB), carrier-suppression double sideband (CS-DSB), etc. Hence, they are widely used in optical fiber communication and microwave photonic systems, such as quadrature amplitude modulation (QAM) [1,2], photonic arbitrary waveform generation [3,4], optical frequency combs [5,6], optoelectronic oscillator [7,8], and highly linear radio over fiber system [9,10] and so on. Modulation depth and half-wave voltage of DPMZMs are two vital electro-optic characteristic parameters for the evaluation of device performance and system applications, especially for high frequency applications.

In the past decades, there are many methods proposed to obtain the electro-optic frequency responses of Mach-Zehnder type modulators [11–21]. The early optical method performs spectral analysis on the optical modulated signal of the MZM with the help of an optical spectrum analyzer (OSA), and extracts the modulation depth and the half-wave voltage of the MZM from the amplitude ratio of different order sidebands [12,13]. However, the OSA-based method requires the MZM to operate at the maximum or minimum transmission points (MATP, MITP) to intensify the 2^nd-order sideband or the 1^st-order sideband, respectively, since the optical modulated spectrum depends on the bias phases of MZMs. In the case of DPMZM under test, the operation of MATP and MITP requires very careful and complicated optimization of three bias voltages, in order to eliminate the bias dependence of the optical modulated spectrum. Besides, the OSA-based method features a resolution of about 2.5 GHz (0.02nm@1550nm), which greatly limits the measurable starting frequency and frequency resolution.

In contrast, the frequency resolution can be largely improved up to Hz level by transforming the measurement from optical domain to electrical domain, in which an electro-optic swept frequency method is widely used with the help of a microwave network analyzer (MNA) [16,17]. The MNA-based measurement is realized by measuring the relative response of an optoelectronic transceiver link including the DPMZM and an assistant PD, where the frequency response of the DPMZM is calibrated by deducting the frequency response of the PD from the cascaded response. Besides the extra optical-to-electrical calibration, the MNA-based method requires an assistant PD whose operation bandwidth must cover the measuring frequency range. Meanwhile, it is hardly qualified for the absolute frequency response measurement such as modulation depth and half-wave voltage. It should be pointed out that the half-wave voltage represents not only the modulation efficiency itself, but also the relative change of the modulation efficiency. Therefore, the relative frequency response can be obtained from the half-wave voltage, but not vice versa.

Recently, we demonstrated a calibration-free method for directly characterizing the frequency response of high-speed DPMZMs based on two-tone and bias-swing modulation [21]. Modulation depth and half-wave voltages are extracted for different modulation frequencies from two sub-MHz heterodyne beating signals generated from the two-tone and bias-swing modulated optical signal, which is free of extra calibration of the PD. Nevertheless, the two-tone method often suffers from low mixing efficiency and signal-to-noise ratio in the measurement. Moreover, the two-tone microwave driving condition with close frequency spacing results in a bulky measurement system.

In this work, we propose a self-referenced method for extracting modulation depth and half-wave voltage of a high-speed DPMZM based on single-tone level control and low-frequency bias swing. In our scheme, a single-tone driving signal is applied on one of the sub-MZMs as well as a low-frequency bias signal on the parent-MZM. The output optical modulated signal is detected by the on-site monitor PD of the DPMZM. The single-tone driving signal and the low-frequency bias signal applied to the DPMZM are mixed after photodetection. The low-frequency signal is then generated in the electrical domain. The functional relationship between the desired low-frequency amplitude and the single-tone driving level is investigated and established, from which the modulation depth and half-wave voltage are extracted with the help of regression analysis. Theoretical description and proof-of-concept experiment are performed to confirm the proposed method. For accuracy, the experiment results are compared with those obtained with the two-tone method and the swept frequency method. Since only low-frequency detection is required, our method enables self-referenced measurement of DPMZM with only one microwave source and an on-site PD, free of any wideband PD and extra calibration for the PD, which is promising for the on-line and on-chip characterization of high-speed DPMZMs.

