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

Xiaoxiao Xue; Xiaoping Zheng; Hanyi Zhang; Bingkun Zhou

doi:10.1364/OE.20.026929

1. 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-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 [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.

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 [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.

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.

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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 [9]. The transfer function of the WaveShaper is denoted as $H_{T} (Ω) = A_{T} (Ω) \exp [j Φ_{T} (Ω)]$ . The microwave signal current at the output of the BPD is then [8]

\begin{matrix} i_{RFo} (ω) = 8 ℜ l_{1} l_{2} \cdot [π V_{RFi} / (4 V_{π})] \times \frac{1}{2 π} \int_{0}^{+ \infty} N (Ω) A_{T} (Ω) \cdot \\ \cos [Ω Δ τ - Φ_{T} (Ω) - θ_{2} ω^{2} / 2] \exp [- j θ_{2} (Ω - Ω_{0}) ω] d Ω, \end{matrix}

where

ω

and

Ω

stand for the microwave and optical frequencies respectively,

ℜ

is the responsivity of the BPD,

V_{RFi}

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,

Δ τ

the time delay induced by the VDL,

θ_{2}

the total dispersion of the DCF (different from [8],

θ_{2}

is used here instead of

β_{2}

in case of confusion),

Ω_{0}

the central frequency of the BOS.

l_{1}

and

l_{2}

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

H_{RF} (ω) = i_{RFo} ​ ​ (ω) R_{L} / V_{RFi}

where

R_{L}

is the load resistant of the BPD. We can consider only the half part of

H_{RF} (ω)

on the positive axis because

H_{RF} (ω) |_{ω \geq 0} = H_{RF}^{*} (- ω) |_{ω \leq 0}

. Suppose that

Δ τ / θ_{2} > 0

and the PSD of the BOS is constant with

N (Ω) = N_{0}

, the MPF’s transfer function is then expressed as

\begin{matrix} {\tilde{H}}_{RF} (ω) = {H_{RF} (ω) |}_{ω \geq 0} \\ = ℜ R_{L} N_{0} l_{1} l_{2} / (2 θ_{2} V_{π}) \cdot H_{b} (ω - Δ τ / θ_{2}) \exp [j (Ω_{0} Δ τ - θ_{2} ω^{2} / 2)] \end{matrix}

Here,

H_{b} (ω)

is the baseband function given by

H_{b} (ω) = θ_{2} \int_{0}^{+ \infty} H_{T}^{*} (Ω) \exp [- j θ_{2} (Ω - Ω_{0}) ω] d Ω = ℱ [h_{b} (t)]

where

h_{b} (t) = H_{T}^{*} (t / θ_{2} + Ω_{0})

the baseband complex impulse response which is a mapping of

H_{T}^{*} (Ω)

with

t = θ_{2} (Ω - Ω_{0})

;

ℱ [□]

the Fourier transform. By programming the WaveShaper, arbitrary amplitude and phase of

H_{b} (ω)

can be achieved. By adjusting the VDL,

H_{b} (ω)

can be shifted to any frequency. Thus the MPF is both highly reconfigurable and widely tunable.

It is worth noting that $h_{b} (t)$ is continuous in time which means the MPF is a continuous-tap FIR filter, $H_{b} (ω)$ can then be deliberately designed to be single-bandpass. The spectral continuity of BOS has long been exploited to implement single-bandpass MPFs [10–12], 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.

Fig. 2 Illustration of complex tap generation.

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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 $1.71 \times 10^{- 21} s^{2}$ . The time resolution $δ t$ and aperture $T$ of $h_{b} (t)$ 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 $H_{b} (ω)$ are given by $1 / T$ and $1 / δ τ$ 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 by

h_{b} (t) = \sin (π B_{e} t) / (π B_{e} t) \times W_{Hann} (t), - T / 2 \leq t \leq T / 2

where

B_{e}

is the RF bandwidth,

W_{Hann} (t)

is the Hanning window function given by

W_{Hann} (t) = 0.5 [1 + \cos (2 π t / T)]

,

T

is the window width. In experiments,

T

was designed to be 21.5 ns. For

B_{e} = 500 MHz

and

1 GHz

, the plots of

h_{b} (t)

,

H_{T} (Ω)

, and

{\tilde{H}}_{RF} (ω)

are shown in Fig. 3(a) –3(c) and 3(d)–3(f), respectively. In Fig. 3(c) and 3(f), both measured and calculated results of

{\tilde{H}}_{RF} (ω)

are shown, and they agree with each other quite well.

