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Abstract
In this work, we propose and demonstrate a self-reference on-chip testing method to obtain the frequency response characteristics of photodiode chips based on photonic sampling and microwave de-embedding. The half-frequency photonic sampling enables self-reference extraction of the combined response of the photodiode chip, the adapter network and the receiver network. The microwave de-embedding under short-open-load-device (SOLD) termination is used to realize on-chip de-embedding of the adapter network and the receiver network in terms of the transmission loss and the impedance mismatch. The proposed on-chip testing method is free of any extra electro-optical transducer standard, which is favorable for performance monitoring in chip evaluation.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Microwave and lightwave technologies have been merged into an interdisciplinary field [1,2], thanks to the strongly emerging applications like high-performance and/or low-latency communications [3,4], high-speed data switching [5–7] and broadband microwave photonic signal processing [7–9]. In these application scenarios, high-speed photodetectors, are basic components to achieve broadband optical/electrical (O/E) conversion, whose frequency response characteristics are of great importance [10].
Currently, there are many methods of measuring the frequency response of photodetectors, which can be categorized into two groups, all-optical and electro-optical schemes. Thereinto, the all-optical schemes based on either heterodyne beat via tunable laser diodes [11–16] or noise beat via an amplified spontaneous emission (ASE) source [17–19] enable ultra-wideband frequency response measurement. However, this method suffers from low frequency resolution due to wavelength drifting or linewidth broadening. As an alternative, electro-optical schemes based on electro-optic frequency sweep (EOFS) [20–22], frequency-shifted heterodyne [23–29] or photonic up-conversion sampling [30,31] can realize a high-resolution measurement. Especially the EOFS scheme is widely used to measure the frequency response of both electro-optic modulators and photodetectors with the assistance of a commercially available off-the-shelf microwave network analyzer (MNA).
Figure 1 shows the schematic diagram of a typical EOFS scheme, where the microwave networks, i.e., SxN and RxN, represent the built-in source and receiver of the MNA, respectively. The EOFS measurement is realized by using an intensity modulator (IM) and a photodiode (PD) as the E/O transmitter and the O/E receiver, respectively [32]. In such a case, there are inevitable electrical components between the SxN and the IM, and between the PD and the RxN, such as microwave cables, connectors, bias-tees, fixtures or probes used to deliver electrical signals from the SxN to the IM and collect electrical signals from the PD to the RxN. These components can be represented by the adapter networks, i.e., SAN and RAN in Fig. 1, which generally have a single coaxial or non-coaxial port. Based on the model in Fig. 1, the measurement results at the reference planes P1-P2 (including the frequency response of the SAN, the IM, the PD and the RAN) can be obtained after correcting the inherent systematic errors by using the two-port electrical/electrical (E/E) calibration under Short-Open-Load-Thru (SOLT) termination [33,34]. The reference planes P1-P2 are cascaded networks of the SAN, the IM, the PD and the RAN, which can be further moved to M1-D2 by de-embedding the SAN and the RAN via the one-port E/E extension under Short-Open-Load (SOL) termination [35]. It is obvious that the measurement results at reference planes M1-D2 actually include the frequency response of the IM and the PD. Therefore, a calibrated IM must be employed as an E/O transducer standard to extract the frequency response of the PD, and vice versa [36,37].
Fig. 1. Schematic diagram of a typical electro-optic frequency sweep scheme. MNA: microwave network analyzer; SxN: built-in source of MNA; SAN: adapter network connected to source; IM: intensity modulator; PD: photodiode; RAN: adapter network connected to receiver; RxN: built-in receiver of MNA.
