Abstract

We explore theoretically the feasibility of using frequency conversion by sum- or difference-frequency generation, enabled by three-wave-mixing, for selectively multiplexing orthogonal input waveforms that overlap in time and frequency. Such a process would enable a drop device for use in a transparent optical network using temporally orthogonal waveforms to encode different channels. We model the process using coupled-mode equations appropriate for wave mixing in a uniform second-order nonlinear optical medium pumped by a strong laser pulse. We find Green functions describing the process, and employ Schmidt (singular-value) decompositions thereof to quantify its viability in functioning as a coherent waveform discriminator. We define a selectivity figure of merit in terms of the Schmidt coefficients, and use it to compare and contrast various parameter regimes via extensive numerical computations. We identify the most favorable regime (at least in the case of no pump chirp) and derive the complete analytical solution for the same. We bound the maximum achievable selectivity in this parameter space. We show that including a frequency chirp in the pump does not improve selectivity in this optimal regime. We also find an operating regime in which high-efficiency frequency conversion without temporal-shape selectivity can be achieved while preserving the shapes of a wide class of input pulses. The results are applicable to both classical and quantum frequency conversion.

© 2013 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. H. Lotz, W. Sauer-Greff, and R. Urbansky, “Spectral efficient coding schemes in optical communications,” Int. J. Optoelectronic Eng.2, 18–25 (2012).
  2. W. Shieh, X. Yi, Y. Ma, and Q. Yang, “Coherent optical OFDM: Has its time come? [Invited],” J. Opt. Netw.7, 234–255 (2008).
    [CrossRef]
  3. M. G. Raymer and K. Srinivasan, “Manipulating the color and shape of single photons,” Phys. Today65, 32–37 (2012).
    [CrossRef]
  4. A. P. Vandevender and P. G. Kwiat, “High efficiency single photon detection via frequency up-conversion,” J. Mod. Opt.51, 1433–1445 (2004).
  5. M. A. Albota and F. C. Wong, “Efficient single-photon counting at 1.55 μm by means of frequency upconversion,” Opt. Lett.29, 1449–1451 (2004).
    [CrossRef] [PubMed]
  6. R. V. Roussev, C. Langrock, J. R. Kurz, and M. M. Fejer, “Periodically poled lithium niobate waveguide sum-frequency generator for efficient single-photon detection at communication wavelengths,” Opt. Lett.29, 1518–1520 (2004).
    [CrossRef] [PubMed]
  7. Y. Ding and Z. Y. Ou, “Frequency downconversion for a quantum network,” Opt. Lett.35, 2491–2593 (2010).
    [CrossRef]
  8. B. Brecht, A. Eckstein, A. Christ, H. Suche, and C. Silberhorn, “From quantum pulse gate to quantum pulse shaper - engineered frequency conversion in nonlinear optical waveguides,” New J. Phys.13, 065029 (2011).
    [CrossRef]
  9. A. Eckstein, B. Brecht, and C. Silberhorn, “A quantum pulse gate based on spectrally engineered sum frequency generation,” Opt. Express19, 13770–13778 (2011).
    [CrossRef] [PubMed]
  10. M. G. Raymer, S. J. van Enk, C. J. McKinstrie, and H. J. McGuinness, “Interference of two photons of different color,” Opt. Commun.283, 747–752 (2010).
    [CrossRef]
  11. H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, “Quantum frequency translation of single-photon states in a photonic crystal fiber,” Phys. Rev. Lett.105, 093604 (2010).
    [CrossRef] [PubMed]
  12. L. Mejling, C. J. McKinstrie, M. G. Raymer, and K. Rottwitt, “Quantum frequency translation by four-wave mixing in a fiber: low-conversion regime,” Opt. Express20, 8367–8396 (2012).
    [CrossRef] [PubMed]
  13. G. Cerullo and S. De Silvestri, “Ultrafast optical parametric amplifiers,” Rev. Sci. Instrum.74, 1 (2003).
    [CrossRef]
  14. B. J. Smith and M. G. Raymer, “Photon wave functions, wave-packet quantization of light, and coherence theory,” New J. Phys.9, 414 (2007).
    [CrossRef]
  15. G. Strang, Introduction to Linear Algebra, 3rd ed. (Wellesley-Cambridge, 1998).
  16. G. J. Gbur, Mathematical Methods for Optical Physics and Engineering (Cambridge, 2011).
  17. S. L. Braunstein, “Squeezing as an irreducible resource,” Phys. Rev. A71, 055801 (2005).
    [CrossRef]
  18. M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics4, 786–791 (2010).
    [CrossRef]
  19. R. Ikuta, Y. Kusaka, T. Kitano, H. Kato, T. Yamamoto, M. Koashi, and N. Imoto, “Wide-band quantum interface for visible-to-telecommunication wavelength conversion,” Nature Commun.2, 1544 (2011).
    [CrossRef]
  20. A. M. Brańczyk, A. Fedrizzi, T. M. Stace, T. C. Ralph, and A. G. White, “Engineered optical nonlinearity for quantum light sources,” Opt. Express19, 55–65 (2011).
    [CrossRef]
  21. J. Huang and P. Kumar, “Observation of quantum frequency conversion,” Phys. Rev. Lett.68, 2153–2156 (1992).
    [CrossRef] [PubMed]
  22. C. J. McKinstrie, L. Mejling, M. G. Raymer, and K. Rottwitt, “Quantum-state-preserving optical frequency conversion and pulse reshaping by four-wave mixing,” Phys. Rev. A85, 053829 (2012).
    [CrossRef]
  23. D. C. Burnham and R. Y. Chiao, “Coherent resonance flourescence excited by short light pulses,” Phys. Rev.188, 667–675 (1969).
    [CrossRef]
  24. Y. Huang and P. Kumar, “Mode-resolved photon counting via cascaded quantum frequency conversion,” Opt. Lett.38, 4 (2013).
    [CrossRef]
  25. M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: Unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A24, 1980–1993 (1981).
    [CrossRef]
  26. R. E. Giacone, C. J. McKinstrie, and R. Betti, “Angular dependence of stimulated Brillouin scattering in homogeneous plasma,” Phys. Plasmas2, 4596–4605 (1995).
    [CrossRef]
  27. R. V. Churchill, Operational Mathematics, 3rd ed. (McGraw-Hill, 1971).
  28. M. G. Raymer, “Quantum state entanglement and readout of collective atomic-ensemble modes and optical wave packets by stimulated Raman scattering,” J. Mod. Opt.51, 1739–1759 (2004).

