Distortion-free spectrum sliced microwave photonic signal processor: analysis, design and implementation

Liwei Li; Xiaoke Yi; Thomas X. H. Huang; Robert A. Minasian

doi:10.1364/OE.20.011517

1. Introduction

Microwave photonic signal processing using optical delay line structures is attractive for processing high speed signals, because it can overcome inherent electronic bottlenecks caused by limited sampling speeds in conventional electrical signal processors. It also offers some significant features such as immunity to electromagnetic interference and large time-bandwidth product [1, 2].

Microwave photonic filters based on finite impulse response (FIR) are particularly of interest because of their inherent flexibility in realizing filters having arbitrary transfer functions [3–6]. A common FIR topology comprises an array of lasers that are modulated and then applied to a linearly chirped fiber Bragg grating (FBG) which forms a discrete time microwave signal processor after photodetection [3]. The use of spectrum slicing of a broadband optical source for the replacement of an optical laser array provides a flexible and scalable solution for realizing multiple taps which is necessary to achieve high resolution signal processing [7–9]. However, a critical issue with the performance of conventional spectrum sliced microwave photonic filters is that it suffers from significant high frequency degradation. This occurs because of the substantial width of the spectral slice, which results in a broad region of the dispersive medium being illuminated rather than a point. This causes a complex interaction in the response, which creates RF frequency response degradation that occurs in addition to and which can dominate over the well-known carrier suppression effect [10]. Although various spectrum slicing techniques have been reported, including Fabry-Perot filters, arrayed waveguide gratings and super-structured FBGs [7–9], in order for spectrum sliced microwave photonic filters to be used practically, it is essential to obtain effective solutions to eliminate this undesirable RF frequency response degradation.

We have reported the first approach based on a multichannel chirped FBG to overcome the dispersion induced RF degradation, which demonstrated an 8-tap filter with discrete tunability [11]. However, the free spectrum range (FSR) of the RF filter was limited by the fixed wavelength spacing of the multichannel chirped FBG [11, 12]. Although cascaded gratings with synchronized tuning have been introduced to improve the tunability of the microwave photonic spectrum sliced filter, this approach is limited to a few taps: e.g. a 5-tap filter was demonstrated in the experiment [12]. In order to increase the filtering resolution, a free-space optical-based approach was recently proposed, and a proof of concept experiment demonstrated the spectrum sliced filtering for a 20-tap FIR filter with the elimination of dispersion induced RF distortion [13]. However, this did not include a detailed theoretical analysis together with experimental verifications for characterizing the functionalities of the spectrum slicing and group delay control for the modulated optical light source, which is essential in order to optimize filter coefficients for high frequency RF filtering. Moreover, the previous approaches [11–13] were restricted to only positive coefficients, which preclude the realization of general RF responses; and also they were limited to static operation i.e. without the ability to switch the filtering function.

In this paper, we propose a new switchable microwave photonic filter based on spectrum slicing of modulated broadband source, which can generate bipolar coefficients for arbitrary RF responses. It offers tunability, reconfigurabiliy, switchability, and the elimination of dispersion induced RF distortion while employing a single device. Detailed theoretical modelling is presented to analyze the filter design for different dispersion schemes. This modeling differs from previous analyses on spectrum sliced microwave photonic filters [10], which focused on the scheme of spectrum slicing before an electro-optic modulator (EOM). In this novel filter study, the modulated broadband optical source is spectrum sliced after a dual-output EOM that generates a modulated bipolar broadband source, and spectrum slicing is subsequently implemented while simultaneously setting the dispersion value within each channel to the opposite value of the dispersive delay element in order to compensate the undesired RF degradation, within one unit. This technique also enables RF filter switchability via software control. Experimental results are presented which verify the theoretical model and demonstrate a multi-tap RF filter with significant improvement of the passband response at high frequencies. The RF response improvement of the new microwave photonic filter for various FSR values and spectrum slice bandwidths is discussed, for both an ideal linear group delay line and for the experimental fiber delay line that has second order group delay. Finally, we demonstrate a switchable bipolar filter with tunability, and a programmable square-top filter configured with more than 30 dB stopband attenuation that displays filter reconfigurability.

