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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 11 — May. 26, 2008
  • pp: 7904–7914
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RF-photonic chirp encoder and compressor for seamless analysis of information flow

Zeev Zalevsky, Amir Shemer, and Shlomo Zach  »View Author Affiliations


Optics Express, Vol. 16, Issue 11, pp. 7904-7914 (2008)
http://dx.doi.org/10.1364/OE.16.007904


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Abstract

In this paper we realize an RF photonic chirp compression system that compresses a continuous stream of incoming RF data (modulated on top of an optical carrier) into a train of temporal short pulses. Each pulse in the train can be separated and treated individually while being sampled by low rate optical switch and without temporal loses of the incoming flow of information. Each such pulse can be filtered and analyzed differently. The main advantage of the proposed system is its capability of being able to handle, seamlessly, high rate information flow with all-optical means and with low rate optical switches.

© 2008 Optical Society of America

1. Introduction

Several and most common applications in which usage of RF photonic approaches was applied deal with generation of true time delay [2–4

2. O. Raz, R. Rotman, Y. Danziger, and M. Tur, “Implementation of photonic true time delay using high-order-mode dispersion compensating fibers,” IEEE Photon. Technol. Lett. 16, 1367–1369 (2004). [CrossRef]

], generation of microwave pulses via optical means [5–7

5. O. Levinson and M. Horowitz, “Generation of Complex Microwave and Millimeter-Wave Pulses Using Dispersion and Kerr Effect in Optical Fiber Systems,” J. Lightwave Technol. 21, 1179–1186 (2003). [CrossRef]

], spectral analysis [8–10

8. 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 Photon. Technol. Lett. 17, 432–434 (2005). [CrossRef]

], optically controlled phased array RADAR receiver [11

11. 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 and Guid. Wave Lett. 5, 414–416 (1995). [CrossRef]

], photonic signal processing and filtering of microwave signals [12–15

12. R. A. Minasian and D. B. Hunter, “Photonic signal processing of microwave signals using fiber Bragg gratings,” Proc. OFC, ThH3, 339–340 (1997).

] and optical delay line filters [16

16. 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]

]. One of the concepts presented for spectral analysis [1

1. Z. Zalevsky, A. Shemer, D. Mendlovic, and S. Zach, “Passive and periodically ultra fast RF-photonic spectral scanner,” Opt. Express 14, 8367–8381 (2006). [CrossRef] [PubMed]

,9

9. 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]

] did not allow temporally seamless processing of information.

In section 2 we present the theoretical description of our setup as well as modeling of its performance. In section 3 we experimentally investigate the proposed system. The paper is concluded in section 4.

2. Theoretical description

2.1 General

The general concept of the proposed configuration is as follows; by passive optical elements and low rate electronics we take a series of low rate train of pulses, temporally extend it using chromatic dispersion, seamlessly modulate RF data on top of it and later on back compress it into a train of pulses having the data encoded within. The temporal extending of the pulses is done using the dispersion in regular fibers. After the modulation of the data, the back compression into the train of pulses is done using chromatic dispersion compensated fiber (DCF). Note that the output of our system is a train of pulses while each pulse is compressing the temporal RF sequence of its corresponding time window.

Several such train pulses containing each an encoding of different RF data can be mixed together. Later on a low rate optical switch can route out a certain pulse, decompress its encoded RF information and process, analyze or filter it.

In this paper we demonstrate the coding configuration which temporally extends the train of pulses, modulates the information on top of the continuous temporal carrier and later on back compresses the carrier with the RF data into a train of pulses. The optical setup for decompressing this information is identical to the system that is used for its compression.

In our experimental demonstration we will show two setups. The first is just a proof of principle while the second follows the outline of the above explanation. The first setup which is presented in Fig. 1 includes two lasers with different wavelengths. The lasers emit up to 2mW of optical power and they are combined using 50/50 coupler hence loosing 50% of the overall power. The light is passed through a modulator that defines a temporal window (the temporal train of pulses) but decrease the overall power by at least 4dB and later on it is amplified with Erbium doped fiber amplifier (EDFA) to regain the power loss due to its operation. In our case we generated temporal window of 40nsec (the temporal width of any pulse in the train of pulses) and the two lasers were of 1557.6nm and 1548.6nm (each laser can provide output power of up to 2mW). A WDM DEMUX filter splits the modulated wavelengths again and each is passed through fibers of different lengths (obviously the original light sources could have been passed through those fibers to begin with but we wanted to present a proof of principle that is as close as possible to the final configuration where broadband light source is used rather than an individual laser). The length difference between the two fibers equals to 3 meters. This difference generates temporal relative delay of about 15nsec:

