Abstract

Photonic radio-frequency (RF) arbitrary waveform generation (AWG) based on spectral shaping and frequency-to-time mapping has received substantial attention. This technique, however, is critically constrained by the far-field condition which imposes strict limits on the complexity of the generated waveforms. The time bandwidth product (TBWP) decreases as the inverse of the RF bandwidth which limits one from exploiting the full TBWP available from modern pulse shapers. Here we introduce a new RF-AWG technique which we call near-field frequency-to-time mapping. This approach overcomes the previous restrictions by predistorting the amplitude and phase of the spectrally shaped optical signal to achieve high fidelity waveforms with radically increased TBWP in the near field region.

© 2013 OSA

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  1. M. Z. Win and R. A. Scholtz, “Ultra-wide bandwidth time-hopping spread-spectrum impulse radio for wireless multiple-access communications,” IEEE Trans. Commun.48(4), 679–689 (2000).
    [CrossRef]
  2. M.-G. Benedetto, T. Kaiser, A. F. Molisch, I. Oppermann, C. Politano, and D. Porcino, UWB communication systems A comprehensive overview (Hindawi Publishing Corporation, 2006).
  3. A. Dezfooliyan and A. M. Weiner, “Evaluation of time domain propagation measurements of UWB systems using spread spectrum channel sounding,” IEEE Trans. Antenn. Propag.60(10), 4855–4865 (2012).
    [CrossRef]
  4. J. D. McKinney, D. E. Leaird, and A. M. Weiner, “Millimeter-wave arbitrary waveform generation with a direct space-to-time pulse shaper,” Opt. Lett.27(15), 1345–1347 (2002).
    [CrossRef] [PubMed]
  5. J. Chou, Y. Han, and B. Jalali, “Adaptive RF-photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett.15(4), 581–583 (2003).
    [CrossRef]
  6. I. S. Lin, J. D. McKinney, and A. M. Weiner, “Photonic synthesis of broadband microwave arbitrary waveforms applicable to ultra-wideband communication,” IEEE Microw. Wirel. Compon. Lett.15(4), 226–228 (2005).
    [CrossRef]
  7. V. Torres-Company, J. Lancis, and P. Andres, “Arbitrary waveform generator based on all-incoherent pulse shaping,” IEEE Photon. Technol. Lett.18(24), 2626–2628 (2006).
    [CrossRef]
  8. J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics1(6), 319–330 (2007).
    [CrossRef]
  9. C. Wang and J. Yao, “Photonic generation of chirped millimeter-wave pulses based on nonlinear frequency-to-time mapping in a nonlinearly chirped fiber bragg grating,” IEEE Trans. Microw. Theory Tech.56(2), 542–553 (2008).
    [CrossRef]
  10. M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics4(2), 117–122 (2010).
    [CrossRef]
  11. J. Yao, “Photonics for ultrawideband communications,” IEEE Microw. Mag.10(4), 82–95 (2009).
    [CrossRef]
  12. A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum.71(5), 1929–1960 (2000).
    [CrossRef]
  13. J. Azana and M. A. Muriel, “Real-time optical spectrum analysis based on the time-space duality in chirped fiber gratings,” IEEE J. Quantum Electron.36(5), 517–526 (2000).
    [CrossRef]
  14. V. Torres-Company, D. E. Leaird, and A. M. Weiner, “Dispersion requirements in coherent frequency-to-time mapping,” Opt. Express19(24), 24718–24729 (2011).
    [CrossRef] [PubMed]
  15. A. Dezfooliyan and A. M. Weiner, “Temporal focusing of ultrabroadband wireless signals using photonic radio frequency arbitrary waveform generation,”Optical Fiber Commun. Conf. (OFC), pp. 1–3 (Anaheim, Calif., 2013).
  16. S. Shen and A. M. Weiner, “Complete dispersion compensation for 400-fs pulse transmission over 10-km fiber link using dispersion compensating fiber and spectral phase equalizer,” IEEE Photon. Technol. Lett.11(7), 827–829 (1999).
    [CrossRef]
  17. A. M. Weiner, Ultrafast Optics (Wiley, 2009).
  18. C. Wang and J. Yao, “Chirped microwave pulse generation based on optical spectral shaping and wavelength-to-time mapping using a sagnac loop mirror incorporating a chirped fiber bragg grating,” J. Lightwave Technol.27(16), 3336–3341 (2009).
    [CrossRef]
  19. B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron.30(8), 1951–1963 (1994).
    [CrossRef]
  20. M. T. Kauffman, A. A. Godil, B. A. Auld, W. C. Banyai, and D. M. Bloom, “Applications of time lens optical-systems,” Electron. Lett.29(3), 268–269 (1993).
    [CrossRef]
  21. A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of 128-element liquid-crystal phase modulator,” IEEE J. Quantum Electron.28(4), 908–920 (1992).
    [CrossRef]
  22. J. T. Willits, A. M. Weiner, and S. T. Cundiff, “Line-by-line pulse shaping with spectral resolution below 890 MHz,” Opt. Express20(3), 3110–3117 (2012).
    [CrossRef] [PubMed]
  23. S. Xiao and A. M. Weiner, “Coherent photonic processing of microwave signals using spatial light modulators: programmable amplitude filters,” J. Lightwave Technol.24(7), 2523–2529 (2006).
    [CrossRef]
  24. A. J. Metcalf, V. Torres-Company, V. R. Supradeepa, D. E. Leaird, and A. M. Weiner, “Fully programmable ultra-complex 2-D pulse shaping,” Conf. of Lasers and Electro-Optics (CLEO), pp. 1–2 (San Jose, Calif., 2012).

