Highly reconfigurable microwave photonic single-bandpass filter with complex continuous-time impulse responses

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 Optical Society of America OCIS codes: (060.5625) Radio frequency photonics; (070.2615) Frequency filtering. References and links 1. J. Capmany, B. Ortega, and D. Pastor, “A tutorial on microwave photonic filters,” J. Lightwave Technol. 24(1), 201–229 (2006). 2. A. Loayssa, J. Capmany, M. Sagues, and J. Mora, “Demonstration of incoherent microwave photonic filters with all-optical complex coefficients,” IEEE Photon. Technol. Lett. 18(16), 1744–1746 (2006). 3. M. Sagues, R. García Olcina, A. Loayssa, S. Sales, and J. Capmany, “Multi-tap complex-coefficient incoherent microwave photonic filters based on optical single-sideband modulation and narrow band optical filtering,” Opt. Express 16(1), 295–303 (2008). 4. X. Yi, T. X. H. Huang, and R. A. Minasian, “Tunable and reconfigurable photonic signal processor with programmable all-optical complex coefficients,” IEEE Trans. Microw. Theory Tech. 58(11), 3088–3093 (2010). 5. E. Hamidi, D. E. Leaird, and A. M. Weiner, “Tunable programmable microwave photonic filters based on an optical frequency comb,” IEEE Trans. Microw. Theory Tech. 58(11), 3269–3278 (2010). 6. M. Song, C. M. Long, R. Wu, D. Seo, D. E. Leaird, and A. M. Weiner, “Reconfigurable and tunable flat-top microwave photonic filters utilizing optical frequency combs,” IEEE Photon. Technol. Lett. 23(21), 1618–1620 (2011). 7. Y. Dai and J. Yao, “Nonuniformly spaced photonic microwave delay-line filters and applications,” IEEE Trans. Microw. Theory Tech. 58(11), 3279–3289 (2010). 8. X. Xue, X. Zheng, H. Zhang, and B. Zhou, “Widely tunable single-bandpass microwave photonic filter employing a non-sliced broadband optical source,” Opt. Express 19(19), 18423–18429 (2011). 9. Finisar Corporation, “Programmable narrow-band filtering using the WaveShaper 1000E and WaveShaper 4000E,” product whitepaper. 10. J. Mora, B. Ortega, A. Díez, J. L. Cruz, M. V. Andrés, J. Capmany, and D. Pastor, “Photonic microwave tunable single-bandpass filter based on a Mach–Zehnder interferometer,” J. Lightwave Technol. 24(7), 2500–2509 (2006). 11. J. H. Lee and Y. M. Chang, “Detailed theoretical and experimental study on single passband, photonic microwave FIR filter using digital micromirror device and continuous-wave supercontinuum,” J. Lightwave Technol. 26(15), 2619–2628 (2008). 12. T. X. Huang, X. Yi, and R. A. Minasian, “Single passband microwave photonic filter using continuous-time impulse response,” Opt. Express 19(7), 6231–6242 (2011). 13. X. Xue, X. Zheng, H. Zhang, and B. Zhou, “All-optical microwave bandpass filter and phase shifter using a broadband optical source and an optical phase modulator,” Opt. Lett. 37(10), 1661–1663 (2012). 14. T. E. Darcie and A. Moye, “Modulation-dependent limits to intensity-noise suppression in microwave-photonic links,” IEEE Photon. Technol. Lett. 17(10), 2185–2187 (2005). #173245 $15.00 USD Received 25 Jul 2012; revised 4 Nov 2012; accepted 5 Nov 2012; published 14 Nov 2012 (C) 2012 OSA 19 November 2012 / Vol. 20, No. 24 / OPTICS EXPRESS 26929


Introduction
Microwave photonic filters (MPFs) which process high-frequency microwave signals in the optical domain have aroused people's great interest in the past decades [1].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-impulseresponse (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][3][4][5][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 [7].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 [8], 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.

Experimental setup and theoretical description
Our experimental setup is shown in Fig. 1.The incoherent light from a BOS (e.g.Erbiumdoped 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 [9], 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.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 [9].The transfer function of the WaveShaper is denoted as where ω and Ω stand for the microwave and optical frequencies respectively, ℜ is the responsivity of the BPD, RFi V the microwave input amplitude, V π the half-wave voltage of the MZM, ( ) N Ω the single-side power spectral density (PSD) of the BOS at the input of C1, τ Δ the time delay induced by the VDL, 2 θ the total dispersion of the DCF (different from θ is used here instead of 2 β in case of confusion), 0 Ω the central frequency of the BOS. 1 l and 2 l 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 RF where L R is the load resistant of the BPD.We can consider only the half part of RF ( ) , the MPF's transfer function is then expressed as Here, b ( ) H ω is the baseband function given by H ω can be shifted to any frequency.Thus the MPF is both highly reconfigurable and widely tunable.H ω can then be deliberately designed to be single-bandpass.The spectral continuity of BOS has long been exploited to implement single-bandpass MPFs [10][11][12], and the concept of "continuous-time impulse response" was first proposed in Ref [12].
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 [13].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.

