Single passband microwave photonic filter using continuous-time impulse response

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

doi:10.1364/OE.19.006231

1. Introduction

Photonic signal processing of microwave signals has attracted considerable interest because it can overcome the inherent bottlenecks of traditional electronic signal processing approaches while also offering attractive features including large time-bandwidth product, and immunity to electromagnetic interference (EMI) [1, 2].

Most of the previously reported microwave photonic filters are fundamentally limited by the presence of multiple harmonic passbands in their frequency response, which intrinsically occurs in all discrete time signal processors [3]. This is undesirable and it significantly restricts the ability of these processors to operate in many signal selection applications that require a wide frequency rejection range. Some techniques, based on a direct synthesis of the microwave filter response via mapping to the shape of an optical filter, have been proposed to obtain a single passband response, by using a combined configuration of a virtually imaged phased array and a spatial light modulator [4], a dual-modulator configuration employing stimulated Brillouin scattering [5], or the use of phase modulation in conjunction with a pair of FBGs [6]. However these approaches have been limited by constraints such as low filtering resolution [4, 6], the presence of a baseband RF response [4], or the inability to implement general RF responses including bipolar taps [4–6]. In the case of spectrum sliced microwave photonic filters, that are attractive in providing a low cost solution for realizing multi-tap filtering [7–9], approaches based on the RF decay effect at high frequencies [9] arising from the linewidth of the spectrum slice have been reported to select the first passband [10–14]. However, these techniques have not demonstrated true single passband filtering because they still retain the baseband response, and they have also exhibited significant attenuation of the first passband e.g. >6 dB, which is not desirable. Moreover since these filters have generated only positive coefficient elements, they cannot realize arbitrary bandpass signal processing functions which require bipolar coefficients. Additionally, these techniques have not utilised the carrier suppression effects within the design process which can add significant benefit to the single passband response.

In this paper, we present the design and synthesis of single passband microwave photonic filters based on a full systematic model, which for the first time investigates the combined effects from both dispersion-induced carrier suppression effects and RF decay effects. This enables the optimum design to be realized, by actually utilizing carrier suppression effects to improve the performance of the filter, for any shape of slice employed. Experimental results demonstrate a high suppression of the multiple unwanted harmonic passbands, while exhibiting only 1.75 dB attenuation of the first passband. Our structure is also capable of realizing bipolar taps, and is programmable through the use of a two-dimensional liquid crystal on silicon (LCoS) pixel array for obtaining reconfigurability [15]. Moreover, we demonstrate frequency tunability, together with a multi-tap, baseband-free square-top, single passband filter, which to our best knowledge is the first demonstration of a programmable microwave photonic filter that displays all these characteristics simultaneously.

2. Single passband microwave photonic filters

Microwave photonic filters can be modeled as linear time-invariant discrete systems. As shown in Fig. 1(a) , their finite impulse responses have a discrete nature and can be expressed as [1]

h (t) = \sum_{n = 0}^{N - 1} h_{n} δ (t - n T)

where N is the number of filter coefficients, T is the basic system delay and h_n is the nth bipolar filter coefficient. The corresponding transfer function can be written as

Fig. 1 Principle of single passband microwave photonics filters. (a) Discrete time impulse response. (b) Frequency response. (c) Low pass filter: time domain, s(t). (d) Low pass filter: frequency domain, S(f_m). (e) Modified impulse response. (f) Modified frequency response.

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H (f_{m}) = \sum_{n = 0}^{N - 1} h_{n} exp (- j 2 π f_{m} n T)

Due to the presence of bipolar filter coefficients, the baseband response that usually exists in a positive-only system is eliminated in the frequency response, as shown in Fig. 1(b). By defining a low-pass filter characteristic, S(f_m) and its inverse Fourier transform time domain signal, s(t) as shown in Fig. 1(d) and Fig. 1(c) respectively, the periodic spectral passbands that normally occur at harmonic frequencies can be suppressed by multiplying H(f_m) by S(f_m). Therefore the modified frequency response, as illustrated in Fig. 1(f), can be derived as,

\bar{H (f_{m})} = H (f_{m}) \cdot S (f_{m})

The modified time domain impulse response, as shown in Fig. 1(e) can be expressed as,

\begin{matrix} \bar{h (t)} = \sum_{n = 0}^{N - 1} h_{n} δ (t - n T) * s (t) \\ = \sum_{n = 0}^{N - 1} h_{n} s (t - n T) \end{matrix}

It can be observed that by converting a designed discrete-time impulse response into a continuous-time impulse response, the periodic spectral passbands at the harmonic frequencies can be suppressed.