2. Operation principle

As shown in Fig. 1, an optical carrier output from a laser diode (LD) is injected into the DPMZM under test, and driven by a single-tone microwave signal v₁(t) = V₁sinω₁t at the RF port of sub-MZM1. Then, the optical carrier is modulated by a low-frequency signal v_b(t) = V_bsinω_bt at the bias port of parent-MZM. Assuming the incident optical field of DPMZM is with the amplitude of E₀ and the angular frequency of ω₀, the output modulated optical field from the DPMZM can be expressed as

(1)$${E_{DPMZM}}(t )= {E_0}{e^{j{\omega _0}t}}\left[ {\left( {{e^{j\frac{{{m_1}}}{2}\sin {\omega_1}t}} + {\gamma_1}{e^{ - j\frac{{{m_1}}}{2}\sin {\omega_1}t + j{\varphi_{b1}}}}} \right) + {\gamma_3}{e^{j{m_b}\sin {\omega_b}t + j{\varphi_{b3}}}}({1 + {\gamma_2}{e^{j{\varphi_{b2}}}}} )} \right]$$

where γ₁, γ₂ and γ₃ are the splitting ratios of the sub-MZM1, the sub-MZM2 and the parent-MZM. The bias phases φ_b₁, φ_b₂ and φ_b₃ are controlled by the bias voltages V_b₁, V_b₂ and V_b₃ of DPMZM. m₁ and m_b are the modulation depths introduced by v₁(t) and v_b(t), and m₁ is defined as

(2)$${m_1} = \frac{{\pi {V_1}}}{{{V_{\pi 1}}}} = \frac{{\pi \sqrt {2{P_1}{Z_L}} }}{{{V_{\pi 1}}}}$$

where V_π₁ is the half-wave voltage of the sub-MZM1, V₁ and P₁ are the driving amplitude and power of the microwave signal applied on the sub-MZM1, and Z_L is the input characteristic impedance. The modulated optical signal is detected by the on-site monitor PD. With the help of Jacobi-Anger expansion, the generated photocurrent signal can be expressed as

(3)$$i(t )= RE_0^2\left\{ \begin{array}{l} 1 + \gamma_1^2 + \gamma_3^2 + \gamma_2^2\gamma_3^2 + 2{\gamma_2}\gamma_3^2\cos {\varphi_{b2}} + 2{\gamma_1}\sum\limits_{n ={-} \infty }^{ + \infty } {{J_n}({{m_1}} )\cos ({n{\omega_1}t - {\varphi_{b1}}} )} \\ \textrm{ + 2}{\gamma_3}\sum\limits_{p ={-} \infty }^{ + \infty } {\sum\limits_{q ={-} \infty }^{ + \infty } {{J_p}\left( {\frac{{{m_1}}}{2}} \right){J_q}({{m_b}} )\cos [{({p{\omega_1} + q{\omega_b}} )t + q\pi - {\varphi_{b3}}} ]} } \\ \textrm{ + 2}{\gamma_2}{\gamma_3}\sum\limits_{p ={-} \infty }^{ + \infty } {\sum\limits_{q ={-} \infty }^{ + \infty } {{J_p}\left( {\frac{{{m_1}}}{2}} \right){J_q}({{m_b}} )\cos [{({p{\omega_1} + q{\omega_b}} )t + q\pi - ({{\varphi_{b2}} + {\varphi_{b3}}} )} ]} } \\ \textrm{ + 2}{\gamma_1}{\gamma_3}\sum\limits_{p ={-} \infty }^{ + \infty } {\sum\limits_{q ={-} \infty }^{ + \infty } {{J_p}\left( {\frac{{{m_1}}}{2}} \right){J_q}({{m_b}} )\cos [{({p{\omega_1} + q{\omega_b}} )t - {\varphi_{b1}}\textrm{ + }{\varphi_{b3}}} ]} } \\ \textrm{ + 2}{\gamma_1}{\gamma_2}{\gamma_3}\sum\limits_{p ={-} \infty }^{ + \infty } {\sum\limits_{q ={-} \infty }^{ + \infty } {{J_p}\left( {\frac{{{m_1}}}{2}} \right){J_q}({{m_b}} )\cos [{({p{\omega_1} + q{\omega_b}} )t - {\varphi_{b1}}\textrm{ + }({{\varphi_{b3}}\textrm{ + }{\varphi_{b2}}} )} ]} } \end{array} \right\}$$

where R is the responsivity of the monitor PD, and J_n(·) (n = 0, ±1, ±2, …) is the nth-order Bessel function of the first kind. From Eq. (3), the amplitude of the desired low-frequency component ω_b is

