## Abstract

We propose and demonstrate a novel switchable microwave photonic filter based on phase modulation. Both a microwave high *Q* bandpass filter and a microwave notch filter with flat passband are achieved respectively. And the switchability between them by tuning the two tunable optical bandpass filters is demonstrated. We also present a theoretical model and analytical expression for the proposed scheme. A frequency response of a high *Q* bandpass filter with a *Q* factor of 327 and a rejection ratio of exceeding 42 dB, and a frequency response of a notch filter with flat passband with a rejection ratio exceeding 34 dB are experimentally obtained. The operation frequency of microwave photonic filter is around 20 GHz.

©2010 Optical Society of America

## 1. Introduction

Microwave photonic filters have been attracting great interest for their advantages compared with electrical filters, such as broad band, light weight, tunability, reconfigurability, and immunity to electromagnetic interference [1–3]. Microwave photonic filters based on optical phase modulation (PM) can obtain negative coefficients easily by phase modulation to intensity modulation (PM-IM) conversion. And PM can eliminate bias drifting problem existing in Mach-Zehnder modulators (MZM) [4]. Therefore, many approaches based on PM have been proposed to achieve bandpass or notch filters, such as using PM and Lyot-Sagnac Loop [5], using PM and dispersion devices [6–9], and using PM and sinusoidal group delay gratings [10]. All these schemes are proposed to obtain a bandpass filter or a notch filter with a finite impulse response (FIR) structure.

In this paper, we propose and demonstrate a novel microwave photonic filter based on PM and two tunable optical bandpass filters (TOBF). The filter has an infinite impulse response (IIR) structure, and it is switchable between a high *Q* bandpass filter and a notch filter with flat passband. The high *Q* bandpass filter is obtained when both of the two TOBFs are blue shift (the center wavelength of TOBF is shorter than the wavelength of optical carrier) or red shift (the center of TOBF is longer than the wavelength of optical carrier), and the notch filter with flat passband is obtained when one TOBF (TOBF1 or TOBF2) is blue shift and the other TOBF (TOBF2 or TOBF1) is red shift. Therefore, both channel selection and channel rejection can be realized in the proposed scheme, and the switching between them can be simply realized by tuning the two TOBFs. Capmany et al has proposed a switchable microwave photonic filter between a bandpass filter and a notch filter [20], with the switchability realized by switching the EOM transfer function over its maximum and minimum value. A high *Q* bandpass filter and a notch filter have been reported in [11] and [12] respectively. The high *Q* bandpass filter realized in [11] cannot be switched to a notch filter, and the subtraction in the notch filter happened in the electrical domain with two photodiodes (PD) [12]. So the notch filter is not all-optical, but hybrid. We use a different method to obtain the negative coefficient. In our scheme, positive and negative coefficients are obtained by two detuned TOBFs, and the subtraction happens directly in the optical domain. Therefore the filter is an all-optical filter. Also, the switchability between a high *Q* bandpass filter and a notch filter is demonstrated and it is realized by simply tuning TOBFs. In the experiment, a high *Q* bandpass filter with a *Q* factor of 327 and a rejection ratio of 42 dB, and a notch filter with flat passband with a rejection ratio exceeding 34 dB are obtained. The operation frequency of the filter is around 20 GHz.

## 2. Experimental setup and principle of analytical model

The proposed experimental setup is shown in Fig. 1 . The laser from a laser diode (LD) is directly modulated by an electrooptic phase modulator (EOPM) and the radio frequency (RF) signal is from“Port1” of the vector network analyzer (VNA).

When the optical carrier is modulated by an EOPM, the amplitude field $E(t)$ can be expressed in the form of

*n*-th order first kind Bessel function. Under small signal modulation condition, only the ±1-st order sidebands need to be considered, and Eq. (2) can be simplified as

In Eq. (3), the amplitudes of the 1-st order sideband and the −1-st order sideband are out of phase [13]. Then the phase modulated signal is injected into “Port2” of the optical coupler (OC) after an optical attenuator (ATT) and the optical power is divided into two parts by OC. One part passes through the OC by “Port4” directly, and the other part gets into the recirculating delay line loop (RDLL) by “Port3”. The RDLL is comprised of an OC, an Erbium-doped fiber amplifier (EDFA), a tunable optical bandpass filter (TOBF1), and an optical variable delay line (OVDL). TOBF1 is detuned from the laser wavelength to realize PM-IM conversion. When the optical carrier is located at opposite slopes of a TOBF, as shown in Fig. 2(a) , the envelopes of converted intensity signals are out of phase [13], as shown in Fig. 2(b). And this can be used to achieve positive and negative coefficients in a microwave photonic filter.

