Abstract

Parametric spectro-temporal analyzer (PASTA) is an entirely new wavelength resolving modality that focuses the spectral information on the temporal axis, enables ultrafast frame rate, and provides comparable resolution and sensitivity to the state-of-art optical spectrum analyzer (OSA). Generally, spectroscopy relies on the allocation of the spectrum onto the spatial or temporal domain, and the Czerny-Turner monochromator based conventional OSA realizes the spatial allocation by a dispersive grating, while the mechanical rotation limits its operation speed. On the other hand, the PASTA system performs the spectroscopy function by a time-lens focusing mechanism, which all-optically maps the spectral information on the temporal axis, and realizes the single-shot spectrum acquisition. Therefore, the PASTA system provides orders of magnitude improvement on the frame rate, as high as megahertz or even gigahertz in principle. In addition to the implementation of the PASTA system, in this paper, we will primarily discuss its performance, including the tradeoff between the frame rate and the wavelength range, factors that affect the wavelength resolution, the conversion efficiency, the power saturation and the polarization sensitivity. Detection bandwidth and high-order dispersion introduced limitations are also under investigation. All these analyses not only provide an overall guideline for the PASTA design, but also help future research in improving and optimizing this new spectrum resolving technology.

© 2013 Optical Society of America

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2013 (1)

C. Zhang, J. Xu, P. C. Chui, and K. K. Y. Wong, “Parametric Spectro-Temporal Analyzer (PASTA) for real-time optical spectrum observation,” Sci. Rep.3, 2064 (2013).
[PubMed]

2011 (1)

C. Zhang, K. K. Y. Cheung, P. C. Chui, K. K. Tsia, and K. K. Y. Wong, “Fiber optical parametric amplifier with high-speed swept pump,” IEEE Photonics Technol. Lett.23(14), 1022–1024 (2011).
[CrossRef]

2010 (1)

2009 (1)

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, “Theory of amplified dispersive Fourier transformation,” Phys. Rev. A80(4), 043821 (2009).
[CrossRef]

2008 (3)

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature456(7218), 81–84 (2008).
[CrossRef] [PubMed]

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics2(1), 48–51 (2008).
[CrossRef]

J. Chou, D. R. Solli, and B. Jalali, “Real-time spectroscopy with subgigahertz resolution using amplified dispersive Fourier transformation,” Appl. Phys. Lett.92(11), 111102 (2008).
[CrossRef]

2007 (1)

J. Chou, O. Boyraz, D. Solli, and B. Jalali, “Femtosecond real-time single-shot digitizer,” Appl. Phys. Lett.91(16), 161105 (2007).
[CrossRef]

2004 (2)

I. V. Rubtsov, R. M. Russo, T. Albers, P. Deria, D. E. Luzzi, and M. J. Therien, “Visible and near-infrared excited-state dynamics of single-walled carbon nanotubes,” Appl. Phys. A Mater. Sci. Process.79(7), 1747–1751 (2004).
[CrossRef]

M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky, “Wide-Band tuning of the gain spectra of one-pump fiber optical parametric amplifiers,” IEEE J. Sel. Top. Quantum Electron.10(5), 1133–1141 (2004).
[CrossRef]

2002 (1)

K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky, “Polarization-independent one-pump fiber optical parametric amplifier,” IEEE Photonics Technol. Lett.14(11), 1506–1508 (2002).
[CrossRef]

2001 (1)

C. V. Bennett and B. H. Kolner, “Aberrations in temporal imaging,” IEEE J. Quantum Electron.37(1), 20–32 (2001).
[CrossRef]

2000 (3)

C. V. Bennett and B. H. Kolner, “Principles of parametric temporal imaging—Part I: System configurations,” IEEE J. Quantum Electron.36(4), 430–437 (2000).
[CrossRef]

C. V. Bennett and B. H. Kolner, “Principles of parametric temporal imaging—Part II: System performance,” IEEE J. Quantum Electron.36(6), 649–655 (2000).
[CrossRef]

