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High resolution coherent spectral analysis method based on Brillouin scattering in an optical fiber

Jiwen Cui, Suwen Zhang, Hong Dang, Yuqi Tian, Zaibin Xu, Ziyun Wang, and Xun Sun

Open Access Open Access

Abstract

High-resolution optical spectral analysis method is of significant importance for those who want to explore the physical world from the frequency domain. Aiming at the resolution degradation of classical coherent optical spectrum analysis (COSA) caused by the mirror phenomenon, this paper modifies the COSA system by introducing two homologous Brillouin scattering beams to serve as the pre-filter and local oscillator (LO), respectively. The central frequencies of the pre-filtered signal and the LO are locked by the Brillouin frequency shifts of those two Brillouin scattering beams. By means of this modification, the pre-filtered signal is located at either the upper-frequency-shifted side or the lower-frequency-shifted sides of the LO but could not exist on both sides of the LO. The proposed method could cancel the mirror phenomenon and thus improve the systematic resolution to 1.3 MHz in theory and 2 MHz in practice.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

High-resolution optical spectral analysis (OSA) is widely used in precision optical measurement. In recent years, it has been witnessed that the demand for higher resolution of measurement objects has increased significantly. For example, the invention of the optical frequency comb enables absolute ranging applications that could take both resolution and measurement range into account. But in practice, such applications are often plugged by the low spectral resolution of commercially available OSAs, and as a result, limiting the unambiguous distance measurable range to millimeter-order (as a contrast, the theoretical measurable distance is close to the coherence length of the optical frequency comb, which is often several kilometers or longer) [1,2]. Furthermore, the usage of the optical frequency comb applications also benefits the calibration of laser spectra [3] and analyte components [4,5], wherein the mismatch between the low-resolution of the current OSAs as well as the fine-structures of the spectra under test will lead to a nonnegligible accuracy decrease.

Classical OSA methods could be categorized as follows. The first one is based on diffraction gratings, its resolution is usually tens of pm and is mainly restricted by the manufacturing accuracy of the gratings [6]. The performance of the grating-based OSAs could also be affected by the rotation demands of the reflective blazed gratings or the chromatic aberration/ polarization asymmetry of the transmission gratings, all of these limit the application of grating-based OSAs in high-precision spectral measurement. The second method utilize the Fabry-Perot interferometers to compact the resolution, despite this method could achieve a resolution of sub-picometer, it always needs to make a tradeoff between the the resolution and the free spectral range [7]. The third method is known as Fourier transform spectrometer which is based on interferometric modulations, but due to the influence of the modulation accuracy and modulation range of the moving mirror, its resolution is only nanometer orders [8,9]. Therefore, it is clear that the above OSAs cannot meet the demand of the measurement requirements of optoelectronic devices [10]. Until the emergence of fiber nonlinearity, many scholars have constructed narrow-band optical filters through the stimulated scattering of fiber to achieve high-resolution spectral analysis. For example, the resolution of the Brillouin optical spectrum analyzer (BOSA) is about 10 to 30 MHz (80 to 240 fm) [11], which is equal to the intrinsic linewidth of the Brillouin gain spectrum (BGS). Therefore, a higher resolution can be achieved by narrowing the line width of BGS. There are cascaded multistage systems to reduce the BGS to 5.8 MHz(46.4 fm) [12]; two attenuation pumps with equal amplitude can be superimposed on a gain pump after Mach-Zehnder Modulator modulation to reduce the BGS to 3.4 MHz (27.2 fm) [13]. And 0.5 MHz (4 fm) spectral resolution has been achieved by constructing Brillouin dynamic grating [14]. Also, many scholars have studied COSA, and achieved 11 MHz (88 fm), 6 MHz (48 fm) and 5 MHz (40 fm) respectively [15,16]. However, the reason why the resolution of the coherent spectrometer is not as good as that of the Brillouin spectrometer is that the coherence principle has some defects. To ensure low power uncertainty, the coherent spectrometer needs to use a band-pass filter, whose system function is a bimodal response. When detecting the broadband light source signal, the resolution of the coherent spectrometer will degrade in advance.

In this paper, we propose a special coherent spectrum analysis method (Brillouin coherent optical spectrum analysis, Brillouin-COSA) to make up for the defects of the classical COSA. In principle, the resolution of this method only depends on the bandwidth of the bandpass filter. In particular, the local oscillator and the signal under test (SUT) for coherent are generated directly or indirectly by two homologous stimulated Brillouin scatterings. The advantage of the way is that the beat is a signal with fixed frequency and only amplitude varying with the sweeping time. Therefore, the process of processing beat signals will be simplified. Considering that the beat frequency is too high to be measured when the Brillouin frequency shift (BFS) of two groups of optical fibers is too large, we skillfully use the linear relationship between temperature and BFS to give a solution.