3. Dispersion-induced RF effects in microwave photonic filters

The principal issue that makes the synthesis of spectrum-sliced microwave photonic filters more complex, is that the finite width of the spectral slice illuminates a region of the dispersive medium, and this causes a complex interaction in the response. This results in both dispersion-induced fading [16] and RF decay effects occurring simultaneously to introduce a low pass filter characteristic into the frequency response of the processor. Using the systematic theory described in [9], which is applicable to stochastic (i.e. spectrum sliced) input fields, we derive the general RF transfer function of the signal processor, for a quadrature-biased electro-optic modulation assuming a small modulation index [9]

H (f_{m}) = \sum_{n = 0}^{N - 1} h_{n} exp (j 2 π f_{m} n T) \cdot cos (π f_{m}^{2} D) \cdot M (f_{m})

where

h_{n}

is the bipolar filter coefficient, f_m is the modulation frequency,

D = d τ / d f

is the group delay slope of the chirped fiber Bragg grating (CFBG). T is the tap delay, and the dispersion induced RF fading due to finite slice width is given as

\begin{matrix} M (f_{m}) = \int_{f_{-}}^{f_{+}} ϕ_{o} (f) \exp (j 2 π f_{m} f \cdot D) d f \\ = (\frac{1}{D}) \int_{t_{-}}^{t_{+}} ϕ_{o} (t / D) \exp (- j 2 π f_{m} t) d t \end{matrix}

with

t_{+} = f_{+} \times D

and

t_{-} = f_{-} \times D

. M(f_m) can be treated as the Fourier transform of the normalized power spectrum

ϕ_{o} (t / D)

, which is expected to be symmetrical and identical for each spectral slice to avoid mismatched filter coefficients. It has a low-pass filter behavior, dependent on the normalized spectrum width with upper frequency (f₊) and lower frequency (f_-), and the group delay slope (D).

From Eq. (5), we observe that the transfer function of the spectrum sliced microwave photonic filter has three terms. The first item in Eq. (5) corresponds to the transfer function of a standard FIR filter. Windowing techniques can be used to tailor the filter coefficient for increasing the filter suppression ratio and for reconfiguring the filter shape, by programming the output power of the spectrum-sliced sources. The second term corresponds to the RF decay due to well-known carrier suppression effect, which is intrinsic to systems that have group delay elements employing dispersion characteristics and which operate with optical signals in a double-sideband modulation scheme. The last term $M (f_{m})$ corresponds to the RF decay arising from the spectral slice width, and accounts for the complex interaction between the finite width of the spectral slice and the dispersive medium. The equation reveals that the RF degradation in the frequency response is independent of the number of filter taps, coefficient weights, and free spectral range (FSR).

By comparing Eq. (5) to Eq. (3) and Eq. (4), it can be seen that the spectrum sliced microwave filter is equivalent to the continuous-time impulse response. Therefore the single passband filter can be regarded as a special case of spectrum sliced signal processors. Equation (5) essentially describes the general analytic transfer function of this class of filters. The low pass filter characteristic, inherent in Eq. (5), that selects the first passband and suppresses the higher order periodic passbands is given by

S (f_{m}) = \cos (π f_{m}^{2} D) M (f_{m})

and comprises the carrier suppression effect and the spectrum-slice induced RF fading effect

M (f_{m})

.

4. Design and analysis

The structure of the true single passband microwave photonic filter is illustrated in Fig. 2 . Amplified spontaneous emission (ASE) from an erbium doped fibre amplifier is used as the broadband source. It is spectrally sliced using a two-dimensional array of LCoS pixels, which can be programmed to provide optical filters with arbitrary centre wavelengths, bandwidths and attenuations [15]. The broadband optical field illuminates the diffraction grating, which disperses each wavelength to a different vertical column on the LCoS. Calculated phase images are then applied to this spatially dispersed signal via the voltage dependent retardation of each pixel in the column. As each wavelength is manipulated by a specific vertical column through advanced phase modulation techniques of the phase front, arbitrary attenuations of different optical wavelengths are obtained by accordingly steering a portion of light to a discard location instead of one of the two output ports. The LCoS acts as optical slicing filters to the ASE source and also as an optical wavelength selective switch that routes wavelengths to one of the two output ports. An input microwave signal is introduced into the system by modulating the spectral slices via a dual-input electro-optic modulator (EOM), and bipolar-coefficients are generated due to the modulation scheme which causes 180° phase difference between the optical fields that come from the two different input ports. The modulated optical signals then travel into a dispersive medium, i.e. CFBG to obtain wavelength dependent group delays and the output light is detected on a photodetector (PD), where an output microwave signal is obtained. The transfer function of the filter is given by Eq. (5).

