Novel programmable microwave photonic filter with arbitrary filtering shape and linear phase

Xiaoqi Zhu; Feiya Chen; Huanfa Peng; Zhangyuan Chen

doi:10.1364/OE.25.009232

1. Introduction

Microwave photonic processing has attracted much attention in recent years [1,2]. The microwave filtering is an important technique of radio frequency (RF) system, which is widely used in radar and communication. With highly increased complexity of RF system, the technology of microwave filter develops towards high frequency, high Q, reconfigurability, and tunability. Compared with traditional electronic filters, microwave photonic filters (MPFs) transcend the bandwidth limitation of electric device, and show great advantage in high sampling frequency, tunability, low loss and immunity to electromagnetic interference [3,4]. Due to its excellent performance, MPF is considered to offer potential to satisfy most of the demands in the future.

One stucture for MPF is the type of infinite impulse response (IIR) filter, which is based on recirculating cavities to provide an infinite number of weighted and delayed input signals. Several methods have been proposed with very high Q factor [5–7]. However, this kind of filters often have low free spectral ranges (FSRs) [7]. The other popular structure for MPF is the type of FIR filter. The multi-tap delay line scheme is the basis of most recent works on this kind of filter. Typically, the light source of MPF is implemented by a multi-wavelength source or by a sliced broadband source. The multi-wavelength source (laser array or optical frequency comb) based MPF is well known for its high Q, tunability and low noise [8,9]. It is also known that only positive taps exist in a classic multi-wavelength MPF which usually functions as a lowpass filter [9]. Many works focus on the realization of bandpass filter with negative taps or complex taps by using polarization modulation [10–12], cladding-mode couplers [13], cross-gain modulation [14], phase-to-intensity modulation conversion [15–17], multiple electro-optic modulators in combination with a dispersive medium [18], π phase inversion and V_π dependence with wavelength in a single electro-optic Mach-Zehnder modulator [19], balanced photo-detection [20], nonuniformly spaced delay lines [18], slow and fast light effects [21–27].

However, multi-wavelength MPFs still have some certain limitations. First, the number of optical wavelengths is finite, so the transfer function is periodic. Second, for the laser array based MPF, it is too expensive to get a high Q factor which requires a large number of lasers. Last, a coherent optical frequency comb will produce strong beat noise in some specific frequency which are multiples of the repeat frequency of the optical frequency comb [9, 28, 29]. Liao et al [29] offers a method to solve this problem by applying group velocity dispersion on the carrier comb before modulation. So this type of filter must operate in the range [mω_r/2, (m + 1)ω_r/2] (m is natural number, ω_r is the repeat angular frequency of the optical frequency comb). Compared with the multi-wavelength MPF, the sliced broadband source based MPF is known for its low cost and aperiodic [30–33]. The presence of nonzero third-order dispersion is the main difficulty for improving Q factor of the sliced broadband source based MPF and several methods have been proposed to compensate the third-order dispersion [31,32].

Recently, the spatial light modulator (For example, Finisar waveshaper) comprising a 2-D array of liquid crystal on silicon (LCoS) pixels, is proposed as novel programmable optical filter and spectrum shaper for the implementation of a reconfigurable MPF. It shows that the spectrum profile of an optical frequency comb has influence on the performance of MPF, for example the Q factor and sidelobe suppression [33–35].

Yi et al [36] reports a method to realize programmable taps of FIR filter with a waveshaper and a chirped fiber Bragg grating. The waveshaper is used to realize single sideband modulation and complex coefficient synthesis. The complex coefficient is generated by controlling the phase difference between the optical comb line and its sidebands. By software programming the complex coefficients, a reconfigurable and tunable shape-invariant multi-tap RF filter with wideband tuning range over the full FSR is demonstrated. However, due to the resolution limitation of the waveshaper, the comb lines and their sidebands are not able to be separated below 10 GHz.

Phase response, especially linear phase response, is also important in radio frequency signal processing, which is widely used in communication [37–40]. Most researches of current MPF studies toward high Q, high frequency and tunability, and have less interest on the phase response. A multiple-passband MPF with arbitrary spectral response and near linear phase response is proposed using nonuniformly spaced multi-taps [40]. The complex coefficient taps are achieved using the nonuniform sampling. Although the amplitude distribution of the taps is symmetric, the spacing of the taps is nonuniform, which leads to a near linear phase response.

