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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 5 — Feb. 28, 2011
  • pp: 4566–4576
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Highly chirped single-bandpass microwave photonic filter with reconfiguration capabilities

Mario Bolea, José Mora, Beatriz Ortega, and José Capmany  »View Author Affiliations


Optics Express, Vol. 19, Issue 5, pp. 4566-4576 (2011)
http://dx.doi.org/10.1364/OE.19.004566


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Abstract

We propose a novel photonic structure to implement a chirped single-bandpass microwave photonic filter based on the amplitude modulation of a broadband optical signal transmitted by a non-linear dispersive element and an interferometric system prior to balanced photodetection. A full reconfigurability of the filter is achieved since amplitude and phase responses can be independently controlled. We have experimentally demonstrated chirp values up to tens of ns/GHz, which is, as far as we know, one order of magnitude better than others achieved by electrical approaches and furthermore, without restrictions in terms of frequency tuning since a frequency operation range up to 40 GHz has been experimentally demonstrated.

© 2011 OSA

1. Introduction

Microwave photonics can be considered a research area where microwave and optical fields converge. The different topics covered by microwave photonics are focused on photonic generation, processing, control and distribution of microwave and millimeter-wave signals. The main interest on microwave photonics lies in the use of photonic technologies to provide functions in microwave systems that are very complex or even impossible to be carried out directly in the radiofrequency (RF) domain. Nevertheless, the great potential of microwave photonics is achieved in Radio-over-Fiber (RoF) systems since it profits from the fiber advantages for the transport and distribution of RF signal such as: low loss, high bandwidth, immunity to electromagnetic interference (EMI) and the possibility of tuning and reconfiguration [1

1. J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007). [CrossRef]

,2

2. J. Yao, “Microwave photonics,” J. Lightwave Technol. 27(3), 314–335 (2009). [CrossRef]

].

Photonic signal processing has attracted a special interest due to the capacity to operate with microwave, millimeter-wave and RF signals free from bandwidth constraint [3

3. J. Capmany, B. Ortega, D. Pastor, and S. Sales, “Discrete-Time optical processing of microwave signals,” J. Lightwave Technol. 23(2), 702–723 (2005). [CrossRef]

]. Moreover, in a RoF environment, the signal processing directly in the optical domain avoids the need of electro-optical and opto-electrical conversions. Microwave photonic filters can be considered as the key element in processing and control systems. Most of the proposed systems in the literature to implement microwave photonic filters are focused on modifying the amplitude response without exploiting the phase characteristics [4

4. J. Capmany, B. Ortega, and D. Pastor, “A tutorial on Microwave Photonic Filters,” J. Lightwave Technol. 24(1), 201–229 (2006). [CrossRef]

]. Nevertheless, the use of filters with dynamic and/or non constant group delay arises great interest in applications where signal processing not only involves the signal amplitude control. In this sense, chirped filters typically present a flat magnitude and quadratic phase characteristic i.e. the delay follows a linear behaviour characterized by a certain slope within the passband [5

5. M. A. G. Laso, T. Lopetegi, M. J. Erro, D. Benito, M. J. Garde, M. A. Muriel, M. Sorolla, and M. Guglielmi, “Real-Time spectrum analysis in microstrip technology,” IEEE Trans. Microw. Theory Tech. 51(3), 705–717 (2003). [CrossRef]

]. This kind of filters has become valuable components in applications which require a careful control over signal temporal characteristics such as high-performance radar, Ultra-Wideband communications and spectral analysis systems involving high bandwidth signal processing [5

5. M. A. G. Laso, T. Lopetegi, M. J. Erro, D. Benito, M. J. Garde, M. A. Muriel, M. Sorolla, and M. Guglielmi, “Real-Time spectrum analysis in microstrip technology,” IEEE Trans. Microw. Theory Tech. 51(3), 705–717 (2003). [CrossRef]

7

7. G. N. Saddik, R. S. Singh, and R. Brown, “Ultra-wideband multifunctional communications/radar system,” IEEE Trans. Microw. Theory Tech. 55(7), 1431–1437 (2007). [CrossRef]

].

