Abstract

The soliton self-frequency shift in As2S3 is investigated theoretically. Detailed simulation under realistic conditions of the propagation of a low peak power pulse in a chalcogenide ridge waveguide shows the concepts of Raman soliton behaviour in silica to be transferrable to As2S3. Quantitatively, differences in the shapes of the Raman spectra in silica and As2S3 are predicted to lead to variations of less than 25 % in the frequency shift rate of a fundamental soliton. Thus we predict the effectiveness of the soliton self-frequency shift in contributing to wide bandwidth generation in low-power supercontinua at mid-infrared wavelengths in this highly nonlinear chalcogenide, as well as other nonlinear processing applications such as digital quantization for optical analogue to digital conversion.

© 2010 Optical Society of America

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    [CrossRef]
  2. J. Gopinath, M. Soljačić, E. Ippen, V. Fuflyigin, W. King, and M. Shurgalin, “Third order nonlinearities in Ge-As-Se-based glasses for telecommunications applications,” J. Appl. Phys. 96, 6931 (2004).
  3. M. Pelusi, F. Luan, T. Vo, M. Lamont, S. Madden, and D. Bulla, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nat. Photonics 3, 139–143 (2009).
    [CrossRef]
  4. J. Van Erps, F. Luan, M. Pelusi, T. Iredale, S. Madden, D.-Y. Choi, D. Bulla, B. Luther-Davies, H. Thienpont, and B. Eggleton, “High-resolution optical sampling of 640-Gb/s data using four-wave mixing in dispersion engineered highly nonlinear As2S3 planar waveguides,” J. Lightwave Technol. 28, 209–215 (2010).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  11. M. R. Lamont, B. Luther-Davies, D.-Y. Choi, S. Madden, and B. J. Eggleton, “Supercontinuum generation in dispersion engineered highly nonlinear γ = 10/W/m) As2S3 chalcogenide planar waveguide,” Opt. Express 16, 14938–14944 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
  15. C. Xu and X. Liu, “Photonic analog-to-digital converter using soliton self-frequency shift and interleaving spectral filters,” Opt. Lett. 28, 986–988 (2003).
    [CrossRef] [PubMed]
  16. R. Pant, C. Xiong, S. Madden, B. L. Davies, and B. J. Eggleton, “Investigation of all-optical analog-to-digital quantization using a chalcogenide waveguide: A step towards on-chip analog-to-digital conversion,” Opt. Commun. 283, 2258–2262 (2010).
    [CrossRef]
  17. R. H. Stolen and E. P. Ippen, “Raman gain in glass optical waveguides,” Appl. Phys. Lett. 22, 276–278 (1973).
    [CrossRef]
  18. R. J. Kobliska and S. A. Solin, “Temperature dependence of the Raman spectrum and the depolarization spectrum of amorphous As2S3,” Phys. Rev. B 8, 756–768 (1973).
    [CrossRef]
  19. K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
    [CrossRef]
  20. J. Laegsgaard, “Mode profile dispersion in the generalised nonlinear Schrödinger equation,” Opt. Express 15, 16110–16123 (2007).
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    [CrossRef]
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  24. A. C. Judge, O. Bang, B. J. Eggleton, B. T. Kuhlmey, E. C. Mägi, R. Pant, and C. M. de Sterke, “Optimization of the soliton self-frequency shift in a tapered photonic crystal fiber,” J. Opt. Soc. Am. B 26, 2064–2071 (2009).
    [CrossRef]
  25. R. Hellwarth, J. Cherlow, and T.-T. Yang, “Origin and frequency dependence of nonlinear optical susceptibilities of glasses,” Phys. Rev. B 11, 964–967 (1975).
    [CrossRef]
  26. C. Xiong, E. Magi, F. Luan, A. Tuniz, S. Dekker, J. S. Sanghera, L. B. Shaw, I. D. Aggarwal, and B. J. Eggleton, “Characterization of picosecond pulse nonlinear propagation in chalcogenide As2S3 fiber,” Appl. Opt. 48, 5467–5474 (2009).
    [CrossRef] [PubMed]
  27. M. R. Lamont, C. M. de Sterke, and B. J. Eggleton, “Dispersion engineering of highly nonlinear As2S3 waveguides for parametric gain and wavelength conversion,” Opt. Express 15, 9458–9463 (2007).
    [CrossRef] [PubMed]
  28. O. Sinkin, R. Holzlohner, J. Zweck, and C. R. Menyuk, “Optimization of the split-step Fourier method in modeling optical-fiber communications systems,” J. Lightwave Technol. 21, 61–68 (2003).
    [CrossRef]
  29. A. V. Gorbach and D. V. Skryabin, “Theory of radiation trapping by the accelerating solitons in optical fibers,” Phys. Rev. A 76, 053803 (2007).
    [CrossRef]
  30. P. Beaud, W. Hodel, B. Zysset, and H. Weber, “Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single–mode optical fiber,” IEEE J. Quantum Electron. 23, 1938–1946 (1987).
    [CrossRef]
  31. V. K. Tikhomirov, L. F. Santos, R. M. Almeida, A. Jha, J. Kobelke, and M. Scheffler, “On the origin of the boson peak in the raman scattering spectrum of As2S3 glass,” J. Non-Cryst. Solids 284, 198–202 (2001).
    [CrossRef]

