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Abstract
We propose and experimentally demonstrate a novel method to realize an optical vector analyzer (OVA) with a largely increased measurement range based on linearly frequency-modulated (LFM) waveform and a recircuiting frequency shifter (RFS) loop. An optical LFM signal is sent into an RFS loop to extend its frequency range by circulating in the loop. At the output of the RFS, the frequency-extended optical LFM signal is launched into a Mach-Zehnder interferometer (MZI1) with the device under test (DUT) incorporated in one arm and a delay line in the other arm. By beating the optical signals from the MZIs at a pair of balanced photodetectors, low-frequency signals are generated, from which the frequency responses of the DUT can be extracted using post-digital signal processing. To eliminate the unwanted influence from the measurement system, another MZI (MZI2) sharing the delay line arm with the MZI1 is used for system self-calibration. Thanks to the largely extended frequency range of the optical LFM signal with the use of the RFS loop, the measurement range of the OVA is highly increased. As a proof of the concept, an experiment is performed in which the magnitude and phase responses of a narrow-band fiber ring resonator (FRR) and a hydrogen cyanide (HCN) gas chamber are measured with the proposed OVA. The measurement results show that a measurement range as broad as 418 GHz and a frequency resolution as high as 0.5 MHz are achieved with a measurement time as short as 400 µs. The key advantages of the proposed OVA include a largely extended measurement range, high measurement speed and high resolution.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent years, emerging optical devices are widely used to manipulate the magnitude and phase of optical signals with a high frequency resolution and a wide bandwidth, which is of fundamental importance in numerous applications, such as optical nanoparticle detection [1], on-chip optical signal processing [2], ultra-sensitive optical sensing [3], and so on. For example, a silica microsphere cavity with a bandwidth of less than 10 MHz [4], a narrow-band phase-shifted FBG with a 30-MHz bandwidth [5], and an ultrahigh-Q silicon racetrack resonator with a Q value of 2.3×106 (150-MHz bandwidth in the 1550-nm band) [6], were proposed to achieve high-resolution microwave photonic signal processing and high-sensitivity optical sensing. Before applying these optical devices into different application scenarios, it is necessary to accurately measure the magnitude and phase responses of the optical devices. To do it, an optical vector analyzer (OVA) with an ultrahigh frequency resolution is a strong candidate. On the other hand, a large measurement range as broad as hundreds of GHz is frequently required to cover the whole transmission (or reflection) spectrum in some applications such as optical characterization of hydrogen cyanide (HCN) [7], waveguide micro-ring resonator [8], and Fano resonator on a silicon photonic chip [9]. Moreover, in some transient events such as plasma and combustion systems [10,11], a fast measurement speed is advantageous to capture the real-time absorption spectrum of the gas which generally varies on a timescale of microseconds.
Previously, most of OVAs are realized based on tunable laser source (TLS) and optical interferometer [12,13]. Thanks to the wide wavelength-swept range of the TLS and the high sensitivity inherent in the homodyne interferometric technique, the OVAs offer a broad measurement range and a large dynamic range, but it has a poor frequency resolution, which is normally a few hundred of MHz, due to the low wavelength resolution of the TLS, making it difficult to obtain high-resolution frequency responses of narrow-band optical components. To address the problem, recently, various OVAs based on microwave photonics (MWP) has been proposed and experimentally demonstrated [14–21]. By up-converting a frequency-swept electrical signal with a frequency resolution as high as kHz to the optical domain via electro-optic modulation, a high-accuracy optical frequency sweeping is realized, which leads to an ultrahigh frequency resolution at a kHz level of the OVAs. To further enhance the performance of the OVAs in terms of frequency resolution, measurement range, accuracy, and dynamic range, great efforts have been made to leverage the MWP technologies [15–21]. For example, the optical frequency comb (OFC)-based method was proposed to increase the measurement range up to 100 GHz [15]. However, the switching time of the tunable optical bandpass filter (BPF) used to select each comb line from the OFC is relatively long, which makes this method unsuitable for high-speed measurement systems. To improve the measurement speed, a high-speed OVA was proposed based on linearly frequency-modulated (LFM) waveform and de-chirp operation, and a measurement time as short as 10 µs was realized [22]. Although the LFM-based OVA provides a high measurement speed, the measurement range is limited by the frequency bandwidth of the optical LFM signal (14.6 GHz), and an extra calibration operation is required to eliminate the unwanted influence from the measurement system.
