1 Introduction

During the past two decades, microwave photonic filters have drawn lots of research attention for their unique advantages such as large bandwidth, good tunability and reconfiguration, the immunity to electromagnetic interference, and the compatibility with the fiber wireless communication system [1–3]. Normally, the frequency responses of the finite impulse response (FIR) MPFs have an inherent periodic feature due to their discrete sampling [4–6]. Single-passband MPF overcoming the periodic feature has also been proposed, which is based on an FMZI sliced broadband optical source (BOS) and a dispersive medium [7]. Other approaches to realizing single-passband MPF have also been presented, such as non-sliced BOS and fiber dispersive medium [8–10], stimulated Brillouin scattering-based RF filtering [11–13], and fiber Bragg grating (FBG)-based single-passband MPF assisted with phase modulator [14, 15]. On the other hand, microwave filters with freely tunable multi-passband are more favorable for practical applications. A selective multi-passband MPF based on a sliced BOS was proposed, in which the number of the passbands can be tuned by adjusting the polarization state via the polarization controller (PC) [16]. MPF with two independent passbands has also been proposed, which is based on phase modulator and an equivalent phase-shifted FBG, and the tunability is realized by adjusting the wavelength of the optical sources employed in the MPF [17]. In this paper, we propose and experimentally demonstrate a dual-passband MPF with two independently tunable passbands based on the sliced BOS and a dispersive medium. Two paralleled FMZIs are taken as the optical spectrum slicer, and in the experiment by tuning the VODL in each sub-FMZI, the central frequencies of two passbands can be tuned freely, and the experimental results show good agreement with the theoretical analysis. The proposed dual-passband MPF shows good tenability and tuning linearity, simple configuration, and the ease of implementation, which has good application potential in the fiber wireless communication and sensing systems.

2 Operation principle and experimental setup

One of the key components in our proposal is the optical spectrum slicer, whose structure is shown in Fig. 1 [18]. The optical spectrum slicer is composed of two paralleled FMZIs as the sub-FMZI in two arms of the main FMZI, and each sub-FMZI consists of two 50:50 optical couplers (OCs) and a PC in one arm of the FMZI in order to achieve the best extinction ratio, and a VODL (VODL1: general photonics, 0–68 mm; VODL2: general photonics, 0–168 mm) in the other arm of the sub-FMZIs, respectively. Supposing the optical path difference (OPD) of one of the sub-FMZIs is ΔL, which is shorter than the coherence length of the optical source, and then, the transmittance of the FMZI can be expressed as:

$$T = \frac{1}{2}\left[ {1 + V{ \cos }\left( {2\pi \frac{\omega }{{\Delta \omega }}} \right)} \right]$$
(1)

where ω is the angular frequency of the light and Δω is determined by the OPD as Δω = (2πc/nΔL), in which c and n are the velocity of the light in vacuum and reflective index of the fiber, respectively. V is the visibility of the sub-FMZI, which is determined by the polarization states of the sub-FMZI. In our experiment, the OPD of the main FMZI is set to be long enough, so that the interference between two sub-FMZIs can be neglected and the incoherent summation of the transmission of two sub-FMZIs would be taken as the output transmission of the optical spectrum slicer.

Fig. 1
figure 1

Schematic diagram of the optical spectrum slicer in the proposed dual-passband MPF

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The BOS in our experimental has a quasi-Gauss distribution S(ω), and the output after the spectrum slicer can be expressed as Eq. (2), where T 1 and T 2 stand for the transmittance of FMZI1 and FMZI2, respectively.

$$S_{\text{out}} \left( \omega \right) = S\left( \omega \right) \times \left[ {T_{1} \left( \omega \right) + T_{2} \left( \omega \right)} \right]$$
(2)

The schematic diagram of our proposed dual-passband MPF is shown in Fig. 2. The light from a BOS (QPHOTONICS QSDM-1550-15) is connected to an optical isolator (ISO) and then launched into the spectrum slicer after which continues optical taps can be obtained. Then, the sliced light is amplified by an erbium-doped fiber amplifier (EDFA, Amonics AEDFA-PA-30) and sent into a PC to align the polarization state with the following Mach–Zehnder modulator (MZM, JDSU 10 GHz). The microwave signal to be processed from the port 1 of the vector network analyzer (VNA, TranscomT5230A) is modulated onto the sliced light via the MZM. Then, the modulated light goes through a coin of standard single-mode fiber (SMF) with the length of 50 km, which works as the dispersive medium in our experiment, and is recovered by the photodiode (PD, OptiLab PD-30). The recovered microwave signal is sent to port 2 of the VNA for measurement.

Fig. 2
figure 2

Schematic diagram of the proposed dual-passband MPF

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The frequency response of the proposed MPF can be expressed as [5],

$$H_{\text{RF}} \left(\Omega \right) \propto \int {S_{\text{out}} \left( \omega \right)} \times \left[ {H^{ * } \left( \omega \right) \times H\left( {\omega +\Omega } \right) + H\left( \omega \right) \times H^{*} \left( {\omega -\Omega } \right)} \right]{\text{d}}\omega$$
(3)

in which S out(ω) is the distribution of the sliced optical source and \(H\left( \omega \right) = \left| {H\left( \omega \right)} \right| \times {\text{e}}^{ - j\phi \left( \omega \right)}\) is the transfer function of the dispersive medium. The phase part of the transfer function can be expressed as the polynomial in Eq. (4).

$$\phi \left( \omega \right) = \phi \left( {\omega_{0} } \right) + \tau \left( {\omega_{0} } \right) \times \left( {\omega - \omega_{0} } \right){\kern 1pt} + \frac{1}{2}\beta \times L\left( {\omega - \omega_{0} } \right){\kern 1pt}^{2} + \frac{1}{3}\chi \times L\left( {\omega - \omega_{0} } \right){\kern 1pt}^{3}$$
(4)

