Abstract

Programmable broadband rf filters are demonstrated using a compact retroreflective optical design with an acousto-optic tunable filter and a chirped fiber Bragg grating. This design enables fast 34 μs domain analog-mode control of rf filter time delays and weights. Two proof-of-concept filters are demonstrated including a two-tap notch filter with >35  dB notch depth and a four-tap bandpass filter. Both filters have 2–8 GHz tunability and a 34μs reset time.

© 2007 Optical Society of America

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References

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  1. N. A. Riza, ed., Selected Papers on Photonic Control Systems for Phased Array Antennas, Vol. MS 136 of SPIE Milestone Series (SPIE, 1997).
  2. K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, and H. J. Shaw, "Optical fiber delay-line signal processing," IEEE Trans. Microwave Theory Tech. 33, 193-210 (1985).
    [CrossRef]
  3. D. Norton, S. Johns, C. Keefer, and R. Soref, "Tunable microwave filtering using high dispersion fiber time delays," IEEE Photon. Technol. Lett. 6, 831-832 (1994).
    [CrossRef]
  4. D. B. Hunter and R. A. Minasian, "Reflectively tapped fiber optic transversal filter using in-fiber Bragg gratings," Electron. Lett. 31, 1010-1012 (1995).
    [CrossRef]
  5. N. You and R. A. Minasian, "A novel high-Q optical microwave processor using hybrid delay-line filters," IEEE Trans. Microwave Theory Tech. 47, 1304-1308 (1999).
    [CrossRef]
  6. J. Capmany, D. Pastor, and B. Ortega, "New and flexible fiber-optic delay-line filters using chirped Bragg gratings and laser arrays," IEEE Trans. Microwave Theory Tech. 47, 1321-1326 (1999).
    [CrossRef]
  7. 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]
  8. M. Y. Frankel and R. D. Esman, "Fiber-optic tunable microwave transversal filter," IEEE Photon. Technol. Lett. 7, 191-193 (1995).
    [CrossRef]
  9. J. Marti, F. Ramos, and R. I. Lamming, "Photonic microwave filter employing multimode optical sources and wideband chirped fiber gratings," Electron. Lett. 34, 1760-1761 (1998).
    [CrossRef]
  10. N. A. Riza, "An optical transversal filter," U.S. patent 5,329,118 (12 July 1994).
  11. B. Moslehi, K. K. Chau, and J. W. Goodman, "Optical amplifiers and liquid-crystal shutters applied to electrically reconfigurable fiber-optic signal processor," Opt. Eng. 32, 574-581 (1993).
    [CrossRef]
  12. D. Dolfi, J. Tabourel, O. Durand, V. Laude, J.-P. Huignard, and J. Chazelas, "Optical architecture for programmable filtering and correlation of microwave signals," IEEE Trans. Microwave Theory Tech. 45, 1467-1471 (1997).
    [CrossRef]
  13. N. A. Riza, M. A. Arain, and F. N. Ghauri, "Tunable microwave/millimeter wave transversal filter using retro-reflective spatial photonics," in Proceedings of the IEEE International Topical Meeting on Microwave Photonics (MWP2004) (IEEE, 2004), pp. 36-39.
  14. N. A. Riza and M. A. Arain, "Programmable broadband radio-frequency transversal filter using compact fiber-optics and digital MEMS-based optical spectral control," Appl. Opt. 43, 3159-3165 (2004).
    [CrossRef] [PubMed]
  15. M. A. Arain and N. A. Riza, "Optoelectronic approach to adaptive radio-frequency transversal filter implementation with negative coefficients by using optical spectrum shaping," Appl. Opt. 45, 2428-2436 (2006).
    [CrossRef] [PubMed]
  16. S. Mansoori and A. Mitchell, "RF transversal filter using an AOTF," IEEE Photon. Technol. Lett. 16, 879-881 (2004).
    [CrossRef]
  17. M. van Buren and N. A. Riza, "Foundations for low-loss fiber gradient-index lens pair coupling with the self-imaging mechanism," Appl. Opt. 42, 550-565 (2003).
    [CrossRef] [PubMed]
  18. N. A. Riza and M. J. Mughal, "Fiber-optic tunable multiwavelength variable attenuator and routing module designs that use bulk acousto-optics," Appl. Opt. 44, 792-799 (2005).
    [CrossRef] [PubMed]
  19. Z. Yaqoob and N. A. Riza, "Bulk acousto-optic wavelength agile filter module for a wavelength-multiplexed optical scanner," Appl. Opt. 44, 2592-2599 (2005).
    [CrossRef] [PubMed]
  20. J. G. Proakis and D. G. Manolakis, Digital Signal Processing: Principles, Algorithms and Applications, 3rd ed. (Prentice-Hall, 1995).
  21. N. A. Riza, "Hybrid Photonic Signal processing for radio frequency signals," in Integrated Optics: Theory and Applications,Proc. SPIE 5956, 71-77 (2005).

