Abstract

We comprehensively analyze multiple WDM channels RZ-to-NRZ format conversion using a single microring resonator. The scheme relies on simultaneous suppression of the first order harmonic components in the spectra of all the RZ channels. An optimized silicon microring resonator with free spectral range of 100 GHz and Q value of 7900 is designed and fabricated for this purpose. Multi-channel RZ-to-NRZ format conversion is demonstrated experimentally at 50 Gbit/s for WDM channels with 200 GHz channel spacing using the fabricated device. Bit error rate (BER) measurements show very good conversion performances for the scheme.

© 2010 OSA

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  1. Y. Yu, X. L. Zhang, J. B. Rosas-Fernández, D. X. Huang, R. V. Penty, and I. H. White, “Simultaneous multiple DWDM channel NRZ-to-RZ regenerative format conversion at 10 and 20 Gb/s,” Opt. Express 17(5), 3964–3969 (2009).
    [CrossRef] [PubMed]
  2. Y. Yu, X. L. Zhang, J. B. Rosas-Fernández, D. X. Huang, R. V. Penty, and I. H. White, “Single SOA based 16 DWDM channels all-optical NRZ-to-RZ format conversions with different duty cycles,” Opt. Express 16(20), 16166–16171 (2008).
    [CrossRef] [PubMed]
  3. Y. Yu, X. L. Zhang, D. X. Huang, L. J. Li, and W. Fu, “20-Gb/s All-optical format conversions from RZ signals with different duty cycles to NRZ signals,” IEEE Photon. Technol. Lett. 19(14), 1027–1029 (2007).
    [CrossRef]
  4. X. Lei, B. C. Wang, V. Baby, I. Glesk, and P. R. Prucnal, “All-optical data format conversion between RZ and NRZ based on a Mach-Zehnder interferometric wavelength converter,” IEEE Photon. Technol. Lett. 15(2), 308–310 (2003).
    [CrossRef]
  5. Y. Zhang, E. M. Xu, D. X. Huang, and X. L. Zhang, “All-optical format conversion from RZ to NRZ utilizing microfiber resonator,” IEEE Photon. Technol. Lett. 21(17), 1202–1204 (2009).
    [CrossRef]
  6. A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36(4), 321–322 (2000).
    [CrossRef]
  7. M. Popovic, “Theory and design of high-index-contrast microphotonic circuits,” Ph.D. thesis (MIT, 2008).
  8. Y. H. Ding, X. L. Zhang, and D. X. Huang, “Elastic polarization converter based on dual microring resonators,” IEEE J. Quantum Electron. 45(8), 1033–1038 (2009).
    [CrossRef]
  9. X. L. Cai, D. X. Huang, and X. L. Zhang, “Numerical analysis of polarization splitter based on vertically coupled microring resonator,” Opt. Express 14(23), 11304–11311 (2006).
    [CrossRef] [PubMed]
  10. F. P. Payne and J. P. R. Lacey, “A theoretical analysis of scattering loss from planar optical waveguides,” Opt. Quantum Electron. 26(10), 977–986 (1994).
    [CrossRef]
  11. W. Y. Chen, R. Grover, T. A. Ibrahim, V. Van, W. N. Herman, P. T. Ho, T. A. Ibrahim, V. Van, W. N. Herman, and P.-T. Ho, “High-finesse laterally coupled single-mode benzocyclobutene microring resonators,” IEEE Photon. Technol. Lett. 16(2), 470–472 (2004).
    [CrossRef]
  12. Y. A. Vlasov and S. J. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express 12(8), 1622–1631 (2004).
    [CrossRef] [PubMed]
  13. R. Stoffer, K. R. Hiremath, M. Hammer, L. Prkna, and J. Ctyroky, “Cylindrical integrated optical microresonators: Modeling by 3-D vectorial coupled mode theory,” Opt. Commun. 256(1-3), 46–67 (2005).
    [CrossRef]

2009 (3)

Y. Zhang, E. M. Xu, D. X. Huang, and X. L. Zhang, “All-optical format conversion from RZ to NRZ utilizing microfiber resonator,” IEEE Photon. Technol. Lett. 21(17), 1202–1204 (2009).
[CrossRef]

Y. H. Ding, X. L. Zhang, and D. X. Huang, “Elastic polarization converter based on dual microring resonators,” IEEE J. Quantum Electron. 45(8), 1033–1038 (2009).
[CrossRef]

