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Simultaneous frequency response measurement of electro-absorption modulation transceivers based on a self-referenced pilot operation

Mengke Wang, Shangjian Zhang, Yutong He, Ying Xu, Zhao Liu, Yali Zhang, Zhiyao Zhang, Heping Li, and Yong Liu

Open Access Open Access

Abstract

An electro-optic method based on a self-referenced pilot operation is proposed for simultaneously characterizing electro-absorption modulation optoelectronic transceivers with a shared setup. Through inserting and extracting the self-referenced pilot, the frequency responses of electro-absorption modulated lasers (EMLs) and photodetectors (PDs) are independently obtained in a single measurement, and any extra optical-to-electrical or electrical-to-optical calibration is avoided. Specifically, the relative frequency response of the EML at fm is determined through the extracted difference-frequency pilot at fp (close to DC), realizing the low-frequency analysis for an EML. The relative frequency response of PD at 2fm+fp is obtained from the amplitude ratio of the extracted sum- and difference-frequency pilots at 2fm+fp and fp under the microwave driving signal at fm, verifying the doubled measuring frequency range. In the proof-of-concept demonstration, the frequency response of an electro-absorption modulation transceiver is measured up to 40 GHz. Thereinto, the frequency response of the EML is obtained by detecting the fixed low-frequency pilot of 10 kHz, and the frequency response of the PD is extracted with frequency-swept modulation to 20 GHz. The experiment results are compared with those obtained with the electro-optic frequency sweeping method to check for accuracy.

© 2021 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

High-speed optoelectronic transceivers are fundamental building blocks in optical fiber communication systems, data centers and microwave photonic links [1]. With the explosive growth of transmission capacity, there occurs an extremely stringent requirement of the transceivers, especially in the 400 Gbit/s optoelectronic transceiver system (4λ×100 Gbit/s 4-level pulse amplitude modulation) [2,3]. Electro-absorption modulation transceivers have attracted continued interest because of their unique advantages of compact structure, low chirp, and large bandwidth [4–6]. The overall performance of an optoelectronic transceiver is normally restricted by the electro-absorption modulated laser (EML) as the electro-optic transmitter and the photodetector (PD) as the optic-electrical receiver, which must be accurately characterized especially when it is operated up to tens of GHz or Gbit/s [7,8].

There are several optical or electrical methods developed to characterize the frequency responses of transmitters and receivers, such as the optical spectrum analysis method, the optical noise beating method, the optical wavelength beating method, the electro-optic frequency sweeping method, and the electro-optic modulation mixing methods. The optical spectrum analysis method is very simple for measuring a modulator (MOD) since it does not require any PD [9–11], however, the frequency resolution and start frequency are limited to be several GHz by the spectral resolution (0.02 nm at 1550 nm) of the grating-based optical spectrum analyzer (OSA). The optical noise or wavelength beating method can be used to measure high-speed PDs with the help of ultra-wideband optical stimulus. Whereas, the optical noise beating method is subjected to small dynamic range and low measurement accuracy [12–14]. The optical wavelength beating method is often affected by the power fluctuation and the wavelength drift of the laser [15,16].

For high-resolution characterization, the optical measurement is transferred to the electrical domain by taking full advantage of electro-optical modulation. The electro-optic frequency sweeping method is the most commonly applied for measuring optoelectronic transceiver devices including a MOD and a PD with the help of a microwave network analyzer (MNA) [17–19]. However, the main difficulty lies in the extra optical-to-electrical (O/E) or electrical-to-optical (E/O) calibration since the measurement result involves the cascade responses of the MOD and the PD. In order to alleviate the calibration, an improved MNA-based method is proposed based on the assumption that an electro-absorption modulator (EAM) can be functioned as both a MOD and a PD with the same frequency response [20]. However, the required three interchange measurements must be operated under exactly the same driving conditions. Recently, the electro-optic modulation mixing methods are proposed based on serial or parallel modulation, which achieve the self-referenced frequency response measurement of transceiver devices including a MOD and a PD with twice electro-optic modulation [21–24]. However, the twice modulation requires an extra modulated optical source covered at least half of the measuring frequency range. In order to mitigate the bandwidth requirement, we also proposed the photonic sampling methods for measuring high-speed Mach-Zehnder modulators (MZMs) and PDs with single electro-optic modulation [25,26], respectively. Nevertheless, it is very difficult for the photonic sampling schemes to characterize an EML due to the inseparable distributed feedback (DFB) laser integrated with the EML. Therefore, a simple method that enables frequency response measurement of high-speed EMLs and PDs in an optoelectronic transceiver, and at the meantime avoids any extra O/E or E/O calibration is of particular interest.