δt=δLcn=3m3.1081.5=15nsec
(1)

where c is the speed of light and n is the refraction index of the fiber. Therefore, the temporal window of 40nsec is expanded to width of 40+15=55nsec. The output is combined again using 50/50 coupler. This generated temporally expanded carrier is to be used for the modulation of the RF information. After the modulation our purpose is to compress the signal back into its original width of 40nsec.

The output of the coupler is passed through a 2×2 optical switch which directs the signals through a loop containing a DCF of -806ps/nm. The control of the switch is synchronized and since the length of the DCF is such that it takes the light 49µsec to circulate the loop, the switch stays in a bypass state until the light is circulated through the loop during two times (it takes about 100µsec) and then the state of the switch is changed to exchange state. The two circulations add the required temporal delay between the two wavelengths on top of which the original information was modulated. Since it takes the light approximately 100µsec to accomplish the full circulation, low speed switch can be used. The accumulated relative delay for those two wavelengths, after the two circulations equals to:

Δt=2·[806psnm]·(1557.6nm1548.6nm)=14.5nsec
(2)

This negative relative delay compresses the signal back to its original temporal width.

After the two rounds the switch passes to its exchange mode and the signals routed towards the optical detector which samples the signal for display purposes. Indeed, since only two lasers i.e. two wavelengths were used, our compression ratio can not be more than two (we will prove it in the sub section dealing with the theoretical modeling). Nevertheless experimenting Fig. 1 demonstrates the basic operation principle.

Fig. 1. Preliminary proof of concept.

Note that the Amp module which is mentioned in Fig. 1 relates to the EDFA device.

The full configuration is presented in Fig. 2. In this setup the modulation of the RF information is performed over spectrally broadband source (e.g. an ASE). The beam is passed thorough an optical modulator (model: JDS/SDL IOAP –MOD 9140 FF1 with modulation bandwidth of up to 10 GHz and 4dB loss) that is modulated using an electronic driver (model: JDS H-301-1110) such that it periodically chops the incoming beam into temporal window of 40nsec. This generates the input train of pulses.

Unlike in Fig. 1 where only two wavelengths were used and the compression factor could not be more than two, here the compression factor is proportional to the spectral bandwidth of the input source (this is modeled and explained in the theoretical modeling sub section). In this case we generate the original train of pulses with proper duty cycle that fits to the compression ratio that may be obtained. That way temporally continuous carrier can be generated and used right after for the RF data modulation.

Fig. 2. Full configuration of spectral chirp coding and temporal sequence compression.

2.2 Theoretical modeling

For proper theoretical modeling of the proposed concept we assume that a temporal train of pulses is generated and injected into our system while each pulse in the train has temporal width of δτ. The pulses in the train are rectangular return to zero (RZ) pulses. The train of pulses is modulated on top of a broadband light source that contains spectral comb, i.e. it has a discrete set of wavelengths that are separated by more than the bandwidth of the RF signal that we intend to modulate later on (this can be obtained for instance at the output of a Fabry-Perot resonator that is illuminated with a white light source or just by combining a plurality of laser using WDM multiplexer as done in optics communication). The white broadband source can be spectrally continuous source as well (such as ASE source) however then various interference effects may be generated between pulses modulated on top of wavelengths having not sufficient spectral separation. For proper theoretical modeling we will assume a source containing spectral comb.

Generally speaking a Gaussian shape pulse having width of δτ (its standard deviation) that is passed through fibers with chromatic dispersion is temporally extended and has the temporal width (its standard deviation) of [17

17. A. W. Lohmann and D. Mendlovic, “Temporal filtering with time lenses,” Appl. Opt. 31, 6212–6219 (1992). [CrossRef] [PubMed]

]:

Δt=δτ2+(β2z(2π·δτ))2
(3)

where β2 is the second order coefficient in the Taylor expansion for β in the phase delay term 2πβ(µ)z where µ is the temporal frequency and z is the propagation distance in the dispersive medium (see also Eq. 6). In our case the effect is a bit different, since our broadband source is composed out of a plurality of discrete narrow band lasers or spectral spikes. Assuming that the number of lasers or spectral spikes contained within our broadband source is N and that the spectral separation between every source or spike is Δµ (µ is the spectral coordinate) then the final temporal width of the pulses is:

