Abstract

A general method for compressing the modulation time–bandwidth product of analog signals is introduced. As one of its applications, this physics-based signal grooming, performed in the analog domain, allows a conventional digitizer to sample and digitize the analog signal with variable resolution. The net result is that frequency components that were beyond the digitizer bandwidth can now be captured and, at the same time, the total digital data size is reduced. This compression is lossless and is achieved through a feature selective reshaping of the signal’s complex field, performed in the analog domain prior to sampling. Our method is inspired by operation of Fovea centralis in the human eye and by anamorphic transformation in visual arts. The proposed transform can also be performed in the digital domain as a data compression algorithm to alleviate the storage and transmission bottlenecks associated with “big data.”

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y. Han and B. Jalali, “Photonic time-stretched analog-to-digital converter: fundamental concepts and practical considerations,” J. Lightwave Technol. 21, 3085–3103 (2003).
    [CrossRef]
  2. A. M. Fard, S. Gupta, and B. Jalali, “Photonic time-stretch digitizer and its extension to real-time spectroscopy and imaging,” Laser Photon. Rev. 7, 207–263 (2013).
    [CrossRef]
  3. K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7, 102–112 (2013).
    [CrossRef]
  4. G. C. Valley, “Photonic analog-to-digital converters,” Opt. Express 15, 1955–1982 (2007).
    [CrossRef]
  5. A. Khilo, S. J. Spector, M. E. Grein, A. H. Nejadmalayeri, C. W. Holzwarth, M. Y. Sander, M. S. Dahlem, M. Y. Peng, M. W. Geis, N. A. DiLello, J. U. Yoon, A. Motamedi, J. S. Orcutt, J. P. Wang, C. M. Sorace-Agaskar, M. A. Popovic, J. Sun, G. Zhou, H. Byun, J. Chen, J. L. Hoyt, H. I. Smith, R. J. Ram, M. Perrott, T. M. Lyszczarz, E. P. Ippen, and F. X. Kartner, “Photonic ADC: overcoming the bottleneck of electronic jitter,” Opt. Express 20, 4454–4469 (2012).
    [CrossRef]
  6. J. Stigwall and S. Galt, “Signal reconstruction by phase retrieval and optical backpropagation in phase-diverse photonic time-stretch systems,” J. Lightwave Technol. 25, 3017–3027 (2007).
    [CrossRef]
  7. W. Ng, T. D. Rockwood, G. A. Sefler, and G. C. Valley, “Demonstration of a large stretch-ratio (M=41) photonic analog-to-digital converter with 8 ENOB for an input signal bandwidth of 10 GHz,” IEEE Photon. Technol. Lett. 24, 1185–1187 (2012).
    [CrossRef]
  8. E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
    [CrossRef]
  9. G. C. Valley, G. A. Sefler, and T. J. Shaw, “Compressive sensing of sparse radio frequency signals using optical mixing,” Opt. Lett. 37, 4675–4677 (2012).
    [CrossRef]
  10. E. D. Diebold, N. K. Hon, Z. Tan, J. Chou, T. Sienicki, C. Wang, and B. Jalali, “Giant tunable optical dispersion using chromo-modal excitation of a multimode waveguide,” Opt. Express 19, 23809–23817 (2011).
    [CrossRef]
  11. J. L. Hunt, B. G. Nickel, and C. Gigault, “Anamorphic images,” Am. J. Phys. 68, 232–237 (2000).
    [CrossRef]
  12. M. H. Asghari and B. Jalali, “Warped dispersive transform and its application to analog bandwidth compression,” in Proceedings of IEEE Photonics Conference (IEEE, 2013), paper TUG 1.1.
  13. P. M. Woodward, Probability and Information Theory with Applications to Radar (Pergamon, 1953).
  14. M. H. Asghari and B. Jalali, “Stereopsis-inspired time-stretched amplified real-time spectrometer (STARS),” IEEE Photon. J. 4, 1693–1701 (2012).
    [CrossRef]
  15. D. R. Solli, S. Gupta, and B. Jalali, “Optical phase recovery in the dispersive Fourier transform,” Appl. Phys. Lett. 95, 231108 (2009).
    [CrossRef]
  16. M. H. Asghari and J. Azana, “Self-referenced temporal phase reconstruction from intensity measurements using causality arguments in linear optical filters,” Opt. Lett. 37, 3582–3584 (2012).
    [CrossRef]
  17. F. Li, Y. Park, and J. Azana, “Linear characterization of optical pulses with durations ranging from the picosecond to the nanosecond regime using ultrafast photonic differentiation,” J. Lightwave Technol. 27, 4623–4633 (2009).
    [CrossRef]
  18. C. Dorrer and I. Kang, “Complete temporal characterization of short optical pulses by simplified chronocyclic tomography,” Opt. Lett. 28, 1481–1483 (2003).
    [CrossRef]
  19. K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, “Theory of amplified dispersive Fourier transformation,” Phys. Rev. A 80, 043821 (2009).
    [CrossRef]
  20. D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2, 48–51 (2008).
    [CrossRef]
  21. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
    [CrossRef]
  22. B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
    [CrossRef]
  23. D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nat. Photonics 6, 463–468 (2012).
    [CrossRef]
  24. K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458, 1145–1149 (2009).
    [CrossRef]
  25. F. Qian, Q. Song, E. Tien, S. K. Kalyoncu, and O. Boyraz, “Real-time optical imaging and tracking of micron-sized particles,” Opt. Commun. 282, 4672–4675 (2009).
    [CrossRef]
  26. C. Zhang, Y. Qiu, R. Zhu, K. K. Y. Wong, and K. K. Tsia, “Serial time-encoded amplified microscopy (STEAM) based on a stabilized picosecond supercontinuum source,” Opt. Express 19, 15810–15816 (2011).
    [CrossRef]
  27. M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456, 81–84 (2008).
    [CrossRef]
  28. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
    [CrossRef]
  29. M. G. F. Wilson and M. C. Bone, “Theory of curved diffraction gratings,” in IEEE Proceedings on Microwaves, Optics and Antennas (IEEE, 1980), pp. 127–132.
  30. G. A. Sefler and G. C. Valley, “Mitigation of group-delay-ripple distortions for use of chirped fiber-Bragg gratings in photonic time-stretch ADCs,” J. Lightwave Technol. 31, 1093–1100 (2013).
    [CrossRef]