In this paper, we propose for the first-time simultaneous frequency response measurement of high-speed EMLs and PDs in an electro-absorption modulation optoelectronic transceiver based on self-referenced pilot operation. As is shown in Fig. 1, the optoelectronic transceiver basically consists of an EML and a PD, where a microwave driving signal is loaded on the EML and looped back to the PD for detection. The low-frequency pilot is applied through the amplitude modulation of the microwave driving signal, and the sum- and difference-frequency pilots are extracted after photodetection, from which the self-referenced frequency responses of the EML and the PD can be independently obtained without any extra O/E or E/O calibration. Meanwhile, the proposed method enables low-frequency detection for measuring high-speed EMLs with a shared setup, and extends twofold frequency range for measuring PDs with a single electro-optic modulation. Theoretical basis is elaborated to support our method as well as the experimental demonstration. The experiment results agree well with those obtained using the MNA-based method, verifying the accuracy of the proposed method.

 figure: Fig. 1.

Fig. 1. Schematic diagram of the proposed self-referenced pilot method, MS: microwave source, LFSG: low-frequency signal generator; EML: electro-absorption modulated laser, PD: photodetector, ESA: electrical spectrum analyzer.

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2. Operation principle

As shown in Fig. 1, the optoelectronic transceiver consists of an EML and a PD for testing. The self-referenced pilot of fp is inserted through amplitude modulation into the microwave signal of fm applied on the EML in the transmitter side, representing by the center frequency of fm and its frequency sidelobes of fm±fp. The optical modulated signal output from the EML is looped back to the PD for pilot extraction at the sum- and difference-frequency components 2fm+fp and fp in the receiver side. Finally, the frequency response M(fm) of the EML can be calculated from the fixed low-frequency component at fp under the same microwave driving level, without considering the effect from the PD because of the fixed low-frequency detection. In the same time, the relative responsivity R(2fm+fp)/R(fp) of the PD can be self-referenced extracted from the amplitude ratio of the sum- and difference-frequency components at 2fm+fp and fp, which is free of any extra calibration for the EML due to the twinborn of sum and difference-frequency.

Mathematically, the microwave driving signal at the frequency of fm is amplitude modulated by a low-frequency pilot signal at the frequency of fp, which can be expressed by [26]

$$v(t )= {V_0} + ({1 + 2{\eta_p}\cos 2\pi {f_p}t} )\cdot {V_m}\cos 2\pi {f_m}t$$
where V0 is the DC component, ηp is the amplitude factor of the pilot signal at fp, and Vm is the amplitude of the microwave driving signal at fm. The amplitude modulated microwave signal is then loaded on the EML, and the optical modulated signal output from the EML is looped back to the PD for photodetection. Under small-signal and narrow-band approximations, the generated photocurrent can be written in terms of the transfer function T by
$${i_{PD}}(t )= R \cdot {I_0} \cdot T[{M \cdot v(t )} ]$$
with the responsivity R of the PD and the optical power I0 of optical carrier. Besides, M·v(t) is the voltage applied to the absorbing layer of EML, and M represents the high-frequency degradation of EML. When the EML is operated under small-signal modulation, the transfer function T can be written as [22]
$$T[{M \cdot v(t )} ]= {e^{ - \Gamma L\alpha [{M \cdot v(t )} ]}}$$
where Γ and L are the optical confinement factor and length of the absorbing layer, and α is the absorption coefficient, which is a linear function of the electric field intensity in the absorbing layer for a certain wavelength.

