Abstract

We propose and experimentally demonstrate a fiber-optics scheme for real-time analog Fourier transform (FT) of a lightwave energy spectrum, such that the output signal maps the FT of the spectrum of interest along the time axis. This scheme avoids the need for analog-to-digital conversion and subsequent digital signal post-processing of the photo-detected spectrum, thus being capable of providing the desired FT processing directly in the optical domain at megahertz update rates. The proposed concept is particularly attractive for applications requiring FT analysis of optical spectra, such as in many optical Fourier-domain reflectrometry (OFDR), interferometry, spectroscopy and sensing systems. Examples are reported to illustrate the use of the method for real-time OFDR, where the target axial-line profile is directly observed in a single-shot oscilloscope trace, similarly to a time-of-flight measurement, but with a resolution and depth of range dictated by the underlying interferometry scheme.

© 2015 Optical Society of America

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References

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2014 (3)

2013 (1)

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7(2), 102–112 (2013).
[Crossref]

2012 (3)

2011 (2)

K. Dolgaleva, A. Malacarne, P. Tannouri, L. A. Fernandes, J. R. Grenier, J. S. Aitchison, J. Azaña, R. Morandotti, P. R. Herman, and P. V. Marques, “Integrated optical temporal Fourier transformer based on a chirped Bragg grating waveguide,” Opt. Lett. 36(22), 4416–4418 (2011).
[Crossref] [PubMed]

L. Froehly, S. Iyer, and F. Vanholsbeeck, “Dual-fibre stretcher and coma as tools for independent 2nd and 3rd order tunable dispersion compensation in a fibre-based ‘scan-free’ time domain optical coherence tomography system,” Opt. Commun. 284(16–17), 4099–4106 (2011).
[Crossref]

2010 (4)

L. Froehly and R. Leitgeb, “Scan-free optical correlation techniques: history and applications to optical coherence tomography,” J. Opt. 12(8), 084001 (2010).
[Crossref]

J. Azaña, “Ultrafast analog all-optical signal processors based on fiber-grating devices,” IEEE Photonics J. 2(3), 359–386 (2010).
[Crossref]

Y. Park and J. Azaña, “Optical signal processors based on a time-spectrum convolution,” Opt. Lett. 35(6), 796–798 (2010).
[Crossref] [PubMed]

W. Wieser, B. R. Biedermann, T. Klein, C. M. Eigenwillig, and R. Huber, “Multi-Megahertz OCT: High quality 3D imaging at 20 million A-scans and 4.5 GVoxels per second,” Opt. Express 18(14), 14685–14704 (2010).
[Crossref] [PubMed]

2008 (2)

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2(1), 48–51 (2008).
[Crossref]

Y. Kim, S. Doucet, and S. LaRochelle, “50-Channel 100-GHz-Spaced Multiwavelength Fiber Lasers With Single-Frequency and Single-Polarization Operation,” IEEE Photonics Technol. Lett. 20(20), 1718–1720 (2008).
[Crossref]

2007 (1)

2005 (2)

2003 (1)

2000 (2)

M. Saruwatari, “All-optical signal processing for terabit/second optical transmission,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1363–1374 (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]

1997 (1)

Y. C. Tong, L. Y. Chan, and H. K. Tsang, “Fiber dispersion or pulse spectrum measurement using a sampling oscilloscope,” Electron. Lett. 33(11), 983–985 (1997).
[Crossref]

1995 (1)

1987 (1)

1977 (1)

D. B. Anderson, J. T. Boyd, M. C. Hamilton, and R. R. August, “An integrated-optical approach to the Fourier transform,” IEEE J. Quantum Electron. 13(4), 268–275 (1977).
[Crossref]

Adam, J.

K. Goda, A. Ayazi, D. R. Gossett, J. Sadasivam, C. K. Lonappan, E. Sollier, A. M. Fard, S. C. Hur, J. Adam, C. Murray, C. Wang, N. Brackbill, D. Di Carlo, and B. Jalali, “High-throughput single-microparticle imaging flow analyzer,” Proc. Natl. Acad. Sci. U.S.A. 109(29), 11630–11635 (2012).
[Crossref] [PubMed]

Ahn, T. J.

Aitchison, J. S.

Anderson, D. B.