2013 (3)

A. M. Fard, S. Gupta, and B. Jalali, “Photonic time-stretch digitizer and its extension to real-time spectroscopy and imaging,” Laser Photon. Rev. 7, 207–263 (2013).
[CrossRef]

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7, 102–112 (2013).
[CrossRef]

G. A. Sefler and G. C. Valley, “Mitigation of group-delay-ripple distortions for use of chirped fiber-Bragg gratings in photonic time-stretch ADCs,” J. Lightwave Technol. 31, 1093–1100 (2013).
[CrossRef]

2012 (7)

A. Khilo, S. J. Spector, M. E. Grein, A. H. Nejadmalayeri, C. W. Holzwarth, M. Y. Sander, M. S. Dahlem, M. Y. Peng, M. W. Geis, N. A. DiLello, J. U. Yoon, A. Motamedi, J. S. Orcutt, J. P. Wang, C. M. Sorace-Agaskar, M. A. Popovic, J. Sun, G. Zhou, H. Byun, J. Chen, J. L. Hoyt, H. I. Smith, R. J. Ram, M. Perrott, T. M. Lyszczarz, E. P. Ippen, and F. X. Kartner, “Photonic ADC: overcoming the bottleneck of electronic jitter,” Opt. Express 20, 4454–4469 (2012).
[CrossRef]

M. H. Asghari and J. Azana, “Self-referenced temporal phase reconstruction from intensity measurements using causality arguments in linear optical filters,” Opt. Lett. 37, 3582–3584 (2012).
[CrossRef]

G. C. Valley, G. A. Sefler, and T. J. Shaw, “Compressive sensing of sparse radio frequency signals using optical mixing,” Opt. Lett. 37, 4675–4677 (2012).
[CrossRef]