In the literature, several approaches in the electrical domain have been proposed to implement chirped delay line filters. Firstly, surface acoustic wave (SAW) devices were proposed as chirped delay lines implemented on stripline [8

8. R. S. Withers, A. C. Anderson, P. V. Wright, and S. A. Reible, “Superconductive tapped delay lines for microwave analog signal processing,” IEEE Trans. Magn. 19(3), 480–484 (1983). [CrossRef]

,9

9. F. Huang, “Low loss quasitransversal microwave filters with specified amplitude and phase characteristics,” Proc. Inst. Electr. Eng. 140, 433–440 (1993).

] and coplanar line [10

10. F. Huang, “Quasitransversal synthesis of microwave chirped filters,” Electron. Lett. 28(11), 1062–1064 (1992). [CrossRef]

] structures. Nevertheless, these technologies were limited to a few gigahertz frequency operation range and exhibited high propagation losses. During the last decade, chirped electromagnetic-bandgap (EBG) structures in microstrip technology operating in reflective mode have been also proposed [11

11. T. Lopetegi, M. A. G. Laso, J. Hernandez, M. Bacaicoa, D. Benito, M. J. Garde, M. Sorolla, and M. Guglielmi, “New microstrip “Wiggly-Line” filters with spurious passband supression,” IEEE Trans. Microw. Theory Tech. 49(9), 1593–1598 (2001). [CrossRef]

, 12

12. M. A. G. Laso, T. Lopetegi, M. J. Erro, D. Benito, M. J. Garde, M. A. Muriel, M. Sorolla, and M. Guglielmi, “Chirped delay lines in microstrip Technology,” IEEE Trans. Microw. Wireless Compon. Lett. 11(12), 486–488 (2001). [CrossRef]

]. Their experimental implementation have been demonstrated for a fixed [5

5. M. A. G. Laso, T. Lopetegi, M. J. Erro, D. Benito, M. J. Garde, M. A. Muriel, M. Sorolla, and M. Guglielmi, “Real-Time spectrum analysis in microstrip technology,” IEEE Trans. Microw. Theory Tech. 51(3), 705–717 (2003). [CrossRef]

, 13

13. J. D. Schwartz, J. Azaña, and D. V. Plant, “Experimental demonstration of real-time spectrum analysis using dispersive microstrip,” IEEE Trans. Microw. Wireless Compon. Lett. 16(4), 215–217 (2006). [CrossRef]

] and tunable [14

14. J. D. Schwartz, I. Arnedo, M. A. G. Laso, T. Lopetegi, J. Azaña, and D. V. Plant, “An electronic UWB continuously tunable time-delay system with nanosecond delays,” IEEE Trans. Microw. Wireless Compon. Lett. 18(2), 103–105 (2008). [CrossRef]

] electrical group-delay time. Nevertheless, the frequency operation range of these devices is restricted to 15 GHz with a maximum group delay slope of 2 ns/GHz due to the excessive losses over long distances [6

6. J. D. Schwartz, J. Azaña, and D. V. Plant, “A Fully Electronic System for the Time Magnification of Ultra-Wideband Signals,” IEEE Trans. Microw. Theory Tech. 55(2), 327–334 (2007). [CrossRef]

]. In order to achieve higher frequencies, substrate integrated waveguides (SIW) have been recently proposed to implement EBG structures which extend the operation frequency range up to several tens of gigahertz [15

15. J. D. Schwartz, R. Abhari, D. V. Plant, and J. Azaña, “Design and analysis of 1-D uniform and chirped electromagnetic bandgap structures in substrate-integrated waveguides,” IEEE Trans. Microw. Theory Tech. 58(7), 1858–1866 (2010). [CrossRef]

], although the group-delay slope only achieves 0.2 ns/GHz as a maximum value. In this sense, the implementation of chirped filters in optical domain becomes a promising solution thanks to the higher frequency operation range and flexibility demonstrated by microwave photonics.