D. B. Anderson, J. T. Boyd, M. C. Hamilton, and R. R. August, “An integrated-optical approach to the Fourier transform,” IEEE J. Quantum Electron. 13(4), 268–275 (1977).
[Crossref]

Ashrafi, R.

August, R. R.

D. B. Anderson, J. T. Boyd, M. C. Hamilton, and R. R. August, “An integrated-optical approach to the Fourier transform,” IEEE J. Quantum Electron. 13(4), 268–275 (1977).
[Crossref]

Ayazi, A.

K. Goda, A. Ayazi, D. R. Gossett, J. Sadasivam, C. K. Lonappan, E. Sollier, A. M. Fard, S. C. Hur, J. Adam, C. Murray, C. Wang, N. Brackbill, D. Di Carlo, and B. Jalali, “High-throughput single-microparticle imaging flow analyzer,” Proc. Natl. Acad. Sci. U.S.A. 109(29), 11630–11635 (2012).
[Crossref] [PubMed]

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]

Azaña, J.

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]

Biedermann, B. R.

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]

Boyd, J. T.

D. B. Anderson, J. T. Boyd, M. C. Hamilton, and R. R. August, “An integrated-optical approach to the Fourier transform,” IEEE J. Quantum Electron. 13(4), 268–275 (1977).
[Crossref]

Brackbill, N.

K. Goda, A. Ayazi, D. R. Gossett, J. Sadasivam, C. K. Lonappan, E. Sollier, A. M. Fard, S. C. Hur, J. Adam, C. Murray, C. Wang, N. Brackbill, D. Di Carlo, and B. Jalali, “High-throughput single-microparticle imaging flow analyzer,” Proc. Natl. Acad. Sci. U.S.A. 109(29), 11630–11635 (2012).
[Crossref] [PubMed]

Calabretta, N.

Capmany, J.

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]

Chan, L. Y.

Y. C. Tong, L. Y. Chan, and H. K. Tsang, “Fiber dispersion or pulse spectrum measurement using a sampling oscilloscope,” Electron. Lett. 33(11), 983–985 (1997).
[Crossref]

Chériaux, G.

Chida, K.

Chou, J.

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2(1), 48–51 (2008).
[Crossref]

Corral, P.

de Waardt, H.

Di Carlo, D.

K. Goda, A. Ayazi, D. R. Gossett, J. Sadasivam, C. K. Lonappan, E. Sollier, A. M. Fard, S. C. Hur, J. Adam, C. Murray, C. Wang, N. Brackbill, D. Di Carlo, and B. Jalali, “High-throughput single-microparticle imaging flow analyzer,” Proc. Natl. Acad. Sci. U.S.A. 109(29), 11630–11635 (2012).
[Crossref] [PubMed]

Dolgaleva, K.

Dorren, H. J. S.

Doucet, S.

Y. Kim, S. Doucet, and S. LaRochelle, “50-Channel 100-GHz-Spaced Multiwavelength Fiber Lasers With Single-Frequency and Single-Polarization Operation,” IEEE Photonics Technol. Lett. 20(20), 1718–1720 (2008).
[Crossref]

Eigenwillig, C. M.

Fard, A. M.

K. Goda, A. Ayazi, D. R. Gossett, J. Sadasivam, C. K. Lonappan, E. Sollier, A. M. Fard, S. C. Hur, J. Adam, C. Murray, C. Wang, N. Brackbill, D. Di Carlo, and B. Jalali, “High-throughput single-microparticle imaging flow analyzer,” Proc. Natl. Acad. Sci. U.S.A. 109(29), 11630–11635 (2012).
[Crossref] [PubMed]

Fernandes, L. A.

Fernández-Pousa, C. R.

Froehly, L.

L. Froehly, S. Iyer, and F. Vanholsbeeck, “Dual-fibre stretcher and coma as tools for independent 2nd and 3rd order tunable dispersion compensation in a fibre-based ‘scan-free’ time domain optical coherence tomography system,” Opt. Commun. 284(16–17), 4099–4106 (2011).
[Crossref]

L. Froehly and R. Leitgeb, “Scan-free optical correlation techniques: history and applications to optical coherence tomography,” J. Opt. 12(8), 084001 (2010).
[Crossref]

Froggatt, M. E.

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]

Gifford, D. K.

Goda, K.

