High-frequency characterization of electro-optic modulation chips based on photonic down-conversion sampling and microwave fixture de-embedding

Yutong He; Ying Xu; Xinhai Zou; Yali Zhang; Zhiyao Zhang; Shangjian Zhang; Yong Liu; Ninghua Zhu; Ninghua Zhu

doi:10.1364/OE.470744

1. Introduction

Integrated optoelectronics holds great promise for realizing low-cost and large-scale solutions to optical communication networks [1–3] and data center optical networks [4–6]. Wideband/high-speed electro-optic modulators (EOMs) and photodetectors (PDs) are in urgent needs for these applications. For example, high-speed EOMs are key components to impose electrical signals onto the intensity of light wave, and their frequency responses including modulation index and half-wave voltages should be characterized to clarify the operation bandwidth in the system applications.

In the past decades, there are lots of methods proposed for measuring frequency responses of EOMs, such as Mach-Zehnder modulators (MZMs), electro-absorption modulators (EAMs), directly modulated lasers (DMLs), which can be categorized into optical spectrum and electrical spectrum methods. The optical spectrum analysis method is achieved by measuring the power ratio of the modulation sidebands with respect to the optical carrier by means of an optical spectrum analyzer (OSA) [7–9]. The measurement is direct and effective for high-frequency and ultra-wideband operation. However, the resolution is restricted to be 1.25 GHz (0.01 nm @ 1550 nm) by the commercially available grating-based OSA. In contrast, the electrical spectrum methods feature high resolution increased up to several orders of magnitude, and typically include the electro-optic frequency sweep (EOFS) method [10–14], the frequency-shifted heterodyne method [15–22] and the photonic down-conversion sampling method [23,24], etc. The EOFS method is widely used to measure the frequency response of both EOMs and PDs with the help of a microwave network analyzer (MNA). Figure 1 shows the schematic diagram of a typical EOFS setup. The reference planes A1-M1 include the built-in source network SxN of the MNA and the adapter network SAN connected to the source port, while the reference planes D2-B2 include the adapter network RAN connected to the receiver port and the built-in receiver network RxN of the MNA. The optoelectronic network is formed by an EOM and a PD in serial as the electrical/optical (E/O) transmitter and the optical/electrical (O/E) receiver, respectively.

Fig. 1. Schematic diagram of a typical electro-optic frequency sweep setup. MNA: microwave network analyzer; SxN: built-in source network of MNA; SAN: adapter network connected to the source port; EOM: electro-optic modulator; PD: photodetector; RAN: adapter network connected to the receiver port; RxN: built-in receiver network of MNA; a_1S: incident wave flowing into the source network; b_2M: scattered wave measured by the receiver network.

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In the case of on-chip testing, the optoelectronic network will have non-coaxial port, and the adapter network SAN and/or RAN generally include microwave fixtures, such as cables, connectors, probes and bias-tees, to deliver electrical signals from the SxN to the EOM and/or collect electrical signals from the PD to the RxN [25]. The frequency response of the SAN, the EOM, the PD and the RAN at the reference planes P1-P2 can be accurately measured after system correction with the full two-port Short-Open-Load-Thru (SOLT) calibration procedure. The combined response of the EOM and the PD can be obtained by de-embedding the adapter networks SAN and RAN, corresponding to moving the test reference planes from P1-P2 to M1-D2. In this case, a calibrated PD must be employed as an O/E transducer standard to extract the frequency response of the EOM, and vice versa [26].