2010 (3)

2009 (3)

2008 (4)

2007 (4)

2006 (1)

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

2004 (1)

J. Gopinath, M. Soljačić, E. Ippen, V. Fuflyigin, W. King, and M. Shurgalin, “Third order nonlinearities in Ge-As-Se-based glasses for telecommunications applications,” J. Appl. Phys. 96, 6931 (2004).

2003 (3)

2001 (1)

V. K. Tikhomirov, L. F. Santos, R. M. Almeida, A. Jha, J. Kobelke, and M. Scheffler, “On the origin of the boson peak in the raman scattering spectrum of As2S3 glass,” J. Non-Cryst. Solids 284, 198–202 (2001).
[CrossRef]

1999 (1)

J. S. Sanghera and I. D. Aggarwal, “Active and passive chalcogenide glass optical fibers for IR applications: a review,” J. Non-Cryst. Solids 256–257, 6–16 (1999).
[CrossRef]

1989 (2)

R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, “Raman response function of silica-core fibers,” J. Opt. Soc. Am. B 6, 1159–1166 (1989).
[CrossRef]

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[CrossRef]

1987 (1)

P. Beaud, W. Hodel, B. Zysset, and H. Weber, “Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single–mode optical fiber,” IEEE J. Quantum Electron. 23, 1938–1946 (1987).
[CrossRef]

1986 (2)

1975 (1)

R. Hellwarth, J. Cherlow, and T.-T. Yang, “Origin and frequency dependence of nonlinear optical susceptibilities of glasses,” Phys. Rev. B 11, 964–967 (1975).
[CrossRef]

1973 (2)

R. H. Stolen and E. P. Ippen, “Raman gain in glass optical waveguides,” Appl. Phys. Lett. 22, 276–278 (1973).
[CrossRef]

R. J. Kobliska and S. A. Solin, “Temperature dependence of the Raman spectrum and the depolarization spectrum of amorphous As2S3,” Phys. Rev. B 8, 756–768 (1973).
[CrossRef]

Aggarwal, I. D.

Almeida, R. M.

V. K. Tikhomirov, L. F. Santos, R. M. Almeida, A. Jha, J. Kobelke, and M. Scheffler, “On the origin of the boson peak in the raman scattering spectrum of As2S3 glass,” J. Non-Cryst. Solids 284, 198–202 (2001).
[CrossRef]

Bang, O.

Beaud, P.

P. Beaud, W. Hodel, B. Zysset, and H. Weber, “Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single–mode optical fiber,” IEEE J. Quantum Electron. 23, 1938–1946 (1987).
[CrossRef]

Blow, K. J.

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[CrossRef]

Bookey, H. T.

Bulla, D.

Cerullo, G.

Cherlow, J.

R. Hellwarth, J. Cherlow, and T.-T. Yang, “Origin and frequency dependence of nonlinear optical susceptibilities of glasses,” Phys. Rev. B 11, 964–967 (1975).
[CrossRef]

Chiodo, N.

Choi, D.-Y.

Coen, S.

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

Davies, B. L.

R. Pant, C. Xiong, S. Madden, B. L. Davies, and B. J. Eggleton, “Investigation of all-optical analog-to-digital quantization using a chalcogenide waveguide: A step towards on-chip analog-to-digital conversion,” Opt. Commun. 283, 2258–2262 (2010).
[CrossRef]

de Sterke, C. M.

Dekker, S.

Dudley, J. M.

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

Eggleton, B.

Eggleton, B. J.

R. Pant, C. Xiong, S. Madden, B. L. Davies, and B. J. Eggleton, “Investigation of all-optical analog-to-digital quantization using a chalcogenide waveguide: A step towards on-chip analog-to-digital conversion,” Opt. Commun. 283, 2258–2262 (2010).
[CrossRef]

C. Xiong, E. Magi, F. Luan, A. Tuniz, S. Dekker, J. S. Sanghera, L. B. Shaw, I. D. Aggarwal, and B. J. Eggleton, “Characterization of picosecond pulse nonlinear propagation in chalcogenide As2S3 fiber,” Appl. Opt. 48, 5467–5474 (2009).
[CrossRef] [PubMed]