(4)$$A({{\omega_b};{m_1}} )= 4RE_0^2{\gamma _3}\left[ {\begin{array}{c} {{\gamma_1}{\gamma_2}\sin ({{\varphi_{b1}} - {\varphi_{b2}} - {\varphi_{b3}}} )- \sin {\varphi_{b3}}}\\ { - {\gamma_2}\sin ({{\varphi_{b2}} + {\varphi_{b3}}} )+ {\gamma_1}\sin ({{\varphi_{b1}} - {\varphi_{b3}}} )} \end{array}} \right]{J_1}({{m_b}} )\cdot {J_0}\left( {\frac{{{m_1}}}{2}} \right)$$

Fig. 1. Schematic diagram of the proposed method, LD: laser diode, DPMZM: dual-parallel Mach-Zehnder modulator, MPD: monitor photodetector, MS: Microwave source, FG: function generator, ESA: electrical spectrum analyzer.

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It can be seen from Eq. (4) that when the low-frequency bias signal is kept with a constant frequency and amplitude, the desired low-frequency component A(ω_b; m₁) changes with the modulation depth m₁, and the corresponding the microwave driving power P₁. In most cases, the modulation depth of the DPMZM is set as m < 3. Therefore, with the help of polynomial expansion, Eq. (4) can be approximately expressed as

(5)$$\sqrt {\frac{{A({{\omega_b};{m_1}} )}}{{A({{\omega_b};0} )}}} \approx 1 - \frac{{m_1^2}}{{32}}\begin{array}{cc} {}&{} \end{array}({{m_1} < 3} )$$

where the desired low-frequency component A(ω_b; m₁) and A(ω_b; 0) represent the cases that the DPMZM is under single-tone driving level with the power of P₁ and zero, respectively. The half-wave voltage can be therefore extracted as follows

(6)$$\sqrt {\frac{{A({{\omega_b};{m_1}} )}}{{A({{\omega_b};0} )}}} = 1 - \frac{{{Z_L}{\pi ^2}}}{{16V_{\pi 1}^2}}{P_1}$$

It can be seen from Eqs. (5) and (6) that the responsivity R of PD is cancelled out by the normalized amplitude A(ω_b; m₁)/A(ω_b; 0), and our measurement is free of calibrating the roll-off responsivity of PD, since the photodetection is performed at the fixed low-frequency ω_b. Eventually, our method realizes self-referenced frequency response measurement of high-speed DPMZMs, including the modulation depth and the half-wave voltage, with the aid of variable single-tone modulation and fixed low-frequency detection. It is also worthy to notice that the sub-MZM2 can be similarly measured by switching the microwave signal to the RF port of the sub-MZM2 while keeping the low-frequency signal to the bias port of the parent-MZM.

It can be seen from Eq. (4) that our method only depends on the normalized amplitude of A(ω_b; m₁)/A(ω_b; 0). Hence, it is independent of the three bias voltages of the DPMZM. In practice, the measurement will benefit from a better signal-to-noise ratio (SNR) of the desired low-frequency component. Therefore, it will be helpful to set the bias phases φ_b₁, φ_b₂ and φ_b₃ close to 0, 0 and π/2 by adjusting the bias voltages V_b₁, V_b₂ and V_b₃ of the DPMZM, respectively. Firstly, the DPMZM is under null modulation, and the output optical intensity of DPMZM is observed and intensified by adjusting the three bias voltages V_b₁, V_b₂ and V_b₃ to set at the maximum transmission bias point (MATB), corresponding to all the bias phases φ_b₁, φ_b₂ and φ_b₃ close to 0. Then, the DPMZM is under bias modulation, and the detected low-frequency component ω_b is observed and intensified by adjusting the bias voltage V_b₃ while keeping the bias voltages V_b₁ and V_b₂ of DPMZM to set the bias phase φ_b₃ close to π/2. After the optimization of the bias phase, the DPMZM is ready for the electro-optic response measurement with the proposed method.

