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Curr. Opt. Photon. 2023; 7(4): 378-386

Published online August 25, 2023 https://doi.org/10.3807/COPP.2023.7.4.378

Copyright © Optical Society of Korea.

Broadband Instantaneous Frequency Measurement System Based on the Dual Paths of the Stimulated Brillouin Scattering Effect

Jiahong Zhang , Weijie Liao

Faculty of Information Engineering and Automation, Kunming University of Science and Technology, Kunming 650500, China

Corresponding author: *zjh_mit@163.com, ORCID 0000-0003-1496-5770

Received: May 2, 2023; Revised: June 20, 2023; Accepted: July 5, 2023

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

A wideband instantaneous frequency measurement (IFM) system is been proposed, designed and analyzed. Phase modulation to intensity modulation conversion is implemented based on the stimulated Brillouin scattering (SBS) effect, and the microwave frequency can be measured by detecting the change in output power. Theoretical analysis shows that the frequency measurement range can be extended to 4fb by adjusting the two sweeping signals of the phase modulators with a difference of 2fb. The IFM system is set up using VPI transmission maker software and the performances are simulated and analyzed. The simulation results show that the measurement range is 0.5−45.96 GHz with a maximum measurement error of less than 9.9 MHz. The proposed IFM system has a wider measurement range than the existing SBS-based IFM system.

Keywords: Instantaneous frequency measurement, Phase modulation, Stimulated Brillouin scattering

OCIS codes: (060.5625) Radio frequency photonics; (070.4340) Nonlinear optical signal processing; (130.4110) Modulators; (290.5900) Scattering, stimulated Brillouin; (350.4010) Microwaves

Instantaneous frequency measurement (IFM) technology can be used to quickly obtain the frequency information of a target for tracking, advance warning and interference purposes, and plays an important role in communications, radar and electronic warfare [1, 2]. With the development of information technology, traditional electronic frequency measurement methods have gradually failed to meet current needs due to the limitation of the electronic bottleneck. The photon-assisted microwave frequency measurement (MFM) method has received attention for its advantages of wider bandwidth, lower loss, anti-electromagnetic interference and larger measurement range [35]. The methods of IFM based on the stimulated Brillouin scattering (SBS) effect have been widely researched due to their adjustable frequency measurement range and lower measurement errors [610].

A multiple MFM scheme is proposed based on the selective conversion of phase modulation to amplitude modulation (PM-IM), which is realized by SBS. The scheme achieves frequency measurements in the 1–9 GHz range with a maximum measurement error of less than 30 MHz [11]. An approach for IFM is proposed based on a PM in combination with an IM. The measurement errors are within ±90 MHz in the frequency range of 0.5–20 GHz [12]. A chip-based approach has achieved multiple-frequency measurement by using the amplitude comparison function (ACF) with a measurement range of up to 38 GHz and a measurement error of 1 MHz [13]. A technique for the IFM is proposed based on SBS in a single-mode optical fiber to achieve multi-MFMs. The measured frequency errors are within 20 MHz within a broadband of 27 GHz [14]. A photonic multiple IFM system is presented and demonstrated based on a swept frequency silicon microring resonator (MRR). Frequency estimation in a range of 5–30 GHz with a measurement error under ±510 MHz is achieved [15]. By scanning the reference frequency during the SBS, the frequency information of the microwave signal to be measured is detected by a mapping between the total output power of the system and the reference frequency, and multi-MFM is achieved. The scheme achieves frequency measurements in the range of 21.42 GHz with a measurement error of less than 5 MHz [16]. A photonic-assisted multiple IFM approach based on SBS and frequency-to-time mapping with high accuracy and a wide frequency measurement range is proposed. The IFM from 6 to 18 GHz is achieved with a measurement error of less than ±1 MHz [17]. A MFM scheme based on SBS and an apodised fiber Bragg grating (AFBG) is proposed. By sweeping a reference frequency during the SBS process, frequency-to-power mapping between the reference frequency and the monitored output optical power of the IFM system is established. A measurement error of less than ±1 MHz within 10.68 GHz to 20 GHz is achieved [18]. In summary, many IFM methods based on SBS effects have been proposed to achieve larger measurement ranges and smaller measurement errors, but not both at the same time.

In this paper, an IFM system based on dual paths of the SBS effect has been proposed and designed. The frequency measurement range can be extended to 4fb by using the two swept signals of the phase modulators with a difference of 2fb. The IFM system has been established and simulated using VPI transmission maker software. The effect of the optical wavelength and power of the pump light on the measurement range and measurement error of the IFM system was also analyzed. The proposed IFM system with dual SBS paths has a larger measurement range.

A schematic diagram of the proposed IFM system based on the dual paths of the SBS effect is shown in Fig. 1. The optical carrier fc is split into two parts by 3 dB optical coupler 1 (OC1) and transmitted in the upper and lower paths. The upper light passes through the 3 dB coupler 2 (OC2) and then splits into two paths that enter into phase modulator 1 (PM1) and phase modulator 2 (PM2), respectively. The output microwave signals from the two swept sources ( fs1 and fs2) are loaded onto the optical carrier through PM1 and PM2, respectively. Figures 2(a) and 2(b) show the first-order sidebands fc + fs1, fcfs1 and fc + fs2, fcfs2 of the modulated signals of PM1 and PM2, which can be expressed as [19].

Figure 1.Schematic diagram of the proposed instantaneous frequency measurement (IFM) system: LD, laser diode; OC, optical coupler; PM, phase modulator; ISO, isolator; HNLF, high nonlinear optical fiber; DPMZM, dual-parallel Mach-Zehnder modulator; EDFA, erbium-doped optical fiber amplifier; PD, photodetector.
Figure 2.Spectrum of the signals. (a) Output from PM1, (b) output from PM2, (c) output from the DPMZM, (d) output from the HNLF1, (e) output from the HNLF2 and (f) output spectrum for fs2 = fs1 + 2fb. PM, phase modulator; DPMZM, dual-parallel Mach-Zehnder modulator; HNLF, high nonlinear optical fiber.

Ep(t)=J0(m)expj2πfct+J1(m)expj2πfc +fs1,2 t+π2J1(m)expj2πfc fs1,2 tπ2

In Eq. (1), m = πV/Vπ is the modulation index, J0(m) and J1(m) are the zero-order and first-order Bessel functions, respectively. The modulated signals from PM1 and PM2 are transmitted unidirectionally through isolator 1 (ISO1) and isolator 2 (ISO2) into highly nonlinear optical fiber 1 (HNLF1) and highly nonlinear optical fiber 2 (HNLF2), respectively, with the same Brillouin frequency shift. The function of the optical isolator is to prevent the pump light from entering the phase modulator in the reverse direction, which will affect the system.

