Abstract

We experimentally demonstrate the nonlinear generation of frequency-dissymmetric sidebands by injecting picosecond pump pulses inside the fundamental mode of a silica-core photonic crystal fiber in its normal dispersion regime. A systematic analysis highlights the fact that this phenomenon is based on the combination of the two major nonlinear effects occurring inside the fiber: self-phase modulation and degenerate four-wave mixing.

© 2013 Optical Society of America

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References

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  1. M. Marhic, Fiber Optical Parametric Amplifiers, Oscillators and Related Devices (Cambridge University, 2012).
  2. J. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
    [CrossRef]
  3. G. Agrawal, Applications of Nonlinear Fiber Optics (Academic, 2008).
  4. J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8, 506–520 (2002).
    [CrossRef]
  5. L. Wang, C. Hong, and S. Friberg, “Generation of correlated photons via four-wave mixing in optical fibers,” J. Opt. B 3, 346–352 (2001).
    [CrossRef]
  6. O. Alibart, J. Fulconis, G. Wong, S. Murdoch, W. Wadsworth, and J. Rarity, “Photon-pair generation using four-wave mixing in a microstructured fiber: theory versus experiment,” New J. Phys. 8, 67 (2006).
    [CrossRef]
  7. J. Fan, A. Migdall, J. Chen, E. Goldschmidt, and A. Ling, “Microstructure fiber-based source of photonic entanglement,” IEEE J. Sel. Top. Quantum Electron. 15, 1724–1732 (2009).
    [CrossRef]
  8. P. Russel, “Photonic-crystal fibers,” J. Lightwave Technol. 24, 4729–4749 (2006).
    [CrossRef]
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    [CrossRef]
  10. S. Coen, A. L. Chau, R. Leonhardt, J. Harvey, J. Knight, W. Wadsworth, and P. Russel, “Supercontinuum generation by stimulated Raman scattering and parametric four-wave mixing in photonic crystal fibers,” J. Opt. Soc. Am. B 19, 753–764 (2002).
    [CrossRef]
  11. P. Roberts, P. Mangan, H. Sabert, F. Couny, T. Birks, J. Knight, and P. Russel, “Control of dispersion in photonic crystal fibers,” J. Opt. Fiber. Commun. Rep. 2, 435–461 (2005).
    [CrossRef]
  12. F. Benabid, J. Knight, G. Antonopoulos, and P. Russel, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
    [CrossRef]
  13. S. Lebrun, P. Delaye, R. Frey, and G. Roosen, “High-efficiency single-mode Raman generation in a liquid-filled photonic bandgap fiber,” Opt. Lett. 32, 337–339 (2007).
    [CrossRef]
  14. G. Agrawal, Nonlinear Fiber Optics (Academic, 2007).
  15. M.-C. Phan Huy, A. Baron, S. Lebrun, R. Frey, and P. Delaye, “Characterization of self-phase modulation in liquid-filled hollow core photonic bandgap fibers,” J. Opt. Soc. Am. B 27, 1886–1893 (2010).
    [CrossRef]
  16. A. Bogris, D. Syvridis, P. Kylemark, and P. Andrekson, “Noise characteristics of dual-pump fiber-optic parametric amplifiers,” J. Lightwave Technol. 23, 2788–2795 (2005).
    [CrossRef]
  17. A. Weiner, Ultrafast Optics (Wiley, 2009).
  18. K. Saitoh and M. Koshiba, “Empirical relations for simple design of photonic crystal fibers,” Opt. Express 13, 267–274 (2005).
    [CrossRef]
  19. M. Koshiba and K. Saitoh, “Applicability of classical optical fiber theories to holey fibers,” Opt. Lett. 29, 1739–1741 (2004).
    [CrossRef]

2010 (1)

2009 (1)

J. Fan, A. Migdall, J. Chen, E. Goldschmidt, and A. Ling, “Microstructure fiber-based source of photonic entanglement,” IEEE J. Sel. Top. Quantum Electron. 15, 1724–1732 (2009).
[CrossRef]

2007 (1)

2006 (3)

O. Alibart, J. Fulconis, G. Wong, S. Murdoch, W. Wadsworth, and J. Rarity, “Photon-pair generation using four-wave mixing in a microstructured fiber: theory versus experiment,” New J. Phys. 8, 67 (2006).
[CrossRef]