Y. Yu, X. L. Zhang, J. B. Rosas-Fernández, D. X. Huang, R. V. Penty, and I. H. White, “Simultaneous multiple DWDM channel NRZ-to-RZ regenerative format conversion at 10 and 20 Gb/s,” Opt. Express 17(5), 3964–3969 (2009).
[CrossRef] [PubMed]

2008 (1)

2007 (1)

Y. Yu, X. L. Zhang, D. X. Huang, L. J. Li, and W. Fu, “20-Gb/s All-optical format conversions from RZ signals with different duty cycles to NRZ signals,” IEEE Photon. Technol. Lett. 19(14), 1027–1029 (2007).
[CrossRef]

2006 (1)

2005 (1)

R. Stoffer, K. R. Hiremath, M. Hammer, L. Prkna, and J. Ctyroky, “Cylindrical integrated optical microresonators: Modeling by 3-D vectorial coupled mode theory,” Opt. Commun. 256(1-3), 46–67 (2005).
[CrossRef]

2004 (2)

Y. A. Vlasov and S. J. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express 12(8), 1622–1631 (2004).
[CrossRef] [PubMed]

W. Y. Chen, R. Grover, T. A. Ibrahim, V. Van, W. N. Herman, P. T. Ho, T. A. Ibrahim, V. Van, W. N. Herman, and P.-T. Ho, “High-finesse laterally coupled single-mode benzocyclobutene microring resonators,” IEEE Photon. Technol. Lett. 16(2), 470–472 (2004).
[CrossRef]

2003 (1)

X. Lei, B. C. Wang, V. Baby, I. Glesk, and P. R. Prucnal, “All-optical data format conversion between RZ and NRZ based on a Mach-Zehnder interferometric wavelength converter,” IEEE Photon. Technol. Lett. 15(2), 308–310 (2003).
[CrossRef]

2000 (1)

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36(4), 321–322 (2000).
[CrossRef]

1994 (1)

F. P. Payne and J. P. R. Lacey, “A theoretical analysis of scattering loss from planar optical waveguides,” Opt. Quantum Electron. 26(10), 977–986 (1994).
[CrossRef]

Baby, V.

X. Lei, B. C. Wang, V. Baby, I. Glesk, and P. R. Prucnal, “All-optical data format conversion between RZ and NRZ based on a Mach-Zehnder interferometric wavelength converter,” IEEE Photon. Technol. Lett. 15(2), 308–310 (2003).
[CrossRef]

Cai, X. L.

Chen, W. Y.

W. Y. Chen, R. Grover, T. A. Ibrahim, V. Van, W. N. Herman, P. T. Ho, T. A. Ibrahim, V. Van, W. N. Herman, and P.-T. Ho, “High-finesse laterally coupled single-mode benzocyclobutene microring resonators,” IEEE Photon. Technol. Lett. 16(2), 470–472 (2004).
[CrossRef]

Ctyroky, J.

R. Stoffer, K. R. Hiremath, M. Hammer, L. Prkna, and J. Ctyroky, “Cylindrical integrated optical microresonators: Modeling by 3-D vectorial coupled mode theory,” Opt. Commun. 256(1-3), 46–67 (2005).
[CrossRef]

Ding, Y. H.

Y. H. Ding, X. L. Zhang, and D. X. Huang, “Elastic polarization converter based on dual microring resonators,” IEEE J. Quantum Electron. 45(8), 1033–1038 (2009).
[CrossRef]

Fu, W.

Y. Yu, X. L. Zhang, D. X. Huang, L. J. Li, and W. Fu, “20-Gb/s All-optical format conversions from RZ signals with different duty cycles to NRZ signals,” IEEE Photon. Technol. Lett. 19(14), 1027–1029 (2007).
[CrossRef]

Glesk, I.

X. Lei, B. C. Wang, V. Baby, I. Glesk, and P. R. Prucnal, “All-optical data format conversion between RZ and NRZ based on a Mach-Zehnder interferometric wavelength converter,” IEEE Photon. Technol. Lett. 15(2), 308–310 (2003).
[CrossRef]

Grover, R.