The microwave signal fx to be measured is loaded onto the optical carrier through a dual parallel Mach Zander intensity modulator (DPMZM), which works on the carrier suppression single-sideband modulation (CS-SSB). The output spectrum of the DPMZM is shown in Fig. 2(c). The output CS-SSB signal is amplified by an erbium-doped fiber amplifier (EDFA) and split into two parts by 3 dB coupler 3 (OC3), and one part is input to HNLF1 through circulator 1 and the other is input to HNLF2 through circulator 2. When the signal light differs from the pump light transmitted in reverse by one Brillouin frequency shift fb, the SBS effect occurs, causing the amplitude of the first-order sideband of the PM to gain or attenuate, thus breaking the sideband balance and achieving PM-IM conversion.

The gain and attenuation spectrums of HNLF1 and HNLF2 are shown in Figs. 2(d) and 2(e) respectively. The gain spectrum g( f ) and the attenuation spectrum a( f ) can be expressed as [20]

g(f)=g02ΔvB/22f2+ΔvB/22+jg04ΔvBff2+ΔvB/22

a(f)=g02ΔvB/22f2+ΔvB/22jg04ΔvBff2+ΔvB/22

in Eq.(2) and Eq.(3), ∆vB is the Brillouin linewidth, g0 = gBIp Leff/Aeff is the line center gain factor of the HNLF, gB is the line center gain, Ip is the power of the pump light, Leff and Aeff are the effective length and effective mode area of HNLF.

When the SBS effect occurs, the PM output optical field can be expressed as

E(t)=ej2πfctJ0(m)+J1(m)expg(fs1,2 fb fx )+a(fs1,2 +fb fx )+j(2πfs1,2 t+π2)J1(m)expj(2πfs1,2t+π2)

From Eq. (4), ignoring the direct current (DC), the output optical power can be written as

P2J0(m)J1(m) G(fs1,2 fb fx )A(fs1,2 +fb fx ) ×cos[ϕg (fs1,2 fb fx )+ϕa (fs1,2 +fb fx ) +2πfs1,2 t+π2]cos[2πfs1,2 t+π2]

in Eq. (5), G( fs1,2fbfx) and A( fs1,2 + fbfx) are the gains and losses introduced by the SBS effect occurring, and ϕg( fs1,2fbfx), ϕa( fs1,2 + fbfx) are the corresponding phase shifts, which can be expressed as

G(fs1,2fbfx)=exp{Re[g(fs1,2fbfx)]} =expg0 2ΔvB /22(f s1,2 fb fx )2+ΔvB /22 A(fs1,2+fbfx)=exp{Re[a(fs1,2+fbfx)]} =expg0 2ΔvB /22(f s1,2 +fb fx )2+ΔvB /22

ϕg(fs1,2fbfx)=Im[g(fs1,2fbfx)]} =g04ΔvB /2(fs1,2fbfx) (fs1,2 fb fx )2+ΔvB /22 ϕa(fs1,2+fbfx)=Im[a(fs1,2+fbfx)]} =g04ΔvB /2(fs1,2+fbfx) (fs1,2 +fb fx )2+ΔvB /22

Therefore, the output of electric field at the PD can be expressed approximately as

Eout(t)=pG(fm)A(fm)cos[ϕg(fm)+ϕa(fm)+2πfs1,2t+π2]cos[2πfs1,2t+π2]

In Eq. (8), ℜ< p> is the response ability of the PD to the input optical power.

For frequency measurement, the PM output signal fc + fs1 is used as the pump light and the DPMZM output signal fc + fx is used as the signal light. When fc + fx is equal to fc + fs1fb or fc + fs1 + fb, the SBS effect occurs and the output power will be changed. Therefore, by scanning fs1 and fs2 and detecting the output power, the frequency fx to be measured can be achieved as the sum of the swept frequency fs and the Brillouin frequency shift fb when the detected output power changes.

As the SBS effect generates both the gain and attenuation spectrums, the signal power changes at fs1fb and fs1 + fb, and the measurable frequency range is 2fb. In this paper, a broadband IFM system based on the dual paths of the SBS effect is proposed, and when the PM signals fs1 and fs2 differ by 2fb, the SBS attenuation spectrum at fc + fs1 and the SBS gain spectrum at fc + fs2 cancel each other, which results in the frequency measurement range increasing to 4fb. The output spectrum is shown in Fig. 2(f).

3.1. Theoretical Analysis

When the optical wavelength λp = 1,550 nm, the Brillouin gain coefficient g0 = 5, the Brillouin frequency shift fb = 11 GHz and the Brillouin linewidth ∆vB = 40 MHz. According to Eq. (5), Fig. 3 shows the relationship between the normalized output power and the known frequencies obtained under different sweeping frequencies of fs1, fs2.

Figure 3.Output power versus known frequencies. (a) fs1, fs2 < fb, (b) fs1, fs2 > fb and fs2fs1 < 2fb, (c) fs1, fs2 > fb and fs2fs1 < 2fb, (d) fs1, fs2 > fb and fs2fs1 = 2fb.

As can be seen in Fig. 3(a), when fs1, fs2 < fb (for fs1 = 3 GHz, fs2 = 9 GHz), with the microwave frequency fx changes from 0 to 44 GHz, the output power at 14 GHz ( fs1 + fb) and 20 GHz ( fs2 + fb) appears as two peaks. Therefore, when detecting the output power changing of photodetector 1 (PD1) and photodetector 2 (PD2), the microwave frequencies under measurement can be determined as fs1 + fb and fs2 + fb, respectively. Under this condition, the measurable frequency range of the IFM system is 11 GHz. As can be seen in Fig. 3(b), when fs1 < fb and fs2 > fb (for fs1 = 5 GHz, fs2 = 15 GHz), and the microwave frequency fx changes from 0 to 44 GHz, the output power at 16 GHz ( fs1 + fb), 4 GHz ( fs2fb) and 26 GHz ( fs2 + fb) appears as three peaks, which results in the measurable frequency range of the IFM system being 22 GHz. As can be seen in Fig. 3(c), when fs2, fs1 > fb, fs2fs1 < 2fb (for fs1 = 15 GHz, fs2 = 20 GHz), and the microwave frequency fx changes from 0 to 44 GHz, the output power at 4 GHz ( fs1fb), 26 GHz ( fs1 + fb), 9 GHz ( fs2fb) and 31 GHz ( fs2 + fb) appears as four peaks, which results in the measurable frequency range of the IFM system being 22 GHz. As can be seen in Fig. 3(d), when fs2, fs1 > fb, and fs2fs1 = 2fb (for fs1 = 12 GHz and fs2 = 34 GHz), when the microwave frequency fx changes from 0 to 44 GHz, the output power at 1 GHz ( fs1fb), 23 GHz ( fs1 + fb), 23 GHz ( fs2fb) and 45 GHz ( fs2 + fb) appears as four peaks, which results in the measurable frequency range of the IFM system being extended to 44 GHz.