Fig. 3 $h_{b} (t)$ , $H_{T} (Ω)$ , and ${\tilde{H}}_{RF} (ω)$ for flat-top passbands with (a-c) $B_{e} = 500 MHz$ and (d-f) $B_{e} = 1 GHz$ . (In (c) and (f), solid: measured, dotted: calculated. See the context for the definition of symbols.)

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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 by

h_{b} (t) = W_{\tan h} (t) \cdot \exp (j π t^{2} / D_{e}), - T / 2 \leq t \leq T / 2

where

D_{e}

is the electrical dispersion in s/Hz,

W_{\tanh} (t)

is the tanh window function given by

W_{\tan h} (t) = 1 + \tan h [β (1 - 2 | 2 t ​ / ​ T |^{α})]

with

α = β = 3

. In experiments, the MPF’s 3-dB bandwidth

B_{e}

was designed to be 3 GHz. For

D_{e} = - 5 ns/GHz

and

- 10 ns/GHz

, the plots of

h_{b} (t)

,

H_{T} (Ω)

, and

{\tilde{H}}_{RF} (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

| D_{e} B_{e} | \approx | θ_{2} b_{o} |

where

b_{o}

is the 3-dB bandwidth of

A_{T} (Ω)

in rad/s. For specified

B_{e}

and

b_{o}

, higher

D_{e}

can be achieved by increasing the optical dispersion

θ_{2}

.

Fig. 4 $h_{b} (t)$ , $H_{T} (Ω)$ , and ${\tilde{H}}_{RF} (ω)$ for chirped passbands with (a-c) $B_{e} = 3 GHz$ , $D_{e} = - 5 ns/GHz$ and (d-f) $D_{e} = - 10 ns/GHz$ . (In (c) and (f), solid: measured, dotted: calculated. See the context for the definition of symbols.)

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3.3. Arbitrary-shape MPF

To implement the arbitrary-shape MPF, $h_{b} (t)$ was digitally calculated from the desired $H_{b} (ω)$ using inverse fast Fourier transform. For demonstration, $H_{b} (ω)$ was designed to be an asymmetric trapezoid which is given by

20 \log (| H_{b} (ω) |) = {\begin{cases} - 30 ω / ω_{1}, ω_{1} \leq ω < 0 \\ 0, 0 \leq ω \leq ω_{2} \\ - \infty, others \end{cases}

where

ω_{1} ~ - 2 GHz

and

ω_{2} ~ 1 GHz

. The phase of

H_{b} (ω)

is 0. It is noted that

h_{b} (t)

is a complex function according the theory of Fourier transform. The plots of

h_{b} (t)

,

H_{T} (Ω)

, and

{\tilde{H}}_{RF} (ω)

are shown in Fig. 5(a) - 5(c), respectively. Good agreements are obtained again between the measured and calculated results of

{\tilde{H}}_{RF} (ω)

in Fig. 5(c).

Fig. 5 $h_{b} (t)$ , $H_{T} (Ω)$ , and ${\tilde{H}}_{RF} (ω)$ for arbitrary-shape passband. (In (c), solid: measured, dotted: calculated. See the context for the definition of symbols.)

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3.4. Tunability and noise reduction

The tunable amplitude responses of the flat-top MPF with $B_{e} = 1 GHz$ are shown in Fig. 6 . The time delay of the VDL needed for a RF bandpass center of $ω_{c}$ is given by $Δ τ = ω_{c} θ_{2}$ . 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.

Fig. 6 Tunable responses of the flat-top MPF with $B_{e} = 1 GHz$ .

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We then investigated the noise-reduction performance of the balanced detection scheme. For simplicity, $H_{T} (Ω)$ was programmed to be a rectangle with a bandwidth of 0.6 THz, thus $H_{b} (ω)$ 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 $m = 4 {(S C R)}^{1 / 2}$ , 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 $m < 0.2$ , 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 $m > 0.2$ , the noise power increases with $m$ . The noise reduction is 5 dB when $m = 0.43$ corresponding to a root-mean-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.

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).

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

Acknowledgments

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

Abstract

1. Introduction

2. Experimental setup and theoretical description

3. Experimental results and discussions

3.1. Flat-top MPF

3.2. Chirped MPF

3.3. Arbitrary-shape MPF

3.4. Tunability and noise reduction

4. Conclusions

Acknowledgments

References and links

Cited By

Figures (7)

Equations (6)

Optics Express