W. Y. Chen, R. Grover, T. A. Ibrahim, V. Van, W. N. Herman, P. T. Ho, T. A. Ibrahim, V. Van, W. N. Herman, and P.-T. Ho, “High-finesse laterally coupled single-mode benzocyclobutene microring resonators,” IEEE Photon. Technol. Lett. 16(2), 470–472 (2004).
[CrossRef]

Hammer, M.

R. Stoffer, K. R. Hiremath, M. Hammer, L. Prkna, and J. Ctyroky, “Cylindrical integrated optical microresonators: Modeling by 3-D vectorial coupled mode theory,” Opt. Commun. 256(1-3), 46–67 (2005).
[CrossRef]

Herman, W. N.

W. Y. Chen, R. Grover, T. A. Ibrahim, V. Van, W. N. Herman, P. T. Ho, T. A. Ibrahim, V. Van, W. N. Herman, and P.-T. Ho, “High-finesse laterally coupled single-mode benzocyclobutene microring resonators,” IEEE Photon. Technol. Lett. 16(2), 470–472 (2004).
[CrossRef]

W. Y. Chen, R. Grover, T. A. Ibrahim, V. Van, W. N. Herman, P. T. Ho, T. A. Ibrahim, V. Van, W. N. Herman, and P.-T. Ho, “High-finesse laterally coupled single-mode benzocyclobutene microring resonators,” IEEE Photon. Technol. Lett. 16(2), 470–472 (2004).
[CrossRef]

Hiremath, K. R.

R. Stoffer, K. R. Hiremath, M. Hammer, L. Prkna, and J. Ctyroky, “Cylindrical integrated optical microresonators: Modeling by 3-D vectorial coupled mode theory,” Opt. Commun. 256(1-3), 46–67 (2005).
[CrossRef]

Ho, P. T.

W. Y. Chen, R. Grover, T. A. Ibrahim, V. Van, W. N. Herman, P. T. Ho, T. A. Ibrahim, V. Van, W. N. Herman, and P.-T. Ho, “High-finesse laterally coupled single-mode benzocyclobutene microring resonators,” IEEE Photon. Technol. Lett. 16(2), 470–472 (2004).
[CrossRef]

Ho, P.-T.

W. Y. Chen, R. Grover, T. A. Ibrahim, V. Van, W. N. Herman, P. T. Ho, T. A. Ibrahim, V. Van, W. N. Herman, and P.-T. Ho, “High-finesse laterally coupled single-mode benzocyclobutene microring resonators,” IEEE Photon. Technol. Lett. 16(2), 470–472 (2004).
[CrossRef]

Huang, D. X.

Y. Yu, X. L. Zhang, J. B. Rosas-Fernández, D. X. Huang, R. V. Penty, and I. H. White, “Simultaneous multiple DWDM channel NRZ-to-RZ regenerative format conversion at 10 and 20 Gb/s,” Opt. Express 17(5), 3964–3969 (2009).
[CrossRef] [PubMed]

Y. H. Ding, X. L. Zhang, and D. X. Huang, “Elastic polarization converter based on dual microring resonators,” IEEE J. Quantum Electron. 45(8), 1033–1038 (2009).
[CrossRef]

Y. Zhang, E. M. Xu, D. X. Huang, and X. L. Zhang, “All-optical format conversion from RZ to NRZ utilizing microfiber resonator,” IEEE Photon. Technol. Lett. 21(17), 1202–1204 (2009).
[CrossRef]

Y. Yu, X. L. Zhang, J. B. Rosas-Fernández, D. X. Huang, R. V. Penty, and I. H. White, “Single SOA based 16 DWDM channels all-optical NRZ-to-RZ format conversions with different duty cycles,” Opt. Express 16(20), 16166–16171 (2008).
[CrossRef] [PubMed]

Y. Yu, X. L. Zhang, D. X. Huang, L. J. Li, and W. Fu, “20-Gb/s All-optical format conversions from RZ signals with different duty cycles to NRZ signals,” IEEE Photon. Technol. Lett. 19(14), 1027–1029 (2007).
[CrossRef]

X. L. Cai, D. X. Huang, and X. L. Zhang, “Numerical analysis of polarization splitter based on vertically coupled microring resonator,” Opt. Express 14(23), 11304–11311 (2006).
[CrossRef] [PubMed]

Ibrahim, T. A.