2. Filter topology

Topology of the new spectrum sliced microwave photonic filter is shown in Fig. 1 . A broadband light source is intensity modulated by a dual-output EOM, which introduces 180° RF phase difference between the modulated light at its dual output ports. Then the modulated bipolar broadband source is launched into port 1 and port 2 of a device that is called a dispersion controlled spectrum slicing filter, which generates spectrum slices with dispersion controllability after the modulation stage. The light then propagates through a linear time delay element, and is finally detected on a photodetector.

Fig. 1 Structure of the microwave photonic processor.

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The dispersion controlled spectrum slicing filter has two input ports that are connected to the modulated bipolar broadband optical source, and it has one output port that feeds into the dispersive group delay element. It is required to generate counter-modulated spectrum slices with desired centre wavelengths, bandwidth, attenuation and dispersion management. By programming single port (either port 1 or port2) or both input ports of the slicing filter, positive taps or bipolar taps can be obtained respectively. Since the dispersion value within each slice is set to be the opposite of the dispersive delay element, it consequently results in a flat group delay region within each channel which eliminates the dispersion induced RF distortion. A free-space optical system based on a two-dimensional array of liquid crystal on silicon (LCoS) pixels can be used to implement these functions [14]. The counter-modulated broadband optical light sources enter the two input ports of the system, which are dispersed to the wavelength-dependent columns of the LCoS pixels. By varying the voltage-controlled phase across the vertical and horizontal dimension of the LCoS, the spectral phase and intensity of the optical signals are simultaneously manipulated. In addition, the optical phase pattern enables the achievement of spectral routing or blocking of the optical signals from either one of the two input ports to the output port of the slicing filter, which forms multiple counter-modulated spectrum slices. Consequently, the configuration can realize tunability, reconfigurability, switching, and dispersion induced RF degradation compensation simultaneously in the microwave photonic filters.

3. Filter principle

The modulated bipolar broadband light source is achieved by amplitude modulating a broadband light source via a dual-output EOM, whose modulation envelope can be described as [15]

s_{0} (t) = \cos (\frac{π}{2 V_{π}} (V_{R F} \cos (2 π f_{m} t) + V_{b i a s} + k V_{π}))

where

V_{π}

is the modulator switching voltage,

V_{R F}

is the amplitude of the RF signal,

f_{m}

is the modulation frequency,

V_{b i a s}

is the bias voltage, which requires

V_{b i a s} = V_{π} / 2

for maximum linearity,

k

is a binary polarity factor,

k = 0

and

k = 1

for the light from the output port 1 and 2 of the dual-output EOM respectively.

After modulation, the counter-modulated broadband light source propagates through the dispersion controlled spectrum slicing filter, which is followed by a linearly dispersive element that is described by $τ (f) = a_{1} f + a_{0}$ , where $f$ is the optical frequency, $a_{1}$ represents the group delay slope and $a_{0}$ is the delay offset. The modulated spectrum slices are created by the slicing filter locating with equal channel spacing ( $Δ f$ ) to maintain a basic time delay of microwave photonic filter, and the FSR of the filter is $F S R = 1 / (a_{1} Δ f)$ , which can be controlled by adjusting the spacing between two consecutive spectrum slices .

We consider $N$ taps of bipolar spectrum sliced sources such that each slice has the central optical frequency $f_{n}$ , and slice amplitude $g_{n} (f)$ , where $n$ = 1, 2, …, $N$ . In order to avoid additional degradation in the RF frequency response caused by unbalanced spectrum slice shapes [10], we design all the spectrum slices to have identical normalized amplitude $g_{0} (f)$ . Thus the slice amplitude can be expressed as $g_{n} (f) = \sqrt{W_{n}} g_{0} (f - f_{n})$ , where $W_{n}$ is the optical power coefficient of the $n^{t h}$ spectrum slice.