W. Ng, T. D. Rockwood, G. A. Sefler, and G. C. Valley, “Demonstration of a large stretch-ratio (M=41) photonic analog-to-digital converter with 8 ENOB for an input signal bandwidth of 10 GHz,” IEEE Photon. Technol. Lett. 24, 1185–1187 (2012).
[CrossRef]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[CrossRef]

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nat. Photonics 6, 463–468 (2012).
[CrossRef]

M. H. Asghari and B. Jalali, “Stereopsis-inspired time-stretched amplified real-time spectrometer (STARS),” IEEE Photon. J. 4, 1693–1701 (2012).
[CrossRef]

2011 (2)

2009 (5)

F. Li, Y. Park, and J. Azana, “Linear characterization of optical pulses with durations ranging from the picosecond to the nanosecond regime using ultrafast photonic differentiation,” J. Lightwave Technol. 27, 4623–4633 (2009).
[CrossRef]

D. R. Solli, S. Gupta, and B. Jalali, “Optical phase recovery in the dispersive Fourier transform,” Appl. Phys. Lett. 95, 231108 (2009).
[CrossRef]

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, “Theory of amplified dispersive Fourier transformation,” Phys. Rev. A 80, 043821 (2009).
[CrossRef]

K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458, 1145–1149 (2009).
[CrossRef]

F. Qian, Q. Song, E. Tien, S. K. Kalyoncu, and O. Boyraz, “Real-time optical imaging and tracking of micron-sized particles,” Opt. Commun. 282, 4672–4675 (2009).
[CrossRef]

2008 (3)

E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[CrossRef]

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2, 48–51 (2008).
[CrossRef]

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456, 81–84 (2008).
[CrossRef]

2007 (3)

2003 (2)

2000 (1)

J. L. Hunt, B. G. Nickel, and C. Gigault, “Anamorphic images,” Am. J. Phys. 68, 232–237 (2000).
[CrossRef]

1997 (1)

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
[CrossRef]

Asghari, M. H.

M. H. Asghari and B. Jalali, “Stereopsis-inspired time-stretched amplified real-time spectrometer (STARS),” IEEE Photon. J. 4, 1693–1701 (2012).
[CrossRef]

M. H. Asghari and J. Azana, “Self-referenced temporal phase reconstruction from intensity measurements using causality arguments in linear optical filters,” Opt. Lett. 37, 3582–3584 (2012).
[CrossRef]

M. H. Asghari and B. Jalali, “Warped dispersive transform and its application to analog bandwidth compression,” in Proceedings of IEEE Photonics Conference (IEEE, 2013), paper TUG 1.1.

Azana, J.

Bone, M. C.

M. G. F. Wilson and M. C. Bone, “Theory of curved diffraction gratings,” in IEEE Proceedings on Microwaves, Optics and Antennas (IEEE, 1980), pp. 127–132.

Boyraz, O.

F. Qian, Q. Song, E. Tien, S. K. Kalyoncu, and O. Boyraz, “Real-time optical imaging and tracking of micron-sized particles,” Opt. Commun. 282, 4672–4675 (2009).
[CrossRef]

Byun, H.

Candes, E. J.

E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[CrossRef]

Chen, J.

Chou, J.

Dahlem, M. S.

Dias, F.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[CrossRef]

Diebold, E. D.

DiLello, N. A.

Dorrer, C.

Dudley, J. M.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[CrossRef]

Erdogan, T.

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
[CrossRef]

Fard, A. M.

A. M. Fard, S. Gupta, and B. Jalali, “Photonic time-stretch digitizer and its extension to real-time spectroscopy and imaging,” Laser Photon. Rev. 7, 207–263 (2013).
[CrossRef]

Foster, M. A.

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456, 81–84 (2008).
[CrossRef]

Gaeta, A. L.

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456, 81–84 (2008).
[CrossRef]

Galt, S.

Geis, M. W.

Genty, G.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[CrossRef]

Geraghty, D. F.

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456, 81–84 (2008).
[CrossRef]

Gigault, C.

