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Abstract
An optical vector network analysis (OVNA) based on double sidebands (DSB) modulation and the Pound Drever Hall (PDH) technique is proposed and demonstrated. The frequency responses measurement of the high Q optical device with high stability are achieved by transmitting the DSB modulation signals through the device. The high stability can be realized by using the PDH feedback loop. Compared with the conventional DSB-based OVNA, the proposed scheme with only one step measurement avoids the complex post-processing. Moreover, the long-term measurement with high stability can also be realized. A proof-of-concept experiment is carried out, which achieves the magnitude and phase responses of the Fabry-Perot interferometer, and there is no frequency response shift even though the test time is up to 90 minutes. The proposed method is simple and stable, which can be potentially applied in characterization and fabrication of high Q optical devices.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Recently, optical devices with high quality factor (Q), which have the capability to manipulate the optical spectrum finely within an ultra-small spectral range, are highly desirable in numerous applications, such as the single molecule detection, on-chip optical signal processing and narrow linewidth laser stabilization and so on [1–4]. Thus, measuring the magnitude and phase responses simultaneously with wide bandwidth and high resolution is of great significance for their design and fabrication, and other key parameters including group delay and insertion loss can be also calculated further [5–7]. Previously, optical vector network analyzers based on interferometry and the modulation phase-shift methods are reported to measure the frequency responses [8–10]. However, the wavelength-swept laser sources required in the systems have low wavelength accuracy and poor wavelength stability, which resulted in a relatively low measurement resolution for ultra-high Q optical devices [11]. In order to solve the problem of low resolution, OVNA based on optical single side-band (SSB) modulation is being developed and receiving increasing attention [12–23]. Owing to the introduction of the high-resolution radio frequency source, sub-MHz resolution can be achieved experimentally in the SSB-based OVNA. Nevertheless, the SSB-based OVNA with the wide measurement range and high measurement accuracy is very hard to be achieved [15]. The sweeping range is mainly restricted by the bandwidth of the optoelectronic devices and the electrical vector network analyzer, and the measurement accuracy cannot be improved perfectly, due to the low sideband suppression ratio (SSR) and high-order sidebands. Besides, the bandpass responses of the device under test (DUT) cannot be measured by the above approach, since the optical carrier has been seriously suppressed while it needs to be located out of the bandpass responses.
To overcome the above problems, an OVNA based on asymmetric double sideband modulation is proposed [24]. Compared with the conventional SSB modulation, the bandwidth is doubled and the errors caused by the unwanted sidebands are avoided efficiently. However, the optical carrier must be shifted to avoid the frequency aliasing problem by employing a dual-drive dual-parallel Mach-Zehner modulator, the stimulated Brillouin scattering effect or an acousto-optic modulator in recent reports [25–27]. Undoubtedly, high cost and complex systems are inevitable in these approaches. As an improvement, a symmetric DSB-based OVNA is proposed, which is a common modulation process, so that the system is dramatically simplified without additional optical filter and RF source as we anticipated [28–30]. However, the DUT needs to be measured twice by adjusting the bias voltage and the frequency responses are obtained with requirement of post-processing. Moreover, for the high Q optical devices with ultra-narrow bandwidth, the optical carrier is hardly in its bandpass or bandstop region without precise control systems, which has limited the practical applications in high Q optical devices.
In this work, we proposed and experimentally demonstrated a high stable OVNA based on symmetric double sidebands modulation and the PDH technique [31]. In the PDH feedback loop, the laser is aligned to one of the DUT’s resonant frequencies. Then the stabilized light is modulated in the OVNA part, which is subsequently beaten after propagating through the DUT. By extracting the magnitude and phase information of double frequency of the driven RF signal, the frequency responses of the DUT can be obtained easily. By applying the proposed OVNA, the high Q optical devices can be measured with only one step measurement, and the complex post-processing is avoided. In addition, the long-term measurement with high stability can be also realized since laser drift is eliminated successfully by using the PDH technique. A proof-of-concept experiment has been performed. When the PDH feedback loop is used, the measurement time is as long as 90 minutes with no frequency response shift and a resolution of 1.2 MHz is achieved.
