In this paper we present passive photonic device performing periodic and ultra fast spectral analysis of RF signals modulated on optical carrier. The spectral scanning is demonstrated in two approaches. First by passing the light through a couple of special bulk periscopes that split the beam into a set of parallel channels or combine a set of channels into one beam. One surface of each periscope is coated with high reflectivity coating such that the set of parallel beams travel several times through the structure due to their partial back reflection in each passage through the periscope. In each passage in the system the channel experience different delay in comparison with the original signal. This relative delay is accumulative and it is generated by placing glass bars with different length for each one of the channels. This structure realizes Finite Impulse Response (FIR) filter that performs the spectral scanning. The second approach involves similar configuration but it is realized with fibers and Y couplers rather than bulk optics. In this case the filter that performs the spectral scanning is an Infinite Impulse Response (IIR) filter having much sharper spectral sampling capability.
© 2006 Optical Society of America
Optical Spectrum Analyzer (OSA) is a widely used device in many optical areas. The OSA is used to map the frequency composition of an incoming signal. It is used mainly in the optical communication industry starting from the O and up to the U bands (1260nm-–675nm). The main application is related to inspection and monitoring of optical networks and devices. There are various optical methods for implementing OSA. One such method is by using Micro Electro-Mechanical Systems (MEMS) [1–2]. It consists of an engine, driving circuit, A/D converter and a PC. It has a wavelength accuracy of 10 pm, scan rate of 1.3 ms, and dynamic range of 33 dB. The heart of the MEMS based OSA is the scanning mirror (12×2 mm) that measures the spectrum continuously and rapidly. Second common approach uses Liquid Crystal (LC) and it is called Fourier Optical Spectrum Analyzer (FOSA) . The FOSA consists of a birefringent filter array with an embedded LC phase modulator. The LC phase modulator is used to control the phase difference between two orthogonally polarized beams and by that avoiding mechanical movement as in conventional Fourier transform spectrometers. Third common method is based on Arrayed Waveguide Grating (AWG) with cascade connection of the AWGs with different channel spacing, through optical switches. The spectral resolution of such system is determined by the narrowest channel spacing [4, 5].
Our main motivation for the OSA realization is related to RF signals. An important application is related to electronic warfare where detection of unknown RF signal embedded in noise is required. By modulating the received RF signal on top of an optical carrier the fast spectral analysis can be done by using optical configuration rather than via RF filters. Such a direction significantly simplifies the system. In this paper we utilize OSA for the RF frequencies within the range of 1GHz-20GHz using either bulk or fiber based RF photonic configuration. The field of RF photonics in general deploys optical based processing techniques into RF signal processing. Such applications include building of photonic RF filters which have a lot of potential due to their capability to obtain high dynamic range, tuning ability and reconfiguration . The concepts of those optical filters are the basis for our RF photonics OSA. An example of such device, operating in wideband, can be seen in the work by Lavielle et al . The device is based on spectral hole burning (SHB). Its features are 2.3GHz instantaneous bandwidth, 500-kHz resolution, and a 32-dB dynamic range. Its RF signal, transferred to the optical carrier with the help of a Mach-Zehnder modulator, and it is analyzed with optical carrier suppression and zooming capabilities.
In former work done by the authors , RF photonic tunable filter was performed by splitting the incoming signal into two paths and delaying one in respect to the other. Therefore, a notch filter with specific band stop was realized. In that work, spectral scanning capabilities were realized by accumulating relative delay between the optical signals due to optical feedback. The main challenge in the devices developed in this paper was obtaining ultra fast spectral scanning (at nano second rate) with high spectral accuracy (MHz range) while using only passive optical elements. All those properties are significantly different from other existing technologies and fit well to the RF photonic application we described. We propose two different integrated electro-optical approaches. The first one is based on bulk realization of high resolution FIR scanning filters. Here the splitting is done in free space and uses multiple beam splitter designated specially for this purpose. We coin this bulk element as periscope. Each ray goes into similar path with different delays. The overall optical power summation of each path, produce the effect of a very sharp band-pass filter. One of the surfaces of the periscope is coated with high reflectivity coating such that usage of two periscopes placed one in front of the other realizes multiple reflection and propagation of beams through the media between the periscopes. The multiple propagations through this media accumulate relative delay between the parallel beams and thus generates different FIR filter in each passage. The realized FIR filter depends upon the number of the optical paths. Detecting the energy of the combined paths at the output of the bulk device provides energetic readout that corresponds to the spectrum of the incoming signal. Since the device is small in dimensions the time between readouts can be small, even in the nano seconds range and thus the spectral mapping is done in nano seconds rate. The spectral scanning system contains only passive bulk optical elements. The second approach is based upon similar concept of optical feedback but realized with fibers rather than bulk optics. In order to obtain sharp band-pass filter that will perform the spectral scanning, we realize IIR configuration. Such configuration has better spectral performance in comparison to the FIR filter.