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7(2), 102–112 (2013).
[Crossref]

K. Goda, A. Ayazi, D. R. Gossett, J. Sadasivam, C. K. Lonappan, E. Sollier, A. M. Fard, S. C. Hur, J. Adam, C. Murray, C. Wang, N. Brackbill, D. Di Carlo, and B. Jalali, “High-throughput single-microparticle imaging flow analyzer,” Proc. Natl. Acad. Sci. U.S.A. 109(29), 11630–11635 (2012).
[Crossref] [PubMed]

Gossett, D. R.

K. Goda, A. Ayazi, D. R. Gossett, J. Sadasivam, C. K. Lonappan, E. Sollier, A. M. Fard, S. C. Hur, J. Adam, C. Murray, C. Wang, N. Brackbill, D. Di Carlo, and B. Jalali, “High-throughput single-microparticle imaging flow analyzer,” Proc. Natl. Acad. Sci. U.S.A. 109(29), 11630–11635 (2012).
[Crossref] [PubMed]

Grenier, J. R.

Hamilton, M. C.

D. B. Anderson, J. T. Boyd, M. C. Hamilton, and R. R. August, “An integrated-optical approach to the Fourier transform,” IEEE J. Quantum Electron. 13(4), 268–275 (1977).
[Crossref]

Herman, P. R.

Hill, M. T.

Huber, R.

Huijskens, F. M.

Hur, S. C.

K. Goda, A. Ayazi, D. R. Gossett, J. Sadasivam, C. K. Lonappan, E. Sollier, A. M. Fard, S. C. Hur, J. Adam, C. Murray, C. Wang, N. Brackbill, D. Di Carlo, and B. Jalali, “High-throughput single-microparticle imaging flow analyzer,” Proc. Natl. Acad. Sci. U.S.A. 109(29), 11630–11635 (2012).
[Crossref] [PubMed]

Iyer, S.

L. Froehly, S. Iyer, and F. Vanholsbeeck, “Dual-fibre stretcher and coma as tools for independent 2nd and 3rd order tunable dispersion compensation in a fibre-based ‘scan-free’ time domain optical coherence tomography system,” Opt. Commun. 284(16–17), 4099–4106 (2011).
[Crossref]

Jalali, B.

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7(2), 102–112 (2013).
[Crossref]

K. Goda, A. Ayazi, D. R. Gossett, J. Sadasivam, C. K. Lonappan, E. Sollier, A. M. Fard, S. C. Hur, J. Adam, C. Murray, C. Wang, N. Brackbill, D. Di Carlo, and B. Jalali, “High-throughput single-microparticle imaging flow analyzer,” Proc. Natl. Acad. Sci. U.S.A. 109(29), 11630–11635 (2012).
[Crossref] [PubMed]

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2(1), 48–51 (2008).
[Crossref]

Joffre, M.

Khoe, G.-D.

Kieffer, J. C.

Kim, Y.

Y. Kim, S. Doucet, and S. LaRochelle, “50-Channel 100-GHz-Spaced Multiwavelength Fiber Lasers With Single-Frequency and Single-Polarization Operation,” IEEE Photonics Technol. Lett. 20(20), 1718–1720 (2008).
[Crossref]

Klein, T.

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]

LaRochelle, S.

A. Malacarne, R. Ashrafi, M. Li, S. LaRochelle, J. Yao, and J. Azaña, “Single-shot photonic time-intensity integration based on a time-spectrum convolution system,” Opt. Lett. 37(8), 1355–1357 (2012).
[Crossref] [PubMed]

Y. Kim, S. Doucet, and S. LaRochelle, “50-Channel 100-GHz-Spaced Multiwavelength Fiber Lasers With Single-Frequency and Single-Polarization Operation,” IEEE Photonics Technol. Lett. 20(20), 1718–1720 (2008).
[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]

Leitgeb, R.

L. Froehly and R. Leitgeb, “Scan-free optical correlation techniques: history and applications to optical coherence tomography,” J. Opt. 12(8), 084001 (2010).
[Crossref]

Lepetit, L.

Li, M.

Liu, Y.

Lonappan, C. K.