2013 (1)

2012 (4)

L. Mejling, C. J. McKinstrie, M. G. Raymer, and K. Rottwitt, “Quantum frequency translation by four-wave mixing in a fiber: low-conversion regime,” Opt. Express20, 8367–8396 (2012).
[CrossRef] [PubMed]

M. G. Raymer and K. Srinivasan, “Manipulating the color and shape of single photons,” Phys. Today65, 32–37 (2012).
[CrossRef]

T. H. Lotz, W. Sauer-Greff, and R. Urbansky, “Spectral efficient coding schemes in optical communications,” Int. J. Optoelectronic Eng.2, 18–25 (2012).

C. J. McKinstrie, L. Mejling, M. G. Raymer, and K. Rottwitt, “Quantum-state-preserving optical frequency conversion and pulse reshaping by four-wave mixing,” Phys. Rev. A85, 053829 (2012).
[CrossRef]

2011 (4)

R. Ikuta, Y. Kusaka, T. Kitano, H. Kato, T. Yamamoto, M. Koashi, and N. Imoto, “Wide-band quantum interface for visible-to-telecommunication wavelength conversion,” Nature Commun.2, 1544 (2011).
[CrossRef]

B. Brecht, A. Eckstein, A. Christ, H. Suche, and C. Silberhorn, “From quantum pulse gate to quantum pulse shaper - engineered frequency conversion in nonlinear optical waveguides,” New J. Phys.13, 065029 (2011).
[CrossRef]

A. M. Brańczyk, A. Fedrizzi, T. M. Stace, T. C. Ralph, and A. G. White, “Engineered optical nonlinearity for quantum light sources,” Opt. Express19, 55–65 (2011).
[CrossRef]

A. Eckstein, B. Brecht, and C. Silberhorn, “A quantum pulse gate based on spectrally engineered sum frequency generation,” Opt. Express19, 13770–13778 (2011).
[CrossRef] [PubMed]

2010 (4)

Y. Ding and Z. Y. Ou, “Frequency downconversion for a quantum network,” Opt. Lett.35, 2491–2593 (2010).
[CrossRef]

M. G. Raymer, S. J. van Enk, C. J. McKinstrie, and H. J. McGuinness, “Interference of two photons of different color,” Opt. Commun.283, 747–752 (2010).
[CrossRef]

H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, “Quantum frequency translation of single-photon states in a photonic crystal fiber,” Phys. Rev. Lett.105, 093604 (2010).
[CrossRef] [PubMed]

M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics4, 786–791 (2010).
[CrossRef]

2008 (1)

2007 (1)

B. J. Smith and M. G. Raymer, “Photon wave functions, wave-packet quantization of light, and coherence theory,” New J. Phys.9, 414 (2007).
[CrossRef]

2005 (1)

S. L. Braunstein, “Squeezing as an irreducible resource,” Phys. Rev. A71, 055801 (2005).
[CrossRef]

2004 (4)

A. P. Vandevender and P. G. Kwiat, “High efficiency single photon detection via frequency up-conversion,” J. Mod. Opt.51, 1433–1445 (2004).

M. G. Raymer, “Quantum state entanglement and readout of collective atomic-ensemble modes and optical wave packets by stimulated Raman scattering,” J. Mod. Opt.51, 1739–1759 (2004).

