## Abstract

A fully electrically tunable microwave photonic filter is realized by the implementation of delay lines based on frequency-time conversion. The frequency response and free spectral range (FSR) of the filter can be engineered by a simple electrical tuning of the delay lines. The method has the capability of being integrated on a silicon photonic platform. In the experiment, a 2-tap tunable microwave photonic filter with a 3-dB bandwidth of 2.55 GHz, a FSR of 4.016 GHz, a FSR maximum tuning range from −354 MHz to 354 MHz and a full FSR translation range is achieved.

©2012 Optical Society of America

## 1. Introduction

Microwave photonic filters (MPFs) with features like broad bandwidth, low loss, light weight, large tunability, and immunity to electromagnetic interference have been investigated intensively recently [1–3]. The processing of microwave signals in the optical domain has attracted much interest in a bundle of applications such as broadband phased array antennas [4], arbitrary waveform generation [5] and radio-over-fiber (RoF) systems [6]. In general, tunable delay lines are the key elements in the implementation of multi-tap complex-coefficient MPFs. In [7], a technique based on optical single sideband (OSSB) modulated signals and a cascade of phase-shifted fiber Bragg gratings (PS-FBG) as tunable delay lines has been presented. However, these PS-FBGs require complex fabrication facilities and special measures to generate the required delays. Tunable delay lines based on the slow light technique have the advantage that the required delay for each tap can be adjusted by a control signal.

To date, various physical mechanisms to produce slow light have been reported in the literature. Among these particularly slow light based on stimulated Brillouin scattering (SBS) is important since it can be carried out at room temperature in optical fibers and at telecommunication wavelengths [8–11]. In [11], slow light based on SBS was incorporated for producing the tunable delay lines in a MPF. However, this is a rather complex scheme since it requires additional devices to generate the optical waves involved and high optical powers to pump the nonlinear interaction. Here, we use tunable delay lines based on frequency-to-time conversion [12] as the MPF taps. In contrast to the other mentioned approaches [7, 11], our method has the capability to be integrated on a silicon photonic platform [13]. To show the possibilities, in the experiment a microwave-photonic filter with a 3-dB bandwidth of 2.55 GHz, a FSR of 4.016 GHz, a FSR maximum tuning range from −354 MHz to 354 MHz and a full-FSR translation range was realized. The paper is organized as follows; section 2 reviews the principles of microwave-photonic filters. Section 3 is dedicated to the introduction, formulation and assessment of the proposed delay line. Section 4 focuses on the experimental setups and corresponding results. Finally, we conclude in section 5.

## 2. Principles of microwave-photonics filters

The operation principles of a finite-impulse response (FIR)-MPF are shown in Fig. 1
. The RF signal (red) is modulated on an optical wave (blue) via an amplitude modulator (AM) with a continuous wave (CW) laser source; the result is fed to a power splitter (1xN) that splits the power between multiple branches. In each branch, there is an attenuator and multiple-*T* buffer to control the intensity and the delay respectively; generating weighted and delayed versions of the original signal. The power combiner (Nx1) combines the power of the different branches. A photodiode converts the output signal back from the optical to the electrical domain. The photodiode behaves as a low-pass filter; i.e. it excludes the higher frequencies. Although the taps’ amplitudes can be controlled via variable optical amplifiers (VOAs), the delays are constant. Thus, in order to achieve complete tunability, the delay in each tap should be also tunable. MPFs operate in the incoherent regime to cancel the optical interference [2].

The following criteria are important for the realization of the delay lines in a tunable MPF with complex coefficients: **Minimum pulse distortion:** The ideal delay-line is an all-pass filter with a linear phase response. However, the real delay lines act as distortive filters. The output signal will be distorted and deviates from the pre-designed MPF response. **Applicability to analogue signals:** The tunable delay line should be able to handle not only bursts and packets but also analogue continuous signals. **Relatively compact or integrated solution:** In MPF implementation, especially the FIR ones (Fig. 1), multiple delay lines are needed to form the whole setup; thus, an integrated solution is essential due to economic reasons. The favourite solutions will be those with the ability of being integrated on a silicon photonic platform.

## 3. Frequency-time conversion (FTC) based tunable photonic delay line

The FTC delay line is based on a basic property of Fourier transformation: “Time shifting of a signal corresponds to the multiplication of its spectrum with linear phase; i.e. $x(t-\Delta t)\leftrightarrow $${e}^{-j\omega \Delta t}X(\omega )$” where ω is the frequency. The basic idea of the FTC based tunable delay line can be seen in Fig. 2 [12]. In the first step, the signal is converted from the frequency to the time domain via a frequency-to-time conversion (FTTC). In this block, the different spectral components of the signal are mapped into the time domain. Therefore, a phase modulator (PM) is used to linearly shift the phase of the incoming signal in time, which eventually results in a linear phase change of the spectrum of the input signal. In order to convert the signal back to the original domain, a time-to-frequency converter (TTFC) is used.

For the FTTC and TTFC blocks, a dispersive device with large group-velocity dispersion (GVD) is used. This can be realized with ring resonators on a silicon photonic substrate [13], arrayed waveguide gratings, chirped fiber Bragg gratings, photonic crystal structures, or even a spool of standard optical fiber. The output spectrum of the setup $Y(\omega )$ can be derived as:

Where $\mathcal{F}\{\xb7\}$ is the Fourier transform operator. Since $\Omega \ll \omega $, the temporal output is:

Where $\Omega $ and $\eta $ are the ramp slope and quadratic phase variation coefficient respectively. $\Omega $ is the inverse of the time required for the ramp to change from the minimum to maximum.