Substituting Eq. (3) into Eq. (2), the photocurrent can be rearranged by expanding the transfer function T in a Taylor series as

$$\begin{aligned} {i_{PD}}(t )&= R \cdot {I_0} \cdot {C_0}\left\{ {1 - \sum\limits_{i = 1}^\infty {{C_i}{{[{M({{f_m}} )\cdot ({1 + 2{\eta_p}\cos 2\pi {f_p}t} )\cdot {V_m}\cos 2\pi {f_m}t} ]}^i}} } \right\}\\ &\textrm{ } = R \cdot {I_0} \cdot {C_0} \cdot \left\{ \begin{array}{l} 1 - {C_1}M({{f_m}} )\cdot ({1 + 2{\eta_p}\cos 2\pi {f_p}t} )\cdot {V_m}\cos 2\pi {f_m}t\\ + {C_2}{M^2}({{f_m}} )\cdot {[{({1 + 2{\eta_p}\cos 2\pi {f_p}t} )\cdot {V_m}\cos 2\pi {f_m}t} ]^2} + \cdots \end{array} \right\} \end{aligned}$$

Thereinto, Ci is a constant, which can be written by

$${C_0} = {e^{ - \Gamma L\alpha ({M \cdot {V_0}} )}} {\kern 12pt}{C_i} = {({\Gamma L} )^i}{\left. {\frac{1}{{i!}}\frac{{{\partial^i}T}}{{\partial {v^i}}}} \right|_{M \cdot {V_0}}},({i = 1,2,3,\ldots } )$$

Therefore, the extracted pilot signals at 2fm+fp and fp after sum- and difference-frequency beating can be easily quantified as

$$A({{f_p}} )= 2{I_0}{C_0}{C_2}{\eta _p}V_m^2{M^2}({{f_m}} )R({{f_p}} )$$
$$A({2{f_m}\textrm{ + }{f_p}} )= {I_0}{C_0}{C_2}{\eta _p}V_m^2{M^2}({{f_m}} )R({2{f_m}\textrm{ + }{f_p}} )$$

In our method, the self-referenced pilot is inserted at the low-frequency fp and close to DC, so that R(fp)≈1 can be satisfied. In this case, the frequency response of EML at fm, and the frequency response of PD at 2fm+fp with respect to the fixed low-frequency pilot at fp can be solved based on Eqs. (5a) and (5b), given by

$$M({{f_m}} )= \sqrt {\frac{1}{{2I{}_0{C_0}{C_2}R({{f_p}} )}}} \cdot \sqrt {\frac{{A({{f_p}} )}}{{{\eta _p}V_m^2}}} = c \cdot \sqrt {\frac{{A({{f_p}} )}}{{{V_m} \cdot {\eta _p}{V_m}}}}$$
$$\frac{{R({2{f_m} + {f_p}} )}}{{R({{f_p}} )}}\textrm{ = }\frac{{2 \cdot A({2{f_m} + {f_p}} )}}{{A({{f_p}} )}}$$

Thereinto, c is related to optical power I0, C0, C2 and responsivity R(fp) of the PD at the fixed low-frequency of fp, which is also a constant, and will not affect the relative frequency response measurement of the EML. Meanwhile, Vm and ηpVm represent the amplitudes of the microwave driving signal at fm and its sidelobe at fm±fp, respectively.