2012

A. Dezfooliyan and A. M. Weiner, “Evaluation of time domain propagation measurements of UWB systems using spread spectrum channel sounding,” IEEE Trans. Antenn. Propag.60(10), 4855–4865 (2012).
[CrossRef]

J. T. Willits, A. M. Weiner, and S. T. Cundiff, “Line-by-line pulse shaping with spectral resolution below 890 MHz,” Opt. Express20(3), 3110–3117 (2012).
[CrossRef] [PubMed]

2011

2010

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics4(2), 117–122 (2010).
[CrossRef]

2009

2008

C. Wang and J. Yao, “Photonic generation of chirped millimeter-wave pulses based on nonlinear frequency-to-time mapping in a nonlinearly chirped fiber bragg grating,” IEEE Trans. Microw. Theory Tech.56(2), 542–553 (2008).
[CrossRef]

2007

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics1(6), 319–330 (2007).
[CrossRef]

2006

V. Torres-Company, J. Lancis, and P. Andres, “Arbitrary waveform generator based on all-incoherent pulse shaping,” IEEE Photon. Technol. Lett.18(24), 2626–2628 (2006).
[CrossRef]

S. Xiao and A. M. Weiner, “Coherent photonic processing of microwave signals using spatial light modulators: programmable amplitude filters,” J. Lightwave Technol.24(7), 2523–2529 (2006).
[CrossRef]

2005

I. S. Lin, J. D. McKinney, and A. M. Weiner, “Photonic synthesis of broadband microwave arbitrary waveforms applicable to ultra-wideband communication,” IEEE Microw. Wirel. Compon. Lett.15(4), 226–228 (2005).
[CrossRef]

2003

J. Chou, Y. Han, and B. Jalali, “Adaptive RF-photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett.15(4), 581–583 (2003).
[CrossRef]

2002

2000

M. Z. Win and R. A. Scholtz, “Ultra-wide bandwidth time-hopping spread-spectrum impulse radio for wireless multiple-access communications,” IEEE Trans. Commun.48(4), 679–689 (2000).
[CrossRef]

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum.71(5), 1929–1960 (2000).
[CrossRef]

J. Azana and M. A. Muriel, “Real-time optical spectrum analysis based on the time-space duality in chirped fiber gratings,” IEEE J. Quantum Electron.36(5), 517–526 (2000).
[CrossRef]

1999

S. Shen and A. M. Weiner, “Complete dispersion compensation for 400-fs pulse transmission over 10-km fiber link using dispersion compensating fiber and spectral phase equalizer,” IEEE Photon. Technol. Lett.11(7), 827–829 (1999).
[CrossRef]

1994

B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron.30(8), 1951–1963 (1994).
[CrossRef]

1993

M. T. Kauffman, A. A. Godil, B. A. Auld, W. C. Banyai, and D. M. Bloom, “Applications of time lens optical-systems,” Electron. Lett.29(3), 268–269 (1993).
[CrossRef]

1992

A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of 128-element liquid-crystal phase modulator,” IEEE J. Quantum Electron.28(4), 908–920 (1992).
[CrossRef]

Andres, P.