In Eq. (4), ω 0 is the central frequency of the optical source, τ(ω 0) is the group delay time at frequency ω 0, β is the dispersion, χ is the dispersion slope of the fiber link, and L is the length of the fiber. So by substituting Eq. (2) into Eq. (3), we can obtain the frequency response of the proposed MPF as,

$$H_{\text{RF}} \left(\Omega \right) \propto \int {S\left( \omega \right) \times \left[ {T_{1} \left( \omega \right) + T_{2} \left( \omega \right)} \right] \times \left[ {H^{*} \left( \omega \right) \times H\left( {\omega +\Omega } \right) + H\left( \omega \right) \times H^{*} \left( {\omega -\Omega } \right)} \right]{\text{d}}\omega }$$
(5)

3 Experimental results

In our experiment, the optical spectra of the BOS, and the EDFA amplified sliced spectrum from the paralleled FMZIs as well as the two individual FMZIs have been measured, and the results are shown in Fig. 3. The central wavelength of the BOS is about 1550 nm, and the 3-dB bandwidth is about 30 nm. From the optical spectra, one can see that the optical combs in Fig. 3c, d contain only one period, respectively, and the sliced spectrum in Fig. 3b can be taken as the superimposition of the optical combs with different periods in Fig. 3c, d.

Fig. 3
figure 3

Spectra of the BOS (a), sliced BOS with paralleled FMZIs (b), and two individual FMZIs (c) and (d)

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The measured frequency responses with individual FMZIs are shown in Fig. 4a, in which the blue line shows the frequency response when the path of FMZI2 is disconnected and the length of VODL1 is set to be 7.65 mm, while the red line shows the frequency response when the path of FMZI1 is disconnected and the length of VODL2 is set to be 125.25 mm. The measured frequency response of the proposed MPF with the paralleled FMZIs is shown in Fig. 4b, and the lengths of the VODL1 and VODL2 are the same as that in Fig. 4a. Figure 4c, d shows the corresponding calculated frequency responses of the MPF. One can see from the experimental results that the central frequency and the shape of the passbands of the dual-passband MPF are identical to that of the MPF with individual FMZIs, respectively. And the theoretical calculation agrees well with the experimental results. The passbands of the proposed dual-passband MPF can also be selectable by inserting optical switches in the optical spectrum slicer.

Fig. 4
figure 4

Measured frequency response of the MPF with separated FMZIs (a) and paralleled FMZIs (b) and the corresponding calculated frequency response (c) and (d)

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The central frequencies of the proposed dual-passband MPF can be tunable by changing the OPD of the sub-FMZIs. In our experiment, the VODLs in each sub-FMZI are tuned to changing the central frequencies of the corresponding passbands, and the experimental result is shown in Fig. 5. In Fig. 5a, the length of VODL2 is fixed at 124.00 mm and the central frequency of the corresponding passband is about 2.43 GHz. By adjusting the length VODL1, the central frequency of the first passband is shifted from 0.552 to 1.752 GHz, while the central frequency of the second passband is fixed at 2.43 GHz without shifting. In the experiment, we also keep the length of the VODL1 at 6 mm, and by adjusting the length of the VODL2, the central frequency of the second passband shifts from 0.479 to 1.933 GHz, while the central frequency of the first passband is fixed at 2.468 GHz without changing. The central frequencies of the passbands can be tuned to higher frequency; however, our measured experiment results are limited to the measurement range of the VNA, and by using VNA with broader bandwidth, passbands with higher frequencies can be measured.

Fig. 5
figure 5

Free tunability of each passband; the length of VODL2 is fixed and VODL1 changes (a) and the length of VODL1 is fixed and VODL2 changes (b)

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Figure 6 shows the measured relationship of the central frequencies and 3-dB bandwidth of the passbands versus the length of corresponding VODL, from which one can see that the proposed dual-passband MPF exhibits a good tuning linearity, and both passbands show an increasing 3-dB bandwidth for higher central frequencies.

Fig. 6
figure 6

Relationships between central frequencies and the 3-dB bandwidth of the corresponding passbands and the length of VODL

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These two passbands of the proposed MPF can also be tuned simultaneously by adjusting both the VODL1 and VODL2 in the sub-FMZIs. Figure 7 shows the measured frequency response of the simultaneously tunable dual-passband MPF, in which the central frequencies of the two passbands of the MPF can be tuned simultaneously and freely without affecting each other, which is very desirable for practical applications compared to traditional multi-passband MPFs with periodic characteristics.

Fig. 7
figure 7

Simultaneously tunability of the proposed dual-passband MPF

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4 Conclusions

In this paper, we have proposed and demonstrated a freely tunable dual-passband MPF with the paralleled FMZIs as the optical spectrum slicer and a dispersive medium. Both theoretical studies and experimental verifications have been carried out. Thanks to the dual-period characteristics of the transmission of the spectrum slicer, the proposed MPF shows a dual-passband frequency response which corresponds to the periods contained in the optical sliced spectrum. The central frequencies of the proposed dual-passband MPF can be tuned freewill by changing the length of the VODLs in each sub-FMZI. Based on this principle, multi-passband MPFs with more passbands can be realized by employing more paralleled FMZIs in the sub-branches of the optical spectrum slicer and designing the OPD between each branch. The proposed MPF enjoys flexible tunability, good tuning linearity, simple configuration and the ease of implementation, which shows a good application potential in fiber wireless communication and sensing systems.