2. Theoretical background

Figure 1
Fig. 1 Block diagram of chirped filter based on a single bandpass photonic filter with differential detection.
shows the block diagram of the proposed chirped single bandpass filter. Firstly, a broadband optical signal, whose power spectral distribution can be properly adjusted, is amplitude modulated by a RF-signal in an external electrooptical modulator (EOM). The modulated signal is launched into a nonlinear dispersive element which can be characterized as a phase filter whose optical transfer function is given by:
HOPT(ω)=ejφ(ω)
(1)
where ω corresponds to the angular optical frequency. Phase dependence can be developed by means of a Taylor expansion around the central frequency of the optical source ω0 [16

16. J. Mora, B. Ortega, A. Díez, J. L. Cruz, M. V. Andrés, J. Capmany, and D. Pastor, “Photonic microwave tunable single-bandpass filter based on a Mach-Zehnder Interferometer,” J. Lightwave Technol. 24(7), 2500–2509 (2006). [CrossRef]

]:
φ(ω)=φ0+φ˙0(ωω0)+12!φ¨0(ωω0)2+13!φ0(ωω0)3
(2)
whereφ˙0is the group-delay time at the central optical frequency ω0 andφ¨0andφ0are the first order dispersion and the dispersion slope, respectively, evaluated at the same frequency.

The optical signal undergoes a group delay time through the dispersive element which can be obtained from Eq. (2) by means of the first order derivative:

τOPT(ω)=dφ(ω)dω=φ˙0+φ¨0(ωω0)+12φ0(ωω0)2
(3)

Following a new derivative order from Eq. (3), the dispersion dependence on the optical frequency is given by:

φ¨(ω)=dτOPT(ω)dω=φ¨0+φ0(ωω0)
(4)

At the output of the nonlinear dispersive element, a Mach-Zehnder Interferometer (MZI) slices the optical spectrum and allows to obtain the different filter taps with a continuous and sinusoidal transfer function T(ω)described as:
T(ω)=12[1+cos(2πωω0Δω)]withΔω=2πΔτ
(5)
where Δω corresponds to the periodicity of the MZI transfer function and Δτ is the optical delay introduced between both arms.

Finally, signal detection is done by means of a balanced photodetector (BPD) whose input ports, P1 and P2, are connected with both MZI output arms. This device realizes the electrical subtraction of the signal detected in both ports to obtain the system transfer function.

In order to understand the system behaviour, we are going to carry out a qualitative analysis making use of numerical simulations whose main results are shown in Fig. 2
Fig. 2 Uniform optical source power distribution with a central optical frequency and a bandwidth of (a) ω1 and δω', (b) ω2 and δω' and (c) ω0 and δω; (d), (e) and (f) and (g), (h) and (i) are the amplitude response and electrical group-delay time, respectively, corresponding to each optical source case.
.

Firstly, a uniform optical source is selected with a δω' bandwidth of 0.5 THz centred at ω1 optical frequency of 191.5 THz (Fig. 2a), a dispersive element characterized by φ¨0=500ps2and φ0=2.5ps3, and an optical delay (Δτ) between MZI arms around 20π ps. As a result, an electrical transfer function with a passband around f1 is obtained as can be observed in Fig. 2d. When the source is centred at 196 THz (ω2) (Fig. 2b), the central frequency of the passband is placed around f2 since dispersion value is different according to Eq. (6), as can be confirmed in the electrical transfer function (Fig. 2e).

Δf=f2-f1f0δωφ¨0φ0
(7)

We also pay attention to the electrical group-delay time obtained in each case. In Fig. 2g, we plot the electrical group-delay when the optical sourced is centred at ω1. As can be observed, it keeps a constant value (τ1) within the passband. On the other hand, when the optical source is centred at ω2 the electrical group-delay time also presents a constant value of τ2 within the passband (Fig. 2h). In both cases, an asymmetry is found out of band which is due the effects of second order dispersion over the electrical transfer function.

In order to show the chirp characteristics of the system, the source is extended to cover the whole optical bandwidth δω giving an electrical group-delay time which presents a linear behaviour within the passband from τ1 and τ2 as can be observed in Fig. 2i. We can obtain from Eq. (3) the electrical group-delay ΔτRF between the passband centred at f1 and f2 which is given by:

ΔτRF=τOPT(ω2)τOPT(ω1)=φ¨0δω
(8)

Note that the electrical group-delay ΔτRF corresponds to the difference optical delay produced in the dispersive element. Thereby, according to the results shown in Fig. 2, the passband generated can be understood as the addition of all the single passband produced around fi with an electrical group-delay τi from the infinitesimal optical source components centred at ωi.