To simplify the O/E calibration procedure, there comes up with many self-calibrated methods for measuring the EOM without the need of an O/E transducer standard, such as the frequency-shifted heterodyne method [15–21] and the photonic down-conversion sampling method [23,24]. We presented an on-wafer probing kit to realize the damage-free and self-calibrated frequency response characterization of an integrated silicon photonic transceiver based on a twice-modulation mixing approach [20,21]. We also reported ultra-wideband and self-reference methods for measuring MZMs based on photonic down-conversion sampling [23], in which the responses of the PD, the adapter network RAN, the receiver network RxN and the mode-locked laser source (MLLS) were eliminated through fixed low-frequency detection. The photonic down-conversion sampling enables the measurement at the reference planes A1-O, however, these methods are only efficient for packaged EOMs with a good impedance match, since the frequency response of EOMs can simply be corrected by deducting the transmission attenuation of the source network SxN and the adapter network SAN while neglecting the impedance mismatch. For the EOM chips, the accuracy will be significantly affected by the multiple reflections or even resonances due to the impedance mismatch among the source network SxN, the adapter network SAN and the EOM chip.

We previously proposed the photonic sampling for measuring the frequency response of PD chips, which is free of any extra E/O transducer standard. For the PD chips without a good impedance match, the measurement accuracy was significantly improved when the reference planes are moved from O-B2 to O-D2 [25]. In this paper, we further proposed the photonic sampling method for measuring the intrinsic modulation index and half-wave voltage of EOM chips at the reference planes M1-O, regardless of what the impedance is. This is the first time, to the best of our knowledge, that the photonic sampling technique has been demonstrated and qualified for measuring on-chip EOMs. In the experiment, the intrinsic modulation index and half-wave voltage of an MZM chip are measured, which fits in with the results obtained by using the EOFS method [10] and the OSA-based method [7].

2. Operation principle

As shown in Fig. 2, an optical pulse train from the MLLS is coupled into the EOM chip under test to sample a frequency-sweep microwave signal generated by the source of the MNA. Then, the sampled optical pulse train is sent into a PD for photodetection and the recovered electrical signal is collected by the receiver of the MNA. In our method, the microwave signal is down-converted to the same low-frequency component, which is contributed by the MLLS, the source network SxN, the adapter network SAN and the EOM chip. Then, a half-frequency microwave signal is carefully set to down-convert to two closely-spaced frequency components to obtain the uneven comb intensity response of the MLLS [25,27]. Thus, the combined response of the source network SxN, the adapter network SAN and the EOM chip is extracted from the down-conversion components by deducting the uneven comb intensity response of the MLLS without the need of any extra O/E transducer standard. Further, the Short-Open-Load-Device (SOLD) termination is implemented to accurately characterize the degradation factor of SxN and SAN in terms of the transmission attenuation and the impedance mismatch [28]. Finally, the power leveling operation [29] is used to track the incident microwave power of the EOM chip. Thus, the intrinsic modulation index and half-wave voltage are obtained by eliminating the effect of SxN and SAN.

Fig. 2. Schematic diagram of the proposed method. MLLS: mode-locked laser source; EOM: electro-optic modulator; DUT: device under test; PD: photodetector; MNA: microwave network analyzer.

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Mathematically, the optical intensity of the optical pulse train from the MLLS can be expressed as

(1)$$P(t )= 2\sum\limits_{n = 0}^N {{p_n}} \cos ({2\pi n{f_r}t} ),$$

where p_n represents the intensity of the nth-order comb of the MLLS, N is an integer representing the effective order of the optical comb, and f_r is the repetition frequency of the MLLS. Then, the optical modulated signal is detected by a PD, and the photocurrent from the PD can be written by

(2)$$\begin{array}{l} {I_n}(t) = {e_{D,B}}(f )R(f )P(t )\{{1 + {\kappa^2} + 2\kappa \cos [{\varphi + {e_{A,M}}({{f_n}} )m({{f_n}} )\cos ({2\pi {f_n}t} )} ]} \}\\ = DC - 8\kappa \sin \varphi {p_0}{e_{D,B}}({{f_n}} )R({{f_n}} ){J_1}[{{e_{A,M}}({{f_n}} )m({{f_n}} )} ]\cos ({2\pi {f_n}t} )\\ + 2\{{1 + {\kappa^2} + 2\kappa \cos \varphi {J_0}[{{e_{A,M}}({{f_n}} )m({{f_n}} )} ]} \}{e_{D,B}}({n{f_r}} )R({n{f_r}} )\sum\limits_{n = 1}^N {{p_n}\cos ({2\pi n{f_r}t} )} \\ - 4\kappa \sin \varphi {e_{D,B}}({{f_n} \pm n{f_r}} )R({{f_n} \pm n{f_r}} ){J_1}[{{e_{A,M}}({{f_n}} )m({{f_n}} )} ]\sum\limits_{n = 1}^N {{p_n}\cos [{2\pi ({{f_n} \pm n{f_r}} )t} ]} +{\cdot}{\cdot} \cdot \end{array}$$