Note that additional works on passive optical IIR filters using ring resonator were done by Madsen  and various different RF photonic configurations used for RF phased array sensors [9–10] and filters  were recently deployed due to their technological potential and capability to obtain high dynamic range, tuning capability and reconfiguration. Several configurations have been suggested using highly dispersive fibers , fiber gratings  and fiber optics prisms7  or arrayed waveguide gratings (AWG) .
Section 2 presents the mathematical analysis and computer simulations for the FIR filters configuration. In section 3 we present technological description of the bulk FIR system concept including some design analysis. Experimental results of the FIR configuration are depicted in section 4. Section 5 presents the second approach for the OSA based upon fibers and Y couplers realizing IIR filters. The paper is concluded in section 6.
2. Mathematical analysis and simulations
The bulk optical configuration realizing FIR based OSA is depicted in Fig. 1(a). This configuration is used for realizing the nano-second fast tunable and reconfigurable RF-photonic spectrum analyzer. The operation principle is as follows: An optical input signal is passed through a shutter that transmits one burst of bits with duty cycle (for the burst) of less than 1/M where M is the number of the required spectral sampling points, e.g. M=40. The length of the transmitted bits burst determines the spectral scanning rate. For simulation purposes we will assume that the burst length is 2nsec. This shutter is also the modulator that modulates the RF signal on top of the optical carrier. It is the only active element in our system. The input bits burst is split between N optical paths or tapes (e.g. N=32) and eventually recombined at the output. In every tape a bar of glass is positioned. The various bars have different lengths. The aim of those bars is to generate relative time delay between the N paths. The larger the number of the tapes N the sharper (and spectrally narrower) is the FIR filter that scans the spectrum of the input signal. Due to the different path lengths, a different delay is generated between each one of the N interfering tapes [see Fig. 1(a)]. The time delay between two adjacent paths (tapes) equals to:
where c is the speed of light and n is the refraction index of glass (the bars are made out of glass).
On both sides of each optical path we place mirrors. Thus, each one of the optical paths is actually a Fabry-Perot resonator. However, it is not really a resonator since the bits burst is shorter than the time that takes the pulses to travel from the reflecting mirror and back. The reflectivity of the mirrors of the resonator (R) should be equal at least to the number of replications we want i.e. M. The length of each path L should be such that the time required by the light to travel back and forth equals to the temporal length of the bits burst (since we require that the generated temporal replicas will not overlap). For bits burst of 2nsec the length should be at least (2×108)×(1×10-9)=20cm (where 2×108 is the speed of light in glass). Note that in order to allow compact realization this length of each path could be folded as depicted in Fig. 1(b). In Fig. 1(b) we present folding of a single optical path. If, for instance, a five times folding is achieved the horizontal dimension will be reduced to 4cm.
The combination (summation) of the N optical paths realizes spectral FIR filter. The length of each bar is different [the portion of glass/ air in every optical tape varies as seen in Fig. 1(a)] such that each replication coming from the Fabry-Perot resonator will contain summation of N signals with different relative delays. The relative delays between the N paths determine the position of the spectral band pass filter (BPF) as known from the FIR theory: Assuming that an incoming sequence s(t), is duplicated N times with relative delay of δt and then summed. For this case one may obtain the following expression:
The Fourier transform of sT equals to:
The filter F is an FIR filter. By tuning the delay between the sequences the position of the filter may be changed. Next we will show that this tuning is obtained by itself.