In this paper, we propose a novel approach to extend the measurement range of the LFM-based OVA using a recircuiting frequency shifter (RFS) loop. In the proposed system, an optical LFM signal is firstly generated by modulating a high-quality electrical LFM signal on an optical carrier using a carrier-suppressed single-sideband modulator (SSBM). By injecting the optical LFM signal into an RFS configuration which mainly consists of a frequency shifter, an optical fiber, and a gain medium [23], the optical signal will be broadly extended in the frequency domain. When the optical LFM signal recirculates in the RFS loop for M rounds, the bandwidth of the optical LFM signal will be extended by a factor of M + 1, which would result in a (M + 1)-times-enlarged measurement range for the LFM-based OVA. At the output of the RFS, the optical LFM signal is launched into a Mach-Zehnder interferometer (MZI1) with the device under test (DUT) incorporated in one arm and a delay line in the other arm. To eliminate the unwanted influence from the measurement system, another MZI (MZI2) sharing the delay line arm with the MZI1 is used for system self-calibration, which not only simplifies the operation of the proposed OVA but also improves the measurement accuracy. By beating the optical signals from the MZIs at a pair of balanced photodetectors, low-frequency signals are generated, from which the frequency responses of the DUT can be extracted using post-digital signal processing. An experimental demonstration is performed, in which the magnitude and phase responses of a narrow-band fiber ring resonator (FRR) and a hydrogen cyanide (HCN) gas chamber are measured. The measurement results show that when the optical LFM signal recirculates in the RFS loop for 37 rounds, a measurement range of 418 GHz and a frequency resolution of 0.5 MHz are achieved within a short measurement time of 400 µs. The key advantages of the proposed OVA include a largely extended measurement range, high measurement speed and high resolution.
2. Principles
2.1 LFM-based OVA
The schematic of the LFM-based OVA is shown in Fig. 1. An optical LFM signal generated by MWP-based techniques is used to interrogate the DUT. Mathematically, its optical filed can be expressed as
where E0 is the complex amplitude, ωc is the initial optical frequency, γ and T are the chirp rate and pulse width of the LFM signal. The optical LFM signal is divided into three portions by a 3×3 optical coupler. One portion transmits through the DUT, and at the output of the DUT the optical signal can be written as [22]
Fig. 1. Schematic of the LFM-based OVA. DUT: device under test; ODL: tunable optical delay line; BPD: balanced photodetector.
In order to eliminate the influence from the measurement MZI (MZI1) and the intensity fluctuation of the laser source, a self-calibration operation is performed by using another MZI (MZI2). The third portion of the optical LFM signal is launched into a tunable optical delay line (ODL). By properly adjusting the time delay induced by the ODL equal to the one of the first portion, the optical field of the calibration signal can be given by
where Ec is the complex amplitude of the calibration signal, and Ec = Ed. Again, the mixed optical signal at the output of the MZI2 is sent to balanced photodetection for de-chirp operation. At the output of BPD2, the AC term of the low-frequency electrical signal can be written as Combining Eqs. (4) and (6), the magnitude and phase responses of the DUT can be calculated by [22]2.2 RFS-based bandwidth extension
In an LFM-based OVA, the measurement range and frequency resolution are determined by the bandwidth and frequency resolution of the optical LFM signal. To increase the measurement range of the OVA, an RFS loop is incorporated to extend the bandwidth of the optical LFM signal. Figure 2(a) shows the schematic of the RFS configuration, which consists a frequency shifter, a length of optical fiber, and a gain medium.