P. Russel, “Photonic-crystal fibers,” J. Lightwave Technol. 24, 4729–4749 (2006).
[CrossRef]

J. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[CrossRef]

2005 (3)

2004 (1)

2003 (1)

2002 (3)

S. Coen, A. L. Chau, R. Leonhardt, J. Harvey, J. Knight, W. Wadsworth, and P. Russel, “Supercontinuum generation by stimulated Raman scattering and parametric four-wave mixing in photonic crystal fibers,” J. Opt. Soc. Am. B 19, 753–764 (2002).
[CrossRef]

F. Benabid, J. Knight, G. Antonopoulos, and P. Russel, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[CrossRef]

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8, 506–520 (2002).
[CrossRef]

2001 (1)

L. Wang, C. Hong, and S. Friberg, “Generation of correlated photons via four-wave mixing in optical fibers,” J. Opt. B 3, 346–352 (2001).
[CrossRef]

Agrawal, G.

G. Agrawal, Applications of Nonlinear Fiber Optics (Academic, 2008).

G. Agrawal, Nonlinear Fiber Optics (Academic, 2007).

Alibart, O.

O. Alibart, J. Fulconis, G. Wong, S. Murdoch, W. Wadsworth, and J. Rarity, “Photon-pair generation using four-wave mixing in a microstructured fiber: theory versus experiment,” New J. Phys. 8, 67 (2006).
[CrossRef]

Andrekson, P.

A. Bogris, D. Syvridis, P. Kylemark, and P. Andrekson, “Noise characteristics of dual-pump fiber-optic parametric amplifiers,” J. Lightwave Technol. 23, 2788–2795 (2005).
[CrossRef]

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8, 506–520 (2002).
[CrossRef]

Antonopoulos, G.

F. Benabid, J. Knight, G. Antonopoulos, and P. Russel, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[CrossRef]

Baron, A.

Benabid, F.

F. Benabid, J. Knight, G. Antonopoulos, and P. Russel, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[CrossRef]

Birks, T.

P. Roberts, P. Mangan, H. Sabert, F. Couny, T. Birks, J. Knight, and P. Russel, “Control of dispersion in photonic crystal fibers,” J. Opt. Fiber. Commun. Rep. 2, 435–461 (2005).
[CrossRef]

Bogris, A.

Chau, A. L.

Chen, J.

J. Fan, A. Migdall, J. Chen, E. Goldschmidt, and A. Ling, “Microstructure fiber-based source of photonic entanglement,” IEEE J. Sel. Top. Quantum Electron. 15, 1724–1732 (2009).
[CrossRef]

Coen, S.

Couny, F.

P. Roberts, P. Mangan, H. Sabert, F. Couny, T. Birks, J. Knight, and P. Russel, “Control of dispersion in photonic crystal fibers,” J. Opt. Fiber. Commun. Rep. 2, 435–461 (2005).
[CrossRef]

Delaye, P.

Dudley, J.

J. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[CrossRef]

Fan, J.

J. Fan, A. Migdall, J. Chen, E. Goldschmidt, and A. Ling, “Microstructure fiber-based source of photonic entanglement,” IEEE J. Sel. Top. Quantum Electron. 15, 1724–1732 (2009).
[CrossRef]

Finazzi, V.

Frey, R.

Friberg, S.

L. Wang, C. Hong, and S. Friberg, “Generation of correlated photons via four-wave mixing in optical fibers,” J. Opt. B 3, 346–352 (2001).
[CrossRef]

Fulconis, J.

O. Alibart, J. Fulconis, G. Wong, S. Murdoch, W. Wadsworth, and J. Rarity, “Photon-pair generation using four-wave mixing in a microstructured fiber: theory versus experiment,” New J. Phys. 8, 67 (2006).
[CrossRef]

Genty, G.

J. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[CrossRef]

Goldschmidt, E.

J. Fan, A. Migdall, J. Chen, E. Goldschmidt, and A. Ling, “Microstructure fiber-based source of photonic entanglement,” IEEE J. Sel. Top. Quantum Electron. 15, 1724–1732 (2009).
[CrossRef]

Hansryd, J.

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8, 506–520 (2002).
[CrossRef]

Harvey, J.

Hedekvist, P.-O.

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8, 506–520 (2002).
[CrossRef]

Hong, C.

