Abstract

We propose and simulate all-optical simultaneous half-adder, half-subtracter, and OR logic gate at 40 Gbit/s based on the cascaded sum-and difference-frequency generation (SFG+DFG) using only one periodically poled lithium niobate (PPLN) waveguide. The SFG and DFG processes generate the Borrow and Carry outputs, respectively. The Sum/Difference and OR are obtained by properly combining the outputs from PPLN after SFG+DFG. The eye diagrams, pulse width, quality-factor (Q-factor), extinction ratio (ER), and tunability are calculated and discussed,showing impressive operation performance.

© 2007 Optical Society of America

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  1. K. E. Stubkjaer, "Semiconductor optical amplifier-based all-optical gates for high-speed optical processing," IEEE J. Sel. Top. Quantum Electron. 6, 1428-1435 (2000).
    [CrossRef]
  2. J. Y. Kim, J. M. Kang, T. Y. Kim, and S. K. Han, "All-optical multiple logic gates with XOR, NOR, OR, and NAND functions using parallel SOA-MZI structures: theory and experiment," J. Lightwave Technol. 24, 3392-3399 (2006).
    [CrossRef]
  3. S. Kim, S. Lee, B. Kang, S. Lee, and J. Park, "All-optical binary half adder using SLALOMs," CLEO/Pacific Rim 2001, 2, II-254-II-255 (2001).
  4. A. J. Poustie, K. J. Blow, A. E. Kelly, and R. J. Manning, "All-optical binary half-adder," Opt. Commun. 156, 22-26 (1998).
    [CrossRef]
  5. J. H. Kim, Y. T. Byun, Y. M. Jhon, S. Lee, D. H. Woo, and S. H. Kim, "All-optical half adder using semiconductor optical amplifier based devices," Opt. Commun. 218, 345-349 (2003).
    [CrossRef]
  6. S. Kumar, D. Gurkan, A. E. Willner, K. Parameswaran, and M. Fejer, "All-optical half adder using a PPLN waveguide and an SOA," OFC 2004, February, 1, 23-27 (2004).
  7. J. E. McGeehan, S. Kumar, and A. E. Willner, "All-optical digital half-subtracter/adder using semiconductor optical amplifiers and a PPLN waveguide," CLEO 2005, May, 2, 1061-1063 (2005).
  8. J. Sun, W. Liu, J. Tian, J. R. Kurz, and M. M. Fejer, "Multichannel wavelength conversion exploiting cascaded second-order nonlinearity in LiNbO3 waveguides," IEEE Photonics Technol. Lett. 15, 1743-1745 (2003).
    [CrossRef]
  9. J. Sun, Z. Ma, D. Liu, and D. Huang, "Wavelength conversion between picosecond pulses using cascaded second-order nonlinearity in LiNbO3 waveguides," Opt. Quantum Electron. 37443-456 (2005).
    [CrossRef]
  10. J. Sun, D. Huang, and D. Liu, "Simultaneous wavelength conversion and pulse compression exploiting cascaded second-order nonlinear processes in LiNbO3 waveguides," Opt. Commun. 259, 321-327 (2006).
    [CrossRef]
  11. J. Wang, J. Sun, C. Luo, and Q. Sun, "Flexible all-optical wavelength conversions of 1.57-ps pulses exploiting cascaded sum- and difference frequency generation (cSFG/DFG) in a PPLN waveguide," Appl. Phys. B 83, 543-548 (2006).
    [CrossRef]
  12. J. Wang, J. Sun, C. Luo, and Q. Sun, "Experimental demonstration of wavelength conversion between ps-pulses based on cascaded sum- and difference frequency generation (SFG+DFG) in LiNbO3 waveguides," Opt. Express 13, 7405-7414 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-19-7405
    [CrossRef] [PubMed]
  13. J. Wang, J. Sun, X. Zhang, X. Yuan, and D. Huang, "Experimental observation of tunable wavelength down- and up-conversions of ultra-short pulses in a periodically poled LiNbO3 waveguide," Opt. Commun. 269, 179-187 (2006).
    [CrossRef]
  14. J. Wang, J. Sun, J. R. Kurz, and M. M. Fejer, "Tunable wavelength conversion of ps-pulses exploiting cascaded sum- and difference frequency generation in a PPLN-fiber ring laser," IEEE Photonics Technol. Lett. 18, 2093-2095 (2006).
    [CrossRef]
  15. J. E. McGeehan, M. Giltrelli, and A. E. Willner, "All-optical digital 3-input AND gate using sum- and difference-frequency generation in a PPLN waveguide," LEOS 2005, July, 179-180 (2005).
  16. J. Wang, J. Sun, and Q. Sun, "Experimental observation of a 1.5 μm band wavelength conversion and logic NOT gate at 40 Gbit/s based on sum-frequency generation," Opt. Lett. 31, 1711-1713 (2006).
    [CrossRef] [PubMed]
  17. J. Sun, and J. Wang, "Simulation of optical NOT gate switching by sum-frequency generation in LiNbO3 waveguides," Opt. Commun. 267, 187-192 (2006).
    [CrossRef]