Fig. 2 Schematic of the true single passband microwave photonic filter.

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The design strategy involves selecting the optimum spectrum slice width in order to tailor the RF degradation effect so that low-pass filter effect comprising both the carrier suppression effect and the spectrum-slice induced RF fading effect, according to Eq. (7), introduces an RF frequency roll-off that suppresses the high-order periodic passbands. This is realized by locating the center frequencies of these unwanted periodic passbands at frequency points that correspond to a large attenuation (ideally null response) of the designated RF low-pass filter curve, through the manipulation of the optical spectral slice shape and its bandwidth. In addition, it is also required that the filter does not have a baseband response in order to realize truly single passband filtering. This is achieved by including negative tap filter coefficients. As an example, we show the design of a 53-tap microwave photonic filter by starting with the standard FIR term contained in the Eq. (5). Figure 3(a) shows the case for uniform bipolar tap coefficients, and Fig. 3(d) shows its corresponding frequency response. Figure 3(b) shows a Gaussian apodized bipolar tap coefficient profile, and Fig. 3(e) shows its corresponding frequency response. Finally, Fig. 3(c) shows bipolar coefficients corresponding to a flat-top filter response, and Fig. 3(f) shows its corresponding frequency response.

Fig. 3 Biploar filter coefficients design. a) Uniform. b) Gaussian. c) Flat-top. Corresponding frequency response. d) Uniform. e) Gaussian. f) Flat-top.

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In the experiments described in Section 5, the LCoS based spectral slice shape is described by [17]

ϕ_{o} (f) = {[erf (\frac{(\frac{B}{2} - f)}{8.41 \times 10^{9}}) - erf (\frac{(- \frac{B}{2} - f)}{8.41 \times 10^{9}})]}^{2}

where

erf (x) = (2 / \sqrt{π}) \int_{0}^{x} e xp (- x^{2}) d x

and B is defined as the device bandwidth (B), equivalent to the 6 dB optical bandwidth for B > 42 GHz. By inserting Eq. (8) into Eq. (7), the dispersion-induced low-pass filter characteristic curve can be numerically evaluated. Figure 4 shows four different optical spectrum-slice widths corresponding to a bandwidth (B) of 40 GHz, 60 GHz, 80 GHz, and 100 GHz, at the center wavelength of 1549.70 nm. We take the group delay slope of dispersive medium to be 335 ps/nm, which is the same as that used in the experiment of Section 5. Figure 5 shows the resulting RF low-pass filter characteristic calculated using Eq. (7), which includes both the spectrum-slice induced RF fading effect and the carrier suppression effect. It can be noted that periodic nulls are present in the responses shown in Fig. 5, and the location of these nulls can be controlled by selecting the spectrum slice width, by means of the two design equations: Eq. (7) and Eq. (8).

Fig. 4 Four different optical spectrum-slice widths corresponding to a bandwidth (B) of (a) 40GHz (b) 60GHz (c) 80GHz (d) 100GHz.

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Fig. 5 RF low-pass filter characteristic, including both the RF fading effect due to the source spectral slice width and the carrier suppression effect, for four different optical spectrum-slice widths of 40GHz, 60GHz, 80GHz, and 100GHz.

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The periodic harmonic passbands that normally occur in FIR filter, as shown in Fig. 3, can be suppressed by utilizing the RF low-pass characteristic curve and designing the spectrum slice bandwidth so that the harmonic passbands are located at the frequencies where strong attenuations occur in RF low-pass characteristic curve. The suppressed kth passband can be calculated from Eq. (7) and is given by

S_{k} = \cos (π {[(k - 0.5) \cdot FSR]}^{2} \cdot D) \cdot M ((k - 0.5) \cdot FSR)

where k = 1,2,3…, and S₁ denoted the first single passband that is to be preserved. The higher-order passbands are designed to be strongly attenuated by means of the RF low-pass characteristic curve, which is realized by selecting the optimum spectrum sliced width in conjunction with the group delay slope of the dispersive medium that is used. Taking the group delay slope of dispersive medium to be 335 ps/nm, which is the same as that used in the experiment of Section 5, and designing for a single passband filter at 5.56GHz, which is the same as that used in the experiment, the optimum design can be found through Eq. (8) and Eq. (9). Figure 6 shows the calculated suppression characteristics for various spectral splice bandwidths for the first (desired) passband and the next second to fourth (undesired) passbands. Figure 6(a) shows the suppressions for the first four passband if the carrier suppression effect is not included, as was done in [14]. For comparison, Fig. 6(b) shows the suppressions for the first four passband if the carrier suppression effect is included. It can be seen that there is a significant difference, and it is important to include the carrier suppression effect. In fact, it can be seen that the carrier suppression effect actually helps in realizing a greater overall suppression performance. For example, it can be observed from Fig. 6 that the minimum suppression level of the third passband is greatly improved from 10dB in Fig. 6(a) to 35dB in Fig. 6(b) with the assistance of the carrier suppression.

