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A new technique that increases the free spectral range (FSR) of a recirculating delay line filter, is presented. The concept is based on a time-compression unit, which is used in conjunction with a frequency-shifting recirculating loop that generates multi-spectral characteristics, and the idea exploits the optical wavelength domain by wavelength-to-time mapping of the taps using an oppositely time-oriented dispersive element so that the taps travel different lengths, to time compress the tap separation. This technique solves, for the first time, the long-standing problem of the small FSR limitation in recirculating microwave photonic delay line filters, opening the way to realize the main functionalities required in microwave photonic filters. Experimental results are presented which demonstrate a large 100-fold increase in the FSR of the bandpass filter response.
©2012 Optical Society of America
1. Introduction
Photonic signal processing, using photonic approaches to condition microwave and radio frequency (RF) signals, is attractive due to the inherent advantages of high time-bandwidth product, immunity to electromagnetic interference (EMI), and its capability to realize dynamic tuning over multi-GHz bandwidths [1,2]. Additionally, since in-fibre signal processors are inherently compatible with fibre optic microwave systems, they can provide connectivity with in-built signal conditioning.
A range of photonic signal processing structures have been reported to realize microwave photonic filters [3–14]. However, finite impulse response (FIR) approaches have difficulty in realizing a large number of taps, which is required for obtaining high-resolution filtering. Infinite impulse response (IIR) approaches are very well suited to generate a multitude of taps using a simple structure, for realizing sharp bandpass filter responses. However, they have always suffered from the important limitation of a low free spectral range (FSR) response. This can be understood from the fact that the FSR is inversely proportional to the loop length of the amplified recirculating delay line IIR structure, and there is a practical limit to the minimum loop length that can be implemented i.e. previously reported IIR recirculating delay line filters [7–14] have exhibited an FSR of around 50 MHz or less. This is a severe limitation for practical applications. In addition to the high-FSR and high-Q requirements, microwave photonic filters need to operate with low noise, and to be tunable with fast control. To date there have been no reports of microwave photonic filters that can meet all these requirements.
In this paper we report a new technique to significantly increase the FSR of an IIR recirculating delay line filter, which also features a very compact structure together with high resolution, tunable filtering and low noise operation. The concept is based on a time-compression unit, which is used in conjunction with a frequency shifting recirculating loop that generates multi-spectral characteristics. This technique solves, for the first time, the long-standing problem of the small FSR limitation in IIR recirculating microwave photonic delay line filters, opening the way to realize the main functionalities required in microwave photonic filters. Experimental results are presented which demonstrate a large 100-fold increase in the FSR of the bandpass filter response.
This paper is organized as follows. The principle of the new technique to increase the FSR of the recirculating delay line filter is presented in Section 2. The analysis of the filter transfer characteristic and the design of the time compression unit to realize a high-resolution large-FSR bandpass filter response are described in Section 3. Experimental results that demonstrate a large-FSR microwave photonic bandpass filter, are presented in Section 4. Finally, conclusions are given in Section 5.
2. Principle of filter FSR increase technique
The structure of the new increased-FSR recirculating delay line processor is shown in Fig. 1 . Light from a laser modulated by the input RF signal is injected into a frequency shifting amplified recirculating delay line (FS-ARDL) loop. It has been previously shown that the FS-ARDL loop can generate a low-noise, high-resolution bandpass filter response without phase induced intensity noise [14], however this previous structure was limited to a low FSR of only 45 MHz [14]. The FS-ARDL loop generates many delayed optical signals with different optical frequencies, and our idea is based on exploiting the optical wavelength domain by wavelength-to-time mapping of the taps to time compress their separation through the use of an oppositely time-oriented dispersive component. This is done by the time compression unit shown in Fig. 1, which in general comprises a dispersive element. As an example, the implementation is shown using a chirped fibre Bragg grating (CFBG) in Fig. 1.
Fig. 1 . Structure of the increased-FSR recirculating delay line filter with a time compression unit; τ << T.