In this paper, we propose and demonstrate a novel optical frequency comb based MPF, which is fully reconfigurable with linear phase. The response of filter is designed using frequency sampling method of finite impulse response (FIR) filter. The linear phase response is realized by the symmetric distribution of filter taps and the DSB modulation. Our work employs an optical frequency comb generator to generate an evenly spaced set of narrow linewidth optical lines. A waveshaper functions as an optical programmable filter which enables us to shape the comb amplitude line by line. According to the sign of designed taps, all comb lines and their sidebands are separated into two different waveshaper outputs, and then detected by a balanced photo-detector (BPD) to generate positive and negative taps. In our proposed scheme, each comb line and its sidebands are operated simultaneously, so the resolution limitation of the waveshaper is not a problem. The tuning range covers from DC to ω_r/2. In the experiment part, we will show four basic types of filter (lowpass, highpass, bandpass and bandstop) and a triple passband filter with arbitrary central frequency and bandwidth. It is the first experimental demonstration of a programmable multiple passband MPF with linear phase response, to the best of our knowledge.

The proposed MPF scheme is also feasible to be implemented in a single chip using the integrated platform [41–44], which will reduce the power consumption and cost, and achieve higher stability and reliability. The key devices of the proposed system have been proposed and demonstrated in recent years, such as integrated programmable optical filter [45–47], integrated optical frequency comb [46–49] and integrated modulator [50,51].

The remaining of the paper is organized as follows. In Section 2, the principle of the multi-wavelength MPF is introduced. This section also describes the influence of different modulation types and higher order fiber dispersion. Section 3 presents the experimental setup and the characterization of the proposed MPF. The last section concludes the paper.

2. Theoretical analysis

The transfer function of a FIR filter can be expressed as

s_{o} = \sum_{n = 0}^{N - 1} h (n) s_{i} (t - n T)

H (ω) = \sum_{n = 0}^{N - 1} h (n) \exp (- j n ω T)

where h(n) is the n_th tap coefficient of the FIR filter. s_o is the output signal. s_i is the input signal. H(ω) is the transfer function of the FIR filter. N is the number of taps. T is the delay time. In the application, frequency sampling method is an essential technique of FIR filter allowing us to design the response of filter in the frequency domain.

For a FIR filter with linear phase response, the necessary and sufficient condition is that h(n) is supposed to be odd symmetric or even symmetric about n = (N-1)/2. The transfer function is rewritten as

H (ω) {=e}^{j φ (ω)} | H (ω) | = {\begin{matrix} e^{- j ω T (N - 1) / 2} \cdot \sum_{n = 0}^{N - 1} h (n) \cos [(\frac{N - 1}{2} - n) ω T)], when h (n) = h (N - 1 - n) \\ e^{j π / 2 - j ω T (N - 1) / 2} \cdot \sum_{n = 0}^{N - 1} h (n) \sin [(\frac{N - 1}{2} - n) ω T)], when h (n) = - h (N - 1 - n) \end{matrix}

where |H(ω)| is the amplitude response and φ(ω) is the phase response. Whether h(n) is odd or even symmetric, the slope of the phase response is T(N-1)/2.

The scheme of the proposed microwave photonic filter is shown in Fig. 1. The repeat angular frequency of optical frequency comb is ω_r. The OFC is modulated by a LiNbO₃ modulator. The modulated signal is sent into a dispersive medium, such as a dispersion compensating fiber (DCF). A programmable optical filter (Finisar waveshaper) is used to shape the comb spectrum and separate all the comb lines and their sidebands into two outputs according to the sign of designed filter taps. A BPD is used to realize the positive and negative filter taps.

Fig. 1 Structure of the proposed filter.

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Assuming the total number of comb lines is N, the optical frequency comb can be expressed as

E_{s} (t) = \sum_{n = 0}^{N - 1} \sqrt{P_{0} (n)} \exp (- j ω_{n} t) = \sum_{n = 0}^{N - 1} \sqrt{P_{0} (n)} \exp [- j (ω_{0} + n ω_{r}) t]

where E_s is the optical field of the comb. P₀(n) is the optical power of the n_th optical comb line. ω₀ is the frequency of the first comb line. ω_n = ω₀ + nω_r is the frequency of the n_th comb line.

The optical frequency comb is modulated by the RF signal. Different type of modulation has different transfer function. Take the DSB modulation biased at linear point as an example, the modulated optical signal can be written as

\begin{array}{l} E_{m} (t) = E_{s} (t) \cos (\frac{π}{4} + \frac{π V_{R F} (t)}{2 V_{π}}) \\ \approx \frac{\sqrt{2}}{2} \sum_{n = 0}^{N - 1} \sqrt{P_{0} (n)} [\frac{1}{2} J_{1} (\frac{π A_{R F}}{2 V_{π}}) e^{- j (ω_{n} t - ω_{R F} t) - j \frac{π}{2}} + J_{0} (\frac{π A_{R F}}{2 V_{π}}) e^{- j ω_{n} t} + \frac{1}{2} J_{1} (\frac{π A_{R F}}{2 V_{π}}) e^{- j (ω_{n} t + ω_{R F} t) + j \frac{π}{2}}] \end{array}

where V_RF = A_RF_·cos(ω_RFt) is the modulated electric signal. A_RF and ω_RF are the amplitude and angular frequency of the RF signal. J_n is the n-order Bessel function.