3.2. Simulation Results

The proposed IFM system is established using VPI transmission maker software. The parameters of the components used are shown in Table 1.

TABLE 1 Parameter settings for instantaneous frequency measurement (IFM) system

DeviceParameterDeviceParameter
LDPower10 dBmSBSBrillouin Gain Coefficient5
Wavelength1,550 nmBrillouin Frequency Shift11 GHz
Linewidth10 MHzBrillouin Linewidth40
PDResponsibility1 A/WEDFAGain5 dB
DPMZMInsert Loss5 dBHNLFFiber Loss0.2 dB/km
Extinction Ratio30 dBFiber Length15 km


When the microwave signal to be measured is input to the DPMZM with steps of 1 GHz in the range of 0–45 GHz, the output power of PD1 and PD2 is recorded. Figure 4 shows the relationship between the recorded power and the unknown microwave frequencies under different swept frequencies. As can be seen in Fig. 4, the output power only changes when the input microwave frequency fx to be measured differs from the PM swept frequency fs by a Brillouin frequency shift fb. Therefore, when detecting a change in the output power of PD1 and PD2, the frequency of the microwave signal to be measured can be determined as the sum of the swept signal frequency fs1 or fs2 and the Brillouin frequency shift fb at that time.

Figure 4.Output power versus known frequencies. (a) fs1, fs2 < fb and fs2fs1 < fb, (b) fs1 < fb, fs2 > fb and fs2fs1 < fb, (c) fs1, fs2 > fb and fs2fs1 < 2fb, and (d) fs1, fs2 > fb and fs2fs1 = 2fb.

When the PM swept frequencies fs1, fs2 < fb (for fs1 = 3 GHz, fs2 = 9 GHz), the output powers from PD1 and PD2 are shown in Fig. 4(a). In Fig. 4(a), it can be seen that two power peaks of −27.800 dBm and −29.178 dBm occurred at 14.0003 GHz and 20.0001 GHz, respectively, which results in the measurement range being within fb. When the PM swept frequencies fs1 < fb, fs2 > fb and fs2fs1 < fb (for fs1 = 5 GHz, fs2 = 15 GHz), the output powers from PD1 and PD2 are shown in Fig. 4(b). In Fig. 4(b), it can be seen that three power peaks of −27.800 dBm, −29.178 dBm, and −29.178 dBm occurred at 16.0004 GHz, 4.0046 GHz and 26.0001 GHz, respectively, which results in the measurement range being within 2fb.

When the PM swept signal frequency fs1, fs2 > fb and fs2fs1 < 2fb (for fs1 = 15 GHz, fs2 = 20 GHz), the output powers from PD1 and PD2 are shown in Fig. 4(c). In Fig. 4(c), it can be seen that four power peaks of −28.034 dBm, −28.0403 dBm, −30.163 dBm and −30.1656 dBm occurred at 4.005 GHz, 26.00006 GHz, 9.0002 GHz and 31.0007 GHz, respectively, which results in the measurement range being within 2fb. When the PM swept frequencies fs1, fs2 > fb and fs2fs1 = 2fb (for fs1 = 12 GHz, fs2 = 34 GHz), the output powers from PD1 and PD2 are shown in Fig. 4(d). It can be seen in Fig. 4(d) that four power peaks of −28.334 dBm, −28.434 dBm, −28.034 dBm and −29.034 dBm occurred at 1.0044 GHz, 23.0096 GHz, 23.0087 GHz and 45.0098 GHz, respectively. Therefore, the loss spectrum generated at fc + fs1 is offset by the gain spectrum generated at fc + fs2, which results in the measurement range increasing from 2fb to 4fb.

In addition, when the frequencies to be measured change in the range of 0.5–44 GHz, and the swept frequencies fs1 and fs2 are swept at 20 MHz intervals in the range 0–45 GHz, the output powers of PD1 and PD2 are simultaneously detected. The measured frequencies according to fs1,2 + fb and the input frequencies are shown in Fig. 5(a). Also, the measurement error is shown in Fig. 5(b). In Figs. 5(a) and 5(b), it can be seen that the measured microwave frequencies are a relatively better match with the input values in the range of 0.5–44 GHz with a maximum error of less than 10 MHz.

Figure 5.Measurement results. (a) The measured frequencies and (b) measurement errors.

Moreover, according to the above theoretical analysis, it is clear that the Brillouin frequency shift fb is the main factor determining the measurable range of the IFM system. Therefore, considering the Brillouin frequency shift fb = 2nf Va/λp (nf = 1.45 is the effective refractive index of the fiber, Va = 5.96 km/s is the speed of sound and λp is the wavelength), the measurement range and measurement error of the IFM system at different wavelengths were simulated using VPI transmission maker software. However, considering that the output wavelength range of current commercial tunable lasers is 1,460 nm–1,620 nm [such as the tunable wavelength range of the Tektronix Wavetune® WTM-230 (Tektronix, OR, USA) is 1,525 nm to 1,625 nm; The tunable wavelength range of the Rohde Schwarz Tunics T25S-HP (Rohde & Schwarz GmbH, Munich, Germany) is 1,460 nm to 1,620 nm]. Therefore, the measurement range and measurement error of the IFM system at wavelengths of 1,500 nm, 1,530 nm, 1,550 nm, 1,580 nm, and 1,600 nm are analyzed. The results are shown in Figs. 6 and 7.

Figure 6.The measurement range at different wavelengths. (a) λp = 1,500 mm; (b) λp = 1,530 mm; (c) λp = 1,550 mm, and (d) λp = 1,600 mm.
Figure 7.Measurement errors at different wavelengths.