J. L. Hunt, B. G. Nickel, and C. Gigault, “Anamorphic images,” Am. J. Phys. 68, 232–237 (2000).
[CrossRef]

Goda, K.

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7, 102–112 (2013).
[CrossRef]

K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458, 1145–1149 (2009).
[CrossRef]

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, “Theory of amplified dispersive Fourier transformation,” Phys. Rev. A 80, 043821 (2009).
[CrossRef]

Grein, M. E.

Gupta, S.

A. M. Fard, S. Gupta, and B. Jalali, “Photonic time-stretch digitizer and its extension to real-time spectroscopy and imaging,” Laser Photon. Rev. 7, 207–263 (2013).
[CrossRef]

D. R. Solli, S. Gupta, and B. Jalali, “Optical phase recovery in the dispersive Fourier transform,” Appl. Phys. Lett. 95, 231108 (2009).
[CrossRef]

Han, Y.

Herink, G.

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nat. Photonics 6, 463–468 (2012).
[CrossRef]

Holzwarth, C. W.

Hon, N. K.

Hoyt, J. L.

Hunt, J. L.

J. L. Hunt, B. G. Nickel, and C. Gigault, “Anamorphic images,” Am. J. Phys. 68, 232–237 (2000).
[CrossRef]

Ippen, E. P.

Jalali, B.

A. M. Fard, S. Gupta, and B. Jalali, “Photonic time-stretch digitizer and its extension to real-time spectroscopy and imaging,” Laser Photon. Rev. 7, 207–263 (2013).
[CrossRef]

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7, 102–112 (2013).
[CrossRef]

M. H. Asghari and B. Jalali, “Stereopsis-inspired time-stretched amplified real-time spectrometer (STARS),” IEEE Photon. J. 4, 1693–1701 (2012).
[CrossRef]

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nat. Photonics 6, 463–468 (2012).
[CrossRef]

E. D. Diebold, N. K. Hon, Z. Tan, J. Chou, T. Sienicki, C. Wang, and B. Jalali, “Giant tunable optical dispersion using chromo-modal excitation of a multimode waveguide,” Opt. Express 19, 23809–23817 (2011).
[CrossRef]

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, “Theory of amplified dispersive Fourier transformation,” Phys. Rev. A 80, 043821 (2009).
[CrossRef]

D. R. Solli, S. Gupta, and B. Jalali, “Optical phase recovery in the dispersive Fourier transform,” Appl. Phys. Lett. 95, 231108 (2009).
[CrossRef]

K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458, 1145–1149 (2009).
[CrossRef]

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2, 48–51 (2008).
[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[CrossRef]

Y. Han and B. Jalali, “Photonic time-stretched analog-to-digital converter: fundamental concepts and practical considerations,” J. Lightwave Technol. 21, 3085–3103 (2003).
[CrossRef]

M. H. Asghari and B. Jalali, “Warped dispersive transform and its application to analog bandwidth compression,” in Proceedings of IEEE Photonics Conference (IEEE, 2013), paper TUG 1.1.

Kalyoncu, S. K.

F. Qian, Q. Song, E. Tien, S. K. Kalyoncu, and O. Boyraz, “Real-time optical imaging and tracking of micron-sized particles,” Opt. Commun. 282, 4672–4675 (2009).
[CrossRef]

Kang, I.

Kartner, F. X.

Khilo, A.

Koonath, P.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[CrossRef]

Kudlinski, A.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[CrossRef]

Lacourt, P. A.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[CrossRef]

Larger, L.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[CrossRef]

Li, F.

Lipson, M.

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456, 81–84 (2008).
[CrossRef]

Lyszczarz, T. M.

Merolla, J. M.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[CrossRef]

Motamedi, A.

Mussot, A.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[CrossRef]

Nejadmalayeri, A. H.

Ng, W.

W. Ng, T. D. Rockwood, G. A. Sefler, and G. C. Valley, “Demonstration of a large stretch-ratio (M=41) photonic analog-to-digital converter with 8 ENOB for an input signal bandwidth of 10 GHz,” IEEE Photon. Technol. Lett. 24, 1185–1187 (2012).
[CrossRef]

Nickel, B. G.