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 H ω are given by 1 T and 1 δτ which are 23.3MHz 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.

Flat-top MPF
For the flat-top MPF, the baseband time-domain impulse response is given by  3(a)-3(c) and 3(d)-3(f), respectively.In Fig. 3(c) and 3(f), both measured and calculated results of  RF ( ) H ω are shown, and they agree with each other quite well.

Arbitrary-shape MPF
To implement the arbitrary-shape MPF, b ( ) h t was digitally calculated from the desired b ( ) H ω using inverse fast Fourier transform.For demonstration, b ( ) H ω was designed to be an asymmetric trapezoid which is given by   Since the dispersion in this paper is twice that used in Ref [8], 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 0 ~12 GHz 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, T ( ) H Ω was programmed to be a rectangle with a bandwidth of 0.6 THz, thus b ( ) H ω 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 8 dBm − .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 [14].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 m can be observed when balanced detection is employed.Detailed plots of the signal and noise power versus m are shown in Fig. 7(c).When <0.2 m , 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 >0.2 m , the noise power increases with m .The noise reduction is 5 dB when 0.43 m = corresponding to a rootmean-square value of 0.3.The result agrees with the theoretical prediction in Ref [14].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.

Conclusions
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 singlebandpass, widely tunable, and highly reconfigurable.Frequency responses with a flat-top, highly chirped, or arbitrary-shape passband were demonstrated, respectively.

Fig. 1 .
Fig. 1.Setup of the fully reconfigurable single-bandpss MPF.BOS: incoherent broadband optical source; C: coupler; PC: polarization controller; MZM: Mach-Zehnder modulator; VDL: variable delay line; DCF: dispersion-compensating fiber; BPD: balanced photodetector.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


t θ = +Ω the baseband complex impulse response which is a mapping of * the Fourier transform.By programming the WaveShaper, arbitrary amplitude and phase of b ( ) H ω can be achieved.By adjusting the VDL, b ( )

Fig. 2 .
Fig. 2. Illustration of complex tap generation.It is worth noting that b ( ) h t is continuous in time which means the MPF is a continuoustap FIR filter, b ( )

δ
and aperture T of b ( ) h t 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 b ( )

Fig. 3 .
Fig. 3. b ( ) h t , T ( ) H Ω , and RF ( ) H ω  h t , T ( ) H Ω , and  RF ( ) H ω are shown in Fig.4(a) -4(c) and 4(d) -4 (f), respectively.The optical and the electrical time delays follow the relationship Ω in rad/s.For specified e B and o b , higher e D can be achieved by increasing the optical dispersion 2 θ .

.
The phase of b ( ) H ω is 0. It is noted that b ( ) h t is a complex function according the theory of Fourier transform.The plots of b ( ) h t , T ( ) H Ω , and  RF ( ) H ω are shown in Fig. 5(a) -5(c), respectively.Good agreements are obtained again between the measured and calculated results of RF ( ) H ω  in Fig. 5(c).

Fig. 5 .
Fig. 5. b ( ) h t , T ( ) H Ω , and RF ( ) H ω  for arbitrary-shape passband.(In (c), solid: measured, dotted: calculated.See the context for the definition of symbols.)3.4.Tunability and noise reduction The tunable amplitude responses of the flat-top MPF with 1GHz e B = are shown in Fig. 6.The time delay of the VDL needed for a RF bandpass center of c ω is given by 2 c τ ω θ Δ =.

Fig. 6 .
Fig. 6.Tunable responses of the flat-top MPF with

Fig. 7 .
Fig. 7. (a), (b) RF output spectra and (c) plots of signal and noise power versus modulation index (the noise bandwidth equals the RF spectrum analyzer's RBW which is 3 MHz). 2 T is the window width.In experiments, T was designed to be 21.5 ns.For 500 MHz e B = and 1GHz , the plots of b ( ) h t , T ( ) H Ω , and  RF ( ) H ω are shown in Fig.