W. Y. Chen, R. Grover, T. A. Ibrahim, V. Van, W. N. Herman, P. T. Ho, T. A. Ibrahim, V. Van, W. N. Herman, and P.-T. Ho, “High-finesse laterally coupled single-mode benzocyclobutene microring resonators,” IEEE Photon. Technol. Lett. 16(2), 470–472 (2004).
[CrossRef]

W. Y. Chen, R. Grover, T. A. Ibrahim, V. Van, W. N. Herman, P. T. Ho, T. A. Ibrahim, V. Van, W. N. Herman, and P.-T. Ho, “High-finesse laterally coupled single-mode benzocyclobutene microring resonators,” IEEE Photon. Technol. Lett. 16(2), 470–472 (2004).
[CrossRef]

Lacey, J. P. R.

F. P. Payne and J. P. R. Lacey, “A theoretical analysis of scattering loss from planar optical waveguides,” Opt. Quantum Electron. 26(10), 977–986 (1994).
[CrossRef]

Lei, X.

X. Lei, B. C. Wang, V. Baby, I. Glesk, and P. R. Prucnal, “All-optical data format conversion between RZ and NRZ based on a Mach-Zehnder interferometric wavelength converter,” IEEE Photon. Technol. Lett. 15(2), 308–310 (2003).
[CrossRef]

Li, L. J.

Y. Yu, X. L. Zhang, D. X. Huang, L. J. Li, and W. Fu, “20-Gb/s All-optical format conversions from RZ signals with different duty cycles to NRZ signals,” IEEE Photon. Technol. Lett. 19(14), 1027–1029 (2007).
[CrossRef]

McNab, S. J.

Payne, F. P.

F. P. Payne and J. P. R. Lacey, “A theoretical analysis of scattering loss from planar optical waveguides,” Opt. Quantum Electron. 26(10), 977–986 (1994).
[CrossRef]

Penty, R. V.

Prkna, L.

R. Stoffer, K. R. Hiremath, M. Hammer, L. Prkna, and J. Ctyroky, “Cylindrical integrated optical microresonators: Modeling by 3-D vectorial coupled mode theory,” Opt. Commun. 256(1-3), 46–67 (2005).
[CrossRef]

Prucnal, P. R.

X. Lei, B. C. Wang, V. Baby, I. Glesk, and P. R. Prucnal, “All-optical data format conversion between RZ and NRZ based on a Mach-Zehnder interferometric wavelength converter,” IEEE Photon. Technol. Lett. 15(2), 308–310 (2003).
[CrossRef]

Rosas-Fernández, J. B.

Stoffer, R.

R. Stoffer, K. R. Hiremath, M. Hammer, L. Prkna, and J. Ctyroky, “Cylindrical integrated optical microresonators: Modeling by 3-D vectorial coupled mode theory,” Opt. Commun. 256(1-3), 46–67 (2005).
[CrossRef]

Van, V.

W. Y. Chen, R. Grover, T. A. Ibrahim, V. Van, W. N. Herman, P. T. Ho, T. A. Ibrahim, V. Van, W. N. Herman, and P.-T. Ho, “High-finesse laterally coupled single-mode benzocyclobutene microring resonators,” IEEE Photon. Technol. Lett. 16(2), 470–472 (2004).
[CrossRef]

W. Y. Chen, R. Grover, T. A. Ibrahim, V. Van, W. N. Herman, P. T. Ho, T. A. Ibrahim, V. Van, W. N. Herman, and P.-T. Ho, “High-finesse laterally coupled single-mode benzocyclobutene microring resonators,” IEEE Photon. Technol. Lett. 16(2), 470–472 (2004).
[CrossRef]

Vlasov, Y. A.

Wang, B. C.

X. Lei, B. C. Wang, V. Baby, I. Glesk, and P. R. Prucnal, “All-optical data format conversion between RZ and NRZ based on a Mach-Zehnder interferometric wavelength converter,” IEEE Photon. Technol. Lett. 15(2), 308–310 (2003).
[CrossRef]

White, I. H.

Xu, E. M.

Y. Zhang, E. M. Xu, D. X. Huang, and X. L. Zhang, “All-optical format conversion from RZ to NRZ utilizing microfiber resonator,” IEEE Photon. Technol. Lett. 21(17), 1202–1204 (2009).
[CrossRef]

Yariv, A.

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36(4), 321–322 (2000).
[CrossRef]

Yu, Y.