2. Principle of operation
The schematic diagram of the proposed OVNA based on double sidebands modulation and the PDH technique is shown in Fig. 1. The measurement system is composed of two key parts, a Pound-Drever-Hall (PDH) feedback loop and a DSB-based OVNA. In the PDH feedback loop, the laser is aligned to one of the resonator’s resonant frequencies when the loop operates, then magnitude and phase of the two ± 1st-order sidebands would be changed with same deviation after the DUT. In the DSB-based OVNA, an optical carrier from a tunable diode laser source is fiber coupled to the phase modulator (PM) via a polarization controller (PC), which ensures an efficient polarization direction before the input port of the PM, subsequently, the optical signal is modulated by a RF signal from the electrical vector network analyzer (EVNA). Then, the double-sideband signal is sent to the DUT, in which the ± 1st-order sidebands undergo same magnitude and phase responses according to the transmission responses of the DUT. A photodetector (PD) is incorporated to convert the optical signal into RF signal, and the weak RF signal is further amplified by an electrical amplifier. Then the phase and magnitude of the electrical component with double frequency of the driven RF signal are detected by the EVNA. By scanning the frequency of the RF source, the total frequency responses of the DUT and measurement system can be obtained, the responses of the measurement system can be removed by a calibration step. Therefore, the accurate magnitude and phase responses of the DUT can be measured.
Fig. 1 (a) Schematic diagram of the proposed OVNA based on DSB modulation and the PDH technique. (b) Optical spectra of the signals at different points. LD: laser diode; PC: polarization controller; PM: phase modulator; DUT: device under test; PD: photo detector; EA: electrical amplifier; LPF: low pass filter; RF: radio frequency; PID: proportional-integral-derivative amplifier; EVNA: electrical vector network analyzer.
Mathematically, the optical fields of the RF modulated signal generated by the PM can be written as
where and are the angular frequencies of the optical carrier and the RF signal, respectively. is the modulation index of the PM, is the amplitude of the RF driving signal, and is the half-wave voltage of the electrical optical modulator (EOM). Based on the Jacobi–Anger expansion, transform the phase-modulated signals in Eq. (1) into the frequency domain, we havewhere is the nth-order Bessel function of the first kind. When the generated optical DSB signal expressed in (2) transmits through a DUT, the magnitude and phase of the carrierand each sideband are changed according to the transmission response of the DUT. Thereby, the optical field at the output of the DUT can be written aswhere , and are the complex transmission responses of the DUT and the measurement system without the DUT, respectively. After the DUT, the optical signal is converted to electrical signal by a PD, the converted photocurrent at frequency is given bywhere is the responsivity of the PD.By using the Pound-Drever-Hall technique, the optical carrier aligned to the resonance of the DUT can be ignored owing to the filtering effect. Besides, the modulated signal is also very small. The beat signal of the suppressed optical carrier and first-order sidebands is weak and is hard to detect. Therefore, the Eq. (2) only contains two first-order sidebands, and then the Eq. (4) in the frequency domain can be rewritten as
The measurement system function can be obtained by using a calibration procedure, in which the DUT is removed and two test ports are directly connected, e.g. . In this case, the photocurrent without DUT can be expressed as
According to Eqs. (5) and (6), the accurate transmission responses of the DUT without measurement error can be obtained, which can be given by
3. Experimental results and discussion
A proof-of-concept experiment for high Q optical devices measurement based on the configuration as shown in Fig. 1 has been implemented. In the DSB-based OVNA, a lightwave with the power of 14.2 dBm is generated by the laser diode (New Focus TLB 6700), which is then modulated by the 40 GHz PM (EOspace), the symmetric DSB signal is thus obtained. After propagating through the Fabry-Perot Interferometer (DUT, Micron Optics), the optical signal is converted into photocurrent by the PD (U2T XPDV2120R) with bandwidth of 40 GHz and responsibility of 0.65 A/W at 1550 nm. Then the magnitude and phase of the photocurrent are extracted by the EVNA (Agilent PNA-X N5244A). Here, the laser is stabilized to the DUT via the PDH technique. The error signal is extracted by comparing the phase of the original radio frequency and the radio frequency after PD using the mixer (Marki M2-0020), which is then sent to the feedback servo (New Focus, LB1005), and the laser wavelength can be controlled precisely by the feedback voltage signal from the servo. An optical spectrum analyzer (Yokogawa AQ6370C) with a resolution of 0.02 nm is employed to monitor the optical spectra at the output of PM.
Figure 2 shows the optical spectra of the optical signal modulated by the swept RF. The modulation frequency is 6 GHz, 8 GHz,10 GHz, 12 GHz, respectively, the modulation index is 0.48. As can be seen, the ± 1st-order sidebands prepared for measuring can be obtained easily. The power of the undesired ± 2nd-order sidebands are much less than that of the ± 1st-order sidebands, which are too weak to affect the measurement accuracy.