As can be seen In Figs. 6 and 7, when λp is 1,500 nm, the measurement range is 0.5–45.96 GHz, and the maximum measurement error is 9.84 MHz. When λp is 1,530 nm, the measurement range is 0.5–44.48 GHz and the maximum measurement error is 9.96 MHz. When λp is 1,550 nm, the measurement range is 0.5–44 GHz and the maximum measurement error is 9.83 MHz. When λp is 1,600 nm, the measurement range is 0.5–43.12 GHz and the maximum measurement error is 8.25 MHz. It can be concluded that as the wavelength increases from 1,500 nm to 1,600 nm, the Brillouin frequency shift fb decreases from 11.49 GHz to 10.78 GHz, which changes the measurement range from 0.5–45.96 GHz to 0.5–43.12 GHz and the measurement error from 9.84 MHz to 8.25 MHz. Therefore, the measurement range of the IFM system can be adjusted by changing the wavelength. However, because of the pump optical power, the HNLF and the ∆vB are determined, and the gain spectrum g( f ) and loss spectrum α( f ) do not vary with the wavelength of the pump light. Therefore, the measurement errors vary little with the wavelength of the pump light.

Furthermore, according to the theoretical analysis, the peak of the Brillouin gain spectrum from the SBS effect increases when the optical power of the pump light is higher, thus enabling the power changes to be detected more easily and further reducing the measurement error. Figure 8 shows the measurement errors of the IFM system when the wavelength is 1,550 nm while the optical powers are 10 dBm, 12 dBm, 14 dBm, and 16 dBm, respectively.

Figure 8.Measurement errors at different powers.

As can be seen in Fig. 8, when the optical powers are 10 dBm, 12 dBm, 14 dBm, and 16 dBm, the measurement errors are within ±9.83 MHz, ±7.69 MHz, ±6.7 MHz, and ±3.08 MHz, respectively, and the maximum measurement errors are 9.83 MHz, 9.90 MHz, 9.00 MHz, and 9.53 MHz. Therefore, it can be concluded that the measurement error of the IFM system can be reduced by increasing the power of the pump light. However, when the power is 16 dBm, with the increase of input frequency, the measurement error range is small and tends to be stable. This comes from the fact that the minimum error of the measurement system depends on the noise.

In addition, a comparison of the performances of existing IFM systems is shown in Table 2. As can be seen in Table 2, in [13], harnessing the photon and phonon interactions in a photonic chip through SBS results in an accurate estimation of multiple frequency measurement up to 38 GHz with errors lower than 1 MHz. In [15], by scanning filtering, unknown frequency information is mapped into time intervals and unknown frequencies can be derived using the frequency-to-time mapping function, which results in a measurement range from 5 to 30 GHz and an error of ±510 MHz. In [16], a simple and feasible frequency measurement scheme using dual-stage SBS and nonlinear fitting is proposed and experimentally demonstrated. The measurement error is less than 5 MHz with a broadband of 21.42 GHz. In [17], a high-accuracy microwave frequency measurement approach with two-step accuracy improvement based on the SBS effect and frequency-to-time mapping is proposed. A measurement range from 6 to 18 GHz is demonstrated with a measurement error of less than ±1 MHz. In [18], a frequency measurement scheme based on SBS and an AFBG is proposed, resulting in a measurement error of less than ±1 MHz within a range of 10.68 GHz to 20 GHz. In this paper, an IFM system based on dual paths of the SBS effect has been proposed and designed. When the PM signals fs1 and fs2 differ by 2fb, the SBS attenuation spectrum at fc + fs1 and the SBS gain spectrum at fc + fs2 cancel each other, which results in the frequency measurement range increasing to 4fb.

TABLE 2 Performances comparison of existing instantaneous frequency measurement (IFM) systems

TimeTechnologyMeasurement Range (GHz)Measurement Error (MHz)
2016SBS on chip [13]9–381
2018MRR [15]5–30510
2019SBS [16]0–21.425
2020SBS + DPMZM [17]6 –181
2022SBS + AFBG [18]10.68–201
2023SBS + PM (this work)0.5–45.969.9


Based on these previous results, the use of integrated optoelectronics can be considered in the future to achieve monolithic integration of the proposed dual paths of the SBS effect, thus reducing the noise of the system and improving measurement accuracy.

In conclusion, a broadband IFM system based on the dual paths of the SBS effect has been proposed, designed and simulated. By changing the swept frequencies and simultaneously detecting the two PDs output powers, the microwave frequency can be measured. The IFM system was established using VPI transmission maker Software, and the microwave frequencies from 0.5–45.96 GHz were measured with a maximum measurement error of 9.9 MHz by setting fs1 to vary from 0 GHz to 22 GHz and fs2 to vary from 23 GHz to 44 GHz. The effect of the optical wavelength and power of the pump light on the measurement range and measurement error are further analyzed. It is concluded that the measurement range of the IFM system can be increased by adjusting the wavelength, and the measurement error can be reduced by increasing the power of the pump light. Compared with the existing IFM systems, the proposed IFM measurement system has a wider measurement range.

Data underlying the results presented in this paper are not publicly available at the time of publication, but may be obtained from the authors upon reasonable request.

National Natural Science Foundation of China (NSFC 62162034); Yunnan Fundamental Research Projects (2022 01AT070189).

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Article

Research Paper

Curr. Opt. Photon. 2023; 7(4): 378-386

Published online August 25, 2023 https://doi.org/10.3807/COPP.2023.7.4.378

Copyright © Optical Society of Korea.

Broadband Instantaneous Frequency Measurement System Based on the Dual Paths of the Stimulated Brillouin Scattering Effect

Jiahong Zhang , Weijie Liao

Faculty of Information Engineering and Automation, Kunming University of Science and Technology, Kunming 650500, China

Correspondence to:*zjh_mit@163.com, ORCID 0000-0003-1496-5770

Received: May 2, 2023; Revised: June 20, 2023; Accepted: July 5, 2023

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A wideband instantaneous frequency measurement (IFM) system is been proposed, designed and analyzed. Phase modulation to intensity modulation conversion is implemented based on the stimulated Brillouin scattering (SBS) effect, and the microwave frequency can be measured by detecting the change in output power. Theoretical analysis shows that the frequency measurement range can be extended to 4fb by adjusting the two sweeping signals of the phase modulators with a difference of 2fb. The IFM system is set up using VPI transmission maker software and the performances are simulated and analyzed. The simulation results show that the measurement range is 0.5−45.96 GHz with a maximum measurement error of less than 9.9 MHz. The proposed IFM system has a wider measurement range than the existing SBS-based IFM system.

Keywords: Instantaneous frequency measurement, Phase modulation, Stimulated Brillouin scattering

I. INTRODUCTION

Instantaneous frequency measurement (IFM) technology can be used to quickly obtain the frequency information of a target for tracking, advance warning and interference purposes, and plays an important role in communications, radar and electronic warfare [1, 2]. With the development of information technology, traditional electronic frequency measurement methods have gradually failed to meet current needs due to the limitation of the electronic bottleneck. The photon-assisted microwave frequency measurement (MFM) method has received attention for its advantages of wider bandwidth, lower loss, anti-electromagnetic interference and larger measurement range [35]. The methods of IFM based on the stimulated Brillouin scattering (SBS) effect have been widely researched due to their adjustable frequency measurement range and lower measurement errors [610].