V. Torres-Company, J. Lancis, and P. Andres, “Arbitrary waveform generator based on all-incoherent pulse shaping,” IEEE Photon. Technol. Lett.18(24), 2626–2628 (2006).
[CrossRef]

Auld, B. A.

M. T. Kauffman, A. A. Godil, B. A. Auld, W. C. Banyai, and D. M. Bloom, “Applications of time lens optical-systems,” Electron. Lett.29(3), 268–269 (1993).
[CrossRef]

Azana, J.

J. Azana and M. A. Muriel, “Real-time optical spectrum analysis based on the time-space duality in chirped fiber gratings,” IEEE J. Quantum Electron.36(5), 517–526 (2000).
[CrossRef]

Banyai, W. C.

M. T. Kauffman, A. A. Godil, B. A. Auld, W. C. Banyai, and D. M. Bloom, “Applications of time lens optical-systems,” Electron. Lett.29(3), 268–269 (1993).
[CrossRef]

Bloom, D. M.

M. T. Kauffman, A. A. Godil, B. A. Auld, W. C. Banyai, and D. M. Bloom, “Applications of time lens optical-systems,” Electron. Lett.29(3), 268–269 (1993).
[CrossRef]

Capmany, J.

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics1(6), 319–330 (2007).
[CrossRef]

Chou, J.

J. Chou, Y. Han, and B. Jalali, “Adaptive RF-photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett.15(4), 581–583 (2003).
[CrossRef]

Cundiff, S. T.

Dezfooliyan, A.

A. Dezfooliyan and A. M. Weiner, “Evaluation of time domain propagation measurements of UWB systems using spread spectrum channel sounding,” IEEE Trans. Antenn. Propag.60(10), 4855–4865 (2012).
[CrossRef]

Godil, A. A.

M. T. Kauffman, A. A. Godil, B. A. Auld, W. C. Banyai, and D. M. Bloom, “Applications of time lens optical-systems,” Electron. Lett.29(3), 268–269 (1993).
[CrossRef]

Han, Y.

J. Chou, Y. Han, and B. Jalali, “Adaptive RF-photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett.15(4), 581–583 (2003).
[CrossRef]

Jalali, B.

J. Chou, Y. Han, and B. Jalali, “Adaptive RF-photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett.15(4), 581–583 (2003).
[CrossRef]

Kauffman, M. T.

M. T. Kauffman, A. A. Godil, B. A. Auld, W. C. Banyai, and D. M. Bloom, “Applications of time lens optical-systems,” Electron. Lett.29(3), 268–269 (1993).
[CrossRef]

Khan, M. H.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics4(2), 117–122 (2010).
[CrossRef]

Kolner, B. H.

B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron.30(8), 1951–1963 (1994).
[CrossRef]

Lancis, J.

V. Torres-Company, J. Lancis, and P. Andres, “Arbitrary waveform generator based on all-incoherent pulse shaping,” IEEE Photon. Technol. Lett.18(24), 2626–2628 (2006).
[CrossRef]

Leaird, D. E.

V. Torres-Company, D. E. Leaird, and A. M. Weiner, “Dispersion requirements in coherent frequency-to-time mapping,” Opt. Express19(24), 24718–24729 (2011).
[CrossRef] [PubMed]

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics4(2), 117–122 (2010).
[CrossRef]

J. D. McKinney, D. E. Leaird, and A. M. Weiner, “Millimeter-wave arbitrary waveform generation with a direct space-to-time pulse shaper,” Opt. Lett.27(15), 1345–1347 (2002).
[CrossRef] [PubMed]

A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of 128-element liquid-crystal phase modulator,” IEEE J. Quantum Electron.28(4), 908–920 (1992).
[CrossRef]

Lin, I. S.

