Abstract

We introduce a novel technique for broadband RF disambiguation which exploits a known jitter imparted onto the sampling rate of an optical pulse source in a subsampled analog optical link. Coarse disambiguation to bandwidths equal to the sample rate is achieved using pure tones as example waveforms by comparing the amplitude of the jitter-induced sidebands relative to the measured signal within the fundamental Nyquist band (frep/2). This sampling technique allows for ultra-wideband signal recovery with a single measurement. In a first-of-its-kind photonics demonstration we show reliable disambiguation for signals with center frequencies spanning 1 MHz – 40 GHz.

© 2014 Optical Society of America

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References

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  1. G. C. Valley, “Photonic analog-to-digital converters,” Opt. Express 15, 1955–1982 (2007).
    [Crossref] [PubMed]
  2. P. W. Juodawlkis, J. J. Hargreaves, R. D. Younger, G. W. Titi, and J. C. Twichell, “Optical down-sampling of wide-band microwave signals,” J. Lightwave Technol. 21, 3116–3124 (2003).
    [Crossref]
  3. J. Kim, M. J. Park, M. H. Perrott, and F. X. Kärtner, “Photonic subsampling analog-to-digital conversion of microwave signals at 40-GHz with higher than 7-ENOB resolution,” Opt. Express 16, 16509–16515 (2008).
    [Crossref] [PubMed]
  4. 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, 341–345 (2014).
    [Crossref] [PubMed]
  5. T. P. McKenna, M. D. Sharp, D. G. Lucarelli, J. A. Nanzer, M. L. Dennis, and T. R. Clark, “Wideband photonic compressive sampling analog-to-digital converter for RF spectrum estimation,” in Proceedings of Optical Fiber Communication Conference, OFC/NFOEC (Anaheim, Calif., 2013), paper OTh3D.1.
    [Crossref]
  6. 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]
  7. B. C. Pile and G. W. Taylor, “Performance of subsampled analog optical links,” J. Lightwave Technol. 39, 1299–1305 (2012).
    [Crossref]
  8. J. D. McKinney and K. J. Williams, “Sampled analog optical links,” IEEE Trans. Microwave Theory Tech. 57, 2093–2099 (2009).
    [Crossref]
  9. J. D. McKinney, V. J. Urick, and J. Briguglio, “Optical comb sources for high dynamic-range single-span long-haul analog optical links,” IEEE Trans. Microwave Theory Tech. 59, 3249–3257 (2011).
    [Crossref]
  10. R. Maleh, G. L. Fudge, F. A. Boyle, and P. E. Pace, “Analog-to-information and the Nyquist folding receiver,” IEEE J. Emerging Sel. Top. Circuits Syst. 2, 564–578 (2012).
    [Crossref]
  11. J. D. McKinney and V. J. Urick, “Radio-frequency down-conversion via sampled analog optical links,” Photon. Tech. Branch, Naval Research Laboratory, NRL/MR/5650–10-9275 (2010).
  12. E. Sorokin, G. Tempea, and T. Brabec, “Measurement of the root-mean-square width and the root-mean-square chirp in ultrafast optics,” J. Opt. Soc. Am. B 17, 146–150 (2000).
    [Crossref]
  13. R. Wu, V. R. Supradeepa, C. M. Long, D. E. Leaird, and A. M. Weiner, “Generation of very flat optical frequency combs from continuous-wave lasers using cascaded intensity and phase modulators driven by tailored radio frequency waveforms,” Opt. Lett. 35, 3234–3236 (2010).
    [Crossref] [PubMed]
  14. D. Von der Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B 39, 201–217 (1986).
    [Crossref]
  15. H. Murata, A. Morimoto, T. Kobayashi, and S. Yamamoto, “Optical pulse generation by electrooptic-modulation method and its application to integrated ultrashort pulse generators,” IEEE J. Sel. Top. Quantum Electron. 6, 1325–1331 (2000).
    [Crossref]

2014 (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, 341–345 (2014).
[Crossref] [PubMed]

2012 (3)

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. C. Pile and G. W. Taylor, “Performance of subsampled analog optical links,” J. Lightwave Technol. 39, 1299–1305 (2012).
[Crossref]

R. Maleh, G. L. Fudge, F. A. Boyle, and P. E. Pace, “Analog-to-information and the Nyquist folding receiver,” IEEE J. Emerging Sel. Top. Circuits Syst. 2, 564–578 (2012).
[Crossref]

2011 (1)

J. D. McKinney, V. J. Urick, and J. Briguglio, “Optical comb sources for high dynamic-range single-span long-haul analog optical links,” IEEE Trans. Microwave Theory Tech. 59, 3249–3257 (2011).
[Crossref]

