1. Introduction

Microwave Photonics is an area under intense research due to the various advantages of processing RF signals in the optical domain instead of using their electric counterparts. Optical fibers show low loss, high bandwidth, immunity to electromagnetic interference, tunability and reconfigurability [1–5]. For the last few years, different approaches have been proposed to implement high performance microwave photonic filters. Nevertheless, most of these filters still suffer from several limitations as pointed out in [1–2]. Carrier suppression effect (CSE) or Dispersion Fading is one example of the limitations shown by these filters reducing its operating frequency range due to the delay line dispersion. CSE can be overcome by using single sideband modulation but then more complex and costly modulation circuitry is needed. Other important issues not easy to achieve with incoherent Microwave Photonics structures are proper base-band rejection and easy tuning techniques for the RF bands filtered.

In this paper, we propose a novel filter structure. The tunable microwave photonic filter exhibits positive and negative coefficients based on the combination of an active mode-locked fiber laser that acts the optical multiwavelength source, a fiber Mach Zehnder (MZ) interferometer cascaded to a 2×1 integrated MZ electro optic modulator (EOM) and a dispersive delay line. This configuration shows some unique features as compared to other structures reported previously. Namely it is free from CSE without requiring single sideband modulation and can provide truly bandpass operation by suppressing the baseband response. In addition, it provides other advantages arising from using the active mode-locked fiber laser as anticipated in [6]: All source modes at the output of the laser have equal polarization and thus the alignment with the EOM is easier and, the output spectrum from the source is itself Gaussian apodized and therefore sidelobe suppression in the filter response is guaranteed.

2. Filter description

The topology of the filter is shown in Fig. 1. An unbalanced MZ structure is achieved by using a 2×2 coupler with a coupling factor c which is connected to a 2×1 electro-optic modulator. The optical path length mismatch for the MZ structure is Δ1 or Δτ = Δ1/v_g as it will be used later. The input coupling constant of the EOM device is given by the factor a² and the output the Y junction is characterised by a coupling constant b ².

 

Fig. 1. Scheme of the RF photonic filter.

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The optical samples are generated by an actively mode-locked fiber laser which has a fixed wavelength separation between adjacent optical taps given by Δλ (or Δω) as shown in (1).

where ω_o is the central optical frequency of the mode-locked fiber laser and E_n is the electrical field amplitude of each laser mode centred in the optical frequency ω_o+ nΔω. The multi-wavelength signal is then launched into the upper arm of the first MZ structure and it is amplitude modulated by the 2×1 MZ modulator. The radiofrequency signal used to modulate the optical signal is generated by a lightwave component analyzer (LCA). A fiber link of length L_F is used as the dispersive element for the transversal filter to introduce a different time delay for each optical sample. If we particularise the analysis for Push-Pull driving of the modulator and we consider the case where the 3 dB input 2×2 coupler and the 3dB Y Branch are ideal, i.e., a²=b²=1/2, it can be demonstrated [7] that the transfer function of the RF filter measured by the LCA is given by:

where

is the transfer function of the original filter and the terms H₁(Ω) and H₂(Ω,ω),

depend on the EOM biasing voltage Vbias through the parameter Δα = π(V_bias/V_π) and the optical differential phase ΔΦ between the arms in the first ΔΦ, ωΔτ+θ_o, where θ_o takes into account the drift of the MZ structure.

It is clearly seen in Eq. (2) how the system shows different behaviour depending on the biasing voltage and the coupling factor c. First, we will consider the case when c = 0 (or c = 1), i.e., the input optical signal E(t) is launched either into the upper or the lower arm of the 2×1 EOM. In this case, there is a null contribution of the term H₂(Ω,ω) and we obtain a typical transfer function when using a the 2×1 EOM [7]:

It is worth noting that a biasing voltage V_bias = 0 is required for operating into the quadrature point for the 2×1 EOM (Δα =0), providing the maximum amplitude response [7]. It is also shown how the CSE effect is taken into account in the second term and thus not avoided in this conventional configuration.

Secondly, we will consider the case of V_bias =V_π /2. In that case the term H₁(Ω) is null for any value of c and the transfer function of the filter becomes

From Eq. (7) it can be clearly seen how the CSE term appears together with the differential phase ΔΦ_n (ΔΦ_n = nΔωΔτ+θ₀) of the MZ in the new filter topology. Then, two important effects can be withdrawn: Firstly, the cosine term is clearly a tap function weighted by the |E_n| terms and featuring sign polarity for the N wavelengths n = [1⋯N] given by the differential phase term ΔΦ_n. Hence, positive and negative optical samples are achieved along the cosine depending on the optical difference path Δl (Δτ) and the separation Δω between adjacent wavelengths. Then, the tunability of the RF filter is not only controlled through Δl, but also with the amount of dispersion β₂L_F. Secondly, the optical differential phase in the MZ has translated into the RF domain as a RF frequency displacement of the standard CSE. This can be seen rewriting Eq. (7) as

We can see how the transfer function shows two terms. Both terms are identical to the initial RF filter H_o(Φ) but shifted to frequencies ± Φ_o, which is given by

where the Free Spectral Range of the original filter is defined as FSR_o =1/(β₂L_F·Δω). In the present configuration, tuning is achieved by changing the optical path difference (Δτ) and the two lobes shift symmetrically from the original filter bands. Then, the tuning range of the RF filter covers a frequency bandwidth up to FSR_o for the case when Δτ is a integer multiple of the laser repetition rate (2π/Δω), crossing along the case of half repetition rate where the tuning is FSR_o/2 It is also clear that the RF phases of both bands, consisting on the drift θ_o and the CSE term (1/2β₂L_FΦ²), only appear in the amplitude response of the filter (|H_RF(Φ)|²) where there is overlapping i.e. (FSR_o and FSR_o/2),Hence, this configuration is free from CSE within its useful tuning range. Similarly, although our configuration is unstable in terms of the optical phase as any other containing a MZ structure, we have experimentally observed that there is no need for thermal stabilization as a change in the optical phase does not affect the amplitude response of the filter.