The laser wavelength is aligned to be located at the band-edge of the CFBG. The CFBG functions as a wavelength-dependent time delay element, so that taps with different wavelengths are reflected at different points along the CFBG. The dispersion slope of the CFBG is designed so that the first tap which passes straight through the optical coupler is reflected at the farthest point along the CFBG. The second tap which circulates once inside the FS-ARDL loop is reflected at a nearer point compared to the first tap, and so on. Hence signals which undergo little delay in the FS-ARDL loop are delayed longer in transiting the CFBG, while conversely signals that are delayed longer in the FS-ARDL experience shorter delays. This equalizes the delay times, and consequently shortens the unit time delay between adjacent taps. Thus the FSR of the microwave photonic filter is increased. The amount of FSR increase depends on the dispersion slope of the CFBG. The steeper the dispersion slope, the more time compression can be achieved and consequently the larger the FSR that can be realized, as discussed in the design procedure described in the next section. It can be noted that the time compression unit can also be inserted within the FS-ARDL loop instead of after the loop, to reduce the tap separation and obtain a large FSR filter response. However in that case, the circulator and the long CFBG cannot be integrated using LiNbO3 together with the other components. Furthermore, the time compression unit inside the loop will introduce more loop loss; therefore a longer EDFA is required for loss compensation. This results in a longer FS-ARDL loop length and hence a longer CFBG is required to obtain the same FSR improvement compared to that when the time compression unit is outside of the FS-ARDL loop.
3. Analysis and simulation
The transfer function for the FS-ARDL structure by itself is given by
where κ is the optical coupler coupling ratio; g is the optical amplifier gain; i is the tap number; N is the total number of taps generated by the FS-ARDL loop that are reflected by the CFBG; l is the optical frequency shifter insertion loss; f is the RF frequency, T = (nL)/c is the delay time corresponding to the FS-ARDL loop length L, n is the fibre refractive index, c is the speed of light in vacuum; tff is the optical modulator insertion loss, Plaser is the laser output optical power, Vπ is the optical modulator switching voltage, and ℜ is the photodiode responsivity. For the FS-ARDL structure by itself, the group delay expression of the ith tap is given bywhere λi is the wavelength of the ith tap: λi = λ0 + iΔλ in which λ0 is the laser wavelength and Δλ is the wavelength shift for each circulation; τc is the time it takes for the light to travel the common path from the modulator, passing the coupler to the photodetector. The time separation between the taps in this case is T = (nL)/c, and hence the filter FSR isWe now consider the time compression and FSR increase. We introduce the time compression unit (which in this case is a CFBG) that has a general group delay expression given bywhere GD0 is a constant, and DCFBG is the dispersion slope of the CFBG. Now cascading the FS-ARDL with the time compression unit, the group delay expression of the ith tap is given byThe time separation between the taps in this case is T – |DCFBGΔλ|, and hence the transfer function for the signal processor shown in Fig. 1 becomeswhere lcir is the insertion loss of the optical circulator, and RCFBG is the reflectivity of the CFBG. The RF fading induced by chromatic dispersion has been neglected, and it can be eliminated by using single side-band (SSB) modulation.The overall filter FSR is given by
The FSR multiplication factor M is given by
From Eq. (8), it can be seen that in order to achieve a large value for the FSR multiplication factor M, it is necessary to design the CFBG characteristic so that |DCFBGΔλ| approaches (nL)/c.The design process to meet a given FSR increase requirement proceeds as follows. For the FS-ARDL having an original FSR0 value and a desired increased value of FSR1, together with the specified Q-factor and hence number of taps N, an optical frequency shift of Δf (or Δλ), where Δf = 2FSR1, is chosen to avoid aliasing assuming SSB modulation. Then the required dispersion slope of the CFBG is obtained from
As an example for illustration, consider an FS-ARDL that has a loop length of 25 cm. This can be implemented using an LiNbO3 integrated frequency shifter and an erbium doped waveguide amplifier (EDWA) or a semiconductor optical amplifier (SOA). From Eq. (2), the filter FSR is only 800 MHz for this FS-ARDL structure. To increase the FSR to 10 GHz, the frequency shift is chosen to be 20 GHz, corresponding to a wavelength shift of Δλ = 0.16 nm for each circulation. Hence, from Eq. (9) a time compression unit with a CFBG having a dispersion slope of 7.14 ns/nm is needed at the output of the frequency shifting loop. To obtain Q-factor of 150 and using Kaiser windowing with α = 1.3 to obtain a filter suppression level of more than 30 dB, 182 taps are needed and the effective spectral span is 14 nm. The length of a CFBG that gives DCFBG = 7.14 ns/nm with a spectral span of 14 nm is 10 m. Even though such a long CFBG is challenging to fabricate, it is commercially available. Chirped fibre Bragg gratings manufactured with a length of > 10 m have been reported [15]. It should also be noted that the CFBG reflective spectrum can be designed to have a window function to suppress the sidelobes amplitudes [16]. As the taps of the FS-ARDL filter have different wavelengths, each of them will experience a different amount of reflection from the CFBG. Therefore tap amplitudes with a windowing function can be realized. A windowing function has been used to improve the performance of the FS-ARDL filter frequency response [17]. Figure 2(a) shows the original limited FSR value of the FS-ARDL filter response, and Fig. 2(b) shows how the FSR has been increased to 10 GHz by the inclusion of the time compression unit.Fig. 2 Simulated frequency response of the 182-tap bandpass filter formed by the FS-ARDL loop (a) without the time compression unit and (b) with the time compression unit.