Without applying the dispersion compensation function of the dispersion controlled spectrum slicing, the $n^{t h}$ RF filter coefficient is given by

{\tilde{L}}_{n} (f_{m}) = s i g n_{n} W_{n} \int_{f_{n -}}^{f_{n +}} g_{0} (f - f_{n}) [g_{0} (f - f_{n} + f_{m}) e^{j a_{1} π f_{m}^{2}} + g_{0} (f - f_{n} - f_{m}) e^{- j a_{1} π f_{m}^{2}}] e^{j 2 π f_{m} a_{1} (f - f_{n})} d f

where

f_{n -}

and

f_{n +}

are the minimum and maximum frequencies of the

n^{t h}

optical spectrum slice,

s i g n_{n}

denotes the polarity of the

n^{t h}

slice, which can be either + 1 or –1 to achieve positive or bipolar tap programmability. Here, the filter coefficient

{\tilde{L}}_{n}

accounts for the complex interaction between the finite width of the modulated spectral slice bandwidth and the dispersive medium within the slice channel that results in an additional degradation in the frequency response of the processor. Note that the carrier suppression effect is embedded in the filter coefficient

{\tilde{L}}_{n}

, which is presented by the exponential terms with the parameter of the group delay slope

(a_{1})

. Therefore it cannot be extracted as a single term, in contrast to the filter coefficient appearing in the previous modelling [10]. In order to enable the high frequency operation in spectrum sliced microwave photonic filters, it is essential to obtain effective solutions to eliminate this undesirable RF degradation.

By applying the dispersion compensation function through the dispersion controlled spectrum slicing filter, the localized dispersion seen by each slice channel is compensated, while the constant time delay step $(Δ t)$ of the microwave photonic filter is maintained as indicated in Fig. 1. This enables the FIR filter to operate free from RF degradation, and the amplitude response of the novel bipolar spectrum sliced microwave photonic filter can be expressed as

| H (f_{m}) | = | \sum_{n = 1}^{N} L_{n} (f_{m}) e^{j 2 π f_{m} n Δ t} |

where L_{n} (f_{m}) = s i g n_{n} W_{n} \int_{f_{n -}}^{f_{n +}} g_{0} (f - f_{n}) [g_{0} (f - f_{n} + f_{m}) + g_{0} (f - f_{n} - f_{m})] d f

L_{n}

is the

n^{t h}

filter coefficient that is a real number coefficient. It can be seen that Eq. (4) is not dispersion related since the impact of group delay slope

(a_{1})

is eliminated via the dispersion controlled spectrum slicing filter. By programming the optical power of spectrum slices, the conventional windowing technique can be used to tailor the filter coefficient to increase the sideband suppression ratio, and this enables the analysis of microwave photonic filter transfer functions with arbitrary spectrum slice shape, power coefficient and polarity.

Figure 2(a) shows the simulated baseband-suppressed filter response for 33 bipolar rectangular spectrum slices having a width of 72 GHz that propagate through a delay line having a dispersion of −150 ps/nm, without applying the dispersion compensation function through the slicing filter. The RF degradation increases rapidly with frequency, which significantly limits the filter response. More than 41 dB degradation is observed at the third passband (14.67 GHz). After applying the dispersion compensation function through the dispersion controlled spectrum slicing filter, the performance can be significantly improved as shown in Fig. 2(b). Similar results can also be obtained for baseband microwave photonic filters that have positive taps only.

Fig. 2 Simulated filter response using 33 bipolar rectangular spectrum slices having a width of 72 GHz: (a) without dispersion compensation (b) with dispersion compensation.

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4. Experimental results and discussion

Experiments were carried out based on the scheme shown in Fig. 1. The broadband source was obtained from an erbium-doped fiber amplifier and after modulation by the dual-output EOM with 20 GHz modulation bandwidth (EOSPACE Inc.) to obtain modulated bipolar signals it was launched into port 1 and port 2 of the dispersion controlled spectrum slicing filter, which was implemented using a commercially-available WaveShaper (Finisar). The device enables multiple programmable slicing filters (minimum bandwidth setting of 10 GHz) within a wavelength range of 1527.4 nm to 1567.5 nm, which determines the largest number of filter coefficients to be realised, given the FSR of the RF filter and the dispersive delay element. Note that there exists a trade off between the maximum achievable group delay slope and the slicing filter bandwidth, where a four-pass configuration can be incorporated to increase the dispersion bandwidth product [16]. A length of optical fiber (Corning MetroCor) was used in the experiment to approximate the linear group delay line and to provide the wideband time delay function for achieving a large number of taps. The group delay of the optical fiber was measured and it showed a dispersion slope factor of $1.9 p s / n m^{2}$ . The average dispersion ( $d$ ) of the fiber within C-band operation was $- 150 p s / n m$ , and the corresponding time delay could be quite accurately described using a second order function in terms of optical frequency $(f)$ as $τ (f) = b_{2} f^{2} + b_{1} f + b_{0}$ , where $b_{2}$ is the quadratic coefficient which is known as fiber second order group delay factor, $b_{1}$ is the group delay linear coefficient, and $b_{0}$ is the fiber group delay offset.

