Frequency response measurement of high-speed electro-optic phase modulators via a single scan based on low-speed photonic sampling and low-frequency detection

Yujia Zhang; Yangxue Ma; Yangxue Ma; Zhiyao Zhang; Lingjie Zhang; Zhen Zeng; Shangjian Zhang; Yong Liu

doi:10.1364/OE.27.032370

1. Introduction

Electro-optic phase modulators, which feature bias-free and linear electric-to-optical signal conversion, have been widely used in applications such as microwave photonics, optical communications and signal processing [1–7]. The frequency response of a phase modulator must be subtly evaluated since it has a great influence on the overall system performance, especially for microwave photonics application. The most direct approach to characterizing the frequency response of a phase modulator is based on optical spectrum analysis, which is achieved by measuring the power ratio of the modulation sideband to the optical carrier at various input microwave frequencies (with identical input microwave power) through an optical spectrum analyzer (OSA) [8]. This method can provide accurate measurement results [9]. Whereas, the frequency measurement resolution is generally low (0.01 nm, i.e., 1.25 GHz@1550 nm), which is limited by the spectral resolution of a commercially-available grating-based OSA [10]. In order to achieve a high-resolution characterization, the frequency response information of the phase modulator should be firstly transferred to the electrical domain via photoelectric conversion, and then be measured through the well-developed electrical domain measurement techniques with a high resolution, such as a vector network analyzer (VNA) and an electrical spectrum analyzer (ESA) [11–17]. In the VNA-based method, phase-to-intensity modulation (PM-IM) conversion should be implemented in advance before photodetection, since phase modulators inherently change the optical phase and keep constant optical envelope [12–18]. The main disadvantage of this method is that extra calibration should be implemented to remove the frequency response of the photodetector and that of the PM-IM conversion architecture based on dispersion or Mach-Zehnder interferometer with unequal arm length [16,17]. In the previous work, we have demonstrated a high-resolution self-calibrating method to measure high-speed electro-optic phase modulators via two-tone modulation and frequency-shifted heterodyne interference [19]. Through employing this method, the frequency response including the S21 curve, the modulation index and the half-wave voltage versus frequency, can be accurately obtained via a single scan by using low-frequency detection. Nevertheless, two tunable microwave sources with their output frequencies synchronously sweeping across the frequency measurement range are needed, which makes this scheme a little complicated.

In this paper, a novel approach to measuring the frequency response of high-speed electro-optic phase modulators is proposed and experimentally demonstrated, which is realized by photonic down-conversion sampling via a low-repetition-rate ultrashort pulse train and PM-IM conversion via a Sagnac loop. This method is featured with single scan, high resolution, low-frequency detection and usage of a single tunable microwave source. Self-calibrating frequency response measurement is achieved by calculating the relative intensity between the Fourier frequency component in the ﬁrst Nyquist frequency range and the direct current (DC) component of the photocurrent. In the experiment, four commercial LiNbO₃-based high-speed electro-optic phase modulators are characterized, where the measured relative frequency response by using the proposed method fits in with that obtained by using the OSA method.

2. Operation principle

Figure 1 shows the schematic diagram of the proposed method. The electro-optic phase modulator under test is inserted into a Sagnac loop to achieve PM-IM conversion, which facilitates measuring its frequency response in the electrical domain. The operation principle of the measurement is briefly described as follows. Low-repetition-rate ultrashort optical pulse train from a passively mode-locked laser (MLL) is split into two branches by the 3-dB optical coupler (OC). In the Sagnac loop, the pulse train propagating in the clockwise (CW) direction is modulated by the input microwave signal (${f_s}$). For the pulse train propagating in the anticlockwise (anti-CW) direction, the modulation can be neglected in the frequency range above multi-hundreds of MHz due to the fact that the high-speed electro-optic phase modulator is a traveling wave device [20,21]. The two counterpropagating pulse trains recombine after circling in the loop via the 3-dB OC, where the two-beam interference achieves partial PM-IM conversion. Then, the partially intensity-modulated optical pulse train is sent to a photodetector (PD) to obtain the low-frequency duplicate of the microwave signal in the first Nyquist frequency range, and the output electrical spectrum is measured by an ESA. The response of the phase modulator at ${f_s}$ can be calculated from the relative intensity between the Fourier frequency component in the ﬁrst Nyquist frequency range and the DC component. Through sweeping ${f_s}$ by the computer-controlled microwave source, the relative frequency response (i.e., the S21 curve) of the phase modulator can be obtained, which is critical for microwave photonics application.

