1 Introduction

Microwave or millimeter wave generation with wideband tuning ability has great potential applications in numerous areas such as radar, signal processing, metrology, electronic warfare, optical and wireless communication systems since it not only can reduce system complexity and cost, but can also make it more convenient and flexible (Yao 2009; Yao and Maleki 1996). For instance, a wideband tunable microwave signal is critical and effective to meet the requirements of the development of frequency diversity radar system, in which multi-frequency and tunable local oscillators are usually necessary. It is well accepted that many electrical approaches such as frequency multiplication can generate high frequency microwave signals. However, the tuning range is always limited. What’s more, a low single side-band (SSB) phase noise cannot be guaranteed, especially at high frequencies.

The optoelectronic oscillator (OEO) attracts great interest due to its advantage of generating high frequency microwave signal with low phase noise. Since it was first reported by Yao and Maleki (1996a), OEO has been widely investigated (Tang et al. 2012; Pan et al. 2015; García and Gasulla 2015; Jiang et al. 2014; Bagnell et al. 2014; Zhou et al. 2014). Now, microwave generation using OEO has been considered a reasonable and very promising solution for obtaining a pure microwave signal, and it has already plays important roles in many fields (Maleki 2011). Generally, an electrical bandpass filter is used as the oscillation mode selection device in an ordinary OEO, which cannot be tuned over a broad frequency band. There is thereby an urgent need but still a significant challenge to generate a microwave with flexible and wideband tunability. Recently, various approaches have been investigated to achieve a tunable OEO (Yang et al. 2013; Zhang et al. 2014; Li and Yao 2012; Xie et al. 2013; Peng et al. 2015). Yang et al. (2013) proposed a dispersion-induced MPF based OEO, which is implemented with a carrier phase-shifted double sideband modulation in a dual-parallel Mach–Zehnder modulator (DPMZM). The central frequency can be tuned by adjusting the DC bias voltage of the DPMZM. Zhang et al. (2014) demonstrated a tunable OEO in which the tuning was realized by changing the length of the tunable delay line. Oscillation frequency from 1 to 12 GHz with a tuning step of 0.5 GHz is generated and could be improved by using an optical source with wider spectral range. To ensure a large tuning range, Li demostrated an OEO by employing a phase modulator (PM) and a phase-shifted fiber Bragg grating (PS-FBG) based microwave photonic filter (MPF), which can support a 3–28 GHz microwave signal generation (Li and Yao 2012). Xie et al. (2013) reported a phase modulator and a tunable optical filter based OEO, by tuning the bandwidth of the optical band-pass filter, a tunable frequency range from 4.74 to 38.38 GHz was realized. In Peng et al. (2015), an ultra-wideband RF generation utilizing a dual-loop optoelectronic oscillator based on stimulated Brillouin scattering was proposed and demonstrated.

In this paper, we propose and experimentally demonstrate a wideband tunable OEO based on a dispersion compensated MPF. The MPF is basically implemented using a narrow linewidth tunable laser source (TLS), a phase modulator, a fiber grating filter structure and a photodetector (PD). Instead of a PS-FBG, a fiber Bragg grating Fabry–Perot (FBG-FP) filter is used to ensure a large enough bandwidth, which is necessary for the generation of high frequency signal. The generated oscillation frequency is equal to the frequency difference between TLS and the notch of the FBG-FP filter and could be tuned simply by changing the TLS wavelength. However, owing to the phase-modulation to intensity-modulation (PM–IM) conversion, FBG-FP filter and long fiber loop with large chromatic dispersion will limit the tuning range of the OEO. A dispersion compensation fiber (DCF) is introduced followed by the SMF to compensate the fiber dispersion so as to overcome this disadvantage and consequently, ultra-wideband tunable signal is achieved experimentally. To prevent the mode hopping and suppress the side modes of the oscillation signal, dual-loop configuration is employed. The SSB phase noise performance of the generated microwave signal is also evaluated under different oscillation frequencies and loop structures. The results shows that the SSB phase noise is very low within the whole tuning range.

2 Principle and theoretical analysis

Figure 1 shows the generation configuration of the proposed OEO. The output of the laser is modulated by a PM and sent into a fiber optical filter through an optical circulator (OC). The optical filter used here is a wideband FBG-FP filter. The light from the output of OC is separated into two fiber links with different fiber length through an optical coupler. The two fiber loops here are used as another comb filter to further suppress the multimode oscillation in the OEO system. After that, the optical signals of each path are fed into two photodetectors (PD) to perform optical-to-electrical conversion respectively. The output electrical signal from each PD is combined using an electrical coupler (EC) and amplified by the power amplifier (PA). Finally, the electrical signal from EC is then applied back to the PM, to close the OEO loop.