According to Eqs. (6) and (7), the frequency response of EML at fm is determined by analyzing the fixed low-frequency pilot of fp (close to DC), which is independent of the responsivity of PD. Meanwhile, the frequency response of PD at 2fm+fp is obtained under the microwave driving at fm, where the frequency response of EML is totally canceled out, proving the self-referenced measurement with doubled frequency range. With the help of the self-referenced pilot insertion and extraction, the method enables independent frequency response measurement of an EML and a PD in an optoelectronic transceiver with a shared setup and a single measurement.

3. Experimental demonstration

In the measurement of optoelectronic transceiver, the optical carrier from the EML is at the center wavelength of 1548.46 nm and the output power of 0 dBm. The EML is biased at the reverse voltage of 3.5 V and driven by a microwave signal up to 40 GHz (R&S SMB 100A). The self-referenced pilot is inserted into the microwave signal through amplitude modulation at 10 kHz, where the pilot frequency can be set at other value as long as the pilot can be distinguished in the electrical spectrum. The PD is biased at the reverse voltage of 2.8 V and used to recover the pilot from the optical modulated signals of the EML. Finally, the desired frequency components including the self-referenced pilot are analyzed by an electrical spectrum analyzer (ESA, R&S FSU50).

Figure 2 shows the measured typical electrical spectra of the difference- and sum-frequency pilots at fp (10 kHz) and 2fm+fp after photodetection, where the electrical spectra of the microwave driving signal at fm and its sidelobe at fm±fp are also shown for reference with the resolution bandwidth (RBW) of 50 Hz and the video bandwidth (VBW) of 200 Hz. For example, in the case of fm=20 GHz, the extracted difference-frequency pilot is measured to be -60.15 dBm at 10 kHz (fp) under the microwave driving amplitudes of V(fm)=Vm=0.458 V (3.21 dBm) and V(fm±fp)=ηpVm=0.228 V (-2.83 dBm). In order to obtain the normalized frequency response of the EML, its frequency response at the low-frequency of 10 MHz (fm) is taken as the reference. In the case of fm=10 MHz, the extracted difference-frequency pilot is measured to be -41.22 dBm at 10 kHz (fp) under the microwave driving amplitudes of V(fm)=Vm=0.623 V (5.89 dBm) and V(fm±fp)=ηpVm=0.338 V (0.57 dBm), as also shown in Fig. 2. Thus, the frequency response of the EML at 20 GHz relative to 10 MHz is calculated to be -6.42 dB based on Eq. (6). Meanwhile, in the case of fm=20 GHz, the extracted sum-frequency pilot at 40.00001 GHz (2fm+fp) is measured to be -70.32 dBm. Therefore, according to Eq. (7), the frequency response of the PD is determined to be -4.16 dB at 40.00001 GHz (2fm+fp) with respect to 10 kHz (fp) through the relative amplitude of the sum- and difference-frequency pilots. Note that the frequency response of the EML at 20 GHz is extracted from the low-frequency pilot at 10 kHz, verifying high-frequency characterization of an EML with fixed low-frequency analysis, and the relative frequency response of the PD at 40.00001 GHz is obtained with microwave driving frequency at 20 GHz, realizing doubled measuring frequency range.

 figure: Fig. 2.

Fig. 2. Measured typical electrical spectra of the difference- and sum-frequency pilots at fp (10 kHz) and 2fm+fp after photodetection under different driving conditions.

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When the microwave driving frequency is swept from DC to 40 GHz, the relative frequency response of the EML can be measured by the fixed difference-frequency pilot analysis at 10 kHz (fp) under the microwave driving level, as displayed in Fig. 3(a). Moreover, the sum-frequency pilot at 2fm+fp can be obtained within the frequency range of 40 GHz, so the relative frequency response of the PD can be extracted based on the relative amplitude of the sum- and difference-frequency pilots at 2fm+fp and fp, as illustrated in Fig. 3(b).

 figure: Fig. 3.

Fig. 3. Measured relative frequency responses of the EML and the PD as a function of frequency.