H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron.6(6), 1173–1185 (2000).
[CrossRef]

1994 (2)

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

M. T. Kauffman, W. C. Banyai, A. A. Godil, and D. M. Bloom, “Time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett.64(3), 270–272 (1994).
[CrossRef]

1993 (1)

N. Yoshizawa and T. Imai, “Stimulated Brillouin scattering suppression by means of applying strain distribution to fiber with cabling,” J. Lightwave Technol.11(10), 1518–1522 (1993).
[CrossRef]

1964 (1)

1930 (1)

M. Czerny and A. F. Turner, “Uber den Astigmatismus bei Spiegelspektrometern,” Z. Phys.61(11–12), 792–797 (1930).
[CrossRef]

Albers, T.

I. V. Rubtsov, R. M. Russo, T. Albers, P. Deria, D. E. Luzzi, and M. J. Therien, “Visible and near-infrared excited-state dynamics of single-walled carbon nanotubes,” Appl. Phys. A Mater. Sci. Process.79(7), 1747–1751 (2004).
[CrossRef]

Banyai, W. C.

M. T. Kauffman, W. C. Banyai, A. A. Godil, and D. M. Bloom, “Time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett.64(3), 270–272 (1994).
[CrossRef]

Bennett, C. V.

C. V. Bennett and B. H. Kolner, “Aberrations in temporal imaging,” IEEE J. Quantum Electron.37(1), 20–32 (2001).
[CrossRef]

C. V. Bennett and B. H. Kolner, “Principles of parametric temporal imaging—Part II: System performance,” IEEE J. Quantum Electron.36(6), 649–655 (2000).
[CrossRef]

C. V. Bennett and B. H. Kolner, “Principles of parametric temporal imaging—Part I: System configurations,” IEEE J. Quantum Electron.36(4), 430–437 (2000).
[CrossRef]

Biedermann, B. R.

Bloom, D. M.

M. T. Kauffman, W. C. Banyai, A. A. Godil, and D. M. Bloom, “Time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett.64(3), 270–272 (1994).
[CrossRef]

Boyraz, O.

J. Chou, O. Boyraz, D. Solli, and B. Jalali, “Femtosecond real-time single-shot digitizer,” Appl. Phys. Lett.91(16), 161105 (2007).
[CrossRef]

Cheung, K. K. Y.

C. Zhang, K. K. Y. Cheung, P. C. Chui, K. K. Tsia, and K. K. Y. Wong, “Fiber optical parametric amplifier with high-speed swept pump,” IEEE Photonics Technol. Lett.23(14), 1022–1024 (2011).
[CrossRef]

Chou, J.

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics2(1), 48–51 (2008).
[CrossRef]

J. Chou, D. R. Solli, and B. Jalali, “Real-time spectroscopy with subgigahertz resolution using amplified dispersive Fourier transformation,” Appl. Phys. Lett.92(11), 111102 (2008).
[CrossRef]

J. Chou, O. Boyraz, D. Solli, and B. Jalali, “Femtosecond real-time single-shot digitizer,” Appl. Phys. Lett.91(16), 161105 (2007).
[CrossRef]

Chui, P. C.

C. Zhang, J. Xu, P. C. Chui, and K. K. Y. Wong, “Parametric Spectro-Temporal Analyzer (PASTA) for real-time optical spectrum observation,” Sci. Rep.3, 2064 (2013).
[PubMed]

C. Zhang, K. K. Y. Cheung, P. C. Chui, K. K. Tsia, and K. K. Y. Wong, “Fiber optical parametric amplifier with high-speed swept pump,” IEEE Photonics Technol. Lett.23(14), 1022–1024 (2011).
[CrossRef]

Czerny, M.