C=ΔτRFΔfφ¨02f0φ0
(9)

From Eq. (9), we can observe that the chirp effect within the passband is a consequence of the use of a nonlinear dispersive element presenting a dispersion slope φ0 which affects the whole optical source spectrum. Note that the sign of the chirp C is determined by the parameter φ0of the dispersive element.

On the other hand, as we can observe in Fig. 3, the baseband component of the filter transfer function has been removed due to the use of balanced photodetection and a single bandpass filter has been achieved. Many structures proposed in the literature increase their complexity in order to remove the baseband component by means of the implementation of negative coefficients of the filter [3

3. J. Capmany, B. Ortega, D. Pastor, and S. Sales, “Discrete-Time optical processing of microwave signals,” J. Lightwave Technol. 23(2), 702–723 (2005). [CrossRef]

,4

4. J. Capmany, B. Ortega, and D. Pastor, “A tutorial on Microwave Photonic Filters,” J. Lightwave Technol. 24(1), 201–229 (2006). [CrossRef]

]. As demonstrated above, our structure allows to benefit from these advantages without an increasing the system complexity.

3. Experimental setup

In the following, we show the capacity of tuning the central frequency of the passband by the adjustment of the VDL in the MZI according to Eq. (6). A 38.4 nm uniform optical source profile was set and two different values of dispersion, φ¨0=525ps2andφ¨0=1050ps2, were induced in the system. For each case, the optical delay of the MZI is adjusted to obtain the central frequency of the passband within a range of frequencies from 5 to 40 GHz in steps of 2.5 GHz. The experimental results (■,●) are plotted in Fig. 6
Fig. 6 Experimental relationship between optical delay in MZI and bandpass central frequency forφ¨0=525ps2 (■) and φ¨0=1050ps2 (●) and the theoretical prediction in dashed line.
and present a linear relationship for each dispersive element with slopes corresponding to both dispersion values of 0.31 and 0.15 GHz/ps, respectively. This linear behaviour was expected from Eq. (6) and the theoretical prediction has been also depicted in Fig. 6 (dashed line), showing an excellent agreement with the experimental results. Note that the passband central frequency can be tuned over a large frequency range since carrier suppression effect is avoided.

In this point, we evaluate the range of the filter bandwidth and chirp values when the central frequency of the filter is fixed. We experimentally demonstrate the dependence of the filter bandwidth and the chirp with the optical bandwidth of the source and the dispersion introduced in the system according to Eqs. (7) and (9), respectively

In the following, the optical source uniform profile was maintained but the optical bandwidth is changed by increasing the number of channels in the OCS. System dispersion is set to φ¨0=1050ps2and φ¨0=525ps2 and the central frequency of the passband in each case was around 15 GHz and 30 GHz by means of optical delays in the MZI of 99.3 and 198.1 psec (forφ¨0=1050ps2) and 49.5 and 98.2 ps (forφ¨0=525ps2). Figure 7
Fig. 7 Experimental relationship between 10-dB bandwidth and optical source width for: φ¨0=525ps2, f0 = 15 GHz (●) and 2φ¨0, f0 (■); (b) φ¨0, 2 · f0 () and2φ¨0, 2·f0 (). Theoretical simulations (dashed line).
shows the experimental results (●, ■, ▼, ▲) for the different cases. We can observe the relationship between 10-dB bandwidth (BW-10dB) of the passband and the optical bandwidth. The higher system dispersion is, the wider passband is, following a linear behaviour between both magnitudes as predicted in Eq. (7). These magnitudes are characterized by slopes of 0.07 and 0.14 GHz/nm for the tuning frequencies of filter at 15 and 30 GHz, respectively. Note the good agreement of the theoretical simulations (dashed line) in Eq. (7) with the experimental measurements.