M. A. Albota and F. C. Wong, “Efficient single-photon counting at 1.55 μm by means of frequency upconversion,” Opt. Lett.29, 1449–1451 (2004).
[CrossRef] [PubMed]

R. V. Roussev, C. Langrock, J. R. Kurz, and M. M. Fejer, “Periodically poled lithium niobate waveguide sum-frequency generator for efficient single-photon detection at communication wavelengths,” Opt. Lett.29, 1518–1520 (2004).
[CrossRef] [PubMed]

2003 (1)

G. Cerullo and S. De Silvestri, “Ultrafast optical parametric amplifiers,” Rev. Sci. Instrum.74, 1 (2003).
[CrossRef]

1995 (1)

R. E. Giacone, C. J. McKinstrie, and R. Betti, “Angular dependence of stimulated Brillouin scattering in homogeneous plasma,” Phys. Plasmas2, 4596–4605 (1995).
[CrossRef]

1992 (1)

J. Huang and P. Kumar, “Observation of quantum frequency conversion,” Phys. Rev. Lett.68, 2153–2156 (1992).
[CrossRef] [PubMed]

1981 (1)

M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: Unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A24, 1980–1993 (1981).
[CrossRef]

1969 (1)

D. C. Burnham and R. Y. Chiao, “Coherent resonance flourescence excited by short light pulses,” Phys. Rev.188, 667–675 (1969).
[CrossRef]

Albota, M. A.

Betti, R.

R. E. Giacone, C. J. McKinstrie, and R. Betti, “Angular dependence of stimulated Brillouin scattering in homogeneous plasma,” Phys. Plasmas2, 4596–4605 (1995).
[CrossRef]

Branczyk, A. M.

Braunstein, S. L.

S. L. Braunstein, “Squeezing as an irreducible resource,” Phys. Rev. A71, 055801 (2005).
[CrossRef]

Brecht, B.

B. Brecht, A. Eckstein, A. Christ, H. Suche, and C. Silberhorn, “From quantum pulse gate to quantum pulse shaper - engineered frequency conversion in nonlinear optical waveguides,” New J. Phys.13, 065029 (2011).
[CrossRef]

A. Eckstein, B. Brecht, and C. Silberhorn, “A quantum pulse gate based on spectrally engineered sum frequency generation,” Opt. Express19, 13770–13778 (2011).
[CrossRef] [PubMed]

Burnham, D. C.

D. C. Burnham and R. Y. Chiao, “Coherent resonance flourescence excited by short light pulses,” Phys. Rev.188, 667–675 (1969).
[CrossRef]

Cerullo, G.

G. Cerullo and S. De Silvestri, “Ultrafast optical parametric amplifiers,” Rev. Sci. Instrum.74, 1 (2003).
[CrossRef]

Chiao, R. Y.

D. C. Burnham and R. Y. Chiao, “Coherent resonance flourescence excited by short light pulses,” Phys. Rev.188, 667–675 (1969).
[CrossRef]

Christ, A.

B. Brecht, A. Eckstein, A. Christ, H. Suche, and C. Silberhorn, “From quantum pulse gate to quantum pulse shaper - engineered frequency conversion in nonlinear optical waveguides,” New J. Phys.13, 065029 (2011).
[CrossRef]

Churchill, R. V.

R. V. Churchill, Operational Mathematics, 3rd ed. (McGraw-Hill, 1971).

De Silvestri, S.

G. Cerullo and S. De Silvestri, “Ultrafast optical parametric amplifiers,” Rev. Sci. Instrum.74, 1 (2003).
[CrossRef]

Ding, Y.

Y. Ding and Z. Y. Ou, “Frequency downconversion for a quantum network,” Opt. Lett.35, 2491–2593 (2010).
[CrossRef]

Eckstein, A.

B. Brecht, A. Eckstein, A. Christ, H. Suche, and C. Silberhorn, “From quantum pulse gate to quantum pulse shaper - engineered frequency conversion in nonlinear optical waveguides,” New J. Phys.13, 065029 (2011).
[CrossRef]

A. Eckstein, B. Brecht, and C. Silberhorn, “A quantum pulse gate based on spectrally engineered sum frequency generation,” Opt. Express19, 13770–13778 (2011).
[CrossRef] [PubMed]

Fedrizzi, A.

Fejer, M. M.

Gbur, G. J.

G. J. Gbur, Mathematical Methods for Optical Physics and Engineering (Cambridge, 2011).

Giacone, R. E.

R. E. Giacone, C. J. McKinstrie, and R. Betti, “Angular dependence of stimulated Brillouin scattering in homogeneous plasma,” Phys. Plasmas2, 4596–4605 (1995).
[CrossRef]

Huang, J.

J. Huang and P. Kumar, “Observation of quantum frequency conversion,” Phys. Rev. Lett.68, 2153–2156 (1992).
[CrossRef] [PubMed]

Huang, Y.

Ikuta, R.

R. Ikuta, Y. Kusaka, T. Kitano, H. Kato, T. Yamamoto, M. Koashi, and N. Imoto, “Wide-band quantum interface for visible-to-telecommunication wavelength conversion,” Nature Commun.2, 1544 (2011).
[CrossRef]

Imoto, N.

R. Ikuta, Y. Kusaka, T. Kitano, H. Kato, T. Yamamoto, M. Koashi, and N. Imoto, “Wide-band quantum interface for visible-to-telecommunication wavelength conversion,” Nature Commun.2, 1544 (2011).
[CrossRef]

Kato, H.

R. Ikuta, Y. Kusaka, T. Kitano, H. Kato, T. Yamamoto, M. Koashi, and N. Imoto, “Wide-band quantum interface for visible-to-telecommunication wavelength conversion,” Nature Commun.2, 1544 (2011).
[CrossRef]

Kitano, T.