A constant filter time delay step $(Δ t)$ can be obtained to avoid RF response distortion by adjusting the spacing between two consecutive spectrum slices. Here $Δ t$ is given by $Δ t = τ (f_{n + 1}) - τ (f_{n})$ , where $f_{n + 1}$ and $f_{n}$ represents the central optical frequency of the ${(n + 1)}^{t h}$ and $n^{t h}$ spectrum slice respectively, $n$ = 1, 2, …, $N$ . The required optical frequency allocation to the slices is obtained by solving the recursive relations substituting the fiber time delay quadratic equation $τ (f)$ , and is given by

f_{n + 1} = f_{n} + [- (f_{n} + 0.5 b_{1} / b_{2}) + \sqrt{f_{n}^{2} + 0.25 b_{1}^{2} / b_{2}^{2} + b_{1} f_{n} / b_{2} + Δ t / b_{2}}]

Figure 3(a) shows the predicted wavelength locations of the 33 channels for the Corning MetroCor fiber used in the experiment, for a filter time delay step of 170 $p s$ . The measured optical spectrum slices obtained using the slicing filter, based on the wavelength allocation and for uniform weighting are shown in Fig. 3(b), and this shows slightly increased channel spacing towards the longer wavelength end in order to provide a constant basic time delay between consecutive taps.

Fig. 3 (a) Simulated wavelength locations of the 33slices; (b) Measured optical spectra of the spectrum slices.

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First, a microwave photonic filter with only positive coefficients was configured by propagating the modulated broadband light source propagated into only one port of the dispersion controlled spectrum slicing filter. Each slice channel was programmed to have a 3dB channel bandwidth of 0.41 nm and a group delay slope of $150 p s / n m$ , which is opposite to the average dispersion of the fiber delay medium. Figure 4 shows the RF filter response measured by a vector network analyser (Agilent N5230A), which displays a filter FSR of 5.87 GHz. In comparison to the case when dispersion compensation is not applied, the RF attenuation degradation at the passband frequencies of 5.87 GHz, 11.74 GHz, and 17.61 GHz is significantly improved by 2.5 dB, 14.7 dB and 25.3 dB respectively. Zoom-in snapshots of the three passband responses are also provided in Fig. 4 together with a comparison to the theory. Excellent agreement can be seen between the theoretical prediction and experimental results in all cases.

Fig. 4 Measured characteristics of the microwave photonic filter with only positive coefficients (a) from 0.01GHz to 20GHz (b)(c)(d) snapshots for three passbands. ——Measured ——Calculated

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Next, a bipolar-coefficient microwave photonic filter, which suppressed the baseband response, was obtained by applying the modulated bipolar broadband light source to both input ports of the dispersion controlled spectrum slicing filter. This realised a bipolar-tap microwave filter which had the same FSR of 5.87 GHz, without changing the rest of the setup. Figure 5 shows the measured RF filter response. In comparison to the case when dispersion compensation is not applied, the RF attenuation degradation at the passband frequencies of 2.93 GHz, 8.81 GHz, and 14.67 GHz was improved by 0.5 dB, 6.5 dB and 39.3 dB respectively, which significantly improved the filter high frequency performance. The excellent agreement between the measurement and theoretical results verifies the analytical theory, as shown in Fig. 5, which also displays zoom-in snapshots of the passband responses.

Fig. 5 Measured characteristics of the bipolar-coefficient microwave photonic filter (a) from 0.01GHz to 20GHz (b)(c)(d) snapshots for three passbands. —— Measured ——Calculated.