Moreover, as another main advantage over the last microwave photonic filter proposals, the chirp within the passband of the filter in our system can be modified by means of the total dispersion introduced in the system. The optical signal is adjusted to a 38.4 nm width uniform profile and the dispersion induced in the system is changed from −105 to −1575 ps2. We measure the electrical group-delay within the passband generated by the photonic filter when it is tuned at 15 and 30 GHz. Absolute value of the slope of the electrical group-delay (|C|) obtained experimentally in each case (■,●) is shown in Fig. 8
Fig. 8 Experimental results for relationship between first order dispersion ( |φ¨0|) and filter chirp within passband when it is tuned at 15 GHz (■) and 30 GHz (). Theoretical prediction for both cases has been added in dashed line.
together with the theoretical prediction according to Eq. (9). As can be observed, the higher system dispersion is, the higher chirp is obtained, following a linear behaviour so that filter chirp is incremented in the same order as system dispersion with values from 1.02 to 17.20 and 0.50 to 8.43 ns/GHz for 15 and 30 GHz respectively. We note as |C| is reduced when the central frequency passband is increased as was predicted from Eq. (9). As was previously mentioned, electrical technologies are restricted in terms of frequency operation range as microstrip structures up to 15 GHz or in terms chirp for SIW which present a maximum value of 0.2 ns/GHz. In this way, the structure that we propose in this paper improves both the frequency operation range and passband chirp. Although the system dispersion is introduced by optical fiber links, in order to achieve a compactness solution it can be used different elements as linearly chirped fiber Bragg gratings (LCFBG). Since it is necessary the use of a broadband dispersive element, this structure can be taken advantage of last wideband LCFBG design and fabrication which can operate over 35 nm range [17

17. S. Wakabayashi and A. Baba, “Design and fabrication of an apodization profile in linearly chirped fiber Bragg gratings for wideband > 35 nm and compact tunable dispersion compensator,” Appl. Opt. 19, 1653–1660 (1980).

].

Finally, as previously shown, we demonstrate the control of the system transfer function by reconfiguring the optical spectrum. As depicted in Fig. 7, the bandwidth of the filter passband can be adjusted by changing the optical bandwidth of the source. In the same way, if the optical power distribution profile is modified, the modulus of the electrical transfer function can be changed. In order to demonstrate it, an apodization factor was applied to the uniform profile (dashed line) as shown in Fig. 9a
Fig. 9 (a) Optical source power distribution, (b) amplitude response and (c) electrical group-delay response for uniform (dashed line) and apodized (solid line) when passband is tuned around 32.5 GHz. CSE when dispersion is −525 ps2 (dotted line).
(solid line), a dispersion of −525 ps2 and the optical delay of the MZI was adjusted to tune the frequency of the passband at 32.5 GHz. In Fig. 9b, amplitude responses obtained with and without apodization of the optical source are plotted. As can be observed, the shape of the passband has been modified with a significant reduction of the secondary lobes and the avoidance of the ripple existing when a uniform profile is used. Figure 9c shows the corresponding electrical-group delay responses which behaviour is independent on the optical source power distribution. Therefore, we have demonstrated a fully control of the amplitude response of the filter independently of the electrical group-delay characteristic within the passband. Carrier Suppression Effect (CSE) curve has been also depicted in both Figs. 9b and 9c (dotted line), but it does not affect to the filter transfer function, although some nulls are present in the passband, as explained above.

4. Conclusion

Acknowledgements

The research leading to these results has received funding from the European Community’s Seventh Framework Programme (FP7) under project 212.352 ALPHA “Architectures for fLexible Photonic Home and Access networks” The authors also wish to acknowledge “Ajudes per a la realització de projectes precompetitius de I+D per a equips d’investigació” GVPRE/2008/250 supported by the Generalitat Valenciana and PROMETEO GVA 2008/092 MICROWAVE PHOTONICS and complementary help for I+D projects for quality groups by Generalitat Valenciana ACOMP/2010/196.

References and links

1.

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007). [CrossRef]

2.

J. Yao, “Microwave photonics,” J. Lightwave Technol. 27(3), 314–335 (2009). [CrossRef]

3.

J. Capmany, B. Ortega, D. Pastor, and S. Sales, “Discrete-Time optical processing of microwave signals,” J. Lightwave Technol. 23(2), 702–723 (2005). [CrossRef]

4.

J. Capmany, B. Ortega, and D. Pastor, “A tutorial on Microwave Photonic Filters,” J. Lightwave Technol. 24(1), 201–229 (2006). [CrossRef]

5.