We have investigated the effects of the non-ideal group delay ripple (GDR) of the CFBG on the filter response. Figure 3(a) shows the effect on the filter bandwidth of the 182-tap FS-ARDL bandpass filter having an FSR of 10 GHz including the time compression unit, for increasing CFBG GDR amplitude. It can be seen the filter has a very good tolerance, and if the GDR of the CFBG is within ± 15 ps, the –3 dB bandwidth of the bandpass filter stays quite constant at 66 MHz and thus the Q factor is maintained around 150. Further simulations were performed to investigate the changes in the filter stopband rejection level for different CFBG GDR values. Figure 3(b) shows the effect on the stopband rejection level of the 182-tap FS-ARDL bandpass filter including the time compression unit, for increasing CFBG GDR amplitude. It can be seen that there is quite a good tolerance, and if the CFBG GDR is within ± 5 ps, the filter maximum stopband rejection level is maintained at or above 30 dB. CFBGs with a group delay ripple of <5 ps and a spectral width of 36 nm have been reported [18].
Fig. 3 (a) The –3 dB bandwidth and (b) the stopband rejection level of the 182-tap FS-ARDL bandpass filter including the time compression unit versus the CFBG group delay ripple.
We have also investigated the results that can be obtained based on an actual grating specification for a commercially available grating, and have carried out simulations based on the specifications of an actual CFBG provided by Promixion. The frequency response of a 182-tap filter having an FSR of 3 GHz formed by a FS-ARDL and a long CFBG having an actual GDR of ± 8.3 ps over the operating range which was provided by the manufacturer, was simulated and is shown in Fig. 4 . It was found that the −3 dB bandwidth of the filter frequency response remains unchanged while the stopband rejection level is around 24 dB. This shows that the commercially available long CFBG can be used to achieve a high-performance large-FSR bandpass filter response. The filter stopband rejection level performance can be improved by using CFBGs with lower GDR, which has been demonstrated [18].
Fig. 4 Simulated frequency response of the 182-tap FS-ARDL bandpass filter including a commercially available CFBG with a GDR of ± 8.3 ps over the operating range.
This structure also has the advantage of providing wideband tuning capability of the bandpass filter center frequency by simply changing the frequency shift value. Since the time separation between the taps is given by T – |DCFBGΔλ|, simply changing the optical frequency shift and hence the wavelength shift Δλ, changes the unit time delay and thus the bandpass filter center frequency. Since the optical frequency shifter which is based on a single-sideband suppressed carrier (SSB-SC) modulator [19] is an electro-optic device, its response time is very fast and high-speed tuning of the filter at nanosecond speed can be obtained. Moreover, the tuning is continuous and it is wideband. Figure 5 shows the frequency tuning characteristics of the 182-tap FS-ARDL bandpass filter including the time compression unit, for different optical frequency shifts. An octave tuning range from 5.3 GHz to 9.8 GHz can be seen, which is obtained by changing the optical frequency shift from 13.75 GHz to 19.375 GHz.
Fig. 5 Simulated frequency response of the 182-tap FS-ARDL bandpass filter including the time compression for different wavelength shifts (corresponding to different optical frequency shifts).
4. Experimental results
Experiments were setup to demonstrate the proof of principle. The experimental setup of the new technique for increasing the FSR of the recirculating delay line filter is shown in Fig. 6 . Since a CFBG was not available, the time compression unit was implemented instead by a WDM fibre Bragg grating (FBG) array which performed the same function at the operating wavelengths. The WDM grating array was connected in parallel via an optical coupler, with the distance separation between consecutive gratings being Δl as shown in Fig. 6. The center wavelength of each FBG was aligned with the wavelength of the tap emanating from the FS-ARDL loop. Hence, each tap was reflected by a different FBG and travelled a different path to the photodetector. By controlling the grating separations, the tap positions in the filter impulse response can be varied and the time separation between taps can be compressed.
A narrow-linewidth laser was used as the optical source and its wavelength was 1552.9 nm. The CW light from the laser was launched into a quadrature-biased electro-optic modulator (EOM) (EOSpace), which was driven by the RF input signal. The modulated optical signal was injected into the FS-ARDL loop formed by a 50:50 optical coupler, which comprised a 15 GHz optical frequency shifter implemented using an SSB-SC modulator (Sumitomo), an erbium-doped fibre amplifier (EDFA) using a 1 m long high-concentration erbium-doped fibre that was pumped by a high power 980 nm pump laser, and an optical bandpass filter to ensure that the taps generated by the FS-ARDL loop were in the 1552 nm band matching the grating wavelengths. The polarization controllers (PC) were used to ensure that the light was aligned to the modulator input polarization and the SSB-SC frequency shifter. The FS-ARDL loop length was 10 m, hence the original FSR of the recirculating delay line filter was 20 MHz.