Fig. 1
figure 1

General configuration of the proposed OEO based on dispersion compensated MPF. OC: optical circulator; PD: photodetector; PA: power amplifier; EC: electrical coupler

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First, the operation principle of the MPF that is incorporated in the OEO is explained as follows:

Assume that the electric field of the light wave from the laser is \(E_{0} (t) = E_{0} \exp \left( {j\omega_{0} t} \right)\). According to the Bessel function of the first kind and ignore the high order sidebands, the output of the PM could be mathematically written as (Qi et al. 2005):

$$E_{1} (t) = E_{0} \cdot \left\{ {J_{0} \left( \beta \right)\exp \left( {j\omega_{0} t} \right) + J_{1} \left( \beta \right)\exp \left[ {j\left( {\omega_{0} t + \omega_{m} t + \pi /2} \right)} \right] - J_{1} \left( \beta \right)\exp \left[ {j\left( {\omega_{0} t - \omega_{m} t - \pi /2} \right)} \right]} \right\}$$
(1)

where \(\beta = \pi V/V_{\pi }\) is the phase modulation index. V and V π are the amplitude of the signal applied to the phase modulator and the half-wave voltage of the phase modulator, respectively.

As can be seen from Eq. (1), when the signal is directly applied to a PD, no signal would be detected. Nevertheless, thanks to the ultra-narrow transmission window of the FBG-FP filter in its reflection band, the signal reflected by FBG-FP filter becomes a SSB modulation signal if one of the first-order sideband falls into the notch of the FBG-FP. In this case, the reflected light of the FBG-FP could be expressed as (assume that upper sideband locates at the notch of the FBG-FP and the transmission coefficient is 100%):

$$E_{1} (t) = E_{0} \cdot \left\{ {J_{0} \left( \beta \right)\exp \left( {j\omega_{0} t} \right) - J_{1} \left( \beta \right)\exp \left[ {j\left( {\omega_{0} t - \omega_{m} t - \pi /2} \right)} \right]} \right\}$$
(2)

Then the microwave signal at the output of the PD can be expressed as:

$$i_{1} (t) \propto \left| {E_{1} \left( t \right)} \right|^{2} \propto J_{0} \left( \beta \right)J_{1} \left( \beta \right)\sin \left( {\omega_{0} t} \right)$$
(3)

Consequently, as seen from Eq. (3), a microwave with the center angular frequency of ω 0 is generated and the frequency is equal to the difference between the notch of the FBG-FP filter and the optical carrier. Thus, when the MPF is closed to form an OEO, the angular frequency of the output signal will be equal to ω 0 (Li and Yao 2012).

However, to obtain a high phase noise, long SMF is usually used in the OEO loop (Jia et al. 2015), which would introduce a PM–IM conversion as well (Zeng and Yao 2005). Thus, the theoretical analysis above should be improved once the SMF dispersion is taken into consideration.

Generally, the amplitude reflection coefficient r(ω) of the FBG-FP filter could be expressed as (Erdogan 1997):

$$r\left( \omega \right) = \frac{{r_{g1} + r_{g2} \exp \left( { - i2\varPhi_{{L_{g} }} } \right)}}{{1 + r_{g1} r_{g2} \exp \left( { - i2\varPhi_{{L_{g} }} } \right)}}$$
(4)

where r g1 and r g2 are the reflection coefficient of each FBG, \(\varPhi_{L} = \beta L_{g}\), L g is the distance between two FBGs. After reflecting by the FBG-FP, Eq. (1) could be rewritten as:

$$\begin{aligned} E_{1} (t) = r\left( {\omega_{0} } \right)E_{0} J_{0} \left( \beta \right)\exp \left( {j\omega_{0} t} \right)\hfill \\+\, r\left( {\omega_{0} + \omega_{m} } \right)E_{0} J_{1} \left( \beta \right)\exp \left[ {j\left( {\omega_{0} t + \omega_{m} t + \pi /2} \right)} \right] \hfill \\-\, r\left( {\omega_{0} - \omega_{m} } \right)E_{0} J_{1} \left( \beta \right)\exp \left[ {j\left( {\omega_{0} t - \omega_{m} t - \pi /2} \right)} \right] \hfill \\ \end{aligned}$$
(5)