ΔT=N·δτ
(4)

while the dispersion of the fiber should fulfill the following condition: the relative temporal displacement of the same temporal pulse corresponding to two adjacent spectral wavelengths in the spectral comb (that are separated by Δµ) will be equal to δτ: That way the pulse is separated into its spectral components (the wavelengths of the spectral comb):

τdis=β2z2·Δμ=β2z·Δλ·c2λ2=δτ
(5)

where τdis is the relative temporal displacement generated due to this dispersion, c is the speed of light and λ is the wavelength: λ·µ=c. This way if the last two equations are fulfilled and if the separation of the pulses in the train is also ΔT, we have generated temporally continues illumination that later on can be back compressed into the train of pulses.

The temporally continues illumination is now being modulated with our continuous flow of RF information. Later on this modulated data stream can be back compressed into a train of pulses with width of δτ (for each pulse) when passed through a DCF based system having opposite value of β2z.

We need also to take care that indeed Eq. (3) is fulfilled, i.e. the number of the spectral spikes or lasers in our broadband source (i.e. N) equals to the ratio between the temporal separation of adjacent pulses in the train divided by the width of each pulse (as stated in Eq. (3)) since only then a continuous extension of the pulse is generated. Therefore, N should be inversely equal to the duty cycle of the original train of pulses.

Since the broadband light source that we used is composed out of a discrete set of wavelengths (colors), the temporal extension is basically a generation of different temporal delay for each pulse that is associated with a different wavelength in the spectral comb. Therefore, the maximal extension of the pulse in the train equals to the number of discrete wavelengths in the illuminating source. Since the spectral separation of those wavelengths is larger than the bandwidth of the modulated signal, the temporal information that is attached to each pulse at each wavelength is not mixed with the other pulses due to their mutual incoherence.

Figure 3(a) clarifies the schematic configuration for the proposed approach. In Fig. 3(b) we present a system application based upon information routing. After the RF data is seamlessly compressed into a train of pulses, several such trains originated from different data sources can be multiplexed together and later on, by using a routing switch, be redirected to different interfacing systems. Since the temporal width of the original pulses in the train of pulses is relatively large (several nsec and in the schemes of Figs. 1 and 2 we even used 40nsec), the individual routing of each RF data source may be realized by slow rate optical switch. After it’s routing the data of each train of compressed pulses can be decompressed and right after be analyzed, processed or stored.

Note that we will also require that the spectral width of each one of the wavelengths in the spectral comb of the illumination source will be narrower than 1/ΔT in order to avoid distortions in compression and decompression.

Fig. 3. (a) Schematic sketch of the operational principle. (b) Application of information routing.

In all the above mentioned derivation we did an approximation that took into account only three terms in the Taylor series for the phase delay β(µ):

β(μ)β0+β1μ+β22μ2
(6)

In the real case higher order terms exist as well. The obtained aberrations depend on the coefficients of those higher terms and their effect on the distortion of the temporal pulses resembles the deformation generated to the focusing spot of spatial imaging lens having coma (corresponds to µ 3) or spherical (corresponds to µ 4) etc aberrations.

In the regular case such aberrations would have caused an extension to the width of the pulses in the train especially when larger bandwidths are involved. Mathematical modeling and estimation of those distortions is presented in Ref. 18

18. M. Born and E. Wolf, Principles of optics: Electromagnetic theory of propagation, interference and diffraction of light, 7 edition (Cambridge University Press, 1999), pp 468–480.

for the analogous case of spatial optics. However, in our case the illuminating broadband source contains a set of spectral spikes and therefore the effect on each one of the pulses in the train is only a distorted displacement of the pulses (each at wavelength corresponding to different spectral spike) rather than deformation of the shape of each pulse (each pulse corresponds to relatively narrow band width). This distortion in displacement occurs in the compression and later on in the decompression stages. The eventual effect is that the light in the output of the dispersion system, prior to the data modulation stage, is not continuous and later on after the decompression it is not back composed into the original set of train of pulses as described in Fig. 3(a). That way the system is no longer completely seamless.