A multiple MFM scheme is proposed based on the selective conversion of phase modulation to amplitude modulation (PM-IM), which is realized by SBS. The scheme achieves frequency measurements in the 1–9 GHz range with a maximum measurement error of less than 30 MHz [11]. An approach for IFM is proposed based on a PM in combination with an IM. The measurement errors are within ±90 MHz in the frequency range of 0.5–20 GHz [12]. A chip-based approach has achieved multiple-frequency measurement by using the amplitude comparison function (ACF) with a measurement range of up to 38 GHz and a measurement error of 1 MHz [13]. A technique for the IFM is proposed based on SBS in a single-mode optical fiber to achieve multi-MFMs. The measured frequency errors are within 20 MHz within a broadband of 27 GHz [14]. A photonic multiple IFM system is presented and demonstrated based on a swept frequency silicon microring resonator (MRR). Frequency estimation in a range of 5–30 GHz with a measurement error under ±510 MHz is achieved [15]. By scanning the reference frequency during the SBS, the frequency information of the microwave signal to be measured is detected by a mapping between the total output power of the system and the reference frequency, and multi-MFM is achieved. The scheme achieves frequency measurements in the range of 21.42 GHz with a measurement error of less than 5 MHz [16]. A photonic-assisted multiple IFM approach based on SBS and frequency-to-time mapping with high accuracy and a wide frequency measurement range is proposed. The IFM from 6 to 18 GHz is achieved with a measurement error of less than ±1 MHz [17]. A MFM scheme based on SBS and an apodised fiber Bragg grating (AFBG) is proposed. By sweeping a reference frequency during the SBS process, frequency-to-power mapping between the reference frequency and the monitored output optical power of the IFM system is established. A measurement error of less than ±1 MHz within 10.68 GHz to 20 GHz is achieved [18]. In summary, many IFM methods based on SBS effects have been proposed to achieve larger measurement ranges and smaller measurement errors, but not both at the same time.

In this paper, an IFM system based on dual paths of the SBS effect has been proposed and designed. The frequency measurement range can be extended to 4fb by using the two swept signals of the phase modulators with a difference of 2fb. The IFM system has been established and simulated using VPI transmission maker software. The effect of the optical wavelength and power of the pump light on the measurement range and measurement error of the IFM system was also analyzed. The proposed IFM system with dual SBS paths has a larger measurement range.

II. SYSTEM STRUCTURE AND PRINCIPLES

A schematic diagram of the proposed IFM system based on the dual paths of the SBS effect is shown in Fig. 1. The optical carrier fc is split into two parts by 3 dB optical coupler 1 (OC1) and transmitted in the upper and lower paths. The upper light passes through the 3 dB coupler 2 (OC2) and then splits into two paths that enter into phase modulator 1 (PM1) and phase modulator 2 (PM2), respectively. The output microwave signals from the two swept sources ( fs1 and fs2) are loaded onto the optical carrier through PM1 and PM2, respectively. Figures 2(a) and 2(b) show the first-order sidebands fc + fs1, fcfs1 and fc + fs2, fcfs2 of the modulated signals of PM1 and PM2, which can be expressed as [19].

Figure 1. Schematic diagram of the proposed instantaneous frequency measurement (IFM) system: LD, laser diode; OC, optical coupler; PM, phase modulator; ISO, isolator; HNLF, high nonlinear optical fiber; DPMZM, dual-parallel Mach-Zehnder modulator; EDFA, erbium-doped optical fiber amplifier; PD, photodetector.
Figure 2. Spectrum of the signals. (a) Output from PM1, (b) output from PM2, (c) output from the DPMZM, (d) output from the HNLF1, (e) output from the HNLF2 and (f) output spectrum for fs2 = fs1 + 2fb. PM, phase modulator; DPMZM, dual-parallel Mach-Zehnder modulator; HNLF, high nonlinear optical fiber.

Ep(t)=J0(m)expj2πfct+J1(m)expj2πfc +fs1,2 t+π2J1(m)expj2πfc fs1,2 tπ2

In Eq. (1), m = πV/Vπ is the modulation index, J0(m) and J1(m) are the zero-order and first-order Bessel functions, respectively. The modulated signals from PM1 and PM2 are transmitted unidirectionally through isolator 1 (ISO1) and isolator 2 (ISO2) into highly nonlinear optical fiber 1 (HNLF1) and highly nonlinear optical fiber 2 (HNLF2), respectively, with the same Brillouin frequency shift. The function of the optical isolator is to prevent the pump light from entering the phase modulator in the reverse direction, which will affect the system.

The microwave signal fx to be measured is loaded onto the optical carrier through a dual parallel Mach Zander intensity modulator (DPMZM), which works on the carrier suppression single-sideband modulation (CS-SSB). The output spectrum of the DPMZM is shown in Fig. 2(c). The output CS-SSB signal is amplified by an erbium-doped fiber amplifier (EDFA) and split into two parts by 3 dB coupler 3 (OC3), and one part is input to HNLF1 through circulator 1 and the other is input to HNLF2 through circulator 2. When the signal light differs from the pump light transmitted in reverse by one Brillouin frequency shift fb, the SBS effect occurs, causing the amplitude of the first-order sideband of the PM to gain or attenuate, thus breaking the sideband balance and achieving PM-IM conversion.

The gain and attenuation spectrums of HNLF1 and HNLF2 are shown in Figs. 2(d) and 2(e) respectively. The gain spectrum g( f ) and the attenuation spectrum a( f ) can be expressed as [20]

g(f)=g02ΔvB/22f2+ΔvB/22+jg04ΔvBff2+ΔvB/22

a(f)=g02ΔvB/22f2+ΔvB/22jg04ΔvBff2+ΔvB/22

in Eq.(2) and Eq.(3), ∆vB is the Brillouin linewidth, g0 = gBIp Leff/Aeff is the line center gain factor of the HNLF, gB is the line center gain, Ip is the power of the pump light, Leff and Aeff are the effective length and effective mode area of HNLF.