In order to simplify the E/O and O/E calibration procedure, an improved method based on quasi-reciprocal approximation is proposed, where an electro-absorption modulator (EAM) is employed to achieve both E/O and O/E conversion with an identical frequency response [38,39]. In our previous work, a frequency-shifted heterodyne method based on two-tone mixing was proposed to achieve self-reference frequency response measurement of PDs without the need of an E/O transducer standard [23,24]. We also presented an on-wafer probing kit to realize damage-free and self-calibrated frequency response characterization of an integrated silicon photonic transceiver based on a twice-modulation mixing approach [26,27]. In addition, we demonstrated an ultra-wideband and self-reference method for measuring PDs through segmental up-conversion based on photonic sampling, in which the uneven responses of both the modulator and the mode-locked laser source (MLLS) were eliminated through the symmetric frequency modulation [30,31]. The photonic sampling method starts at the reference planes A1-B2, and enables self-reference measurement at the reference planes O-B2. Nevertheless, this method is only efficient for packaged photodetectors with a good impedance match, since the frequency response characteristics of PDs are simply corrected by deducting the transmission attenuation (i.e., neglecting the impedance mismatch) of the RAN and the RxN. As is known to all, the impedance mismatch will contribute to multiple reflections or even resonances in the electrical transmission path [36,40]. Hence, for the on-chip test with a poor impedance match, the measurement accuracy of the photonic sampling method will be significantly reduced when the reference planes are moved from O-B2 to O-D2, and the impedance mismatch is still ignored.
In this paper, we present an improved self-reference photonic sampling method to measure the frequency response of PD chips. The prominent advantage of the proposed method lies in that an accurate measurement can still be realized without an impedance match. To the best of our knowledge, this is the first time that the photonic sampling technique has been demonstrated and qualified for the self-reference frequency response measurement of PD chips. In the experiment, the intrinsic frequency response of a surface-coupled PD chip is measured, which fits in with the measurement results obtained by using the conventional EOFS methods [35,36].
2. Operation principle
Figure 2 shows the schematic diagram of the proposed self-reference photonic sampling method for measuring the frequency response of PD chips. An optical pulse train from a MLLS is sent into an IM to sample a half-frequency sweep microwave signal from the built-in source of an MNA. The sampled optical pulse train is then coupled into the PD chip under test and collected by the built-in receiver of the MNA. In the generated electrical spectrum, the comb-like frequency components are contributed by the MLLS, the PD chip, the RAN and the RxN, while the sampling frequency components are contributed by the MLLS, the SxN, the SAN, the IM, the PD chip, the RAN and the RxN. In the proposed method, the uneven spectrum lines of the MLLS are firstly characterized by comparing the amplitudes of the sampling frequency components. Hence, the combined response of the PD chip, the RAN and the RxN is extracted from the comb-like frequency components without the need of any extra E/O transducer standard. Then, an on-chip one-port test of reflection coefficients under Short-Open-Load-Device (SOLD) termination is implemented to accurately characterize the degradation factor of the RAN and the RxN in terms of the transmission attenuation and the impedance mismatch. Therefore, the intrinsic frequency response of the PD chip is obtained after de-embedding the RAN and the RxN.
Fig. 2. Schematic diagram of the proposed method and the photographs of the PD chip coupled by a cleaved single-mode fiber and a microwave probe. MLLS: mode-locked laser source; IM: intensity modulator; PD: photodiode; DUT: device under test; MNA: microwave network analyzer.
Mathematically, the optical pulse train from the MLLS can be expressed by the comb-like power spectrum located at its center frequency as
where fr is the tooth spacing (also the repetition rate) of the optical pulse train, N is an integer representing the effective order of the optical comb, and p0 and pn are the power of the center frequency component and the frequency components with frequency shifts of nfr, respectively. The optical pulse train from the MLLS samples the microwave signal (fn) from the built-in source of the MNA through electro-optic modulation in the IM, and is then detected by the PD chip under test. The recovered electrical signal in the built-in receiver of the MNA can be expressed asIn order to calibrate the uneven response of the MLLS, we use the half-frequency photonic sampling defined by fn≈nfr/2 (n=1, 2, …, N) to guarantee that fn is close to nfr–fn, i.e., fn≈nfr–fn. In this case, eD,B(fn)R(fn)≈eD,B(nfr−fn)R(nfr−fn). Therefore, the comb intensity of the MLLS can be calculated based on Eqs. (4a) and (4b) as follows
where p0 is the DC power of the MLLS. Substituting Eq. (5) into Eq. (3), the combined response of the PD chip, the RAN and the RxN corresponding to the reference planes O-B2 can be written asIn order to obtain the individual response of the PD chip at the reference planes O-D2, the degradation factor eD,B of the reference planes D2-B2 is required to be characterized and subtracted from the combined response of the reference planes O-B2. Figure 3 shows the signal flow graph of the PD chip, the RAN and the RxN, in which apd, Гpd and b2M are the output voltage wave, the reflection coefficient of the PD chip, and the measured voltage wave of the built-in receiver of MNA, respectively. ГRxN and γRxN in Fig. 3 represent the intrinsic systematic responses of the reflection coefficient and transmission attenuation of the RxN, respectively, which can be determined by using two-port E/E calibration [36] and receiver leveling techniques [41] in the system correction of the MNA.