A DCF is used as a dispersion medium to achieve the required time delay. An additional phase term θ(ω) is added to the signal after transmission over DCF, which can be written as

θ (ω) = \frac{β_{2} L}{2} {(ω - ω_{0})}^{2}

where β₂ is the second-order fiber dispersion and the higher order dispersion is negligible. L is the length of the DCF. The optical signal after transmission in DCF is

\begin{array}{l} E_{D} (t) = \frac{\sqrt{2}}{2} \sum_{n = 0}^{N - 1} \sqrt{P_{0} (n)} [\frac{- 1}{2} J_{1} (\frac{π A_{R F}}{2 V_{π}}) e^{- j [ω_{n} t - ω_{R F} t + θ (ω_{n} - ω_{R F}) + j \frac{π}{2}]} \\ + J_{0} (\frac{π A_{R F}}{2 V_{π}}) e^{- j (ω_{n} t + θ (ω_{n}))} + \frac{1}{2} J_{1} (\frac{π A_{R F}}{2 V_{π}}) e^{- j [ω_{n} t + ω_{R F} t + θ (ω_{n} + ω_{R F}) - j \frac{π}{2}]}] \end{array}

A waveshaper is used to shape the comb spectrum and separate all the comb lines and their sidebands into two outputs according to the sign of designed filter taps. Denoting P_s(n) to be the optical power of the n_th wavelength after the waveshaper, the received signal after BPD is

\begin{array}{l} I_{o} (t) = A_{D} \cos (\frac{β_{2} L ω_{R F}^{2}}{2}) [\sum_{n, h (n) > 0} P_{s} (n) \cos (ω_{R F} t + n β_{2} L ω_{R F} ω_{r}) - \sum_{n, h (n) < 0} P_{s} (n) \cos (ω_{R F} t + n β_{2} L ω_{R F} ω_{r})] \\ = A_{D} \cos (\frac{β_{2} L ω_{R F}^{2}}{2}) \sum_{n = 0}^{N - 1} sign [h (n) \cdot P_{s} (n)] \cos {ω_{R F} [t -(- n β_{2} L ω_{r})]} \end{array}

where A_D is a frequency-independent coefficient, and can be expressed as

A_{D} = α R Z J_{0} (\frac{π A_{R F}}{2 V_{π}}) J_{1} (\frac{π A_{R F}}{2 V_{π}})

where Z is the load resistance of the photo-detector(PD). α is the loss of the link. R is the responsivity of the PD. By separating all comb lines into two different paths and detecting in a balanced PD, positive and negative taps are achieved.

From (8), The transfer function of the proposed system within frequency range [0, ω_r/2] is expressed as

H (ω) = G (ω) \sum_{n = 0}^{N - 1} [sign (h (n)) \cdot P_{s} (n)] \exp (- j n ω T)

where

T =- β_{2} ω_{r} L

G (ω) = A_{D} \cos (β_{2} L ω^{2} / 2)

Comparing (10) with (2), a programmable microwave photonic filter is realized. The tap value h(n) is achieved from the term sign[h(n)]·P_s(n).

The basic procedure to generate a desired transfer function is:

(1) Generate h(n) of FIR filter using the frequency sampling method and a given tap number N. h(n) is symmetric about n = (N−1)/2.
(2) Shape the OFC spectrum line by line using the waveshaper. Program the amplitude response of each comb line and its sideband according to the absolute value of h(n).
(3) Program the output path of each comb line and its sideband using the waveshaper, according to the sign of h(n).
(4) Detect the signals using a BPD.

For symmetrically distributed filter taps which satisfy h(n) = h(N−1−n), the transfer function is

H (ω) =G(ω) \cdot e^{- j ω T (N - 1) / 2} \cdot \sum_{n = 0}^{N - 1} [si g n (h (n)) \cdot P_{s} (n)] \cos [(\frac{N - 1}{2} - n) ω T)]

G(ω) is a frequency dependent function, which has different expression in different kind of modulation.

