## Abstract

A microwave photonic filter is demonstrated with both tunable center frequency and bandwidth. This filter is switchable from all-pass, bandpass to notch filter, and the notch filter is a result of the subtraction of a bandpass filter from an all-pass filter based on a balanced photodetector. The all-pass filter is achieved based on a single wavelength radio over fiber link, and the bandpass one is acquired by using the spectrum-sliced broadband optical source. Theoretical analysis and experimental results show that both the center frequency and the bandwidth of the notch filter can be widely tuned.

© 2015 Optical Society of America

## 1. Introduction

Microwave photonic filter (MPF) is a hot research topic and is found to be very potential in application fields such as in radar systems, wireless communication, and radio astronomy [1]. The advantage of MPF includes wide band, high selectivity [2], tunability [3], reconfigurability [4, 5 ], and immunity to electromagnetic interference. In millimeter wave process techniques, the notch filter is a common signal processing stage to clean the clutter and noise from the wanted signals [6].

Several MPF approaches with notch responses have been proposed [7–14 ]. Most of them are based on delay taps. However, the number of their taps are usually just two, which limits the selectivity of notch response. A dual-output electro-optic modulator is used to present an equivalent two-tap negative tap notch filter [8]. Its tap delay is influenced by the length of fiber loop or the grating reflector, as a result the response is periodic with a free spectral range (FSR) of only 45.4MHz. A microwave photonic notch filter with complex taps can be realized based on slow and fast light effects in a semiconductor optical amplifier [9]. This work makes the filter response tunable, but the FSR is 9.4 MHz which is limited by the optical fiber length difference between two taps. Four-wave mixing and cross-gain modulation in a semiconductor optical amplifier can be employed to demonstrate a notch photonic filter [10]. The number of taps is enlarged to four, but the FSR is limited at the level of 100MHz. Based on a Sagnac loop that comprises an off-loop-center electro absorption modulator and a wavelength dependent delay [11], a notch filter with an improvement of FSR to 6.1GHz is presented. However, the filter has merely two taps. An MPF switchable between a bandpass filter and a notch filter is demonstrated based on phase modulation and a fiber loop that comprises two tunable optical bandpass filters [12]. The filter has an infinite impulse response structure, which is equivalent to a larger number of taps. However, the FSR is only 4.9MHz. Another kind of approach for microwave photonic notch filter is reported based on stimulated brillouin scattering (SBS) effect [13]. The approach needs a highly precise control on the biases of the modulator and a careful managing on the light polarization for the SBS process which is polarization dependent. Moreover, a report on the linearity performance of the SBS-based MPF is that the frequency response changes with the power of input signal [15]. Recently, a notch filter was demonstrated by using six well-designed tap weights [14]. The frequency response is periodic with a FSR of 4.7GHz. However, the filter suffers from a narrower Nyquist zone [16] because of the nonuniform tap distribution, and it is not a linear-phase filter because the shaped taps are asymmetrical. Moreover, the working frequency of the method is limited by the resolution of Fourier domain optical processor (FDOP).

In this paper, a notch MPF is proposed and demonstrated with continuously tunable center frequency and bandwidth based on an all-pass filter minus a bandpass filter. The all-pass component and the bandpass component share the same optical link, but the former is realized based on a single-frequency light and the latter is based on a spectrum-sliced broadband optical source. Theoretical analysis on the transfer function is presented. Experiment results show that the notch filter is not periodic and can be adjusted by tuning the center frequency and bandwidth of the bandpass filter.

## 2. Theoretical principle

The schematic diagram of the proposed MPF is illustrated in Fig. 1 . The optical power and optical angle frequency of the laser source is ${P}_{o}$ and ${\omega}_{o}$, respectively. The spectrum-sliced broadband optical source (BOS) is first confined within the optical angle frequency range between ${\omega}_{1}$ and ${\omega}_{2}$ (${\omega}_{1}<{\omega}_{2}$) via the FDOP, and then sliced via a Mache-Zehnder interferometer (MZI) which is constructed by two 50/50 optical couplers and a variable delay line (VDL). The FDOP works as a programmable optical filter. The single-frequency light and the broadband light are coupled together and then single-side-band modulated to carry the radio frequency (RF) signal. The modulated light is fed into a dispersion fiber, and then launched into a wavelength division multiplexer (WDM). The WDM splits the light into two parts: Port B only includes the laser part; Port C only includes the BOS part. A balanced photodetector (BPD) is employed to detect the two parts, respectively.