J. L. Hunt, B. G. Nickel, and C. Gigault, “Anamorphic images,” Am. J. Phys. 68, 232–237 (2000).
[CrossRef]

Orcutt, J. S.

Park, Y.

Peng, M. Y.

Perrott, M.

Popovic, M. A.

Qian, F.

F. Qian, Q. Song, E. Tien, S. K. Kalyoncu, and O. Boyraz, “Real-time optical imaging and tracking of micron-sized particles,” Opt. Commun. 282, 4672–4675 (2009).
[CrossRef]

Qiu, Y.

Ram, R. J.

Rockwood, T. D.

W. Ng, T. D. Rockwood, G. A. Sefler, and G. C. Valley, “Demonstration of a large stretch-ratio (M=41) photonic analog-to-digital converter with 8 ENOB for an input signal bandwidth of 10 GHz,” IEEE Photon. Technol. Lett. 24, 1185–1187 (2012).
[CrossRef]

Ropers, C.

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nat. Photonics 6, 463–468 (2012).
[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[CrossRef]

Salem, R.

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456, 81–84 (2008).
[CrossRef]

Sander, M. Y.

Sefler, G. A.

Shaw, T. J.

Sienicki, T.

Smith, H. I.

Solli, D. R.

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nat. Photonics 6, 463–468 (2012).
[CrossRef]

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, “Theory of amplified dispersive Fourier transformation,” Phys. Rev. A 80, 043821 (2009).
[CrossRef]

D. R. Solli, S. Gupta, and B. Jalali, “Optical phase recovery in the dispersive Fourier transform,” Appl. Phys. Lett. 95, 231108 (2009).
[CrossRef]

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2, 48–51 (2008).
[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[CrossRef]

Song, Q.

F. Qian, Q. Song, E. Tien, S. K. Kalyoncu, and O. Boyraz, “Real-time optical imaging and tracking of micron-sized particles,” Opt. Commun. 282, 4672–4675 (2009).
[CrossRef]

Sorace-Agaskar, C. M.

Spector, S. J.

Stefani, A.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[CrossRef]

Stigwall, J.

Sun, J.

Sylvestre, T.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[CrossRef]

Tan, Z.

Tien, E.

F. Qian, Q. Song, E. Tien, S. K. Kalyoncu, and O. Boyraz, “Real-time optical imaging and tracking of micron-sized particles,” Opt. Commun. 282, 4672–4675 (2009).
[CrossRef]

Tsia, K. K.

C. Zhang, Y. Qiu, R. Zhu, K. K. Y. Wong, and K. K. Tsia, “Serial time-encoded amplified microscopy (STEAM) based on a stabilized picosecond supercontinuum source,” Opt. Express 19, 15810–15816 (2011).
[CrossRef]

K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458, 1145–1149 (2009).
[CrossRef]

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, “Theory of amplified dispersive Fourier transformation,” Phys. Rev. A 80, 043821 (2009).
[CrossRef]

Turner-Foster, A. C.

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456, 81–84 (2008).
[CrossRef]

Valley, G. C.

Wakin, M. B.

E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[CrossRef]

Wang, C.

Wang, J. P.

Wetzel, B.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[CrossRef]

Wilson, M. G. F.

M. G. F. Wilson and M. C. Bone, “Theory of curved diffraction gratings,” in IEEE Proceedings on Microwaves, Optics and Antennas (IEEE, 1980), pp. 127–132.

Wong, K. K. Y.

Woodward, P. M.

P. M. Woodward, Probability and Information Theory with Applications to Radar (Pergamon, 1953).

Yoon, J. U.

Zhang, C.

Zhou, G.

Zhu, R.

