Abstract

Pulse compression processing based on stimulated Brillouin scattering (SBS) in an optical fiber is theoretically and experimentally demonstrated. Broadband microwave signal is electro-optically modulated onto the pump lightwave that is launched into one end of the fiber. Acoustic wave in the fiber inherits the amplitude and phase information of the pump lightwave and thus the coupling between the acoustic wave and pump lightwave leads to the auto-correlated process of the pump lightwave as well as the modulated microwave signal. Derivation of the SBS coupling equations shows that the short-pulse probe lightwave amplified by the pump lightwave possesses the nature of auto-correlation formula. All-optical pulse compression of the broadband microwave signal is implemented after a subtraction between the detected probe pulse with and without SBS. A proof-of-concept experiment is carried out. The pulse compression of a linear frequency-modulated microwave signal with 1 GHz sweep range at the carrier frequency of 4.3 GHz is successfully realized, which well matches the theoretical analysis.

© 2016 Optical Society of America

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Broadband instantaneous frequency measurement based on stimulated Brillouin scattering

Xin Long, Weiwen Zou, and Jianping Chen
Opt. Express 25(3) 2206-2214 (2017)

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2015 (4)

2014 (3)

2013 (1)

B. J. Eggleton, C. G. Poulton, and R. Pant, “Inducing and harnessing stimulated Brillouin scattering in photonic integrated circuits,” Adv. Opt. Photonics 5(4), 536–587 (2013).
[Crossref]

2012 (2)

2011 (2)

X. Bao and L. Chen, “Recent progress in Brillouin scattering based fiber sensors,” Sensors (Basel) 11(4), 4152–4187 (2011).
[Crossref] [PubMed]

L. Zhang, L. Zhan, K. Qian, J. Liu, Q. Shen, X. Hu, and S. Luo, “Superluminal propagation at negative group velocity in optical fibers based on Brillouin lasing oscillation,” Phys. Rev. Lett. 107(9), 093903 (2011).
[Crossref] [PubMed]

2009 (2)

2008 (1)

2007 (3)

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

Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318(5857), 1748–1750 (2007).
[Crossref] [PubMed]

G. C. Valley, “Photonic analog-to-digital converters,” Opt. Express 15(5), 1955–1982 (2007).
[Crossref] [PubMed]

2006 (1)

J. Sun, Y. Dai, X. Chen, Y. Zhang, and S. Xie, “Stable dual-wavelength DFB fiber laser with separate resonant cavities and its application in tunable microwave generation,” IEEE Photonics Technol. Lett. 18(24), 2587–2589 (2006).
[Crossref]

2005 (2)

K. Y. Song, M. Herráez, and L. Thévenaz, “Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering,” Opt. Express 13(1), 82–88 (2005).
[Crossref] [PubMed]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94(15), 153902 (2005).
[Crossref] [PubMed]

1973 (1)

D. R. Morgan, “Surface acoustic wave devices and applications,” Ultrasonics 11(3), 121–131 (1973).
[Crossref]

Bao, X.

X. Bao and L. Chen, “Recent progress in Brillouin scattering based fiber sensors,” Sensors (Basel) 11(4), 4152–4187 (2011).
[Crossref] [PubMed]

Berizzi, F.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507(7492), 341–345 (2014).
[Crossref] [PubMed]

Bigelow, M. S.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94(15), 153902 (2005).
[Crossref] [PubMed]

Bogoni, A.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507(7492), 341–345 (2014).
[Crossref] [PubMed]

P. Ghelfi, F. Scotti, F. Laghezza, and A. Bogoni, “Photonic generation of phase-modulated RF signals for pulse compression techniques in coherent radars,” J. Lightwave Technol. 30(11), 1638–1644 (2012).
[Crossref]

Boyd, R. W.

Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318(5857), 1748–1750 (2007).
[Crossref] [PubMed]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94(15), 153902 (2005).
[Crossref] [PubMed]

Byun, H.

Capmany, J.

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

Capria, A.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507(7492), 341–345 (2014).
[Crossref] [PubMed]

Chen, J.

Chen, L.

X. Bao and L. Chen, “Recent progress in Brillouin scattering based fiber sensors,” Sensors (Basel) 11(4), 4152–4187 (2011).
[Crossref] [PubMed]

Chen, X.

J. Sun, Y. Dai, X. Chen, Y. Zhang, and S. Xie, “Stable dual-wavelength DFB fiber laser with separate resonant cavities and its application in tunable microwave generation,” IEEE Photonics Technol. Lett. 18(24), 2587–2589 (2006).
[Crossref]

Choi, D.-Y.

Cook, C. E.

C. E. Cook, “Pulse compression-key to more efficient radar transmission,” in Proceedings of the Institute of Radio Engineers (IEEE, 1960), pp. 310–316.
[Crossref]

Dahlem, M. S.