The output of “Port4” consists of two components: one straight-through component (from “Port2” to “Port4”) and one component comprised of recirculating output taps (from “Port1” to “Port4”). The recirculating output taps have been converted to intensity signals, while the straight-through component is still carrying phase signal. Then the straight-through component and recirculating output taps are all injected into TOBF2. The straight-through component is converted to intensity signal by TOBF2 and it comprises the all-pass component of the microwave photonic filter. The all-pass component can be expressed as

*κ*denotes optical coupling ratio of OC (from Port 2 to Port 4).

From Eq. (4), we can obtain the optical intensity of all-pass component

Here, we neglect the DC component and the $2{\omega}_{m}$ component (under small signal modulation condition). From Eq. (5), we can conclude that the coefficient carrying ${\omega}_{m}$ signal is ${P}_{0}\kappa \sqrt{{\alpha}_{20}}{J}_{0}(\frac{\pi {V}_{pp}}{2{V}_{\pi}}){J}_{1}(\frac{\pi {V}_{pp}}{2{V}_{\pi}})(\sqrt{{\alpha}_{21}}-\sqrt{{\alpha}_{2-1}})$ and a phase shift by $\pi /2$is added. From Eq. (5), the all-pass transfer function can be expressed as

The transfer function of bandpass filter can be obtained similarly. When the *n*-th tap passes through TOBF2, the optical amplitude field is

*G*denotes the optical power gain of EDFA, ${\alpha}_{10}$, ${\alpha}_{11}$, and ${\alpha}_{1-1}$ denote optical attenuation of optical carrier, the 1-st order sideband, and the −1-st order sideband by TOBF1 respectively.

By neglecting DC and $2{\omega}_{m}$ components, we can obtain the optical power that carries ${\omega}_{m}$ from Eq. (7)

In Eq. (8), we can see that the coefficient carrying ${\omega}_{m}$signal after *n* loop circles is ${P}_{0}{(1-\kappa )}^{2}{\kappa}^{n-1}{G}^{n}{(\sqrt{{\alpha}_{10}})}^{n}\sqrt{{\alpha}_{20}}{J}_{0}(\frac{\pi {V}_{pp}}{2{V}_{\pi}}){J}_{1}(\frac{\pi {V}_{pp}}{2{V}_{\pi}})[{(\sqrt{{\alpha}_{11}})}^{n}\sqrt{{\alpha}_{21}}-{(\sqrt{{\alpha}_{1-1}})}^{n}\sqrt{{\alpha}_{2-1}}]$ and also a phase shift by $\pi /2$ is added. In our scheme, the laser coherence time ${\tau}_{coh}$is far less than the basic time delay *T* (${\tau}_{coh}\ll T$). So, the microwave photonic bandpass filter is an incoherent filter [2,16], and the bandpass filter transfer function can be expressed as

*T*is the time delay caused by optical delay line of the RDLL. At last, the combined optical signals are sent to a photo-detector (PD) to be converted to electrical microwave signals.

It should be noted that the first tap in the bandpass filter is delayed by *T* comparing with the all-pass tap. Hence, the bandpass filter is delayed by *T* comparing with the all-pass component. And correspondingly, there is a phase shift of ${e}^{-j\omega T}$in the bandpass component (being included in${e}^{-j(n\omega T+\pi /2)}$of Eq. (9)) comparing with the all-pass component. Therefore, when the bandpass component and the all-pass component are summed before the PD, the optical interference between the optical bandpass component and the all-pass component is negligible (${\tau}_{coh}\ll T$). Thus, the final microwave response is equal to the parallel connection of the all-pass microwave filter and the bandpass filter, and the final transfer function is the addition of the bandpass transfer function and the all-pass transfer function [17,18]. Thus, we can obtain the final response function from Eq. (6) and Eq. (9)