Am. J. Phys. (1)

J. L. Hunt, B. G. Nickel, and C. Gigault, “Anamorphic images,” Am. J. Phys. 68, 232–237 (2000).
[CrossRef]

Appl. Phys. Lett. (1)

D. R. Solli, S. Gupta, and B. Jalali, “Optical phase recovery in the dispersive Fourier transform,” Appl. Phys. Lett. 95, 231108 (2009).
[CrossRef]

IEEE Photon. J. (1)

M. H. Asghari and B. Jalali, “Stereopsis-inspired time-stretched amplified real-time spectrometer (STARS),” IEEE Photon. J. 4, 1693–1701 (2012).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

W. Ng, T. D. Rockwood, G. A. Sefler, and G. C. Valley, “Demonstration of a large stretch-ratio (M=41) photonic analog-to-digital converter with 8 ENOB for an input signal bandwidth of 10 GHz,” IEEE Photon. Technol. Lett. 24, 1185–1187 (2012).
[CrossRef]

IEEE Signal Process. Mag. (1)

E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[CrossRef]

J. Lightwave Technol. (5)

Laser Photon. Rev. (1)

A. M. Fard, S. Gupta, and B. Jalali, “Photonic time-stretch digitizer and its extension to real-time spectroscopy and imaging,” Laser Photon. Rev. 7, 207–263 (2013).
[CrossRef]

Nat. Photonics (3)

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7, 102–112 (2013).
[CrossRef]

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2, 48–51 (2008).
[CrossRef]

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, “Fluctuations and correlations in modulation instability,” Nat. Photonics 6, 463–468 (2012).
[CrossRef]

Nature (3)

K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458, 1145–1149 (2009).
[CrossRef]

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456, 81–84 (2008).
[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[CrossRef]

Opt. Commun. (1)

F. Qian, Q. Song, E. Tien, S. K. Kalyoncu, and O. Boyraz, “Real-time optical imaging and tracking of micron-sized particles,” Opt. Commun. 282, 4672–4675 (2009).
[CrossRef]

Opt. Express (4)

Opt. Lett. (3)

Phys. Rev. A (1)

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, “Theory of amplified dispersive Fourier transformation,” Phys. Rev. A 80, 043821 (2009).
[CrossRef]

Sci. Rep. (1)

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).
[CrossRef]

Other (3)

M. H. Asghari and B. Jalali, “Warped dispersive transform and its application to analog bandwidth compression,” in Proceedings of IEEE Photonics Conference (IEEE, 2013), paper TUG 1.1.

P. M. Woodward, Probability and Information Theory with Applications to Radar (Pergamon, 1953).

M. G. F. Wilson and M. C. Bone, “Theory of curved diffraction gratings,” in IEEE Proceedings on Microwaves, Optics and Antennas (IEEE, 1980), pp. 127–132.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1.
Fig. 1.

Comparison of the conventional time-stretch transform (left) and proposed anamorphic transform (right). Both are performed prior to sampling, and they boost the analog-to-digital converter (ADC)’s sampling rate. However, for a given bandwidth compression factor M, the anamorphic transform leads to a shorter record length with fewer samples. ωm is the envelope frequency.

Fig. 2.
Fig. 2.

(a) Proposed anamorphic transformation is performed using a filter with a tailored frequency-dependent GD placed prior to the ADC. The complex field of the transformed signal is measured, and the input signal is reconstructed using backpropagation. (b) Arbitrary input signal; inset shows its field spectrum. (c) MID of the signal after it is subjected to a filter with S-shaped GD (see inset). The MID is a 3D plot showing the dependence of the envelope intensity (color) on time and envelope frequency. For comparison, the MID of the input signal without the filter is shown in the inset. The anamorphic transform reduces the signal envelope bandwidth, but it does not lead to a proportional increase in its time duration. The complex interference patterns arise because the system is in the near field. ωm=0 corresponds to the carrier frequency.

Fig. 3.
Fig. 3.

(a) Anamorphic transformation in the case of a filter with a quadratic phase profile (linear GD). (b) MID. The input signal is the same as that in Fig. 2. ωm=0 corresponds to the carrier frequency.

Fig. 4.
Fig. 4.

(a) Input signal. (b) MID of the input signal without any filter. ωm=0 corresponds to the carrier frequency. The anamorphic transform of this input signal is shown in Fig. 6.