2010 (1)

2009 (1)

J. D. McKinney and K. J. Williams, “Sampled analog optical links,” IEEE Trans. Microwave Theory Tech. 57, 2093–2099 (2009).
[Crossref]

2008 (1)

2007 (1)

2003 (1)

2000 (2)

H. Murata, A. Morimoto, T. Kobayashi, and S. Yamamoto, “Optical pulse generation by electrooptic-modulation method and its application to integrated ultrashort pulse generators,” IEEE J. Sel. Top. Quantum Electron. 6, 1325–1331 (2000).
[Crossref]

E. Sorokin, G. Tempea, and T. Brabec, “Measurement of the root-mean-square width and the root-mean-square chirp in ultrafast optics,” J. Opt. Soc. Am. B 17, 146–150 (2000).
[Crossref]

1986 (1)

D. Von der Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B 39, 201–217 (1986).
[Crossref]

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, 341–345 (2014).
[Crossref] [PubMed]

Bogoni, A.

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

Boyle, F. A.

R. Maleh, G. L. Fudge, F. A. Boyle, and P. E. Pace, “Analog-to-information and the Nyquist folding receiver,” IEEE J. Emerging Sel. Top. Circuits Syst. 2, 564–578 (2012).
[Crossref]

Brabec, T.

Briguglio, J.

J. D. McKinney, V. J. Urick, and J. Briguglio, “Optical comb sources for high dynamic-range single-span long-haul analog optical links,” IEEE Trans. Microwave Theory Tech. 59, 3249–3257 (2011).
[Crossref]

Capria, A.

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

Clark, T. R.

T. P. McKenna, M. D. Sharp, D. G. Lucarelli, J. A. Nanzer, M. L. Dennis, and T. R. Clark, “Wideband photonic compressive sampling analog-to-digital converter for RF spectrum estimation,” in Proceedings of Optical Fiber Communication Conference, OFC/NFOEC (Anaheim, Calif., 2013), paper OTh3D.1.
[Crossref]

Dennis, M. L.

T. P. McKenna, M. D. Sharp, D. G. Lucarelli, J. A. Nanzer, M. L. Dennis, and T. R. Clark, “Wideband photonic compressive sampling analog-to-digital converter for RF spectrum estimation,” in Proceedings of Optical Fiber Communication Conference, OFC/NFOEC (Anaheim, Calif., 2013), paper OTh3D.1.
[Crossref]

Fudge, G. L.

R. Maleh, G. L. Fudge, F. A. Boyle, and P. E. Pace, “Analog-to-information and the Nyquist folding receiver,” IEEE J. Emerging Sel. Top. Circuits Syst. 2, 564–578 (2012).
[Crossref]

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, 341–345 (2014).
[Crossref] [PubMed]

Hargreaves, J. J.

Juodawlkis, P. W.

Kärtner, F. X.

Kim, J.

Kobayashi, T.

H. Murata, A. Morimoto, T. Kobayashi, and S. Yamamoto, “Optical pulse generation by electrooptic-modulation method and its application to integrated ultrashort pulse generators,” IEEE J. Sel. Top. Quantum Electron. 6, 1325–1331 (2000).
[Crossref]

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, 341–345 (2014).
[Crossref] [PubMed]

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, 341–345 (2014).
[Crossref] [PubMed]

Leaird, D. E.

Long, C. M.

Lucarelli, D. G.

T. P. McKenna, M. D. Sharp, D. G. Lucarelli, J. A. Nanzer, M. L. Dennis, and T. R. Clark, “Wideband photonic compressive sampling analog-to-digital converter for RF spectrum estimation,” in Proceedings of Optical Fiber Communication Conference, OFC/NFOEC (Anaheim, Calif., 2013), paper OTh3D.1.
[Crossref]

Malacarne, A.

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

Maleh, R.

R. Maleh, G. L. Fudge, F. A. Boyle, and P. E. Pace, “Analog-to-information and the Nyquist folding receiver,” IEEE J. Emerging Sel. Top. Circuits Syst. 2, 564–578 (2012).
[Crossref]

McKenna, T. P.

T. P. McKenna, M. D. Sharp, D. G. Lucarelli, J. A. Nanzer, M. L. Dennis, and T. R. Clark, “Wideband photonic compressive sampling analog-to-digital converter for RF spectrum estimation,” in Proceedings of Optical Fiber Communication Conference, OFC/NFOEC (Anaheim, Calif., 2013), paper OTh3D.1.
[Crossref]

McKinney, J. D.

