A Single Source Microwave Photonic Filter Using a Novel Single-mode Fiber to Multimode Fiber Coupling Technique References and Links

In this paper we present a fully tunable and reconfigurable single-laser multi-tap microwave photonic FIR filter that utilizes a special SM-to-MM combiner to sum the taps. The filter requires only a single laser source for all the taps and a passive component, a SM-to-MM combiner, for incoherent summing of signal. The SM-to-MM combiner does not produce optical interference during signal merging and is phase-insensitive. We experimentally demonstrate an eight-tap filter with both positive and negative programmable coefficients with excellent correspondence between predicted and measured values. The magnitude response shows a clean and accurate function across the entire bandwidth, and proves successful operation of the FIR filter using a SM-to-MM combiner. Photonic microwave filtering using coherently coupled integrated ring resonators, " Microw. High-quality online-reconfigurable microwave photonic transversal filter with positive and negative coefficients, " IEEE Photon. Microwave photonic filter with tunability, reconfigurability and bipolar taps, " Electron. Incoherent bipolar tap microwave photonic filter based on balanced bridge electro-optic modulator, " Electron. High-performance microwave transversal filter using fiber Bragg grating arrays, " IEEE Photon. Fibre optic microwave and millimetre-wave filter with high density sampling and very high sidelobe suppression using subnanometre optical spectrum slicing, " Electron. Lett. Photonic microwave filter based on spectrum slicing with reconfiguration capability, " Electron. Photonic notch filter without optical coherence limitations, " J. Integrated photonic microwave bandpass filter incorporating a polymeric microring resonator, " Jpn. Signal beating elimination using single-mode fiber to multimode fiber coupling, " Opt. Low-loss many-to-one fiber couplers with few or single-moded inputs and a multi-mode output, " Fiber and Integrated Opt.


Introduction
The application of optical fiber as photonic signal processors to process high-speed RF data is becoming more important as bandwidth and reconfigurability demands increase [1].Indeed, microwave photonic filters (MPFs) have the advantage of having wide bandwidth operation, low loss across the entire bandwidth, and immunity to electromagnetic interference (EMI) [2].The bandwidth of coaxial cables is limited by frequency-dependent losses which increase with higher frequencies so that traditional RF and electronics cannot practically handle wide bandwidths in the GHz range.Fortunately, processing in the optical domain takes advantage of the broadband capabilities and low dispersion of optical delay schemes [2].Moreover, MPFs can be made to be extremely lightweight and compact, with full tunability and reconfigurability.
MPFs can be grouped into two broad categories, single-source MPFs (SSMPFs) and multi-source MPFs (MSMPFs) [2].MSMPFs operate in the regime of incoherence, defined by systems in which the coherence time of the multiple optical sources is much less than the time delays of the filter.MSMPF's are optically phase independent and are unaffected by environmental conditions such as temperature variations, mechanical vibrations, etc, and for this reason most of the architectures implemented to date are based on this method [2].Initially, MSMPF's could only be implemented with positive coefficients, severely limiting their operation, but innovative schemes for implementing negative coefficients have since been proposed [3][4][5].Fully tunable and programmable weighting using free space methods such as spatial light modulators [3] and multi-port programmable wavelength processors [4] have been demonstrated.A simple technique using a 1X2 dual output Mach-Zehnder modulator (MZM) to achieve negative weighting by using phased-inversed dual outputs is shown in [5].
Drawbacks to this approach are that MSMPF architectures are spectrally inefficient, can become complicated, and are not practical for scaling [2].MSMPFs filters require either a wavelength-specific optical source for each tap or complicated spectral slicing techniques [6][7][8][9][10].MSMPF's using arrays of distributed-feedback (DFB) lasers and wavelength-division multiplexed (WDM) filters have been demonstrated with one laser per tap [6].In addition, many techniques for slicing a broadband optical source have been proposed such as using a Fabry-Perot filter comb [7], fiber-Bragg gratings (FBGs) [8], and optical filters [9].However, these methods spectrally slice a broadband source generated from an amplified spontaneous emission (ASE) noise source, which has random fluctuation of phase and amplitude that contributes to noise and instability in the system [10].