Zhang, X. L.

Y. Yu, X. L. Zhang, J. B. Rosas-Fernández, D. X. Huang, R. V. Penty, and I. H. White, “Simultaneous multiple DWDM channel NRZ-to-RZ regenerative format conversion at 10 and 20 Gb/s,” Opt. Express 17(5), 3964–3969 (2009).
[CrossRef] [PubMed]

Y. H. Ding, X. L. Zhang, and D. X. Huang, “Elastic polarization converter based on dual microring resonators,” IEEE J. Quantum Electron. 45(8), 1033–1038 (2009).
[CrossRef]

Y. Zhang, E. M. Xu, D. X. Huang, and X. L. Zhang, “All-optical format conversion from RZ to NRZ utilizing microfiber resonator,” IEEE Photon. Technol. Lett. 21(17), 1202–1204 (2009).
[CrossRef]

Y. Yu, X. L. Zhang, J. B. Rosas-Fernández, D. X. Huang, R. V. Penty, and I. H. White, “Single SOA based 16 DWDM channels all-optical NRZ-to-RZ format conversions with different duty cycles,” Opt. Express 16(20), 16166–16171 (2008).
[CrossRef] [PubMed]

Y. Yu, X. L. Zhang, D. X. Huang, L. J. Li, and W. Fu, “20-Gb/s All-optical format conversions from RZ signals with different duty cycles to NRZ signals,” IEEE Photon. Technol. Lett. 19(14), 1027–1029 (2007).
[CrossRef]

X. L. Cai, D. X. Huang, and X. L. Zhang, “Numerical analysis of polarization splitter based on vertically coupled microring resonator,” Opt. Express 14(23), 11304–11311 (2006).
[CrossRef] [PubMed]

Zhang, Y.

Y. Zhang, E. M. Xu, D. X. Huang, and X. L. Zhang, “All-optical format conversion from RZ to NRZ utilizing microfiber resonator,” IEEE Photon. Technol. Lett. 21(17), 1202–1204 (2009).
[CrossRef]

Electron. Lett. (1)

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36(4), 321–322 (2000).
[CrossRef]

IEEE J. Quantum Electron. (1)

Y. H. Ding, X. L. Zhang, and D. X. Huang, “Elastic polarization converter based on dual microring resonators,” IEEE J. Quantum Electron. 45(8), 1033–1038 (2009).
[CrossRef]

IEEE Photon. Technol. Lett. (4)

Y. Yu, X. L. Zhang, D. X. Huang, L. J. Li, and W. Fu, “20-Gb/s All-optical format conversions from RZ signals with different duty cycles to NRZ signals,” IEEE Photon. Technol. Lett. 19(14), 1027–1029 (2007).
[CrossRef]

X. Lei, B. C. Wang, V. Baby, I. Glesk, and P. R. Prucnal, “All-optical data format conversion between RZ and NRZ based on a Mach-Zehnder interferometric wavelength converter,” IEEE Photon. Technol. Lett. 15(2), 308–310 (2003).
[CrossRef]

Y. Zhang, E. M. Xu, D. X. Huang, and X. L. Zhang, “All-optical format conversion from RZ to NRZ utilizing microfiber resonator,” IEEE Photon. Technol. Lett. 21(17), 1202–1204 (2009).
[CrossRef]

W. Y. Chen, R. Grover, T. A. Ibrahim, V. Van, W. N. Herman, P. T. Ho, T. A. Ibrahim, V. Van, W. N. Herman, and P.-T. Ho, “High-finesse laterally coupled single-mode benzocyclobutene microring resonators,” IEEE Photon. Technol. Lett. 16(2), 470–472 (2004).
[CrossRef]

Opt. Commun. (1)

R. Stoffer, K. R. Hiremath, M. Hammer, L. Prkna, and J. Ctyroky, “Cylindrical integrated optical microresonators: Modeling by 3-D vectorial coupled mode theory,” Opt. Commun. 256(1-3), 46–67 (2005).
[CrossRef]

Opt. Express (4)

Opt. Quantum Electron. (1)

F. P. Payne and J. P. R. Lacey, “A theoretical analysis of scattering loss from planar optical waveguides,” Opt. Quantum Electron. 26(10), 977–986 (1994).
[CrossRef]

Other (1)