Fig. 1. Schematic diagram of the proposed method. MLL: mode-locked lasers; PC: polarization controller; OC: optical coupler; PD: photodetector; ESA: electrical spectrum analyzer.

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Mathematically, for an MLL with a central frequency of ${f_0}$ and a repetition rate of ${f_r}$, the optical field of the output pulse train can be expressed as

(1)$$\begin{aligned} {S_{MLL}}(t ) &= {F_0}\sum\limits_{l ={-} \infty }^{ + \infty } {p({t - {l \mathord{\left/ {\vphantom {l {{f_r}}}} \right.} {{f_r}}}} )} \\ &= \sum\limits_{n\textrm{ ={-} }N}^N {\{{{p_n}{e^{j[{2\pi ({{f_0} + n{f_r}} )t} ]}} + {p_n}{e^{ - j[{2\pi ({{f_0} + n{f_r}} )t} ]}}} \}} , \end{aligned}$$

where ${F_0}$ and $p(t )$ are the amplitude and the time-domain envelope of the optical pulse. N is an integer determined by the spectral width of the MLL. ${p_n}$ is the amplitude of the corresponding optical mode.

The CW-propagating optical pulse train and the anti-CW-propagating one before entering the phase modulator can be written as

(2)$${S_{CW - beforePM}}(t )= \frac{{\sqrt 2 }}{2}{S_{MLL}}(t ),$$

(3)$${S_{anti - CW - beforePM}}(t )= \frac{{\sqrt 2 }}{2}{S_{MLL}}(t ){e^{j\frac{\pi }{2}}},$$

where the additional phase shift of ${\pi \mathord{\left/ {\vphantom {\pi 2}} \right.} 2}$ is introduced by the directional coupling in the OC. In the phase modulator, the CW-propagating optical pulse train is modulated by a single-tone microwave signal in the form of ${V_{in}} = V\cos ({2\pi {f_s}t} )$, and the anti-CW-propagating one can be regarded as modulation-free in the frequency range above multi-hundreds of MHz. Therefore, the optical field of the CW-propagating and the anti-CW-propagating signals arriving at port two of the optical circulator can be written as

(4)$${S_{CW}}(t )= \frac{1}{2}{S_{MLL}}(t ){e^{jm({{f_s}} )\cos ({2\pi {f_s}t} )}}{e^{{{j\pi } \mathord{\left/ {\vphantom {{j\pi } 2}} \right.} 2}}},$$

(5)$${S_{anti - CW}}(t )= \frac{1}{2}{S_{MLL}}(t ){e^{{{j\pi } \mathord{\left/ {\vphantom {{j\pi } 2}} \right.} 2}}}{e^{j\varphi }},$$

where $m({{f_s}} )$ is the modulation index at ${f_s}$. $\varphi $ is the phase difference between the CW-propagating and the anti-CW-propagating light. It should be pointed out that, although the pigtail of the 3-dB OC is single-mode fiber, the pigtail of the electro-optic phase modulator is generally polarization-maintaining fiber. Therefore, $\varphi $ can be tuned via changing the status of the polarization controller in the measurement setup. The output optical field from the Sagnac loop is the summation of Eq. (4) and Eq. (5), which can be expressed as

(6)$${S_r}(t )= {S_{MLL}}(t ){e^{{{j\pi } \mathord{\left/ {\vphantom {{j\pi } 2}} \right.} 2}}}{e^{{{jm({{f_s}} )\cos ({2\pi {f_s}t} )} \mathord{\left/ {\vphantom {{jm({{f_s}} )\cos ({2\pi {f_s}t} )} 2}} \right.} 2} + j{\varphi \mathord{\left/ {\vphantom {\varphi 2}} \right.} 2}}} \cdot \cos \left[ {\frac{\varphi }{2} - \frac{{m({{f_s}} )}}{2}\cos ({2\pi {f_s}t} )} \right],$$

It can be seen from Eq. (6) that partial PM-IM conversion is achieved, and can be used to achieve frequency response measurement after photodetection.