*ℜ*is the PD responsivity. In our model, we treat the TOBF1 and TOBF2 as a super-Gaussian filter and a Gaussian filter, respectively. In Eq. (10), the amplitude attenuation coefficients of the TOBF1 and TOBF2 can be expressed as ${\alpha}_{1}=\mathrm{exp}(-\frac{{(\lambda -{\lambda}_{0})}^{4}}{{\sigma}_{1}^{4}})$ and ${\alpha}_{2}=\mathrm{exp}(-\frac{{(\lambda -{\lambda}_{0})}^{2}}{{\sigma}_{{}^{2}}^{2}})$, respectively. Then we can obtain ${\alpha}_{10}=\mathrm{exp}(-\frac{{({\lambda}_{c}-{\lambda}_{0})}^{4}}{{\sigma}_{1}^{4}})$, ${\alpha}_{11}=\mathrm{exp}(-\frac{{({\lambda}_{c}+\Delta \lambda -{\lambda}_{0})}^{4}}{{\sigma}_{1}^{4}})$, ${\alpha}_{1-1}=\mathrm{exp}(-\frac{{({\lambda}_{c}-\Delta \lambda -{\lambda}_{0})}^{4}}{{\sigma}_{1}^{4}})$, ${\alpha}_{20}=\mathrm{exp}(-\frac{{({\lambda}_{c}-{\lambda}_{0})}^{2}}{{\sigma}_{2}^{2}})$, ${\alpha}_{21}=\mathrm{exp}(-\frac{{({\lambda}_{c}+\Delta \lambda -{\lambda}_{0})}^{2}}{{\sigma}_{2}^{2}})$ and ${\alpha}_{2-1}=\mathrm{exp}(-\frac{{({\lambda}_{c}-\Delta \lambda -{\lambda}_{0})}^{2}}{{\sigma}_{2}^{2}})$ respectively. $\Delta \lambda $ denotes the optical wavelength difference between the first order sideband and the carrier.

As can be seen from Eq. (10), there are two poles in the transfer function. And they are located at

andrespectively.When the detuning of TOBF1 is the same as TOBF2 (both are blue shift or both are red shift), the envelopes of converted intensity signals are in phase, as seen in Fig. 2. So the overall response of the microwave photonic filter is equal to the all-pass component adding the band-pass component, and it is also a bandpass filter. This process is shown in Fig. 3 .

When the detuning of TOBF1 is opposite to TOBF2 (one blue shift and the other red shift), as shown in Fig. 2, the envelopes of converted intensity signals are out of phase. At this time, the overall response is equal to the all-pass component minus the bandpass component. When the power of all-pass signals is nearly equal to the power of resonance signals, notches are obtained at frequencies that are resonance frequencies in the bandpass filter. This is shown in Fig. 4 .

## 3. Experimental results and discussion

In order to verify the switchable microwave photonic filter, we carry out experiments with the configuration shown in Fig. 1. The laser wavelength from LD (Agility 3205, linewidth 10 MHz) is set at 1550.42 nm, the bandwidth of TOBF1 (Newport, TBF-1550-1.0) is 1 nm, and the bandwidth of TOBF2 (Santec, OTF-300) is 0.3 nm. The key parameters of other key components are as follows: the EOPM (Convega March-40) has a 3 dB bandwidth of 40 GHz, EDFA has a small signal gain of about 20 dB and the saturation output power is about 10 dBm, PD (SHF AG Berlin) has a 3 dB bandwidth of 40 GHz, and the maximal sweeping frequency of VNA (Anritsu MS4642A) is 20 GHz. At first, we tune TOBF1 at 1550.08 nm, and TOBF2 at 1550.28 nm to make both of the two TOBFs blue shift relative to laser wavelength. And the spectrum relationship between two TOBFs and phase modulated signal is shown in Fig. 5(a) . A 50:50 OC is incorporated to comprise the RDLL. The optical spectrum measured before the PD is shown in Fig. 5(b). We can see that the 1-st order sideband is suppressed and the optical power around the −1-st order sideband is very high. But we think the optical power around the −1-st order sideband is comprised of two components: the power of −1-st order sideband and the power of recirculating amplified spontaneous emission (RASE). The amplified spontaneous emission (ASE) in EDFA is selected by TOBF1 and recirculated in the RDLL. The RASE can be amplified by EDFA consecutively until reaching the steady state. At the same time, the optical carrier and two sidebands are attenuated by TOBF1 and amplified by EDFA consecutively until reaching the steady state. In Fig. 5(b), no 1-st order sideband is observed. The large attenuation of the 1-st order sideband is caused by recirculating attenuation by TOBF1 in the RDLL and TOBF2 after the RDLL.