2006 (7)

J. Y. Kim, J. M. Kang, T. Y. Kim, and S. K. Han, "All-optical multiple logic gates with XOR, NOR, OR, and NAND functions using parallel SOA-MZI structures: theory and experiment," J. Lightwave Technol. 24, 3392-3399 (2006).
[CrossRef]

J. Sun, D. Huang, and D. Liu, "Simultaneous wavelength conversion and pulse compression exploiting cascaded second-order nonlinear processes in LiNbO3 waveguides," Opt. Commun. 259, 321-327 (2006).
[CrossRef]

J. Wang, J. Sun, C. Luo, and Q. Sun, "Flexible all-optical wavelength conversions of 1.57-ps pulses exploiting cascaded sum- and difference frequency generation (cSFG/DFG) in a PPLN waveguide," Appl. Phys. B 83, 543-548 (2006).
[CrossRef]

J. Wang, J. Sun, X. Zhang, X. Yuan, and D. Huang, "Experimental observation of tunable wavelength down- and up-conversions of ultra-short pulses in a periodically poled LiNbO3 waveguide," Opt. Commun. 269, 179-187 (2006).
[CrossRef]

J. Wang, J. Sun, J. R. Kurz, and M. M. Fejer, "Tunable wavelength conversion of ps-pulses exploiting cascaded sum- and difference frequency generation in a PPLN-fiber ring laser," IEEE Photonics Technol. Lett. 18, 2093-2095 (2006).
[CrossRef]

J. Wang, J. Sun, and Q. Sun, "Experimental observation of a 1.5 μm band wavelength conversion and logic NOT gate at 40 Gbit/s based on sum-frequency generation," Opt. Lett. 31, 1711-1713 (2006).
[CrossRef] [PubMed]

J. Sun, and J. Wang, "Simulation of optical NOT gate switching by sum-frequency generation in LiNbO3 waveguides," Opt. Commun. 267, 187-192 (2006).
[CrossRef]

2005 (2)

2003 (2)

J. H. Kim, Y. T. Byun, Y. M. Jhon, S. Lee, D. H. Woo, and S. H. Kim, "All-optical half adder using semiconductor optical amplifier based devices," Opt. Commun. 218, 345-349 (2003).
[CrossRef]

J. Sun, W. Liu, J. Tian, J. R. Kurz, and M. M. Fejer, "Multichannel wavelength conversion exploiting cascaded second-order nonlinearity in LiNbO3 waveguides," IEEE Photonics Technol. Lett. 15, 1743-1745 (2003).
[CrossRef]

2000 (1)

K. E. Stubkjaer, "Semiconductor optical amplifier-based all-optical gates for high-speed optical processing," IEEE J. Sel. Top. Quantum Electron. 6, 1428-1435 (2000).
[CrossRef]

1998 (1)

A. J. Poustie, K. J. Blow, A. E. Kelly, and R. J. Manning, "All-optical binary half-adder," Opt. Commun. 156, 22-26 (1998).
[CrossRef]

Blow, K. J.

A. J. Poustie, K. J. Blow, A. E. Kelly, and R. J. Manning, "All-optical binary half-adder," Opt. Commun. 156, 22-26 (1998).
[CrossRef]

Byun, Y. T.

J. H. Kim, Y. T. Byun, Y. M. Jhon, S. Lee, D. H. Woo, and S. H. Kim, "All-optical half adder using semiconductor optical amplifier based devices," Opt. Commun. 218, 345-349 (2003).
[CrossRef]

Fejer, M. M.