The output current from the PD can be written as

(7)$$\begin{array}{l} {I_{PD}}(t )\propto R(f ){S_r}(t )S_r^ \ast (t )\\ = \sum\limits_{n ={-} N}^N {\sum\limits_{l ={-} N}^N {{p_n}{p_l}} } \left\{ \begin{array}{l} R({({n - l} ){f_r}} )\cdot [{1 + \cos \varphi \cdot {J_0}({m({{f_s}} )} )} ]\cdot \cos ({2\pi ({n - l} ){f_r}t} )\\ + 2R({({n - l} ){f_r} \pm {f_s}} )\cdot \sin \varphi \cdot {J_1}({m({{f_s}} )} )\cdot \cos ({2\pi ({n{f_r} - l{f_r} \pm {f_s}} )t} )+ \cdots \end{array} \right\}, \end{array}$$

where $R(f )$ is the responsivity of the PD at f. It can be seen from Eq. (7) that the response information of the modulator at ${f_s}$ has been transferred to numerous frequency duplicates. Since the bandwidth of the MLL is large (multi-nm to multi-tens-of nm), i.e., N is huge, there is always a frequency duplicate falling into the first Nyquist frequency range of $0 - {{{f_r}} \mathord{\left/ {\vphantom {{{f_r}} 2}} \right.} 2}$, which is defined as Fourier frequency ${f_F}$, and can be written as

(8)$${f_F} = \left\{ \begin{array}{l} {f_s} - k{f_r}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} rem({{{{f_s}} \mathord{\left/ {\vphantom {{{f_s}} {{f_r}}}} \right.} {{f_r}}}} )\le {{{f_r}} \mathord{\left/ {\vphantom {{{f_r}} 2}} \right.} 2}\\ k{f_r} - {f_s}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} rem({{{{f_s}} \mathord{\left/ {\vphantom {{{f_s}} {{f_r}}}} \right.} {{f_r}}}} )> {{{f_r}} \mathord{\left/ {\vphantom {{{f_r}} 2}} \right.} 2} \end{array} \right.,$$

where $k = round({{{{f_s}} \mathord{\left/ {\vphantom {{{f_s}} {{f_r}}}} \right.} {{f_r}}}} )$ denotes that ${{{f_s}} \mathord{\left/ {\vphantom {{{f_s}} {{f_r}}}} \right.} {{f_r}}}$ is rounded to the nearest integer, and $rem(x )$ represents the remainder of x.

The amplitude of the Fourier frequency component ${I_F}$ and that of the DC component ${I_{DC}}$ can be extracted from Eq. (7) as

(9)$${I_F} = 2{E_k}R({{f_F}} )\cdot \sin \varphi \cdot {J_1}({m({{f_s}} )} ),$$

(10)$${I_{DC}} = {E_0}R(0 )\cdot [{1 + \cos \varphi \cdot {J_0}({m({{f_s}} )} )} ],$$

where ${E_k}$ is expressed as

(11)$${E_k} = 2\sum\limits_{n ={-} N}^N {{p_n}{p_{n + k}}} ,$$

Since the MLL bandwidth is greatly larger than the frequency measurement range, an approximation can be made as

(12)$${E_0} \approx {E_1} \approx {E_2} \approx \ldots \approx {E_n},$$

Additionally, under small-signal modulation, ${J_0}({m({{f_s}} )} )\approx 1$. Hence, the response of the modulator at ${f_s}$ is calculated by