Although the RASE appeared around the −1-st order sideband, the RASE does not affect the stability of microwave photonic filter. In fact, the microwave photonic filter is very stable during our experiment. Under this condition, a high Q bandpass microwave photonic filter is obtained and the frequency response with OVDL being tuned with about 10 ps interval is shown in Fig. 6 . The experiment1 (simulation1), experiment2 (simulation2), and experiment 3 (simulation3) are corresponding to the OVDL with 40 ps, 30 ps, and 20 ps, respectively. And we give simulation results based on Eq. (10) and the simulation results and experimental results show good agreement. In the experiment, the measured $FSR=4.9$MHz, and $\Delta {f}_{3dB}=15.0$kHz. Thus the corresponding $Q=FSR/\Delta f=327$. And the rejection ratio exceeds 42 dB.

As stated in the earlier part, there are two poles in the transfer function. The *Q* value of the microwave bandpass filter is determined by the locations of the two poles. And the locations of the two poles are determined by the coupling ratio of OC, the loss of TOBF1 and gain of EDFA in the RDLL, which can be seen from Eq. (11) and Eq. (12). A higher *Q* value can be obtained when the poles become nearer to 1. And the bandpass filter can achieve a high *Q* when the TOBF1 is properly tuned. Moreover, two poles are helpful to increase the *Q* value [21]. And two poles can increase the stopband rejection and narrow the skirt region [19].

When the two TOBFs are oppositely detuned, a notch filter is obtained. We take TOBF1 blue shift and TOBF2 red shift for example. We tune TOBF1 at 1549.48 nm, and TOBF2 at 1550.49 nm, respectively. The relationship between the two TOBFs and phase modulated signal is shown in Fig. 7(a) . And the optical spectrum before PD is shown in Fig. 7(b). We can see that both of the two sidebands still exist. But the offsets between the optical carrier and the two first order sidebands are enlarged because of the two detuned TOBFs. Under this condition, a notch filter with flat passband is obtained and the rejection ratio exceeds 34 dB. The limited notch depth is caused by power offset between bandpass signal and all-pass signal. And the power offset is affected by the detuning degree of TOBFs. When the two TOBFs are tuned that the power of bandpass signal is precisely equal to the power of all-pass signal, a very deep notch can be obtained (ideally minus infinity). The microwave frequency response is shown in Fig. 8 . The experiment4 (simulation4), experiment5 (simulation5), and experiment6 (simulation6) are corresponding to the OVDL with 20 ps, 10 ps, and 0 ps, respectively. When the TOBFs are tuned from the case that both are blue shift (or both are red shift) to the case that one is blue shift and the other is red shift, we can observe that passbands are switched to notches, by comparing experiment3 in Fig. 6 and experiment4 in Fig. 8. This is because that the notches in the notch filter are from all-pass signals minus resonance signals, as we have discussed. By tuning the OVDL with about 10 ps interval, we can obtain a tunable notch filter with flat passband. Also, we give a simulation about the notch filter with flat passband based on Eq. (10). The measured and predicted frequency responses are shown in Fig. 8. We can see that the experimental results and the predicted results show good agreement.

The stability of TOBFs will affect the stability of microwave photonic filter greatly. Because slightly response fluctuation of TOBF will cause the PM-IM conversion changed. But during the experiment, the TOBFs show good stability and the response of microwave photonic filter is very stable.