Fig. 6 Suppression characteristics at different spectral splice bandwidths for the first (desired) passband and the next second to fourth (undesired) passbands (a) without carrier suppression effect and (b) with carrier suppression effect.

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The optimum design is obtained by choosing a spectral slice bandwidth that simultaneously minimizes the attenuation of the first (desired) passband and which maximizes the suppression of the higher order passbands suppression relative to the first passband. In this case, the optimum spectral slice width can be found to be 49GHz from Fig. 6(b). For illustration, the suppressions of the first four passbands for four different spectrum slice bandwidths are shown in Fig. 7 . From Fig. 7(b) it can be seen that the 49GHz spectrum slice bandwidth provides the best design, resulting in only a small attenuation of 1.75dB for the first passband while at the same time suppressing the higher order passbands by more than 29dB. It can also be noted that this optimum spectral slice width of 49GHz, is different to the design guideline reported in [14] that proposed choosing a finesse of 2 to provide the most effective suppression, which while true for the sinusoidal and Gaussian cases considered in [14] which also excluded carrier suppression effects, does not hold for the general case. In fact the inclusion of the carrier suppression effect and the use of general spectral slice shapes actually helps in improving the overall response, which is the reason why the present results demonstrate a high suppression of the multiple unwanted harmonic passbands, while exhibiting only 1.75 dB attenuation of the first (wanted) passband, compared to over 6 dB attenuation of the first passband reported in [14].

Fig. 7 Passband suppressions due to the dispersion-induced RF low-pass characteristic for spectrum sliced bandwidths (B) of: (a) 40GHz, (b) 49GHz, (c) 65GHz and (d) 80GHz.

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5. Experimental results

Experiments were first conducted to verify the theoretical model of RF low-pass characteristic curve, as described by Eq. (7). In order to measure the transfer functions of the microwave photonic filter itself over the relevant frequency range, the response roll-off due to the cables, the EOM and the photodetector were calibrated out. Different spectrum sliced sources were generated using the programmable LCoS device (Finisar WaveShaper 4000E), and the RF transfer functions were measured after photodetection to determine the experimental RF low-pass characteristic curve. The experimental setup was similar to that shown in Fig. 2. Only one slicing filter was activated for obtaining a single optical power spectrum slice with various specified bandwidths. The optical field was then modulated by the input RF signal before being applied to the dispersive group delay line (335ps/nm), and the output was detected by a photodetector. By comparing the swept input RF signals, the RF transfer functions were measured from the output signals on a network analyser, and this provided the RF low-pass characteristic curve for each spectrum slice width. The theoretical calculations were obtained by evaluating the measured optical spectrum through Eq. (7).

First, a spectrum slice bandwidth of 80GHz used, as shown in Fig. 8(a) . The spectrum width and the slope of the dispersive CFBG induce the RF low-pass characteristic response, including the RF fading due to slice width and the carrier suppression effect, and this was measured on the network analyzer. The measured RF response corresponding to the 80GHz spectrum sliced width source is shown in Fig. 8(b), together with a comparison to the theoretical predictions. Excellent agreement can be seen. Figure 8(c) and 8(d) shows the results for a 100GHz spectrum sliced width source. Again, a very good match is observed between the measurements and predictions, which confirm the validity of the model presented to calculate the RF low-pass characteristic curve.

Fig. 8 Spectrum slice bandwidth of (a) 80GHz (b) the corresponding RF low-pass characteristic curve. Spectrum slice bandwidth of (c) 100GHz (d) the corresponding RF low-pass characteristic curve.