M. A. G. Laso, T. Lopetegi, M. J. Erro, D. Benito, M. J. Garde, M. A. Muriel, M. Sorolla, and M. Guglielmi, “Real-Time spectrum analysis in microstrip technology,” IEEE Trans. Microw. Theory Tech. 51(3), 705–717 (2003). [CrossRef]

6.

J. D. Schwartz, J. Azaña, and D. V. Plant, “A Fully Electronic System for the Time Magnification of Ultra-Wideband Signals,” IEEE Trans. Microw. Theory Tech. 55(2), 327–334 (2007). [CrossRef]

7.

G. N. Saddik, R. S. Singh, and R. Brown, “Ultra-wideband multifunctional communications/radar system,” IEEE Trans. Microw. Theory Tech. 55(7), 1431–1437 (2007). [CrossRef]

8.

R. S. Withers, A. C. Anderson, P. V. Wright, and S. A. Reible, “Superconductive tapped delay lines for microwave analog signal processing,” IEEE Trans. Magn. 19(3), 480–484 (1983). [CrossRef]

9.

F. Huang, “Low loss quasitransversal microwave filters with specified amplitude and phase characteristics,” Proc. Inst. Electr. Eng. 140, 433–440 (1993).

10.

F. Huang, “Quasitransversal synthesis of microwave chirped filters,” Electron. Lett. 28(11), 1062–1064 (1992). [CrossRef]

11.

T. Lopetegi, M. A. G. Laso, J. Hernandez, M. Bacaicoa, D. Benito, M. J. Garde, M. Sorolla, and M. Guglielmi, “New microstrip “Wiggly-Line” filters with spurious passband supression,” IEEE Trans. Microw. Theory Tech. 49(9), 1593–1598 (2001). [CrossRef]

12.

M. A. G. Laso, T. Lopetegi, M. J. Erro, D. Benito, M. J. Garde, M. A. Muriel, M. Sorolla, and M. Guglielmi, “Chirped delay lines in microstrip Technology,” IEEE Trans. Microw. Wireless Compon. Lett. 11(12), 486–488 (2001). [CrossRef]

13.

J. D. Schwartz, J. Azaña, and D. V. Plant, “Experimental demonstration of real-time spectrum analysis using dispersive microstrip,” IEEE Trans. Microw. Wireless Compon. Lett. 16(4), 215–217 (2006). [CrossRef]

14.

J. D. Schwartz, I. Arnedo, M. A. G. Laso, T. Lopetegi, J. Azaña, and D. V. Plant, “An electronic UWB continuously tunable time-delay system with nanosecond delays,” IEEE Trans. Microw. Wireless Compon. Lett. 18(2), 103–105 (2008). [CrossRef]

15.

J. D. Schwartz, R. Abhari, D. V. Plant, and J. Azaña, “Design and analysis of 1-D uniform and chirped electromagnetic bandgap structures in substrate-integrated waveguides,” IEEE Trans. Microw. Theory Tech. 58(7), 1858–1866 (2010). [CrossRef]

16.

J. Mora, B. Ortega, A. Díez, J. L. Cruz, M. V. Andrés, J. Capmany, and D. Pastor, “Photonic microwave tunable single-bandpass filter based on a Mach-Zehnder Interferometer,” J. Lightwave Technol. 24(7), 2500–2509 (2006). [CrossRef]

17.

S. Wakabayashi and A. Baba, “Design and fabrication of an apodization profile in linearly chirped fiber Bragg gratings for wideband > 35 nm and compact tunable dispersion compensator,” Appl. Opt. 19, 1653–1660 (1980).

