Abstract

The performance of all-optical switches is a compromise between the achievable bandwidth of the switched signal and the energy requirement of the switching operation. In this work we consider a system consisting of a photonic crystal cavity coupled to two input and two output waveguides. As a specific example of a switching application, we investigate the demultiplexing of an optical time division multiplexed signal. To quantify the energy-bandwidth trade-off, we introduce a figure of merit for the detection of the demultiplexed signal. In such investigations it is crucial to consider patterning effects, which occur on time scales that are longer than the bit period. Our analysis is based on a coupled mode theory, which allows for an extensive investigation of the influence of the system parameters on the switching dynamics. The analysis is shown to provide new insights into the ultrafast dynamics of the switching operation, and the results show optimum parameter ranges that may serve as design guidelines in device fabrication.

© 2011 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Soljačić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nature Mater. 3, 211–219 (2004).
    [CrossRef]
  2. J. Y. Lee, L. H. Yin, G. P. Agraval, and P. M. Fauchet, “Ultrafast optical switching based on nonlinear polarization rotation in silicon waveguides,” Opt. Express 18, 11514–11523 (2010).
    [CrossRef] [PubMed]
  3. M. Waldow, T. Plotzing, M. Gottheil, M. Forst, and J. Bolten, “25 ps all-optical switching in oxygen implanted silicon-on-insulator microring resonator,” Opt. Express 16, 7693–7702 (2008).
    [CrossRef] [PubMed]
  4. C. Husko, A. De Rossi, S. Combré, Q. V. Tran, F. Raineri, and C. W. Wong, “Ultrafast all-optical modulation in GaAs photonic crystal cavities,” Appl. Phys. Lett. 94, 021111 (2009).
    [CrossRef]
  5. K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4, 477–483 (2010).
    [CrossRef]
  6. L. O’Faolain, D. M. Beggs, T. P. White, T. Kampfrath, K. Kuipers, and T. F. Krauss, “Compact optical switches and modulators based on dispersion engineered photonic crystals,” IEEE Photon. J. 2, 404–414 (2010).
    [CrossRef]
  7. O. Wada, “Recent progress in semiconductor-based photonic signal-processing devices,” IEEE J. Sel. Top. Quantum Electron. 17, 309–319 (2011).
    [CrossRef]
  8. P. A. Andrekson, H. Sunnerud, S. Oda, T. Nishitani, and J. Yang, “Ultrafast, atto-Joule switch using fiber parametric amplifier operated in saturation,” Opt. Express 16, 10956–10961 (2008).
    [CrossRef] [PubMed]
  9. J. Xu, X. Zhang, and J. Mørk, “Investigation of patterning effects in ultrafast SOA-based optical switches,” IEEE J. Quantum Electron. 46, 87–94 (2010).
    [CrossRef]
  10. J. B. Khurgin, “Performance of nonlinear photonic crystal devices at high bit rates,” Opt. Lett. 30, 643–645 (2005).
    [CrossRef] [PubMed]
  11. M. F. Yanik, S. Fan, M. Soljacic, and J. D. Joannopoulos, “All-optical transistor action with bistable switching in a photonic crystal cross-waveguide geometry,” Opt. Lett. 28, 2506–2508 (2003).
    [CrossRef] [PubMed]
  12. J. Bravo-Abad, S. Fan, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Modeling nonlinear optical phenomena in nanophotonics,” J. Lightwave Technol. 25, 2539–2546 (2007).
    [CrossRef]
  13. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals, Molding the Flow of Light (Princeton University Press, 2008)
  14. H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
    [CrossRef] [PubMed]
  15. J. Mørk, F. Öhmann, and S. Bischoff, “Analytical expression for the bit error rate of cascaded all-optical regenerators,” Photon. Technol. Lett. 15, 1479–1481 (2003).
    [CrossRef]
  16. R. W. Boyd, Nonlinear Optics (Academic Press, 2008)

2011 (1)

O. Wada, “Recent progress in semiconductor-based photonic signal-processing devices,” IEEE J. Sel. Top. Quantum Electron. 17, 309–319 (2011).
[CrossRef]

2010 (4)

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4, 477–483 (2010).
[CrossRef]