Fig. 2. (a) Schematic of recircuiting frequency shifter (RFS)-based bandwidth extension; (b) Schematic of the optical frequency shifter.
An optical LFM signal with a bandwidth of (ωc, ωc+F) and a pulse width of T is divided into two portions by an optical coupler. One portion heads forward to the measurement system while the other portion is injected into the RFS loop, in which the LFM signal is delayed by TR by a length of optical fiber, and frequency-shifted by F using a frequency shifter.
In the RFS loop, the optical frequency shifter is realized with a dual-parallel Mach–Zehnder modulator (DP-MZM), which is driven by a pair of quadrature RF signals, as shown in the upper portion of Fig. 2(b). The spectra evaluation in the DP-MZM is shown in the lower portion of Fig. 2(b). By properly controlling DC1 and DC2, the two sub-MZMs are biased at the minimum transmission point (MITP), and carrier-suppressed double-sideband (CS-DSB) modulation is realized. By adjusting DC3 to introduce a 90° phase difference to the two sub-MZMs, carrier-suppressed single-sideband (CS-SSB) modulation can be done, and therefore an optical frequency shifter is realized.
To avoid the overlap of the pulses, the time delay (TR) induced by the optical fiber is slightly larger than the pulse width (T) of the input LFM signal. To compensate the propagation loss in the RFS loop, a gain medium is used to amplify the optical signal. When the optical LFM signal recirculates in the RFS loop for M rounds, at the output of the RFS loop the optical signal can be expressed as
3. Experimental setup and results
The experimental setup of the proposed OVA is shown in Fig. 3. A narrow-linewidth fiber laser (NKT, Adjustik E15) is used to generate an optical carrier (point A), which is then launched into an MZM. The MZM is biased at the MITP to achieve CS-DSB modulation (point B). A high-performance arbitrary waveform generator (AWG, Keysight M8195A) with a sampling rate of 65 GSa/s is employed to generate a high-quality electrical LFM signal. The start frequency, stop frequency, pulse width, and period of the electrical LFM signal are set to be 6 GHz, 18 GHz, 9.8 µs, and 400 µs, respectively. The electrical LFM signal is amplified using a microwave amplifier and then sent to the MZM. After the modulation, the CS-DSB signal is launched into a tunable optical bandpass filter (BPF1, Finisar waveshaper 1000S), where the negative first-order sideband is selected. After power amplification with an erbium-doped fiber amplifier (EDFA), the generated optical LFM signal is launched into the RFS loop (point C).
Fig. 3. Experimental setup of the proposed LFM-based OVA. MZM: Mach-Zehnder modulator; BPF: optical bandpass filter; EDFA: erbium-doped fiber amplifier; DP-MZM: double parallel Mach–Zehnder modulator; DUT: device under test; ODL: optical delay line; MZI: Mach-Zehnder interferometer; BPD: balance photodetector; DSP module: digital-signal-processing module.
In the RFS loop, the frequency shifter is realized with a DP-MZM, which is driven by a pair of quadrature RF signals. By biasing the two sub-MZMs at the MITP and introducing a 90° phase difference to the two sub-MZMs, CS-SSB modulation can be done. Due to the time delay difference between the DUT path and the reference path (τ2-τ1, τ2>τ1), the generated low-frequency beat signal has a reduced pulse width of T-(τ2-τ1) (rather than T), and the effective bandwidth of the optical LFM signal launched into the RFS loop is reduced to be 11 GHz accordingly. To enable frequency continuity of the frequency-extended LFM signal, the frequency shifting induced by the DP-MZM is also set to be 11 GHz, and the AWG used to generate the electrical LFM signal and the microwave synthesizer used to generate the 11-GHz RF signal are synchronized rigidly. An EDFA is used in the loop for round-trip loss compensation and a BPF (BPF2, Santec OTF-970) is used to remove the amplified spontaneous emission (ASE) noise induced by the EDFA. In the experiments, the bandwidth of BPF2 is set to be 3.5 nm. To avoid overlap between successive LFM signals, a 2-km-long single-mode fiber is used in the RFS loop, which has a time delay of 10 µs.