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We also investigated the effect of the second-order group delay of the dispersive optical fiber on the RF performance of the microwave photonic filter, by deriving the filter coefficient considering both the second order and linear group delay factor of the dispersive element, which is given by

\begin{array}{l} L'_{n} (f_{m}) = s i g n_{n} W_{n} \int_{f_{n -}}^{f_{n +}} g_{0} (f - f_{n}) [\begin{array}{l} g_{0} (f - f_{n} + f_{m}) e^{j (2 b_{2} f + (b_{1} - d)) π f_{m}^{2}} \\ + g_{0} (f - f_{n} - f_{m}) e^{- j (2 b_{2} f + (b_{1} - d)) π f_{m}^{2}} \end{array}] \\ \times e^{j 2 π f_{m} [b_{2} (f^{2} - f_{^{n}}^{2}) + (b_{1} - d) (f - f_{n})]} d f \end{array}

Here the dispersion value within each channel of the dispersive controlled spectrum slicing filter is set as –d, which is the opposite of the average dispersion of the fiber. It can be seen the residual secondary delay term generates a phase factor to the filter coefficient

(L'_{n} (f_{m}))

, which causes a complex interaction to the filter response.

Figure 6 shows a comparison between the RF passband responses of the 33-tap bipolar filter with an FSR of 5.87 GHz and around the third passband over a span of 12.5-17 GHz, when an ideal linear time delay line is used and when the actual experimental fiber delay line exhibiting second order group delay, are used as the delay medium. A difference of 0.23 dB between the two RF responses is observed at the third filter passband. The RF responses at the lower frequency passbands (< 8.81 GHz) are also compared and a maximum RF difference of less than 0.06 dB is observed. These results show that the fiber second order group delay effect is negligible for frequencies below 20 GHz, once the multiple spectrum slices are relocated to maintain a constant delay step. Note that the typical dispersion slope of Corning standard single mode optical fiber is only $0.8 p s / n m^{2}$ for accumulating the $150 p s / n m$ dispersion value, which is even less than the Corning MetroCor fiber used in the experiment.

Fig. 6 Comparison between the RF passband responses of the 33-tap bipolar filter, when an ideal linear time delay line is used and when the actual experimental fiber delay line, which exhibits second order group delay, are used as the delay medium.

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We further investigated the filter performance improvement for different FSR values and for different spectrum slice bandwidths, for either an ideal linear optical delay line or for the MetroCor second order fiber group delay line used in the experiments. Figure 7 shows the RF response amplitude improvement of the simulated 33-tap bipolar-coefficient filter response, over the first few passbands for various FSR values of 5 GHz, 7 GHz, 9 GHz and 11 GHz respectively. The results show that the RF response is significantly improved by implementing the dispersion controlled slicing filter, especially at high frequency. Note that the RF filter based on the experimental fiber delay line performs quite similarly to the RF filter that uses the ideal linear optical delay line, for the first three passbands. Further improvement of the RF amplitude passband response can be achieved by reducing the second order group delay factor of the dispersive fiber. By comparing Figs. 7(a) and 7(b) it can be seen that over 11dB further improvement at the fourth passband of the 7 GHz FSR (at 24.5 GHz), can be realized if the second order group delay factor in the dispersive optical fiber is compensated, and this can be achieved by using cascaded optical fibers [17]. Nevertheless, for both cases, the RF response improvements at the fourth filter passband are all beyond 25 dB, which proves that this filter design is effective for different FSR values.

Fig. 7 Simulated 33-tap RF response improvement for the first to the fourth passbands for different filter FSR values: (a) using an ideal linear delay line (b) using the experimental delay line that has second order group delay effects. Circles, 5 GHz; squares, 7 GHz; triangles, 9 GHz; crosses, 11GHz.

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We also investigated the RF response improvement for different bandwidths of the spectrum slices. The results are illustrated in Fig. 8 . In the simulation, a super-Gaussian shape was used to model the shape of the experimental spectrum sliced source, and an RF filter with an FSR of 11GHz was used as an example in the simulation. Again, the new microwave photonic filter enables the achievement of a significant RF improvement at the filter passbands. For the RF frequencies of less than 27.5 GHz, the RF improvement of the filter based on the two schemes, the ideal linear delay line and the experimental fiber delay are comparable. Moreover, the simulation results show that at the fourth passband RF frequency, which is as high as 38.5 GHz, the RF response improvement using the experimental MetroCor fiber delay line can be further improved by around 10 dB if the second group delay factor is reduced.