The third case we would like to point out is the case when an arbitrary value of the EOM biasing voltage and the coupling factor c of the MZ structure is used. In this case the transfer function of the RF filter has a contribution that is identical to the initial RF filter H_o(Φ) which is related to the term H₁(Φ). In addition, it shows another contribution which is not more than a version of the original RF filter shifted a certain frequency Φ_o through the term H₂(Φ,ω). Controlling the parameter Δα and c, we obtain the conventional response of the RF photonic filter or the novel response.

3. Experimental Analysis

The transversal filter was implemented using an actively mode-locked fiber laser driven by an external 10 GHz RF signal. The mode-locked fiber laser provides a multiwavelength signal that is used to obtain around 40 different carriers. Inset of Fig. 1 shows the optical signal launched into the MZ structure which correspond to a distribution of discrete optical taps with an optical frequency separation equal to the repetition rate of the laser (~ 0.08 nm for this case). The central wavelength of the multiwavelength is λ _o = 1550 nm. This multi-tap source is fed to a 50/50 coupler where each one of its output arms is connected to one of the inputs of the 2×1 EOM where the optical carriers are amplitude modulated by a RF signal of frequency Φ=2πf which is generated with the LCA. The 2·1 EOM (V_π= 14 V) was driven in Push-Pull configuration. Finally, a SMF-28 fiber of length L_F = 50 km was used as the dispersive element in the filter, (15.8 ps/km nm). Figure 2 shows the experimental results of the transfer function of the filter for different configurations. Figure 2(a) shows the transfer function when c = 1, i.e., when the multi-wavelength source is launched just into one of the arms of the 2x1 EOM. The 2×1 EOM acts as a conventional modulator and the filter shows a FSR_o = 15.78 GHz [2]. Figure 2(b) shows the case for an EOM biasing voltage of 7 V. As shown in Eq. (8), the RF filter shows no baseband component and splits the original pass-band lobe at FSR₀ into two side lobes when there is an optical path difference in the MZ structure. Figure 2(b) depicts the case when the optical path difference Δ1 corresponds to a delay time of 22.6 ps. For higher delays, the two lobes, H_o(Φ-Φ_o) and H_o(Φ+Φ_o), approach each other until they superimpose (measured for a delay of 50 ps). Then, when Δτ > 50 ps, the lobes cross each other up to reach the baseband and FSR_o positions (as Fig. 2(a)), for a time delay of 100ps. This result is in agreement with the 10GHz repetition rate of the mode-locked laser.

 

Fig. 2. Transfer function of (a) the original filter and (b) for a delay time in the MZ of 22.6 ps.

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Figure 3(a) illustrates the tunability of the filter and shows the shifted frequency f_o of the side lobes as a function of the time delay Δτ between the arms of the MZ structure. The filled circles correspond to the measured FSR of the filter and the solid line is the theoretical prediction, showing a useful tuning range of FSR₀/2. The experimental slope (0.16 GHz/ps) is in good agreement with the theoretical prediction. In order to show the performance of the RF filter, Fig. 3(b) corresponds to the 1dB, 3dB and 15 dB bandwidths of the RF filters versus the time delay Δτ. We can observe that the shape of the RF filter remains invariant when the time delay is changed when tuning the filter. In order to complete the experimental characterization, we measured the amplitude of the base-band and the pass-band of the filter as a function of the EOM biasing voltage. According to our previous theoretical model, the base-band is related to the term H₁(Φ) and the RF pass-band is related to the term H₂(Φ). Figure 4(a) shows the amplitude of the base-band and the pass-band corresponding to the MZ time delay shown in Fig. 2(b) as a function of the EOM biasing voltage. It is clear the good agreement between the theoretical prediction (line) and the experiment (points). In particular, we can see how V_bias =V_π /2 yields to eliminate the base-band and maximize the amplitude of the pass-band.

Finally, Fig. 4(b) shows the experimental CSE (dashed line) measured for the fiber link that we used in the experimental set-up and the amplitude of the different RF pass-bands values which have been implemented. As predicted earlier, when the MZ structure is disable, the CSE appears in the transfer function of the RF filter. However, the amplitude of the RF filter remains constant when the novel configuration is used, as shown in the inset, which shows the different RF filters around the first notch of the CSE which is located at 8.9 GHz.

 

Fig. 3. Frequency f_o and bandwidths Δf of RF filters versus the optical delay time Δτ. Theoretical calculation (solid line) and experimental results (filled squares).

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Fig. 4. Amplitude Response of (a) the base band and the RF band-pass for f_o = 4.25 GHz versus the EOM biasing voltage and (b) of the RF bands for different values of f_o (circles) and conventional CSE (dashed line). Inset: Detail of the transfer function of the RF filters around the first notch of CSE.

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4. Conclusions

We have presented a full theoretical and experimental analysis of a novel all-optical microwave photonic filter that combines a mode-locked fiber laser, which acts as a multi-tap wavelength source and a MZ structure in cascade to a 2×1 EOM. We have theoretically presented and experimentally demonstrated several interesting properties of this novel configuration: the filter is free from the carrier suppression effect and thus it does not require single sideband modulation. It also shows positive and negative coefficients due to its own MZ structure and the tunability can be achieved by controlling the optical path difference. Other MZ configurations are currently under investigation. The present configuration can be changed by introducing different optical filters such as fiber Bragg gratings to modify the phase relationship in the MZ cavity to configure more specific responses for the positive and negative taps.