Figure 2 presents some simulation results obtained for 32 tapped delay lines added in fields (same polarization required for coherent addition). Figure 2(a) depicts the spectral BPF. Each filter is realized by different replication of the input bits burst. The delay between the different tapes that is obtained prior to their entry to the resonator is a non accumulative delay. Assuming that this fixed delays between adjacent tapes is: ΔtAT =50psec (1cm in glass). The relative delay between the various tapes inside the resonator (generated due to the glass bars) is an accumulative delay that is increased with every replication. Assuming that this relative delay between adjacent replications is ΔtAR=10psec (2mm in glass). Connecting those notations to Fig. 1(a) means that Δy=5mm and δx is approximately 3mm [since the difference between two adjacent paths within the resonator is the portion of the path that is done in glass instead of in free air, so the difference in the refraction index is only Δn= 1.5–1=0.5 and thus δx equals to (3×108/0.5) ×(5×10-12)=3 mm]. Note that since the delay ΔtAR is accumulated while the delay ΔtAT is fixed, if we detect replication number k its overall relative delay equals to: δt= ΔtAT+k ΔtAR. Note that the idea of having fixed as well as accumulating delay is very important in order to obtain more or less continuous and uniform scanning of the spectrum. If only accumulated delay would have been used, the scanning would have been completely non uniform since the spectral position of the BPF is proportional to 1/δt [see Eq. (3)] while δt itself is linearly accumulated. Following this explanation, the simulation of Fig. 2(b) presents the spectral scanning obtained with the parameters previously specified. Note that every replication generates a BPF with different spectral position. In Fig. 2(b) every replication is plotted with different color and also has a numbering. There are 6 replications.
Note also that in the simulation the various paths (tapes) may be added with weighting coefficients following for instance the Kaiser window (e.g. of order 3.5). The Kaiser window may be mathematically expressed as:
where I0 is the zero order modified Bessel function and α, β are parameters of the window. m is the window’s index. Increasing the order of the Kaiser window from 3.5 to 6, for instance, will further decrease the spectral side lobes [seen in Fig. 2(c)] but will also enlarge the width of the BPF.
The plot of the Kaiser window that we used in the simulation as the coefficients for the FIR filter with N=32 tapes, is seen in Fig. 2c.
Note that the suggested device may basically be generated in lithographic recording on polymers and that the same folding as was generated for the horizontal dimension may as well be applied for the vertical one. This is even recommended since without folding, the overall dimension of the vertical axis is 32×Δy=16cm. A folding factor of 3 will reduce the device’s vertical dimension to 5.3cm [the folding for the vertical axis will be realized in same way as described by Fig. 1(b)].
If after the output mirror an SLM is placed while each of its pixels affects different optical path, the weightings of those various paths could be changed. That way a reconfigurable spectral analyzer may be realized since the weightings and the paths’ number influences the shape of the BPF. The scanning rate itself corresponds to the temporal length of the bits burst which in our case was 2nsec. The overall spectral scanning takes M times 2nsec which equals to 80nsec in our example. The spectral resolution is less than 900MHz [see Fig. 2(a)] which is approximately 10psec.
3. Technological overview
The experimental system built to investigate the performance of the suggested approach was composed out of several main blocks according to the technological overview presented above and as can be seen in Fig. 3.
We produced RF signal by using Rhodes and Schwartz RF signal generator of up to 2.2 GHz to modulate 1550nm laser transmitter of up to 2 GHz. Then the signal passed through optical EDFA pre-amplifier (to increase its intensity) and through 1×2 fast optical switch produced by Civcom Ltd. This fast switch which acts also as shutter was realized by cascading two Civcom’s 1 by 2 switches. The problem is that although the switches have fast optical response (approximately 200nsec), their electrical driver is limited to operation frequency of 10KHz. Thus in order to be able to generate short input bits burst sequence we used an RC circuit that was inserted between the electrical drivers of both switches such that we actually constructed an optical AND gate. Since the first switch’s driver was connected to a pulse generator and the second one was connected to the same generator but had a delayed electric control command and since only when both switches are open the light could come through into the optical system, an optical logic AND gate was realized. By playing with the RC parameters very short pulse sequence could be generated (corresponding to the RC delay). Note that the shutter had extinction ratio of about 30dB and it was enough to significantly attenuate the residual light and thus avoid its effect on the system performance.