I. S. Lin, J. D. McKinney, and A. M. Weiner, “Photonic synthesis of broadband microwave arbitrary waveforms applicable to ultra-wideband communication,” IEEE Microw. Wirel. Compon. Lett.15(4), 226–228 (2005).
[CrossRef]

McKinney, J. D.

I. S. Lin, J. D. McKinney, and A. M. Weiner, “Photonic synthesis of broadband microwave arbitrary waveforms applicable to ultra-wideband communication,” IEEE Microw. Wirel. Compon. Lett.15(4), 226–228 (2005).
[CrossRef]

J. D. McKinney, D. E. Leaird, and A. M. Weiner, “Millimeter-wave arbitrary waveform generation with a direct space-to-time pulse shaper,” Opt. Lett.27(15), 1345–1347 (2002).
[CrossRef] [PubMed]

Muriel, M. A.

J. Azana and M. A. Muriel, “Real-time optical spectrum analysis based on the time-space duality in chirped fiber gratings,” IEEE J. Quantum Electron.36(5), 517–526 (2000).
[CrossRef]

Novak, D.

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics1(6), 319–330 (2007).
[CrossRef]

Patel, J. S.

A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of 128-element liquid-crystal phase modulator,” IEEE J. Quantum Electron.28(4), 908–920 (1992).
[CrossRef]

Qi, M.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics4(2), 117–122 (2010).
[CrossRef]

Scholtz, R. A.

M. Z. Win and R. A. Scholtz, “Ultra-wide bandwidth time-hopping spread-spectrum impulse radio for wireless multiple-access communications,” IEEE Trans. Commun.48(4), 679–689 (2000).
[CrossRef]

Shen, H.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics4(2), 117–122 (2010).
[CrossRef]

Shen, S.

S. Shen and A. M. Weiner, “Complete dispersion compensation for 400-fs pulse transmission over 10-km fiber link using dispersion compensating fiber and spectral phase equalizer,” IEEE Photon. Technol. Lett.11(7), 827–829 (1999).
[CrossRef]

Torres-Company, V.

V. Torres-Company, D. E. Leaird, and A. M. Weiner, “Dispersion requirements in coherent frequency-to-time mapping,” Opt. Express19(24), 24718–24729 (2011).
[CrossRef] [PubMed]

V. Torres-Company, J. Lancis, and P. Andres, “Arbitrary waveform generator based on all-incoherent pulse shaping,” IEEE Photon. Technol. Lett.18(24), 2626–2628 (2006).
[CrossRef]

Wang, C.

C. Wang and J. Yao, “Chirped microwave pulse generation based on optical spectral shaping and wavelength-to-time mapping using a sagnac loop mirror incorporating a chirped fiber bragg grating,” J. Lightwave Technol.27(16), 3336–3341 (2009).
[CrossRef]

C. Wang and J. Yao, “Photonic generation of chirped millimeter-wave pulses based on nonlinear frequency-to-time mapping in a nonlinearly chirped fiber bragg grating,” IEEE Trans. Microw. Theory Tech.56(2), 542–553 (2008).
[CrossRef]

Weiner, A. M.

A. Dezfooliyan and A. M. Weiner, “Evaluation of time domain propagation measurements of UWB systems using spread spectrum channel sounding,” IEEE Trans. Antenn. Propag.60(10), 4855–4865 (2012).
[CrossRef]

J. T. Willits, A. M. Weiner, and S. T. Cundiff, “Line-by-line pulse shaping with spectral resolution below 890 MHz,” Opt. Express20(3), 3110–3117 (2012).
[CrossRef] [PubMed]

V. Torres-Company, D. E. Leaird, and A. M. Weiner, “Dispersion requirements in coherent frequency-to-time mapping,” Opt. Express19(24), 24718–24729 (2011).
[CrossRef] [PubMed]

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics4(2), 117–122 (2010).
[CrossRef]

S. Xiao and A. M. Weiner, “Coherent photonic processing of microwave signals using spatial light modulators: programmable amplitude filters,” J. Lightwave Technol.24(7), 2523–2529 (2006).
[CrossRef]