L. O’Faolain, D. M. Beggs, T. P. White, T. Kampfrath, K. Kuipers, and T. F. Krauss, “Compact optical switches and modulators based on dispersion engineered photonic crystals,” IEEE Photon. J. 2, 404–414 (2010).
[CrossRef]

J. Xu, X. Zhang, and J. Mørk, “Investigation of patterning effects in ultrafast SOA-based optical switches,” IEEE J. Quantum Electron. 46, 87–94 (2010).
[CrossRef]

J. Y. Lee, L. H. Yin, G. P. Agraval, and P. M. Fauchet, “Ultrafast optical switching based on nonlinear polarization rotation in silicon waveguides,” Opt. Express 18, 11514–11523 (2010).
[CrossRef] [PubMed]

2009 (1)

C. Husko, A. De Rossi, S. Combré, Q. V. Tran, F. Raineri, and C. W. Wong, “Ultrafast all-optical modulation in GaAs photonic crystal cavities,” Appl. Phys. Lett. 94, 021111 (2009).
[CrossRef]

2008 (2)

2007 (1)

2005 (1)

2004 (1)

M. Soljačić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nature Mater. 3, 211–219 (2004).
[CrossRef]

2003 (2)

J. Mørk, F. Öhmann, and S. Bischoff, “Analytical expression for the bit error rate of cascaded all-optical regenerators,” Photon. Technol. Lett. 15, 1479–1481 (2003).
[CrossRef]

M. F. Yanik, S. Fan, M. Soljacic, and J. D. Joannopoulos, “All-optical transistor action with bistable switching in a photonic crystal cross-waveguide geometry,” Opt. Lett. 28, 2506–2508 (2003).
[CrossRef] [PubMed]

1990 (1)

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[CrossRef] [PubMed]

Agraval, G. P.

Andrekson, P. A.

Barber, P. W.

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[CrossRef] [PubMed]

Beggs, D. M.

L. O’Faolain, D. M. Beggs, T. P. White, T. Kampfrath, K. Kuipers, and T. F. Krauss, “Compact optical switches and modulators based on dispersion engineered photonic crystals,” IEEE Photon. J. 2, 404–414 (2010).
[CrossRef]

Bischoff, S.

J. Mørk, F. Öhmann, and S. Bischoff, “Analytical expression for the bit error rate of cascaded all-optical regenerators,” Photon. Technol. Lett. 15, 1479–1481 (2003).
[CrossRef]

Bolten, J.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic Press, 2008)

Bravo-Abad, J.

Combré, S.

C. Husko, A. De Rossi, S. Combré, Q. V. Tran, F. Raineri, and C. W. Wong, “Ultrafast all-optical modulation in GaAs photonic crystal cavities,” Appl. Phys. Lett. 94, 021111 (2009).
[CrossRef]

De Rossi, A.

C. Husko, A. De Rossi, S. Combré, Q. V. Tran, F. Raineri, and C. W. Wong, “Ultrafast all-optical modulation in GaAs photonic crystal cavities,” Appl. Phys. Lett. 94, 021111 (2009).
[CrossRef]

Fan, S.

Fauchet, P. M.

Forst, M.

Gottheil, M.

Hill, S. C.

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[CrossRef] [PubMed]

Husko, C.

C. Husko, A. De Rossi, S. Combré, Q. V. Tran, F. Raineri, and C. W. Wong, “Ultrafast all-optical modulation in GaAs photonic crystal cavities,” Appl. Phys. Lett. 94, 021111 (2009).
[CrossRef]

Joannopoulos, J. D.

J. Bravo-Abad, S. Fan, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Modeling nonlinear optical phenomena in nanophotonics,” J. Lightwave Technol. 25, 2539–2546 (2007).
[CrossRef]

M. Soljačić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nature Mater. 3, 211–219 (2004).
[CrossRef]

M. F. Yanik, S. Fan, M. Soljacic, and J. D. Joannopoulos, “All-optical transistor action with bistable switching in a photonic crystal cross-waveguide geometry,” Opt. Lett. 28, 2506–2508 (2003).
[CrossRef] [PubMed]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals, Molding the Flow of Light (Princeton University Press, 2008)

Johnson, S. G.

J. Bravo-Abad, S. Fan, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Modeling nonlinear optical phenomena in nanophotonics,” J. Lightwave Technol. 25, 2539–2546 (2007).
[CrossRef]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals, Molding the Flow of Light (Princeton University Press, 2008)

Kampfrath, T.