2006

2005

2004

2003

1999

N. You and R. A. Minasian, "A novel high-Q optical microwave processor using hybrid delay-line filters," IEEE Trans. Microwave Theory Tech. 47, 1304-1308 (1999).
[CrossRef]

J. Capmany, D. Pastor, and B. Ortega, "New and flexible fiber-optic delay-line filters using chirped Bragg gratings and laser arrays," IEEE Trans. Microwave Theory Tech. 47, 1321-1326 (1999).
[CrossRef]

1998

J. Marti, F. Ramos, and R. I. Lamming, "Photonic microwave filter employing multimode optical sources and wideband chirped fiber gratings," Electron. Lett. 34, 1760-1761 (1998).
[CrossRef]

1997

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]

D. Dolfi, J. Tabourel, O. Durand, V. Laude, J.-P. Huignard, and J. Chazelas, "Optical architecture for programmable filtering and correlation of microwave signals," IEEE Trans. Microwave Theory Tech. 45, 1467-1471 (1997).
[CrossRef]

1995

D. B. Hunter and R. A. Minasian, "Reflectively tapped fiber optic transversal filter using in-fiber Bragg gratings," Electron. Lett. 31, 1010-1012 (1995).
[CrossRef]

M. Y. Frankel and R. D. Esman, "Fiber-optic tunable microwave transversal filter," IEEE Photon. Technol. Lett. 7, 191-193 (1995).
[CrossRef]

1994

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

1993

B. Moslehi, K. K. Chau, and J. W. Goodman, "Optical amplifiers and liquid-crystal shutters applied to electrically reconfigurable fiber-optic signal processor," Opt. Eng. 32, 574-581 (1993).
[CrossRef]

1985

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, and H. J. Shaw, "Optical fiber delay-line signal processing," IEEE Trans. Microwave Theory Tech. 33, 193-210 (1985).
[CrossRef]

Arain, M. A.

Capmany, J.

J. Capmany, D. Pastor, and B. Ortega, "New and flexible fiber-optic delay-line filters using chirped Bragg gratings and laser arrays," IEEE Trans. Microwave Theory Tech. 47, 1321-1326 (1999).
[CrossRef]

Chau, K. K.

B. Moslehi, K. K. Chau, and J. W. Goodman, "Optical amplifiers and liquid-crystal shutters applied to electrically reconfigurable fiber-optic signal processor," Opt. Eng. 32, 574-581 (1993).
[CrossRef]

Chazelas, J.

D. Dolfi, J. Tabourel, O. Durand, V. Laude, J.-P. Huignard, and J. Chazelas, "Optical architecture for programmable filtering and correlation of microwave signals," IEEE Trans. Microwave Theory Tech. 45, 1467-1471 (1997).
[CrossRef]

Coppinger, F.

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]

Cutler, C. C.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, and H. J. Shaw, "Optical fiber delay-line signal processing," IEEE Trans. Microwave Theory Tech. 33, 193-210 (1985).
[CrossRef]

Dolfi, D.