Fig. 4. Optical spectra of the generated carrier-suppressed double-sideband (CS-DSB) signal (blue curve) and carrier-suppressed single-sideband (CS-SSB) signal (red curve).
Fig. 5. Spectral responses of a narrow-band fiber ring resonator (FRR) measured by LFM-based OVA. (a) Magnitude response and (b) phase response.
The measurement system mainly consists of a measurement MZI (MZI1) and a calibration MZI (MZI2). The device under test (DUT) is incorporated in the upper arm of MZI1, and a delay fiber is added in the other arm. By beating the optical signals from MZI1 at a balanced photodetector (BPD1), a low-frequency signal is generated, in which the magnitude and phase responses of the DUT can be extracted using post-digital signal processing. To eliminate the influence from the measurement MZI (MZI1) and the intensity fluctuation of the laser source, the calibration MZI (MZI2) is used and its optical path difference (OPD) is equal to the one of MZI1. Since the frequencies of the low-frequency electrical signals IMZI-1 and IMZI-2 generated by MZI1 and MZI2 are proportional to the OPDs of the two MZIs [24], time delay equality can be evaluated by simply using a fast Fourier transform (FFT) algorithm. When the frequencies of IMZI-1 and IMZI-2 are identical, the OPD of MZI2 is equal to the one of MZI1. Two balanced photodetectors (BPDs, Thorlabs PDB450C-AC) with a bandwidth of 150 MHz are employed to down-convert the signal from the optical domain to the electrical domain. The electrical signals from the BPDs are recorded by a real-time oscilloscope (OSC) with a sampling rate of 2.5 GSa/s and then processed using a personal computer.
Fig. 6. (a) Measured optical spectra of the LFM signals at the input (blue curve) and output (red curve) ports of the RFS loop. The inset shows the optical spectra of signals at the input (blue curve) and output (red curve) ports of the DP-MZM. (b) Relative optical frequency changed as a function of time of the input (inset) and output optical LFM signals.
Fig. 7. Spectral responses of the narrow-band FRR measured using the proposed wideband LFM-based OVA. (a) Magnitude response and (b) phase response. (c) and (d) are the zoom-in view of the magnitude and phase responses within a range of 340-351 GHz.
Figure 4 (blue curve) shows the optical spectrum of the generated CS-DSB signal when an electrical LFM signal with a frequency bandwidth from 6 to18 GHz is applied to the MZM. By properly controlling the DC bias of the MZM and the power of the electrical LFM signal, the optical carrier and high-order sidebands are suppressed by 25 dB compared with the first-order sidebands. To achieve CS-SSB modulation, a sharp-edge optical BPF is employed to select the negative first-order sideband of the CS-DSB signal, and the optical spectrum of the CS-SSB signal is shown in Fig. 4 (red curve).
Firstly, a narrow-band FRR is used as the DUT, and the measurement results are shown in Fig. 5. The FRR is constructed by connecting the input port and the output port of a 50/50 optical coupler. The cavity length is 13.7 cm, which corresponds to a theoretical free spectral range (FSR) of 750 MHz. Figure 5(a) shows the measured magnitude response of the FRR. Periodical frequency response could be seen, and the measured FSR is 750.4 MHz, which matches well with the theoretical one. Due to the time delay difference between the DUT path and the reference path (τ2-τ1, τ2>τ1), the generated low-frequency beat signal has a reduced pulse width of T-(τ2-τ1) (rather than T), and the measurement range of the OVA is reduced to be 11 GHz accordingly (rather than 12 GHz). In this case, 14 periods can be observed. Figure 5(b) shows the measured phase response of the FRR. Periodical phase jump of 2π can be observed at resonances.