3. Experimental demonstration

In our experiment, an optical carrier at the wavelength of 1550.01 nm is injected into the DPMZM (Fujitsu FTM7962) via a polarization controller. The single-tone driving signal comes from a microwave synthesizer (R&S SMB100A) which is applied on the RF port of sub-MZM1 or sub-MZM2, working as RF modulation of the optical carrier. The low-frequency signal applied on the bias port of the parent-MZM comes from a function generator (Hantek HDG2102B), which is kept within the bandwidth of bias port of the parent MZM, typically at 100 kHz. The output signal of the monitor PD of DPMZM is collected by a low-noise amplifier and analyzed by an electrical spectrum analyzer (ESA).

Before measurement, the bias voltages of the DPMZM are optimized as follows. Firstly, the DPMZM is set under null modulation by switching off the output of both the microwave source and the function generator, and all the bias voltages V_b₁, V_b₂ and V_b₃ are adjusted to maximize the optical intensity of the DPMZM. Then, the DPMZM is set under bias modulation by switching on the output of the function generator while switching off the output of the microwave source, and the bias voltage V_b₃ of DPMZM is regulated to maximize the electrical amplitude of the detected frequency component f_b. In this case, the bias voltages V_b₁, V_b₂ and V_b₃ are optimized at 1.30 V, 1.25 V and 3.90 V, respectively.

Our measurement is divided into two steps. In the case of measuring A(f_b; 0), the DPMZM is driven under bias modulation by switching on the output of the function generator while switching off the output of the microwave source. In the case of measuring A(f_b; m₁), the DPMZM is driven under RF modulation by switching on both outputs of the microwave source and the function generator. Figure 2 illustrates the measured electrical power of the detected low-frequency f_b (100 kHz) at different single-tone frequencies and levels, where the measured A(f_b; 0) is shown as a benchmark for normalization. As can be seen from Fig. 2, the detected low-frequency component f_b will become stronger larger when increasing the single-tone driving power. For example, in the case of f₁ = 10 GHz, the amplitude of A(f_b; 0) is measured to be 3.465 mV (-39.21 dBm). The amplitudes A(f_b; m₁) are measured to be 3.389 mV (-39.40 dBm), 3.312 mV (-39.60 dBm), 3.162 mV (-40.00 dBm), 2.990 mV (-40.49 dBm), corresponding to the driving level of 4.485 mW (6.52 dBm), 9.060 mW (9.57 dBm), 18.097 mW (12.58 dBm), 28.769 mW (14.59 dBm), respectively. As shown in Fig. 3, the modulation depths at 10 GHz are solved to be m₁= 0.596 at P₁= 6.52 dBm, m₁= 0.846 at P₁= 9.57 dBm, m₁= 1.196 at P₁= 12.58 dBm, and m₁= 1.508 at P₁= 14.59 dBm, respectively, based on Eq. (5). Therefore, the corresponding half-wave voltages are calculated to be 3.534 V, 3.532 V, 3.534 V and 3.533 V, respectively. In order to improve the accuracy, the linear regression analysis between the normalized low-frequency component A(f_b; m₁)/A(f_b; 0) and the microwave driving power P₁ is performed based on Eq. (6), from which the half-wave voltages of DPMZM are extracted with least square fitting method. For example, the half-wave voltage at 10 GHz is calculated to be 3.533 V from the linear regression slope (LRS). Note that both the modulation depth and half-wave voltage at 10 GHz are obtained from the low-frequency component at 100 kHz, verifying the self-referenced measurement with fixed low-frequency detection. The modulation depth and the microwave driving power are measured at other single-tone frequencies according to Eq. (6), and are illustrated in Fig. 3. Figure 4 shows the regression curves at different driving frequencies between the normalized amplitude of A(f_b; m₁)/A(f_b; 0) and the single-tone driving level P₁. The according half-wave voltages are acquired and shown in Fig. 5(a).

Fig. 2. Measured electrical power of low-frequency signal under different frequencies when the single-tone driving level is set to be (a) 7 dBm, (b) 10 dBm, (c) 13 dBm, (d) 15 dBm, respectively.

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Fig. 3. Measured modulation depths as a function modulation frequency under different frequencies when the single-tone driving level is set to be (a) 7 dBm, (b) 10 dBm, (c) 13 dBm, (d) 15 dBm, respectively.

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Fig. 4. Linear regression analysis between low-frequency components and single-tone driving level.

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Fig. 5. (a) Measured half-wave voltages with our method and two-tone method; (b) Relative frequency responses measured with our method, the two-tone method and the MNA-based method.