Based on the signal flow in Fig. 3, the degradation factor eD,B can be characterized by [40]
To obtain the scattering parameters of the RAN and the PD chip, the one-port reflection coefficients ($\Gamma _M^S$, $\Gamma _M^O$, $\Gamma _M^L$ and $\Gamma _M^D$) at the reference plane P2 are measured when the RAN is terminated with four different impedance substrates (Short, Open, Load and Device, i.e., SOLD) at the coplanar contact of the microwave probe. The scattering parameters of the RAN are determined by using the following expressions [35]
With the help of the measured reflection coefficients, the degradation factor eD,B can be calculated based on Eqs. (7a)–(8d), and the frequency response of the PD chip can be obtained by removing the impact of the RAN and the RxN. Thus, the measurement of the intrinsic frequency response of the PD chip can be realized based on half-frequency photonic sampling and SOLD-based microwave de-embedding, which corresponds to moving the reference planes from A1-B2 to O-D2.
If the device under test and the adapter network are featured with a good impedance match, the reflection coefficients Гpd, $S_{11}^{RAN} $ and $S_{22}^{RAN} $ can be considered to be zero, and the degradation factor eD,B will degenerate into the total transmission attenuation γT of the RAN and the RxN.
3. Experimental results and discussion
In the experiment, an optical pulse train centered at 1559.12 nm and with a 3-dB spectrum width of 0.9 nm is generated by a home-made fiber-based MLLS, whose repetition rate is measured to be 21.939 MHz. The optical pulse train enters an IM (EOSpace AX-1×2-OMSS-20-PFA-SFA), where it samples the half-frequency sweep microwave signal from the built-in source of an MNA (Keysight N5225A). After sampling, the optical signal with an average power lower than −15dBm is coupled into an InGaAs/InP p-i-n PD chip by using a cleaved single-mode fiber, where the PD chip is electrically contacted by a microwave probe (GGB 50A-GSG) as shown in Fig. 2. The adapter network SAN includes a microwave cable, and the adapter network RAN includes a microwave probe and another bias-tee network. The MNA is operated at the frequency-offset mode, where the source frequency is set to be fn, and the response frequency is set to be nfr, fn and nfr−fn, respectively. It is noted that there is not obvious difference between the optical spectrum before and after IM, due to the MHz-level repetition frequency of MLLS and the GHz-level resolution of optical spectrum analyzer (OSA).
Firstly, the comb intensity of the MLLS is characterized by setting the frequency of the half-frequency sweep microwave signal to be fn=nfr/2−0.5 MHz (n=1,2,3…). In this case, the relative comb intensity pn/p0 can be derived from the amplitude comparison between the sampling components at fn and nfr−fn based on Eq. (5). Figure 4 presents the measurement results. The narrow 3-dB spectrum width (0.9 nm) of the MLLS serves as the major contribution to the uneven response of the MLLS in the measured results. The comb frequency components V(nfr) are measured at the reference planes A1-B2, and the combined response of R(nfr)eD,B(nfr) is determined at the reference planes O-B2 after subtracting the relative comb intensity of the MLLS. According to Eq. (5) and (6), we normalize the measured comb frequency components V(nfr) as a relative response V(nfr)/V(0). As the impact of the SxN, the SAN and the IM is fully removed, the half-frequency photonic sampling enables self-reference O/E response measurement without any extra E/O transducer standard, which corresponds to moving the reference planes from A1-B2 to O-B2.