G (ω) = {\begin{matrix} A_{S} \exp (j β_{2} L ω^{2} / 2), Single-sideband modulation \\ A_{P} \sin (β_{2} L ω^{2} / 2), Phase-modulation \\ A_{D} \cos (β_{2} L ω^{2} / 2), Double-sideband modulation \end{matrix}

where A_x (x = S, P, D) is a frequency-independent coefficient related to the modulation format.

When a single sideband modulation is used, an additional phase response, which is proportional to ω², is added to the transfer function. In this case, the amplitude response |H(ω)| is in accord with the designed curve, however the condition of linear phase response is no longer satisfied.

When a phase modulation is used, a sinusoidal amplitude response, which has large attenuation in the low frequency range, is added to the transfer function. In this case, the amplitude response of filter has great constraint in the low frequency range.

When a DSB modulation is used, an additional cosine amplitude response is added to transfer function, as shown in Fig. 2. In this case, there is a bandwidth limitation to the amplitude response |H(ω)| due to the dispersion β₂L, meanwhile the condition linear phase response φ(ω) is still satisfied. It is feasible to pre-compensate the amplitude fluctuation within an appropriate frequency range. In Fig. 2, the dispersion coefficient of DCF is 130 ps/(km·nm), and the length of DCF is 1 km. The 3-dB bandwidth is 18 GHz for the additional amplitude response G(ω). The amplitude response |H(ω)| of FIR filter is able to be pre-compensated below 18 GHz.

Fig. 2 Amplitude response G(ω) of DSB modulation caused by the fiber dispersion.

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Considering the situation that the third order fiber dispersion β₃ is no longer negligible and the DSB modulation is used, (10) can be rewritten as

H (ω) = A_{D} \sum_{n = 0}^{N - 1} [si g n (h (n)) \cdot P_{s} (n)] \cos (\frac{β_{2} L ω^{2}}{2} + \frac{n β_{3} L ω^{2} ω_{r}}{2}) \exp (- j (n ω β_{2} L ω_{r} + \frac{1}{6} β_{3} L ω^{3} + \frac{n^{2}}{2} β_{3} L ω_{r}^{2} ω))

Although β₃ is not negligible, it is so small that |nβ₃Lω²ω_r| << |β₂Lω²|,|nβ₃Lω²ω_r| <<1 and β₃Lω³ → 0 in the frequency range from DC to ω_r. So (15) can be simplify as

H (ω) \approx A_{D} \cos (\frac{β_{2} L ω^{2}}{2}) \sum_{n = 0}^{N - 1} P_{s} (n) \exp (- j (n ω β_{2} L ω_{r} + \frac{n^{2}}{2} β_{3} L ω_{r}^{2} ω))

It is obvious that the time delay between adjacent taps is no longer fixed but increase linearly with the tap n, which is expressed as T(n).

T (n) = β_{2} L ω_{r} + \frac{1}{2} β_{3} L ω_{r}^{2} + n β_{3} L ω_{r}^{2}

The existence of β₃ will lead to some deviations between experimental and theoretical response. Considering the real dispersion of the fiber, |β₃/β₂|<10⁻¹⁴. The total number of taps is about 100, so |n²β₃Lω²ω_r| is much smaller than |nωβ₂Lω_r|. For our proposed MPF, the 3_rd and higher order fiber dispersion don't have significant influence.

3. Experimental results

The experimental setup is shown in Fig. 3. The optical frequency comb is generated by an optical frequency comb generator (OptoComb WTEC-01-25). A Mach-Zehnder modulator is biased at π/2 point to realize the DSB modulation. The modulated signal is transported in a 1 km DCF and then amplified in an EDFA. A waveshaper (Finisar 4000S) is used to shape the OFC spectrum and separate all comb lines and their sidebands into two different paths. A balanced photo-detector with 40 GHz bandwidth (u²t BPDV2150R) is used to achieve positive filter taps and negative filter taps. A vector network analyzer is used to measure the transfer function.

Fig. 3 Experimental setup of the proposed filter.

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The spectrum of the optical frequency comb output from comb generator is shown in Fig. 4(a). The repeat frequency of the optical frequency comb is 35 GHz. The spectrum profile of the optical frequency comb is triangular. In order to guarantee enough optical signal to noise ratio (OSNR) for every comb line, the central 101 comb lines with more than 20 dB OSNR are used in the FIR filter. The differences between the designed comb profile and the original one is programmed as the attenuation values in the waveshaper. An example of the positive and negative taps is shown as Figs. 4(b) and 4(c). These taps are generated using frequency sampling design method. To satisfy the linear phase condition, these taps are symmetric about the 51th comb line.