where e_A_,M is the degradation factor of SxN and SAN corresponding to the reference planes A1-M1, e_D_,B is the degradation factor of RAN and RxN corresponding to the reference planes D2-B2, κ and φ represent the asymmetric factor and the bias phase of the EOM, respectively, m and R are the modulation index of the EOM and the responsivity of the PD, respectively, J₀ and J₁ are the zero-order and first-order Bessel function of the first kind, respectively.

In our method, the microwave frequency is carefully set as

(3)$${f_n} = n{f_r} + \varDelta f,\textrm{ }n = 1,2,3, \cdot{\cdot} \cdot$$

to down-convert to the same low-frequency Δf (0 < Δf < f_r/2). In the case of small-signal approximations, the desired down-conversion components can be simply expressed as

(4)$$V({{f_n};\varDelta f} )\approx 2\kappa \sin \varphi R({\varDelta f} ){e_{D,B}}({\varDelta f} ){p_n}{e_{A,M}}({{f_n}} )m({{f_n}} ).$$

which includes the contributions from the MLLS, the source network SxN, the adapter network SAN, the MZM, the PD, the adapter network RAN and the receiver network RxN. As the responsivity of the PD and the degradation factor e_D_,B are constant at the same low-frequency, the combined response of the SxN, the SAN and the EOM can be obtained from the measured down-conversion components without the need of calibrating the PD, the RAN and the RxN

(5)$$\frac{{{e_{A,M}}({{f_n}} )m({{f_n}} )}}{{{e_{A,M}}({{f_1}} )m({{f_1}} )}} = \frac{{{p_1}}}{{{p_n}}}\frac{{V({{f_n};\varDelta f} )}}{{V({{f_1};\varDelta f} )}}.$$

The uneven comb intensity response of the MLLS (p_n/p₁) can be extracted by using half-frequency photonic sampling defined by f’_n≈nf_r/2 (n = 1,2,3…). In this case, e_A,M(f’_n)M(f’_n)e_D,B(f’_n)R(f’_n)≈e_A,M(nf_r−f’_n)M(nf_r−f’_n)e_D,B(nf_r−f’_n)R(nf_r−f’_n). Therefore, the uneven comb intensity response of the MLLS can be calculated as follows [25]

(6)$$\frac{{{p_n}}}{{{p_1}}} = \frac{{V({f_n^{\prime};n{f_r} - f_n^{\prime}} )}}{{V({f_n^{\prime};f_n^{\prime}} )}}.$$

Thus, the relative modulation index m can be obtained by subtracting the uneven comb intensity response of the MLLS V(f’_n) in Eq. (6) from the measured down-conversion components V(f_n;Δf) in Eq. (4), as

(7)$$\frac{{m({{f_n}} )}}{{m({{f_1}} )}} = \frac{{V({f_n^{\prime};f_n^{\prime}} )}}{{V({f_n^{\prime};n{f_r} - f_n^{\prime}} )}}\frac{{V({{f_n};\varDelta f} )}}{{V({{f_1};\varDelta f} )}}\frac{{{e_{A,M}}({{f_1}} )}}{{{e_{A,M}}({{f_n}} )}}.$$

To further obtain the degradation factor e_A_,M, we investigate the signal flow graph in Fig. 3 and have

