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Relative frequency response measurement of Mach-Zehnder modulators utilizing dual-carrier modulation and low-frequency detection

Yujia Zhang, Weiqiang Lyu, Yaowen Zhang, Yutong He, Chao Jing, Shangjian Zhang, Zhiyao Zhang, and Yong Liu

Open Access Open Access

Abstract

A self-calibrated approach is proposed to measure the relative frequency response of Mach-Zehnder modulators (MZMs) based on dual-carrier modulation and low-frequency detection. In this scheme, a dual-carrier is generated by combining a continuous-wave light from a distributed feedback laser diode with its frequency-shifted replica. Through modulating the dual-carrier by a frequency-scanned single-tone microwave signal via the MZM under test biased at its minimum transmission point, a fixed low-frequency heterodyne signal carrying the electro-optic modulation response information is generated after photodetection, from which the relative frequency response of the MZM can be obtained. In the experiment, the relative frequency response of a commercial MZM is measured by using the proposed method, where the result fits in with those obtained by using the conventional optical spectrum analysis method and the microwave network analysis method. The proposed method features self-calibration, high frequency resolution, low-frequency detection, and usage of only a single frequency-scanned microwave source, which is favorable for characterizing the microwave performance of MZMs in backbone optical communication and microwave photonic systems.

© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

High-speed electro-optic Mach-Zehnder modulators (MZMs) are elementary and essential components in backbone optical communication and microwave photonic systems [1–6]. Characterizing the frequency response of MZMs with a high frequency resolution is of great importance to improve the system performance due to the following reasons. Firstly, digital signal processing (DSP) technology has been widely employed in high-speed optical communication to enhance the transmission performance, which has the ability to compensate for the signal distortion introduced by the frequency response variation of the MZMs. Secondly, the link gain of a broadband microwave photonic system is closely related to the frequency response of the MZMs, which can be flattened through equalization. To achieve those functionalities, the frequency response of MZMs must be well characterized in advance.

Optical spectrum analysis is a classical method to measure the frequency response of electro-optic modulators based on an optical spectrum analyzer (OSA) [7]. By monitoring the relative optical power of the modulation sideband and the carrier, the frequency response of the modulator under test can be obtained. However, the starting frequency and the measurement resolution of this method are generally limited to be about 2.5 GHz (i.e., 0.02 nm@1550 nm) by the spectral resolution of the commercially-available grating-based OSA. To achieve a high frequency resolution measurement, electrical spectrum analysis method has been proposed and widely used with the assistance of a microwave network analyzer (MNA) [8–10]. In this method, the frequency response of the modulator is measured by applying a frequency-scanned single-tone microwave signal onto the MZM under test, and analyzing the recovered signal from an assisted photodetector (PD). The operation bandwidth of the PD must cover the interesting frequency range. In addition, the frequency response of the assisted PD must be calibrated to obtain the intrinsic frequency response characteristic of the modulator [11–13]. In order to simplify the measurement process, a self-calibrated method has been proposed based on frequency-shifted heterodyning [14–16]. In this method, the desired optical spectrum components are transferred to the electrical spectrum with a high fidelity, which facilitates high-resolution measurement in the electrical domain. This method alleviates about half bandwidth requirement for the assisted PD, and avoids the calibration for the uneven frequency response of the PD. To ease the detection bandwidth requirement, a two-tone modulation method has been proposed to achieve frequency response measurement of high-speed MZMs via utilizing a low-speed PD [17]. In this method, self-calibrated measurement is realized via low-frequency detection, but at the expense of using a synchronous frequency-scanned two-tone microwave stimulus. Another low-frequency detection method is also proposed based on photonic down-conversion sampling via a low-repetition-rate ultra-short pulse train, which can achieve self-calibrated microwave characterization of MZMs by using a single microwave source [18]. However, due to the large spectrum width of the passively mode-locked laser, the measured frequency response of the MZM is an average value in a large wavelength range. In addition, the passively mode-locked laser may suffer from repetition frequency drift, which must be precisely controlled to obtain the accurate frequency response of the MZM.