Fig. 5.
Fig. 5.

Comparison of the linear and nonlinear filter GD profiles that result in the same output envelope bandwidth. As observed in Fig. 6, the nonlinear GD results in a smaller time duration. ω=0 corresponds to the carrier frequency.

Fig. 6.
Fig. 6.

Time–bandwidth compression using the AST in the far-field regime. (a) Comparison of the output envelope spectra for filters with linear GD (solid blue line) and with the tailored nonlinear GD, i.e., AST (dotted red line). The input signal is shown in Fig. 4, and the filter GD profiles are shown in Fig. 5. (b) Comparison of the temporal outputs for the two filters. (c) Comparison of the recovered with the original signal. In both cases, the envelope bandwidth is reduced from 1 THz to 8 GHz; however, the temporal length, and hence the number of samples needed to represent it, is nearly 40% lower with the AST. The signal captured with the same 8 GHz ADC but without AST is also shown in (c). MID plots are shown in Fig. 7. ωm=0 corresponds to the carrier frequency.

Fig. 7.
Fig. 7.

Left and right figures show the MID of the signal in Fig. 6, when the filter has linear and nonlinear (S-shaped) GD, respectively. In both cases, the envelope bandwidth is reduced from 1 THz to 8 GHz; however, the temporal length, and hence the number of samples needed to represent the signal, is nearly 40% lower with the anamorphic transform. MID is used to identify the optimum GD profile. ωm=0 corresponds to the carrier frequency.

Fig. 8.
Fig. 8.

(a) Input signal. (b) MID of the input signal. The anamorphic transform of this input signal is shown in Fig. 10. ωm=0 corresponds to the carrier frequency.

Fig. 9.
Fig. 9.

Comparison of the linear and nonlinear filter GD profiles that result in the same output envelope bandwidth. As observed in Fig. 10, the nonlinear GD results in a smaller time duration. ω=0 corresponds to the carrier frequency.

Fig. 10.
Fig. 10.

Time–bandwidth compression using the AST in the near-field regime. (a) Comparison of the output envelope spectra for filters with linear GD (solid blue line) and with nonlinear (S-shaped) GD (dotted red line). The input signal is shown in Fig. 8, and the filter GD profiles are shown in Fig. 9. (b) Comparison of the temporal outputs for the two filters. (c) Comparison of the recovered signal with the original signal. In both cases, the envelope bandwidth is reduced from 40 to 16 GHz; however, the temporal length, and hence the number of samples needed to represent the signal, is nearly 35% lower with the AST. The captured signal with the same 16 GHz ADC but without AST is also shown in (c). MID plots are shown in Fig. 11. ωm=0 corresponds to the carrier frequency.

Fig. 11.
Fig. 11.

Left and right figures show the MID of the signal in Fig. 10, when the filter has a linear or nonlinear (S-shaped) GD, respectively. In both cases the envelope bandwidth is reduced from 40 to 16 GHz; however, the temporal length, and hence the number of samples needed to represent it, is nearly 35% lower with the anamorphic transform. MID is used to design the optimum GD profile.

Equations (8)

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

Ii(ωm)=FT{|Ei(t)|2},
Ii(ωm)=E˜i(ω)E˜i*(ω+ωm)dω,
Io(ωm)=E˜i(ω)E˜i*(ω+ωm)ej(β(ω)β(ω+ωm))dω.
AST{E˜i(ω)}(ωm)=E˜i(ω)E˜i*(ω+ωm)ej·ωm·[β(ω+ωm)β(ω)ωm]dω.
AST{E˜i(ω)}(ωm)=E˜i(ω)E˜i*(ω+ωm)ej·ωm·τ(ω)dω.
MID(ωm,t)=E˜i(ω)E˜i*(ω+ωm)ej·ωm·[β(ω+ωm)β(ω)ωm]ejωtdω.
τ(ω)=A·tan1(B·ω),
DFT{E˜i(ω)}(t)=|E˜i(ω)ej·β2ω22ej·ω·tdω|2.

Metrics