J. D. McKinney, V. J. Urick, and J. Briguglio, “Optical comb sources for high dynamic-range single-span long-haul analog optical links,” IEEE Trans. Microwave Theory Tech. 59, 3249–3257 (2011).
[Crossref]

J. D. McKinney and K. J. Williams, “Sampled analog optical links,” IEEE Trans. Microwave Theory Tech. 57, 2093–2099 (2009).
[Crossref]

J. D. McKinney and V. J. Urick, “Radio-frequency down-conversion via sampled analog optical links,” Photon. Tech. Branch, Naval Research Laboratory, NRL/MR/5650–10-9275 (2010).

Morimoto, A.

H. Murata, A. Morimoto, T. Kobayashi, and S. Yamamoto, “Optical pulse generation by electrooptic-modulation method and its application to integrated ultrashort pulse generators,” IEEE J. Sel. Top. Quantum Electron. 6, 1325–1331 (2000).
[Crossref]

Murata, H.

H. Murata, A. Morimoto, T. Kobayashi, and S. Yamamoto, “Optical pulse generation by electrooptic-modulation method and its application to integrated ultrashort pulse generators,” IEEE J. Sel. Top. Quantum Electron. 6, 1325–1331 (2000).
[Crossref]

Nanzer, J. A.

T. P. McKenna, M. D. Sharp, D. G. Lucarelli, J. A. Nanzer, M. L. Dennis, and T. R. Clark, “Wideband photonic compressive sampling analog-to-digital converter for RF spectrum estimation,” in Proceedings of Optical Fiber Communication Conference, OFC/NFOEC (Anaheim, Calif., 2013), paper OTh3D.1.
[Crossref]

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]

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, 341–345 (2014).
[Crossref] [PubMed]

Pace, P. E.

R. Maleh, G. L. Fudge, F. A. Boyle, and P. E. Pace, “Analog-to-information and the Nyquist folding receiver,” IEEE J. Emerging Sel. Top. Circuits Syst. 2, 564–578 (2012).
[Crossref]

Park, M. J.

Perrott, M. H.

Pile, B. C.

B. C. Pile and G. W. Taylor, “Performance of subsampled analog optical links,” J. Lightwave Technol. 39, 1299–1305 (2012).
[Crossref]

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, 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, 341–345 (2014).
[Crossref] [PubMed]

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]

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, 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, 341–345 (2014).
[Crossref] [PubMed]

Sefler, G. A.

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]

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, 341–345 (2014).
[Crossref] [PubMed]

Sharp, M. D.

T. P. McKenna, M. D. Sharp, D. G. Lucarelli, J. A. Nanzer, M. L. Dennis, and T. R. Clark, “Wideband photonic compressive sampling analog-to-digital converter for RF spectrum estimation,” in Proceedings of Optical Fiber Communication Conference, OFC/NFOEC (Anaheim, Calif., 2013), paper OTh3D.1.
[Crossref]

Sorokin, E.

Supradeepa, V. R.

Taylor, G. W.

B. C. Pile and G. W. Taylor, “Performance of subsampled analog optical links,” J. Lightwave Technol. 39, 1299–1305 (2012).
[Crossref]

Tempea, G.

Titi, G. W.

Twichell, J. C.

Urick, V. J.

J. D. McKinney, V. J. Urick, and J. Briguglio, “Optical comb sources for high dynamic-range single-span long-haul analog optical links,” IEEE Trans. Microwave Theory Tech. 59, 3249–3257 (2011).
[Crossref]

J. D. McKinney and V. J. Urick, “Radio-frequency down-conversion via sampled analog optical links,” Photon. Tech. Branch, Naval Research Laboratory, NRL/MR/5650–10-9275 (2010).

Valley, G. C.

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]

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

Vercesi, V.

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

Von der Linde, D.

D. Von der Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B 39, 201–217 (1986).
[Crossref]

Weiner, A. M.

Williams, K. J.

J. D. McKinney and K. J. Williams, “Sampled analog optical links,” IEEE Trans. Microwave Theory Tech. 57, 2093–2099 (2009).
[Crossref]

Wu, R.

Yamamoto, S.

H. Murata, A. Morimoto, T. Kobayashi, and S. Yamamoto, “Optical pulse generation by electrooptic-modulation method and its application to integrated ultrashort pulse generators,” IEEE J. Sel. Top. Quantum Electron. 6, 1325–1331 (2000).
[Crossref]

Younger, R. D.