Two concepts were considered for the optical system. One approach is depicted in Fig 3(a) and it is based on using two periscopes and two mirrors. This is the basic approach mentioned also in the introduction. The first periscope, which we coin the entrance periscope, was produced such that it splits the incoming signal into 16 parallel beams (see Fig. 3(b)). The transmission and reflection coefficients are 95% and 5% respectively. After splitting the optical signal a semi reflecting mirror was inserted to perform the spectral scanning, i.e. the replications in time. This mirror was made such that it reflects and transmits 50% of the arriving energy. This was the main cause for energy loses in that system. However, since we were interested in identifying the relative intensity in each frequency, we used EDFA for compensating that. From that point the light of each tape passed through different time delay caused by bars of glass having different lengths (and refraction index of 1.5). Those glasses had AR coating to reduce energy loss in each round. The beam went into a second mirror with reflectivity and transmission of R= 95%, T=5% respectively. This way a major part of the signal went back for the second scan while its remaining energy proceeded to the output folding and combing second periscope which had reflection and transmission coefficients of R=50% and T=50% respectively. The combined beams are detected by a slow rate detector for sensing the energy fluctuations. The sensed energy is the spectrum of the incoming signal.
The second approach for this bulk realization is seen in Fig. 3(c). It is based on similar concept but used only one periscope. In this approach the second mirror is replaced with mirror having reflectivity coefficient (R) of 100% and the second periscope is removed. Thus, instead of summing the different paths by using the periscope (and loosing energy that way), we used a big aperture lens. The lens focused the rays onto the slow rate detector that has large sensing area of 2×2 mm.
4. Experimental results
The slow rate detector used in the system was a free space detector with bandwidth of 1GHz. The detector output was connected to high rate sampling scope (HP TDS5054), which has bandwidth of 0.5GHz with 5G samples/sec. The system was constructed as depicted in Fig. 3(c) because of lack in optical intensity at the output of the system.
In the experiments we show the two major claims of this paper. First, that the shape of the BPF that scans the spectrum is related to the number of the optical tapes and their relative weightening. Second, that indeed the proposed system performs the desired spectral scanning.
We have constructed the configuration of Fig. 3(c) and used three tapes. The theory as presented by Eq. 3 predicts that the anticipated BPF should have two blocking frequencies (the number of blocking frequencies equals to the number of tapes minus one). The relative delay between adjacent tapes was realized by placing AR coated glass bars having varied lengths. The length difference was Δx=24cm which corresponds to time delay δt that equals to:
this provides frequency blocking at frequency of 1.25GHz (=1/0.8nsec). If we observe the third replication then the zero transmission frequency will be 1.25GHz/3=417MHz. Note that we used 2Δx since in the configuration of Fig. 3(c), for each replication, the light passes through the delay twice (on his way to the mirror and on his way back). Figure 4(a) presents several results captured for various input frequencies (we captured much more figures than that). The upper part of each figure is the transmission of the temporal signal and the lower part is its Fourier transform (FFT). The frequency of each measurement is specified on the right side of the figure. From all the figures that were captured we computed the BPF i.e. the spectral transmission of the OSA as depicted in Fig. 4(b). Indeed two blocking frequencies were obtained at around 415MHz and at 830MHz, as anticipated from the theory [see Eq. (3)].