L. Wang, C. Hong, and S. Friberg, “Generation of correlated photons via four-wave mixing in optical fibers,” J. Opt. B 3, 346–352 (2001).
[CrossRef]

Knight, J.

P. Roberts, P. Mangan, H. Sabert, F. Couny, T. Birks, J. Knight, and P. Russel, “Control of dispersion in photonic crystal fibers,” J. Opt. Fiber. Commun. Rep. 2, 435–461 (2005).
[CrossRef]

F. Benabid, J. Knight, G. Antonopoulos, and P. Russel, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[CrossRef]

S. Coen, A. L. Chau, R. Leonhardt, J. Harvey, J. Knight, W. Wadsworth, and P. Russel, “Supercontinuum generation by stimulated Raman scattering and parametric four-wave mixing in photonic crystal fibers,” J. Opt. Soc. Am. B 19, 753–764 (2002).
[CrossRef]

Koshiba, M.

Kylemark, P.

Lebrun, S.

Leonhardt, R.

Li, J.

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8, 506–520 (2002).
[CrossRef]

Ling, A.

J. Fan, A. Migdall, J. Chen, E. Goldschmidt, and A. Ling, “Microstructure fiber-based source of photonic entanglement,” IEEE J. Sel. Top. Quantum Electron. 15, 1724–1732 (2009).
[CrossRef]

Mangan, P.

P. Roberts, P. Mangan, H. Sabert, F. Couny, T. Birks, J. Knight, and P. Russel, “Control of dispersion in photonic crystal fibers,” J. Opt. Fiber. Commun. Rep. 2, 435–461 (2005).
[CrossRef]

Marhic, M.

M. Marhic, Fiber Optical Parametric Amplifiers, Oscillators and Related Devices (Cambridge University, 2012).

Migdall, A.

J. Fan, A. Migdall, J. Chen, E. Goldschmidt, and A. Ling, “Microstructure fiber-based source of photonic entanglement,” IEEE J. Sel. Top. Quantum Electron. 15, 1724–1732 (2009).
[CrossRef]

Monro, T.

Murdoch, S.

O. Alibart, J. Fulconis, G. Wong, S. Murdoch, W. Wadsworth, and J. Rarity, “Photon-pair generation using four-wave mixing in a microstructured fiber: theory versus experiment,” New J. Phys. 8, 67 (2006).
[CrossRef]

Phan Huy, M.-C.

Rarity, J.

O. Alibart, J. Fulconis, G. Wong, S. Murdoch, W. Wadsworth, and J. Rarity, “Photon-pair generation using four-wave mixing in a microstructured fiber: theory versus experiment,” New J. Phys. 8, 67 (2006).
[CrossRef]

Richardson, D.

Roberts, P.

P. Roberts, P. Mangan, H. Sabert, F. Couny, T. Birks, J. Knight, and P. Russel, “Control of dispersion in photonic crystal fibers,” J. Opt. Fiber. Commun. Rep. 2, 435–461 (2005).
[CrossRef]

Roosen, G.

Russel, P.

P. Russel, “Photonic-crystal fibers,” J. Lightwave Technol. 24, 4729–4749 (2006).
[CrossRef]

P. Roberts, P. Mangan, H. Sabert, F. Couny, T. Birks, J. Knight, and P. Russel, “Control of dispersion in photonic crystal fibers,” J. Opt. Fiber. Commun. Rep. 2, 435–461 (2005).
[CrossRef]

F. Benabid, J. Knight, G. Antonopoulos, and P. Russel, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[CrossRef]

S. Coen, A. L. Chau, R. Leonhardt, J. Harvey, J. Knight, W. Wadsworth, and P. Russel, “Supercontinuum generation by stimulated Raman scattering and parametric four-wave mixing in photonic crystal fibers,” J. Opt. Soc. Am. B 19, 753–764 (2002).
[CrossRef]

Sabert, H.

P. Roberts, P. Mangan, H. Sabert, F. Couny, T. Birks, J. Knight, and P. Russel, “Control of dispersion in photonic crystal fibers,” J. Opt. Fiber. Commun. Rep. 2, 435–461 (2005).
[CrossRef]

Saitoh, K.

Syvridis, D.

Wadsworth, W.