K. Goda, A. Ayazi, D. R. Gossett, J. Sadasivam, C. K. Lonappan, E. Sollier, A. M. Fard, S. C. Hur, J. Adam, C. Murray, C. Wang, N. Brackbill, D. Di Carlo, and B. Jalali, “High-throughput single-microparticle imaging flow analyzer,” Proc. Natl. Acad. Sci. U.S.A. 109(29), 11630–11635 (2012).
[Crossref] [PubMed]

Maestre, H.

Malacarne, A.

Marques, P. V.

Mora, J.

Morandotti, R.

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]

Murray, C.

K. Goda, A. Ayazi, D. R. Gossett, J. Sadasivam, C. K. Lonappan, E. Sollier, A. M. Fard, S. C. Hur, J. Adam, C. Murray, C. Wang, N. Brackbill, D. Di Carlo, and B. Jalali, “High-throughput single-microparticle imaging flow analyzer,” Proc. Natl. Acad. Sci. U.S.A. 109(29), 11630–11635 (2012).
[Crossref] [PubMed]

Noda, J.

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]

Ortega, B.

Park, Y.

Pastor, D.

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]

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]

Sadasivam, J.

K. Goda, A. Ayazi, D. R. Gossett, J. Sadasivam, C. K. Lonappan, E. Sollier, A. M. Fard, S. C. Hur, J. Adam, C. Murray, C. Wang, N. Brackbill, D. Di Carlo, and B. Jalali, “High-throughput single-microparticle imaging flow analyzer,” Proc. Natl. Acad. Sci. U.S.A. 109(29), 11630–11635 (2012).
[Crossref] [PubMed]

Sales, S.

Saruwatari, M.

M. Saruwatari, “All-optical signal processing for terabit/second optical transmission,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1363–1374 (2000).
[Crossref]

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]

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]

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]

Siddiqui, M.

Soller, B. J.

Solli, D. R.

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2(1), 48–51 (2008).
[Crossref]

Sollier, E.

K. Goda, A. Ayazi, D. R. Gossett, J. Sadasivam, C. K. Lonappan, E. Sollier, A. M. Fard, S. C. Hur, J. Adam, C. Murray, C. Wang, N. Brackbill, D. Di Carlo, and B. Jalali, “High-throughput single-microparticle imaging flow analyzer,” Proc. Natl. Acad. Sci. U.S.A. 109(29), 11630–11635 (2012).
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Srivatsa, A.

Takada, K.

Tannouri, P.

Tong, Y. C.

Y. C. Tong, L. Y. Chan, and H. K. Tsang, “Fiber dispersion or pulse spectrum measurement using a sampling oscilloscope,” Electron. Lett. 33(11), 983–985 (1997).
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Tozburun, S.

Tsang, H. K.

Y. C. Tong, L. Y. Chan, and H. K. Tsang, “Fiber dispersion or pulse spectrum measurement using a sampling oscilloscope,” Electron. Lett. 33(11), 983–985 (1997).
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Vakoc, B. J.

Vanholsbeeck, F.

L. Froehly, S. Iyer, and F. Vanholsbeeck, “Dual-fibre stretcher and coma as tools for independent 2nd and 3rd order tunable dispersion compensation in a fibre-based ‘scan-free’ time domain optical coherence tomography system,” Opt. Commun. 284(16–17), 4099–4106 (2011).
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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).
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K. Goda, A. Ayazi, D. R. Gossett, J. Sadasivam, C. K. Lonappan, E. Sollier, A. M. Fard, S. C. Hur, J. Adam, C. Murray, C. Wang, N. Brackbill, D. Di Carlo, and B. Jalali, “High-throughput single-microparticle imaging flow analyzer,” Proc. Natl. Acad. Sci. U.S.A. 109(29), 11630–11635 (2012).
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Appl. Opt. (2)

Electron. Lett. (1)

Y. C. Tong, L. Y. Chan, and H. K. Tsang, “Fiber dispersion or pulse spectrum measurement using a sampling oscilloscope,” Electron. Lett. 33(11), 983–985 (1997).
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IEEE Photonics J. (1)

J. Azaña, “Ultrafast analog all-optical signal processors based on fiber-grating devices,” IEEE Photonics J. 2(3), 359–386 (2010).
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IEEE Photonics Technol. Lett. (1)