D. Dolfi, J. Tabourel, O. Durand, V. Laude, J.-P. Huignard, and J. Chazelas, "Optical architecture for programmable filtering and correlation of microwave signals," IEEE Trans. Microwave Theory Tech. 45, 1467-1471 (1997).
[CrossRef]

Durand, O.

D. Dolfi, J. Tabourel, O. Durand, V. Laude, J.-P. Huignard, and J. Chazelas, "Optical architecture for programmable filtering and correlation of microwave signals," IEEE Trans. Microwave Theory Tech. 45, 1467-1471 (1997).
[CrossRef]

Esman, R. D.

M. Y. Frankel and R. D. Esman, "Fiber-optic tunable microwave transversal filter," IEEE Photon. Technol. Lett. 7, 191-193 (1995).
[CrossRef]

Frankel, M. Y.

M. Y. Frankel and R. D. Esman, "Fiber-optic tunable microwave transversal filter," IEEE Photon. Technol. Lett. 7, 191-193 (1995).
[CrossRef]

Ghauri, F. N.

N. A. Riza, M. A. Arain, and F. N. Ghauri, "Tunable microwave/millimeter wave transversal filter using retro-reflective spatial photonics," in Proceedings of the IEEE International Topical Meeting on Microwave Photonics (MWP2004) (IEEE, 2004), pp. 36-39.

Goodman, J. W.

B. Moslehi, K. K. Chau, and J. W. Goodman, "Optical amplifiers and liquid-crystal shutters applied to electrically reconfigurable fiber-optic signal processor," Opt. Eng. 32, 574-581 (1993).
[CrossRef]

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, and H. J. Shaw, "Optical fiber delay-line signal processing," IEEE Trans. Microwave Theory Tech. 33, 193-210 (1985).
[CrossRef]

Huignard, J.-P.

D. Dolfi, J. Tabourel, O. Durand, V. Laude, J.-P. Huignard, and J. Chazelas, "Optical architecture for programmable filtering and correlation of microwave signals," IEEE Trans. Microwave Theory Tech. 45, 1467-1471 (1997).
[CrossRef]

Hunter, D. B.

D. B. Hunter and R. A. Minasian, "Reflectively tapped fiber optic transversal filter using in-fiber Bragg gratings," Electron. Lett. 31, 1010-1012 (1995).
[CrossRef]

Jackson, K. P.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, and H. J. Shaw, "Optical fiber delay-line signal processing," IEEE Trans. Microwave Theory Tech. 33, 193-210 (1985).
[CrossRef]

Jalali, B.

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]

Johns, S.

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

Keefer, C.

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

Lamming, R. I.

J. Marti, F. Ramos, and R. I. Lamming, "Photonic microwave filter employing multimode optical sources and wideband chirped fiber gratings," Electron. Lett. 34, 1760-1761 (1998).
[CrossRef]

Laude, V.

D. Dolfi, J. Tabourel, O. Durand, V. Laude, J.-P. Huignard, and J. Chazelas, "Optical architecture for programmable filtering and correlation of microwave signals," IEEE Trans. Microwave Theory Tech. 45, 1467-1471 (1997).
[CrossRef]

Manolakis, D. G.

J. G. Proakis and D. G. Manolakis, Digital Signal Processing: Principles, Algorithms and Applications, 3rd ed. (Prentice-Hall, 1995).

Mansoori, S.

S. Mansoori and A. Mitchell, "RF transversal filter using an AOTF," IEEE Photon. Technol. Lett. 16, 879-881 (2004).
[CrossRef]

Marti, J.

J. Marti, F. Ramos, and R. I. Lamming, "Photonic microwave filter employing multimode optical sources and wideband chirped fiber gratings," Electron. Lett. 34, 1760-1761 (1998).
[CrossRef]

Minasian, R. A.