Fig. 8 Simulated 33-tap RF Response improvement for the first to the fourth passbands for different bandwidth spectrum slices, with an FSR of 11 GHz: (a) using the ideal linear delay line (b) using the experimental delay line that has second order group delay effects. Circles, 30 GHz; squares, 50 GHz; triangles, 70 GHz; crosses, 90 GHz.

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The tunability and reconfigurability of the microwave photonic filter was demonstrated via software control of the spectrum slice center frequencies and the corresponding tap weight. Here, a 33-tap microwave photonic filter was implemented to demonstrate the passband tunability. This was achieved by decreasing the spectrum slice spacing by programming the slice center frequencies through the dispersion controlled spectrum slicing filter; while keeping each channel dispersion value the same. Figure 9(a) shows the filter response of a 33-tap tuned from 5.87 GHz to 11.03 GHz. By routing every other spectrum slice to the alternative port of the slicing filter, a switched baseband-suppressed filter with 33 bipolar taps was obtained and is presented in Fig. 9(b). Excellent agreement can be seen from the comparison between the measured and calculated RF response.

Fig. 9 Measured 33-tap filter RF response (a) tuned to a passband of 11 GHz (b) switched baseband-suppressed filter with 33 bipolar taps. —— Measured —— Calculated.

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Finally, a 33-tap bipolar coefficient microwave photonic filter that had a flat-top response, and which had a switchable capability was demonstrated. A Gaussian-sinc windowing function which synthesizes both positive and negative coefficients was applied by adjusting the amplitude of the dispersion controlled optical slicing filter to spectrally filter the modulated broadband light source directed from port 1 and port 2 of the dual-output EOM respectively. Figure 10 shows RF measurements along with the filter tap profiles illustrated in the insets. A square-shape RF response centered at 11.03 GHz and having a 3 dB bandwidth of 0.99 GHz is displayed in Fig. 10(a). It has a shape factor of 1.6, which is defined as the ratio of −20 dB to −3 dB bandwidth. The filter has over 30 dB stopband rejection and has a flat-top passband. The amplitude of the filter passband ripple is less than 0.12 dB. By switching every other optical slice to the alternative port of the dispersion controlled slicing filter in order to alternate the polarity of these filter coefficients, the RF filter can be switched off, as shown in Fig. 10(b).

Fig. 10 Measured 33-tap square-top RF filter response (a) bipolar Gaussian-sinc profile (b) switched bipolar Gaussian-sinc profile.

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5. Conclusion

A new switchable microwave photonic filter based on a novel spectrum slicing technique has been presented. The processor enables programmable multi-tap generation with general transfer function characteristics and offers tunability, reconfigurabiliy, and switchability. It is based on connecting a dispersion controlled spectrum slicing filter after the modulated bipolar broadband light source, which consequently creates multiple spectrum slices with bipolarity, and compensates dispersion induced RF degradation simultaneously within a single device. A detailed theoretical model for this microwave photonic filter design has been presented. Experimental results have been presented which verify the model, and demonstrate a 33 bipolar-tap microwave filter with significant reduction of passband attenuations at high frequencies. The RF response improvement of the new microwave photonic filter has been investigated, for both an ideal linear group delay line and for the experimental fiber delay line that has second order group delay and the results have shown that this new structure is effective for RF filters with various FSR values and spectrum slice bandwidths. Finally, we have demonstrated a switchable bipolar filter that has a square-top bandpass filter response with more than 30 dB stopband attenuation that can be switched on/off via software control.

Acknowledgments

The research was supported by the Australian Research Council. The authors also would like to acknowledge Shanghai Jiaotong Open Project program of the State Key Laboratory of Advanced Optical Communication Systems and Networks, and valuable discussions with Dr. M. Roelens, Dr. S. Frisken and Dr. S. Poole from Finisar Australia.

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Distortion-free spectrum sliced microwave photonic signal processor: analysis, design and implementation

Abstract

1. Introduction

2. Filter topology

3. Filter principle

4. Experimental results and discussion

5. Conclusion

Acknowledgments

References and Links

Cited By

Figures (10)

Equations (6)

Optics Express