Y. Kim, S. Doucet, and S. LaRochelle, “50-Channel 100-GHz-Spaced Multiwavelength Fiber Lasers With Single-Frequency and Single-Polarization Operation,” IEEE Photonics Technol. Lett. 20(20), 1718–1720 (2008).
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Nat. Photonics (2)

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2(1), 48–51 (2008).
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K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7(2), 102–112 (2013).
[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).
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Opt. Commun. (1)

L. Froehly, S. Iyer, and F. Vanholsbeeck, “Dual-fibre stretcher and coma as tools for independent 2nd and 3rd order tunable dispersion compensation in a fibre-based ‘scan-free’ time domain optical coherence tomography system,” Opt. Commun. 284(16–17), 4099–4106 (2011).
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Opt. Express (4)

Opt. Lett. (4)

Proc. Natl. Acad. Sci. U.S.A. (1)

K. Goda, A. Ayazi, D. R. Gossett, J. Sadasivam, C. K. Lonappan, E. Sollier, A. M. Fard, S. C. Hur, J. Adam, C. Murray, C. Wang, N. Brackbill, D. Di Carlo, and B. Jalali, “High-throughput single-microparticle imaging flow analyzer,” Proc. Natl. Acad. Sci. U.S.A. 109(29), 11630–11635 (2012).
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M. Li, A. Malacarne, S. LaRochelle, J. Yao, and J. Azaña, “Reconfigurable and Single-Shot Chirped Microwave Pulse Compression Using a Time-Spectrum Convolution System”, IEEE Intern. Topical Meeting on Microwave Photonics 2011, PD paper, Singapore, (2011).

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Supplementary Material (3)

NameDescription
» Visualization 1: MP4 (15460 KB)      Visualization 1
» Visualization 2: MP4 (11371 KB)      Visualization 2
» Visualization 3: AVI (578 KB)      Visualization 3

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Figures (11)

Fig. 1
Fig. 1 Conceptual comparison between a system employing the Fourier transform of consecutive incoming energy spectra through electronic digital processing (a) and one based on the proposed analog real-time optical spectrum Fourier transformation (RT-OSFT) (b).
Fig. 2
Fig. 2 Principle of RT-OSFT. The equation given for the output signal waveform is a particular case of the more general result in Eq. (1), assuming that the input signal spectrum to be processed is symmetric.
Fig. 3
Fig. 3 Processed input energy spectra (left) and corresponding output temporal waveforms (blue) and time-scaled Fourier transform magnitude of the input spectrum (red) (right), in the case of rectangular-shaped envelope of the input optical spectrum (see Visualization 1).
Fig. 4
Fig. 4 Processed input energy spectra (left) and corresponding output temporal waveforms (blue) and time-scaled Fourier transform magnitude of the input spectrum (red) (right), in the case of double Gaussian-shaped envelope of the input optical spectrum (see Visualization 2).
Fig. 5
Fig. 5 Processed input energy spectrum (left) and corresponding output temporal waveform (blue) and time-scaled Fourier transform magnitude of the input spectrum (red) (right), in the case of 5.5nm-width continuous incoherent rectangular spectrum.
Fig. 6
Fig. 6 Working principle of the proposed optical reflectometry method based on RT-OSFT.
Fig. 7
Fig. 7 Experimental setup for a proof-of-concept of the proposed optical reflectometry concept, in the case of maximization of the depth range. The dispersion and interferometer stages are interchanged with respect to the theoretical scheme in Fig. 6. The splitter is a 3-dB fiber coupler.
Fig. 8
Fig. 8 Temporal output signal for steps of 1mm, in case of maximization of the depth range.
Fig. 9
Fig. 9 Experimental setup for the optimization of the spatial resolution.
Fig. 10
Fig. 10 Temporal output signal for steps of 0.1mm (a); temporal signal position (b) and spatial resolution (c) versus distance of the target, in case of optimizing the spatial resolution.
Fig. 11
Fig. 11 Temporal signal acquired in single shot by the real-time oscilloscope before (green) and after (orange) the I-Q demodulator (left). Measurement of the system sensitivity (right) (see Visualization 3).

Equations (2)

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S( t Φ ¨ )cos( D m 2 t 2 ){ s( ω = D m t )exp( j D m 2 t 2 ) } with s( ω )=FT{ S( t Φ ¨ ) }
D m << 8π ( | Φ ¨ |Δω ) 2

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