The optical spectrum before modulation can be given by

Suppose that the microwave signal given by $\mathrm{cos}\left(\Omega t\right)$ where $\Omega $ is the RF frequency. Under the small signal modulation condition, the optical spectrum of the modulated light can be written as

where $m$ is the modulation index. The optical fiber is modeled as an optical phase filter given by $\Phi \left(\omega \right)=\mathrm{exp}(-j{\beta}_{2}L{\omega}^{2}/2)$, where ${\beta}_{2}$ and $L$ is the second-order dispersion and the length of the fiber, respectively. Thus, the light after fiber dispersion isThen, the laser light and the broadband light at Port A is divided. For Port B, the laser light is time delayed for ${\tau}_{0}$ by the VDL with a spectrum written as

In the branch of Port C, the broadband light spectrum is

When $\Re $ is the responsivity of the photodiode, the RF output of the BPD is the difference of two photodiodes

Thus, the Fourier transfer of $i\left(t\right)$is

By substituting Eq. (5) and Eq. (6) into Eq. (8), ${E}_{i}\left(\Omega \right)$ can be calculated and we obtain the RF transfer function

Based on theoretical analysis, $H\left(\Omega \right)$ is the subtraction of two terms: the first term is an all-pass response; the second term is a bandpass response [19]. The bandpass component has two passbands at $\Omega =0$ and $\Omega ={\Omega}_{2}$. The shape of the former passband is just a half of the latter passband. And the latter passband we concern should be theoretically 6dB lower than the former one.

The RF transfer function can be a notch filter if the all-pass response minus the bandpass response, as shown in Fig. 2 . In order to obtain a notch at ${\Omega}_{2}$, we need to make $H\left({\Omega}_{2}\right)=0$. When $\Omega $ is near to ${\Omega}_{2}$, $\left|H\left(\Omega \right)\right|\approx {P}_{0}\mathrm{exp}\left(-j{\beta}_{2}{\omega}_{0}\Omega -j\Omega {\tau}_{0}\right)-{H}_{0}\left(\Omega -{\Omega}_{2}\right)/2$. Thus, the amplitude of the bandpass response and the all-pass response should be matched at the frequency ${\Omega}_{2}$. Thus, an amplitude match condition should be satisfied:

The condition infers that the optical power at Port B is theoretically 3dB lower than the optical power at Port C. The function of the VDL is true time delay which is independent of ${\Omega}_{2}$. The group time delay of the laser light is different from the BOS in the dispersion module. Without the VDL to match these two delays, we cannot acquire a notch when a delay difference is between the all-pass and bandpass filters. After matched, the VDL needs no adjusting unless the center wavelength of the BOS changes. Under the amplitude match condition, the MPF has two notches: the frequency of the first notch is ${\Omega}_{1}$; the frequency of the second notch is ${\Omega}_{2}$. A simulation result is shown in Fig. 3 , where the simulation condition is according to the experiment part.

The frequency ${\Omega}_{2}$ can be tuned by the MZI without changing the filter shape according to Eq. (9). Another slicing way is to directly use the FPOP to shape the spectrum of the BOS. In this way, the interferometer is not needed in the approach, but a FPOP with high resolution is required. Let $H\left({\Omega}_{1}\right)=0$, then the frequency of the first notch satisfies

It indicates that ${\Omega}_{1}$ is half the −6dB bandwidth of the bandpass filter. Therefore, the value of ${\Omega}_{1}$ and the bandwidth of the bandpass filter are of the same order of magnitude. Further, if the filter shape is Gaussian, ${\Omega}_{1}$ is less than the −3dB bandwidth of the bandpass filter. When the frequency value of the second notch is tuned, the filter shape and bandwidth do not change so that the first notch is stable.

Finally, the bandwidth of the notch filter can be tuned with the spectrum of the BOS. When decreasing the bandwidth of the BOS, the bandwidth of the bandpass filter gets larger so that the stopband of the notch filter becomes larger. In addition, the bandwidth of the bandpass filter at the base band will become larger as well as the value of ${\Omega}_{1}$. Even so, because the bandwidth is usually very small, the value of ${\Omega}_{1}$ are much less than ${\Omega}_{2}$. In this way, the first notch is separated from the second notch in the frequency domain. Similarly, two passbands of the bandpass response are also separated away.

## 3. Experimental results and discussion

To prove the concept, the experiment setup is illustrated in Fig. 4 . The broadband light is from the spontaneous emission of an erbium-doped fiber amplifier (EDFA). Then, the BOS is filtered with the waveshaper I (Finisar 4000S), and then coupled with a laser (Emcore). The RF signal is single-side-band modulated by employing a dual-parallel Mach-Zehnder modulator (DPMZM, Fujitsu, 40Gbps) with a 90 degree hybrid coupler (Agilent 87310B). The total dispersion of the dispersion compensation fiber (Corning) is 1700$p{s}^{2}/rad$ cascaded with an EDFA. The waveshaper II (Fiberhome) is used to split the light into a BPD (u2t photonics). A VDL (General Photonics) is used to match the time delay. An optical spectrum analyzer (Advantest Q8384) is used to measure the optical spectrum, and a vector network analyzer (VNA, Agilent N5242A) is used to measure the frequency response.