Dai, Y.

J. Sun, Y. Dai, X. Chen, Y. Zhang, and S. Xie, “Stable dual-wavelength DFB fiber laser with separate resonant cavities and its application in tunable microwave generation,” IEEE Photonics Technol. Lett. 18(24), 2587–2589 (2006).
[Crossref]

DiLello, N. A.

Eggleton, B. J.

D. Marpaung, B. Morrison, M. Pagani, R. Pant, D.-Y. Choi, B. Luther-Davies, S. J. Madden, and B. J. Eggleton, “Low-power, chip-based stimulated Brillouin scattering microwave photonic filter with ultrahigh selectivity,” Optica 2(2), 76–83 (2015).
[Crossref]

B. J. Eggleton, C. G. Poulton, and R. Pant, “Inducing and harnessing stimulated Brillouin scattering in photonic integrated circuits,” Adv. Opt. Photonics 5(4), 536–587 (2013).
[Crossref]

Gaeta, A. L.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94(15), 153902 (2005).
[Crossref] [PubMed]

Gauthier, D. J.

Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318(5857), 1748–1750 (2007).
[Crossref] [PubMed]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94(15), 153902 (2005).
[Crossref] [PubMed]

Geis, M. W.

Ghelfi, P.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507(7492), 341–345 (2014).
[Crossref] [PubMed]

P. Ghelfi, F. Scotti, F. Laghezza, and A. Bogoni, “Photonic generation of phase-modulated RF signals for pulse compression techniques in coherent radars,” J. Lightwave Technol. 30(11), 1638–1644 (2012).
[Crossref]

Grein, M. E.

He, Z.

Herráez, M.

Holzwarth, C. W.

Hotate, K.

Hoyt, J. L.

Hu, X.

L. Zhang, L. Zhan, K. Qian, J. Liu, Q. Shen, X. Hu, and S. Luo, “Superluminal propagation at negative group velocity in optical fibers based on Brillouin lasing oscillation,” Phys. Rev. Lett. 107(9), 093903 (2011).
[Crossref] [PubMed]

Ippen, E. P.

Kärtner, F. X.

Khilo, A.

Laghezza, F.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507(7492), 341–345 (2014).
[Crossref] [PubMed]

P. Ghelfi, F. Scotti, F. Laghezza, and A. Bogoni, “Photonic generation of phase-modulated RF signals for pulse compression techniques in coherent radars,” J. Lightwave Technol. 30(11), 1638–1644 (2012).
[Crossref]

Lazzeri, E.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507(7492), 341–345 (2014).
[Crossref] [PubMed]

Leaird, D. E.

Li, X.

Li, Y.

Liu, J.

L. Zhang, L. Zhan, K. Qian, J. Liu, Q. Shen, X. Hu, and S. Luo, “Superluminal propagation at negative group velocity in optical fibers based on Brillouin lasing oscillation,” Phys. Rev. Lett. 107(9), 093903 (2011).
[Crossref] [PubMed]

Long, X.

Luo, S.

L. Zhang, L. Zhan, K. Qian, J. Liu, Q. Shen, X. Hu, and S. Luo, “Superluminal propagation at negative group velocity in optical fibers based on Brillouin lasing oscillation,” Phys. Rev. Lett. 107(9), 093903 (2011).
[Crossref] [PubMed]

Luther-Davies, B.

Lyszczarz, T. M.

Madden, S. J.

Malacarne, A.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507(7492), 341–345 (2014).
[Crossref] [PubMed]

Marpaung, D.

Morgan, D. R.

D. R. Morgan, “Surface acoustic wave devices and applications,” Ultrasonics 11(3), 121–131 (1973).
[Crossref]

Morrison, B.

Motamedi, A.

Nejadmalayeri, A. H.

Novak, D.

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

Okawachi, Y.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94(15), 153902 (2005).
[Crossref] [PubMed]

Onori, D.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507(7492), 341–345 (2014).
[Crossref] [PubMed]

Orcutt, J. S.

Pagani, M.

Pant, R.

D. Marpaung, B. Morrison, M. Pagani, R. Pant, D.-Y. Choi, B. Luther-Davies, S. J. Madden, and B. J. Eggleton, “Low-power, chip-based stimulated Brillouin scattering microwave photonic filter with ultrahigh selectivity,” Optica 2(2), 76–83 (2015).
[Crossref]

B. J. Eggleton, C. G. Poulton, and R. Pant, “Inducing and harnessing stimulated Brillouin scattering in photonic integrated circuits,” Adv. Opt. Photonics 5(4), 536–587 (2013).
[Crossref]

Peng, M. Y.