Fig. 8. Spectral responses of an HCN gas chamber measured by the proposed wideband LFM-based OVA. (a) Magnitude response and (b) phase response. (c) and (d) are the zoom-in view of the magnitude and phase responses within a range of 216-232 GHz.
To expand the measurement range of the LFM-based OVA, an RFS loop is introduced into the system. Figure 6(a) shows the measured optical spectra of the LFM signals at the input (blue curve) and output (red curve) ports of the RFS loop. It can be observed that the bandwidth of the output optical LFM signal is increased to 3.5 nm, which is limited by the bandwidth of BPF2. In the RFS loop, a DP-MZM is used as the optical frequency shifter. The optical spectra of signals at the input (blue curve) and output (red curve) ports of the DP-MZM is shown in the inset of Fig. 6(a). By controlling the DC biases and the phase difference between two RF signals injected into the two sub-MZMs, an optical CS-SSB signal is generated, and the negative first-order sideband is suppressed by 28 dB compared with the positive first-order sideband. In the RFS loop, the CS-SSB signal is amplified by an EDFA, while the residual negative first order sideband power is too small to be amplified by the EDFA.
In the experiments, the optical LFM signal recirculates in the RFS loop for 37 rounds, which leads to a 38-times-enlarged bandwidth of the output LFM signal. When the optical LFM signal is launched into MZI2, a low-frequency sinusoidal beat signal (IMZI−2(t)) is generated, and the instantaneous phase (Δφ) of the beat signal is proportional to the frequency chirp [25,26]. The instantaneous phase can be acquired using an equation written by tan−1{IMZI−2(t)/H[IMZI−2(t)]}, where H[] represents Hilbert transform, and an unwrap operation is implemented to obtain the absolute instantaneous phase variation [25,26]. The relative optical frequency with respect to time can be determined by cΔφ/2πnΔL, where c is the velocity of light in vacuum, n is the refractive index of the fiber core, and ΔL is the length of the delay fiber. Figure 6(b) shows the measured relative optical frequency of the input (inset) and output optical LFM signals of the RFS loop. It can be observed that the bandwidth of the optical LFM signal is increased from 11 GHz to 418 GHz by using the RFS loop.
Then, the proposed wideband LFM-based OVA is used to measure the magnitude and phase resoponses of the FRR within a significantly extended range of 418 GHz. Figures 7(a) and 7(b) show the overall magnitude and phase responses of the FRR, and Figs. 7(c) and 7(d) show the zoom-in view within a range of 340-351 GHz. Periodical resonator modes can be clearly observed both in the magnitude response and the phase response. The measurement results match well with the results given in Fig. 5, which is measured using the OVA based on CS-SSB modulation [22]. This means that the proposed LFM-based OVA is capable of characterizing optical components within a wide bandwidth of 418 GHz. The total measurement time is 400 µs, corresponding to 0.4 ns/point.
Finally, the proposed wideband LFM-based OVA is used to measure the frequency responses of a 30-cm-long HCN gas chamber at room temperature (24 °C) and at a pressure of 25 Torr. The measured magnitude and phase responses are shown in Figs. 8(a) and 8(b), respectively, and 5 absorption lines can be observed within a measurement range of 418 GHz. Figures 8(c) and 8(d) show the zoom-in view of the measured magnitude and phase responses within a range of 216-232 GHz. According to the known spectroscopic model from HITRAN, a Voigt curve is used to fit the transmission spectrum of the HCN gas sample [27]. As shown in Fig. 8(c), the red curve and the navy-blue curve represent the measured data and the Voigt-fitted data, respectively. It can be observed that the Voigt curve fits well with the measured data, and the R-square value (Goodness of Fit) is calculated to be 0.999.