The other category of MPFs is SSMPFs.To date, most SSMPFs operate in the coherent regime, in which the coherence time of the filter source is much longer than the filter's time delays and rely on coherent field summations to create the filter [2].Unlike MSMPFs, SSMPFs such as this suffer from optical coherence noise known as beating during summation, and are extremely sensitive to the environment.Some new developments in integrated photonics to avoid optical interference effects, such as techniques using coupled silica ring resonators [1], double-pass modulation [11], CMOS ring resonators [12], polymeric microring resonators [13], and silica-waveguide technologies [14], have allowed for some development in the field of coherent MPFs.Unfortunately, these techniques are limited to simple few-tap filters and are still affected by phase sensitivity due to environmental conditions.Because of this reason, SSMPFs based on coherent schemes are not generally implemented in practice [2].
However, if optical interference effects can be fully suppressed, SSMPFs have great potential to be simpler, requiring only a single arbitrary narrow linewidth laser for a multipletap filter, and can be easily implemented in existing telecommunications systems [1].They have the potential be scaled more easily than MSMPFs.Negative coefficients are intrinsic to the system and are implemented using simple phase shifts to create destructive interference.
In this paper we propose a SSMPF that combines the advantages of MSMPFs and SSMPFs while retaining none of their disadvantages.We implement a filter using a singlemode-to-multimode (SM-MM) fiber combiner to combine the coherent taps of our filter using an incoherent method.Our filter has full control over its profile and uses thermo-optic controlled attenuators to provide 20 dB range of weighting and tunable fiber delay lines.Moreover, our SSMPF uses a 1X2 complementary, π-shifted Mach-Zehnder modulator (MZM) to implement coefficients usually used in incoherent MSMPFs [5].
The novelty of our finite impulse response (FIR) filter is in its use of SM-MM fiber coupling to avoid coherent interference beating [15,16].Our FIR filter is phase-insensitive and the effect of interferometric beating is insignificant.By utilizing a SM-to-MM fiber combiner, our filter overcomes the traditional roadblocks of coherent SSMPFs while keeping the primary advantage of conventional MSMPFs: robustness to interferometric beating.
Moreover, unlike MSMPF's that need either a laser array or to employ spectral slicing, our filter retains the primary advantage of SSMPF's: one laser source is used for a simple filter architecture.Indeed, the primary advantage of our FIR filter is size, weight, and power.In most practical applications a large number of taps are needed [2], and in photonic beamformers the need for filters with large arrays of many taps exist.WDM schemes begin to become bulky with a large number of taps as one laser source is needed for each tap, and spectral slicing methods are limited by the available spectral bandwidth as well as the spectral sliced resolution of each tap.We have the ability to easily scale the filter using just one laser (paired with an amplifier).Thus, our filter can provide an improvement over both ordinary MSMPF and SMMPF schemes.

Theory
Our architecture is based on the novel use of a single-mode to multimode (SM-to-MM) fiber combiner, which was first proposed by the coauthors in [15], to construct a multi-tap FIR filter.The device is an all-passive fiber-based approach to prevent undesired beating during signal merging and detection [15].The main principle behind the combiner is the signal coupling from several individual single-mode fibers to different spatial positions or modes inside a multimode fiber.The combiner offers the advantage of phase-insensitivity and coupling without optical interference.
Optical interference in the form of beating between two optical signals operating at the same wavelength has previously been a limiting factor that degrades the filter frequency response profile.Typically single-mode fused couplers are used to combine signals.However, when two coherent optical signals are combined using a conventional fused coupler, the resulting coupling is phase sensitive and depends on the relative phase difference of the inputs.Signals from different input fibers generally have different instantaneous phases due to different lengths of travel through the fiber as well as environmental changes such as temperature and pressure.Thus, the fluctuation in the relative phase between the two inputs results in instantaneous changes in the coupling ratio and the output power of the coupler, resulting in interference noise or beating at the output.This optical beat noise is severe and cannot be overlooked since it has a squared power relationship.