The experiment was designed to demonstrate an FSR increase by a factor of 100. A ten-tap filter was used to verify the principle of operation using ten FBGs having a wavelength separation of 0.12 nm (15 GHz) at the center wavelengths of 1552.072 nm, 1552.192 nm, 1552.312 nm, 1552.432 nm, 1552.552 nm, 1552.672 nm, 1552.792 nm, 1552.912 nm, 1553.032 nm and 1553.152 nm . The FBG bandwidth was around 7.5 GHz so that each FBG reflected just one tap. The FBGs were arranged in a parallel configuration so that each reflected tap experienced a similar amount of loss when it passed through the time compression unit. An optical coupler was used to split the optical signal at the output of the FS-ARDL loop into ten different paths, and an EDFA was placed before and after it to compensate for the coupler losses. Each path length to the FBGs was designed to be Δl longer than the adjacent one, and this length difference Δl enabled control of the unit time delay of the overall structure. For instance the first tap, which does not circulate the FS-ARDL loop, has the wavelength of the laser λ1, and after passing through the optical coupler can only be reflected by FBG1. Letting lc be the length of the common path from the EOM, to the 50:50 coupler and then to the circulator, which is travelled by every tap, and denoting l1 as the length between the optical circulator and FBG1, then the time it takes for the first tap to reach the photodetector is
The second tap, which circulates once inside the FS-ARDL loop, has the wavelength λ2 = λ1 + Δλ, and after passing through the optical coupler can only be reflected by FBG2. Designing the length from the optical coupler to the FBG2 to be l2 = l1 – Δl, then the time it takes for the second tap to reach the photodetector isSimilarly, the time for the mth tap to reach the photodetector photodetector isHence, the time difference between two adjacent taps reaching the photodetector isThe loop length L is fixed, as determined by the length of the components inside the loop, however the FBG pathway difference Δl can be adjusted. Here the objective is to demonstrate an FSR increase by a factor of 100, and since the original FSR was 20 MHz hence the final FSR should be 2 GHz. Therefore we set L – 2Δl to be 10 cm, so that the FSR of the overall structure is 2 GHz.First, the frequency response of the FS-ARDL filter alone was measured for reference on a network analyser. The results are shown in Fig. 7 , and the filter exhibits an FSR of 20 MHz.
Next, the frequency response of the FS-ARDL together with the time compression unit was measured on the network analyser. The results are shown in Fig. 8 , which shows that the FSR of the filter has been increased to 2 GHz. This verifies that the inclusion of the time compression unit increases the FSR of the optical delay line based bandpass filter by a factor of 100-fold. The filter response exhibited stable performance even though the laser source had a narrow linewidth, which showed that it was free of coherent interference effects. The predicted response of the FS-ARDL cascaded with the time compression FBG array unit is also shown in Fig. 8. Good agreement between theory and measurements can be seen.
Fig. 8 Measured and simulated frequency response of the FS-ARDL filter together with the time compression unit.
5. Conclusion
A new technique that increases the FSR of a recirculating delay line filter, has been presented. In addition to significantly increasing the FSR by two orders of magnitude, it also features the ability to be implemented in a compact structure, with high-resolution performance, tunable filtering, and coherence free low noise operation. The concept is based on a time-compression unit, which is used in conjunction with a frequency-shifting recirculating loop that generates multi-spectral characteristics, and the idea exploits the optical wavelength domain by wavelength-to-time mapping of the taps using an oppositely time-oriented dispersive component such as a grating to time compress the tap separation. The grating acts as a wavelength dependent time delay element which causes the taps that have different optical frequencies to travel different lengths, and by designing the dispersion slope and the frequency shift, the length differences compensate for the long unit time delay of the loop, thus increasing the frequency response FSR of the overall structure.
This technique solves, for the first time, the long-standing problem of the small FSR limitation in recirculating microwave photonic delay line filters, opening the way to realize the main functionalities required in microwave photonic filters. Experimental results have been presented which demonstrate a large 100-fold increase in the FSR of the bandpass filter response. The new all-optical microwave photonic filter offers large-FSR bandpass filtering with coherence-free low-noise performance, which can be integrated in optical fibre microwave transmission systems.
Acknowledgment
This work was supported by the Australian Research Council. The authors gratefully acknowledge Xudong Wang for his assistance in the experiments.
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