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In order to verify the accuracy of the proposed method, the relative frequency responses of the EML and the PD are measured with the electro-optic frequency sweeping method by using the MNA (Agilent N5235A), respectively, in which the built-in source of the MNA is swept at the same microwave driving frequency. In the MNA method, the frequency response of the EML under test cascaded with an assisted PD or the PD under test cascaded with an assisted modulator is firstly obtained. Then, the frequency response of the assisted PD or modulator is measured with the electro-optic modulation mixing method [21]. Therefore, the frequency response of the EML under test or PD under test itself can be calibrated by subtracting the frequency response of the assisted PD or the assisted modulator from the cascade responses. In addition, the relative frequency response of the EML+PD is estimated by combining the obtained frequency responses of the EML and PD in the proposed method, and is also measured with the MNA method for comparison. Figure 4 illustrates the measured relative frequency responses of PD, EML and EML+PD by employing the proposed method and the MNA method with or without calibration. The good consistency between these two methods proves that the proposed method achieves the self-referenced frequency response measurement of the electro-absorption modulation optoelectronic transceivers with a shared setup.

 figure: Fig. 4.

Fig. 4. Measured relative frequency responses of PD, EML and EML+PD with the proposed method and the MNA method.

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In our method, the relative frequency response of EML or PD at any frequency is extracted by simply varying the frequency fm of the microwave driving signal loaded onto the EML. In this case, the frequency resolution of the proposed method is mainly determined by the swept step of the microwave source (MS) and the RBW of the ESA, which can theoretically reach 10 Hz level. In our measurement, the MS and the ESA are controlled by a computer via NI-VISA bus. A matlab program is used to set the MS and acquire data from the ESA. Much time is spent on the control and communication among the computer, the MS and the ESA. To speed up our measurement, one possible way is to use the ESA to synchronize and control the MS for efficiency.

4. Measurement uncertainty

For the accuracy, the measurement uncertainty for the EML or the PD under test is investigated. In our experiment, the measurement uncertainty mainly comes from the error of the measured electrical spectra, since our method is based on the electrical spectra pilot analysis of the optical modulated signal. Besides, it is noted that the approximate relationship of R(fp)≈1 will not introduce extra uncertainty since the responsivity R(fp) of PD at this fixed frequency is a constant (close to 1).

In the EML measurement, the frequency response has an error dependence on the desired frequency component as following

$$\frac{{\delta M({{f_m}} )}}{{M({{f_m}} )}}\textrm{ = }\frac{1}{2} \cdot \left[ {\frac{{\delta A({{f_p}} )}}{{A({{f_p}} )}} + \frac{{\delta {V_m}}}{{{V_m}}} + \frac{{\delta ({{\eta_p}{V_m}} )}}{{{\eta_p}{V_m}}}} \right]$$
which is deduced from the total derivative of Eq. (6). According to the specification of the ESA, the maximum uncertainty of the measured electrical amplitude is 0.1 dB, corresponding to a relative error of no more than 1.16% [=(100.1/20-1)×100%]. Thus, the frequency response of the EML at any frequency has a relative error of no more than 1.74% (=0.5×1.16%×3). In practice, the frequency response of the EML at any frequency with respect to a fixed low frequency is calculated during the experiment, so the total relative error of less than 3.48% (=1.74%×2) might be delivered to the extracted relative frequency response of the EML in the worst case.

In the PD measurement, the measurement uncertainty can be simply derived from the total differential of Eq. (7), given by

$$\frac{{\delta {R_f}}}{{{R_f}}} = \frac{{\delta A({2{f_m}\textrm{ + }{f_p}} )}}{{A({2{f_m}\textrm{ + }{f_p}} )}}\textrm{ + }\frac{{\delta A({{f_p}} )}}{{A({{f_p}} )}}$$

Therefore, the total relative error of frequency response measurement for PD is no more than 2.32% (=1.16%×2) in the worst case.