Instead of combining individual input signals using a single-mode fused coupler, the SMto-MM combiner combines the inputs from multiple single-mode fibers into a single piece of multimode fiber.A traditional SM-SM coupler only allows a portion of the input signal to be launched into the output, but the SM-MM combiner allows the entire signal to be launched into the output.It has been shown in [15] and [16] that by launching signals at slightly different spatial positions, different inputs are coupled into different modes of the multimode fiber.The input signals are coupled into the multimode fiber with minimal or no coherent interaction.The combined signal at the output of the combiner can be completely captured by a photodetector with a sufficiently large active area.The SM-to-MM combiner is insensitive to relative phase differences between signals and thus can avoid any optical beat noise [15].
There is an upper limit on the scalability of the SM-MM combiner, since the outputs of the each the single-mode fibers must be able to fit inside the multimode fiber.For a 62.5 μm multimode fiber, the combiner can combine up to 56 fibers assuming that the multimode fiber has ~500 modes, and for a 100 μm fiber, a maximum of 113 outputs can be combined assuming ~1000 modes [16].Indeed, this is the main limitation of the device, and architecture, as there is a hard limit to its scalability.The limitation can be overcome by using two or more such devices combined with a MM-MM coupler, which, of course, increases complexity.
The SM-MM combiner we use in this experiment has an input consisting of eight standard single-mode fibers that do not require any polarization control.The output consists of a 100 μm multimode fiber.The eight SM fibers are arranged in a 2X4 array with eight 300 μm collimating lenses.The SM-MM combiner has an insertion loss of < 1 dB.
Figure 1(a) shows the experimental setup for measuring the suppression of beat noise using the SM-to-MM combiner [15].A continuous-wave (CW) light source is modulated by a 1.25 Gb/s pseudorandom binary sequence (PRBS) electrical signal using an electro-optic intensity modulator.The non-return-to-zero (NRZ) is split into two different branches using a SM-SM optical coupler.The two branches are then combined using a traditional SM-SM coupler for Case I and the SM-MM combiner for Case II.A comparison on signal beating will be made between the two cases [15].
The input PRBS signal is shown in Fig. 1(b).From Fig. 1(c), we can see that a significant amount of beating can be observed at the output for a conventional SM-SM coupler, and the eye diagram is closed.We can see that beating is severely reduced when a SM-MM combiner is used for signal combining and a widely opened eye diagram is the result, as in Fig. 1

(d).
There remains a small amount of residual beat noise, resulting from the imperfect orthogonality of the modes carrying different signals.Experimental demonstration showing the prevention of beat noise during signal merging by using a SM-MM combiner is shown.Moreover, the use of short coherent length laser will not eliminate the beating problem.In [15], the authors show the coherent (no path difference), partial coherent, and incoherent case, and beating is observed in all cases.Even if the coherent length of the laser is shorter than our delay, beating will be observed if a standard SM-SM coupler is used.However, our motivation is that with SM-MM combiner, it can greatly suppress the beating problem, despite the delay.Thus, we can use it for higher bandwidth filters.

Experimental setup
An N + 1 tap FIR filter is characterized by the classical discrete difference equation: where x[n-Nτ] represents N th tap given by the input signal, x[n], delayed by Nτ and weighted by a scalar coefficient of b N .y[n] represents the filtered output signal.An FIR filter simply represents the sum of weighted samples successively delayed by multiples of τ.The transfer function in the frequency domain of an FIR filter associated with ideal sampling is traditionally given by: 0 ( ) exp( ) The spectral profile of an FIR filter is periodic with period of 1/τ and is symmetric around DC and also symmetric around +/−1/(2τ).This term 1/τ is commonly referred to as the filter free spectral range (FSR) and represents the periodicity associated with the filter.The filter profile shape within each period is determined by the weighting of each delayed sample and consists of a series of peaks and notches.
Figure 2 shows the architecture for our single-source multi-tap FIR filter, which replicates Eq. ( 1) by creating a system of delayed and weighted samples.Only one distributed feedback (DFB) laser with wavelength 1553.54 nm with a line width of 0.5 nm is used as the optical carrier for the 8-tap FIR filter.The narrow-linewidth laser can be at any wavelength that is compatible with the fiber.The output of the laser is injected into a polarization controller before entering a dual output electro-optics Mach-Zehnder modulator (EOM), which is used to create both positive and negative tap coefficients [5].The RF signal to be processed by the FIR filter drives the EOM, modulating that signal onto the optical carrier.The modulated optical signals at the two outputs of the EOM are complimentary to one another.The approach is to bias each of the modulator outputs on opposite parts of the linear portions of the modulator transfer function so that the RF input signals (the carrier frequency) are π-shifted with each other after modulation [5].We use this complimentary output to implement negative coefficients, as the optical intensities of the RF signal will destructively interfere when summed.The modulator has a modulation bandwidth of over 20 GHz, with a V π of 4.1 V and an extinction ratio of 19 dB.Moreover, both outputs have an insertion loss of 3.7 dB, so that the intensities of both branches are equal.