If the signal passes through a dispersive device (for example, the long SMF), it could be given by:

$$\begin{aligned} E_{1} (t) = r\left( {\omega_{0} } \right)E_{0} J_{0} \left( \beta \right)\exp \left[ {j\omega_{0} t + j\varphi_{0} } \right] \hfill \\+\, r\left( {\omega_{0} + \omega_{m} } \right)E_{0} J_{1} \left( \beta \right)\exp \left[ {j\left( {\omega_{0} t + \omega_{m} t + \pi /2} \right) + j\varphi_{ + 1} } \right] \hfill \\-\, r\left( {\omega_{0} - \omega_{m} } \right)E_{0} J_{1} \left( \beta \right)\exp \left[ {j\left( {\omega_{0} t - \omega_{m} t - \pi /2} \right) + j\varphi_{ - 1} } \right] \hfill \\ \end{aligned}$$
(6)

where φ 0, φ +1, and φ −1 are the additional phase delay of the carrier, upper sideband and the lower sideband induced by the dispersion of the long SMF, which can be express by an expansion in a Taylor series. For the uniform FBG based FBG-FP filter, fiber grating induced dispersion could be negligibly. Meanwhile, taking the whole frequency band into consideration and ignoring dc component and the high order harmonics, the recovered RF signal could be simplified as follows (Meslener 1984):

$$E_{1} (t) \propto \sqrt {A + B - C\cos \left[ {2\pi cLD\left( {\frac{{f_{m}^{2} }}{{f_{0}^{2} }}} \right)} \right]} \cos \left( {\omega_{0} t + \varPhi } \right)$$
(7)

where \(A = R^{2} \left( {\omega_{0} } \right)R^{2} \left( {\omega_{0} + \omega_{m} } \right),B = R^{2} \left( {\omega_{0} } \right)R^{2} \left( {\omega_{0} - \omega_{m} } \right),C = - 2R^{2} \left( {\omega_{0} } \right)R\left( {\omega_{0} + \omega_{m} } \right)R\left( {\omega_{0} - \omega_{m} } \right)\), R is the amplitude reflectivity of the FBG-FP filter, Φ is the phase of the synthetic signal. f m and f 0 are the frequency of the modulation signal and the carrier, respectively. D is the group velocity dispersion in SMF, L is the SMF length, c is the light velocity in vacuum. Hence, the detection signal at the output of the PD is:

$$V \propto \left| {E_{1} (t)} \right|^{2} \propto A + B - C\cos \left[ {2\pi cLD\left( {\frac{{f_{m}^{2} }}{{f_{0}^{2} }}} \right)} \right]$$
(8)

According to Eq. (7) and Eq. (8), the open loop frequency response of the MPF with different carrier wavelength and different SMF length could be calculated and depicted in Fig. 2.

Fig. 2
figure 2

Simulation results of the frequency response. a Frequency response at different input wavelength when the SMF length is 4 km; b frequency response at different SMF length when the input wavelength is fixed at 1549.96 nm

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Here, in Fig. 2, the notch wavelength of FBG-FP filter is set to be 1550 nm, and the TLS wavelength is initially set to be 1549.96 nm, indicating that the frequency difference between TLS and the notch of the FBG-FP filter is 5 GHz. The group velocity dispersion of the SMF is set to be 17 ps/(nm·km). As we can see from Fig. 2a, it is obvious that the result is the consequence of the SMF dispersion induced PM–IM conversion. As increasing the difference between the notch of the FBG-FP and the TLS wavelength, the frequency peak moves to high frequency accordingly. However, due to the PM–IM conversion, the response peaks are covered by the SMF dispersion induced frequency response profile and consequently, the peak amplitude is not that obvious at high response frequencies. Therefore, the dispersion of the SMF is a key factor that would limit the highest oscillation frequency of an OEO. Figure 2b shows the frequency response of the MPF with different SMF length under a certain TLS wavelength. We can conclude that shorter fiber should be employed so as to obtain a high frequency oscillation. Nevertheless, this is not easy for obtaining very low phase noise. Thus, in order to achieve broad frequency tuning range and low phase noise, it’s critical to suppress the SMF dispersion in the OEO.