2. Principle

2.1 Mirror phenomena of the classical COSA

A schematic diagram of the classical COSA system is illustrated in Fig. 1(a) [17]. The LO and SUT keep the same polarization state and enter a coupler for heterodyne interference. After that, a balanced photodetector (BPD) is used to convert the heterodyne interference signal into an electrical signal, and a resolution bandwidth (RBW) filter is used to filter it. Finally, through a power detector to detect the filtered signal, the spectral information of the SUT can be recovered. The video bandwidth (VBW) filter in Fig. 1(a) is utilized to reduce the 1/f noise of the interferometry setup and smooth the measurement results.

 figure: Fig. 1.

Fig. 1. Schematic diagram of the Brillouin-COSA system. (a) The structure of the classic COSA; (b) structure of Brillouin-COSA; (c) The observation device of the beat signal of Brillouin-LO and Brillouin-SUT, in which TLS works in an untuned state. Note the electrical parts used in the three figures are exactly the same.

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In the classical COSA, the beat signal in the frequency domain can be simplified as [18]:

$${U_{\textrm{beat}}}(\omega )= \cos \left[ {\frac{{{\omega^2}}}{{4\pi \gamma }} + \frac{{{{({{\omega_0} - {\omega_{\textrm{SUT}}}} )}^2}}}{{4\pi \gamma }} - \frac{\pi }{4}} \right]$$
where, ω0 and γ represent the initial angular frequency and sweeping rate of the swept LO; ωSUT is the angular frequency of the SUT. The spectral information of the SUT can be extracted from Ubeat(ω):
$${X_{\textrm{SUT}}}({\omega + {\omega_0} + 2\pi \gamma t} )= {U_{\textrm{beat}}}(\omega )\cdot {H_\textrm{B}}(\omega )\cdot {H_{\textrm{PD}}}(\omega )$$
where, HB(ω) represents the amplitude-frequency function of the bandpass filter, and HPD(ω) represents the system function of the power detector.

Figure 2 simulates the results of Eq. (2) when the SUTs contain only one or two spectral components. It could be found that: 1. The systematic response to a single-frequency SUT includes two peaks mirror-symmetric to the center frequency of the SUT (Fig. 2(a)); 2. The total response to a dual-frequency SUT is approximately equal to the superposition of the individual responses to the single-frequency components(Fig. 2(b) & Fig. 2(c)); 3. When the interval between the peaks of the SUT exceeds (2*ωc+dω), two peaks could be distinguished clearly (Fig. 2(b)); 4. Once the interval between the peaks decrease to less than (2*ωc+dω), the obtained results start to aliasing, and thus cause resolution degradation (Fig. 2(b)).

 figure: Fig. 2.

Fig. 2. Schematic diagram of the classic COSA measuring single-frequency and dual-frequency signals: (a) SUT is a single frequency signal; and SUT is a dual-frequency signal with a frequency spacing of 4ωc in (b) and 2ωc in (c), respectively. For comparison purposes, the amplitude of each impulse in the SUTs is set to 0.8.

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2.2 Principle of Brillouin-COSA

As shown in Fig. 2(b), a Brillouin-COSA system is proposed to cancel the resolution degradation caused by mirror phenomena. The light from the tunable laser source (TLS) is amplified and split by an erbium-doped fiber amplifier (EDFA) and a 50:50 optical coupler (coupler 1). In the upper limb, the amplified light pumped the stimulated Brillouin scattering (SBS) inside the delay fiber 1, and the scattered light flows back to the circulator 1 to serve as the Brillouin local oscillator (Brillouin-LO). In the lower limb, the amplified light pass through circulator 2 and is partially scattered back to form the Brillouin signals under test (Brillouin-SUT). In the Brillouin-COSA, the SBS occurring in delay fiber 2 is equivalent to a pre-filter compressing the spectrum of the SUT, and mirror phenomena could be canceled by introducing a frequency difference between the Brillouin-LO and the Brillouin-SUT. After that, a 50:50 optical coupler (coupler 2) combines the Brillouin-LO and the Brillouin-SUT for heterodyne interferometry measurement.

Figure 3 depicts the schematic diagram of a peak normalized Brillouin gain spectrum, the horizontal axis represents the frequency difference between the SBS and the pump. The center position of the Brillouin gain spectrum is called Brillouin frequency shift (BFS), which could fluctuate several or tens of MHz depending on the material, processing, and external environment. Therefore, Brillouin-COSA uses this feature to make the Brillouin-LO and Brillouin-SUT perform coherent detection to eliminate the mirror problem of the classical COSA.

 figure: Fig. 3.

Fig. 3. Schematic diagram of the Brillouin gain spectrum in the SMF.