Fig. 4 Optical spectra of (a) the optical frequency comb, and the waveshaper outputs for (b) positive taps, and (c) negative taps.

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For a 1-km DCF with the dispersion coefficient of 130 ps/(km·nm), the delay time T is 36 ps, and the corresponding sampling rate is 27.76 GHz. According to Nyquist sampling theory, we can program the frequency response within 13.88 GHz.

Figure 5 shows 4 basic types of filter response (lowpass, highpass, bandpass and bandstop) generated by our experiment. The parameters, including center frequencies, cut-off frequencies, sidelobe suppression, passband ripples and rejection ratios, of these filters are designed by frequency sampling design method of FIR filter. The theoretical response curves are shown in dashed lines, while the experimental results are represented by solid lines. While designing the FIR filters, the amplitude attenuation caused by DSB modulation is pre-compensated at the same time. Figure 5(a) shows the response of lowpass filters. The fluctuation in the passband is below 3 dB. The cut-off frequencies are 2.78 GHz, 5.55 GHz, 8.33 GHz and 11.10 GHz respectively, which agree with the theoretical values. Figure 5(b) shows the response of four highpass filters with the cut-off frequencies of 2.78 GHz, 5.55 GHz, 8.33 GHz and 11.10 GHz respectively. Figure 5(c) is the response of four bandpass filters. The center frequencies of 2.78 GHz, 5.55 GHz, 8.33 GHz and 11.10 GHz respectively, which accord with the theoretical values. The sidelobe suppression is about 30 dB. Figure 5(d) is the response of four bandstop filters. The center frequencies are 2.78 GHz, 5.55 GHz, 8.33 GHz and 11.10 GHz respectively, and the stopband suppression is more than 15 dB. The phase responses of all these filters are linear in the passband.

Fig. 5 Normalized S21 response of (a) lowpass filters; (b) highpass filters; (c) bandpass filters; (d) bandstop filters. (Solid lines: experimental results. Dashed lines: theoretical curves).

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The accuracy of the designed filter has also been tested. Figure 6 shows the theoretical and experimental results of a typical triple passband filter. In fact, more passbands with arbitrary passband spacing, bandwidth, central frequency and even shape are also practical. However, there are 101 taps used in our experiment, which means only 101 frequency values are able to be designed. An increasing of passbands number will decrease the rejection ratio and roll-off slope. The distribution of the taps is shown as Figs. 4(b) and 4(c). The center frequencies of passband are 2.63 GHz, 5.90 GHz and 11.50 GHz, respectively. In Fig. 6, the blue lines show the theoretical amplitude and phase responses, which describe the ideal transfer function with only 2nd order fiber dispersion. The yellow lines are the simulation results with both 2nd and 3rd order fiber dispersion. The red lines are the experimentally measured amplitude and phase response.

Fig. 6 (a) Normalized amplitude response and (b) phase response of a triple passband filter (Blue line: Response with only 2nd order dispersion; Yellow line: Response with 2nd and 3rd order dispersion; Red line: Experimental result)

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The measured amplitude response shows a good agreement with the theoretical result. However, the measured phase response shows some deviations compared with the theoretical curve, which is mainly caused by 3rd and higher order fiber dispersion. When only the 2nd order fiber dispersion is considered, the theoretical phase response in the stopband is nearly zero. The existence of 3rd and higher order fiber dispersion will worsen the suppression in the stopband, and lead to additional phase response. The theoretical curve with both 2nd and 3rd order fiber dispersion is closer to the experimental result. Though the measured phase response does not match up with the theoretical curve in the stopband, the slope of theoretical curve in the pass band, which plays a much more important role than the absolute value, accords exactly with the experimental result. The measured slopes in all three passbands are 1800 ps, and agree well with the theoretical slope ∂φ/∂ω = T(N-1)/2 = 1800 ps.

4. Summary

In this paper, a novel comb based microwave photonic filter is proposed and demonstrated. The responses of filter, including central frequency, cut-off frequency, bandwidth, sidelobe suppression, passband ripple are all programmable using frequency sampling method of FIR filter. The double sideband modulation and symmetric distribution of filter taps are used to maintain the linear phase condition. A larger number taps of FIR filter may have a better performance such as higher Q factor and higher frequency resolution. To expand the tuning rage, a smaller time delay is needed. Considering the situation that the filter must operate in the range [0, ω_r/2], we can achieve a wider tuning range by increasing the repeat frequency and diminishing the fiber dispersion and fiber length.