5. Discussion and conclusion

Different from the electro-optic frequency sweeping method, the method enables the self-referenced frequency response measurement of the EML and the PD, and does not depend on the availability of a standard PD or a standard MOD for extra calibrations. Compared with electro-optic modulation mixing methods based on serial or parallel modulation, the method enables the high-frequency response measurement for the EML and the PD with a single electro-optic modulation. Superior to the photonic sampling methods, the method makes full use of the DFB laser integrated with the EML as the optical source, and realizes the simultaneous characterization of the EML and the PD with a shared setup and a single measurement.

In summary, we have demonstrated an electro-optic method based on self-referenced pilot operation for simultaneous frequency response measurement of high-speed EMLs and PDs in an electro-absorption modulation optoelectronic transceiver. Through inserting and extracting the self-referenced pilot, the frequency response of the EML at fm is obtained with low-frequency analysis in a shared setup, which is free of any extra O/E calibration. Meanwhile, the frequency response of the PD at 2fm+fp is determined with the doubled measuring frequency range, which is also independent of any extra E/O calibration.

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.

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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 (4)
Fig. 1.
Fig. 1. Schematic diagram of the proposed self-referenced pilot method, MS: microwave source, LFSG: low-frequency signal generator; EML: electro-absorption modulated laser, PD: photodetector, ESA: electrical spectrum analyzer.

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Fig. 2.
Fig. 2. Measured typical electrical spectra of the difference- and sum-frequency pilots at fp (10 kHz) and 2fm+fp after photodetection under different driving conditions.

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Fig. 3.
Fig. 3. Measured relative frequency responses of the EML and the PD as a function of frequency.

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Fig. 4.
Fig. 4. Measured relative frequency responses of PD, EML and EML+PD with the proposed method and the MNA method.

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Equations (11)

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v ( t ) = V 0 + ( 1 + 2 η p cos ⁡ 2 π f p t ) ⋅ V m cos ⁡ 2 π f m t
i P D ( t ) = R ⋅ I 0 ⋅ T [ M ⋅ v ( t ) ]
T [ M ⋅ v ( t ) ] = e − Γ L α [ M ⋅ v ( t ) ]
i P D ( t ) = R ⋅ I 0 ⋅ C 0 { 1 − ∑ i = 1 ∞ C i [ M ( f m ) ⋅ ( 1 + 2 η p cos ⁡ 2 π f p t ) ⋅ V m cos ⁡ 2 π f m t ] i }   = R ⋅ I 0 ⋅ C 0 ⋅ { 1 − C 1 M ( f m ) ⋅ ( 1 + 2 η p cos ⁡ 2 π f p t ) ⋅ V m cos ⁡ 2 π f m t + C 2 M 2 ( f m ) ⋅ [ ( 1 + 2 η p cos ⁡ 2 π f p t ) ⋅ V m cos ⁡ 2 π f m t ] 2 + ⋯ }
C 0 = e − Γ L α ( M ⋅ V 0 ) C i = ( Γ L ) i 1 i ! ∂ i T ∂ v i | M ⋅ V 0 , ( i = 1 , 2 , 3 , … )
A ( f p ) = 2 I 0 C 0 C 2 η p V m 2 M 2 ( f m ) R ( f p )
A ( 2 f m  +  f p ) = I 0 C 0 C 2 η p V m 2 M 2 ( f m ) R ( 2 f m  +  f p )
M ( f m ) = 1 2 I 0 C 0 C 2 R ( f p ) ⋅ A ( f p ) η p V m 2 = c ⋅ A ( f p ) V m ⋅ η p V m
R ( 2 f m + f p ) R ( f p )  =  2 ⋅ A ( 2 f m + f p ) A ( f p )
δ M ( f m ) M ( f m )  =  1 2 ⋅ [ δ A ( f p ) A ( f p ) + δ V m V m + δ ( η p V m ) η p V m ]
δ R f R f = δ A ( 2 f m  +  f p ) A ( 2 f m  +  f p )  +  δ A ( f p ) A ( f p )
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