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We know that the envelope of the Brillouin gain spectrum can be expressed by Lorentz function L1,2(Ω) [19]:

$${L_{1,2}}(\Omega )= \frac{{{{({{{{\Gamma _{\textrm{B1,2}}}} / 2}} )}^2}}}{{{{({\Omega - {\Omega _{\textrm{B1,2}}}} )}^2} + {{({{{{\Gamma _{\textrm{B1,2}}}} / 2}} )}^2}}}$$
where, ΓB represents the full width at half maxima (FWHM) of the Brillouin gain spectrum and is 10∼30 MHz in Corning SMF-28e; ΩB represents the BFS in the SMF; and the subscripts 1 and 2 represent the values in the two groups of fibers respectively, and also represent the variables related to Brillouin-LO and Brillouin-SUT. Assuming that the tunable laser source has the sweeping speed of γ and the initial angular frequency of ω0, the center frequencies of Brillouin-LO and Brillouin-SUT can be expressed as:
$${\omega _{1}}(t )= {\omega _{0}} + 2\pi \gamma t - {\Omega _{{B1}}}$$
$${\omega _2}(t )= {\omega _{0}} + 2\pi \gamma t - {\Omega _{\textrm{B}2}}$$
Then, in the range of ±Δω1 and ±Δω2 of the center frequencies of Brillouin-LO and Brillouin-SUT respectively, the minimum variation of recording frequency is δω, then the frequency distribution of Brillouin-LO and Brillouin-SUT can be written as follows:
$${\Omega _1}(t )= {\omega _{0}} + 2\pi \gamma t - {\Omega _{{B1}}} + m\delta \omega ,m \in [{ - M,M} ]$$
$${\Omega _2}(t )= {\omega _{0}} + 2\pi \gamma t - {\Omega _{{B2}}} + n\delta \omega ,n \in [{ - N,N} ]$$
In Eq. (6) and (7), M=Δω1/δω; N=Δω2/δω.

Since there is only one pump in the system, the initial phase of the two can be ignored. Then, the phases of Brillouin-LO and Brillouin-SUT can be obtained by integrating Ω1(t) and Ω2(t). And the amplitudes of Brillouin-LO and Brillouin-SUT can be obtained according to the corresponding amplitudes of different frequency components. Therefore, the Brillouin-LO and Brillouin-SUT used for coherence can be written as:

$${E_{{\textrm{B - LO}}}}(t )= \sum\limits_{m ={-} M}^M {{l_{{1,}m}}{e^{j({{\omega_{0}}t - {\Omega _{{B1}}}t + m\delta \omega t + \pi \gamma {t^2}} )}}}$$
$${E_{\textrm{B - SUT}}}(t )= \sum\limits_{n ={-} N}^N {{l_{{2,}n}}{e^{j({{\omega_{0}}t - {\Omega _{{B2}}}t + n\delta \omega t + \pi \gamma {t^2}} )}}}$$
in Eq. (8) and (9), l1,m and l2,n represents the corresponding amplitude of each frequency component in L1,2(Ω) in the time domain, respectively.

The transfer function of the four-port optical coupler with a splitting ratio δ is:

$$\left( \begin{array}{l} {E_3}(t )\\ {E_4}(t )\end{array} \right) = \left( {\begin{array}{{cc}} {\sqrt \delta }&{j{\kern 1pt} \sqrt {1 - \delta } }\\ {j\sqrt \delta }&{\sqrt {1 - \delta } } \end{array}} \right)\left( \begin{array}{l} {E_1}(t )\\ {E_2}(t )\end{array} \right)$$
where, the subscripts 1 and 2 indicate input ports; 3 and 4 indicate output ports. After connecting Brillouin-LO and Brillouin-SUT to the coupler4 (δ=0.5), the output signal can be obtained as:
$$\left( \begin{array}{l} {E_3}(t )\\ {E_4}(t )\end{array} \right) = \left( \begin{array}{l} \frac{{\sqrt 2 }}{2}\left[ {\sum\limits_{m ={-} M}^M {{l_{1,m}}{e^{j({{\omega_{p}}t - {\Omega _{{B1}}}t + m\delta \omega t + \pi \gamma {t^2}} )}}} + j\sum\limits_{n ={-} N}^N {{l_{2,n}}{e^{j({{\omega_{p}}t - {\Omega _{{B2}}}t + n\delta \omega t + \pi \gamma {t^2}} )}}} } \right]\\ \frac{{\sqrt 2 }}{2}\left[ {j\sum\limits_{m ={-} M}^M {{l_{1,m}}{e^{j({{\omega_{p}}t - {\Omega _{{B1}}}t + m\delta \omega t + \pi \gamma {t^2}} )}}} + \sum\limits_{n ={-} N}^N {{l_{2,n}}{e^{j({{\omega_{p}}t - {\Omega _{{B2}}}t + n\delta \omega t + \pi \gamma {t^2}} )}}} } \right] \end{array} \right)$$
When connecting the output of coupler 4 to the balanced photodetector, according to i$/vprop;$E(t)E* (t), the optical intensity at two individual photodetectors of the balanced photodetector can be written as:
$${i_1} = \frac{1}{2}\sum\limits_{m ={-} M}^M {l_{1,m}^{2}} + \frac{1}{2}\sum\limits_{n ={-} N}^N {l_{2,n}^{2}} + \sum\limits_{m{\kern 1pt} ={-} M}^M {\sum\limits_{n ={-} N}^N {{l_{1,m}}{l_{2,n}}\cos [{({n - m} )t\delta \omega + \Delta {\Omega _\textrm{B}}t} ]} }$$
$${i_2} = \frac{1}{2}\sum\limits_{m ={-} M}^M {l_{1,m}^{2}} + \frac{1}{2}\sum\limits_{n ={-} N}^N {l_{2,n}^{2}} - \sum\limits_{m{\kern 1pt} ={-} M}^M {\sum\limits_{n ={-} N}^N {{l_{1,m}}{l_{2,n}}\cos [{({n - m} )t\delta \omega + \Delta {\Omega _\textrm{B}}t} ]} }$$
in Eq. (12) and (13), ΔΩ=ΩB1-ΩB2, represents the difference of the BFS in two sets of delayed fibers; and the autocorrelation component of the beam has been removed. After the photocurrent passes through the trans-impedance amplifier inside the balanced photodetector, the voltage signal output by the balanced photodetector is:
$${u_{\textrm{beat}}}(t )= R({{i_1} - {i_2}} )= 8R\cos ({\Delta {\Omega _\textrm{B}}t} )\sum\limits_{m{\kern 1pt} = 0}^M {{l_{1,m}}\cos ({mt\delta \omega } )\sum\limits_{n = 0}^N {{l_{2,n}}\cos ({nt\delta \omega } )} }$$
where, R is the responsivity of two individual photodetectors of the balanced photodetector.