R. Ikuta, Y. Kusaka, T. Kitano, H. Kato, T. Yamamoto, M. Koashi, and N. Imoto, “Wide-band quantum interface for visible-to-telecommunication wavelength conversion,” Nature Commun.2, 1544 (2011).
[CrossRef]

Koashi, M.

R. Ikuta, Y. Kusaka, T. Kitano, H. Kato, T. Yamamoto, M. Koashi, and N. Imoto, “Wide-band quantum interface for visible-to-telecommunication wavelength conversion,” Nature Commun.2, 1544 (2011).
[CrossRef]

Kumar, P.

Y. Huang and P. Kumar, “Mode-resolved photon counting via cascaded quantum frequency conversion,” Opt. Lett.38, 4 (2013).
[CrossRef]

J. Huang and P. Kumar, “Observation of quantum frequency conversion,” Phys. Rev. Lett.68, 2153–2156 (1992).
[CrossRef] [PubMed]

Kurz, J. R.

Kusaka, Y.

R. Ikuta, Y. Kusaka, T. Kitano, H. Kato, T. Yamamoto, M. Koashi, and N. Imoto, “Wide-band quantum interface for visible-to-telecommunication wavelength conversion,” Nature Commun.2, 1544 (2011).
[CrossRef]

Kwiat, P. G.

A. P. Vandevender and P. G. Kwiat, “High efficiency single photon detection via frequency up-conversion,” J. Mod. Opt.51, 1433–1445 (2004).

Langrock, C.

Lotz, T. H.

T. H. Lotz, W. Sauer-Greff, and R. Urbansky, “Spectral efficient coding schemes in optical communications,” Int. J. Optoelectronic Eng.2, 18–25 (2012).

Ma, L.

M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics4, 786–791 (2010).
[CrossRef]

Ma, Y.

McGuinness, H. J.

M. G. Raymer, S. J. van Enk, C. J. McKinstrie, and H. J. McGuinness, “Interference of two photons of different color,” Opt. Commun.283, 747–752 (2010).
[CrossRef]

H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, “Quantum frequency translation of single-photon states in a photonic crystal fiber,” Phys. Rev. Lett.105, 093604 (2010).
[CrossRef] [PubMed]

McKinstrie, C. J.

C. J. McKinstrie, L. Mejling, M. G. Raymer, and K. Rottwitt, “Quantum-state-preserving optical frequency conversion and pulse reshaping by four-wave mixing,” Phys. Rev. A85, 053829 (2012).
[CrossRef]

L. Mejling, C. J. McKinstrie, M. G. Raymer, and K. Rottwitt, “Quantum frequency translation by four-wave mixing in a fiber: low-conversion regime,” Opt. Express20, 8367–8396 (2012).
[CrossRef] [PubMed]

M. G. Raymer, S. J. van Enk, C. J. McKinstrie, and H. J. McGuinness, “Interference of two photons of different color,” Opt. Commun.283, 747–752 (2010).
[CrossRef]

H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, “Quantum frequency translation of single-photon states in a photonic crystal fiber,” Phys. Rev. Lett.105, 093604 (2010).
[CrossRef] [PubMed]

R. E. Giacone, C. J. McKinstrie, and R. Betti, “Angular dependence of stimulated Brillouin scattering in homogeneous plasma,” Phys. Plasmas2, 4596–4605 (1995).
[CrossRef]

Mejling, L.

C. J. McKinstrie, L. Mejling, M. G. Raymer, and K. Rottwitt, “Quantum-state-preserving optical frequency conversion and pulse reshaping by four-wave mixing,” Phys. Rev. A85, 053829 (2012).
[CrossRef]

L. Mejling, C. J. McKinstrie, M. G. Raymer, and K. Rottwitt, “Quantum frequency translation by four-wave mixing in a fiber: low-conversion regime,” Opt. Express20, 8367–8396 (2012).
[CrossRef] [PubMed]

Mostowski, J.

M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: Unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A24, 1980–1993 (1981).
[CrossRef]

Ou, Z. Y.

Y. Ding and Z. Y. Ou, “Frequency downconversion for a quantum network,” Opt. Lett.35, 2491–2593 (2010).
[CrossRef]

Radic, S.

H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, “Quantum frequency translation of single-photon states in a photonic crystal fiber,” Phys. Rev. Lett.105, 093604 (2010).
[CrossRef] [PubMed]

Rakher, M. T.

M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics4, 786–791 (2010).
[CrossRef]

Ralph, T. C.

Raymer, M. G.

C. J. McKinstrie, L. Mejling, M. G. Raymer, and K. Rottwitt, “Quantum-state-preserving optical frequency conversion and pulse reshaping by four-wave mixing,” Phys. Rev. A85, 053829 (2012).
[CrossRef]

M. G. Raymer and K. Srinivasan, “Manipulating the color and shape of single photons,” Phys. Today65, 32–37 (2012).
[CrossRef]

L. Mejling, C. J. McKinstrie, M. G. Raymer, and K. Rottwitt, “Quantum frequency translation by four-wave mixing in a fiber: low-conversion regime,” Opt. Express20, 8367–8396 (2012).
[CrossRef] [PubMed]

H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, “Quantum frequency translation of single-photon states in a photonic crystal fiber,” Phys. Rev. Lett.105, 093604 (2010).
[CrossRef] [PubMed]

M. G. Raymer, S. J. van Enk, C. J. McKinstrie, and H. J. McGuinness, “Interference of two photons of different color,” Opt. Commun.283, 747–752 (2010).
[CrossRef]

B. J. Smith and M. G. Raymer, “Photon wave functions, wave-packet quantization of light, and coherence theory,” New J. Phys.9, 414 (2007).
[CrossRef]

M. G. Raymer, “Quantum state entanglement and readout of collective atomic-ensemble modes and optical wave packets by stimulated Raman scattering,” J. Mod. Opt.51, 1739–1759 (2004).