To estimate the generated distortion due to this effect let us take into account the comma as well as spherical aberrations:

β(μ)β0+β1μ+β22μ2+β36μ3+β424μ4
(7)

while the coefficients of β3 and β4 correspond to the comma and the spherical aberrations respectively. Instead of the result presented in Eq. (5), the relative displacement of two pulses corresponding to adjacent spectral wavelengths in the spectral comb (that are separated by Δµ) is becoming:

τdis=β2z·Δμ2+β3z·Δμ26+β4z·Δμ324
(8)

Since now the relative temporal displacement τdis is no longer proportional to the spectral separation between the wavelengths of the spectral comb (i.e. Δµ) the temporal extension will not be uniform and continuous. However, since the coefficients of β3 and β4 are relatively small in comparison to β2, we will choose the spectral bandwidth of the source not to be too large such that those distortions will be negligible. We will choose:

Δμmin{3β2β3,4β3β4}
(9)

For instance, assuming fiber having β2=20 [ps2/km], β3=0.14 [ps3/km] and β4=0.11 [ps4/km] yields that one must set Δµ to be much less than 5 THz which is Δλ of 40nm. This suits well with the ITU grid of optics communication and the laser sources that are available in that industry having spectral separation of Δλ of less than 1nm (therefore choosing Δλ of less than 1nm fulfills the condition of Eq. (9)).

In addition since the temporal width of each pulse in the original train is large comparably to the bandwidth of the modulated RF data, the shape of the pulse itself is less relevant in its effect over the overall performance of the proposed system since the temporal extension as well as compression is not due to the shape of the pulse or its bandwidth but rather due to the fact that the illumination source is a broadband source (e.g. containing spectral comb). Due to this as well as due to the spectral structure of the illumination there is almost no interaction between temporally adjacent pulses in the train. Therefore, the modulation extinction ratio is hardly affected and no special request needs to be added for the performance of the electro-optical modulator that is responsible for the modulation of the RF data on top of the optical carrier [20

20. E. Shumakher, A. Hayat, A. Freimain, M. Nazarathy, and G. Eisenstein, “Timing extraction of a 10 Gbit/s NRZ signal using an electro-optic multiplication scheme,” IEEE Photonic Technol. Lett. 16, 2353–2355 (2004). [CrossRef]

].

3. Experimental investigation

Due to equipment limitations (related to the optical power level) we have constructed only the setup described in Fig. 1. However its operation principle is identical to the general setup of Fig. 2 and its experimental investigation may provide with the proof of principle that we wish to obtain. In Figs. 4 and 5 we present the experimental results for the temporal extension of the pulses in the train as well as its compression after adding the modulation of the RF data.

Fig. 4. Experimental results using δL=1.5m (a). Output after chromatic delay of ≈8 ns (the two channels with their combination). (b) The same as in 4(a) but with data modulation. (c) Output after decreasing the chromatic delay in the DCF (i.e. the temporal compression). (d) The same as in 4(c) but with data modulation.

In Fig. 4 we present experimental results for δL=1.5m. In Fig. 4(a) we present the output after chromatic delay of approximately 8nsec (we show both wavelengths after their combination). In Fig. 4(b) we present the same as in Fig. 4(a) but with the data modulation. One may see that indeed the two wavelengths have relative temporal delay and that after their combination the modulated information appears over temporally extended pulse.

In Fig. 4(c) we present the output after decreasing the chromatic delay in the DCF (i.e. the temporal compression). Indeed now the two wavelengths have much smaller relative temporal delay. In Fig. 4(d) we present the same as in Fig. 4(c) but with the data modulation (i.e. the compression back to the train of pulses was applied over the modulated signals of Fig. 4(b)). In all the figures of Fig. 4 we have the measurement of each channel as well as their summation in solid blue line. The time base in Fig. 4 is 20nsec per square.

In Fig. 5 additional experimental results are presented. There we used δL=3m. In Fig. 5(a) we show the output after chromatic delay of approximately 16nsec (the two channels with their combination). We performed temporal extension of the pulses in the train of pulses. Figure 5(b) is the same as in Fig. 5(a) but with the data modulation. Figure 5(c) presents the output after decreasing the chromatic delay using DCF, i.e. after the temporal compression. Figure 5(d) is the same as 5(c) but with the data modulation (i.e. the compression is applied over the modulated data of Fig. 5(b)). In all the figures of Fig. 5 we have the measurement of each channel as well as their summation in solid blue line. The time base in Fig. 5 is 20nsec per square.