Perrott, M.

Pinna, S.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507(7492), 341–345 (2014).
[Crossref] [PubMed]

Popovic, M. A.

Porzi, C.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507(7492), 341–345 (2014).
[Crossref] [PubMed]

Poulton, C. G.

B. J. Eggleton, C. G. Poulton, and R. Pant, “Inducing and harnessing stimulated Brillouin scattering in photonic integrated circuits,” Adv. Opt. Photonics 5(4), 536–587 (2013).
[Crossref]

Qian, K.

L. Zhang, L. Zhan, K. Qian, J. Liu, Q. Shen, X. Hu, and S. Luo, “Superluminal propagation at negative group velocity in optical fibers based on Brillouin lasing oscillation,” Phys. Rev. Lett. 107(9), 093903 (2011).
[Crossref] [PubMed]

Ram, R. J.

Rashidinejad, A.

Sander, M. Y.

Scaffardi, M.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507(7492), 341–345 (2014).
[Crossref] [PubMed]

Schweinsberg, A.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94(15), 153902 (2005).
[Crossref] [PubMed]

Scotti, F.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507(7492), 341–345 (2014).
[Crossref] [PubMed]

P. Ghelfi, F. Scotti, F. Laghezza, and A. Bogoni, “Photonic generation of phase-modulated RF signals for pulse compression techniques in coherent radars,” J. Lightwave Technol. 30(11), 1638–1644 (2012).
[Crossref]

Serafino, G.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507(7492), 341–345 (2014).
[Crossref] [PubMed]

Sharping, J. E.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94(15), 153902 (2005).
[Crossref] [PubMed]

Shen, Q.

L. Zhang, L. Zhan, K. Qian, J. Liu, Q. Shen, X. Hu, and S. Luo, “Superluminal propagation at negative group velocity in optical fibers based on Brillouin lasing oscillation,” Phys. Rev. Lett. 107(9), 093903 (2011).
[Crossref] [PubMed]

Shi, J.-W.

Smith, H. I.

Song, K. Y.

Sorace-Agaskar, C. M.

Spector, S. J.

Sun, J.

Thévenaz, L.

Valley, G. C.

Vercesi, V.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507(7492), 341–345 (2014).
[Crossref] [PubMed]

Wang, J. P.

Weiner, A. M.

Wun, J.-M.

Xie, S.

J. Sun, Y. Dai, X. Chen, Y. Zhang, and S. Xie, “Stable dual-wavelength DFB fiber laser with separate resonant cavities and its application in tunable microwave generation,” IEEE Photonics Technol. Lett. 18(24), 2587–2589 (2006).
[Crossref]

Yang, G.

Yang, S.

Yao, J.

Yoon, J. U.

Zhan, L.

L. Zhang, L. Zhan, K. Qian, J. Liu, Q. Shen, X. Hu, and S. Luo, “Superluminal propagation at negative group velocity in optical fibers based on Brillouin lasing oscillation,” Phys. Rev. Lett. 107(9), 093903 (2011).
[Crossref] [PubMed]

Zhang, H.

Zhang, J.

Zhang, L.

L. Zhang, L. Zhan, K. Qian, J. Liu, Q. Shen, X. Hu, and S. Luo, “Superluminal propagation at negative group velocity in optical fibers based on Brillouin lasing oscillation,” Phys. Rev. Lett. 107(9), 093903 (2011).
[Crossref] [PubMed]

Zhang, Y.

J. Sun, Y. Dai, X. Chen, Y. Zhang, and S. Xie, “Stable dual-wavelength DFB fiber laser with separate resonant cavities and its application in tunable microwave generation,” IEEE Photonics Technol. Lett. 18(24), 2587–2589 (2006).
[Crossref]

Zhou, G. R.

Zhu, Z.

Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318(5857), 1748–1750 (2007).
[Crossref] [PubMed]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94(15), 153902 (2005).
[Crossref] [PubMed]

Zou, W.

Adv. Opt. Photonics (1)

B. J. Eggleton, C. G. Poulton, and R. Pant, “Inducing and harnessing stimulated Brillouin scattering in photonic integrated circuits,” Adv. Opt. Photonics 5(4), 536–587 (2013).
[Crossref]

IEEE Photonics Technol. Lett. (1)

J. Sun, Y. Dai, X. Chen, Y. Zhang, and S. Xie, “Stable dual-wavelength DFB fiber laser with separate resonant cavities and its application in tunable microwave generation,” IEEE Photonics Technol. Lett. 18(24), 2587–2589 (2006).
[Crossref]

J. Lightwave Technol. (2)

Nat. Photonics (1)

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

Nature (1)

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507(7492), 341–345 (2014).
[Crossref] [PubMed]

Opt. Express (6)