M. Czerny and A. F. Turner, “Uber den Astigmatismus bei Spiegelspektrometern,” Z. Phys.61(11–12), 792–797 (1930).
[CrossRef]

Deria, P.

I. V. Rubtsov, R. M. Russo, T. Albers, P. Deria, D. E. Luzzi, and M. J. Therien, “Visible and near-infrared excited-state dynamics of single-walled carbon nanotubes,” Appl. Phys. A Mater. Sci. Process.79(7), 1747–1751 (2004).
[CrossRef]

Droppleman, L. A.

Eigenwillig, C. M.

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,” Nature456(7218), 81–84 (2008).
[CrossRef] [PubMed]

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,” Nature456(7218), 81–84 (2008).
[CrossRef] [PubMed]

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,” Nature456(7218), 81–84 (2008).
[CrossRef] [PubMed]

Goda, K.

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, “Theory of amplified dispersive Fourier transformation,” Phys. Rev. A80(4), 043821 (2009).
[CrossRef]

Godil, A. A.

M. T. Kauffman, W. C. Banyai, A. A. Godil, and D. M. Bloom, “Time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett.64(3), 270–272 (1994).
[CrossRef]

Haus, H. A.

H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron.6(6), 1173–1185 (2000).
[CrossRef]

Huber, R.

Imai, T.

N. Yoshizawa and T. Imai, “Stimulated Brillouin scattering suppression by means of applying strain distribution to fiber with cabling,” J. Lightwave Technol.11(10), 1518–1522 (1993).
[CrossRef]

Jalali, B.

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, “Theory of amplified dispersive Fourier transformation,” Phys. Rev. A80(4), 043821 (2009).
[CrossRef]

J. Chou, D. R. Solli, and B. Jalali, “Real-time spectroscopy with subgigahertz resolution using amplified dispersive Fourier transformation,” Appl. Phys. Lett.92(11), 111102 (2008).
[CrossRef]

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics2(1), 48–51 (2008).
[CrossRef]

J. Chou, O. Boyraz, D. Solli, and B. Jalali, “Femtosecond real-time single-shot digitizer,” Appl. Phys. Lett.91(16), 161105 (2007).
[CrossRef]

Kauffman, M. T.

M. T. Kauffman, W. C. Banyai, A. A. Godil, and D. M. Bloom, “Time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett.64(3), 270–272 (1994).
[CrossRef]

Kazovsky, L. G.

M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky, “Wide-Band tuning of the gain spectra of one-pump fiber optical parametric amplifiers,” IEEE J. Sel. Top. Quantum Electron.10(5), 1133–1141 (2004).
[CrossRef]

K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky, “Polarization-independent one-pump fiber optical parametric amplifier,” IEEE Photonics Technol. Lett.14(11), 1506–1508 (2002).
[CrossRef]

Klein, T.

Kolner, B. H.

C. V. Bennett and B. H. Kolner, “Aberrations in temporal imaging,” IEEE J. Quantum Electron.37(1), 20–32 (2001).
[CrossRef]

C. V. Bennett and B. H. Kolner, “Principles of parametric temporal imaging—Part II: System performance,” IEEE J. Quantum Electron.36(6), 649–655 (2000).
[CrossRef]

C. V. Bennett and B. H. Kolner, “Principles of parametric temporal imaging—Part I: System configurations,” IEEE J. Quantum Electron.36(4), 430–437 (2000).
[CrossRef]

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

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,” Nature456(7218), 81–84 (2008).
[CrossRef] [PubMed]

Luzzi, D. E.

I. V. Rubtsov, R. M. Russo, T. Albers, P. Deria, D. E. Luzzi, and M. J. Therien, “Visible and near-infrared excited-state dynamics of single-walled carbon nanotubes,” Appl. Phys. A Mater. Sci. Process.79(7), 1747–1751 (2004).
[CrossRef]

Marhic, M. E.