N. You and R. A. Minasian, "A novel high-Q optical microwave processor using hybrid delay-line filters," IEEE Trans. Microwave Theory Tech. 47, 1304-1308 (1999).
[CrossRef]

D. B. Hunter and R. A. Minasian, "Reflectively tapped fiber optic transversal filter using in-fiber Bragg gratings," Electron. Lett. 31, 1010-1012 (1995).
[CrossRef]

Mitchell, A.

S. Mansoori and A. Mitchell, "RF transversal filter using an AOTF," IEEE Photon. Technol. Lett. 16, 879-881 (2004).
[CrossRef]

Moslehi, B.

B. Moslehi, K. K. Chau, and J. W. Goodman, "Optical amplifiers and liquid-crystal shutters applied to electrically reconfigurable fiber-optic signal processor," Opt. Eng. 32, 574-581 (1993).
[CrossRef]

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, and H. J. Shaw, "Optical fiber delay-line signal processing," IEEE Trans. Microwave Theory Tech. 33, 193-210 (1985).
[CrossRef]

Mughal, M. J.

Newton, S. A.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, and H. J. Shaw, "Optical fiber delay-line signal processing," IEEE Trans. Microwave Theory Tech. 33, 193-210 (1985).
[CrossRef]

Norton, D.

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

Ortega, B.

J. Capmany, D. Pastor, and B. Ortega, "New and flexible fiber-optic delay-line filters using chirped Bragg gratings and laser arrays," IEEE Trans. Microwave Theory Tech. 47, 1321-1326 (1999).
[CrossRef]

Pastor, D.

J. Capmany, D. Pastor, and B. Ortega, "New and flexible fiber-optic delay-line filters using chirped Bragg gratings and laser arrays," IEEE Trans. Microwave Theory Tech. 47, 1321-1326 (1999).
[CrossRef]

Proakis, J. G.

J. G. Proakis and D. G. Manolakis, Digital Signal Processing: Principles, Algorithms and Applications, 3rd ed. (Prentice-Hall, 1995).

Ramos, F.

J. Marti, F. Ramos, and R. I. Lamming, "Photonic microwave filter employing multimode optical sources and wideband chirped fiber gratings," Electron. Lett. 34, 1760-1761 (1998).
[CrossRef]

Riza, N. A.

M. A. Arain and N. A. Riza, "Optoelectronic approach to adaptive radio-frequency transversal filter implementation with negative coefficients by using optical spectrum shaping," Appl. Opt. 45, 2428-2436 (2006).
[CrossRef] [PubMed]

Z. Yaqoob and N. A. Riza, "Bulk acousto-optic wavelength agile filter module for a wavelength-multiplexed optical scanner," Appl. Opt. 44, 2592-2599 (2005).
[CrossRef] [PubMed]

N. A. Riza, "Hybrid Photonic Signal processing for radio frequency signals," in Integrated Optics: Theory and Applications,Proc. SPIE 5956, 71-77 (2005).

N. A. Riza and M. J. Mughal, "Fiber-optic tunable multiwavelength variable attenuator and routing module designs that use bulk acousto-optics," Appl. Opt. 44, 792-799 (2005).
[CrossRef] [PubMed]

N. A. Riza and M. A. Arain, "Programmable broadband radio-frequency transversal filter using compact fiber-optics and digital MEMS-based optical spectral control," Appl. Opt. 43, 3159-3165 (2004).
[CrossRef] [PubMed]

M. van Buren and N. A. Riza, "Foundations for low-loss fiber gradient-index lens pair coupling with the self-imaging mechanism," Appl. Opt. 42, 550-565 (2003).
[CrossRef] [PubMed]

N. A. Riza, M. A. Arain, and F. N. Ghauri, "Tunable microwave/millimeter wave transversal filter using retro-reflective spatial photonics," in Proceedings of the IEEE International Topical Meeting on Microwave Photonics (MWP2004) (IEEE, 2004), pp. 36-39.