I. S. Lin, J. D. McKinney, and A. M. Weiner, “Photonic synthesis of broadband microwave arbitrary waveforms applicable to ultra-wideband communication,” IEEE Microw. Wirel. Compon. Lett.15(4), 226–228 (2005).
[CrossRef]

J. D. McKinney, D. E. Leaird, and A. M. Weiner, “Millimeter-wave arbitrary waveform generation with a direct space-to-time pulse shaper,” Opt. Lett.27(15), 1345–1347 (2002).
[CrossRef] [PubMed]

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum.71(5), 1929–1960 (2000).
[CrossRef]

S. Shen and A. M. Weiner, “Complete dispersion compensation for 400-fs pulse transmission over 10-km fiber link using dispersion compensating fiber and spectral phase equalizer,” IEEE Photon. Technol. Lett.11(7), 827–829 (1999).
[CrossRef]

A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of 128-element liquid-crystal phase modulator,” IEEE J. Quantum Electron.28(4), 908–920 (1992).
[CrossRef]

Willits, J. T.

Win, M. Z.

M. Z. Win and R. A. Scholtz, “Ultra-wide bandwidth time-hopping spread-spectrum impulse radio for wireless multiple-access communications,” IEEE Trans. Commun.48(4), 679–689 (2000).
[CrossRef]

Wullert, J. R.

A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of 128-element liquid-crystal phase modulator,” IEEE J. Quantum Electron.28(4), 908–920 (1992).
[CrossRef]

Xiao, S.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics4(2), 117–122 (2010).
[CrossRef]

S. Xiao and A. M. Weiner, “Coherent photonic processing of microwave signals using spatial light modulators: programmable amplitude filters,” J. Lightwave Technol.24(7), 2523–2529 (2006).
[CrossRef]

Xuan, Y.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics4(2), 117–122 (2010).
[CrossRef]

Yao, J.

J. Yao, “Photonics for ultrawideband communications,” IEEE Microw. Mag.10(4), 82–95 (2009).
[CrossRef]

C. Wang and J. Yao, “Chirped microwave pulse generation based on optical spectral shaping and wavelength-to-time mapping using a sagnac loop mirror incorporating a chirped fiber bragg grating,” J. Lightwave Technol.27(16), 3336–3341 (2009).
[CrossRef]

C. Wang and J. Yao, “Photonic generation of chirped millimeter-wave pulses based on nonlinear frequency-to-time mapping in a nonlinearly chirped fiber bragg grating,” IEEE Trans. Microw. Theory Tech.56(2), 542–553 (2008).
[CrossRef]

Zhao, L.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics4(2), 117–122 (2010).
[CrossRef]

Electron. Lett.

M. T. Kauffman, A. A. Godil, B. A. Auld, W. C. Banyai, and D. M. Bloom, “Applications of time lens optical-systems,” Electron. Lett.29(3), 268–269 (1993).
[CrossRef]

IEEE J. Quantum Electron.

A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of 128-element liquid-crystal phase modulator,” IEEE J. Quantum Electron.28(4), 908–920 (1992).
[CrossRef]

B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron.30(8), 1951–1963 (1994).
[CrossRef]

J. Azana and M. A. Muriel, “Real-time optical spectrum analysis based on the time-space duality in chirped fiber gratings,” IEEE J. Quantum Electron.36(5), 517–526 (2000).
[CrossRef]

IEEE Microw. Mag.

J. Yao, “Photonics for ultrawideband communications,” IEEE Microw. Mag.10(4), 82–95 (2009).
[CrossRef]

IEEE Microw. Wirel. Compon. Lett.

I. S. Lin, J. D. McKinney, and A. M. Weiner, “Photonic synthesis of broadband microwave arbitrary waveforms applicable to ultra-wideband communication,” IEEE Microw. Wirel. Compon. Lett.15(4), 226–228 (2005).
[CrossRef]

IEEE Photon. Technol. Lett.