Through two self-heterodyne experiments, we found that the BFS of the two sets of delay fibers used differed by about 25 MHz, that is, ΔΩ/(2π)=(ΩB1-ΩB2)/ (2π) = 25 MHz. For the convenience of analysis, the conditions of Δω1=Δω2 and l1,m= l2,m are given. When TLS sweeps from 1549.99 nm to 1550 nm at a speed of 1nm/s, the simulation results are shown in Fig. 4.

 figure: Fig. 4.

Fig. 4. The beat of Brillouin-LO and Brillouin-SUT: (a) in the time domain, ubeat(t) and (b) in the frequency domain, Ubeat(ω).

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From the simulation results in the frequency domain, it can be seen that the beat signals of Brillouin-LO and Brillouin-SUT are distributed on both sides with 25 MHz as the center, which is exactly the difference between the BFS in the two groups of fibers. And it is the intensity information of the SUT that is modulated on the 25 MHz signal. Then, a 10th-order Butterworth bandpass filter with a center frequency of 25 MHz and a bandwidth of 1 MHz is selected as the resolution bandwidth filter:

$${H_{\textrm{RBW}}}(\omega )= \frac{1}{{\sqrt {1 + {{\left( {\frac{{\omega - 2\pi \times 25\textrm{MHz}}}{{{{({2\pi \times 1\textrm{MHz}} )} / 2}}}} \right)}^{20}}} }}$$
The subsequent processing of the filtering results is similar to the classical COSA, which requires the use of a power detector (to obtain the envelope) and a video bandwidth filter (to remove noise). The time domain processing method has been analyzed in detail in Ref. [16–18,20]. In the frequency domain, we can also give an envelope detection method similar to the root mean square value:
$$Y(\omega )= \sqrt {\frac{1}{{\delta {\omega _{\textrm{opt}}}}}{{\int_0^{\delta {\omega _{\textrm{opt}}}} {|{X(\omega )} |} }^2}d\omega }$$
where, δωopt represents the optimal distance between adjacent peaks suitable for integration in X(ω); and X(ω) (=Ubeat(ω)HRBW(ω)) represents the filtering result of the resolution bandwidth filter. The corresponding processing results are shown in Fig. 5.

 figure: Fig. 5.

Fig. 5. (a) The filtering result of the resolution bandwidth filter, X(ω); (b) Envelope extraction result, Y(ω).

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It could be found that the output of the Brillouin-COSA is unimodal, while the output of the classical COSA is bimodal (Fig. 2(a)). The comparison between Figs. 5(b) and 2(a) indicates that the introduction of the Brillouin pre-filter could effectively suppress the mirror phenomenon, and the resolution of the proposed Brillouin-COSA is thus enhanced. In case that the Brillouin frequency shifts of the Brillouin-LO and Brillouin-SUT are too different, the beat frequency of the heterodyne signal could probably exceed the bandwidth of the balanced photodetector, and finally disable the spectrum analysis. To solve this problem, we utilize an oil-bath heater to control the ambient temperature of the fiber spool. The variation trend between the Brillouin frequency shift and the fiber temperature is approximately linear [21,22]:

$${\Omega _\textrm{B}}(T )= {\Omega _{{{\rm B}}\textrm{0}}}\textrm{ + }{c_\textrm{T}}({T - {T_0}} )$$
where, ΩB0 is the BFS at room temperature T0; and cT represents the linear coefficient between temperature and BFS. Through this method, the center frequency ΔΩB of the output signal will be reduced, which satisfies the Nyquist sampling theorem. Thence, the problem of measuring SUT is solved.