Opt. Lett. (2)

Optica (3)

Phys. Rev. Lett. (2)

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94(15), 153902 (2005).
[Crossref] [PubMed]

L. Zhang, L. Zhan, K. Qian, J. Liu, Q. Shen, X. Hu, and S. Luo, “Superluminal propagation at negative group velocity in optical fibers based on Brillouin lasing oscillation,” Phys. Rev. Lett. 107(9), 093903 (2011).
[Crossref] [PubMed]

Science (1)

Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318(5857), 1748–1750 (2007).
[Crossref] [PubMed]

Sensors (Basel) (1)

X. Bao and L. Chen, “Recent progress in Brillouin scattering based fiber sensors,” Sensors (Basel) 11(4), 4152–4187 (2011).
[Crossref] [PubMed]

Ultrasonics (1)

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[Crossref]

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[Crossref]

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[Crossref]

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Figures (7)

Fig. 1
Fig. 1 The SBS process and the excitation of the acoustic wave. (a) Illustration for the symbols. EP: pump lightwave, which is modulated by an LFM pulse. Q: acoustic wave. ES: short-pulse probe lightwave. ES’: received probe pulse. (b) Pump lightwave is injected at z = 0 while the counter-propagating probe lightwave is launched at z = L. (c) The first time when the two lightwaves meet each other and acoustic wave is generated. (d) ‘New’ acoustic waves are stimulated while ‘old’ ones last for a lifetime and disappear finally. (e) Amplified probe lightwave is detected at the near end of the fiber.
Fig. 2
Fig. 2 Simulation results for the pulse compression based on the SBS process. The pump lightwave is modulated by an LFM pulse with 1 GHz sweep range and the probe lightwave is a short pulse with 0.5 ns duration. (a) The detected probe power with and without the pump lightwave. The inset shows the log scale of the vertical axis. (b) The subtracted power is compared to the small signal approximation and the squared ideal pulse compression.
Fig. 3
Fig. 3 Experimental setup for pulse compression of the broadband microwave frequency based on SBS process. DFB-LD: distributed-feedback laser. PC: polarization controller. EOM: electro-optic modulator. EDFA: erbium-doped fiber amplifier. ISO: isolator. SSBM: single sideband modulator. PD: photo-detector.
Fig. 4
Fig. 4 Time profile (a) and short-time Fourier transform (b) of the LFM pulse to be processed. The LFM pulse has 1 μs duration and 1 GHz sweep range. Time profile (c) and short-time Fourier transform (d) of the pump lightwave that is modulated by the LFM pulse.
Fig. 5
Fig. 5 Experiment results for the pulse compression based on the SBS process. (a) The detected probe power with and without the pump lightwave injected. (b) The pulse compression achieved by the subtraction in (a) is compared with the squared ideal pulse compressions of the LFM pulses before and after the modulation [see Figs. 4(a) and 4(c)].
Fig. 6
Fig. 6 The full width of the compressed mainlobe as a function of the sweeping bandwidth of the LFM pulse.
Fig. 7
Fig. 7 Analysis on the distortions that induced by the pulse duration (τS) of the probe lightwave and the phonon lifetime. (a) Comparison between the squared pulse compression of |yP(t)|2 and subtracted signal of |ΔES(t)|2 with different τS. (b) Relative distortions caused by the phonon lifetime τp for different LFM pulse bandwidths B. Horizontal coordinate is normalized by the factor of 1/B.

Equations (13)

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( t +Γ )Q( z,t )=i g 1 E P ( z,t ) E S ( z,t ),
( z + 1 v t ) E P ( z,t )=i g 2 E S ( z,t )Q( z,t ),
( z 1 v t ) E S ( z,t )=i g 2 E P ( z,t ) Q ( z,t ),
E P ( z,t )= E P0 ( t z v ),
E S ( z,t )= E S0 ( t Lz v ),
Q( z,t )=i g 1 t E P0 ( τ z v ) E S0 ( τ Lz v ) e Γ( tτ ) dτ,
E S ( t+T )= g B v 8 τ p { E S0 ( t )[ u( t ) y P ( t ) e Γ t ] }+ E S0 ( t ),
y P ( t )= E P0 ( t ) E P0 ( t ),
s( t+T ) | E S ( t+T ) | 2 | E S0 ( t ) | 2 = | Δ E S ( t ) | 2 +2Re{ Δ E S ( t ) E S0 ( t ) },
s( t+T )2Re{ Δ E S ( t ) E S0 ( t ) },whent< τ S ,
s( t+T ) | Δ E S ( t ) | 2 ,whent τ S ,
R 1 B .
δ= [ | y P ( t ) | 2 | Δ E S ( t ) | 2 ] / | y P ( t ) | 2 .

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