It should be noticed that in the scheme, the PM-IM conversion is realized by detuned optical bandpass filters. The optical bandpass filter is a passive optical component, and the speed of PM-IM conversion nearly has no limit. This is different from negative coefficients obtained by wavelength conversion based on cross gain modulation (XGM) in a semiconductor optical amplifier (SOA) [14,15]. In an SOA, the speed of wavelength conversion is limited by carrier recovery time of SOA. The proposed microwave photonic filter is able to operate at very high frequency. In our experiment, the central frequency of the microwave photonic filter is around 20 GHz. This is limited by the maximum frequency from the VNA (20 GHz). But in practical application, the operation frequency is only limited by the speed of EOPM or PD when incorporating TOBFs with large enough bandwidth. When higher speed EOPM and PD are used, microwave photonic filter with TOBFs of proper bandwidth can operate at 40 GHz or 60 GHz. It is noticeable that there is low frequency response limitation in the microwave photonic filter caused by PM-IM conversion. Usually, the response of microwave photonic filters is concentrated on high frequency performance, and high frequency operation is an advantage compared with electrical filters. We will have a discussion about the frequency limitation and the influences of the bandwidth and shape of TOBF on microwave photonic filter in the next part.

## 4. Discussion

#### 4.1 Limitations and the influences of TOBFs on the microwave photonic filter

Although the microwave photonic filter can work at high frequency, but when a certain TOBF (a certain response shape and a certain bandwidth) is given, limitations are imposed on the response of microwave photonic filter. The limitations include low frequency response and high frequency response.

The frequency response of the microwave photonic filter at low frequency is not so well as the frequency responses at higher frequency. This is caused by the gradual slope of TOBFs. The optical carrier is located at the slope of the TOBF to produce imbalance operation on the two first order sidebands and thus realize PM-IM conversion [13]. When the modulation frequency is low, the two first order sidebands are very close to the optical carrier. And the PM-IM conversion efficiency is low (the intensity signal converted by OBPF1, as shown in Fig. 9 ). When the modulation frequency is higher, the interval between the optical carrier and the sideband gets larger, and the amplitude of converted intensity signal is larger. So the power of microwave signal in passband of microwave filter at higher frequency is larger than that at lower frequency. This is the low frequency limitation.

Figure 9 shows the PM-IM conversion process when the phase modulated signal is converted by three optical bandpass filters (OBPF) with different slopes. According to Eq. (5), the power of converted intensity signal is linear with respect of the amplitude attenuation difference of the two sidebands. So, steeper slope can produce larger intensity signal. This can be seen by comparing converted intensity signals by TOBF1 and TOBF2 in Fig. 9. We assume there is an ideal TOBF whose slopes are vertical, such as OBPF3 shown in Fig. 9. When the optical carrier is located just in the passband of OBPF3, large intensity power can be obtained even under low frequency modulation. The ideal OBPF3 can overcome the low frequency response limitation of microwave filter. However, in fact, optical filter with vertical slopes does not exist. But OBPFs with steep slopes can reduce the low frequency limitation. The steeper the slope is, the smaller the low frequency limitation is.

The shape of passband can influence the microwave filter response. A TOBF usually has an unflat passband (Gaussian shape or super Gaussian shape). The unflat optical passband causes unflat microwave frequency response [13]. And the microwave frequency response is the microwave frequency response of conventional bandpass (or notch) filter multiplied by PM-IM conversion envelope. If we want to obtain a perfect flat microwave frequency response, a TOBF with flat passband and stopband is needed, such as TOBF3 as shown in Fig. 9. After TOBF3, the optical power difference between the 1-st order and the −1-st order sideband is constant under different modulation frequencies (the 1-st order sideband must be located in the passband), and the amplitude of converted intensity signal is constant at different modulation frequencies. Thus a microwave photonic filter with flat envelope is expected to be obtained.

The bandwidth of TOBF will affect the high frequency response of microwave filter. High frequency modulation can increase the frequency interval of the two first order sidebands. When the frequency of modulation signal is very high, both of the two sidebands are attenuated greatly and the converted intensity signal is very weak. So, in order to achieve high frequency response, a TOBF with large bandwidth is needed. However, larger bandwidth can increase noise in the RDLL and cause the microwave filter deteriorated. TOBF with smaller bandwidth can reduce the noise but can increase the loss in the RDLL, causing microwave filter deteriorated too. So, TOBFs in the scheme must be chosen with proper bandwidth.

So, in order to obtain a high quality microwave photonic filter, the TOBFs in the scheme should be properly designed. And apodized fiber Bragg gratings could be used to obtain TOBFs with steeper slope and flatter passband.