The RF-modulated signal exits from the complementary ports of the EOM, and both the positive and π-shifted negative outputs enter different 1:4 optical splitters to create four positive and four negative taps (eight taps total).Any configuration of positive/ negative taps can be reconfigured, and we are not limited to four taps of each.
The positive and negative taps are inserted directly into an 8-channel optical attenuator to easily control the weights (b N ) shown in Eq. ( 1) through a computer or any electronic circuit providing a controllable voltage.The attenuators are internally controlled by a thermo-optic effect based voltage and have a total range of 20 dB of attenuation.The attenuators have a quick response time of 0.1 dB per 10 μs.
Tunable fiber-optic delay lines then delay the modulated and weighted taps.Any arbitrary delay can be implemented, but we chose to delay each tap by increments of 400 ps for a true-time delay (TTD) system.This corresponds to the τ's in Eq. ( 1).Any delay up to instrumental resolution can be implemented.Finally, all the taps are combined at the SM-MM combiner, and the output is detected by a photodetector.Of course, there is a different delay between each input of the SM-MM combiner, but these can be offset by the tunable delay lines already in the system or by splicing the input fibers.The SM-MM combiner also exhibits a certain amount of loss, though small, ranging from 0.15 to 0.87 dB, that are different for each tap.As the differing losses are small, the optical attenuator easily compensates them.
The frequency profile of the output signal is determined by the frequency profile of the designed filter governed by the weight and delay of each tap.Our architecture offers full reconfigurability and tunability, and any combination of positive or negative taps, weights and delays can be achieved.Furthermore, the novelty of the filter is its use of the SM-MM combiner which allows the architecture to be easily scalable to at least one hundred taps while using a single laser by simply adding splitters and optical amplifiers, up to the limit imposed by the ASE of the optical amplifiers.The optical weights, which are integrated sixteen per chip and electrically controlled, do not limit the scalability of this architecture, nor does the addition of tunable optical delays.

Experimental results and discussion
The transfer function of the system is experimentally measured using the setup as described in Fig. 2. A network analyzer is used to measure the transfer function of the filter.In making the measurements, we accounted for the frequency response of both the modulator and photodiode and de-embed it from the data of the entire system that was captured.We first designed and experimentally demonstrated a coherent 8-tap FIR filter with unity weights.The two examples presented in this paper were not chosen to show a specific type of filter but instead demonstrate the stability of the filter weights, precision of the weighting, and the range of the attenuators.We showcase the novelty and operation of the SM-MM combiner in our data measurements.The calculated and measured magnitude responses are shown in Fig. 3.The predicted magnitude of the frequency response of the filter is shown by the dark blue curve.The tap weights are designed to be as close to unity as we could obtain ([ ) and the delays between consecutive taps are spaced 400 ps apart.The measured response is shown by the light green dotted curve and shows a close match between the predicted and measured responses.Thus, we show the successful implementation of the SM-to-MM fiber combiner in the FIR filter.We are able to obtain a maximum attenuation of ~45 dB at the notches, which is great performance for an 8-tap filter.Next, to show tunability and reconfigurability of our architecture, we wanted to show extreme weighting with the attenuator.The filter shown in Fig. 4 changes some weights of the filter to by adjusting the optical attenuator to provide an attenuation of 20 dB.The coefficients of the new 8-tap filter are close to [1 0 −1.122 0 −0.6166 0 1.1482 0] with the delays between consecutive taps being 400 ps again.Again, the predicted magnitude of the frequency response of the filter is shown by the dark blue curve and the dotted green curve represents the measured response.We notice that this filter can be considered as a 4-tap filter with consecutive delays of 800 ps.The bandwidth as shown in Fig. 4 changes to 1.25 GHz (from 2.5 GHz in Fig. 3) as expected when the delays are doubled.