3. Experiment and results

3.1 Experimental setup

To verify the Brillouin-COSA approach, an experimental setup was integrated according to Fig. 2(b). The TLS is the Tunics Reference external cavity tunable laser produced by Yenista Optics in France, with a tuning range of 1530 nm∼1625 nm. The narrow linewidth fiber laser, which is the source of the SUT, is the CoSF-D-ER-M laser produced by CONNET, with a center wavelength of 1550 nm and a nominal linewidth of less than 1 kHz.The pump is amplified by the EDFA-C-PM-CW-MB erbium-doped fiber amplifier produced by Opeak in China. The fiber model is Corning SMF-28e, and the length of each group is 10km. The model of ESA is Keysight N9010A, and its measurement range is from 10Hz to 3GHz. The device for adjusting the temperature of the optical fiber is the MR-5015 precision constant temperature oil tank produced by AIKOM in China. The working temperature of this device is 5 to 65°C (maximum 110°C ), and the temperature control stability can reach ±0.002°C /10min. The balanced photodetector is the PDB450C produced by Thorlabs with a coverage of 800‒1700 nm. The PD1 and PD2 are Thorlabs PDA05CF2 InGaAs photodetectors. The resolution bandwidth filter is made by AD4817 with a high gain-bandwidth product of 1 GHz. The power detector is made by AD8361 which has a working bandwidth up to 2.5 GHz. The video bandwidth filters are made by OP37 with a medium gain-bandwidth product of 63 MHz. All signals are finally collected by the PCI-1714UL data acquisition card produced by Advantech in China with a maximum sampling rate of 10 MHz. And use the computer to display the spectrum of the SUT.

3.2 Mirror problem measurement experiment

To observe the mirror phenomenon, a simple COSA system is constructed based on Fig. 2(a). The LO is directly provided by the tunable laser source. And SUT is the intensity-modulated signal obtained by a LiNbO3 intensity modulator modulating the light source output by a fiber laser with a line width of 1kHz, where the frequency spacing of the intensity-modulated signal is equal to the modulation frequency. A 10th-order Butterworth filter of 2 MHz center frequency and 1 MHz bandwidth is as the resolution bandwidth filter and a 25 kHz lowpass filter is as the video bandwidth filter of COSA system. Figure 6 shows that the COSA system measures modulated signals with a peak spacing of 10 MHz and 5 MHz, respectively. It can be seen that the three input signals correspond to the six output signals due to the mirror phenomenon. When the modulation frequency decreases, the output signal quickly aliases. This causes resolution degradation.

 figure: Fig. 6.

Fig. 6. Use the intensity-modulated signal to demonstrate the mirror phenomenon of COSA: (a) the modulation frequency is 10 MHz and (b) the modulation frequency is 5 MHz.

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3.3 Verification of the Brillouin-COSA principle

To give the relevant information of the Brillouin filter, we used the self-heterodyne principle as shown in Fig. 7 to measure the SBS. The experiment also needs to use a dual-parallel input electro-optic modulator (Eospace's IQ-0DKS-25-PFA-PFA-LV electro-optic modulator, its working wavelength is 1550 nm, and the 3 dB modulation bandwidth is greater than 20 GHz) and a microwave source (the 1431/A type produced by CLP 41, which can provide RF/microwave signals with a frequency between 10 MHz and 18 GHz).

 figure: Fig. 7.

Fig. 7. Use the self-heterodyne principle to measure the Brillouin filter, in which SUT and PD2 are not connected in this experiment, which is set for the subsequent verification of the pre-filtering effect of the Brillouin filter on the SUT.

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In the experiment of self heterodyne, the frequency of the modulated signal from the microwave source is 10 GHz (the pump is shifted by 10 GHz, which is convenient to beat with SBS); The pump power of SBS is about 16 dBm. The corresponding measurement result is shown in Fig. 8, which is the average result of five groups of data. The linewidth of SBS is about 10.5 MHz estimated by Lorentz fitting.

 figure: Fig. 8.

Fig. 8. Brillouin filter measured by heterodyne principle

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To test the filtering effect of the Brillouin filter on SUT, we connect the SUT to the optical isolator and connect the output of optical attenuator 2 to PD 2 for observation based on the principle shown in Fig. 7. And the SUT is provided by narrow linewidth fiber laser, a cosf-d-er-m laser produced by CONNET company, whose central wavelength is 1550 nm and nominal linewidth is less than 1 kHz. The corresponding measurement results are shown in Fig. 9, where the Brillouin gain is about 30 dB.

 figure: Fig. 9.

Fig. 9. Pre-filtering effect of Brillouin filter on SUT

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Then, we utilize the ESA to monitor the beat signal formed by Brillouin-LO and Brillouin-SUT (the principle is shown in Fig. 1(c)). Figure 10(a) demonstrates the beat spectrum captured by a high-speed photodiode (PD, Newport 1414), it appears as a single peak with a central frequency of about 30 MHz, which is consistent with the envelope of Fig. 4(b). Limited by the slew rate of the chip, the center bandwidth and gain of the filter cannot be increased at the same time. Therefore, in this paper, the BFS of a Brillouin beam is moved by temperature control, so that the center of the beat signal falls to 2MHz. At this time, the beat signal observed by the balanced photodetector and ESA is shown in Fig. 10(b).

 figure: Fig. 10.