Now after showing that the spectral scanning BPF coincides with the theory we want to show the spectral scanning itself. For that we repeated the same measurement as before but over the sixth rather than the third replica (k=6 instead of k=3). In case that is relevant for the configuration we realized where we set the fixed delay ΔtAT to be zero, the anticipation from the theory is that the blocking frequencies should be reduced by a factor of 2 (since k which is the number of the replication is increased by a factor of 2). We isolated the sixth replica by directing the right mirror of Fig. 3(c) such that the third and the sixth replicas were separated in space and allowed us doing their individual spectral characterizations. Figure 5(a) presents several samples while in the upper part one may see the transmitted temporal input signal and the lower part of each figure is its FFT. The samples were taken at frequencies of: 119MHz, 200MHz, 286MHz, 355MHz, 469MHz and 584MHz. Following those results the chart of Fig. 5(b) was plotted. Indeed the first blocking frequency is now at around 200MHz and the second around 400MHz. Indeed this experiment verifies the theory claiming that we have obtained spectral scanning while each replication corresponds to different spectral sampling with the generated BPF.
Note that a plot of the optical setup is depicted in Fig. 6(a) and in Fig. 6(b). In Fig. 6(a) one can see the set up depicted in Fig. 3(c).. In this setup, one periscope is used with 3 delay glasses in different lengths and a mirror to perform the scanning. The output is converged using a lens into high speed free space detector. In Fig. 6(b) one may also see the spatial distribution of 16 light spots coming out of the periscope (having 16 outputs) and that are later on recombined into one single spot (in the experiment we described in section 4 we have used 3 tapes rather than 16 but we have tested the system also with 16 tapes). Note also that the filter that we realized is an FIR filter and thus the relative delay between the channels is in the scale of nsec (large number of optical periods) and thus the sensitivity of the filter to phase errors between the optical paths (tapes) is relatively small, e.g. the various channels can actually be combined also in intensities.
5. Fibers based realization
In the previous section we have demonstrated the realization of the spectral scanning using FIR filters. The main difficulty of that setup is that in order to realize narrow BPF one needs large number of tapes. In this section we present different realization based upon fibers that generates very narrow spectral scanning. The fine spectral scanning is generated by using IIR rather than FIR filters. In this concept only two fiber loops are required for the narrow spectral BPF (rather than 32 or more as in the previous sections).
Let us consider the system of Fig. 7. It contains two Y couplers. It realizes a two term IIR filter:
where r1 and t1 and r2 and t2 are the field splitting ratios of the right and left Y-couplers respectively.
Δt is the time that takes to the light to travel through the feedback fiber loop. Note that + =1 and + =1. Since y(t)=t1y′(t) one has the following equation:
After performing a Fourier transform one obtains:
which implies that the ratio between the input spectrum X(ν) and the output spectrum Y(ν) equals to:
The minima for the transmitted frequencies are obtained at:
which leads to:
The maximum transmission is obtained at:
For example in Fig. 8 one may see the simulation of the IIR filter for the case of Δt=0.5nsec, r1 =0.99 and r2 =0.98. As inspected from the theory the first passed frequency is at 2GHz.
Note that this time the temporal difference Δt is related to the length of the feedback fiber loop:
where c/n is the light velocity in the fiber. Obviously as may be seen from Eq. 11 the length of the feedback fiber ΔL, can be multiplicities of the value obtained in Eq. 12 and those multiplicities correspond to using different values for m (Eq. 11) which are larger than one.
So far we have presented the theory for an all-optical realization of a single IIR filter. However, in order to use the proposed approach for spectral scanning and detection of RF carrier, one needs to vary this relative time delay Δt [a delay between the input and output signals x(t) and y(t) respectively]. The optical realization of such an all-optical tunable scanning module may be done following Fig. 9.