N. A. Riza, ed., Selected Papers on Photonic Control Systems for Phased Array Antennas, Vol. MS 136 of SPIE Milestone Series (SPIE, 1997).

N. A. Riza, "An optical transversal filter," U.S. patent 5,329,118 (12 July 1994).

Shaw, H. J.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, and H. J. Shaw, "Optical fiber delay-line signal processing," IEEE Trans. Microwave Theory Tech. 33, 193-210 (1985).
[CrossRef]

Soref, R.

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

Tabourel, J.

D. Dolfi, J. Tabourel, O. Durand, V. Laude, J.-P. Huignard, and J. Chazelas, "Optical architecture for programmable filtering and correlation of microwave signals," IEEE Trans. Microwave Theory Tech. 45, 1467-1471 (1997).
[CrossRef]

Trinh, P. D.

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]

Tur, M.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, and H. J. Shaw, "Optical fiber delay-line signal processing," IEEE Trans. Microwave Theory Tech. 33, 193-210 (1985).
[CrossRef]

van Buren, M.

Yaqoob, Z.

Yegnanarayanan, S.

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]

You, N.

N. You and R. A. Minasian, "A novel high-Q optical microwave processor using hybrid delay-line filters," IEEE Trans. Microwave Theory Tech. 47, 1304-1308 (1999).
[CrossRef]

Appl. Opt.

Electron. Lett.

D. B. Hunter and R. A. Minasian, "Reflectively tapped fiber optic transversal filter using in-fiber Bragg gratings," Electron. Lett. 31, 1010-1012 (1995).
[CrossRef]

J. Marti, F. Ramos, and R. I. Lamming, "Photonic microwave filter employing multimode optical sources and wideband chirped fiber gratings," Electron. Lett. 34, 1760-1761 (1998).
[CrossRef]

IEEE Photon. Technol. Lett.

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]

M. Y. Frankel and R. D. Esman, "Fiber-optic tunable microwave transversal filter," IEEE Photon. Technol. Lett. 7, 191-193 (1995).
[CrossRef]

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

S. Mansoori and A. Mitchell, "RF transversal filter using an AOTF," IEEE Photon. Technol. Lett. 16, 879-881 (2004).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

D. Dolfi, J. Tabourel, O. Durand, V. Laude, J.-P. Huignard, and J. Chazelas, "Optical architecture for programmable filtering and correlation of microwave signals," IEEE Trans. Microwave Theory Tech. 45, 1467-1471 (1997).
[CrossRef]

N. You and R. A. Minasian, "A novel high-Q optical microwave processor using hybrid delay-line filters," IEEE Trans. Microwave Theory Tech. 47, 1304-1308 (1999).
[CrossRef]

J. Capmany, D. Pastor, and B. Ortega, "New and flexible fiber-optic delay-line filters using chirped Bragg gratings and laser arrays," IEEE Trans. Microwave Theory Tech. 47, 1321-1326 (1999).
[CrossRef]

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, and H. J. Shaw, "Optical fiber delay-line signal processing," IEEE Trans. Microwave Theory Tech. 33, 193-210 (1985).
[CrossRef]

Opt. Eng.

B. Moslehi, K. K. Chau, and J. W. Goodman, "Optical amplifiers and liquid-crystal shutters applied to electrically reconfigurable fiber-optic signal processor," Opt. Eng. 32, 574-581 (1993).
[CrossRef]

Proc. SPIE

N. A. Riza, "Hybrid Photonic Signal processing for radio frequency signals," in Integrated Optics: Theory and Applications,Proc. SPIE 5956, 71-77 (2005).

Other

J. G. Proakis and D. G. Manolakis, Digital Signal Processing: Principles, Algorithms and Applications, 3rd ed. (Prentice-Hall, 1995).

N. A. Riza, M. A. Arain, and F. N. Ghauri, "Tunable microwave/millimeter wave transversal filter using retro-reflective spatial photonics," in Proceedings of the IEEE International Topical Meeting on Microwave Photonics (MWP2004) (IEEE, 2004), pp. 36-39.