3 Experimental results and discussion

The experimental setup of the proposed OEO is shown in Fig. 3. A TLS (ID Photonics CoBrite DX4) with a tunable range from 1510 to 1590 nm and a highest output power of 16 dBm is used as the light source. A polarization controller (PC) is adopted to adjust the polarization of the light in order to obtain a deep modulation. The PM (Photline MPZ-LN-40) has a 3 dB bandwidth of 32 GHz and a half-wave voltage of 7 V. Two cascaded amplifiers (PA1, Keysight N4985A and PA2, SHF S807) with the respective frequency gain range of 100 kHz–50 GHz and 60 kHz–50 GHz are used to amplify the electrical signal. The SMF lengths for the two loops are about 600 m and 4 km. To overcome the PM–IM conversion illustrated above, two DCFs are used to compensate the SMF induced dispersion in each loop. The dispersion factor of the DCF is about − 140 ps/(nm km) at 1550 nm and the length of the two DCFs are about 90 and 340 m, respectively. An optical spectrum analyzer (OSA, YOKOGAWA AQ6370D) and an electrical spectrum analyzer (ESA, Keysight N9040B) are used to monitor the optical and electrical spectrum. The FBG-FP fiber filter used is composed of two wavelength matched Bragg gratings with appropriate separation, which are written by the phase mask scanning technique with an excimer laser. When the cavity length reduces to several millimeters, single resonance peak can be achieved within the FBG reflection band by carefully optimizing the cavity and FBG parameters (Barmenkov et al. 2006). Due to the high reflectivity of each FBG, an ultra-narrow pass band is generated in the reflection band. The optical spectrum of the FBG-FP filter used in the experiment is shown in Fig. 4.

Fig. 3
figure 3

Schematic diagram of the experimental setup. TLS: tunable laser source; PM: phase modulator; FBG: fiber Bragg grating; PC: polarization controller; DCF: dispersion compensation fiber; SMF: single mode fiber; OSA: optical spectrum analyzer; ESA: electrical spectrum analyzer

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Fig. 4
figure 4

Optical transmission and reflection spectrum of the FBG-FP filter obtained by OSA

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As depicted in Fig. 4, the transmission window of the FBG-FP locates at 1552.256 nm. Due to the low resolution of the OSA (0.02 nm), the detail feature of the transmission peak cannot be observed clearly. However, the 3 dB bandwidth of the passband of the FBG-FP is measured to be 77 MHz using a microwave modulation method (Li et al. 2012), indicating a high Q-factor of 2.51 × 106.

To investigate the frequency response of the MPF in the OEO, we measure the open loop response between PM and PA using a Vector Network Analyzer (VNA, Agilent N5244A). For comparison, the frequency response with and without inserting the DCF are both tested. Figure 5a–c shows the superposed frequency response of the MPF before and after the DCF is used when the passband frequency is located at 21.1, 30.7 and 40.5 GHz, respectively. As depicted in Fig. 5, when no DCF is used, the signal to noise ratio of the passband drops dramatically at high frequencies due to the strong PM–IM conversion caused by SMF dispersion, which agrees well with the theoretical analysis above. Then two DCFs are used followed by the SMF and the result is much improved. Although the amplitude of the response peak drops as well, the PM–IM conversion induced by SMF is much suppressed. Figure 5d depicts the superposed frequency response when the passband frequencies are 10.4, 21.1, 30.7 and 40.5 GHz after DCF is utilized. Since the measurement is implemented between the phase modulator and the power amplifier, the frequency response is superposition of the dual-loop structure response. Hence, the frequency response is a little bit modulated.

Fig. 5
figure 5

Frequency response before and after the DCF is utilized when the passband frequency is tuned at a 21.1 GHz, b 30.7 GHz and c 40.5 GHz. d Frequency response of the MPF after DCF is utilized

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Then the loop is closed and the OEO performance is measured. Figure 6 shows the electrical spectrum of the OEO under two different frequency spans of 100 kHz and 1 MHz when the oscillation frequency is about 10.74 GHz. The 3 and 20 dB bandwidth of the generated signal are 1.12 and 2.63 kHz, respectively. In Fig. 6b, although there several low-level side modes, the side mode suppression ratio (SMSR) is almost 70 dB and no mode hopping is observed. The first obvious side mode occurs nearly 330 kHz offset the oscillation frequency, which is caused by the short loop of the OEO.