L. O’Faolain, D. M. Beggs, T. P. White, T. Kampfrath, K. Kuipers, and T. F. Krauss, “Compact optical switches and modulators based on dispersion engineered photonic crystals,” IEEE Photon. J. 2, 404–414 (2010).
[CrossRef]

Khurgin, J. B.

Krauss, T. F.

L. O’Faolain, D. M. Beggs, T. P. White, T. Kampfrath, K. Kuipers, and T. F. Krauss, “Compact optical switches and modulators based on dispersion engineered photonic crystals,” IEEE Photon. J. 2, 404–414 (2010).
[CrossRef]

Kuipers, K.

L. O’Faolain, D. M. Beggs, T. P. White, T. Kampfrath, K. Kuipers, and T. F. Krauss, “Compact optical switches and modulators based on dispersion engineered photonic crystals,” IEEE Photon. J. 2, 404–414 (2010).
[CrossRef]

Lai, H. M.

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[CrossRef] [PubMed]

Lee, J. Y.

Leung, P. T.

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[CrossRef] [PubMed]

Matsuo, S.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4, 477–483 (2010).
[CrossRef]

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals, Molding the Flow of Light (Princeton University Press, 2008)

Mørk, J.

J. Xu, X. Zhang, and J. Mørk, “Investigation of patterning effects in ultrafast SOA-based optical switches,” IEEE J. Quantum Electron. 46, 87–94 (2010).
[CrossRef]

J. Mørk, F. Öhmann, and S. Bischoff, “Analytical expression for the bit error rate of cascaded all-optical regenerators,” Photon. Technol. Lett. 15, 1479–1481 (2003).
[CrossRef]

Nishitani, T.

Notomi, M.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4, 477–483 (2010).
[CrossRef]

Nozaki, K.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4, 477–483 (2010).
[CrossRef]

O’Faolain, L.

L. O’Faolain, D. M. Beggs, T. P. White, T. Kampfrath, K. Kuipers, and T. F. Krauss, “Compact optical switches and modulators based on dispersion engineered photonic crystals,” IEEE Photon. J. 2, 404–414 (2010).
[CrossRef]

Oda, S.

Öhmann, F.

J. Mørk, F. Öhmann, and S. Bischoff, “Analytical expression for the bit error rate of cascaded all-optical regenerators,” Photon. Technol. Lett. 15, 1479–1481 (2003).
[CrossRef]

Plotzing, T.

Raineri, F.

C. Husko, A. De Rossi, S. Combré, Q. V. Tran, F. Raineri, and C. W. Wong, “Ultrafast all-optical modulation in GaAs photonic crystal cavities,” Appl. Phys. Lett. 94, 021111 (2009).
[CrossRef]

Sato, T.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4, 477–483 (2010).
[CrossRef]

Shinya, A.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4, 477–483 (2010).
[CrossRef]

Soljacic, M.

Sunnerud, H.

Tanabe, T.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4, 477–483 (2010).
[CrossRef]

Taniyama, H.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4, 477–483 (2010).
[CrossRef]

Tran, Q. V.

C. Husko, A. De Rossi, S. Combré, Q. V. Tran, F. Raineri, and C. W. Wong, “Ultrafast all-optical modulation in GaAs photonic crystal cavities,” Appl. Phys. Lett. 94, 021111 (2009).
[CrossRef]

Wada, O.

O. Wada, “Recent progress in semiconductor-based photonic signal-processing devices,” IEEE J. Sel. Top. Quantum Electron. 17, 309–319 (2011).
[CrossRef]

Waldow, M.

White, T. P.

L. O’Faolain, D. M. Beggs, T. P. White, T. Kampfrath, K. Kuipers, and T. F. Krauss, “Compact optical switches and modulators based on dispersion engineered photonic crystals,” IEEE Photon. J. 2, 404–414 (2010).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals, Molding the Flow of Light (Princeton University Press, 2008)

Wong, C. W.

C. Husko, A. De Rossi, S. Combré, Q. V. Tran, F. Raineri, and C. W. Wong, “Ultrafast all-optical modulation in GaAs photonic crystal cavities,” Appl. Phys. Lett. 94, 021111 (2009).
[CrossRef]

Xu, J.