O. Alibart, J. Fulconis, G. Wong, S. Murdoch, W. Wadsworth, and J. Rarity, “Photon-pair generation using four-wave mixing in a microstructured fiber: theory versus experiment,” New J. Phys. 8, 67 (2006).
[CrossRef]

S. Coen, A. L. Chau, R. Leonhardt, J. Harvey, J. Knight, W. Wadsworth, and P. Russel, “Supercontinuum generation by stimulated Raman scattering and parametric four-wave mixing in photonic crystal fibers,” J. Opt. Soc. Am. B 19, 753–764 (2002).
[CrossRef]

Wang, L.

L. Wang, C. Hong, and S. Friberg, “Generation of correlated photons via four-wave mixing in optical fibers,” J. Opt. B 3, 346–352 (2001).
[CrossRef]

Weiner, A.

A. Weiner, Ultrafast Optics (Wiley, 2009).

Westlund, M.

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8, 506–520 (2002).
[CrossRef]

Wong, G.

O. Alibart, J. Fulconis, G. Wong, S. Murdoch, W. Wadsworth, and J. Rarity, “Photon-pair generation using four-wave mixing in a microstructured fiber: theory versus experiment,” New J. Phys. 8, 67 (2006).
[CrossRef]

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

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8, 506–520 (2002).
[CrossRef]

J. Fan, A. Migdall, J. Chen, E. Goldschmidt, and A. Ling, “Microstructure fiber-based source of photonic entanglement,” IEEE J. Sel. Top. Quantum Electron. 15, 1724–1732 (2009).
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. B (1)

L. Wang, C. Hong, and S. Friberg, “Generation of correlated photons via four-wave mixing in optical fibers,” J. Opt. B 3, 346–352 (2001).
[CrossRef]

J. Opt. Fiber. Commun. Rep. (1)

P. Roberts, P. Mangan, H. Sabert, F. Couny, T. Birks, J. Knight, and P. Russel, “Control of dispersion in photonic crystal fibers,” J. Opt. Fiber. Commun. Rep. 2, 435–461 (2005).
[CrossRef]

J. Opt. Soc. Am. B (3)

New J. Phys. (1)

O. Alibart, J. Fulconis, G. Wong, S. Murdoch, W. Wadsworth, and J. Rarity, “Photon-pair generation using four-wave mixing in a microstructured fiber: theory versus experiment,” New J. Phys. 8, 67 (2006).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Rev. Mod. Phys. (1)

J. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[CrossRef]

Science (1)

F. Benabid, J. Knight, G. Antonopoulos, and P. Russel, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[CrossRef]

Other (4)

G. Agrawal, Nonlinear Fiber Optics (Academic, 2007).

M. Marhic, Fiber Optical Parametric Amplifiers, Oscillators and Related Devices (Cambridge University, 2012).

A. Weiner, Ultrafast Optics (Wiley, 2009).

G. Agrawal, Applications of Nonlinear Fiber Optics (Academic, 2008).

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Figures (13)

Fig. 1.
Fig. 1.

Measured (black curves) intensity spectra (in logarithmic scale) for an hyperbolic secant pulse (with an injected peak power equal to 407 W) at the input (a) and at the output (b) of a third-order nonlinear medium, with the simulated (red) spectra [see Eq. (5)] using parameters α=0.17m1, T0=1.1ps, ΦNL,max=6π, and z=0.97m and a central wavelength equal to 815 nm.

Fig. 2.
Fig. 2.

Calculated phase-matching curve (black) and amplification gain profile based on the GVD measurement (plotted with a pump peak power value of 200 W). Inset: scanning electronic microscopy (SEM) image of the transverse structure of our silica-core PCF.

Fig. 3.
Fig. 3.

Experimental setup used to observe frequency-dissymmetric FWM in our PCF. (Obj., microscope objective; HWP, half-wave plate; Imag., imaging lens.)

Fig. 4.
Fig. 4.

Example of frequency-dissymmetric spectrum, which has been observed when injecting picosecond hyperbolic secant pulses at 815 nm inside the fundamental mode of the PCF (OSA resolution: 2 nm, i.e., 0.9 THz). The spectral width of the injected beam is increased by a factor of about 100 due to SPM.

Fig. 5.
Fig. 5.

Comparison between the experimental location of the generated sidebands (for a quasi-constant injected pump peak power of about 200 W) with the phase-matching curve. The white straight line (y=x) corresponds to the value of λinj. Inset: typical spectrum observed in zone II.b, with double-maximum sidebands.

Fig. 6.
Fig. 6.