Equation (3) shows some interesting points: The induced delay$\Delta t=2\Omega \eta $ can be tuned both by variation of the ramp slope and the dispersive elements’ phase variation coefficient. Hence, the delay or advancement of the signal can be tuned by the variation of the sign and phase modulation slope ($\Omega $) which is achievable by controlling the RF arbitrary waveform generators (RF AWG). Second, since the induced delay is independent of the incoming signal bandwidth, higher fractional delays can be achieved with shorter signals. This characteristic leads to a high time-bandwidth product. Third, there is an additional linear phase modulation term $\mathrm{exp}(j\text{\hspace{0.17em}}\Omega t)$ that shifts the optical signal from $\omega $ to $\omega +\Omega $. Therefore, another linear phase modulation term with negative slope $\mathrm{exp}(-j\text{\hspace{0.17em}}\Omega t)$ is required if the original optical spectrum is to be recovered.

## 4. Experimental setup

#### 4.1 Tunable phase shifter/delay line characterization

In the experimental setup illustrated in Fig. 2, we use a dispersion compensation module for the FTTC block with a dispersion of −1247 ps/nm. The first phase-modulator (PM) (Avanex 20 Gbps) is modulated with a positive ramp $\Omega t+{\Phi}_{0}$ generated by the RF AWG. The phase ${\Phi}_{0}$ can be controlled by the starting point of the generated ramp. As TTFC block, we use a spool of 75 km of fiber (with the overall dispersion of 1252 ps/nm). Finally, the second phase modulation with the negative slope (-$\Omega t$ generated by the RF AWG as well) returns back the optical signal to the original frequency. There remains a tunable phase shift of ${\Phi}_{0}$ and delay of $\Delta t=2\Omega \eta $. A vectorial network analyzer (VNA) is used to characterize the suggested setup (Fig. 2). Port 1 of the VNA sweeps the frequency in the range of 1 GHz to 19 GHz and port 2 measures the output RF signal. Therefore, the phase shift of the recovered RF signal is obtained for each${\Phi}_{0}$. For the measurements shown in Fig. 3(a)
, we have changed ${\Phi}_{0}$ in the span of −180° to 180° in steps of 45°, but kept the ramp slope $\Omega $ unchanged. As can be seen, the phase shift is nearly independent of the employed microwave frequency (phase deviations (< ± 9°) translate into the MPF’s response distortions). Therefore, it is possible to use this RF phase shifter to generate complex coefficients in the MPF with a tunable range of one FSR. The phase shift ripples are caused by the measurement errors and the non-ideality of the generated ramp. To test the tunable delay line, the same setup is employed but the initial phase ${\Phi}_{0}$ is kept constant while the ramp slope $\Omega $ is changed. Meanwhile, the delay or advancement between the applied signal of port 1 of VNA and the measured signal of port 2 of VNA is calculated. The results are shown in Fig. 3(b). The small deviations from the dashed line _{$\Delta t=2\Omega \eta $} especially for higher ramp rates are due to the fact that the ramps are approximated with piecewise-constant waveforms. This approximation converges to a linear ramp as the ramp slope ($\Omega $) decreases.

#### 4.2 2-tap filter implementation

The proposed method has been experimentally verified for a proof-of-concept 2-tap MPF shown in Fig. 4
. Two laser sources (${\lambda}_{1}=1550.8nm$ and ${\lambda}_{2}=1549.8nm$) are used for the two branches to guarantee an incoherent regime [2]. The RF signals with a bandwidth of around 10 GHz are fed to two 20 Gbps amplitude modulators; The output of the tunable delay line combines with the signal of the lower branch through an optical power combiner and is detected by a photodiode. The overall transfer function is_{$H(\omega )=1+\mathrm{exp}(j\text{\hspace{0.17em}}{\Phi}_{0}-j\omega t)$}. From the black plot in Fig. 5
, it can be derived that the filter has a 3-dB bandwidth of 2.55 GHz and a FSR of 4.016 GHz if the ramp slope is 1 GHz and the phase ${\Phi}_{0}$ is unchanged.

### 4.2.1 MPF frequency response translation

Theoretically, if the complex coefficients are varied by shifting the phase by $n{\Phi}_{0}$, for a multi-tap MPF with delay difference *T,* the translated frequency response of the filter is:

*N = 2*) are shown in Fig. 5. As can be seen, a phase shift of 360° can be obtained and the frequency response can be tuned over the whole FSR.

### 4.2.2 FSR adjustment by delay tuning

In a multi-tap complex coefficient filter, the delay/advancement among branches can be controlled independently, which corresponds to a FSR adjustment. For a multi-tap MPF with constant delay difference *T*, this can be written as:

Where $\beta $(the delay difference scaling factor) is also the FSR scaling factor. By measuring the frequency response for four different delays/advancements by a VNA, we show that the maximum FSR tuning range of the MPF is from ± 149 MHz up to ± 345MHz (Fig. 6(a) -6(d)). The frequency responses of both amplitude and phase modulators affect the MPF response which leads to an attenuation of the higher frequency content and induces the differences between the simulations and the experimental results.

## 5. Conclusions

We have presented a fully electrically tunable microwave photonic filter realized by the implementation of delay lines based on frequency-time conversion. Besides the capability to be integrated on a silicon photonic platform [13], these delays have the potential to achieve very high delay/advancement. The maximum achievable values are restricted only by the phase modulation slope and the phase variation coefficient. In the proof-of-concept experiments, we have shown a 2-tap MPF with a 3-dB bandwidth of 2.55 GHz, a FSR of 4.016 GHz, a FSR maximum tuning range from −354 MHz to 354 MHz and a full FSR translation range. Table 1 compares the results of the presented system in comparison to other MPF implementations [7, 11].

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