(13)$${J_1}({m({{f_s}} )} )= \frac{{R(0 )}}{{2R({{f_F}} )}}\frac{{{I_F}}}{{{I_{DC}}}}\frac{{1 + \cos \varphi }}{{\sin \varphi }},$$

If the frequency sweeping step is equal to the repetition rate of the MLL, ${f_F}$ is a constant, i.e., ${{R(0 )} \mathord{\left/ {\vphantom {{R(0 )} {R({{f_F}} )}}} \right.} {R({{f_F}} )}}$ is a constant, during the measurement process. In addition, ${{({1 + \cos \varphi } )} \mathord{\left/ {\vphantom {{({1 + \cos \varphi } )} {\sin \varphi }}} \right.} {\sin \varphi }}$ is a constant during the measurement. Hence, relative frequency response of the modulator can be obtained via a single scan, which is free of calibrating the PD response. In practice, the repetition rate of a passive MLL can be as low as multi-MHz. A high-resolution measurement can be achieved through using the proposed method. In addition, single-scan measurement with a higher resolution can also be realized through reducing the frequency sweeping step when the responsivity of the PD in the frequency range of $0 - {{{f_r}} \mathord{\left/ {\vphantom {{{f_r}} 2}} \right.} 2}$ is flat.

3. Experimental results and discussion

In the experiment, the ultrashort optical pulse train is from a passively mode-locked erbium-doped fiber laser (Calmar FPL-02CFF) with a central wavelength of 1550.2 nm, a repetition rate of 96.9 MHz and a 3-dB spectral width of 11.1 nm. The test units are four commercial LiNbO3-based high-speed electro-optic phase modulators including two 20 Gb/s modulators (EOSPACE PM-5S5-20-PFA-PFA-UV) labeled as sample 1 and sample 2, and two 40 Gb/s modulators (EOSPACE PM-DV5-40-PFA-PFA-LV) labeled as sample 3 and sample 4. The single-tone microwave signals applied to the phase modulators are generated by a tunable microwave source (R&S SMB100A), where the frequency is swept from 0.9990 GHz to 40.0497 GHz with a step of 96.9 MHz. The intensity-modulated optical pulse train from the Sagnac loop is detected by a 20 Gb/s photodetector (HP 11982A), and the output electrical spectra are measured by an ESA (R&S FSU50). In order to verify the validation of the measurement results utilizing the proposed method, the frequency responses of the four phase modulators are also measured by using the OSA method, where a grating-based optical spectrum analyzer (YOKOGAWA AQ6370C) is employed to directly measure the output optical spectra of the phase modulators.

Figure 2 shows the measured electrical spectra in the frequency range of 0 to 100 MHz for sample 2 when the input microwave frequency ${f_s}$ is tuned to be 4.0029 GHz, 7.9758 GHz, 11.9487 GHz and 15.6309 GHz, respectively. It can be seen from Fig. 2 that, after photonic down-conversion sampling, any input single-tone microwave signal has been copied to the frequency duplicate in the first Nyquist frequency range of 0-48.45 MHz, where ${f_F}\textrm{ = 30}{\kern 1pt} {\kern 1pt} \textrm{MHz}$ fits in with the theoretical result in Eq. (8).

Fig. 2. Measured electrical spectra from the PD when the input microwave frequency is tuned to be 4.0029 GHz, 7.9758 GHz, 11.9487 GHz and 15.6309 GHz, respectively.