J. Xu, X. Zhang, and J. Mørk, “Investigation of patterning effects in ultrafast SOA-based optical switches,” IEEE J. Quantum Electron. 46, 87–94 (2010).
[CrossRef]

Yang, J.

Yanik, M. F.

Yin, L. H.

Young, K.

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[CrossRef] [PubMed]

Zhang, X.

J. Xu, X. Zhang, and J. Mørk, “Investigation of patterning effects in ultrafast SOA-based optical switches,” IEEE J. Quantum Electron. 46, 87–94 (2010).
[CrossRef]

Appl. Phys. Lett. (1)

C. Husko, A. De Rossi, S. Combré, Q. V. Tran, F. Raineri, and C. W. Wong, “Ultrafast all-optical modulation in GaAs photonic crystal cavities,” Appl. Phys. Lett. 94, 021111 (2009).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. Xu, X. Zhang, and J. Mørk, “Investigation of patterning effects in ultrafast SOA-based optical switches,” IEEE J. Quantum Electron. 46, 87–94 (2010).
[CrossRef]

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

O. Wada, “Recent progress in semiconductor-based photonic signal-processing devices,” IEEE J. Sel. Top. Quantum Electron. 17, 309–319 (2011).
[CrossRef]

IEEE Photon. J. (1)

L. O’Faolain, D. M. Beggs, T. P. White, T. Kampfrath, K. Kuipers, and T. F. Krauss, “Compact optical switches and modulators based on dispersion engineered photonic crystals,” IEEE Photon. J. 2, 404–414 (2010).
[CrossRef]

J. Lightwave Technol. (1)

Nat. Photonics (1)

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4, 477–483 (2010).
[CrossRef]

Nature Mater. (1)

M. Soljačić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nature Mater. 3, 211–219 (2004).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Photon. Technol. Lett. (1)

J. Mørk, F. Öhmann, and S. Bischoff, “Analytical expression for the bit error rate of cascaded all-optical regenerators,” Photon. Technol. Lett. 15, 1479–1481 (2003).
[CrossRef]

Phys. Rev. A (1)

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[CrossRef] [PubMed]

Other (2)

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals, Molding the Flow of Light (Princeton University Press, 2008)

R. W. Boyd, Nonlinear Optics (Academic Press, 2008)

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 (9)

Fig. 1
Fig. 1

(a) The switching structure investigated with a central cavity and two input and two output waveguides. An example of a steady state Ez -field distribution with inputs from the left and the bottom is overlaid on the structure. (b) CMT model of the structure in (a) with an illustration of the parameters entering Eqs. (1) and (2).

Fig. 2
Fig. 2

Illustration of the power spectra of the signal and control as well as the Lorentzian transmission spectra of the cavity modes.

Fig. 3
Fig. 3

(a) Ratio of output energy to input pulse width as a function of the input peak power for a square pulse. The different curves correspond to different pulse widths, while the cavity linewidth is fixed. The dashed red line shows the characteristic bistability curve found from the steady state solution of Eq. (1). (b) The same as (a), but for a Gaussian pulse. Notice the different scales on the P inS 0 -axis in (a) and (b). The green dots indicate local extrema in the output as a function of P inS 0 . (c) Input (black) and output (red) power of a Gaussian pulse with input powers corresponding to the green dots in (b). The curve of the input power has been scaled to be comparable to the output. The values of input power and output energy are given in units of [10−3 ε 0 ca/χ (3)] and [ε 0 a 2/χ (3)], respectively. The parameters in both (a), (b), and (c) are: Δω S = 2.344 × 10−3 c/a and δ S = 3Δω S.

Fig. 4
Fig. 4

(a) The top graph shows the input signal, when the target bit slot is “0” and the following bits are all “1”s. The middle graph shows the input control pulse. The lower graph shows the corresponding signal output, and U outS 0 { 1 } is given by the blue area under the curve. (b) The top graph shows the input signal, when the target bit is “1” followed by 9 “0”s. The middle graph shows the control pulse. The lower graph shows the corresponding signal output, and U outS 1 { 0 } is the area under the curve. (c) The left graph shows the detected energy for a pseudo random binary signal consisting of 215 – 1 bits. The red lines indicate the worst case scenario energies, U outS 1 { 0 } and U outS 0 { 1 } . The right graph shows the corresponding probability distribution function (pdf).