When the SBS effect occurs, the PM output optical field can be expressed as

E(t)=ej2πfctJ0(m)+J1(m)expg(fs1,2 fb fx )+a(fs1,2 +fb fx )+j(2πfs1,2 t+π2)J1(m)expj(2πfs1,2t+π2)

From Eq. (4), ignoring the direct current (DC), the output optical power can be written as

P2J0(m)J1(m) G(fs1,2 fb fx )A(fs1,2 +fb fx ) ×cos[ϕg (fs1,2 fb fx )+ϕa (fs1,2 +fb fx ) +2πfs1,2 t+π2]cos[2πfs1,2 t+π2]

in Eq. (5), G( fs1,2fbfx) and A( fs1,2 + fbfx) are the gains and losses introduced by the SBS effect occurring, and ϕg( fs1,2fbfx), ϕa( fs1,2 + fbfx) are the corresponding phase shifts, which can be expressed as

G(fs1,2fbfx)=exp{Re[g(fs1,2fbfx)]} =expg0 2ΔvB /22(f s1,2 fb fx )2+ΔvB /22 A(fs1,2+fbfx)=exp{Re[a(fs1,2+fbfx)]} =expg0 2ΔvB /22(f s1,2 +fb fx )2+ΔvB /22

ϕg(fs1,2fbfx)=Im[g(fs1,2fbfx)]} =g04ΔvB /2(fs1,2fbfx) (fs1,2 fb fx )2+ΔvB /22 ϕa(fs1,2+fbfx)=Im[a(fs1,2+fbfx)]} =g04ΔvB /2(fs1,2+fbfx) (fs1,2 +fb fx )2+ΔvB /22

Therefore, the output of electric field at the PD can be expressed approximately as

Eout(t)=pG(fm)A(fm)cos[ϕg(fm)+ϕa(fm)+2πfs1,2t+π2]cos[2πfs1,2t+π2]

In Eq. (8), ℜ< p> is the response ability of the PD to the input optical power.

For frequency measurement, the PM output signal fc + fs1 is used as the pump light and the DPMZM output signal fc + fx is used as the signal light. When fc + fx is equal to fc + fs1fb or fc + fs1 + fb, the SBS effect occurs and the output power will be changed. Therefore, by scanning fs1 and fs2 and detecting the output power, the frequency fx to be measured can be achieved as the sum of the swept frequency fs and the Brillouin frequency shift fb when the detected output power changes.

As the SBS effect generates both the gain and attenuation spectrums, the signal power changes at fs1fb and fs1 + fb, and the measurable frequency range is 2fb. In this paper, a broadband IFM system based on the dual paths of the SBS effect is proposed, and when the PM signals fs1 and fs2 differ by 2fb, the SBS attenuation spectrum at fc + fs1 and the SBS gain spectrum at fc + fs2 cancel each other, which results in the frequency measurement range increasing to 4fb. The output spectrum is shown in Fig. 2(f).

III. RESULTS AND DISCUSSION

3.1. Theoretical Analysis

When the optical wavelength λp = 1,550 nm, the Brillouin gain coefficient g0 = 5, the Brillouin frequency shift fb = 11 GHz and the Brillouin linewidth ∆vB = 40 MHz. According to Eq. (5), Fig. 3 shows the relationship between the normalized output power and the known frequencies obtained under different sweeping frequencies of fs1, fs2.

Figure 3. Output power versus known frequencies. (a) fs1, fs2 < fb, (b) fs1, fs2 > fb and fs2fs1 < 2fb, (c) fs1, fs2 > fb and fs2fs1 < 2fb, (d) fs1, fs2 > fb and fs2fs1 = 2fb.

As can be seen in Fig. 3(a), when fs1, fs2 < fb (for fs1 = 3 GHz, fs2 = 9 GHz), with the microwave frequency fx changes from 0 to 44 GHz, the output power at 14 GHz ( fs1 + fb) and 20 GHz ( fs2 + fb) appears as two peaks. Therefore, when detecting the output power changing of photodetector 1 (PD1) and photodetector 2 (PD2), the microwave frequencies under measurement can be determined as fs1 + fb and fs2 + fb, respectively. Under this condition, the measurable frequency range of the IFM system is 11 GHz. As can be seen in Fig. 3(b), when fs1 < fb and fs2 > fb (for fs1 = 5 GHz, fs2 = 15 GHz), and the microwave frequency fx changes from 0 to 44 GHz, the output power at 16 GHz ( fs1 + fb), 4 GHz ( fs2fb) and 26 GHz ( fs2 + fb) appears as three peaks, which results in the measurable frequency range of the IFM system being 22 GHz. As can be seen in Fig. 3(c), when fs2, fs1 > fb, fs2fs1 < 2fb (for fs1 = 15 GHz, fs2 = 20 GHz), and the microwave frequency fx changes from 0 to 44 GHz, the output power at 4 GHz ( fs1fb), 26 GHz ( fs1 + fb), 9 GHz ( fs2fb) and 31 GHz ( fs2 + fb) appears as four peaks, which results in the measurable frequency range of the IFM system being 22 GHz. As can be seen in Fig. 3(d), when fs2, fs1 > fb, and fs2fs1 = 2fb (for fs1 = 12 GHz and fs2 = 34 GHz), when the microwave frequency fx changes from 0 to 44 GHz, the output power at 1 GHz ( fs1fb), 23 GHz ( fs1 + fb), 23 GHz ( fs2fb) and 45 GHz ( fs2 + fb) appears as four peaks, which results in the measurable frequency range of the IFM system being extended to 44 GHz.

3.2. Simulation Results

The proposed IFM system is established using VPI transmission maker software. The parameters of the components used are shown in Table 1.

TABLE 1. Parameter settings for instantaneous frequency measurement (IFM) system.

DeviceParameterDeviceParameter
LDPower10 dBmSBSBrillouin Gain Coefficient5
Wavelength1,550 nmBrillouin Frequency Shift11 GHz
Linewidth10 MHzBrillouin Linewidth40
PDResponsibility1 A/WEDFAGain5 dB
DPMZMInsert Loss5 dBHNLFFiber Loss0.2 dB/km
Extinction Ratio30 dBFiber Length15 km


When the microwave signal to be measured is input to the DPMZM with steps of 1 GHz in the range of 0–45 GHz, the output power of PD1 and PD2 is recorded. Figure 4 shows the relationship between the recorded power and the unknown microwave frequencies under different swept frequencies. As can be seen in Fig. 4, the output power only changes when the input microwave frequency fx to be measured differs from the PM swept frequency fs by a Brillouin frequency shift fb. Therefore, when detecting a change in the output power of PD1 and PD2, the frequency of the microwave signal to be measured can be determined as the sum of the swept signal frequency fs1 or fs2 and the Brillouin frequency shift fb at that time.

Figure 4. Output power versus known frequencies. (a) fs1, fs2 < fb and fs2fs1 < fb, (b) fs1 < fb, fs2 > fb and fs2fs1 < fb, (c) fs1, fs2 > fb and fs2fs1 < 2fb, and (d) fs1, fs2 > fb and fs2fs1 = 2fb.