Fig. 10. ESA measures the beat signals of Brillouin-LO and Brillouin-SUT, in which multiple sets of data are not collected for averaging in order to show the real signal. (a) At room temperature, the center frequency of the beat signal is 25 MHz when the temperature controller is not turned on.; (b) The center frequency of the beat signal can be adjusted to 2 MHz by adjusting the temperature controller.

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After that, the result of filtering Fig. 10(b) with 2MHz and 1MHz filters is shown in Fig. 11. It can be seen that the signal line width after filtering is about 1.3MHz. This difference may be caused by factors such as electrical noise and component parameter errors. Therefore, to achieve higher resolution, a resolution bandwidth filter with accurate bandwidth can be customized.

 figure: Fig. 11.

Fig. 11. The output signal of the resolution bandwidth filter measured by ESA.

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To further illustrate the advantages of Brillouin-COSA (Fig. 2(b)), SUT continues to use the same intensity-modulated signal as in COSA. The difference is that, as shown in Fig. 12(a), Brillouin-COSA can directly distinguish intensity-modulated signals with a frequency spacing of 5 MHz that cannot be measured by the COSA system. Next, reduce the modulation frequency to 2 MHz (Fig. 12(b)), it can be seen that Brillouin-COSA can still distinguish. Taking into account the error of the subsequent power detector, the value achieved by Brillouin-COSA is very close to the actual bandwidth (1.3 MHz) of the resolution bandwidth filter. This shows that the theory of Brillouin-COSA is correct. It not only makes up for the shortcomings of COSA, but also can more than double the resolution. Also, the ultimate resolution achieved by this method has yet to be verified.

 figure: Fig. 12.

Fig. 12. Use intensity-modulated signal to test the resolution of Brillouin-COSA system: (a) the modulation frequency is 5 MHz and (b) the modulation frequency is 2 MHz.

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3.4 OSA of fine spectrum structures

In this section, the proposed Brillouin-COSA system is used to measure optical signals with repetition frequency and broadband optical signals to verify the measurement capabilities of Brillouin-COSA on different occasions. And compare the results with a commercial grating spectrometer produced by Anritsu in Japan, which has a resolution of 30 pm, to verify the accuracy of Brillouin-COSA measurement.

First, the wide amplified spontaneous emission source (ASE) passes through two Fabry-Perot etalons with different free spectral ranges to obtain similar frequency comb light sources (Fig. 13(a)). The Brillouin-COSA system is equivalent to an optical frequency comb light source with a measurement repetition frequency of 5 GHz (40 pm) and 0.1 GHz (0.8 pm), as shown in Fig. 13, to verify the measurement capability of the comb light source. It can be seen from the comparison result that Brillouin-COSA can measure in-depth spectral information. It should be pointed out that the bottom noise in the measurement results mainly comes from the intensity noise of ASE. In Fig. 13(c), the reason for the greater noise is that the polarization controller is manually adjusted, and the light of the other polarization state is completely extinct.

 figure: Fig. 13.

Fig. 13. Measurement of SUT with repetition frequency: (a) the principle of frequency comb signal generation; (b) the repetition frequency is 5 GHz (40pm) and (c) the repetition frequency is 0.1 GHz (0.8pm).

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Then, the ASE spectrum of the phase-shifted fiber Bragg grating (PS-FBG) is measured using the Brillouin-COSA system. The characteristic of the output signal is a broadband spectrum, and there is a narrowband window in it (Fig. 14(a)). By detecting this kind of broadband spectral signal, Brillouin-COSA ‘s large-range measurement capability can be explained. The unfiltered measurement results are shown in Fig. 14(b). Comparing the filtered result, as shown in Fig. 14(c), with the measurement result of a reliable commercial spectrometer, the wavelength position of the measurement result of the Brillouin-COSA system is consistent, but the spectrum information revealed by Brillouin-COSA is more.

 figure: Fig. 14.

Fig. 14. Analysis of reflectance spectrum of PS-FBG: (a) generation principle of broadband signal with measurement mark; (b) unfiltered measurement results and (c) filtered measurement results.

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4. Discussion

In COSA, in order to have lower power uncertainty, it is impossible to use a low-pass filter for homodyne detection. For this reason, it is necessary to use a band-pass filter to extract a signal of a specific frequency. But at the same time, there is also the mirroring problem. When TLS scans, it will inevitably pass through the SUT, which results in the same frequency of the beat signal generated on the left and right sides of the SUT. Finally, the measurement relationship of the COSA system is that one input corresponds to two outputs. The output is a mirror image relationship with the SUT. Combining the bandwidth Δf and center frequency f0 of the resolution bandwidth filter, it can be given that the limit resolution δfCOSA of COSA is:

$$\delta {f_{\textrm{COSA}}} = 2{f_0} + \Delta f$$
the maximum value represented by Eq. (18) is 5 MHz, which is also the maximum resolution that COSA can achieve at present.

