Abstract: We propose a novel structure of complex-tap microwave photonic filter (MPF) employing an incoherent broadband optical source (BOS) and a programmable optical spectrum processor. By tailoring the optical spectral amplitude and phase, arbitrary complex continuous-time impulse responses of the MPF can be constructed. Frequency responses with a single flat-top, highly chirped, or arbitrary-shape passband are demonstrated, respectively. The passband center can also be tuned in a wide range only limited by the opto-electrical devices. To the best of our knowledge, it is the first demonstration of an incoherent-BOS-based MPF which is single-bandpass, widely tunable, and highly reconfigurable with complex taps.
© 2012 OSA
Microwave photonic filters (MPFs) which process high-frequency microwave signals in the optical domain have aroused people’s great interest in the past decades . The potential applications of MPFs include ultra-wideband radar, radio astronomy, high-speed microwave communications, etc. One important advantage of MPFs over their electrical counterparts is high reconfigurability. By tailoring the tap weights (or “coefficients”), flexible finite-impulse-response (FIR) MPFs can be implemented. For an ideal FIR MPF with full reconfigurability, each coefficient should be complex and can be adjusted arbitrarily. The direct way to implement complex-tap MPFs is to manipulate the microwave phase photonically in each tap. Various structures have been proposed in this scope based on the heterodyne method [2–6]. Single-sideband modulation (SSB) is employed, and the phase of the optical carrier is then adjusted. The optical phase change is translated to the microwave domain through heterodyning of the carrier with the sideband at the photodetector. Ideal complex taps can be generated, but the system complexity is high because wideband microwave 90° hybrid coupler or high-resolution optical spectrum processing is needed to implement SSB and optical carrier phase tuning. Another approximate method is using non-uniformly spaced optical carrier wavelengths . By tuning the wavelength of each tap from the uniform position, an extra time delay is introduced to the microwave signal resulting in an equivalent phase shift. However, since the phase shift depends linearly on the microwave frequency, the complex tap is narrow-band. The function of the MPF is still limited.
In this paper, we propose a novel complex-tap MPF employing an incoherent broadband optical source (BOS) and a programmable optical spectrum processor. Equivalent “electrical slicing” of the BOS is employed , and complex coefficients are generated by tuning the localized slicing phase. It is worth noting that our structure looks similar to that in Refs [5, 6]. which uses coherent frequency combs. In comparison, our method has a reduced complexity since it only needs double-sideband suppressed-carrier (DSB-SC) modulation other than SSB. Furthermore, by taking advantage of low cost and spectral continuity of the BOS, arbitrary complex continuous-time impulse responses can be implemented, giving rise to a highly reconfigurable single passband in the frequency domain. The passband center can also be widely tuned by changing the slicing period. Differential detection is further employed to significantly reduce the optical intensity noise. To our knowledge, it is the first demonstration of a single-bandpass complex-tap MPF with high reconfigurability and wide tunability.
2. Experimental setup and theoretical description
Our experimental setup is shown in Fig. 1 . The incoherent light from a BOS (e.g. Erbium-doped fiber amplifier (EDFA) or light-emitting diode (LED)) is polarized and split into two branches via a 1 × 2 coupler (C1). One branch is modulated by the microwave input via a single-drive Mach-Zehnder modulator (MZM) biased at the minimum transport point. The other branch is spectrum tailored via a WaveShaper which is a commercial programmable optical processor , and time delayed via a variable optical delay line (VDL). The two branches are then combined again in the same polarization via a 2 × 2 coupler (C2). The two outputs of C2 go through a dispersive element which is a length of dispersion-compensating fiber (DCF) in opposite directions via two circulators and differentially detected.
Under small-signal modulation, two sidebands are generated for each frequency component of the BOS in the MZM branch. When the sidebands are combined with the tailored carriers from the WaveShaper branch via C2, a 180°-shift is introduced in the sideband-carrier differential phase between the two outputs of C2. At the balanced photodetector (BPD), microwave signal currents are generated through beating of the sidebands with the corresponding carriers, and noise currents are generated mainly through beating of the carriers with each other. Thus the signals at the two inputs of the BPD are counter-phase while the noises are in-phase. The output of the BPD is given by subtraction of the two inputs. The total signal amplitude is then doubled while the noises are eliminated.