Fig. 5. Experimental results using δL=3m (a) Output after chromatic delay of ≈16 ns (the two channels with their combination). (b) The same as in 5(a) but with data modulation. (c) Output after decreasing the chromatic delay in the DCF (i.e. after the temporal compression). (d) The same as in 5(c) but with data modulation.

Note that in Fig. 4 as well as in Fig. 5 we present the temporal expansions, data modulation and eventually the optical compression of a single pulse out of the original train of pulses (the digital scope captures and displays periodic signals).

4. Conclusions

In this paper we have presented a new approach for temporal seamless capability for analyzing and processing of RF photonic information flow using all-optical and electro-optical low rate devices. The concept is based upon a configuration which takes a broadband source modulates it into a train of pulses, then temporally expands those pulses to generate temporally continuous carrier. On top of this carrier a seamless RF data is being modulated. This data is later on compressed. The temporal extension as well as compression is done using the property of chromatic dispersion existing in regular fibers as well as DCFs.

Each pulse in the generated output train of pulses (that encodes within the seamless RF data) can be dealt separately with low rate electronics since the temporal width of the pulses in the train is relatively large. Several trains of pulses having encoding of different RF data sources can be mixed together and later on routed away by low rate switch and then be decompressed, analyzed, filtered or stored.

Preliminary experimental demonstration of the proposed concept was presented.

References and links

1.

Z. Zalevsky, A. Shemer, D. Mendlovic, and S. Zach, “Passive and periodically ultra fast RF-photonic spectral scanner,” Opt. Express 14, 8367–8381 (2006). [CrossRef] [PubMed]

2.

O. Raz, R. Rotman, Y. Danziger, and M. Tur, “Implementation of photonic true time delay using high-order-mode dispersion compensating fibers,” IEEE Photon. Technol. Lett. 16, 1367–1369 (2004). [CrossRef]

3.

R. Rotman, O. Raz, and M. Tur, “Analysis of a true time delay photonic beam former for transmission of a linear frequency-modulated waveform,” J. Lightwave Technol. 23, 4026–4036 (2005). [CrossRef]

4.

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]

5.

O. Levinson and M. Horowitz, “Generation of Complex Microwave and Millimeter-Wave Pulses Using Dispersion and Kerr Effect in Optical Fiber Systems,” J. Lightwave Technol. 21, 1179–1186 (2003). [CrossRef]

6.

H. Chi and J. Yao, “An approach to photonic generation of high-frequency phase-coded RF pulses,” IEEE Photon. Technol. Lett. 19, 768–770 (2007). [CrossRef]

7.

A. Zeitouny, S. Stepanov, O. Levinson, and M. Horowitz, “Optical generation of linearly chirped microwave pulses using fiber Bragg gratings,” IEEE Photon. Technol. Lett. 17, 660–662 (2005). [CrossRef]

8.

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 Photon. Technol. Lett. 17, 432–434 (2005). [CrossRef]

9.

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]

10.

V. Lavielle, I. Lorgere, J. L. Le Gout, S. Tonda, and D. Dolfi, “Wideband versatile radio-frequency spectrum analyzer,” Opt. Lett. 28, 384–386. (2003). [CrossRef] [PubMed]

11.

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 and Guid. Wave Lett. 5, 414–416 (1995). [CrossRef]

12.

R. A. Minasian and D. B. Hunter, “Photonic signal processing of microwave signals using fiber Bragg gratings,” Proc. OFC, ThH3, 339–340 (1997).

13.

D. Norton, S. Johns, C. Keefer, and R. Soref, “Tunable microwave filter using high dispersion fiber time delays,” IEEE Photon. Technol. Lett. 6, 831–832 (1994). [CrossRef]

14.

M. Y. Frankel and R. D. Esman, “Fiber optic tunable microwave transversal filter,” IEEE Photon. 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 Photon. Technol. Lett. 9, 339–341 (1997). [CrossRef]

16.

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]

17.

A. W. Lohmann and D. Mendlovic, “Temporal filtering with time lenses,” Appl. Opt. 31, 6212–6219 (1992). [CrossRef] [PubMed]

18.

M. Born and E. Wolf, Principles of optics: Electromagnetic theory of propagation, interference and diffraction of light, 7 edition (Cambridge University Press, 1999), pp 468–480.

19.