The Brillouin-COSA constructed by introducing two beams of homologous Brillouin scattering perfectly solves the problem of mirroring in COSA. After the optical filter equivalent to Brillouin scattering pre-filters the SUT, it is equivalent to loading the information contained in the SUT onto the Brillouin scattering. It keeps “movement”, so the mirror effect is avoided. Due to the homology relationship, the BFS of the two Brillouin scattering is different, but they maintain stable coherence, thereby generating a fixed-frequency beat signal, which is different from the constantly changing frequency in COSA, which is more convenient for measurement. Correspondingly, the resolution δfBrillouin-COSA of Brillouin-COSA depends only on the bandwidth Δf of the resolution bandwidth filter in principle:

$$\delta {f_{\textrm{Brillouin - COSA}}} = \Delta f$$
The actual bandwidth of the resolution bandwidth filter used in the test in this article is 1.3 MHz, but due to the defects of the subsequent circuit, the actual resolution of Brillouin-COSA is 2 MHz. But according to Brillouin-COSA ‘s measurement of intensity-modulated signals with a frequency spacing of 2 MHz, it can be inferred that it can easily achieve 1 MHz and higher spectral resolution. However, what is the highest resolution that Brillouin-COSA can achieve requires the establishment of a detailed input and output relationship power error model for analysis, which has not been discussed in this article. Of course, it is also necessary to design corresponding resolution bandwidth filters and power detectors for experimental verification. In addition, we considered the situation that the Nyquist sampling theorem could not be satisfied between the signal obtained by Brillouin-COSA and the digital acquisition card when the BFS difference between the two sets of delay fibers was too large. This situation can be adjusted by adding a temperature controller to one group of BFS longer delay fibers to indirectly reduce the frequency of the Brillouin-COSA output signal. The BFS of the two groups of fibers and the relationship with the temperature change are measured by self-heterodyne interference experiments, where the temperature coefficient of the BFS in the delay fiber 2 placed in the temperature controller is 1.1 MHz/°C . Of course, if there is a high-speed data acquisition card, it can be omitted the use of a temperature controller and directly perform measurements.

5. Summary

In conclusion, we have proposed a special spectral analysis method Brillouin-COSA by combining the Brillouin scattering and classical COSA detection. The detailed design scheme and derivation process of Brillouin-COSA ‘s realization method and working principle are given. The spectral resolution of this method just depends on the bandwidth of the band-pass filter. For this reason, a resolution bandwidth filter with a center frequency of 2 MHz and a bandwidth of about 1 MHz is designed for verification. After testing, the real bandwidth of the resolution bandwidth filter is 1.3 MHz, which makes the spectral resolution of the Brillouin-COSA system only 2 MHz (16 fm). Experiments show that Brillouin-COSA solves the mirror problem in COSA and doubles the resolution. Finally, using Brillouin-COSA to measure the optical signal with repetition frequency obtained by an amplified spontaneous emission source and two Fabry-Perot etalons to verify the detection ability of the optical frequency comb light source, and detect the reflectance spectrum of a phase-shifted fiber Bragg grating to verify the measurement of the broadband spectrum signal ability. Compared with the measurement results of a commercial grating spectrometer, the measurement accuracy of Brillouin-COSA is verified.

This article mainly verifies the principle and applicability of the Brillouin-COSA system. However, the spectral resolution that Brillouin-COSA can be achieved in the future by designing band-pass filters with accurate bandwidths.

Funding

National Natural Science Foundation of China (52075131); Science Fund for Distinguished Young Scholars of Heilongjiang Province (JQ2019E002).

Acknowledgment

We are very grateful to Pengcheng Hu for providing some key experimental devices

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.

References

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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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Figures (14)
Fig. 1.
Fig. 1. Schematic diagram of the Brillouin-COSA system. (a) The structure of the classic COSA; (b) structure of Brillouin-COSA; (c) The observation device of the beat signal of Brillouin-LO and Brillouin-SUT, in which TLS works in an untuned state. Note the electrical parts used in the three figures are exactly the same.

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Fig. 2.
Fig. 2. Schematic diagram of the classic COSA measuring single-frequency and dual-frequency signals: (a) SUT is a single frequency signal; and SUT is a dual-frequency signal with a frequency spacing of 4ωc in (b) and 2ωc in (c), respectively. For comparison purposes, the amplitude of each impulse in the SUTs is set to 0.8.

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Fig. 3.
Fig. 3. Schematic diagram of the Brillouin gain spectrum in the SMF.

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Fig. 4.
Fig. 4. The beat of Brillouin-LO and Brillouin-SUT: (a) in the time domain, ubeat(t) and (b) in the frequency domain, Ubeat(ω).

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Fig. 5.
Fig. 5. (a) The filtering result of the resolution bandwidth filter, X(ω); (b) Envelope extraction result, Y(ω).

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Fig. 6.
Fig. 6. Use the intensity-modulated signal to demonstrate the mirror phenomenon of COSA: (a) the modulation frequency is 10 MHz and (b) the modulation frequency is 5 MHz.