J. Wang, J. Sun, J. R. Kurz, and M. M. Fejer, "Tunable wavelength conversion of ps-pulses exploiting cascaded sum- and difference frequency generation in a PPLN-fiber ring laser," IEEE Photonics Technol. Lett. 18, 2093-2095 (2006).
[CrossRef]

J. Sun, W. Liu, J. Tian, J. R. Kurz, and M. M. Fejer, "Multichannel wavelength conversion exploiting cascaded second-order nonlinearity in LiNbO3 waveguides," IEEE Photonics Technol. Lett. 15, 1743-1745 (2003).
[CrossRef]

Han, S. K.

Huang, D.

J. Sun, D. Huang, and D. Liu, "Simultaneous wavelength conversion and pulse compression exploiting cascaded second-order nonlinear processes in LiNbO3 waveguides," Opt. Commun. 259, 321-327 (2006).
[CrossRef]

J. Wang, J. Sun, X. Zhang, X. Yuan, and D. Huang, "Experimental observation of tunable wavelength down- and up-conversions of ultra-short pulses in a periodically poled LiNbO3 waveguide," Opt. Commun. 269, 179-187 (2006).
[CrossRef]

J. Sun, Z. Ma, D. Liu, and D. Huang, "Wavelength conversion between picosecond pulses using cascaded second-order nonlinearity in LiNbO3 waveguides," Opt. Quantum Electron. 37443-456 (2005).
[CrossRef]

Jhon, Y. M.

J. H. Kim, Y. T. Byun, Y. M. Jhon, S. Lee, D. H. Woo, and S. H. Kim, "All-optical half adder using semiconductor optical amplifier based devices," Opt. Commun. 218, 345-349 (2003).
[CrossRef]

Kang, J. M.

Kelly, A. E.

A. J. Poustie, K. J. Blow, A. E. Kelly, and R. J. Manning, "All-optical binary half-adder," Opt. Commun. 156, 22-26 (1998).
[CrossRef]

Kim, J. H.

J. H. Kim, Y. T. Byun, Y. M. Jhon, S. Lee, D. H. Woo, and S. H. Kim, "All-optical half adder using semiconductor optical amplifier based devices," Opt. Commun. 218, 345-349 (2003).
[CrossRef]

Kim, J. Y.

Kim, S. H.

J. H. Kim, Y. T. Byun, Y. M. Jhon, S. Lee, D. H. Woo, and S. H. Kim, "All-optical half adder using semiconductor optical amplifier based devices," Opt. Commun. 218, 345-349 (2003).
[CrossRef]

Kim, T. Y.

Kurz, J. R.

J. Wang, J. Sun, J. R. Kurz, and M. M. Fejer, "Tunable wavelength conversion of ps-pulses exploiting cascaded sum- and difference frequency generation in a PPLN-fiber ring laser," IEEE Photonics Technol. Lett. 18, 2093-2095 (2006).
[CrossRef]

J. Sun, W. Liu, J. Tian, J. R. Kurz, and M. M. Fejer, "Multichannel wavelength conversion exploiting cascaded second-order nonlinearity in LiNbO3 waveguides," IEEE Photonics Technol. Lett. 15, 1743-1745 (2003).
[CrossRef]

Lee, S.

J. H. Kim, Y. T. Byun, Y. M. Jhon, S. Lee, D. H. Woo, and S. H. Kim, "All-optical half adder using semiconductor optical amplifier based devices," Opt. Commun. 218, 345-349 (2003).
[CrossRef]

Liu, D.

J. Sun, D. Huang, and D. Liu, "Simultaneous wavelength conversion and pulse compression exploiting cascaded second-order nonlinear processes in LiNbO3 waveguides," Opt. Commun. 259, 321-327 (2006).
[CrossRef]

J. Sun, Z. Ma, D. Liu, and D. Huang, "Wavelength conversion between picosecond pulses using cascaded second-order nonlinearity in LiNbO3 waveguides," Opt. Quantum Electron. 37443-456 (2005).
[CrossRef]

Liu, W.

J. Sun, W. Liu, J. Tian, J. R. Kurz, and M. M. Fejer, "Multichannel wavelength conversion exploiting cascaded second-order nonlinearity in LiNbO3 waveguides," IEEE Photonics Technol. Lett. 15, 1743-1745 (2003).
[CrossRef]

Luo, C.