M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: Unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A24, 1980–1993 (1981).
[CrossRef]

Rottwitt, K.

C. J. McKinstrie, L. Mejling, M. G. Raymer, and K. Rottwitt, “Quantum-state-preserving optical frequency conversion and pulse reshaping by four-wave mixing,” Phys. Rev. A85, 053829 (2012).
[CrossRef]

L. Mejling, C. J. McKinstrie, M. G. Raymer, and K. Rottwitt, “Quantum frequency translation by four-wave mixing in a fiber: low-conversion regime,” Opt. Express20, 8367–8396 (2012).
[CrossRef] [PubMed]

Roussev, R. V.

Sauer-Greff, W.

T. H. Lotz, W. Sauer-Greff, and R. Urbansky, “Spectral efficient coding schemes in optical communications,” Int. J. Optoelectronic Eng.2, 18–25 (2012).

Shieh, W.

Silberhorn, C.

A. Eckstein, B. Brecht, and C. Silberhorn, “A quantum pulse gate based on spectrally engineered sum frequency generation,” Opt. Express19, 13770–13778 (2011).
[CrossRef] [PubMed]

B. Brecht, A. Eckstein, A. Christ, H. Suche, and C. Silberhorn, “From quantum pulse gate to quantum pulse shaper - engineered frequency conversion in nonlinear optical waveguides,” New J. Phys.13, 065029 (2011).
[CrossRef]

Slattery, O.

M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics4, 786–791 (2010).
[CrossRef]

Smith, B. J.

B. J. Smith and M. G. Raymer, “Photon wave functions, wave-packet quantization of light, and coherence theory,” New J. Phys.9, 414 (2007).
[CrossRef]

Srinivasan, K.

M. G. Raymer and K. Srinivasan, “Manipulating the color and shape of single photons,” Phys. Today65, 32–37 (2012).
[CrossRef]

M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics4, 786–791 (2010).
[CrossRef]

Stace, T. M.

Strang, G.

G. Strang, Introduction to Linear Algebra, 3rd ed. (Wellesley-Cambridge, 1998).

Suche, H.

B. Brecht, A. Eckstein, A. Christ, H. Suche, and C. Silberhorn, “From quantum pulse gate to quantum pulse shaper - engineered frequency conversion in nonlinear optical waveguides,” New J. Phys.13, 065029 (2011).
[CrossRef]

Tang, X.

M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics4, 786–791 (2010).
[CrossRef]

Urbansky, R.

T. H. Lotz, W. Sauer-Greff, and R. Urbansky, “Spectral efficient coding schemes in optical communications,” Int. J. Optoelectronic Eng.2, 18–25 (2012).

van Enk, S. J.

M. G. Raymer, S. J. van Enk, C. J. McKinstrie, and H. J. McGuinness, “Interference of two photons of different color,” Opt. Commun.283, 747–752 (2010).
[CrossRef]

Vandevender, A. P.

A. P. Vandevender and P. G. Kwiat, “High efficiency single photon detection via frequency up-conversion,” J. Mod. Opt.51, 1433–1445 (2004).

White, A. G.

Wong, F. C.

Yamamoto, T.

R. Ikuta, Y. Kusaka, T. Kitano, H. Kato, T. Yamamoto, M. Koashi, and N. Imoto, “Wide-band quantum interface for visible-to-telecommunication wavelength conversion,” Nature Commun.2, 1544 (2011).
[CrossRef]

Yang, Q.

Yi, X.

Int. J. Optoelectronic Eng. (1)

T. H. Lotz, W. Sauer-Greff, and R. Urbansky, “Spectral efficient coding schemes in optical communications,” Int. J. Optoelectronic Eng.2, 18–25 (2012).

J. Mod. Opt. (2)

A. P. Vandevender and P. G. Kwiat, “High efficiency single photon detection via frequency up-conversion,” J. Mod. Opt.51, 1433–1445 (2004).

M. G. Raymer, “Quantum state entanglement and readout of collective atomic-ensemble modes and optical wave packets by stimulated Raman scattering,” J. Mod. Opt.51, 1739–1759 (2004).