M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky, “Wide-Band tuning of the gain spectra of one-pump fiber optical parametric amplifiers,” IEEE J. Sel. Top. Quantum Electron.10(5), 1133–1141 (2004).
[CrossRef]

K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky, “Polarization-independent one-pump fiber optical parametric amplifier,” IEEE Photonics Technol. Lett.14(11), 1506–1508 (2002).
[CrossRef]

Megill, L. R.

Rubtsov, I. V.

I. V. Rubtsov, R. M. Russo, T. Albers, P. Deria, D. E. Luzzi, and M. J. Therien, “Visible and near-infrared excited-state dynamics of single-walled carbon nanotubes,” Appl. Phys. A Mater. Sci. Process.79(7), 1747–1751 (2004).
[CrossRef]

Russo, R. M.

I. V. Rubtsov, R. M. Russo, T. Albers, P. Deria, D. E. Luzzi, and M. J. Therien, “Visible and near-infrared excited-state dynamics of single-walled carbon nanotubes,” Appl. Phys. A Mater. Sci. Process.79(7), 1747–1751 (2004).
[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,” Nature456(7218), 81–84 (2008).
[CrossRef] [PubMed]

Shafer, A. B.

Solli, D.

J. Chou, O. Boyraz, D. Solli, and B. Jalali, “Femtosecond real-time single-shot digitizer,” Appl. Phys. Lett.91(16), 161105 (2007).
[CrossRef]

Solli, D. R.

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, “Theory of amplified dispersive Fourier transformation,” Phys. Rev. A80(4), 043821 (2009).
[CrossRef]

J. Chou, D. R. Solli, and B. Jalali, “Real-time spectroscopy with subgigahertz resolution using amplified dispersive Fourier transformation,” Appl. Phys. Lett.92(11), 111102 (2008).
[CrossRef]

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics2(1), 48–51 (2008).
[CrossRef]

Therien, M. J.

I. V. Rubtsov, R. M. Russo, T. Albers, P. Deria, D. E. Luzzi, and M. J. Therien, “Visible and near-infrared excited-state dynamics of single-walled carbon nanotubes,” Appl. Phys. A Mater. Sci. Process.79(7), 1747–1751 (2004).
[CrossRef]

Tsia, K. K.

C. Zhang, K. K. Y. Cheung, P. C. Chui, K. K. Tsia, and K. K. Y. Wong, “Fiber optical parametric amplifier with high-speed swept pump,” IEEE Photonics Technol. Lett.23(14), 1022–1024 (2011).
[CrossRef]

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, “Theory of amplified dispersive Fourier transformation,” Phys. Rev. A80(4), 043821 (2009).
[CrossRef]

Turner, A. F.

M. Czerny and A. F. Turner, “Uber den Astigmatismus bei Spiegelspektrometern,” Z. Phys.61(11–12), 792–797 (1930).
[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,” Nature456(7218), 81–84 (2008).
[CrossRef] [PubMed]

Uesaka, K.

K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky, “Polarization-independent one-pump fiber optical parametric amplifier,” IEEE Photonics Technol. Lett.14(11), 1506–1508 (2002).
[CrossRef]

Wieser, W.

Wong, K. K. Y.

C. Zhang, J. Xu, P. C. Chui, and K. K. Y. Wong, “Parametric Spectro-Temporal Analyzer (PASTA) for real-time optical spectrum observation,” Sci. Rep.3, 2064 (2013).
[PubMed]

C. Zhang, K. K. Y. Cheung, P. C. Chui, K. K. Tsia, and K. K. Y. Wong, “Fiber optical parametric amplifier with high-speed swept pump,” IEEE Photonics Technol. Lett.23(14), 1022–1024 (2011).
[CrossRef]

M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky, “Wide-Band tuning of the gain spectra of one-pump fiber optical parametric amplifiers,” IEEE J. Sel. Top. Quantum Electron.10(5), 1133–1141 (2004).
[CrossRef]

K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky, “Polarization-independent one-pump fiber optical parametric amplifier,” IEEE Photonics Technol. Lett.14(11), 1506–1508 (2002).
[CrossRef]

Xu, J.