A. J. Lowery, S. Wang, and M. Premaratne, “Calculation of power limit due to fiber nonlinearity in optical OFDM systems,” Opt. Express 15, 13282–13287 (2007). [CrossRef] [PubMed]

20.

E. Shumakher, A. Hayat, A. Freimain, M. Nazarathy, and G. Eisenstein, “Timing extraction of a 10 Gbit/s NRZ signal using an electro-optic multiplication scheme,” IEEE Photonic Technol. Lett. 16, 2353–2355 (2004). [CrossRef]

OCIS Codes
(230.2090) Optical devices : Electro-optical devices
(250.5300) Optoelectronics : Photonic integrated circuits

ToC Category:
Optical Devices

History
Original Manuscript: November 20, 2007
Revised Manuscript: March 6, 2008
Manuscript Accepted: March 6, 2008
Published: May 19, 2008

Citation
Zeev Zalevsky, Amir Shemer, and Shlomo Zach, "RF-photonic chirp encoder and compressor for seamless analysis of information flow," Opt. Express 16, 7904-7914 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-11-7904


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References

  1. Z. Zalevsky, A. Shemer, D. Mendlovic, and S. Zach, "Passive and periodically ultra fast RF-photonic spectral scanner," Opt. Express 14, 8367-8381 (2006). [CrossRef] [PubMed]
  2. O. Raz, R. Rotman, Y. Danziger, and M. Tur, "Implementation of photonic true time delay using high-order-mode dispersion compensating fibers," IEEE Photon. Technol. Lett. 16, 1367-1369 (2004). [CrossRef]
  3. R. Rotman, O. Raz, and M. Tur, "Analysis of a true time delay photonic beam former for transmission of a linear frequency-modulated waveform," J. Lightwave Technol. 23, 4026-4036 (2005). [CrossRef]
  4. 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]
  5. O. Levinson and M. Horowitz, "Generation of Complex Microwave and Millimeter-Wave Pulses Using Dispersion and Kerr Effect in Optical Fiber Systems," J. Lightwave Technol. 21, 1179-1186 (2003). [CrossRef]
  6. H. Chi and J. Yao, "An approach to photonic generation of high-frequency phase-coded RF pulses," IEEE Photon. Technol. Lett. 19, 768-770 (2007). [CrossRef]
  7. A. Zeitouny, S. Stepanov, O. Levinson, and M. Horowitz, "Optical generation of linearly chirped microwave pulses using fiber Bragg gratings, " IEEE Photon. Technol. Lett. 17, 660-662 (2005). [CrossRef]
  8. 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 Photon. Technol. Lett. 17, 432-434 (2005). [CrossRef]
  9. 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]
  10. V. Lavielle, I. Lorgere, J. L. Le Gout, S. Tonda, and D. Dolfi, "Wideband versatile radio-frequency spectrum analyzer," Opt. Lett. 28, 384-386. (2003). [CrossRef] [PubMed]
  11. H. R. Fetterman, Y. Chang, D. C. Scott, S. R. Forrest,  et al., "Optically controlled phased array radar receiver using SLM switched real time delays," IEEE Microwave and Guid. Wave Lett. 5, 414-416 (1995). [CrossRef]
  12. R. A. Minasian and D. B. Hunter, "Photonic signal processing of microwave signals using fiber Bragg gratings," Proc. OFC, ThH3, 339-340 (1997).
  13. D. Norton, S. Johns, C. Keefer, and R. Soref, "Tunable microwave filter using high dispersion fiber time delays," IEEE Photon. Technol. Lett. 6, 831-832 (1994). [CrossRef]
  14. M. Y. Frankel and R. D. Esman, "Fiber optic tunable microwave transversal filter," IEEE Photon. 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 Photon. Technol. Lett. 9, 339-341 (1997). [CrossRef]
  16. 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]
  17. A. W. Lohmann and D. Mendlovic, "Temporal filtering with time lenses," Appl. Opt. 31, 6212-6219 (1992). [CrossRef] [PubMed]
  18. M. Born and E. Wolf, Principles of optics: Electromagnetic theory of propagation, interference and diffraction of light, 7th ed. (Cambridge University Press, 1999), pp 468-480.
  19. A. J. Lowery, S. Wang, and M. Premaratne, "Calculation of power limit due to fiber nonlinearity in optical OFDM systems," Opt. Express 15, 13282-13287 (2007). [CrossRef] [PubMed]
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