J. Opt. Netw. (1)

Nat. Photonics (1)

M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics4, 786–791 (2010).
[CrossRef]

Nature Commun. (1)

R. Ikuta, Y. Kusaka, T. Kitano, H. Kato, T. Yamamoto, M. Koashi, and N. Imoto, “Wide-band quantum interface for visible-to-telecommunication wavelength conversion,” Nature Commun.2, 1544 (2011).
[CrossRef]

New J. Phys. (2)

B. Brecht, A. Eckstein, A. Christ, H. Suche, and C. Silberhorn, “From quantum pulse gate to quantum pulse shaper - engineered frequency conversion in nonlinear optical waveguides,” New J. Phys.13, 065029 (2011).
[CrossRef]

B. J. Smith and M. G. Raymer, “Photon wave functions, wave-packet quantization of light, and coherence theory,” New J. Phys.9, 414 (2007).
[CrossRef]

Opt. Commun. (1)

M. G. Raymer, S. J. van Enk, C. J. McKinstrie, and H. J. McGuinness, “Interference of two photons of different color,” Opt. Commun.283, 747–752 (2010).
[CrossRef]

Opt. Express (3)

Opt. Lett. (4)

Phys. Plasmas (1)

R. E. Giacone, C. J. McKinstrie, and R. Betti, “Angular dependence of stimulated Brillouin scattering in homogeneous plasma,” Phys. Plasmas2, 4596–4605 (1995).
[CrossRef]

Phys. Rev. (1)

D. C. Burnham and R. Y. Chiao, “Coherent resonance flourescence excited by short light pulses,” Phys. Rev.188, 667–675 (1969).
[CrossRef]

Phys. Rev. A (3)

M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: Unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A24, 1980–1993 (1981).
[CrossRef]

S. L. Braunstein, “Squeezing as an irreducible resource,” Phys. Rev. A71, 055801 (2005).
[CrossRef]

C. J. McKinstrie, L. Mejling, M. G. Raymer, and K. Rottwitt, “Quantum-state-preserving optical frequency conversion and pulse reshaping by four-wave mixing,” Phys. Rev. A85, 053829 (2012).
[CrossRef]

Phys. Rev. Lett. (2)

J. Huang and P. Kumar, “Observation of quantum frequency conversion,” Phys. Rev. Lett.68, 2153–2156 (1992).
[CrossRef] [PubMed]

H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, “Quantum frequency translation of single-photon states in a photonic crystal fiber,” Phys. Rev. Lett.105, 093604 (2010).
[CrossRef] [PubMed]

Phys. Today (1)

M. G. Raymer and K. Srinivasan, “Manipulating the color and shape of single photons,” Phys. Today65, 32–37 (2012).
[CrossRef]

Rev. Sci. Instrum. (1)

G. Cerullo and S. De Silvestri, “Ultrafast optical parametric amplifiers,” Rev. Sci. Instrum.74, 1 (2003).
[CrossRef]

Other (3)

G. Strang, Introduction to Linear Algebra, 3rd ed. (Wellesley-Cambridge, 1998).

G. J. Gbur, Mathematical Methods for Optical Physics and Engineering (Cambridge, 2011).

R. V. Churchill, Operational Mathematics, 3rd ed. (McGraw-Hill, 1971).

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 (20)

Fig. 1
Fig. 1

Green function rs(t, t′) in low-conversion limit for medium length L = 1 and Gaussian pump duration τp = 1. (a)βr = βp = 1, βs = −1, (b)βr = 4, βs = 2, βp = 3, (c)βr = 3.5, βs = βp = 1.5, (d)βr = 3.5, βs = 1.5, βp = 1

Fig. 2
Fig. 2

Low-conversion Green function for βr = 8, βs = 4, βp = 6, τp = 0.707, L = 1. Top view and perspective view.

Fig. 3
Fig. 3

Low converison Green function for (a)βr = βp = 1, βs = −1, τp = 0.1, L = 1. For (b)βr = 2, βs = βp = 0, τp = 0.1, L = 1.

Fig. 4
Fig. 4

Temporal Schmidt modes for the case in Fig. 3(b) βr = βp = 1, βs = −1, τp = 0.1, L = 1. (a) First two input modes. (b) Corresponding output modes. First modes are in blue. Second modes are in red.

Fig. 5
Fig. 5

(a), (b) Low-conversion Green function with higher-order pump pulse and βr = βp = 1, βs = −1, τp = 0.1, L = 1. (c) Dominant input Schmidt mode. (d) Dominant output Schmidt mode.

Fig. 6
Fig. 6

Numerically determined conversion efficiencies of the first five Schmidt modes for the SSVM case in Fig. 3(b) for various γ̄. The resulting selectivities S is given in the legend.

Fig. 7
Fig. 7

The first three s input (a, c) and r output (b, d) Schmidt modes for γ̄ = 0.5(a, b), 2.0(c, d), for parameters from Fig. 3(b). Numerical results.

Fig. 8
Fig. 8

Distortion of the first Schmidt modes (r input (a) and s output (b)) with increasing γ̄, for parameters from Fig. 3(b). Numerical results.

Fig. 9
Fig. 9

Selectivity vs. γ̄ for Gaussian pumps of various widths. βs = 0, βp = 2, βr = 4, L = 1. Numerical results.

Fig. 10
Fig. 10

Conversion efficiencies for the first ten Schmidt modes for various γ̄ and Gaussian pump widths (τp). βs = 0, βp = 2, βr = 4, L = 1. Numerical results.

Fig. 11
Fig. 11

The first three s input (a,c,e) and r output (b,d,f) Schmidt modes for γ̄ = 3.36, and τp = 0.1(a,b), 0.7(c,d), and 2.0(e,f). βs = 0, βp = 2, βr = 4, L = 1. Numerical results.