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Fig. 7.
Fig. 7. Use the self-heterodyne principle to measure the Brillouin filter, in which SUT and PD2 are not connected in this experiment, which is set for the subsequent verification of the pre-filtering effect of the Brillouin filter on the SUT.

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Fig. 8.
Fig. 8. Brillouin filter measured by heterodyne principle

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Fig. 9.
Fig. 9. Pre-filtering effect of Brillouin filter on SUT

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Fig. 10.
Fig. 10. ESA measures the beat signals of Brillouin-LO and Brillouin-SUT, in which multiple sets of data are not collected for averaging in order to show the real signal. (a) At room temperature, the center frequency of the beat signal is 25 MHz when the temperature controller is not turned on.; (b) The center frequency of the beat signal can be adjusted to 2 MHz by adjusting the temperature controller.

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Fig. 11.
Fig. 11. The output signal of the resolution bandwidth filter measured by ESA.

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Fig. 12.
Fig. 12. Use intensity-modulated signal to test the resolution of Brillouin-COSA system: (a) the modulation frequency is 5 MHz and (b) the modulation frequency is 2 MHz.

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Fig. 13.
Fig. 13. Measurement of SUT with repetition frequency: (a) the principle of frequency comb signal generation; (b) the repetition frequency is 5 GHz (40pm) and (c) the repetition frequency is 0.1 GHz (0.8pm).

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Fig. 14.
Fig. 14. Analysis of reflectance spectrum of PS-FBG: (a) generation principle of broadband signal with measurement mark; (b) unfiltered measurement results and (c) filtered measurement results.

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Equations (19)

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U beat ( ω ) = cos ⁡ [ ω 2 4 π γ + ( ω 0 − ω SUT ) 2 4 π γ − π 4 ]
X SUT ( ω + ω 0 + 2 π γ t ) = U beat ( ω ) ⋅ H B ( ω ) ⋅ H PD ( ω )
L 1 , 2 ( Ω ) = ( Γ B1,2 / 2 ) 2 ( Ω − Ω B1,2 ) 2 + ( Γ B1,2 / 2 ) 2
ω 1 ( t ) = ω 0 + 2 π γ t − Ω B 1
ω 2 ( t ) = ω 0 + 2 π γ t − Ω B 2
Ω 1 ( t ) = ω 0 + 2 π γ t − Ω B 1 + m δ ω , m ∈ [ − M , M ]
Ω 2 ( t ) = ω 0 + 2 π γ t − Ω B 2 + n δ ω , n ∈ [ − N , N ]
E B - LO ( t ) = ∑ m = − M M l 1 , m e j ( ω 0 t − Ω B 1 t + m δ ω t + π γ t 2 )
E B - SUT ( t ) = ∑ n = − N N l 2 , n e j ( ω 0 t − Ω B 2 t + n δ ω t + π γ t 2 )
( E 3 ( t ) E 4 ( t ) ) = ( δ j 1 − δ j δ 1 − δ ) ( E 1 ( t ) E 2 ( t ) )
( E 3 ( t ) E 4 ( t ) ) = ( 2 2 [ ∑ m = − M M l 1 , m e j ( ω p t − Ω B 1 t + m δ ω t + π γ t 2 ) + j ∑ n = − N N l 2 , n e j ( ω p t − Ω B 2 t + n δ ω t + π γ t 2 ) ] 2 2 [ j ∑ m = − M M l 1 , m e j ( ω p t − Ω B 1 t + m δ ω t + π γ t 2 ) + ∑ n = − N N l 2 , n e j ( ω p t − Ω B 2 t + n δ ω t + π γ t 2 ) ] )
i 1 = 1 2 ∑ m = − M M l 1 , m 2 + 1 2 ∑ n = − N N l 2 , n 2 + ∑ m = − M M ∑ n = − N N l 1 , m l 2 , n cos ⁡ [ ( n − m ) t δ ω + Δ Ω B t ]
i 2 = 1 2 ∑ m = − M M l 1 , m 2 + 1 2 ∑ n = − N N l 2 , n 2 − ∑ m = − M M ∑ n = − N N l 1 , m l 2 , n cos ⁡ [ ( n − m ) t δ ω + Δ Ω B t ]
u beat ( t ) = R ( i 1 − i 2 ) = 8 R cos ⁡ ( Δ Ω B t ) ∑ m = 0 M l 1 , m cos ⁡ ( m t δ ω ) ∑ n = 0 N l 2 , n cos ⁡ ( n t δ ω )
H RBW ( ω ) = 1 1 + ( ω − 2 π × 25 MHz ( 2 π × 1 MHz ) / 2 ) 20
Y ( ω ) = 1 δ ω opt ∫ 0 δ ω opt | X ( ω ) | 2 d ω
Ω B ( T ) = Ω B 0  +  c T ( T − T 0 )
δ f COSA = 2 f 0 + Δ f
δ f Brillouin - COSA = Δ f
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