OCIS Codes
(060.0060) Fiber optics and optical communications : Fiber optics and optical communications
(060.5625) Fiber optics and optical communications : Radio frequency photonics

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: November 2, 2010
Revised Manuscript: January 21, 2011
Manuscript Accepted: January 26, 2011
Published: February 24, 2011

Citation
Mario Bolea, José Mora, Beatriz Ortega, and José Capmany, "Highly chirped single-bandpass microwave photonic filter with reconfiguration capabilities," Opt. Express 19, 4566-4576 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-5-4566


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References

  1. J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007). [CrossRef]
  2. J. Yao, “Microwave photonics,” J. Lightwave Technol. 27(3), 314–335 (2009). [CrossRef]
  3. J. Capmany, B. Ortega, D. Pastor, and S. Sales, “Discrete-Time optical processing of microwave signals,” J. Lightwave Technol. 23(2), 702–723 (2005). [CrossRef]
  4. J. Capmany, B. Ortega, and D. Pastor, “A tutorial on Microwave Photonic Filters,” J. Lightwave Technol. 24(1), 201–229 (2006). [CrossRef]
  5. M. A. G. Laso, T. Lopetegi, M. J. Erro, D. Benito, M. J. Garde, M. A. Muriel, M. Sorolla, and M. Guglielmi, “Real-Time spectrum analysis in microstrip technology,” IEEE Trans. Microw. Theory Tech. 51(3), 705–717 (2003). [CrossRef]
  6. J. D. Schwartz, J. Azaña, and D. V. Plant, “A Fully Electronic System for the Time Magnification of Ultra-Wideband Signals,” IEEE Trans. Microw. Theory Tech. 55(2), 327–334 (2007). [CrossRef]
  7. G. N. Saddik, R. S. Singh, and R. Brown, “Ultra-wideband multifunctional communications/radar system,” IEEE Trans. Microw. Theory Tech. 55(7), 1431–1437 (2007). [CrossRef]
  8. R. S. Withers, A. C. Anderson, P. V. Wright, and S. A. Reible, “Superconductive tapped delay lines for microwave analog signal processing,” IEEE Trans. Magn. 19(3), 480–484 (1983). [CrossRef]
  9. F. Huang, “Low loss quasitransversal microwave filters with specified amplitude and phase characteristics,” Proc. Inst. Electr. Eng. 140, 433–440 (1993).
  10. F. Huang, “Quasitransversal synthesis of microwave chirped filters,” Electron. Lett. 28(11), 1062–1064 (1992). [CrossRef]
  11. T. Lopetegi, M. A. G. Laso, J. Hernandez, M. Bacaicoa, D. Benito, M. J. Garde, M. Sorolla, and M. Guglielmi, “New microstrip “Wiggly-Line” filters with spurious passband supression,” IEEE Trans. Microw. Theory Tech. 49(9), 1593–1598 (2001). [CrossRef]
  12. M. A. G. Laso, T. Lopetegi, M. J. Erro, D. Benito, M. J. Garde, M. A. Muriel, M. Sorolla, and M. Guglielmi, “Chirped delay lines in microstrip Technology,” IEEE Trans. Microw. Wireless Compon. Lett. 11(12), 486–488 (2001). [CrossRef]
  13. J. D. Schwartz, J. Azaña, and D. V. Plant, “Experimental demonstration of real-time spectrum analysis using dispersive microstrip,” IEEE Trans. Microw. Wireless Compon. Lett. 16(4), 215–217 (2006). [CrossRef]
  14. J. D. Schwartz, I. Arnedo, M. A. G. Laso, T. Lopetegi, J. Azaña, and D. V. Plant, “An electronic UWB continuously tunable time-delay system with nanosecond delays,” IEEE Trans. Microw. Wireless Compon. Lett. 18(2), 103–105 (2008). [CrossRef]
  15. J. D. Schwartz, R. Abhari, D. V. Plant, and J. Azaña, “Design and analysis of 1-D uniform and chirped electromagnetic bandgap structures in substrate-integrated waveguides,” IEEE Trans. Microw. Theory Tech. 58(7), 1858–1866 (2010). [CrossRef]
  16. J. Mora, B. Ortega, A. Díez, J. L. Cruz, M. V. Andrés, J. Capmany, and D. Pastor, “Photonic microwave tunable single-bandpass filter based on a Mach-Zehnder Interferometer,” J. Lightwave Technol. 24(7), 2500–2509 (2006). [CrossRef]
  17. S. Wakabayashi and A. Baba, “Design and fabrication of an apodization profile in linearly chirped fiber Bragg gratings for wideband > 35 nm and compact tunable dispersion compensator,” Appl. Opt. 19, 1653–1660 (1980).

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