V. Torres-Company, J. Lancis, and P. Andres, “Arbitrary waveform generator based on all-incoherent pulse shaping,” IEEE Photon. Technol. Lett.18(24), 2626–2628 (2006).
[CrossRef]

S. Shen and A. M. Weiner, “Complete dispersion compensation for 400-fs pulse transmission over 10-km fiber link using dispersion compensating fiber and spectral phase equalizer,” IEEE Photon. Technol. Lett.11(7), 827–829 (1999).
[CrossRef]

J. Chou, Y. Han, and B. Jalali, “Adaptive RF-photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett.15(4), 581–583 (2003).
[CrossRef]

IEEE Trans. Antenn. Propag.

A. Dezfooliyan and A. M. Weiner, “Evaluation of time domain propagation measurements of UWB systems using spread spectrum channel sounding,” IEEE Trans. Antenn. Propag.60(10), 4855–4865 (2012).
[CrossRef]

IEEE Trans. Commun.

M. Z. Win and R. A. Scholtz, “Ultra-wide bandwidth time-hopping spread-spectrum impulse radio for wireless multiple-access communications,” IEEE Trans. Commun.48(4), 679–689 (2000).
[CrossRef]

IEEE Trans. Microw. Theory Tech.

C. Wang and J. Yao, “Photonic generation of chirped millimeter-wave pulses based on nonlinear frequency-to-time mapping in a nonlinearly chirped fiber bragg grating,” IEEE Trans. Microw. Theory Tech.56(2), 542–553 (2008).
[CrossRef]

J. Lightwave Technol.

Nat. Photonics

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics4(2), 117–122 (2010).
[CrossRef]

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics1(6), 319–330 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Rev. Sci. Instrum.

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum.71(5), 1929–1960 (2000).
[CrossRef]

Other

A. Dezfooliyan and A. M. Weiner, “Temporal focusing of ultrabroadband wireless signals using photonic radio frequency arbitrary waveform generation,”Optical Fiber Commun. Conf. (OFC), pp. 1–3 (Anaheim, Calif., 2013).

A. M. Weiner, Ultrafast Optics (Wiley, 2009).

M.-G. Benedetto, T. Kaiser, A. F. Molisch, I. Oppermann, C. Politano, and D. Porcino, UWB communication systems A comprehensive overview (Hindawi Publishing Corporation, 2006).

A. J. Metcalf, V. Torres-Company, V. R. Supradeepa, D. E. Leaird, and A. M. Weiner, “Fully programmable ultra-complex 2-D pulse shaping,” Conf. of Lasers and Electro-Optics (CLEO), pp. 1–2 (San Jose, Calif., 2012).

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Figures (7)

Fig. 1
Fig. 1

(a-b) Frequency and time domain variables for optical waveforms. (c-d) Frequency and time domain variables for RF waveforms. We use subscript “RF” for all RF quantities.

Fig. 2
Fig. 2

Frequency-to-time mapping phenomenon. When the shaped spectrum propagates through a dispersive element, different wavelengths travel at different speeds (only four wavelengths are shown for illustration). For sufficiently large chromatic dispersion, we get a linear frequency-dependent time delay which maps the power spectrum to the temporal intensity profile.

Fig. 3
Fig. 3

Simulating the generation of a linear down-chirp RF waveform over frequencies from baseband to ~20 GHz with time aperture of ~125 ns, corresponding to a TBWP of ~2500. (a-c) Waveforms from conventional frequency-to-time mapping. The generated RF waveform is badly distorted, and certain frequencies are strongly attenuated. (d-f) Waveforms from near-field frequency-to-time mapping. An undistorted chirp is obtained, and the RF spectrum extends smoothly out to ~20 GHz.

Fig. 4
Fig. 4

Experimental setup (only main components are shown). Output pulses of a mode-locked laser are sent through a pulse shaper with spectral resolution of ~10 GHz. The pulse shaper can be programmed either according to the conventional FTM method in which the desired waveform is sculpted onto the optical power spectrum or according to the Near-Field Frequency-to-Time mapping (NF-FTM) algorithm. In NF-FTM the spectral shaping of FTM is modulated as prescribed by an assumed quadratic temporal phase factor (virtual time lens) resulting in both amplitude and phase spectral shaping. In either case, the generated signals are stretched in a dispersive element, and then the RF signals are detected by a high-speed photodiode (PD).