Appl. Phys. B (1)

D. Von der Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B 39, 201–217 (1986).
[Crossref]

IEEE J. Emerging Sel. Top. Circuits Syst. (1)

R. Maleh, G. L. Fudge, F. A. Boyle, and P. E. Pace, “Analog-to-information and the Nyquist folding receiver,” IEEE J. Emerging Sel. Top. Circuits Syst. 2, 564–578 (2012).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

H. Murata, A. Morimoto, T. Kobayashi, and S. Yamamoto, “Optical pulse generation by electrooptic-modulation method and its application to integrated ultrashort pulse generators,” IEEE J. Sel. Top. Quantum Electron. 6, 1325–1331 (2000).
[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 Trans. Microwave Theory Tech. (2)

J. D. McKinney and K. J. Williams, “Sampled analog optical links,” IEEE Trans. Microwave Theory Tech. 57, 2093–2099 (2009).
[Crossref]

J. D. McKinney, V. J. Urick, and J. Briguglio, “Optical comb sources for high dynamic-range single-span long-haul analog optical links,” IEEE Trans. Microwave Theory Tech. 59, 3249–3257 (2011).
[Crossref]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (1)

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, 341–345 (2014).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (1)

Other (2)

J. D. McKinney and V. J. Urick, “Radio-frequency down-conversion via sampled analog optical links,” Photon. Tech. Branch, Naval Research Laboratory, NRL/MR/5650–10-9275 (2010).

T. P. McKenna, M. D. Sharp, D. G. Lucarelli, J. A. Nanzer, M. L. Dennis, and T. R. Clark, “Wideband photonic compressive sampling analog-to-digital converter for RF spectrum estimation,” in Proceedings of Optical Fiber Communication Conference, OFC/NFOEC (Anaheim, Calif., 2013), paper OTh3D.1.
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 Setup for short pulse (optical comb) generation and the subsampled analog link.
Fig. 2
Fig. 2 (a) Optical comb spectra from output of cascaded modulators, showing comb lines within ∼1dB variation falling within Δfrms ≈ 225 GHz. (b) Measured intensity autocorrelation of the compressed optical pulse, indicatinga6ps pulse (intensity) duration.
Fig. 3
Fig. 3 RF gain as a function of input frequency for the subsampled analog link. The measured gain data are shown by the circles and the gain calculated from Eq. (13) is shown by the gray line.
Fig. 4
Fig. 4 Depiction of the change in SPR as a function of frequency, 300 MHz (n = 0), 4.7 GHz (n = 1), and 34.7 GHz (n = 7). The growth is n2 as predicted, where the ratio grows from line 1 to 7 by 49-times (16.9 dB).
Fig. 5
Fig. 5 SPR growth as a function of frequency and alias band normalized to the SPR at frep = 5 GHz. A plot of n2 is overlayed showing agreement with a quadratic growth profile. The metered bar below the plot label the alias (n) bands.
Fig. 6
Fig. 6 The alias band as determined over a set of 1000 random input frequencies. The correspondance between input frequency and frequency disambiguation is excellent to 40 GHz.

Equations (13)

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i ( t ) = p ( t ) [ 1 + v in ( t ) * h mzm ( t ) ] * h pd ( t ) * h lpf ( t )
P rf ( ω ) = 1 2 I avg 2 | P sp ( ω ) | 2 | H pd ( ω ) | 2 | H lp ( ω ) | 2 R o + 1 2 π 2 I avg 2 | P sp ( ω ) * V in ( ω ) V π ( ω ) | 2 | H pd ( ω ) | 2 | H lp ( ω ) | 2 R o .
p ( t ) = p ˜ ( t ) * n = δ ( t n T ) ,
P sp ( ω ) = P ˜ ( ω ) P o × n = δ ( ω n ω rep ) .
p ( t ) = p ˜ ( t ) * n = δ ( t n T + Δ T ) ,
p ( t ) = p ˜ ( t ) * n = δ ( t n T ) + δ ( t n T ) Δ T = n = p ˜ ( t n T ) + d d t p ˜ ( t n T ) Δ T .
Δ T = T J ( t )
P sp ( ω ) = P ˜ ( ω ) P o n = δ ( ω n ω rep ) + P ˜ ( ω ) P o n = j n ω rep T δ ( ω n ω rep ) * S J ( ω ) .
SPR comb = [ n ω rep T | S j ( ω ) | ] 2 .
SPR sig = SPR comb = [ n ω rep T | S j ( ω ) | ] 2 .
J ( t ) = κ V j ω j sin ( ω j t ) ,
SPR sig = SPR comb = SPR = ( n 2 κ V j f j ) 2 .
G n ( ω in ) = [ π I avg V π ( ω in ) ] 2 | P sp ( n ω rep ) | 2 | H pd ( n ω rep ω in ) | 2 | H lp ( n ω rep ω in ) | 2 R i R o

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