For proper operation we need to assume that the input signal x(t) is time limited. As before, this time limitation is obtained in the electro-optical (EO) modulator that modulates the incoming RF information on optical carrier. In addition to the modulation the EO modulator temporally chops the incoming signal and converts it into a time limited package of information. The left optical feedback having length of L0 realizes temporal replications of the input signal x(t). The temporal width of the package of x(t) after being multiplied by the speed of light in the fiber equals to L0 . Our aim is that each replication of x(t) will be added to y(t) with different relative delay Δt in order to realize tunable IIR filter. To achieve this we have added additional feedback loop. The first replication of x(t) is added to y(t) after being temporally delayed by the time taking light to travel a distance of L1 . The second replication of x(t) will already be added with y(t) that was temporally delayed by the time taking light to travel a distance of L2 +L1 since part of the energy is coupled to the second loop (having length of L2 ). The third replication of x(t) will have a temporal delay due to distance of 2L2 +L1 since it corresponds to light that traveled once through the loop L1 and twice through the loop L2 . Other replications will accumulate more and more relative delay following the same explanation. Note that the lengths of the three optical feedback loops should be such that the separation time between the various replications will be smaller than the time that takes to stabilize and reach the steady state in the IIR loop. Let us assume that the number of passes needed for stabilization is M [it is proportional to 1/(1-r1r2)] then the temporal sampling insights should be chosen carefully as well as the lengths of the fiber loops such that the sampling will capture the insights that correspond to light that traveled a distance of ML1 for the first replica, M(L1 +L2 ) for the second and M(L1 +2L2 ) for the third replica etc. Other combinations of number of passing times through L1 and L2 provide non desired information.
The main advantage of the design of Fig. 9 is that the tunable spectral scanning is obtained with only three optical feedback loops and yet the realized spectral filter is very sharp (see Eq. 9) which is the main benefit in using the IIR filters. Note that in this configuration, as before, a slow rate detector that samples the energy of each replication actually displays the spectrum of the input signal x(t), since each replication is filtered by a different IIR filter.
5.2. Experimental results
We produced the RF carrier by using Rhodes and Schwartz RF signal generator capable of going to frequencies of up to 2.2 GHz in order to modulate 1550nm laser transmitter capable of being modulated by frequencies of up to 2 GHz. Then the signal was inserted into EDFA pre-amplifier for increasing its intensity and thorough a 1×2 fast optical switch produced by Civcom. The Civcom’s switch acted also as shutter and generated the temporally limited packages of x(t). This fast shutter was actually realized by cascading two Civcom’s 1 by 2 switches as was done in the experiments in the previous sections. Here as well, by playing with the RC parameters very short pulse sequence could be generated (corresponding to the RC delay).
The IIR filter (Fig. 7) was built with two Y couplers with energy splitting factor of 99%–1%. The slow rate detector used in the system had bandwidth of 100 MHz. We wanted the central frequency for observation to be at around 50MHz. Using Eq. 11, one can calculate that for v0 =15MHz the delay should be Δt=6.66μsec and this leads to a fiber length of L=20m. The detector output was connected to a high sampling rate scope (HP TDS5054), which enabled us to take the results. The first taken results are shown in Fig. 11.
The Cyan line (upper line) represents the real time optical signal and the red line (lower line) represents its real time FFT. Here the measurements were taken at frequency of 48MHz, 55.5MHz and 63MHz. Those measurements correspond to spectral bandwidth of 15MHz which contains the stop band for frequencies of 48MHz and 63MHz while the center of the pass band is 55.5MHz. One can see from Fig. 11 that 12dB of attenuation for the stop band frequency was obtained. The same experiment was done with feedback fiber loop of L=200m. This corresponds to central pass band frequency of 1.5MHz with a delay of Δt=0.666μsec. The results are shown in Fig. 12 and as before, the Cyan line represents the real time optical signal and the red line is the signal’s real time FFT. The Gray line is fixed FFT for a signal at 9.935 MHz. It is displayed for comparison reasons. Here the filter bandwidth is 3MHz and the sampling points for the stop band, that were tested in the experiment, were at frequencies of 9.916MHz and 10.53MHz while the pass band points are for frequencies of 6.995MHz and 9.935MHz.
In this paper we have presented a novel approach for realizing optical spectral analyzer for RF signals via photonic passive configuration. Two possibilities were presented. In the first the RF-photonic spectral analyzer was built using bulk optics where periodically scanning finite impulse response filters were generated. In the second possibility infinite impulse response was realized using fiber based configuration. The main advantages of the suggested systems is that they perform continuous and uniform scanning of the spectrum of the input RF signal while the system contains only static and passive elements. In addition, the spectral scanning rate is in nano second rate and thus ultra fast spectral scanning is obtained. The realized scanning filter may also have high spectral resolution in the range of MHz. Experimental results as well as numerical simulations demonstrated the operation principle for both configurations. The main practical limiting factor of the proposed approach is related to the losses in each pass through the system during the spectral scanning process and therefore the limited number of the replicas that may be obtained. Since this number is the number of the spectral samples it is important to increase it as much as possible.