Fig. 6
figure 6

Electrical spectrum of the oscillation signal at about 10.74 GHz. a Electrical spectrum of the signal at 100 kHz Span and resolution bandwidth (RBW) of 1 kHz. b Electrical spectrum of the signal at 1 MHz Span and RBW of 1 kHz

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Then the tunability of the OEO system is investigated. The TLS power is set to be 16 dBm and the wavelength is tuned at 1552.23 nm at the beginning. By adjusting the TLS wavelength, the oscillation frequency tunability of the OEO is measured. Similarly, the oscillation results of the OEO before and after using the DCF are both measured. When no DCF is used in the OEO loop, a highest tuning frequency of 27 GHz is obtained, which is attributed to the SMF dispersion analyzed above. However, a tunable signal from 2 to 44 GHz can be generated after DCF is inserted, as shown in Fig. 7a. The power decrease at high frequencies is resulted from the uneven frequency response of the electrical devices in the system, for example the PM and PA. The harmonics may be primarily caused by the low saturation power of the RF amplifiers. The result demonstrates that by employing the DCF in the OEO loop to cancel the dispersion induced PM–IM conversion, higher frequency operation could be obtained. Theoretically, the oscillation frequency can reach much higher since the reflection bandwidth of the FBG-FP filter is wide enough. However, due to the limitation of the device bandwidth used in the experiment, the highest frequency observed is only 44.30 GHz, which would be improved by utilizing the devices with much broader bandwidth. Figure 7b shows the measured − 3 dB bandwidth of the generated signal during the tuning process. The result demonstrates that the bandwidth keeps almost stable under different oscillation frequencies.

Fig. 7
figure 7

a Superposed electrical spectrum of the generated tunable oscillation signal ranging from 2 to 44 GHz; b 3 dB bandwidth change of the generated signal during the tuning process

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To evaluate the SSB phase noise of the proposed OEO, the output oscillation signal is measured. Firstly, the SSB phase noise is investigated under different oscillation frequencies. Figure 8a shows the measured SSB phase noise of the oscillation frequency of 9.61, 19.21, 30.50 and 44.30 GHz. The SSB phase noise remains to less than – 110 dBc/Hz at an offset of 10 kHz for all the oscillation frequencies above, which are − 117.78, − 119.84, − 115.83, − 113.92 dBc/Hz, respectively. By recording the SSB phase noise of different oscillation frequencies at the offset of 10 kHz, the relationship of between SSB phase noise and the oscillation frequencies could be obtained, as depicted in Fig. 9b. The results demonstrated that the SSB phase noise is almost independent of the oscillation frequency. A little phase noise decrease at high oscillation frequency may be caused by the reduced gain, which could be overcome by using a TLS with higher output power or a PA with higher gain (Yao and Maleki 1996a, b).

Fig. 8
figure 8

Measured SSB phase noise results. a SSB phase noise at the four different oscillation frequencies; b SSB phase noise at an offset of 10 kHz under different oscillation frequencies

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Fig. 9
figure 9

Measured SSB phase noise for the single-loop and dual-loop configuration at the oscillation frequency of 10 GHz

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To prevent the mode hopping and suppress the undesired side modes of the oscillation signal, dual-loop configuration is applied in our system. Figure 9 shows the SSB phase noise for the single-loop and dual-loop configuration at the oscillation frequency of 10 GHz.

The measurement of single-loop in Fig. 9 is configured with the respective disconnection of the PD1 and PD2 depicted in Fig. 3. As demonstrated in Fig. 9, the SSB phase noise for the dual-loop is much lower than the short single-loop. What’s more, comparing with phase noise of the long single-loop, the side modes are well suppressed. Finally, the frequency stability is evaluated. During the measurement, a maximum frequency drift of less than 100 kHz can be observed and no mode hopping is found within half an hour when the oscillating signal is around 10 GHz. Since the OEO is operated at a laboratory environment without any mechanical, thermal and acoustic isolation, the use of a wavelength-stabilized laser source and a well-packaged and temperature-controlled FBG-FP would be necessary to increase the system long-term stability for practical applications.

4 Conclusion

This paper demonstrates a wideband tunable dual-loop OEO based on a phase modulated MPF system, which is implemented using a TLS, a phase modulator, a FBG-FP filter and a PD. The oscillation frequency of the OEO is equal to the frequency between TLS and the notch frequency of the FBG-FP filter. The oscillation frequency can be simply changed by the adjusting the TLS wavelength. By utilizing a section of DCF followed by the SMF to compensate the long SMF dispersion, the highest tuning frequency can be improved from 28 to 44 GHz, which could be further improved by employing devices with larger bandwidth. Meanwhile, to suppress the mode hopping and the side modes of the oscillation signal, dual-loop configuration is adopted. The SSB phase noise is measured to be less than – 110 dBc/Hz at an offset of 10 kHz within the whole frequency range.