In the experiment, we realize a fully programmable filter in the range from DC to 13.88 GHz using 101 taps. Four basic types of filters (lowpass, highpass, bandpass and bandstop) with different bandwidths, cut-off frequencies and center frequencies are generated. Also a triple passband filter is realized in our experiment. To the best of our knowledge, it is the first demonstration of a programmable multiple passband MPF with linear phase response. The Experiment shows good agreement with the theoretical result.

Acknowledgment

This work is supported by National Natural Science Foundation of China (Grant No. 61690194 and Grant No. 61401005).

References and links

1. J. Capmany, J. Mora, I. Gasulla, J. Sancho, J. Lloret, and S. Sales, “Microwave photonic signal processing,” J. Lightwave Technol. 31(4), 571–586 (2013). [CrossRef]

2. R. A. Minasian, “Photonic signal processing of microwave signal,” IEEE Trans. Microw. Theory Tech. 54(2), 832–846 (2006). [CrossRef]

3. J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007). [CrossRef]

4. D. Dolfi, “New trends in optoelectronics for radar, EW and communication systems,” in IEEE International Topical Meeting on Microwave Photonics (2011).

5. B. Ortega, J. Mora, J. Capmany, D. Pastor, and R. Garcia-Olcina, “Highly selective microwave photonic filters based on active optical recirculating cavity and tuned modulator hybrid structure,” Electron. Lett. 41(20), 1113–1135 (2005). [CrossRef]

6. E. Xu, X. Zhang, L. Zhou, Y. Zhang, Y. Yu, X. Li, and D. Huang, “Ultrahigh-Q microwave photonic filter with Vernier effect and wavelength conversion in a cascaded pair of active loops,” Opt. Lett. 35(8), 1242–1244 (2010). [CrossRef] [PubMed]

7. J. Liu, N. Guo, Z. Li, C. Yu, and C. Lu, “Ultrahigh-Q microwave photonic filter with tunable Q value utilizing cascaded optical-electrical feedback loops,” Opt. Lett. 38(21), 4304–4307 (2013). [CrossRef] [PubMed]

8. J. Capmany, D. Pastor, and B. Ortega, “New and flexible fiber-optic delay-line filters using chirped Bragg grattings and laser arrays,” IEEE Trans. Microw. Theory Tech. 47(7), 1321–1326 (1999). [CrossRef]

9. E. Hamidi, D. E. Leaird, and A. M. Weiner, “Tunable programmable microwave photonic fitlers based on an optical frequency comb,” IEEE Trans. Microw. Theory Tech. 58(11), 3269–3278 (2010). [CrossRef]

10. Y. Zhang and S. Pan, “Tunable multitap microwave photonic filter with all complex coefficients,” Opt. Lett. 38(5), 802–804 (2013). [CrossRef] [PubMed]

11. J. P. Yao and Q. Wang, “Photonic microwave bandpass filter with negative coefficients using a polarization modulator,” IEEE Photonics Technol. Lett. 19(9), 644–646 (2007). [CrossRef]

12. Q. Wang and J. P. Yao, “Multitap photonic microwave filters with arbitrary positive and negative coefficients using a polarization modulator and an optical polarizer,” IEEE Photonics Technol. Lett. 20(2), 78–80 (2008). [CrossRef]

13. S. C. Chan, Q. Liu, Z. Wang, and K. S. Chiang, “Tunable negative-tap photonic microwave filter based on a cladding-mode coupler and an optically injected laser of large detuning,” Opt. Express 19(13), 12045–12052 (2011). [CrossRef] [PubMed]

14. M. D. Manzanedo, J. Mora, and J. Capmany, “Continuously tunable microwave photonic filter with negative coefficients using cross-phase modulation in an SOA-MZ interferometer,” IEEE Photonics Technol. Lett. 20(7), 526–528 (2008). [CrossRef]

15. F. Zeng, J. Wang, and J. Yao, “All-optical microwave bandpass filter with negative coefficients based on a phase modulator and linearly chirped fiber Bragg gratings,” Opt. Lett. 30(17), 2203–2205 (2005). [CrossRef] [PubMed]

16. J. Wang, F. Zeng, and J. P. Yao, “All-optical microwave bandpass filter with negative coefficients based on PM-IM conversion,” IEEE Photonics Technol. Lett. 17(10), 2176–2178 (2005). [CrossRef]

17. J. Mora, J. Capmany, A. Loayssa, and D. Pastor, “Novel technique for implementing incoherent microwave photonic filters with negative coefficients using phase modulation and single sideband selection,” IEEE Photonics Technol. Lett. 18(18), 1943–1945 (2006). [CrossRef]

18. Y. Yan and J. Yao, “A tunable photonic microwave filter with a complex coefficient using an optical RF phase shifter,” IEEE Photonics Technol. Lett. 19(19), 1472–1474 (2007). [CrossRef]

19. V. Borja, L. C. Juan, and M. Javier, “Multi-tap all-optical microwave filter with negative coefficients based on multiple optical carriers and dispersive media,” in IEEE International Topical Meeting on Microwave Photonics (2005).