When the PM swept frequencies fs1, fs2 < fb (for fs1 = 3 GHz, fs2 = 9 GHz), the output powers from PD1 and PD2 are shown in Fig. 4(a). In Fig. 4(a), it can be seen that two power peaks of −27.800 dBm and −29.178 dBm occurred at 14.0003 GHz and 20.0001 GHz, respectively, which results in the measurement range being within fb. When the PM swept frequencies fs1 < fb, fs2 > fb and fs2fs1 < fb (for fs1 = 5 GHz, fs2 = 15 GHz), the output powers from PD1 and PD2 are shown in Fig. 4(b). In Fig. 4(b), it can be seen that three power peaks of −27.800 dBm, −29.178 dBm, and −29.178 dBm occurred at 16.0004 GHz, 4.0046 GHz and 26.0001 GHz, respectively, which results in the measurement range being within 2fb.

When the PM swept signal frequency fs1, fs2 > fb and fs2fs1 < 2fb (for fs1 = 15 GHz, fs2 = 20 GHz), the output powers from PD1 and PD2 are shown in Fig. 4(c). In Fig. 4(c), it can be seen that four power peaks of −28.034 dBm, −28.0403 dBm, −30.163 dBm and −30.1656 dBm occurred at 4.005 GHz, 26.00006 GHz, 9.0002 GHz and 31.0007 GHz, respectively, which results in the measurement range being within 2fb. When the PM swept frequencies fs1, fs2 > fb and fs2fs1 = 2fb (for fs1 = 12 GHz, fs2 = 34 GHz), the output powers from PD1 and PD2 are shown in Fig. 4(d). It can be seen in Fig. 4(d) that four power peaks of −28.334 dBm, −28.434 dBm, −28.034 dBm and −29.034 dBm occurred at 1.0044 GHz, 23.0096 GHz, 23.0087 GHz and 45.0098 GHz, respectively. Therefore, the loss spectrum generated at fc + fs1 is offset by the gain spectrum generated at fc + fs2, which results in the measurement range increasing from 2fb to 4fb.

In addition, when the frequencies to be measured change in the range of 0.5–44 GHz, and the swept frequencies fs1 and fs2 are swept at 20 MHz intervals in the range 0–45 GHz, the output powers of PD1 and PD2 are simultaneously detected. The measured frequencies according to fs1,2 + fb and the input frequencies are shown in Fig. 5(a). Also, the measurement error is shown in Fig. 5(b). In Figs. 5(a) and 5(b), it can be seen that the measured microwave frequencies are a relatively better match with the input values in the range of 0.5–44 GHz with a maximum error of less than 10 MHz.

Figure 5. Measurement results. (a) The measured frequencies and (b) measurement errors.

Moreover, according to the above theoretical analysis, it is clear that the Brillouin frequency shift fb is the main factor determining the measurable range of the IFM system. Therefore, considering the Brillouin frequency shift fb = 2nf Va/λp (nf = 1.45 is the effective refractive index of the fiber, Va = 5.96 km/s is the speed of sound and λp is the wavelength), the measurement range and measurement error of the IFM system at different wavelengths were simulated using VPI transmission maker software. However, considering that the output wavelength range of current commercial tunable lasers is 1,460 nm–1,620 nm [such as the tunable wavelength range of the Tektronix Wavetune® WTM-230 (Tektronix, OR, USA) is 1,525 nm to 1,625 nm; The tunable wavelength range of the Rohde Schwarz Tunics T25S-HP (Rohde & Schwarz GmbH, Munich, Germany) is 1,460 nm to 1,620 nm]. Therefore, the measurement range and measurement error of the IFM system at wavelengths of 1,500 nm, 1,530 nm, 1,550 nm, 1,580 nm, and 1,600 nm are analyzed. The results are shown in Figs. 6 and 7.

Figure 6. The measurement range at different wavelengths. (a) λp = 1,500 mm; (b) λp = 1,530 mm; (c) λp = 1,550 mm, and (d) λp = 1,600 mm.
Figure 7. Measurement errors at different wavelengths.

As can be seen In Figs. 6 and 7, when λp is 1,500 nm, the measurement range is 0.5–45.96 GHz, and the maximum measurement error is 9.84 MHz. When λp is 1,530 nm, the measurement range is 0.5–44.48 GHz and the maximum measurement error is 9.96 MHz. When λp is 1,550 nm, the measurement range is 0.5–44 GHz and the maximum measurement error is 9.83 MHz. When λp is 1,600 nm, the measurement range is 0.5–43.12 GHz and the maximum measurement error is 8.25 MHz. It can be concluded that as the wavelength increases from 1,500 nm to 1,600 nm, the Brillouin frequency shift fb decreases from 11.49 GHz to 10.78 GHz, which changes the measurement range from 0.5–45.96 GHz to 0.5–43.12 GHz and the measurement error from 9.84 MHz to 8.25 MHz. Therefore, the measurement range of the IFM system can be adjusted by changing the wavelength. However, because of the pump optical power, the HNLF and the ∆vB are determined, and the gain spectrum g( f ) and loss spectrum α( f ) do not vary with the wavelength of the pump light. Therefore, the measurement errors vary little with the wavelength of the pump light.

Furthermore, according to the theoretical analysis, the peak of the Brillouin gain spectrum from the SBS effect increases when the optical power of the pump light is higher, thus enabling the power changes to be detected more easily and further reducing the measurement error. Figure 8 shows the measurement errors of the IFM system when the wavelength is 1,550 nm while the optical powers are 10 dBm, 12 dBm, 14 dBm, and 16 dBm, respectively.

Figure 8. Measurement errors at different powers.

As can be seen in Fig. 8, when the optical powers are 10 dBm, 12 dBm, 14 dBm, and 16 dBm, the measurement errors are within ±9.83 MHz, ±7.69 MHz, ±6.7 MHz, and ±3.08 MHz, respectively, and the maximum measurement errors are 9.83 MHz, 9.90 MHz, 9.00 MHz, and 9.53 MHz. Therefore, it can be concluded that the measurement error of the IFM system can be reduced by increasing the power of the pump light. However, when the power is 16 dBm, with the increase of input frequency, the measurement error range is small and tends to be stable. This comes from the fact that the minimum error of the measurement system depends on the noise.