In this paper, a self-calibrated method for measuring the frequency response of broadband MZMs is proposed based on dual-carrier modulation and low-frequency detection. Compared with the frequency-shifted heterodyning method, the bandwidth requirement of the PD is greatly reduced. Compared with the two-tone modulation method, only a single tunable microwave source is required, which simplifies the measurement setup. Compared with the photonic down-conversion sampling method, the wide-spectrum-induced average effect is avoided in the measurement. A proof-of-concept experiment is carried out to demonstrate the proposed method, where the measured frequency response of a commercial MZM by using the proposed method fits in with those obtained by the OSA and the MNA methods. In addition, a guideline to enhancing the measurement accuracy is also presented.

2. Operation principle

Figure 1 shows the schematic diagram of the proposed method. Continuous-wave (CW) light with a center frequency of fc from a laser diode is divided into two branches via an optical coupler (OC). In the upper branch, the center frequency of the CW light is shifted to fc+f0 by using a frequency shifter. Then, it is combined with the CW light directly from the lower branch via another OC to generate a dual-carrier, of which the frequency interval is equal to f0. The dual-carrier is modulated in the MZM under test by a single-frequency microwave signal with a frequency of fs. The MZM is biased at its minimum transmission point to achieve carrier-suppressed double-sideband (CS-DSB) modulation. Hence, two modulation sidebands are generated, where the −1st-order sideband includes frequency components at fc-fs and fc+f0-fs, and the +1st-order sideband includes frequency components at fc+fs and fc+f0 + fs. Both of the modulation sidebands carry the modulation response information at fs. After photodetection, heterodyne products at f0 are generated, whose power is relative to the modulation response information at fs. Therefore, through sweeping fs by using a calibrated MNA, the modulation frequency response information of the MZM can be obtained by measuring the corresponding power of the fixed low-frequency component at f0. The relative frequency response of the MZM can be calculated through power normalization, where the measured power at a low frequency is generally used as a reference.

 figure: Fig. 1.

Fig. 1. Schematic diagram of the proposed dual-carrier modulation method to measure the frequency response of an MZM. LD: laser diode, FS: frequency shifter, MZM: Mach-Zehnder modulator, PD: photodetector, MNA: microwave network analyzer.

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Mathematically, the optical field of the generated dual-carrier can be expressed as

$${E_{in}} = \frac{1}{{1 + \gamma }}{E_0}{e^{j2\pi {f_c}t}}[{1 + \gamma {e^{j2\pi {f_0}t + j\varphi }}} ]$$
where E0 and fc are the amplitude and the center frequency of the CW light, respectively. f0 is the frequency shift of the CW light introduced by the frequency shifter in the upper branch.1: γ is the amplitude ratio of the optical field from the lower branch and the upper branch. φ is the phase difference of the optical field between the upper branch and lower branch.

The dual-carrier is modulated by a single-frequency microwave signal with a frequency of fs in the MZM biased at its minimum transmission point. The output optical field is expressed as

$${E_{out}} = \frac{1}{{1 + \gamma }}{E_0}{e^{j2\pi {f_c}t}}[{1 + \gamma {e^{j2\pi {f_0}t + j\varphi }}} ]\cos \left( {\frac{\pi }{2} + \frac{{m({{f_s}} )}}{2}\cos ({2\pi {f_s}t} )} \right)$$
where m(fs) is the modulation index of the MZM at fs.

After photodetection, the output current is calculated by using Jacobi-Anger expansion as

$$\begin{array}{l} I \propto R(f ){E_{out}}E_{out}^ \ast{=} \\ \textrm{ = }\frac{1}{2}\frac{1}{{{{({1\textrm{ + }\gamma } )}^2}}}E_0^2\left\{ \begin{array}{l} R(0 )({1 + {\gamma^2}} )- R(0 ){J_0}({m({{f_s}} )} )- R(0 ){\gamma^2}{J_0}({m({{f_s}} )} )\\ + 2\gamma R({{f_0}} )\cos ({2\pi {f_0}t + \varphi } )- 2\gamma R({{f_0}} ){J_0}({m({{f_s}} )} )\cos ({2\pi {f_0}t + \varphi } )\\ + 2({1 + {\gamma^2}} )R({2{f_s}} ){J_2}({m({{f_s}} )} )\cos ({4\pi {f_s}t} )\\ + 2\gamma R({2{f_s} + {f_0}} ){J_2}({m({{f_s}} )} )\cos ({2\pi ({2{f_s} + {f_0}} )+ \varphi } )\\ + 2\gamma R({2{f_s} - {f_0}} ){J_2}({m({{f_s}} )} )\cos ({2\pi ({2{f_s} - {f_0}} )- \varphi } )\\ + \ldots \end{array} \right\} \end{array}$$
where Jn(x) is the nth-order Bessel function of the first kind. R(f) is the responsivity of the PD at f. The desired current component at f0 can be calculated by applying Bessel series expansion as
$$I({{f_0};{f_s}} )\propto E_0^2R({{f_0}} )\frac{\gamma }{{{{({1\textrm{ + }\gamma } )}^2}}}\{{1 - {J_0}[{m({{f_s}} )} ]} \}\approx \frac{{E_0^2\gamma }}{{4{{({1\textrm{ + }\gamma } )}^2}}}R({{f_0}} ){m^2}({{f_s}} )$$