C. Zhang, J. Xu, P. C. Chui, and K. K. Y. Wong, “Parametric Spectro-Temporal Analyzer (PASTA) for real-time optical spectrum observation,” Sci. Rep.3, 2064 (2013).
[PubMed]

Yoshizawa, N.

N. Yoshizawa and T. Imai, “Stimulated Brillouin scattering suppression by means of applying strain distribution to fiber with cabling,” J. Lightwave Technol.11(10), 1518–1522 (1993).
[CrossRef]

Zhang, C.

C. Zhang, J. Xu, P. C. Chui, and K. K. Y. Wong, “Parametric Spectro-Temporal Analyzer (PASTA) for real-time optical spectrum observation,” Sci. Rep.3, 2064 (2013).
[PubMed]

C. Zhang, K. K. Y. Cheung, P. C. Chui, K. K. Tsia, and K. K. Y. Wong, “Fiber optical parametric amplifier with high-speed swept pump,” IEEE Photonics Technol. Lett.23(14), 1022–1024 (2011).
[CrossRef]

Appl. Phys. A Mater. Sci. Process. (1)

I. V. Rubtsov, R. M. Russo, T. Albers, P. Deria, D. E. Luzzi, and M. J. Therien, “Visible and near-infrared excited-state dynamics of single-walled carbon nanotubes,” Appl. Phys. A Mater. Sci. Process.79(7), 1747–1751 (2004).
[CrossRef]

Appl. Phys. Lett. (3)

J. Chou, O. Boyraz, D. Solli, and B. Jalali, “Femtosecond real-time single-shot digitizer,” Appl. Phys. Lett.91(16), 161105 (2007).
[CrossRef]

J. Chou, D. R. Solli, and B. Jalali, “Real-time spectroscopy with subgigahertz resolution using amplified dispersive Fourier transformation,” Appl. Phys. Lett.92(11), 111102 (2008).
[CrossRef]

M. T. Kauffman, W. C. Banyai, A. A. Godil, and D. M. Bloom, “Time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett.64(3), 270–272 (1994).
[CrossRef]

IEEE J. Quantum Electron. (4)

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

C. V. Bennett and B. H. Kolner, “Aberrations in temporal imaging,” IEEE J. Quantum Electron.37(1), 20–32 (2001).
[CrossRef]

C. V. Bennett and B. H. Kolner, “Principles of parametric temporal imaging—Part I: System configurations,” IEEE J. Quantum Electron.36(4), 430–437 (2000).
[CrossRef]

C. V. Bennett and B. H. Kolner, “Principles of parametric temporal imaging—Part II: System performance,” IEEE J. Quantum Electron.36(6), 649–655 (2000).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky, “Wide-Band tuning of the gain spectra of one-pump fiber optical parametric amplifiers,” IEEE J. Sel. Top. Quantum Electron.10(5), 1133–1141 (2004).
[CrossRef]

H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron.6(6), 1173–1185 (2000).
[CrossRef]

IEEE Photonics Technol. Lett. (2)

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C. Zhang, J. Xu, P. C. Chui, and K. K. Y. Wong, “Parametric Spectro-Temporal Analyzer (PASTA) for real-time optical spectrum observation,” Sci. Rep.3, 2064 (2013).
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Figures (8)

Fig. 1
Fig. 1

Principle of the time-lens focusing mechanism, compared with the ADFT mechanism. (a) Schematic diagram shows the relative temporal position between two wavelengths across the PASTA system; (b) calculated temporal ray diagram of the time-lens focusing, illustrates the temporal transformation of two wavelengths along the system, and how they are separated and focused on the focal plane; (c) and (d) corresponding schematic and temporal ray diagrams of the ADFT mechanism.