(8)$${e_{A,M}} = \frac{{{a_{1D}}}}{{{a_{1S}}}} = \frac{{{\gamma ^{SxN}}S_{21}^{SAN}}}{{1 - {\Gamma ^{SxN}}S_{11}^{SAN} - S_{22}^{SAN}{\Gamma _{EOM}} + {\Gamma ^{SxN}}S_{11}^{SAN}S_{22}^{SAN}{\Gamma _{EOM}} - {\Gamma ^{SxN}}S_{21}^{SAN}S_{12}^{SAN}{\Gamma _{EOM}}}},$$

where a_1S and a_1D are the incident wave at the reference plane A1 and M1, respectively. Г^SxN and γ^SxN are the reflection coefficient and the transmission coefficient of the source network SxN, respectively, Г_EOM is the reflection coefficient of the EOM, and $S_{11}^{SAN}$, $S_{22}^{SAN}$, $S_{12}^{SAN}$, and $S_{21}^{SAN}$ are the scattering parameters of the SAN. In Eq. (8), the numerator term represents the transmission attenuation of SxN and SAN, and the denominator term represents the impedance mismatch among SxN, SAN and EOM.

Fig. 3. Signal flow graph of SxN, SAN and EOM.

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To obtain the scattering parameters of the SAN and the EOM, the one-port reflection coefficients ($\Gamma _M^S$, $\Gamma _M^O$, $\Gamma _M^L$, and $\Gamma _M^D$) at the reference plane M1 are measured when the SAN is terminated with four different impedances (Short, Open, Load and Device under test, i.e., SOLD). The scattering parameters can be calculated as follows

(9a)$$S_{11}^{SAN} = \Gamma _M^L,$$

(9b)$$S_{22}^{SAN} = \frac{{\Gamma _M^S + \Gamma _M^O - 2\Gamma _M^L}}{{\Gamma _M^O - \Gamma _M^S}},$$

(9c)$$S_{21}^{SAN}S_{12}^{SAN} = \frac{{2({\Gamma _M^S - \Gamma _M^L} )({\Gamma _M^O - \Gamma _M^L} )}}{{\Gamma _M^O - \Gamma _M^S}},$$

(9d)$${\Gamma _{EOM}} = \frac{{({\Gamma _M^D - \Gamma _M^L} )({\Gamma _M^O - \Gamma _M^S} )}}{{({\Gamma _M^D - \Gamma _M^L} )({\Gamma _M^S + \Gamma _M^O - 2\Gamma _M^L} )+ 2({\Gamma _M^S - \Gamma _M^L} )({\Gamma _M^O - \Gamma _M^L} )}}.$$

When the repetition frequency f_r of the MLLS is about tens of megahertz, the modulation index m(f₁) can be approximately calculated by

(10)$$m({{f_1}} )\approx \frac{{{{ {4V({{f_1};{f_1}} )} |}_{\varphi = \frac{\pi }{2}}}}}{{V({0;{f_r}} )|{_{\varphi = 0}} - {{ {V({0;{f_r}} )} |}_{\varphi = \frac{\pi }{2}}}}}$$

The modulation index at f_n can be therefore determined by substituting Eqs. (6) and (8)–(10) into Eq. (7). Furthermore, the power wave a_1S of the source network of the MNA can be determined with the help of the power leveling technique, and the half-wave voltage V_π of the EOM can be calculated by

(11)$${V_\pi }({{f_n}} )= \frac{{\pi {e_{A,M}}({{f_n}} )\cdot {a_{1s}}}}{{m({{f_n}} )}}\sqrt {{Z_r}}$$

which corresponds to moving the reference planes from A1-B2 to M1-O.

From the theoretical derivation, our method is applicable for characterizing the EOM including those chips without a good impedance match. If the device under test and the adapter network are featured with a good impedance match, the reflection coefficients can be considered to be zero, and the degradation factor will degenerate into the total transmission attenuation of SxN and SAN.