Based on Eq. (4), the relative frequency response of the MZM can be calculated as

$${S_{21}}({{f_s}} )= \frac{{I({{f_0};{f_s}} )}}{{I({{f_0};{f_{sr}}} )}} = \frac{{{m^2}({{f_s}} )}}{{{m^2}({{f_{sr}}} )}}$$
where fsr is a referenced frequency. In general, fsr is set to be in the low frequency range, e.g., fsr = 1 GHz. It can be seen from Eq. (5) that the relative frequency response can be measured based on the proposed dual-carrier modulation, featuring single-scan, fixed low-frequency detection and calibration-free of PD response.

3. Experimental results and discussion

A proof-of-concept experiment is carried out to verify the feasibility of the proposed method. In the experiment, a distributed feedback (DFB) laser diode centered at 1550.036 nm is employed to generate CW light with a power of 12.5 dBm. In the upper branch, an acousto-optic frequency shifter (CETC F-YSG100-2) with a frequency shift amount of 100 MHz is used to shift the center wavelength of the CW light. A commercial 20-Gb/s dual-output MZM (EOSPACE AX-1×2-0MSS-20-PFA-SFA) is used as the device under test, whose direct current (DC) bias voltage is finely adjusted by using a high-accuracy power supply (Agilent E3620A) to achieve CS-DSB modulation. The modulated optical signal is detected by using a PD (HP 11982A). A calibrated four-port MNA (Keysight N5225A) is used to generate the frequency-scanned single-tone microwave signal applied to the MZM and to measure the power of the recovered signal at f0 from the PD.

Figure 2(a) presents the optical spectrum of the generated dual-carrier, in which the two optical tones cannot be distinguished due to the poor resolution (0.02 nm) of the employed OSA (YOKOGAWA AQ6370C). To measure the fine spectral structure of the generated dual-carrier, a heterodyne system is constructed [16]. In the heterodyne measurement system, a dual-drive Mach-Zehnder modulator (DD-MZM) driven by a single-tone microwave signal at 12.75 GHz is used to generate the reference light. Figure 2(b) exhibits the measured electrical spectrum of the heterodyne signal by using an electrical spectrum analyzer (R&S FSU50). It can be clearly seen from Fig. 2(b) that a dual-carrier with a frequency interval of 100 MHz is successfully generated. Figure 2(c) shows the electrical spectrum of the heterodyne signal from the PD, where the dual-carrier is directly sent to achieve photodetection. The extremely narrow spectrum line at 100 MHz indicates that the generated dual-carrier has an excellent coherence, which is beneficial for achieving a high-resolution measurement.

 figure: Fig. 2.

Fig. 2. (a) Optical spectrum of the generated dual-carrier, (b) electrical spectrum of the generated dual-carrier measured by using the heterodyne measurement system, and (c) electrical spectrum of the heterodyne signal through directly injecting the generated dual-carrier into the PD.

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Figure 3 shows the optical spectrum from the MZM biased at the minimum transmission point, where the frequency and the power of the applied single-tone microwave signal are set to be 10 GHz and 13 dBm, respectively. The carrier suppression ratio is measured to be 10.4 dB, which indicates that the MZM works in CS-DSB modulation status. In addition, the higher-order modulation sidebands are much lower than the 1st-order modulation sidebands, which guarantees that their influence on the measurement is negligible. Figure 4 exhibits the measured electrical spectra from the PD when fs is set to be 10 GHz, 20 GHz, 30 GHz and 40 GHz, respectively, and the driving power for all frequencies is set to be 13 dBm. It can be clearly seen from Fig. 4 that the power of the generated single-tone signal at 100 MHz decreases as the modulation frequency increases, which is attributed to the degradation of the modulation efficiency of the MZM.

 figure: Fig. 3.