J. Wang, J. Sun, C. Luo, and Q. Sun, "Flexible all-optical wavelength conversions of 1.57-ps pulses exploiting cascaded sum- and difference frequency generation (cSFG/DFG) in a PPLN waveguide," Appl. Phys. B 83, 543-548 (2006).
[CrossRef]

J. Wang, J. Sun, C. Luo, and Q. Sun, "Experimental demonstration of wavelength conversion between ps-pulses based on cascaded sum- and difference frequency generation (SFG+DFG) in LiNbO3 waveguides," Opt. Express 13, 7405-7414 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-19-7405
[CrossRef] [PubMed]

Ma, Z.

J. Sun, Z. Ma, D. Liu, and D. Huang, "Wavelength conversion between picosecond pulses using cascaded second-order nonlinearity in LiNbO3 waveguides," Opt. Quantum Electron. 37443-456 (2005).
[CrossRef]

Manning, R. J.

A. J. Poustie, K. J. Blow, A. E. Kelly, and R. J. Manning, "All-optical binary half-adder," Opt. Commun. 156, 22-26 (1998).
[CrossRef]

Poustie, A. J.

A. J. Poustie, K. J. Blow, A. E. Kelly, and R. J. Manning, "All-optical binary half-adder," Opt. Commun. 156, 22-26 (1998).
[CrossRef]

Stubkjaer, K. E.

K. E. Stubkjaer, "Semiconductor optical amplifier-based all-optical gates for high-speed optical processing," IEEE J. Sel. Top. Quantum Electron. 6, 1428-1435 (2000).
[CrossRef]

Sun, J.

J. Sun, D. Huang, and D. Liu, "Simultaneous wavelength conversion and pulse compression exploiting cascaded second-order nonlinear processes in LiNbO3 waveguides," Opt. Commun. 259, 321-327 (2006).
[CrossRef]

J. Wang, J. Sun, C. Luo, and Q. Sun, "Flexible all-optical wavelength conversions of 1.57-ps pulses exploiting cascaded sum- and difference frequency generation (cSFG/DFG) in a PPLN waveguide," Appl. Phys. B 83, 543-548 (2006).
[CrossRef]

J. Wang, J. Sun, and Q. Sun, "Experimental observation of a 1.5 μm band wavelength conversion and logic NOT gate at 40 Gbit/s based on sum-frequency generation," Opt. Lett. 31, 1711-1713 (2006).
[CrossRef] [PubMed]

J. Sun, and J. Wang, "Simulation of optical NOT gate switching by sum-frequency generation in LiNbO3 waveguides," Opt. Commun. 267, 187-192 (2006).
[CrossRef]

J. Wang, J. Sun, X. Zhang, X. Yuan, and D. Huang, "Experimental observation of tunable wavelength down- and up-conversions of ultra-short pulses in a periodically poled LiNbO3 waveguide," Opt. Commun. 269, 179-187 (2006).
[CrossRef]

J. Wang, J. Sun, J. R. Kurz, and M. M. Fejer, "Tunable wavelength conversion of ps-pulses exploiting cascaded sum- and difference frequency generation in a PPLN-fiber ring laser," IEEE Photonics Technol. Lett. 18, 2093-2095 (2006).
[CrossRef]

J. Wang, J. Sun, C. Luo, and Q. Sun, "Experimental demonstration of wavelength conversion between ps-pulses based on cascaded sum- and difference frequency generation (SFG+DFG) in LiNbO3 waveguides," Opt. Express 13, 7405-7414 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-19-7405
[CrossRef] [PubMed]

J. Sun, Z. Ma, D. Liu, and D. Huang, "Wavelength conversion between picosecond pulses using cascaded second-order nonlinearity in LiNbO3 waveguides," Opt. Quantum Electron. 37443-456 (2005).
[CrossRef]

J. Sun, W. Liu, J. Tian, J. R. Kurz, and M. M. Fejer, "Multichannel wavelength conversion exploiting cascaded second-order nonlinearity in LiNbO3 waveguides," IEEE Photonics Technol. Lett. 15, 1743-1745 (2003).
[CrossRef]

Sun, Q.

Tian, J.

J. Sun, W. Liu, J. Tian, J. R. Kurz, and M. M. Fejer, "Multichannel wavelength conversion exploiting cascaded second-order nonlinearity in LiNbO3 waveguides," IEEE Photonics Technol. Lett. 15, 1743-1745 (2003).
[CrossRef]

Wang, J.