The WaveShaper is base on Liquid Crystal on Silicon (LCoS) technique, and acts as a programmable optical filter with arbitrary amplitude and phase responses . The transfer function of the WaveShaper is denoted as . The microwave signal current at the output of the BPD is then 8], is used here instead of in case of confusion), the central frequency of the BOS. and represent the amplitude transmission factors from the input of C1 to the input of the BPD through the MZM branch and through the WaveShaper branch, respectively. The MPF’s transfer function is given by where is the load resistant of the BPD. We can consider only the half part of on the positive axis because . Suppose that and the PSD of the BOS is constant with , the MPF’s transfer function is then expressed as
It is worth noting that is continuous in time which means the MPF is a continuous-tap FIR filter, can then be deliberately designed to be single-bandpass. The spectral continuity of BOS has long been exploited to implement single-bandpass MPFs [10–12], and the concept of “continuous-time impulse response” was first proposed in Ref . Nevertheless, the physical principle of complex tap generation in our scheme can be explained from the view of a discrete-tap MPF. As shown in Fig. 2 , the broadband optical spectrum is divided into many small sections. Each section corresponds to one tap, and acts as a photonic microwave phase shifter . The RF output amplitude of each phase shifter can be adjusted by changing the optical amplitude while the phase adjusted by changing the localized slicing phase. By programming the WaveShaper, fully reconfigurable complex taps are generated.
3. Experimental results and discussions
In experiments, we used a flat-gain EDFA as the BOS. The available spectral width was about 4 THz. The commercial WaveShaper had a spectral resolution of about 10 GHz. The total dispersion of the DCF was . The time resolution and aperture of are calculated to be 107 ps and 43.0 ns respectively. According to the Fourier transform theory, the reconfigurable spectral resolution and window width of the RF transfer function are given by and which are 23.3 MHz and 9.31 GHz respectively. To demonstrate the flexible reconfigurability, the MPF’s passband was configured to be flat-top, chirped, or even with arbitrary shape, while the passband center was tuned to 6 GHz.
3.1. Flat-top MPF
For the flat-top MPF, the baseband time-domain impulse response is given byFig. 3(a) –3(c) and 3(d)–3(f), respectively. In Fig. 3(c) and 3(f), both measured and calculated results of are shown, and they agree with each other quite well.
3.2. Chirped MPF
Chirped microwave filters are widely used in the pulse-compression technique. The baseband time-domain impulse response of the chirped MPF is given byFig. 4(a) – 4(c) and 4(d) –4 (f), respectively. The optical and the electrical time delays follow the relationship where is the 3-dB bandwidth of in rad/s. For specified and , higher can be achieved by increasing the optical dispersion .
3.3. Arbitrary-shape MPF
To implement the arbitrary-shape MPF, was digitally calculated from the desired using inverse fast Fourier transform. For demonstration, was designed to be an asymmetric trapezoid which is given byFig. 5(a) - 5(c), respectively. Good agreements are obtained again between the measured and calculated results of in Fig. 5(c).
3.4. Tunability and noise reduction
The tunable amplitude responses of the flat-top MPF with are shown in Fig. 6 . The time delay of the VDL needed for a RF bandpass center of is given by . Since the dispersion in this paper is twice that used in Ref , the required time delay range of the VDL for the same RF tuning range is doubled. Limited by the VDL we had at hand, only a range of is shown here. However, by using an appropriate VDL, the RF bandpass center can be tuned in a wide range only limited by the opto-electrical devices.
We then investigated the noise-reduction performance of the balanced detection scheme. For simplicity, was programmed to be a rectangle with a bandwidth of 0.6 THz, thus was a sinc function. The passband center was tuned to 10 GHz. The responsivity of the BPD was 0.7 A/W, and the optical power at each input was . The RF input signal was a single tone of 10 GHz. The intensity modulation index is calculated from the measured sideband-to-carrier ratio (SCR) according to , by replacing the BOS with a single-wavelength laser. It has been investigated that the modulation-induced noise increment forms a basic limit to the performance of balanced detection . The RF output spectra with balanced detection or with only one single input of the BPD are shown in Fig. 7(a) and 7(b). An obvious increment of the noise ground level with increasing can be observed when balanced detection is employed. Detailed plots of the signal and noise power versus are shown in Fig. 7(c). When , the noise reduction is limited by the unbalance of the two optical paths denoted in Fig. 1 by doted arrows. This unbalance in our experiments is mainly attributed to the polarization dependent loss and dispersion. In this region, an improvement of the signal-to-noise ratio (SNR) of roughly 14 dB can be achieved. When , the noise power increases with . The noise reduction is 5 dB when corresponding to a root-mean-square value of 0.3. The result agrees with the theoretical prediction in Ref . quite well. It is noteworthy that a SNR increment of 11 dB is still achieved at this point because the RF signal power is 6 dB higher with balanced detection than that with one single input.
In conclusion, we have proposed a novel complex-tap MPF employing a low-cost incoherent BOS and a commercial optical spectrum processor. The MPF’s transfer function was single-bandpass, widely tunable, and highly reconfigurable. Frequency responses with a flat-top, highly chirped, or arbitrary-shape passband were demonstrated, respectively.
This work is supported by the 973 Project under grant Nos. 2012CB315603/04, China Postdoctoral Science Foundation under grant No. 2012M520275, and National Nature Science Foundation of China (NSFC) under grant Nos. 60736003, 61025004, and 61032005.
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