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In order to confirm the accuracy of our method, we make a comparison between the proposed method and the two-tone method. Illustrated in Fig. 5(a) are the half-wave voltages of the sub-MZM1 and sub-MZM2 respectively, where the experimental results have an excellent consistency between our method and the two-tone method. The normalized frequency responses (the reference frequency at 1 GHz) of the two methods are calculated from the formula -20*Log₁₀V_π and are plotted in Fig. 5(b). For further verification, the DPMZM is measured with the MNA swept frequency method. Firstly, the cascaded response of the DPMZM and a broadband PD is obtained by an MNA after a full two-port electrical-to-electrical calibration. Then, the relative frequency response of PD is determined with the help of the optical frequency-detuned heterodyne method [22]. Hereafter, the frequency response of the DPMZM is calibrated by subtracting the frequency response of PD from the cascaded response. Figure 5(b) exhibits the relative frequency responses measured with the proposed method, the two-tone method, and the MNA swept frequency method. It can be seen that good consistency between the proposed method and the MNA method with optical-to-electrical calibration proves the self-referenced frequency response measurements of DPMZMs. Prior to the two-tone method, our method requires only a single-tone signal and achieves the modulation depth and half-wave voltage measurements of DPMZMs.

4. Measurement uncertainty

For the accuracy, we investigate the uncertainty of the linear regression slope given by [23]

(7)$$\frac{{\delta {V_\pi }}}{{{V_\pi }}} = \frac{{\sqrt {\frac{1}{{n - 2}}\sum\limits_{i = 1}^n {{{\left( {\frac{{A({{f_b};{m_{1i}}} )}}{{A({{f_b};0} )}} - \frac{{\hat{A}({{f_b};{m_{1i}}} )}}{{\hat{A}({{f_b};0} )}}} \right)}^\textrm{2}}} \cdot ({n\overline {P_{1i}^2} - n{{\overline {{P_{1i}}} }^2}} )} }}{{2\sum\limits_{i = 1}^n {\left( {\frac{{A({{f_b};{m_{1i}}} )}}{{A({{f_b};0} )}} - \frac{{\overline A ({{f_b};{m_{1i}}} )}}{{\overline A ({{f_b};\textrm{0}} )}}} \right)({{P_{1i}} - \overline {{P_{1i}}} } )} }},({i = 1,2,\ldots ,n} )$$

where n is the number of sample data points for every frequency, $\bar{x}$ and $\hat{x}$ represent the average value and the fitted value of x, respectively. According to the measurement, the total uncertainty of half-wave voltages V_π is estimated and illustrated in Fig. 6. It can be seen that the uncertainty of our measurement is estimated at no more than 3.5% in the worst cases.

Fig. 6. Estimated uncertainty of half-wave voltage in the interesting frequency range.

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5. Discussion and conclusion

Different from the OSA-based method, our method avoids bias dependence and achieves high-resolution measurement in the electrical domain. Compared with the MNA sweep frequency method, our method enables electro-optic frequency response measurement including modulation depth and half-wave voltage without the need of a standard broadband PD for extra calibrations. Superior to the two-tone method, it requires only a single-tone microwave source to drive the DPMZM under test.

In summary, we have proposed and experimentally demonstrated a self-referenced method for measuring the electro-optic frequency response parameters of high-speed DPMZMs based on variable single-tone modulation and fixed low-frequency detection. The modulation depth and half-wave voltage of high-speed DPMZMs can be extracted by observing the fixed low-frequency components, which are free of any broadband PD and extra optical to electrical calibration. Besides, the measurement frequency range can be larger than 40GHz, as long as the microwave source supports the operation. The method is promising for the on-line or on-chip characterization of high-speed DPMZMs by using low-frequency on-site or off-site monitor PD.

Funding

National Key Research and Development Program of China (2018YFE0201900); National Natural Science Foundation of China (61927821); Fundamental Research Funds for the Central Universities (ZYGX2019Z011).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

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Self-referenced electro-optic response measurement of dual-parallel Mach-Zehnder modulators employing single-tone level control and low-frequency bias swing

Abstract

1. Introduction

2. Operation principle

3. Experimental demonstration

4. Measurement uncertainty

5. Discussion and conclusion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (6)

Equations (7)

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