To further move the reference planes from O-B2 to O-D2, the system correction of the MNA is performed at two coaxial ports (P1 and P2) by using the SOLT calibration and receiver leveling techniques, from which the reflection coefficient ГRxN and transmission attenuation γRxN of the MNA receiver are extracted as shown in Fig. 5.
Fig. 5. Measured responses of the RxN with SOLT calibration and reflection coefficients of the RAN under SOLD termination.
After system correction, the one-port reflection coefficients (($\Gamma _M^S$, $\Gamma _M^O$, $\Gamma _M^L$ and $\Gamma _M^D$) are measured at the coaxial port P2 of the MNA when the RAN is terminated with Short-Open-Load impedance substrates (GGB CS-5) and the PD chip at the coplanar tip of the microwave probe, respectively. The measured reflection coefficients are also exhibited in Fig. 5. Therefore, the scattering parameters ($S_{11}^{RAN}$, $S_{12}^{RAN}$, $S_{21}^{RAN}$, and $S_{22}^{RAN}$) of the RAN can be determined based on Eqs. (8a)–(8c), which are shown in Fig. 6. The reflection coefficient Гpd of the PD chip can also be extracted from the measured reflection coefficient $\Gamma _M^D$ based on Eq. (8d). As shown in Fig. 6, the PD chip has a strong reflection, which reveals its poor impedance match. Figure 7 illustrates the degradation factor eD,B, the impedance mismatch γPD,RAN between the PD chip and the RAN, the total transmission attenuation γT of the RAN and the RxN, and the impedance mismatch γRAN,RxN between the RAN and the RxN. It can be seen from Fig. 7 that the degradation factor is highly related to the impedance mismatch between the PD chip, the RAN and the RxN. Therefore, it is necessary to take the impedance mismatch into account when chips are under test, especially for those chips with poor impedance match. Finally, the frequency response of the PD chip is obtained by removing the impact of the RAN and the RxN, which is shown in Fig. 8. Thus, the frequency response of the PD chip can be measured based on half-frequency photonic sampling and SOLD-based microwave de-embedding, which corresponds to moving the reference planes from A1-B2 to O-D2.
In order to check the measurement accuracy, we also implement the conventional EOFS measurement by using an identical setup except that the MLLS is replaced by a continuous-wave laser diode. In this case, the built-in source and receiver of the MNA are swept at the same frequency. The MNA measurement starts from the reference planes P1-P2 by means of a two-port SOLT calibration, from which the combined response of the SAN, the IM, the PD chip and the RAN is directly obtained. With similar 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. In order to further move the reference planes from M1-D2 to O-D2, the frequency response of the IM is characterized by using a pair of E/O and O/E transducer standards (Agilent N4373) for an extra calibration. After the calibration, the frequency response of the PD chip can be obtained. Figure 9 presents the measurement results obtained by using the conventional EOFS method and the proposed method. It can be seen from Fig. 9 that the measurement result based on the photonic sampling method fits in with that based on the EOFS method after calibration, which verifies the feasibility of the proposed method. Moreover, the measured reflection coefficients in Fig. 6 (i.e., the Гpd) reveal the impedance mismatch of the PD chip under test, which indicates that the proposed method is robust to impedance mismatch of the on-chip devices.
4. Conclusion
In summary, a novel method for measuring the frequency response of PD chips is proposed and demonstrated based on photonic sampling and microwave de-embedding. The half-frequency photonic sampling enables the self-reference measurement of the combined response of the PD chip, the RAN and the RxN. The microwave de-embedding based on SOLD termination achieves the on-chip extraction of the individual frequency response of the PD chip by de-embedding the RAN and the RxN in terms of the transmission loss and the impedance mismatch. In the experiment, the frequency response of a surface-coupled PD chip is measured, and the consistency between the proposed method and the conventional EOFS method is investigated to check the measurement accuracy. The on-chip measurement without any extra E/O transducer standards is promising for non-invasively extracting intrinsic frequency response characteristics in the course of chip fabrication, and is also helpful for more predictable yield before device packaging.
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).
Acknowledgements
The authors express heartfelt thanks to the 44th research institute of China Electronics Technology Group Corporation (CETC) for providing the PD chips.
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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