M. Popovic, “Theory and design of high-index-contrast microphotonic circuits,” Ph.D. thesis (MIT, 2008).

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Figures (11)

Fig. 1
Fig. 1

Principle of the multi-channel RZ-to-NRZ format conversion, illustrated here for two channels. (a) and (b) show the eye diagrams of two different input RZ signals at 50 Gbit/s with 200 GHz channel spacing. (c) Spectrum transformation of the RZ-to-NRZ format conversion for the two channels utilizing the through transmission of the MRR. (d) Transformed converted NRZ spectra. (e) to (g) show the eye diagrams of the converted NRZ channels for single channel format conversion without AWG, as well as two channels operation after the MRR and ripples suppression by the AWG. In this illustration, r 2 = 0.35 and a = 0.94 for the MRR and the 3 dB bandwidth of the Gaussian AWG is 65 GHz.

Fig. 2
Fig. 2

(a) Q factor and (b) amplitude ripples of the converted NRZ signal versus Q value of the MRR and bandwidth of the OBPF for 50 Gbit/s format conversion.

Fig. 3
Fig. 3

(a) Illustration of the detuning between the notches of the through transmission and the first order harmonic components of the RZ spectrum. (b) Q factor and amplitude ripple of the converted NRZ signal as a function of frequency detuning Δf (or equivalent temperature deviation). Q = 8000, FWHM = 65 GHz.

Fig. 4
Fig. 4

(a) Cross section and (b) corresponding TE0 mode profile of the electric field of the designed waveguide calculated by the full vectorial mode matching method [8,9].

Fig. 5
Fig. 5

(a) Calculated effective index dispersion of the designed waveguide for the TE0 mode. (b) Calculated power coupling coefficient and Q value of the MRR as a function of the coupling gap for the TE0 mode.

Fig. 6
Fig. 6

(a) Scanning electron microscope (SEM) top view image of the fabricated device before BCB spinning. The inset is a close-up view of the coupling area between the ring and the straight waveguide. (b) Optical microscope picture of the fabricated device. The MRR is under the micro heater. (c) Measured transmission of the fabricated MRR.

Fig. 7
Fig. 7

Experimental setup for the multiple WDM channels RZ-to-NRZ format conversion.

Fig. 8
Fig. 8

(a) Spectra of the RZ signal at the transmitter and converted NRZ signals at the MRR and AWG outputs. The spectrum of a NRZ modulated signal is also shown as a reference. Eye diagrams of the input RZ (b), reference NRZ (c) and converted NRZ (d) signals. (e) BER measurements of the original RZ and of the converted NRZ signals after the MRR and the AWG, as well as of an electrically generated reference NRZ-OOK signal.

Fig. 9
Fig. 9

Spectra of the four WDM channel signal. (a) WDM RZ signal. (b) Converted WDM NRZ signal.

Fig. 10
Fig. 10

Measured eye diagrams of (a) single RZ signal, (b) WDM RZ signals after decorrelation, (c) original reference NRZ signal, and (d)~(g) converted NRZ signals for channels 1 to 4.

Fig. 11
Fig. 11

(a) Back-to-back BER measurement of the RZ channels (single channel operation, with and without AWG, as well as WDM operation) (b) BER measurement of the converted NRZ channels in single channel and WDM operation, as well as an electrically generated reference NRZ signal. (c) Power penalties of the RZ signal output from the AWG for single and multiple WDM channels cases, compared to the original RZ signals without AWG. (d) Power penalty of the output converted NRZ signal for single and multiple WDM channels cases, compared to the reference electrically modulated NRZ signal. Power penalties are measured at BER of 10−9.

Equations (5)

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t = r [ 1 a exp ( j θ ) ] 1 a r 2 exp ( j θ )
Δ n ( Δ T ) n ( T 0 ) 0.01587 ( Δ T T 0 ) + 0.002392 ( Δ T T 0 ) 2
n s i ( λ ) =  3 .476-0 .07805 ( λ -1.55 ) +0.082 ( λ -1.55 ) 2
α = S ( n c o r e 2 n s i d e 2 ) 2 k 0 3 4 π n c o r e i n n e r s i d e E 2 d y + o u t e r s i d e E 2 d y E 2 d a
S = 2 σ 2 L c 0 π d θ 1 + L c 2 k 0 2 ( n e f f n s i d e cos θ ) 2

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