References and links
1 . T. Saitoh , T. Nakamura , and K. Y. Takahashi , “ High-speed (1.3 ms/scan) optical spectrum analyzer utilizing MEMS scanning mirror ” ECOC, Royal Inst. of Technol. 562 – 563 , 3 , Kista, Sweden ( 2004 ).
2 . Y. Takahashi , “ High-speed MEMS-OSA and its application to fiber sensors ,” SPIE Proceedings 5502 , 33 – 38 ( 2004 ). [CrossRef]
3 . Y. Q. Lu , F. Du , Y.H. Wu , and S. T. Wu “ Liquid-crystal-based Fourier optical spectrum analyzer without moving parts ,” Jpn. J. Appl. Phys. Part 2-Letters 44 , 291 – 293 ( 2005 ). [CrossRef]
4 . T. Y. Itoh , Y. Aizawa , K. T. Kurokawa , and H. Tsuda , “ Optical spectrum analyzer based on arrayed waveguide grating for high-speed optical communication systems ,” IEEE Photonics Technol. Lett. 17 , 432 – 434 ( 2005 ). [CrossRef]
5 . K. Takada , H. Yamada , and K. Okamoto , “ Optical spectrum analyzer using cascaded AWGs with different channel spacings ,” IEEE Photonics Technol. Lett. 11 , 863 – 864 ( 1999 ). [CrossRef]
6 . Z. Zalevsky , A. Shemer , V. Eckhouse , D. Mendlovic , and S. Zach , “ RF-Photonic Filter for Highly Resolved and Ultra-Fast Information Extraction ,” J. Opt. Soc. Am. A 22 , 1668 – 1677 ( 2005 ). [CrossRef]
8 . C. K. Madsen , “ General IIR optical filter design for WDM applications using all-pass filters ,” J. Lightwave Technol. 18 , 860 – 868 ( 2000 ). [CrossRef]
9 . H. R. Fetterman , Y. Chang , D. C. Scott , and S. R. Forrest , et al., “ Optically controlled phased array radar receiver using SLM switched real time delays ,” IEEE Microwave Guid. Wave Lett. 5 , 414 – 416 ( 1995 ). [CrossRef]
10 . L. Xu , R. Taylor , and S. R. Forrest , “ True time-delay phased-array antenna feed system based on optical heterodyne techniques ,” IEEE Photon. Technol. Lett. 8 , 160 – 162 ( 1996 ). [CrossRef]
11 . R. A. Minasian and D. B. Hunter , “ Photonic signal processing of microwave signals using fiber Bragg gratings ,” Proc. OFC , ThH3 339 – 340 ( 1997 ).
12 . D. Norton , S. Johns , C. Keefer , and R. Soref , “ Tunable microwave filter using high dispersion fiber time delays ,” IEEE Photonics Technol. Lett 6 , 831 – 832 ( 1994 ). [CrossRef]
13 . J. Campany , D. Pastor , and B. Ortega , “ New and flexible fiber-optics delay line filters using chirped fiber Bragg gratings and laser arrays ,” IEEE Trans. Microwave Theory Tech. 47 , 1321 – 1326 ( 1999 ). [CrossRef]
14 . M. Y. Frankel and R. D. Esman , “ Fiber optic tunable microwave transversal filter ,” IEEE Photonics Technol. Lett. 7 , 191 – 193 ( 1995 ). [CrossRef]
15 . F. Coppinger , S. Yegnanarayanan , P. D. Trinh , and B. Jalali , “ Continuously tunable photonic radio-frequency notch filter ,” IEEE Photonics Technol. Lett. 9 , 339 – 341 ( 1997 ). [CrossRef]