4. Discussion
In the proposed LFM-based OVA, a 38-times enlarged measurement range is achieved when the optical LFM signal recirculates in the RFS loop for 37 rounds. The improvement factor is determined by the circulation number of the LFM signal, which is mainly limited by the accumulation of the ASE noise in the RFS loop. Recently, several methods have been proposed to suppress the ASE noise by exploiting the spatial-hole-burning effect in an unpumped erbium-doped fiber (EDF), which may help to further increase the circulation number [28]. Therefore, it is promising to extend the measurement range of the LFM-based OVA up to a few THz. In the meanwhile, the measurement time is determined by the pulse width of the electrical LFM signal and the circulation number. Therefore, by shortening the pulse width of the electrical LFM signal and using a shorter delay fiber in the RFS loop, a much higher measurement speed can be achieved.
In the experiment, an optical LFM signal with a pulse width of 9.8 µs is launched into the RFS loop to extend its frequency range by circulating in the loop. Theoretically, the frequency resolution of the LFM-based OVA is inversely proportional to the pulse width of the LFM signal [22], and the theoretical frequency resolution can reach 100 kHz. Thanks to the linear time-frequency relationship of the LFM signal, the frequency resolution of the LFM-based OVA would be the bandwidth of the signal divided by the total sampling points [22]. Therefore, a frequency resolution as high as 0.5 MHz (12 GHz/(2.5 GSa/s×9.8 µs)) is achieved. It is worth noting that the frequency resolution remains unchanged when the bandwidth of the LFM signal is extended by the RFS loop.
Different from the work reported in [22], firstly, an RFS loop is incorporated in the system to significantly increase the measurement range up to 418 GHz; secondly, to eliminate the unwanted influence produced by the measurement MZI and the intensity fluctuation of the laser source, a self-calibration process is performed. In the experiment, the calibration process is performed with the use of the MZI2. In this way, the measurement signal and the calibration signal can be simultaneously acquired at the two channels of the measurement system.
In the measurement of phase response, when the frequency error of the optical LFM signal (induced by the finite linewidth of the laser source and the frequency error of the electrical LFM signal) is considered, the optical field of the LFM signal (given by Eq. (1)) should be rewritten as
Figure 9 shows the comparison between the OVA systems without and with the calibration MZI (MZI2). Figure 9(a) shows the probability density of the phase fluctuation obtained from the phase response measured with the proposed LFM-based OVA without the calibration MZI. As can be seen, the phase fluctuation distributes within ± 2°, and the standard deviation of the phase fluctuation is 0.7°. Figure 9(b) shows the probability density of the phase fluctuation obtained from the phase response measured with the proposed LFM-based OVA with the calibration MZI. As can be seen, the phase fluctuation distributes within ± 1°, and the standard deviation of the phase fluctuation is 0.3°, which verifies the effectiveness of the calibration MZI in improving the measurement accuracy of the phase response characterization.
Fig. 9. Probability density of the phase fluctuation for the LFM-based OVA when the calibration MZI (MZI2) is (a) not used and (b) used.
5. Conclusion
In conclusion, we have proposed and demonstrated a novel method to extend the measurement range of the LFM-based OVA using an RFS loop. To achieve a high frequency resolution, a high-quality optical LFM signal was generated via electro-optic modulation. By properly controlling the parameters of the LFM signal (such as the bandwidth, pulse width, period, etc.) and the RFS loop (such as the frequency shift, delay time, etc.), a 38-times-enlarged measurement range has been achieved without extra switching time. As a proof of the concept, the magnitude and phase responses of a narrow-band FRR and an HCN gas chamber were measured using the proposed system. A measurement range as broad as 418 GHz and a frequency resolution as high as 0.5 MHz are achieved with a measurement time as short as 400 µs. The proposed high-performance OVA is promising to be a powerful tool for characterization of various emerging optical devices and will find wide applications in frontier research, such as molecular dynamics, on-chip optical signal processing, ultra-sensitive optical sensing, and so on.
Funding
National Key Research and Development Program of China (No. 2018YFE0201800, No. 2019YFB220330).
Disclosures
The authors declare no conflicts of interest.
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