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According to Eq. (13), the frequency response can be calculated from the relative intensity between the Fourier frequency and the DC components. However, the DC component cannot be accurately measured by the ESA with an alternating current (AC) coupling employed in the experiment. Therefore, the amplitude of the current at ${f_r}$ is used as the substitute. This substitution is valid since the amplitude of the DC component and the ${f_r}$ component are nearly the same in theory (Simulation result indicates that the amplitude difference is smaller than 0.0001 dB when the 3-dB spectral width of the MLL is 11.1 nm.) Fig. 3 exhibits the measured relative frequency response (i.e., the S21 curve) of the four phase modulators, where the red line represents the measurement results using the proposed method, and the blue dots denote those using the OSA method. The good match between the measurement results by using the two test methods indicates that the proposed method can be utilized to accurately measure the microwave characteristic of a phase modulator with a high resolution (96.9 MHz in the experiment). It should be noted that the minimum measurable frequency is about 4 GHz in the OSA method, which is limited by the spectral resolution of the OSA employed in the experiment (0.02 nm). Below 4 GHz, the modulation sidebands are difficult or even unable to be distinguished from the optical carrier.

Fig. 3. Measured relative frequency response (i.e., the S21 curve) of (a) sample 1, (b) sample 2, (c) sample 3 and (d) sample 4.

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It should be pointed out that only relative frequency response is obtained in the experiment. In order to acquire the absolute frequency response (i.e., half-wave voltage versus frequency), the polarization states in the Sagnac loop must be well understood. This is difficult since the polarization state is uncertain in the Sagnac loop which is not fully composed of polarization-maintaining fiber. However, it has no influence on the measurement accuracy of the relative frequency response (the most critical characteristic of the phase modulators). It should also be pointed out that, for an electro-optic phase modulator with single-mode fiber as its pigtail (i.e., the Sagnac loop is fully composed of single-mode fiber), $\varphi $ is always equal to zero in theory. In such a case, there is no 1^st-order modulation sidebands according to Eq. (6). Instead, the 2^nd-order modulation sidebands can be utilized to measure the relative frequency response of the phase modulator based on the proposed method. In addition, the proposed method is also applicable for an electro-optic intensity modulator. When it is applied to measure an electro-optic intensity modulator, the Sagnac loop and the optical circulator in Fig. 1 should be removed, since no PM-IM conversion is needed in the measurement. Furthermore, the absolute frequency response (i.e. half-wave voltage and the modulation index) of an electro-optic intensity modulator can be obtained by using this method, since both the polarization state and the bias condition are known.

Finally, it should be pointed out that the measured S21 curve of the phase modulator is the microwave characteristic at the central wavelength of the MLL. If the S21 curves at different wavelengths are required, a wavelength-tunable MLL should be employed to complete the measurement. In addition, the MLL in the experimental setup can be replaced by any coherent broadband optical source such as dissipative soliton source, supercontinuum generated by an MLL. Incoherent broadband optical source, such as an amplified spontaneous emission (ASE) one, cannot be employed in the experimental setup to achieve measurement.

4. Conclusion

In summary, we have proposed and experimentally demonstrated an approach to measuring the frequency response of high-speed electro-optic phase modulators via a single scan. This method utilizes a Sagnac loop architecture to achieve PM-IM conversion, and employs low-speed photonic sampling to transfer the response information at a high frequency to the low-frequency duplicate in the first Nyquist frequency range. In this method, the frequency response of any high-speed electro-optic phase modulator is calculated from the relative intensity between the Fourier frequency component in the ﬁrst Nyquist frequency range and the DC component, which can be achieved through low-frequency detection and analysis, and is free of PD response calibration. In the experiment, the relative frequency responses of two 20 Gb/s LiNbO₃-based electro-optic phase modulators and two 40 Gb/s samples were measured with a resolution of 96.9 MHz by using the proposed method, which fit in with those obtained by using the OSA method.

Funding

National Key R&D Program of China (2018YFE0201900); National Natural Science Foundation of China (61575037, 61927821, 61875240, 61421002); Fundamental Research Funds for the Central Universities (ZYGX2019Z011).

Disclosures

The authors declare no conflicts of interest.

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Frequency response measurement of high-speed electro-optic phase modulators via a single scan based on low-speed photonic sampling and low-frequency detection

Abstract

1. Introduction

2. Operation principle

3. Experimental results and discussion

4. Conclusion

Funding

Disclosures

References

Cited By

Figures (3)

Equations (13)

Optics Express