Fig. 5
Fig. 5

(a) Variation of the FoM as a function of the signal detuning δ S and control detuning δ C for Δω SS = 10 and Δω CC = 2. The top graph corresponds to a control energy of U inC = 0.155 ε 0 a 2/χ (3), while the bottom graph corresponds to U inC = 1.6 ε 0 a 2/χ (3). (b) Same as (a), except the cavity linewidths are related to the pulse bandwidths by Δω SS = 0.06 and Δω CC = 2.

Fig. 6
Fig. 6

(a) The maximum of the FoM found by varying (δ S, δ C) as a function of U inC and Δω S. (b) The transmission of the signal pulse, U outS 1 { 0 } / U inS 1 { 0 } , corresponding to the maximum of the FoM in (a). The black lines indicate discontinuity boundaries, where the transmission suddenly changes value. (c) The value of δ S max / Ω S corresponding to the maximum of the FoM in (a). The white lines indicate discontinuity boundaries. (d) The value of δ C max / Ω C , which corresponds to the maximum of the FoM in (a).

Fig. 7
Fig. 7

(a) The maximum value of U outS rel ( δ S / Ω S ) , defined in Eq. (8), plotted as a function of the bandwidth ratio between the pulse and the cavity. (b) The value of δ SS where the maximum in (a) occurs (solid black) and a cross section of δ S max / Ω S at U inC = 0.105 ε 0 a 2/χ (3) from Fig. 6(c) (dashed red). (c) The transmission corresponding to the maximum in (a) (solid black) and a cross section of the transmission at U inC = 0.105 ε 0 a 2/χ (3) from Fig. 6(b) (dashed red).

Fig. 8
Fig. 8

(a) The maximum FoM found by varying (δ S, δ C) as a function of U inC and Δω C. (b) The transmission of the signal, U outS 1 { 0 } / U inS 1 { 0 } , corresponding to the maximum of the FoM in (a). As in Fig. 6(b), the white line indicates a discontinuity boundary, where the transmission suddenly changes value. (c) The value of δ S max / Ω S corresponding to the maximum of the FoM. The discontinuity boundary is also shown with a black line. (d) The value of δ C max / Ω C , which corresponds to the maximum of the FoM along with the discontinuity boundary.

Fig. 9
Fig. 9

(a) Minimum required control energy to obtain different values of the FoM (indicated by the different curves) as a function of the signal bit rate. (b) The ratio of the linewidth of cavity mode C and the pulse spectral width corresponding to the minimum energies shown in (a). The diferent curves correspond to the same values of the FoM as in (a). In both (a) and (b), the parameter values from Sec. 4 have been used.

Equations (11)

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

d S outS d t = i δ S S outS + i 1 τ S ( P outS P SS + 2 P outC P SC ) S outS 1 τ S ( S outS S inS )
d S outC d t = i δ C S outC + i 1 τ C ( P outC P CC + 2 P outS P CS ) S outC 1 τ C ( S outC S inC ) .
1 P i j = 2 ε 0 ε r max c ω i c κ i j Q i Q j χ max ( 3 ) ,
δ S eff = δ S 1 τ S ( P outS P SS + 2 P outC P SC ) .
P inS ( t ) = P inS 0 exp [ ln ( 2 ) ( 2 t Δ t S ) 2 ] ,
P inS ( t ) = P inS 0 Θ ( t ) , Θ ( t ) = { 1 for t 0 0 for t < 0 .
P outS ( t ) = P inS 0 Δ ω S 2 Δ ω S 2 + 4 δ S 2 [ 1 + exp ( Δ ω S t ) 2 exp ( Δ ω S t / 2 ) cos ( δ S t ) Θ ( t ) ,
FoM = U outS 1 { 0 } U outS 0 { 1 } .
U outS = P inS 0 Δ t S π 4 X e ln ( 2 ) ( X i 2 Y ) 2 ( Erfc [ ln ( 2 ) ( X i 2 Y ) ] + e i 8 ln ( 2 ) X Y Erfc [ ln ( 2 ) ( X + i 2 Y ) ] ) ,
X = Δ ω S Ω S , Y = δ S Ω S , and Erfc ( z ) = 1 2 π 0 z e t 2 d t .
U outS rel ( δ S / Ω S ) = | d U outS d ( δ S / Ω S ) | 1 U outS .

Metrics