Fig. 12
Fig. 12

Proposed mechanism for shape-preserving frequency conversion in the short-pump “symmetrically counter-propagating signals” regime.

Fig. 13
Fig. 13

The first three s input (a,c) and r output (b,d) Schmidt modes for γ̄ = 3.36, τp = 0.5, and βp = 2.5(a,b), and 3.5(c,d). βs = 0, βs = 0, βr = 4, L = 1. Numerical results.

Fig. 14
Fig. 14

Selectivity vs. γ̄ for Gaussian pumps of various widths and various βp. βs = 0, βr = 4, L = 1. Numerical results.

Fig. 15
Fig. 15

Selectivity vs. γ̄ for Gaussian pumps of various τp and βr. βp = 4, βs = 0, L = 1. Numerical results.

Fig. 16
Fig. 16

The first three s input (a,c,e) and r output (b,d,f) Schmidt modes for γ̄ = 0.5, τp = 0.5, and βr = 3.0(a,b), 1.5(c,d), and 0.5(e,f). βp = 4, βs = 0, L = 1. Numerical results.

Fig. 17
Fig. 17

The first five dominant conversion efficiencies for the parameters in Fig. 3(b) and 6, for various γ̄, SSVM regime. Derived via SVD of the exact Green function Grs(t, t′) (Eq. (17c)).

Fig. 18
Fig. 18

Green function for parameters in Fig. 3(a), τp = 0.01, top and perspective-views, for (a)γ̄ = 1.0, (b)γ̄ = 2.0, (c)γ̄ = 3.0.

Fig. 19
Fig. 19

Selectivity vs. γ̄ for parameters from Fig. 3(b) and 6, for various pump widths (τp), using Grs(t, t′) in Eq. (17c).

Fig. 20
Fig. 20

Selectivity vs. γ ¯ β r s L for parameters from Fig. 3(b), with various βrsL. The joined plot for βrsL = 0.1 = τp has a lower maximum than all other plots.

Tables (1)

Tables Icon

Table 1 Conversion efficiencies for the first four dominant Schmidt modes for the Green functions from Fig. 1. γ̄ = γ/βrs.

Equations (56)