In addition, a comparison of the performances of existing IFM systems is shown in Table 2. As can be seen in Table 2, in [13], harnessing the photon and phonon interactions in a photonic chip through SBS results in an accurate estimation of multiple frequency measurement up to 38 GHz with errors lower than 1 MHz. In [15], by scanning filtering, unknown frequency information is mapped into time intervals and unknown frequencies can be derived using the frequency-to-time mapping function, which results in a measurement range from 5 to 30 GHz and an error of ±510 MHz. In [16], a simple and feasible frequency measurement scheme using dual-stage SBS and nonlinear fitting is proposed and experimentally demonstrated. The measurement error is less than 5 MHz with a broadband of 21.42 GHz. In [17], a high-accuracy microwave frequency measurement approach with two-step accuracy improvement based on the SBS effect and frequency-to-time mapping is proposed. A measurement range from 6 to 18 GHz is demonstrated with a measurement error of less than ±1 MHz. In [18], a frequency measurement scheme based on SBS and an AFBG is proposed, resulting in a measurement error of less than ±1 MHz within a range of 10.68 GHz to 20 GHz. In this paper, an IFM system based on dual paths of the SBS effect has been proposed and designed. When the PM signals fs1 and fs2 differ by 2fb, the SBS attenuation spectrum at fc + fs1 and the SBS gain spectrum at fc + fs2 cancel each other, which results in the frequency measurement range increasing to 4fb.

TABLE 2. Performances comparison of existing instantaneous frequency measurement (IFM) systems.

TimeTechnologyMeasurement Range (GHz)Measurement Error (MHz)
2016SBS on chip [13]9–381
2018MRR [15]5–30510
2019SBS [16]0–21.425
2020SBS + DPMZM [17]6 –181
2022SBS + AFBG [18]10.68–201
2023SBS + PM (this work)0.5–45.969.9


Based on these previous results, the use of integrated optoelectronics can be considered in the future to achieve monolithic integration of the proposed dual paths of the SBS effect, thus reducing the noise of the system and improving measurement accuracy.

IV. CONCLUSION

In conclusion, a broadband IFM system based on the dual paths of the SBS effect has been proposed, designed and simulated. By changing the swept frequencies and simultaneously detecting the two PDs output powers, the microwave frequency can be measured. The IFM system was established using VPI transmission maker Software, and the microwave frequencies from 0.5–45.96 GHz were measured with a maximum measurement error of 9.9 MHz by setting fs1 to vary from 0 GHz to 22 GHz and fs2 to vary from 23 GHz to 44 GHz. The effect of the optical wavelength and power of the pump light on the measurement range and measurement error are further analyzed. It is concluded that the measurement range of the IFM system can be increased by adjusting the wavelength, and the measurement error can be reduced by increasing the power of the pump light. Compared with the existing IFM systems, the proposed IFM measurement system has a wider measurement range.

DISCLOSURES

The authors declare no conflicts of interest.

DATA AVAILABILITY

Data underlying the results presented in this paper are not publicly available at the time of publication, but may be obtained from the authors upon reasonable request.

FUNDING

National Natural Science Foundation of China (NSFC 62162034); Yunnan Fundamental Research Projects (2022 01AT070189).

Fig 1.

Figure 1.Schematic diagram of the proposed instantaneous frequency measurement (IFM) system: LD, laser diode; OC, optical coupler; PM, phase modulator; ISO, isolator; HNLF, high nonlinear optical fiber; DPMZM, dual-parallel Mach-Zehnder modulator; EDFA, erbium-doped optical fiber amplifier; PD, photodetector.
Current Optics and Photonics 2023; 7: 378-386https://doi.org/10.3807/COPP.2023.7.4.378

Fig 2.

Figure 2.Spectrum of the signals. (a) Output from PM1, (b) output from PM2, (c) output from the DPMZM, (d) output from the HNLF1, (e) output from the HNLF2 and (f) output spectrum for fs2 = fs1 + 2fb. PM, phase modulator; DPMZM, dual-parallel Mach-Zehnder modulator; HNLF, high nonlinear optical fiber.
Current Optics and Photonics 2023; 7: 378-386https://doi.org/10.3807/COPP.2023.7.4.378

Fig 3.

Figure 3.Output power versus known frequencies. (a) fs1, fs2 < fb, (b) fs1, fs2 > fb and fs2fs1 < 2fb, (c) fs1, fs2 > fb and fs2fs1 < 2fb, (d) fs1, fs2 > fb and fs2fs1 = 2fb.
Current Optics and Photonics 2023; 7: 378-386https://doi.org/10.3807/COPP.2023.7.4.378

Fig 4.

Figure 4.Output power versus known frequencies. (a) fs1, fs2 < fb and fs2fs1 < fb, (b) fs1 < fb, fs2 > fb and fs2fs1 < fb, (c) fs1, fs2 > fb and fs2fs1 < 2fb, and (d) fs1, fs2 > fb and fs2fs1 = 2fb.
Current Optics and Photonics 2023; 7: 378-386https://doi.org/10.3807/COPP.2023.7.4.378

Fig 5.

Figure 5.Measurement results. (a) The measured frequencies and (b) measurement errors.
Current Optics and Photonics 2023; 7: 378-386https://doi.org/10.3807/COPP.2023.7.4.378

Fig 6.

Figure 6.The measurement range at different wavelengths. (a) λp = 1,500 mm; (b) λp = 1,530 mm; (c) λp = 1,550 mm, and (d) λp = 1,600 mm.
Current Optics and Photonics 2023; 7: 378-386https://doi.org/10.3807/COPP.2023.7.4.378

Fig 7.

Figure 7.Measurement errors at different wavelengths.
Current Optics and Photonics 2023; 7: 378-386https://doi.org/10.3807/COPP.2023.7.4.378

Fig 8.

Figure 8.Measurement errors at different powers.
Current Optics and Photonics 2023; 7: 378-386https://doi.org/10.3807/COPP.2023.7.4.378

TABLE 1 Parameter settings for instantaneous frequency measurement (IFM) system

DeviceParameterDeviceParameter
LDPower10 dBmSBSBrillouin Gain Coefficient5
Wavelength1,550 nmBrillouin Frequency Shift11 GHz
Linewidth10 MHzBrillouin Linewidth40
PDResponsibility1 A/WEDFAGain5 dB
DPMZMInsert Loss5 dBHNLFFiber Loss0.2 dB/km
Extinction Ratio30 dBFiber Length15 km

TABLE 2 Performances comparison of existing instantaneous frequency measurement (IFM) systems

TimeTechnologyMeasurement Range (GHz)Measurement Error (MHz)
2016SBS on chip [13]9–381
2018MRR [15]5–30510
2019SBS [16]0–21.425
2020SBS + DPMZM [17]6 –181
2022SBS + AFBG [18]10.68–201
2023SBS + PM (this work)0.5–45.969.9

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