In the experiment, the optical spectrum of the BOS is firstly carved into Gaussian profile by the waveshaper I. The −3dB optical bandwidth is 3nm. The optical spectrum after modulation is shown in Fig. 5(a) : the left part is the sliced BOS; the right part is a single-frequency light with a wavelength of around 1552.5nm. Then, it is divided into two ports by the waveshaper II. The single-frequency part is fed into Port B with the optical spectrum shown in Fig. 5(b). The spectrum at Port C is shown in Fig. 5(c) which merely includes the BOS part. After tuning the time delay of the VDL and the optical power of the single-frequency light, a notch filter can be obtained. In Fig. 5(d), the stopband center frequency is 10.03GHz with a stopband attenuation of 37dB, and the −3dB stopband bandwidth is around 292MHz. In addition, it has a quadratic phase response as shown in Fig. 6 . The optical power at Port B is 3.7dB lower than the optical power at Port C. This notch response is a result of the all-pass response shown in Fig. 5(e) minus the bandpass response shown in Fig. 5(f). Here, the all-pass response is measured by switching off the BOS. The phenomenon that this response is slope is because it includes the frequency responses of the modulator and the photodiode [15]. The bandpass response has the same center frequency as the notch one, and it is measured by switching the laser light off. In Fig. 5(f), the −3dB bandwidth is around 163MHz. In a word, the filter can be switchable from all-pass, bandpass to notch filter.

The frequency of the second notch can be adjusted by tuning the MZI without any change to the filter shape. In the experiment, the center frequency is tuned from 2GHz to 17GHz, and the results are shown in Fig. 7 . For the bandpass filter, their base band does not change and the shape of the second passband remains invariant when tuning the frequency. The −3dB bandwidth at the base band are around 80MHz. Meanwhile, notches responses are shown in Fig. 7(b). The frequency of the first notch is stable at around 130MHz that is less than the −3dB bandwidth at the second notch. Meanwhile, the frequency of the first notch is far less than the working frequency of the second notch.

Finally, the bandwidth of the MPF can be adjusted by tuning the bandwidth of the BOS. As shown in Fig. 8 , we do not change the center wavelength of the BOS and only adjust the −3dB bandwidth of the BOS to 2nm. Consequently, the corresponding bandpass and notch filters are listed in Fig. 9 . In Fig. 9(a), the −3dB bandwidth for 2nm is 240MHz. And in Fig. 9(b), the −3dB stopband bandwidth for 2nm is around 428MHz. Here, when the passband filter is transferred into the notch filter, two −3 dB bandwidth are different. It is because that the notch filter is based on the amplitude of the all-pass filter minus the amplitude of the bandpass filter. The −3dB stopband bandwidth of notch response is mapped from the −10.7dB bandwidth of the bandpass response. In Fig. 9(a), the −10.7dB bandwidth for 2nm is 451MHz. Then, comparing these experimental results of 2nm with 3nm, it indicates that the bandwidth of the MPF can get smaller by increasing the bandwidth of the BOS.

In this paper, two filters are necessary. One filter is used to filter the BOS; the other one is used to split the single laser from the BOS. In order to quickly verify the principle, we use two waveshapers in the experiment. It results in a high system cost. Moreover, a way to reduce the cost is to use fiber Bragg gratings (FBG) with optical circulators to work as the filters. Take the second filter as an example, we can send the light into the FBG via an optical circulator. When the Bragg wavelength is just equal to the laser wavelength, the reflected light only includes the laser light and the transmitted light only contains the BOS part. In addition, limited by the devices in the laboratory, the fiber is used in the experiment and it has a large time delay. If replacing the fiber with a chirped FBG [18] with large dispersion, the time delay of this filter can be much smaller. Finally, the noise and spurious free dynamic range level of this system can be found in our previous work [19] that had the similar experimental devices as this work.

## 4. Conclusion

In conclusion, we propose and demonstrate an MPF with switchable frequency responses. The notch filter is achieved by an all-pass filter based on a single-frequency light minus a bandpass filter based on a spectrum-sliced broadband optical source in a balanced photodetector. Thus, the frequency response can be reconfigured from all-pass, bandpass to notch filter. The experiment demonstrates that the filter has widely tuned center frequency and bandwidth with both notch response and bandpass response.

## Acknowledgments

This work was partly supported by National 973 Program under grant No.2012CB315603-04, National Natural Science Foundation of China under grants No.61025004, 61032005, 61321004, 61420106003, and 61427813.

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