N. A. Riza, ed., Selected Papers on Photonic Control Systems for Phased Array Antennas, Vol. MS 136 of SPIE Milestone Series (SPIE, 1997).

N. A. Riza, "An optical transversal filter," U.S. patent 5,329,118 (12 July 1994).

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Figures (5)

Fig. 1
Fig. 1

Proposed retroreflective design programmable broadband rf transversal filter using compact CFBG fiber optics and an AOTF.

Fig. 2
Fig. 2

Optical spectrum of the implemented two-tap rf notch filters showing the approximate equal strengths of the filter weights, their 0.75   nm 3 dB widths, and interwavelength spacings Δ λ of (a) 4.6   nm and (b) 2.1   nm to produce rf notches at 3.1 and 6.75 GHz, respectively.

Fig. 3
Fig. 3

Normalized frequency domain impulse response H ( f ) of the demonstrated rf notch filter with the null frequency set at (a) 3.09 GHz and (b) 6.75 GHz.

Fig. 4
Fig. 4

Optical spectrum of the implemented four-tap rf FIR filters showing the relative strengths of the filter weights and their interwavelength spacing Δ λ of (a) 5.58   nm and (b) 5.61   nm .

Fig. 5
Fig. 5

Normalized frequency domain impulse response H(f) of the demonstrated four-tap rf filters with the mainlobe frequency centered at approximately 5.1 GHz and weights of (a) Fig. 4(a) design and (b) Fig. 4(b) design.

Equations (89)

Equations on this page are rendered with MathJax. Learn more.

> 35   dB
34 μ s
1562   nm
z 0
z 0
τ d
τ d
PD 1
PD 2
PD 1
PD 2
τ d
PD 1
PD 2
Δ λ r
τ min = Δ λ r D c g .
D c g
D c g = 2 L g Δ λ chirp c n e f f ,
Δ λ chirp
L g
n e f f
τ min
f max
f max
f max = 1 2 τ min .
Δ λ chirp
N Δ λ chirp / Δ λ r
τ max, N
f min, N
τ max, N = Δ λ chirp D c g N 1 ,
f min, N = 1 2 τ max, N .
r ( t ) = n = 0 N 1 A n s ( t n τ ) ,
r ( t )
δ ( t )
h ( t ) = n = 0 N 1 A n δ ( t n τ ) .
H ( f ) = { n = 0 N 1 A n δ ( t n τ ) } .
A n = A
H ( f ) = 2 A × sin ( N π f τ ) N   sin ( π f τ ) ,
f = 1 / τ
N = 2
A n = A
r ( t ) = n = 0 1 A s ( t n τ ) = A [ s ( t ) + s ( t τ ) ] .
s ( t ) = δ ( t )
H ( f ) = 2 A   cos ( π f τ ) .
f null = ( 2 k + 1 ) f 0
f 0 = 1 / 2 τ
k = 0 , 1 , 2 , , K
( TeO 2 )
1640   nm
1544   nm
1544   nm
z 0
D c g = 35.2 ps / nm
1551.1   nm
Δ λ
4.6   nm
0.75   nm
1551.1   nm
Δ λ
4.6   nm
0.75   nm
± 0.06   nm
0.75   nm
Δ λ = 0.75   nm
τ min = 26.4   ps
f max = 18.94   GHz
Δ λ chirp = 22.88   nm
τ max = 805.4   ps
f min  2 = 621   MHz
Δ λ = 4.6   nm
τ = Δ λ D c g
1556.6   nm
5.58   nm
1557.08   nm
Δ λ
5.61   nm
τ = 196.95   ps
f = 1 / τ 5.1   GHz
34 μ s
5 μ s
TeO 2
0.75   nm
Δ λ
4.6   nm
2.1   nm
H ( f )
Δ λ
5.58   nm
5.61   nm

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