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

( z + β r t ) A r ( z , t ) = i γ A p ( t β p z ) A s ( z , t ) ,
( z + β s t ) A s ( z , t ) = i γ A p * ( t β p z ) A r ( z , t ) ,
E p ( z , t ) = A p ( t β p z ) exp [ i ( k p z ω p t ) ] .
A j ( L , t ) = k = r , s G j k ( t , t ) A k ( 0 , t ) d t .
G r r ( t , t ) = n τ n Ψ n ( t ) ψ n * ( t ) , G r s ( t , t ) = n ρ n Ψ n ( t ) ϕ n * ( t ) ,
G s s ( t , t ) = n τ n * Φ n ( t ) ϕ n * ( t ) , G s r ( t , t ) = n ρ n * Φ n ( t ) ψ n * ( t ) .
S : = | ρ 1 | 4 n = 1 | ρ n | 2 1 .
A r ( t ) | in = n a n ψ n ( t ) , A r ( t ) | out = n c n Ψ n ( t ) ,
A s ( t ) | in = n b n ϕ n ( t ) , A s ( t ) | out = n d n Φ n ( t ) .
c n = τ n a n + ρ n b n ,
d n = τ n b n ρ n a n ,
G ˜ r s ( ω , ω ) = d t d t exp [ i ω t ] G r s ( t , t ) exp [ i ω t ] = n ρ n Ψ ˜ n ( ω ) ϕ ˜ n * ( ω ) .
A r ( L , t ) = A r ( 0 , t β r L ) + i 0 L d z κ ( z , t ) A s ( z , t r ) ,
A s ( L , t ) = A s ( 0 , t β s L ) + i 0 L d z κ * ( z , t ) A r ( z , t s ) ,
A r ( L , t ) A r ( 0 , t r ) + i 0 L d z κ ( z , t ) A s ( 0 , t r ) ,
A s ( L , t ) A s ( 0 , t s ) + i 0 L d z κ * ( z , t ) A r ( 0 , t s ) ,
A j ( L , t ) A j ( 0 , t j ) + d t G ¯ j k ( t , t ) A k ( 0 , t ) | k j ,
G ¯ r s ( t , t ) = i γ β r s A p ( β r p t β s p ( t β r L ) β r s ) H ( t t + β r L ) H ( t t β s L ) ,
G ¯ s r ( t , t ) = i γ * β r s A p * ( β r p ( t β s L ) β s p t β r s ) H ( t t + β s L ) H ( t t β r L ) ,
slope = d t d t | max = β s β p β r β p .
G ¯ ˜ r s ( ω , ω ) = i γ β r s A ˜ p ( 0 , ω ω ) exp [ i L β r ( ω ω ) β s p / β r s ] × sin ( ω ¯ β r s L ) ω ¯ exp [ i L ω ¯ ( β r + β s ) ] = g 1 ( ω ω ) × g 2 ( ω ¯ ) ,
z A r ( z , t ) = i γ A p ( t β p z ) A s ( z , t ) ,
z A s ( z , t ) = i γ A p ( t β p z ) A r ( z , t ) ,
A r ( L , t ) = A r ( 0 , t ) cos [ P ( L ) ] + i A s ( 0 , t ) sin [ P ( L ) ] ,
A s ( L , t ) = A s ( 0 , t ) cos [ P ( L ) ] + i A r ( 0 , t ) sin [ P ( L ) ] ,
G r r ( t , t ) = H ( τ τ ) δ ( ζ ζ ) γ ¯ η / ξ J 1 { 2 γ ¯ η ξ } H H ( τ , τ , ζ , ζ ) ,
G s r ( t , t ) = i γ ¯ A p * ( τ ) J 0 { 2 γ ¯ η ξ } H H ( τ , τ , ζ , ζ ) ,
G r s ( t , t ) = i γ ¯ A p ( τ ) J 0 { 2 γ ¯ η ξ } H H ( τ , τ , ζ , ζ ) ,
G s s ( t , t ) = δ ( τ τ ) H ( ζ ζ ) γ ¯ A p * ( τ ) A p ( τ ) ζ / η J 1 { 2 γ ¯ η ξ } H H ( τ , τ , ζ , ζ ) .
( z + β r p t ) A r ( z , t ) = i γ A p ( t ) A s ( z , t ) ,
( z + β s p t ) A s ( z , t ) = i γ * A p * ( t ) A r ( z , t ) .
( z + β r p t ) A r ( z , t ) = i γ P ( t ) exp [ i θ ( t ) ] A s ( z , t ) ,
z A s ( z , t ) = i γ * P ( t ) exp [ i θ ( t ) ] A r ( z , t ) .
G r s ( t , t ) = j ρ j Ψ j ( t ) ϕ n * ( t ) .
Ψ j ( t ) = k U j k β r , k ( t ) ; ϕ j * ( t ) = l V j l B s , l * ( t ) ,
G r s ( t , t ) = k , l [ j U j k ρ j V j l ] B r , k ( t ) B s , l * ( t ) = k , l [ G ¯ r s ] k l B r , k ( t ) B s , l * ( t ) .
A r ( L , t ) = i γ ¯ t β r L t β s L d t A p ( t ) J 0 { 2 γ ¯ η ξ } A s ( 0 , t )
= i γ L β r s L 0 β r s L d t A p ( t + t β r L ) A s ( 0 , t + t β r L ) J 0 [ 2 γ L β r s L ( t t + t β r L t β r L + β r s L | A p ( x ) | 2 d x ) 1 / 2 ] .
g y 0 y d t J 0 [ | g | t ( y t ) y ] = 2 sin ( g 2 )
A r ( L , t ) = i A s ( t β r L ) sin [ γ L A p ( t β r L ) ] ,
( z + β r t ) A ¯ r ( z , t ) = i γ A p ( t β p z ) A ¯ s ( z , t ) ,
( z + β s t ) A ¯ s ( z , t ) = i γ A p * ( t β p z ) A ¯ r ( z , t ) .
τ A r ( τ , ζ ) = i γ ¯ A p ( τ ) A s ( τ , ζ ) ,
ζ A s ( τ , ζ ) = i γ ¯ A p * ( τ ) A r ( τ , ζ ) ,
τ A r ( τ , s ) = i γ ¯ A p ( τ ) A s ( τ , s ) ,
s A s ( τ , s ) = i γ ¯ A p * ( τ ) A r ( τ , s ) + δ ( τ τ ) ,
A r ( τ , s ) = i γ ¯ A p ( τ ) s exp [ γ ¯ 2 η ( τ , τ ) / s ] H ( τ τ ) ,
A s ( τ , s ) = δ ( τ τ ) s [ γ ¯ 2 A p * ( τ ) A p ( τ ) s 2 ] exp [ γ ¯ 2 η ( τ , τ ) / s ] H ( τ τ ) .
A r ( τ , ζ ) = i γ ¯ A p ( τ ) J 0 { 2 γ ¯ η ( τ , τ ) ξ } H H ( τ , τ , ζ , ζ ) ,
A s ( τ , ζ ) = δ ( τ τ ) H ( ξ ) γ ¯ A p * ( τ ) A p ( τ ) ξ / η ( τ , τ ) × J 1 { 2 γ ¯ η ( τ , τ ) ξ } H H ( τ , τ , ζ , ζ ) ,
r A r ( τ , s ) = i γ ¯ A p ( τ ) A s ( τ , s ) + δ ( τ τ ) ,
s A s ( τ , s ) = i γ ¯ A p * ( τ ) A r ( τ , s ) ,
A r ( τ , s ) = exp [ γ ¯ 2 η ( τ , τ ) / s ] H ( τ τ ) ,
A s ( τ , s ) = i γ ¯ A p * ( τ ) s exp [ γ ¯ 2 η ( τ , τ ) / s ] H ( τ τ ) .
A r ( τ , ζ ) = H ( τ τ ) δ ( ζ ζ ) γ ¯ η ( τ , τ ) / ξ × J 1 { 2 γ ¯ η ( τ , τ ) ξ } H H ( τ , τ , ζ , ζ ) ,
A s ( τ , ζ ) = i γ ¯ A p * ( τ ) J 0 { 2 γ ¯ η ( τ , τ ) ξ } H H ( τ , τ , ζ , ζ ) .

Metrics