20. N. You and R. A. Minasian, “Synthesis of WDM grating-based optical microwave filter with arbitrary impulse response,” in International Topical Meeting on Microwave Photonics (MWP, 1999), pp. 223–226. [CrossRef]

21. Y. Dai and J. Yao, “Nonuniformly-spaced photonic microwave delayline filter,” Opt. Express 16(7), 4713–4718 (2008). [CrossRef] [PubMed]

22. S. Sales, W. Xue, J. Mork, and I. Gasulla, “Slow and fast light effects and their applications tomicrowave photonics using semiconductor optical amplifiers,” IEEE Trans. Microw. Theory Tech. 58(11), 3022–3038 (2010). [CrossRef]

23. F. Ohman, K. Yvind, and J. Mork, “Slow light in a semiconductor waveguide for true-time delay applications in microwave photonics,” IEEE Photonics Technol. Lett. 19(15), 1145–1147 (2007). [CrossRef]

24. W. Xue, Y. Chen, F. Öhman, S. Sales, and J. Mørk, “Enhancing light slow-down in semiconductor optical amplifiers by optical filtering,” Opt. Lett. 33(10), 1084–1086 (2008). [CrossRef] [PubMed]

25. W. Xue, S. Sales, J. Capmany, and J. Mørk, “Microwave phase shifter with controllable power response based on slow- and fast-light effects in semiconductor optical amplifiers,” Opt. Lett. 34(7), 929–931 (2009). [CrossRef] [PubMed]

26. W. Xue, S. Sales, J. Capmany, and J. Mørk, “Wideband 360 degrees microwave photonic phase shifter based on slow light in semiconductor optical amplifiers,” Opt. Express 18(6), 6156–6163 (2010). [CrossRef] [PubMed]

27. J. Sancho, J. Lloret, I. Gasulla, S. Sales, and J. Capmany, “Fully tunable 360° microwave photonic phase shifter based on a single semiconductor optical amplifier,” Opt. Express 19(18), 17421–17426 (2011). [CrossRef] [PubMed]

28. V. R. Supradeepa, C. M. Long, R. Wu, F. Ferdous, E. Hamidi, D. E. Leaird, and A. M. Weiner, “Comb-based radio frequency photonic filters with rapid tunability and high selectivity,” Nat. Photonics 6(3), 186–194 (2012). [CrossRef]

29. J. Liao, X. Xue, H. Wen, S. Li, X. Zheng, H. Zhang, and B. Zhou, “A spurious frequencies suppression method for optical frequency comb based microwave photonic filter,” Laser Photonics Rev. 7(4), 34–38 (2013). [CrossRef]

30. J. Mora, L. R. Chen, and J. Capmany, “Single-bandpass microwave photonic filter with tuning and reconfiguration capabilities,” J. Lightwave Technol. 26(15), 2663–2670 (2008). [CrossRef]

31. X. Xue, X. Zheng, H. Zhang, and B. Zhou, “Analysis and compensation of third-order dispersion induced RF distortions in highly reconfigurable microwave photonic filters,” J. Lightwave Technol. 31(13), 2263–2270 (2013). [CrossRef]

32. D. Zou, X. Zheng, S. Li, H. Zhang, and B. Zhou, “High-Q microwave photonic filter with self-phase modulation spectrum broadening and third-order dispersion compensation,” Chin. Opt. Lett. 12(8), 080601 (2014). [CrossRef]

33. J. H. Lee, Y. M. Chang, Y.-G. Han, S. B. Lee, and H. Y. Chung, “Fully reconfigurable photonic microwave transversal filter based on digital micromirror device and continuous-wave, incoherent supercontinuum source,” Appl. Opt. 46(22), 5158–5167 (2007). [CrossRef] [PubMed]

34. Y. Yu, S. Li, J. Liao, X. Zheng, H. Zhang, and B. Zhou, “Improving suppression ratio of microwave photonic filters using high-precision spectral shaping,” Opt. Eng. 54(5), 050501 (2015). [CrossRef]

35. L. Li, X. Yi, T. X. H. Huang, and R. Minasian, “High-resolution single bandpass microwave photonic filter with shape-invariant tunability,” IEEE Photonics Technol. Lett. 26(1), 82–85 (2014). [CrossRef]

36. 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). [CrossRef]

37. F. Li, X. Zhang, Q. Meng, L. Sun, Q. Zhang, C. Li, S. Li, A. He, H. Li, and Y. He, “Superconducting filter with a linear phase for third-generation mobile communications,” Supercond. Sci. Technol. 20(7), 611–615 (2007). [CrossRef]

38. D. Sridhar, “Efficient OFDM PAPR reduction method using linear phase variation,” in International Journal of Electronics Communication & Computer Engineering (2011).