Fig. 3. Optical spectrum from the MZM under test biased at the minimum transmission point.

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 figure: Fig. 4.

Fig. 4. Measured electrical spectra from the PD when fs is set to be 10 GHz, 20 GHz, 30 GHz and 40 GHz, respectively.

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Figure 5 presents the measured relative frequency response of the MZM, in which the blue line, the red line and the black circles denote the measurement results obtained by using the proposed method, the MNA method and the OSA method, respectively. In the measurement based on the OSA method, experimental setup in [7] is used. CW light from the DFB laser diode serves as the optical carrier directly. Through adjusting the DC bias voltage to make the MZM work at its quadrature point, the power of the carrier and the modulation sideband under different driving frequencies but with an identical driving power is measured by using the OSA. The modulation indices and the half-wave voltages at different driving frequencies are calculated by solving the Bessel functions based on the relative power of the carrier and the modulation sidebands [7]. The relative frequency response is calculated as S21 = 20lg(1/Vπ), where Vπ denotes the half-wave voltage versus modulation frequency of the MZM. Due to the spectral resolution limitation of the employed OSA, the modulation sidebands cannot be distinguished from the optical carrier if fs is small. Hence, the frequency response of the MZM is unable to be measured when fs is smaller than 4 GHz as shown in Fig. 5. In the measurement based on the MNA method, experimental setup in [8] is utilized. CW light from the DFB laser diode also serves as the optical carrier directly. Firstly, the total frequency response of the cascaded MZM and PD are measured by using the calibrated MNA. Then, the frequency response of the PD is measured by using another self-calibrated PD frequency response characterization method [19]. Finally, the frequency response of the PD is deducted from the measured total frequency response to obtain the intrinsic frequency response of the MZM. The results in Fig. 5 indicate that the proposed method is feasible for charactering the frequency response of MZMs with a high resolution. Nevertheless, the measured frequency response beyond 30 GHz by using the proposed method is higher than that obtained by using the MNA method as shown in Fig. 5. The reason can be summarized as follows. In the high-frequency range, the modulation efficiency of the MZM degrades. Therefore, the carrier suppression ratio after electro-optic modulation is lower than that in Fig. 3 due to the decrease of the modulation index. In this condition, the heterodyne signal between the two optical tones in the vestigial carrier (also located at 100 MHz) introduces a non-ignorable overestimation of the frequency response.

 figure: Fig. 5.

Fig. 5. Measured relative frequency response of the MZM by using the proposed method (blue line), the MNA method (red line) and the OSA method (black circles).

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In fact, the optical carrier cannot be completely suppressed in an MZM due to the limited extinction ratio (generally in the range of 20–30 dB for a commercial MZM), which is induced by the unsymmetrical Mach-Zehnder interferometer architecture in the device fabrication process. Therefore, the vestigial carrier inevitably introduces a measurement error into the proposed method. In the measurement, the carrier suppression ratio may further degrade compared with that in Fig. 3 due to the DC bias drift and the relatively low modulation index of the MZM. Although the carrier suppression ratio can be enhanced through increasing the driving power, the appearance of higher-order modulation sidebands (e.g., 3rd-order modulation sidebands, including two groups of two optical tones separated by 100 MHz) may also induce an extra measurement error. Figure 6 exhibits the calculated measurement errors under various modulation indices and DC bias deviations, where the extinction ratio of the MZM is set to be 26 dB (corresponding the measured value). The calculation result indicates that the measurement error gradually varies from 1.0 dB under m = 0.4 to −0.2 dB under m = 0.9. Therefore, through properly setting the modulation index in the measurement, the frequency response measurement error beyond 30 GHz as shown in Fig. 5 can be greatly reduced. The calculation results also indicate that a small DC bias drift from the minimum transmission point has little influence on the measurement accuracy. Finally, it should be pointed out that the proposed method is only applicable for the intensity modulator with a large extinction ratio (>20 dB). The most suitable devices include lithium niobate (LN)-based MZMs and lithium niobate on insulator (LNOI)-based MZMs, which are generally with extinction ratios in the range of 20–30 dB.

 figure: Fig. 6.

Fig. 6. Calculated measurement errors under various modulation indices and DC bias deviations.