3. Experimental results

In the experiment, a fiber-based MLLS at the center wavelength of 1559.5 nm is used to generate an optical pulse train with the repetition frequency of 19.91 MHz. The optical pulse train is then coupled into a MZM chip through a cleaved single-mode fiber to sample microwave signal generated by the source of a MNA and applied on the coplanar electrode of the MZM chip through a microwave probe (GGB 40A). After the sampling, the optical modulation signal is sent into a PD for photodetection, and the down-conversion electrical signal is detected by the receiver of the MNA.

We firstly evaluate the uneven comb intensity response of the MLLS, where the stimulus frequency of MNA is set to as f’_n= nf_r/2−0.5 MHz (n = 1, 2, 3…, 1000), and the reception frequency is set to be f’_n and nf_r/2-f’_n. Figure 4 shows the measured frequency components under half-frequency sampling and the uneven comb intensity response of the MLLS. Secondly, the MNA is operated to characterize the MZM chip, where the stimulus frequency is set to be f_n= nf_r+ Δf (Δf = 1MHz, n = 1, 2, 3…, 2000) and the reception frequency is set to be a fixed value at Δf. From the measured down-conversion components, the combined response of the source network SxN, the adapter network SAN and the MZM chip can be obtained by subtracting the uneven comb intensity response of the MLLS (p_n/p₁). As the impact of the RAN and the RxN is eliminated, the half-frequency photonic sampling enables self-reference E/O response measurement without any extra O/E transducer standard, corresponding to moving the reference planes from A1-B2 to A1-O.

Fig. 4. (a) Measured sampled components and (b) calculated response of the uneven comb intensity.

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To further move the reference planes from A1-O to M1-O, the system correction of the MNA is performed at the coaxial port (P1) by using OSL calibration, from which the reflection coefficient Г^SxN and the transmission coefficient γ^SxN of the source network SxN are extracted as shown in Fig. 5(a). After system correction, the reflection coefficients ($\Gamma _M^S$, $\Gamma _M^O$, $\Gamma _M^L$, and $\Gamma _M^D$) are measured at the coaxial port (P1) when the RAN is terminated with Short-Open-Load impedance substrates (GGB CS-5) and the MZM chip at the coplanar tip of the microwave probe, respectively, as shown in Fig. 5(a). Therefore, the reflection coefficients ($S_{11}^{RAN}$, $S_{12}^{RAN}$) and the transmission coefficient ($S_{21}^{SAN}$, $S_{12}^{SAN}$) can be determined based on Eqs. (9a)–(9c), which are shown in Fig. 5(b). The reflection coefficient Г_EOM of the MZM chip can also be extracted from the measured reflection coefficient $\Gamma _M^D$ based on Eq. (8d), as shown in Fig. 6. It can be found from the Smith chart in Fig. 6 that the SAN introduces a short length of transmission line due to the on-wafer probe and results in the trace rotation. After microwave de-embedding, the trace rotation is minimized while still maintaining a trajectory that follows a phase rotation due to the electrical delay of the travelling-wave electrodes of the MZM chip. The impedance of the MZM chip is located at about 90 Ω instead of the reference impedance (50Ω), indicating the imperfect impedance match.

Fig. 5. (a) Measured scattering parameters of the SxN and reflection coefficients of the SAN under SOL termination, and (b) extracted scattering parameters of the SAN.

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Fig. 6. Measured reflection coefficients on a Smith chart.

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With the scattering parameters of SxN and SAN, the degradation factors e_A_,M are calculated by Eq. (9), as shown in Fig. 7, from which the relative modulation index (m(f_n)/m(f₁)) of the MZM chip is obtained by de-embedding the source network SxN and the adapter network SAN, which corresponds to moving the reference planes from A1-B2 to M1-O. For comparison, the combined response of the SxN, the SAN and the MZM chip are also illustrated n the same figure. One can see that the degradation factor is highly related to the transmission attention and impedance mismatch among the SxN, the SAN and the MZM chip. Therefore, it is necessary to take the impedance mismatch and the attenuation into account when MZM chips are under test, especially for those chips without a good impedance match.