39. G. Venanzoni, A. Morini, and M. Farina, “Practical design of a high power L-band linear phase filter for radar applications,” Microw. Opt. Technol. Lett. 53(12), 2717–2721 (2011). [CrossRef]

40. C. Wang and J. Yao, “A nonuniformly space microwave photonic filter using a spatially discrete chirped FBG,” IEEE Photonics Technol. Lett. 25(19), 1889–1892 (2013). [CrossRef]

41. E. J. Norberg, R. S. Guzzon, J. S. Parker, L. A. Johansson, and L. A. Coldren, “Programmable photonic microwave filters monolithically integrated in InP/InGaAsP,” J. Lightwave Technol. 29(11), 1611–1619 (2011). [CrossRef]

42. R. S. Guzzon, E. J. Norberg, J. S. Parker, L. A. Johansson, and L. A. Coldren, “Integrated InP-InGaAsP tunable coupled ring optical bandpass filters with zero insertion loss,” Opt. Express 19(8), 7816–7826 (2011). [CrossRef] [PubMed]

43. P. Dong, N. N. Feng, D. Feng, W. Qian, H. Liang, D. C. Lee, B. J. Luff, T. Banwell, A. Agarwal, P. Toliver, R. Menendez, T. K. Woodward, and M. Asghari, “GHz-bandwidth optical filters based on high-order silicon ring resonators,” Opt. Express 18(23), 23784–23789 (2010). [CrossRef] [PubMed]

44. N. N. Feng, P. Dong, D. Feng, W. Qian, H. Liang, D. C. Lee, J. B. Luff, A. Agarwal, T. Banwell, R. Menendez, P. Toliver, T. K. Woodward, and M. Asghari, “Thermally-efficient reconfigurable narrowband RF-photonic filter,” Opt. Express 18(24), 24648–24653 (2010). [CrossRef] [PubMed]

45. J. Wang, Y. Xuan, A. J. Metcalf, P. Wang, X. Xue, D. E. Leaird, A. M. Weiner, and M. Qi, A multi-channel thermally reconfigurable SiN spectral shaper,” in CLEO:2014, OSA Technical Digest (online) (Optical Society of America, 2014), paper SM3G.4.

46. F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. Tom, and A. M. Weiner, Spectral line-by-line pulse shaping of an on-chip microresonator frequency comb,” in CLEO: 2011 - Laser Science to Photonic Applications (OSA, 2011).

47. D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photonics Rev. 7(4), 506–538 (2013). [CrossRef]

48. T. Kippenberg, “Microresonator-based optical frequency combs,” in Conference on Lasers and Electro-Optics 2012, OSA Technical Digest (online) (Optical Society of America, 2012), paper CF3M.1. [CrossRef]

49. M. A. Foster, J. S. Levy, O. Kuzucu, K. Saha, M. Lipson, and A. L. Gaeta, “Silicon-based monolithic optical frequency comb source,” Opt. Express 19(15), 14233–14239 (2011). [CrossRef] [PubMed]

50. C. Haffner, W. Heni, Y. Fedoryshyn, J. Niegemann, A. Melikyan, D. L. Elder, B. Baeuerle, Y. Salamin, A. Josten, U. Koch, C. Hoessbacher, F. Ducry, L. Juchli, A. Emboras, D. Hillerkuss, M. Kohl, L. R. Dalton, C. Hafner, and J. Leuthold,”All-plasmonic Mach-Zehnder modulator enabling optical high-speed communication at the microscale,” Nat. Photonics 9(8), 525–528 (2015). [CrossRef]

51. L. Alloatti, R. Palmer, S. Diebold, K. P. Pahl, B. Chen, R. Dinu, M. Fournier, J. Fedeli, T. Zwick, W. Freude, C. Koos, and J. Leuthold, “100 GHz silicon–organic hybrid modulator,” Light Sci. Appl. 3(5), e173 (2014). [CrossRef]

Novel programmable microwave photonic filter with arbitrary filtering shape and linear phase

Abstract

1. Introduction

2. Theoretical analysis

3. Experimental results

4. Summary

Acknowledgment

References and links

Cited By

Figures (6)

Equations (17)

Optics Express