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4. Conclusion

In summary, we have proposed and experimentally demonstrated an approach to measuring the relative frequency response of high-speed MZMs based on dual-carrier modulation and low-frequency detection, which is free of extra PD frequency response calibration. Through using a frequency shifter with a small frequency shift, this method has the ability to achieve high-resolution frequency response characterization of MZMs. In the measurement, the high-frequency response of the MZM is obtained by measuring the power of the heterodyne signal at a fixed low frequency, which greatly reduce the bandwidth requirement of the PD compared with the frequency-shifted heterodyning method. In addition, the proposed method only needs a single frequency-scanned microwave source, which simplifies the hardware and control requirement compared with the two-tone modulation method. The maximum measurable frequency range is determined by the maximum frequency of the stimulus from the MNA. Nevertheless, the two optical tones in the vestigial carrier may introduce a non-ignorable measurement error, especially in the high-frequency band. Therefore, the proposed method is only applicable for the MZM with a large extinction ratio (>20 dB), and the power of the stimulus from the MNA should be properly set in the measurement to decrease the vestigial carrier-induced measurement error. In the proposed method, through employing a tunable laser source, the relative frequency response of the MZM at different wavelengths can be measured, which eliminates the wide-spectrum-induced average effect in the photonic down-conversion sampling method.

Funding

National Key Research and Development Program of China (2019YFB2203800); National Natural Science Foundation of China (61927821); Fundamental Research Funds for the Central Universities (ZYGX2019Z011, ZYGX2020ZB012).

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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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.

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Figures (6)
Fig. 1.
Fig. 1. Schematic diagram of the proposed dual-carrier modulation method to measure the frequency response of an MZM. LD: laser diode, FS: frequency shifter, MZM: Mach-Zehnder modulator, PD: photodetector, MNA: microwave network analyzer.

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Fig. 2.
Fig. 2. (a) Optical spectrum of the generated dual-carrier, (b) electrical spectrum of the generated dual-carrier measured by using the heterodyne measurement system, and (c) electrical spectrum of the heterodyne signal through directly injecting the generated dual-carrier into the PD.

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Fig. 3.
Fig. 3. Optical spectrum from the MZM under test biased at the minimum transmission point.

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Fig. 4.
Fig. 4. Measured electrical spectra from the PD when fs is set to be 10 GHz, 20 GHz, 30 GHz and 40 GHz, respectively.

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Fig. 5.
Fig. 5. Measured relative frequency response of the MZM by using the proposed method (blue line), the MNA method (red line) and the OSA method (black circles).

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Fig. 6.
Fig. 6. Calculated measurement errors under various modulation indices and DC bias deviations.

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Equations (5)

Equations on this page are rendered with MathJax. Learn more.

E i n = 1 1 + γ E 0 e j 2 π f c t [ 1 + γ e j 2 π f 0 t + j φ ]
E o u t = 1 1 + γ E 0 e j 2 π f c t [ 1 + γ e j 2 π f 0 t + j φ ] cos ⁡ ( π 2 + m ( f s ) 2 cos ⁡ ( 2 π f s t ) )
I ∝ R ( f ) E o u t E o u t ∗ =  =  1 2 1 ( 1  +  γ ) 2 E 0 2 { R ( 0 ) ( 1 + γ 2 ) − R ( 0 ) J 0 ( m ( f s ) ) − R ( 0 ) γ 2 J 0 ( m ( f s ) ) + 2 γ R ( f 0 ) cos ⁡ ( 2 π f 0 t + φ ) − 2 γ R ( f 0 ) J 0 ( m ( f s ) ) cos ⁡ ( 2 π f 0 t + φ ) + 2 ( 1 + γ 2 ) R ( 2 f s ) J 2 ( m ( f s ) ) cos ⁡ ( 4 π f s t ) + 2 γ R ( 2 f s + f 0 ) J 2 ( m ( f s ) ) cos ⁡ ( 2 π ( 2 f s + f 0 ) + φ ) + 2 γ R ( 2 f s − f 0 ) J 2 ( m ( f s ) ) cos ⁡ ( 2 π ( 2 f s − f 0 ) − φ ) + … }
I ( f 0 ; f s ) ∝ E 0 2 R ( f 0 ) γ ( 1  +  γ ) 2 { 1 − J 0 [ m ( f s ) ] } ≈ E 0 2 γ 4 ( 1  +  γ ) 2 R ( f 0 ) m 2 ( f s )
S 21 ( f s ) = I ( f 0 ; f s ) I ( f 0 ; f s r ) = m 2 ( f s ) m 2 ( f s r )
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