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Next, experiments were conducted to demonstrate high-order FIR filters with a single passband response. The design realized a microwave photonic filter having 53 taps, with its first passband centered at 2.28GHz (which corresponded to a fundamental delay time of 180ps and an FSR 5.56GHz). Using the results obtained in Section 4, the optimum spectral slice width of 49GHz was employed, and 53 spectral slices were generated by the LCoS multiple optical filtering with identical 49GHz bandwidths. The spacing between successive two slices was programmed according to group delay slope of CFBG to obtain the constant system delay of 180ps. Internal switching function routed the slices to either input port of a commercial dual-input EOM, according to the required tap polarity. The non-flat ASE output curve was compensated by programming the attenuations of LCoS optical filters. In addition, different weighting profiles for the filter coefficients were implemented, to demonstrate reconfigurability. Figure 9(a) shows the measured optical power spectrum for a uniform alternately bipolar tap filter coefficient profile, and Fig. 9(b) shows the corresponding measured frequency response normalized to the first passband. The measured 3-dB bandwidth of the RF bandpass filter is 0.09GHz. It can be observed that the baseband resonance has been eliminated, and that the higher order periodic passbands, expected at 8.34GHz and 13.9GHz, have been suppressed by over 29dB. This confirms the design strategy. Figure 9(c) shows a Gaussian windowed alternately bipolar tap filter coefficient profile, and Fig. 9(d) shows the corresponding measured frequency response. The RF bandpass filter has a 3-dB bandwidth of 0.12GHz, and again the baseband response is eliminated and over 29dB of suppression over sidebands and higher-order periodic passband is demonstrated. Figure 9(e) shows the measured optical power spectrum for bipolar filter coefficients that result in a flat-top filter response, and Fig. 9(f) shows the corresponding measured frequency response. The RF bandpass filter had a 3-dB bandwidth of 0.35GHz and passband ripples of less than +/−0.35dB. Again the baseband response has been eliminated, and in addition to the flat-top response, the single passband microwave photonic filter exhibited over 29dB suppression of higher-order periodic passbands. Zoom-in snapshots of three single passband responses spanning 1.5-4GHz are provided in Fig. 10 together with a comparison to the theory. In all cases, stable RF responses were observed. The stability is mainly dependent on the power fluctuation of the broadband power source, however the broadband source used obtained from the ASE source (Amonics) had less than +/− 0.02dB power variation over 8 hours and no stability issues in the filter response were observed.

Fig. 9 53-tap high-order microwave photonic filters with (a) uniform bipolar tap profile and (b) the corresponding measured RF response; (c) Gaussian weighted bipolar tap profile and (d) the corresponding measured RF response; (e) bipolar filter coefficients that result in a flat-top filter response and (f) the corresponding measured RF response.

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Fig. 10 Measured frequency response (1.5-4GHz span). (a) Uniform weighted bipolar coefficients (b) Gaussian weighted bipolar coefficients. (c) Flat-top weighted bipolar coefficients

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Finally, we experimentally demonstrated the frequency tuning ability of the flat-top single passband filter. The measured RF response of the microwave photonic filter exhibiting tunability is shown in Fig. 11 , which had passband ripples of less than +/− 0.35dB. This was obtained by changing the system delays to 180ps, 190ps, 200ps, 210ps and 225ps, which corresponded to the tuned centre frequencies of the single passband filter shown in Fig. 11. The tuning was realized by modifying the RF low-pass characteristic curve and altering the wavelength separation between any two spectral slices, and was accomplished using only software control without changing the rest of the structure.

Fig. 11 Measured RF responses of the flat-top microwave photonic filter showing tunability.

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6. Conclusion

This paper has presented a single passband microwave photonic filter that has high resolution, with multiple-taps and baseband-free response as well as exhibiting a square-top passband, tunability and reconfiguration. A full systematic model for single passband microwave photonic filters has been used to account for arbitrary spectrum slice shapes, which for the first time has investigated the combined effects from both the dispersion-induced carrier suppression effect and the RF decay effect due to the spectrum slice width and has enabled the optimum design to be realized by utilizing the carrier suppression effect to improve the filter performance. Experimental results have demonstrated a high suppression of the multiple unwanted harmonic passbands, while exhibiting only 1.75 dB attenuation of the first passband. Our structure is also capable of realizing bipolar taps, and is programmable through the use of a two-dimensional liquid crystal on silicon (LCoS) pixel array, and demonstrates frequency tunability. To our best knowledge, this is the first demonstration of a programmable microwave photonic filter that simultaneously displays a single passband together with a multiple-tap, baseband-free, square-top, as well as exhibiting tunability and reconfiguration.

Acknowledgments

The work was supported by the Australian Research Council. The authors gratefully acknowledge valuable discussions with Dr. M. Roelens and Dr. S. Poole from Finisar Australia.

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Single passband microwave photonic filter using continuous-time impulse response

Abstract

1. Introduction

2. Single passband microwave photonic filters

3. Dispersion-induced RF effects in microwave photonic filters

4. Design and analysis

5. Experimental results

6. Conclusion

Acknowledgments

References and Links

Cited By

Figures (11)

Equations (9)

Optics Express