Fig. 2
Fig. 2

Detailed experimental setup of PASTA system, pump stretching and output dispersion share the same spool of DCF. EDFA: erbium-doped fiber amplifier; FBG: fiber Bragg grating; AM: amplitude modulator; PC: polarization controller; C/L: C-band and L-band WDM coupler.

Fig. 3
Fig. 3

Relation between the pump dispersion and the output dispersion at different wavelength. To ensure the pump stretching GDD is twice of the output GDD, the pump pulse should pass the same 16.3-km DCF twice. However, since the pump wavelength (1555 nm) had larger dispersion than the signal wavelength (1543.5 nm), another 13.6-km SMF was employed to compensate it.

Fig. 4
Fig. 4

The stationary performance of the PASTA system, with 100-MHz frame rate and four equally-spaced CW sources under test: (a) the stretched pump traces with the interference fringes; (b) the idler traces generated after the first-stage FWM; (c) four CW sources with different wavelength were captured by PASTA system.

Fig. 5
Fig. 5

Resolution performance of the PASTA system, with two close CW sources separated by 30 pm. The electrical trace was captured with 16-GHz electrical bandwidth (black dashed line), and compared with the simulated optical output pulse train (red solid line).

Fig. 6
Fig. 6

Two sets of time-lens focusing configurations in temporal ray diagram, with (a) or without (b) the input dispersion. The input GDD value affects the temporal aperture of the PASTA system.

Fig. 7
Fig. 7

Implementation of the time-lens by parametric mixing with linear chirped pump. (a) Mechanism of the two-stage FWM, a swept-source pumped FWM added with a CW source pumped FWM; (b) spectra of the two-stage FWM, as well as the wavelength conversion efficiency. The blue dash-dotted lines correspond to the gain spectra (right vertical axis).

Fig. 8
Fig. 8

Input conditions of the signal for the PASTA system. (a) The relation between the output intensity and the input power, in log-log scale. (b) Output intensity changed with the SOP of input signal, in linear scale.

Tables (1)

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Table 1 Analogous Quantities between the Space-lens and Time-lens System

Equations (14)

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E s ( t ) = I s × rect ( t T ) × exp ( i 2 π c λ 0 t )
E ¯ s ( ω )= I s 2π Tsinc[ T 2π ( ω 2πc λ 0 ) ]
E s '( t )= E s ( t ) t f ( t )
E o ( t )= F 1 { E ¯ s '( ω ) G o ( ω ) } = 1 2π + [ + E s ( t' ) t f ( t' ) exp( iωt' )dt' ] G o ( ω )exp( iωt )dω = + g o ( tt' ) E s ( t' ) t f ( t' )dt' = I s g o ( t ) + exp[ i( 1 Φ o 1 Φ f ) t ' 2 2 ] E s ( t' )exp( i t Φ o t' )dt'
E o ( t )= g o ( t ) E ¯ s ( t Φ o )
E o ( t )= 1 2πi Φ o exp( i t 2 2 Φ o ) I s 2π Tsinc[ T 2π Φ f ( t 2πc λ 0 Φ f ) ]
I( t )= | E o ( t ) | 2 = I s T 2 4 π 2 | Φ o | sinc 2 [ T 2π Φ f ( t 2πc λ 0 Φ f ) ]
t= 2πc Φ f λ 0 = ω 0 Φ f
Δt= 2πc Φ f λ 0 2 Δλ
Δ t o =0.4429×2× 2π Φ f T
Δ t e = t PW = 2ln2 π f BW ,
Δλ= λ 0 2 2πc Φ f Δt={ λ 0 2 2πc Φ f Δ t o = 0.4429×2 λ 0 2 cT (optical field limited) λ 0 2 2πc Φ f Δ t e = λ 0 2 ln2 π 2 c Φ f f BW (electrical field limited)
λ BW = λ 0 2 2πc Φ f T
N eff = λ BW Δλ = T Δ t e

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