To verify the feasibility of the proposed scheme, the laser is stabilized to the resonant frequency of the DUT via the PDH technique. The ± 1st-order sidebands, which carry with the same frequency responses after passing through the DUT, are converted into double frequency of the driven RF signal by the PD. Therefore, the frequency responses of the DUT can be obtained easily by extracting the magnitude and phase information of doublefrequency. As shown in Fig. 3, the magnitude and phase responses of the DUT can be measured by the proposed DSB-based OVNA when the modulation index is 0.48. The DUT is the Fabry-Perot Interferometer. It is clear that the measurement range is from 3 GHz to 13 GHz offset the optical carrier. When compared with the SSB-based OVNA, the frequency response near the optical carrier can be measured accurately since the optical filter is not required in the proposed DSB-based OVNA. In addition, the measurement points can be increased to 32001, so the proposed DSB-OVNA can have sub-MHz resolution theoretically when the measurement range is 10 GHz.
Fig. 3 (a) Magnitude and (b) phase responses of the DUT measured by the proposed DSB-based OVNA in the wideband range.
High stability is that the calculative ability of the measurement system can stay the same at a long period of time, which mainly includes the short-term and long-term stability. In the DSB-based OVNA systems with low stability, high resolution spectroscopy and accurate tests of fundamental physical constants are hard to achieve. However, the stability of the system is mainly determined by the laser. Therefore, it is very critical and valuable to improve the stability of laser source.
In this work, the center frequency of the laser is aligned to one of the DUT’s resonant frequencies via the PDH technique. Hence, the OVNA system with PDH feedback control loop can be operated stably for a very long time. Figure 4 shows the magnitude and phase responses of the DUT measured by the proposed OVNA with PDH servo loop at various test time point. As can be seen, the measured magnitude and phase responses are almost coincident even when the test time is up to 90 minutes, which agrees well with the theoretical prediction. Nevertheless, when the PDH feedback control loop is removed from the proposed OVNA, the errors in the frequency responses induced by the unwanted laser frequency drift become obvious, as shown in Fig. 5. It can be observed clearly that two repeated magnitude and phase responses with different frequency deviation appear at various test time point. It is mainly ascribed that the laser deviates from DUT’s resonant frequencies under free running without PDH feedback control loop, then the responses in the left and that in the right are measured respectively by + 1st and −1st-order sidebands one by one, causing aliasing effect in the responses. Therefore, the PDH technique is the key for the DSB-based OVNA to operate in a long term with high stability. Though only the periodic devices can be measured, the proposed OVNA would have great application prospects because of the rapid development of the periodic ultra-high Q resonators.
Fig. 4 (a) Magnitude and (b) phase responses of the DUT measured by the proposed OVNA with PDH feedback loop at various test time point.
Fig. 5 (a) Magnitude and (b) phase responses of the DUT measured by the proposed OVNA without PDH feedback loop at various test time point.
4. Conclusion
In conclusion, a high stable OVNA based on symmetric double sidebands modulation and the PDH technique has been proposed and experimentally demonstrated. The frequency responses of the high Q optical device are measured successfully with high stability by transmitting both ± 1st-order sidebands of the DSB modulation through the device. The high stability can be realized by using the PDH feedback control loop for stabilizing the laser, thus, the stability of the DSB-based OVNA is improved. Compared with the conventional DSB-based OVNA, only one step measurement is required and the complex post-processing is avoided. The key advantage of the proposed scheme is that the long-term measurement with high stability can be realized by using the PDH feedback loop. In the experiment, the magnitude and phase responses of the Fabry-Perot interferometer is achieved, and no aliasing of the frequency responses even when the test time reaches up to 90 minutes. Our proposed scheme shows a potential application in the fields of the high spectral efficiency optical communication and high-accuracy optical metrology.
Funding
National Natural Science Foundation of China (NSFC) (61501051, 61625104, 61431003); Fundamental Research Funds for the Central Universities (500418777); Fund of State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications (BUPT) (No. IPOC2017ZT01) and China Postdoctoral Science Foundation (Grant No. 2017M610826).
Acknowledgments
Many thanks to Long Ye for invaluable help in the laboratory testing of our scheme. Many thanks to Jinliang Liu for useful discussions.
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