#### 4.2 The key factor that limits the${Q}_{N}$factor

In this section, we will discuss how to obtain high rejection selectivity in a notch filter. We can define a parameter as

where $FSR$ is free spectral range, and $\Delta {f}_{3dB}$ is the bandwidth of a notch that drops 3 dB from the peak of passband, as shown in Fig. 10 . In Eq. (11), the parameter${Q}_{N}$ is used to measure the notch filter rejection selectivity of a notch filter. A large ${Q}_{N}$ shows that a notch filter has good rejection selectivity. In the experiment, the measured $FSR$ and $\Delta {f}_{3dB}$ are 4.9 MHz and 0.6 MHz, respectively. And the corresponding ${Q}_{N}$ is 8.2.We can see that the rejection selectivity is not very large. This can be explained as follows. The notches are formed by subtraction of all-pass component and the bandpass component. So only when the power of an all-pass signal and the power of a resonance signal are balanced that can a deep notch be obtained. When the$\Delta {f}_{3dB}$of the bandpass filter becomes smaller, the $\Delta {f}_{3dB}$ of the notch filter will also become smaller. Thus, if we want to obtain a high rejection selectivity (high ${Q}_{N}$ factor) notch filter, we must increase the *Q* factor of the bandpass filter. We give a simulation result that reveals the relationship between the ${Q}_{N}$ factor and *Q* factor, as shown in Fig. 11
. We can see that the ${Q}_{N}$ factor is linear with respect to the *Q* factor.

In our scheme, the power of all-pass signals is lower than the power of resonance signals when the TOBF1 is slightly detuned (as shown in Fig. 5(a)). This is because that the resonance signals are amplified by EDFA in RDLL and many taps are overlapped to strengthen amplitudes of resonance signals while the power of all-pass signals is not amplified. Therefore, in order to balance the power of all-pass signals and the power of resonance signals, we could reduce the power of resonance signals. So the TOBF1 is detuned larger to increase the loss in the ring and reduce the power of resonance signals. This can be seen by comparing Fig. 5(a) and Fig. 6(a). However, larger loss in the ring leads to the *Q* factor decreased. Thus the ${Q}_{N}$ factor of the notch filter is low. So in order to obtain a notch filter with a high ${Q}_{N}$ factor and a high rejection ratio, the bandpass filter must achieve a high *Q* factor and the power of bandpass component and all-pass component must be matched simultaneously. A method to increase the *Q* and${Q}_{N}$factor simultaneously is to increase the coupling ratio of OC. When the coupling ratio *κ* is increased, the power of all-pass signal is increased, and the TOBF1 is detuned less than before to balance the power of all-pass signal and bandpass signal. Thus the Q factor and${Q}_{N}$factor are both increased. This can also be concluded from Eq. (10). When the coupling ratio is increased, the two poles (${z}_{p1}=\kappa G\sqrt{{\alpha}_{10}{\alpha}_{11}}$,${z}_{p2}=\kappa G\sqrt{{\alpha}_{10}{\alpha}_{1-1}}$) of the transfer function (Eq. (10) are increased nearer to the unit circle. Thus, the *Q* and${Q}_{N}$factor are both increased [11,19].

## 4. Conclusions

We have theoretically and experimentally demonstrated a novel microwave photonic filter based on phase modulation. The microwave photonic filter can be switched between a high Q bandpass filter and a notch filter with flat passband by simply tuning two tunable optical bandpass filters. Thus the filter can be used on the occasion that one microwave signal is selected and rejected alternatively. By tuning the OVDL, the microwave photonic filter can be tuned to extract or suppress different microwave signals. The negative coefficient is obtained by PM-IM conversion, and PM-IM conversion is realized by detuned TOBFs, so the speed of PM-IM conversion is nearly no limit and the scheme has potential to operate at very high frequency. The influences of shape and bandwidth of TOBF on microwave photonic filter are also discussed. When adopting TOBF with proper bandwidth and shape, the ultimate limit of the microwave photonic filter is from the EOPM and the PD. If higher speed EOPM and PD are incorporated, the microwave photonic filter could operate at even higher frequencies.

## Acknowledgements

This work is supported by the National Basic Research Program of China (Grant No. 2006CB302805), the National Natural Science Foundation of China (NNSFC) (Grant No. 60901006), and the Program for New Century Excellent Talents in Ministry of Education of China (Grant No. NCET-04-0715).

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