J. Wang, J. Sun, X. Zhang, X. Yuan, and D. Huang, "Experimental observation of tunable wavelength down- and up-conversions of ultra-short pulses in a periodically poled LiNbO3 waveguide," Opt. Commun. 269, 179-187 (2006).
[CrossRef]

J. Wang, J. Sun, C. Luo, and Q. Sun, "Flexible all-optical wavelength conversions of 1.57-ps pulses exploiting cascaded sum- and difference frequency generation (cSFG/DFG) in a PPLN waveguide," Appl. Phys. B 83, 543-548 (2006).
[CrossRef]

J. Sun, and J. Wang, "Simulation of optical NOT gate switching by sum-frequency generation in LiNbO3 waveguides," Opt. Commun. 267, 187-192 (2006).
[CrossRef]

J. Wang, J. Sun, and Q. Sun, "Experimental observation of a 1.5 μm band wavelength conversion and logic NOT gate at 40 Gbit/s based on sum-frequency generation," Opt. Lett. 31, 1711-1713 (2006).
[CrossRef] [PubMed]

J. Wang, J. Sun, J. R. Kurz, and M. M. Fejer, "Tunable wavelength conversion of ps-pulses exploiting cascaded sum- and difference frequency generation in a PPLN-fiber ring laser," IEEE Photonics Technol. Lett. 18, 2093-2095 (2006).
[CrossRef]

J. Wang, J. Sun, C. Luo, and Q. Sun, "Experimental demonstration of wavelength conversion between ps-pulses based on cascaded sum- and difference frequency generation (SFG+DFG) in LiNbO3 waveguides," Opt. Express 13, 7405-7414 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-19-7405
[CrossRef] [PubMed]

Woo, D. H.

J. H. Kim, Y. T. Byun, Y. M. Jhon, S. Lee, D. H. Woo, and S. H. Kim, "All-optical half adder using semiconductor optical amplifier based devices," Opt. Commun. 218, 345-349 (2003).
[CrossRef]

Yuan, X.

J. Wang, J. Sun, X. Zhang, X. Yuan, and D. Huang, "Experimental observation of tunable wavelength down- and up-conversions of ultra-short pulses in a periodically poled LiNbO3 waveguide," Opt. Commun. 269, 179-187 (2006).
[CrossRef]

Zhang, X.

J. Wang, J. Sun, X. Zhang, X. Yuan, and D. Huang, "Experimental observation of tunable wavelength down- and up-conversions of ultra-short pulses in a periodically poled LiNbO3 waveguide," Opt. Commun. 269, 179-187 (2006).
[CrossRef]

Appl. Phys. B (1)

J. Wang, J. Sun, C. Luo, and Q. Sun, "Flexible all-optical wavelength conversions of 1.57-ps pulses exploiting cascaded sum- and difference frequency generation (cSFG/DFG) in a PPLN waveguide," Appl. Phys. B 83, 543-548 (2006).
[CrossRef]

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

K. E. Stubkjaer, "Semiconductor optical amplifier-based all-optical gates for high-speed optical processing," IEEE J. Sel. Top. Quantum Electron. 6, 1428-1435 (2000).
[CrossRef]

IEEE Photonics Technol. Lett. (2)

J. Sun, W. Liu, J. Tian, J. R. Kurz, and M. M. Fejer, "Multichannel wavelength conversion exploiting cascaded second-order nonlinearity in LiNbO3 waveguides," IEEE Photonics Technol. Lett. 15, 1743-1745 (2003).
[CrossRef]

J. Wang, J. Sun, J. R. Kurz, and M. M. Fejer, "Tunable wavelength conversion of ps-pulses exploiting cascaded sum- and difference frequency generation in a PPLN-fiber ring laser," IEEE Photonics Technol. Lett. 18, 2093-2095 (2006).
[CrossRef]

J. Lightwave Technol. (1)

Opt. Commun. (5)

A. J. Poustie, K. J. Blow, A. E. Kelly, and R. J. Manning, "All-optical binary half-adder," Opt. Commun. 156, 22-26 (1998).
[CrossRef]

J. H. Kim, Y. T. Byun, Y. M. Jhon, S. Lee, D. H. Woo, and S. H. Kim, "All-optical half adder using semiconductor optical amplifier based devices," Opt. Commun. 218, 345-349 (2003).
[CrossRef]

J. Sun, and J. Wang, "Simulation of optical NOT gate switching by sum-frequency generation in LiNbO3 waveguides," Opt. Commun. 267, 187-192 (2006).
[CrossRef]