Evolution of λsource as a function of λinj. Crosses: anomalous dispersion regime and internal sideband (in the transition regime) results. Dots: external sideband (in the transition regime) results. Straight line (y=x): value of λinj. For values of λinj higher than 870 nm, λsource remains equal to λinj (the corresponding crosses, which are not plotted here, are still on the straight line).

Fig. 7.
Fig. 7.

Difference between internal and external maximum power level (in dB) as a function of the injected wavelength. For injected wavelengths higher than 834 nm (resp. lower than 825 nm) typically, the power difference between the two maxima can be evaluated with good reliability only on the idler (resp. signal) sideband; that is why only idler (resp. signal) data is plotted.

Fig. 8.
Fig. 8.

Average injected power used for the spectrum measurements presented in this subsection. Our experimental criterion was to keep, on the OSA, approximately the same sideband power level for all the measured spectra. This experimental data interestingly highlights a trend showing that the injected power has to be increased when λinj decreases from λ0. The solid line is a guideline.

Fig. 9.
Fig. 9.

Measured spectrum networks for λinj={873;830;825}nm and Pinj varying typically between 170 and 290 W for λinj=873nm, between 230 and 510 W for λinj=830nm, and between 330 and 530 W for λinj=825nm (OSA resolution: 2 nm). For λinj=873nm, we see the apparition of a cascade FWM process when Pinj is above 230 W typically.

Fig. 10.
Fig. 10.

Measured sideband power level (from spectra in Fig. 9) plotted as a function of the total injected power. Filled symbols: signal; empty symbols: idler; circles: anomalous dispersion regime (with λinj=873nm); squares: normal dispersion regime (with λinj=825nm); upward and downward triangles: internal and external maxima, respectively, in the transition regime (with λinj=830nm). The dashed and solid lines correspond to the simulation results with an interaction length LFWM=Leff=0.9Lfiber and LFWM=0.8Leff=0.7Lfiber, respectively.

Fig. 11.
Fig. 11.

Measured spectra for λinj=873nm and with an OSA spectral resolution of 2 nm. Black solid lines correspond to the simulation results [based on Eqs. (7) and (11)] with LFWM=0.8Leff=0.7Lfiber and pump peak powers equal to the injected peak powers: {175; 210; 225; 240} W.

Fig. 12.
Fig. 12.

Example of SPM-broadened spectrum recorded in linear scale and with an OSA resolution of 0.2 nm. Pinj is proportional to the integral of the entire spectrum (red); Puseful,828nm and Puseful,834nm are proportional to the integrals of the green part and the blue part, respectively (with the same proportionality factor).

Fig. 13.
Fig. 13.

Measured sideband power level plotted as a function of the “right” useful power Puseful,828nm. (See caption of Fig. 10.)

Tables (1)

Tables Icon

Table 1. Properties of Our Silica-Core PCF

Equations (15)

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ΦNL,max(z)=γPpLeff(z)=γPp1eαzα,
γ=ωpn2(I)cAeff,
δω(t)=ΦNL(t)t.
Δλ(z)Δλ(z=0)ΦNL,max(z).
I(ω;z)=I0eαzT02sech2(πωT02)×F22({12+iωT02,12iωT02},{12,1},iΦNL,max(z))×F22({12iωT02,12+iωT02},{12,1},iΦNL,max(z)),
β(ωs)+β(ωi)2β(ωp)+2γPp=0.
G(ωp;ω)=(γPpg(ωp;ω))2sinh2(g(ωp;ω)LFWM),
g(ωp;ω)=Δk(ωp;ω)2(2γPpΔk(ωp;ω)2)
Δk(ωp;ω)=2β(ωp)β(ω)β(2ωpω).
Gmax(ωp;ωs)=sinh2(γPpLFWM)=sinh2(ΦNL,maxLFWMLeff),
P(ωp;ω;Δω)=h4π2ωΔω2ω+Δω2(G(ωp;ω)12)ωdω.
P(ωp;ω;Δω)h4π2ωΔω(G(ωp;ω)12),
Pmax(ωp;ωs;Δω)h4π2ωsΔωsinh2(ΦNL,maxLFWMLeff).
β2(ω)=(K0+K1ω+K2ω2+K3ω3),
K0=1.8110500896234425·1024,K1=2.1530389065354214·1039,K2=8.706787346496974·1055,K3=1.2061182225010229·1070.

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