The filters shown in Figs. 3 and 4 show a close match between the predicted and measured responses, and discrepancies will be discussed later.The matching profile of the magnitude response at both the peaks and notches show the accuracy of the FIR filter along with a working SM-to-MM combiner.The FSR of the overall responses are 2.5 GHz and 1.25 GHz, equal to the inverse of the delays spaced at 400 and 800 ps.The frequency of the notches and peaks are the same as those of the theoretical response, showing that the extreme accuracy of the delays.
The general profiles of the filters very closely match theoretical values, except for the fact that the notches of the magnitude response sometimes are not as accurate as the prediction.Computer-controlled attenuator boards were used in our experiments, which produced slight fluctuations in optical power, resulting in unavoidable inaccuracy of tap amplitudes.In order to increase performance, electronic circuit boards controlling attenuator voltage can provide a more stable weighting, and resolution of 35.10 μV can be achieved with standard voltage electronic control boards.
A FIR filter's FSR is related to the inverse of the incremental delay between successive taps, and FSR can be increased simply by utilizing shorter fiber delay lines between each of the taps.We used 400 ps delays in this paper, resulting in a FSR of 2.5 GHz.This is by no means the limit of the architecture.The optical delay lines do not limit the FSR of the system.For example by simply using 100 ps delays, we can easily create a MPF with a 10 GHz FSR.The authors were limited by a 3 GHz network analyzer, so only a 2.5 GHz filter was shown.In [15], the coauthors show that the SM-MM works well for coherent (no path difference), partial coherent, and incoherent case.Thus, we are confident that the scheme will work for higher bandwidth with shorter delay.In the end, the FSR is limited only by the resolution of the delay lines and the operating frequencies of the photodetector, and FSR of hundreds of GHz can be easily reached.By simply splitting an extra tap from the laser source, the filter taps can be easily scaled without needing to introduce additional lasers with a different wavelength or complicate the architecture.
The magnitude response of the FIR filter is error-free and nearly noise-free, and the overall measured response is clean and robust over the entire 2.5 GHz range, showing the successful coupling of the SM-to-MM combiner.To show the advantage of using the SM-MM combiner, we replicated the filters above using a traditional SM coupler.The beat noise was so strong that the filter profile was constantly changing and could not be stabilized.To show this, we took a continuous set of 8 data sets with a 30 s interval between measurements using our network analyzer and graphed them side by side in Figs. 5 and 6, corresponding to the same filters shown in Figs. 1 and 2. The filter profiles vastly change from one to another between measurements and do not reach a steady-state profile.The traditional method is not acceptable for implementing an optical FIR filter.

Conclusion
We propose and experimentally demonstrate a fully tunable and reconfigurable 8-tap FIR filter using a SM-to-MM fiber combiner.Optical interference from coherent summing and sensitivity from phase fluctuations have traditionally made SSMPF filters less popular than MSMPF filters.However, we introduce the use of a combiner that spatially couples the input signals into a piece of multimode fiber eliminating optical interference.Our architecture only requires a single wavelength narrowband laser source and can be built into existing fiber optic systems.Thus, the major drawbacks of MSMPF, their spectrally inefficiency, complexity, and bulkiness, can be overcome, and we have a filter that combines the advantages of both SSMPFs and MSMPFs.Our architecture is fully reconfigurable and tunable.Optical attenuators with quick response times provide weights, while tunable optical fibers provide delays.Since only a single laser is used, the architecture can be easily scaled merely by adding additional splitters and optical amplifiers up to the limit imposed by the ASE of the optical amplifiers.
An 8-tap filter was experimentally demonstrated.Close agreement between predicted and measured magnitude responses was observed, evidence of accurate matching of tap coefficients and delays.Successful implementation of the SM-to-MM fiber combiner was evident by the excellent stability and low noise was shown by the system.The combiner eliminates interference and phase noise as desired and filter operation is stable and robust.

Fig. 1 .
Fig. 1. a. Experimental Setup b.Input signal c.Signal combination with SM-SM coupler d.Signal combination using SM-MM combiner.