Fig. 5
Fig. 5

Generating down-chirp RF waveform over frequencies from baseband to ~41 GHz with time aperture of ~6.8 ns, corresponding to a TBWP of ~280. (a-c) Waveforms from conventional frequency-to-time mapping. Generated RF waveform is badly distorted and certain frequencies are strongly attenuated. (d-f) Waveforms from near-field frequency-to-time mapping. An undistorted chirp signal is obtained and the RF spectrum extends smoothly out to ~41 GHz with less than 5 dB roll-off in respect to the 4 GHz frequency components.

Fig. 6
Fig. 6

(a) Experimental result versus simulation for the generated chirp waveform with time aperture of ~6.8 ns and bandwidth of ~41 GHz. (b) we overlay these curves on top of each other and zoom in on different parts of the waveform to show details. The agreement between the simulation and experimental results is excellent.

Fig. 7
Fig. 7

Upper bounds of the achievable waveforms based on conventional FTM and NF-FTM for two shapers with assumed spectral resolutions of 1 GHz and 10 GHz and optical bandwidth of 5THz. Conventional FTM is restricted to the space below the “far-field limit” for which good waveform fidelity is maintained, whereas NF-FTM is bounded only by the “optical bandwidth” and “pulse shaper resolution” limits.

Tables (1)

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Table 1 Variables and their meaning.*

Equations (21)

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a out ( t )exp( j t 2 2 ψ 2 ) + a in ( t )exp( j t 2 2 ψ 2 )exp( j t t ψ 2 )d t .
| a out ( t ) | 2 Limit Fa r Field | exp( j t 2 2 ψ 2 ) + a FTM ( t )exp( j t t ψ 2 )d t | 2 = | A FTM ( ω=t/ ψ 2 ) | 2 .
| ( T/2 ) 2 2 ψ 2 |< π 8 T 2 π <| ψ 2 | | ψ 2min |= T 2 π 1 π δ f 2 .
B RF 0.5 δ t RF = 2 π δf = δ t RF /| ψ 2 | 0.5 2 π δ f | ψ 2 | < 0.5 2 π δ f | ψ 2min | (3) 0.25×δf.
T RF Nδ t RF = B δf δ t RF B 1 δf 0.5 B RF (4) B 0.25 B RF 0.5 B RF 0.125 B ( B RF ) 2 .
TBW P FTM (5) 0.125B B RF .
a NFFTM ( t )= a FTM ( t )exp( j t 2 2 ψ 2 ).
ϕ n = δ t 2 (nN/2) 2 2 ψ 2 1nN.
δ ϕ max =| ϕ N ϕ N1 | = (8) δ t 2 2| ψ 2 | ( N1 ) δ t 2 2| ψ 2 | N= δ t 2 2| ψ 2 | B δf δt~1/B 1 B 2 | ψ 2 | δf .
δ ϕ max (9) 1 B 2 | ψ 2 | δf = 2 π δf = δ t RF /| ψ 2 | π B 1 δ t RF δ t RF ~0.5/ B RF 2π B B RF .
Δ f inst = 1 2π δϕ δt 1 2π δ ϕ max δt δt~1/B δ ϕ max 2π B (10) B RF .
Δ f inst (11) B RF B (10) δ ϕ max 2π.
δ ϕ max (10) 2π B B RF B RF <0.125×B δ ϕ max < π 4 .
T RF =Nδ t RF = B δf δ t RF δ t RF ~0.5/ B RF B δf 0.5 B RF .
TBW P NFFTM 0.5 B δf .
| A NFFTM ( ω ) | 2 | + a NFFTM ( t )exp( jω t )d t | 2
= equatio n (7) | + a FTM ( t )exp( j t 2 2 ψ 2 )exp( jω t )d t | 2
= | [ + a FTM ( t )exp( j t 2 2 ψ 2 )exp( jω t )d t ] * | 2
= t t | + a FTM * ( t )exp( j t 2 2 ψ 2 )exp( jω t )d t | 2
= a FTM * ( t )= a FTM ( t ) | + a FTM ( t )exp( j t 2 2 ψ 2 )exp( jω t )d t | 2 .
| a out ( t ) | 2 | + a FTM ( t )exp( j t 2 2 ψ 2 )exp( j t t ψ 2 )d t | 2 .

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