J. Sun, D. Huang, and D. Liu, "Simultaneous wavelength conversion and pulse compression exploiting cascaded second-order nonlinear processes in LiNbO3 waveguides," Opt. Commun. 259, 321-327 (2006).
[CrossRef]

J. Wang, J. Sun, X. Zhang, X. Yuan, and D. Huang, "Experimental observation of tunable wavelength down- and up-conversions of ultra-short pulses in a periodically poled LiNbO3 waveguide," Opt. Commun. 269, 179-187 (2006).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Opt. Quantum Electron. (1)

J. Sun, Z. Ma, D. Liu, and D. Huang, "Wavelength conversion between picosecond pulses using cascaded second-order nonlinearity in LiNbO3 waveguides," Opt. Quantum Electron. 37443-456 (2005).
[CrossRef]

Other (4)

S. Kim, S. Lee, B. Kang, S. Lee, and J. Park, "All-optical binary half adder using SLALOMs," CLEO/Pacific Rim 2001, 2, II-254-II-255 (2001).

S. Kumar, D. Gurkan, A. E. Willner, K. Parameswaran, and M. Fejer, "All-optical half adder using a PPLN waveguide and an SOA," OFC 2004, February, 1, 23-27 (2004).

J. E. McGeehan, S. Kumar, and A. E. Willner, "All-optical digital half-subtracter/adder using semiconductor optical amplifiers and a PPLN waveguide," CLEO 2005, May, 2, 1061-1063 (2005).

J. E. McGeehan, M. Giltrelli, and A. E. Willner, "All-optical digital 3-input AND gate using sum- and difference-frequency generation in a PPLN waveguide," LEOS 2005, July, 179-180 (2005).

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Figures (6)

Fig. 1.
Fig. 1.

Digital gate-level diagram and logical truth table for the half-adder, half-subtracter, and OR logic gate. The Sum and Difference outputs are identical.

Fig. 2.
Fig. 2.

Schematic diagram of single-PPLN-based all-optical half-adder, half-subtracter, and OR logic gate. TF: tunable filter, VOA: variable optical attenuator, TDL: tunable delay line.

Fig. 3.
Fig. 3.

Input and output waveforms for the half-adder, half-subtracter, and OR logic gate: (a) input signal A, (b) input signal B, (c) Sum/Difference output (XOR), (d) Carry output (AND) of sum-frequency wave, (e) Carry output (AND) of idler wave, (f) Borrow output of A-B, (g) Borrow output of B-A, (h) OR output (A+Ā∙B), (i) OR output (B+AB̄).

Fig. 4.
Fig. 4.

Eye diagrams for the half-adder, half-subtracter, and OR logic gate: (a) input signal A,(b) input signal B, (c) Sum/Difference output (XOR), (d) Carry output (AND) of sum-frequency wave, (e) Carry output (AND) of idler wave, (f) Borrow output of A-B, (g) Borrow output of B-A, (h) OR output (A + Ā∙B), (i) OR output (B+AB̄).

Fig. 5.
Fig. 5.

Dependence of (a) idler pulse width, (b) Q-factor, (c) extinction ratio on the length of the PPLN waveguide.

Fig. 6.
Fig. 6.

Dependence of Q-factor (Sum/Difference, Borrows, OR) and extinction ratio (Sum/Difference, Borrows) on (a)(b) pump wavelength, idler wavelength and (c)(d) wavelengths of signals A, B.

Equations (9)

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

A SA z + β 1 SA A SA t + i 2 β 2 SA 2 A SA t 2 = SA κ SFG A SB * A SF exp ( k SFG z )
A SB z + β 1 SB A SB t + i 2 β 2 SB 2 A SB t 2 = SB κ SFG A SA * A SF exp ( k SFG z )
A SF z + β 1 SF A SF t + i 2 β 2 SF 2 A SF t 2 = SF κ SFG A SA A SB exp ( k SFG z ) + SF κ DFG A P A i exp ( i Δ k DFG z )
A P z + β 1 P A P t + i 2 β 2 P 2 A P t 2 = P κ DFG A i * A SF exp ( i Δ k DFG z )
A i z + β 1 i A i t + i 2 β 2 i 2 A i t 2 = i κ DFG A P * A SF exp ( i Δ k DFG z )
κ SFG = d eff 2 μ 0 cn SA n SB n SF A eff
κ DFG = d eff 2 μ 0 cn P n i n SF A eff
Δ k SFG = k SF k SA k SB 2 π Λ
Δ k DFG = k SF k P k i 2 π Λ

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