Fig. 7. Extracted degradation factor, the incident power of SxN, and the retrieved combined response of the SxN, the SAN and the MZM chip.

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The modulation index m(f₁) is measured by applying load modulation and no-load modulation. In this case, the power of V(f₁;f₁)|_φ_=π/2 and V(0;f_r)|_φ₌₀−V(0;f_r)|_φ_=π/2 are measured to be -69.17 dBm and -55.16 dBm, respectively, the modulation index m(f₁) is therefore calculated to be 0.159. Note that the bias phase of MZM is observed through the amplitude of the modulation frequency f₁, where the maximum and minimum correspond to the bias phase of π/2 and 0, respectively. Besides, the incident power (a_1S) of the source network SxN is measured with the power leveling technique, from which the half-wave voltage of the MZM chip is derived based on Eq. (11). Thus, the intrinsic modulation index and half-wave voltage of the MZM chip can be retrieved based on photonic down-conversion sampling and microwave fixture de-embedding, which corresponds to moving the test reference planes from A1-B2 to M1-O.

For the accuracy, the OSA-based method and the conventional EOFS method are also investigated with a CW laser as the laser source. In the OSA-based measurement, the MZM chip is under the same driving condition while the optical modulated signal is analyzed by an OSA. The modulation index and half-wave voltage are extracted from the ratio between the optical carrier and the modulated sidebands. It is worthy noticing that the OSA-based measurement starts from 10 GHz due to the resolution limit of the commercially available grating-based OSA [8]. The EOFS measurement is initially operated at the reference planes P1-P2 with the help of a two-port SOLT calibration, from which the combined response of the SAN, the EOM chip, the PD and the RAN is directly obtained. With one-port extension procedures at the coaxial port P1 and P2, the SAN and the RAN can be separately de-embedded, which corresponds to moving the reference planes from P1-P2 to M1-D2. Then, the frequency response of the PD is calibrated with a pair of E/O and O/E transducer standards (Agilent N4373), which corresponds to moving the reference planes from M1-D2 to M1-O. After the calibration, the frequency response of the MZM chip is obtained. In Fig. 8, the modulation index under the same driving power are consist with the normalized frequency response of EOFS method after O/E calibration, while both the modulation index and half-wave voltages from our measurement fit in with those obtained with the OSA-based method, which verifies the feasibility of the proposed method.

Fig. 8. Measurement results under the same driving power with the OSA method, the EOFS method and the proposed method.

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4. Conclusion

In summary, a new extraction method for the intrinsic frequency responses of EOM chips is proposed and demonstrated based on photonic down-conversion sampling and microwave fixture de-embedding. The photonic down-conversion sampling enables self-reference extracting the combined response of the source network, the adapter network and the EOM chip, while the microwave de-embedding based on OSL calibration enables on-chip extraction of the intrinsic modulation index of the EOM chip. Moreover, the power leveling technique is used to track the incident microwave power of the source network to obtain the intrinsic half-wave voltage of the chip. In the experiment, the measured results fit in with the results obtained by using the OSA-based method and the EOFS method. Prior to our work for PD in [25], we complete the photonic sampling for characterizing both EOM chips and PD chips with self-reference and on-chip capability, corresponding to the reference planes M1-O or O-D2. Our scheme is applicable for measuring EOM chips even without a good impedance match and is also free of any extra O/E transducer standards. We believe it is promising for non-invasive characterization of high-speed EOM chips during fabrication.

Funding

National Key Research and Development Program of China (2018YFE0201900); National Natural Science Foundation of China (61927821, 61901069); 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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High-frequency characterization of electro-optic modulation chips based on photonic down-conversion sampling and microwave fixture de-embedding

Abstract

1. Introduction

2. Operation principle

3. Experimental results

4. Conclusion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (8)

Equations (14)

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