A. C. Judge, O. Bang, B. J. Eggleton, B. T. Kuhlmey, E. C. Mägi, R. Pant, and C. M. de Sterke, “Optimization of the soliton self-frequency shift in a tapered photonic crystal fiber,” J. Opt. Soc. Am. B 26, 2064–2071 (2009).
[CrossRef]

M. R. Lamont, B. Luther-Davies, D.-Y. Choi, S. Madden, and B. J. Eggleton, “Supercontinuum generation in dispersion engineered highly nonlinear γ = 10/W/m) As2S3 chalcogenide planar waveguide,” Opt. Express 16, 14938–14944 (2008).
[CrossRef] [PubMed]

D.-I. Yeom, E. C. Mägi, M. R. E. Lamont, M. A. F. Roelens, L. Fu, and B. J. Eggleton, “Low-threshold supercontinuum generation in highly nonlinear chalcogenide nanowires,” Opt. Lett. 33, 660–662 (2008).
[CrossRef] [PubMed]

M. R. Lamont, C. M. de Sterke, and B. J. Eggleton, “Dispersion engineering of highly nonlinear As2S3 waveguides for parametric gain and wavelength conversion,” Opt. Express 15, 9458–9463 (2007).
[CrossRef] [PubMed]

Fu, L.

Fuflyigin, V.

J. Gopinath, M. Soljačić, E. Ippen, V. Fuflyigin, W. King, and M. Shurgalin, “Third order nonlinearities in Ge-As-Se-based glasses for telecommunications applications,” J. Appl. Phys. 96, 6931 (2004).

Genty, G.

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

Gopinath, J.

J. Gopinath, M. Soljačić, E. Ippen, V. Fuflyigin, W. King, and M. Shurgalin, “Third order nonlinearities in Ge-As-Se-based glasses for telecommunications applications,” J. Appl. Phys. 96, 6931 (2004).

Gorbach, A. V.

A. V. Gorbach and D. V. Skryabin, “Theory of radiation trapping by the accelerating solitons in optical fibers,” Phys. Rev. A 76, 053803 (2007).
[CrossRef]

Gordon, J. P.

Haus, H. A.

Hellwarth, R.

R. Hellwarth, J. Cherlow, and T.-T. Yang, “Origin and frequency dependence of nonlinear optical susceptibilities of glasses,” Phys. Rev. B 11, 964–967 (1975).
[CrossRef]

Herrmann, J.

A. V. Husakou, and J. Herrmann, “Supercontinuum generation in photonic crystal fibers made from highly nonlinear glasses,” Appl. Phys. B 77, 227–234 (2003).
[CrossRef]

Hodel, W.

P. Beaud, W. Hodel, B. Zysset, and H. Weber, “Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single–mode optical fiber,” IEEE J. Quantum Electron. 23, 1938–1946 (1987).
[CrossRef]

Holzlohner, R.

Hu, J.

Husakou, A. V.

A. V. Husakou, and J. Herrmann, “Supercontinuum generation in photonic crystal fibers made from highly nonlinear glasses,” Appl. Phys. B 77, 227–234 (2003).
[CrossRef]

Ippen, E.

J. Gopinath, M. Soljačić, E. Ippen, V. Fuflyigin, W. King, and M. Shurgalin, “Third order nonlinearities in Ge-As-Se-based glasses for telecommunications applications,” J. Appl. Phys. 96, 6931 (2004).

Ippen, E. P.

R. H. Stolen and E. P. Ippen, “Raman gain in glass optical waveguides,” Appl. Phys. Lett. 22, 276–278 (1973).
[CrossRef]

Iredale, T.

Jha, A.

N. D. Psaila, R. R. Thomson, H. T. Bookey, S. Shen, N. Chiodo, R. Osellame, G. Cerullo, A. Jha, and A. K. Kar, “Supercontinuum generation in an ultrafast laser inscribed chalcogenide glass waveguide,” Opt. Express 15, 15776–15781 (2007).
[CrossRef] [PubMed]

V. K. Tikhomirov, L. F. Santos, R. M. Almeida, A. Jha, J. Kobelke, and M. Scheffler, “On the origin of the boson peak in the raman scattering spectrum of As2S3 glass,” J. Non-Cryst. Solids 284, 198–202 (2001).
[CrossRef]

Judge, A. C.

Kar, A. K.

King, W.

J. Gopinath, M. Soljačić, E. Ippen, V. Fuflyigin, W. King, and M. Shurgalin, “Third order nonlinearities in Ge-As-Se-based glasses for telecommunications applications,” J. Appl. Phys. 96, 6931 (2004).

Kobelke, J.

V. K. Tikhomirov, L. F. Santos, R. M. Almeida, A. Jha, J. Kobelke, and M. Scheffler, “On the origin of the boson peak in the raman scattering spectrum of As2S3 glass,” J. Non-Cryst. Solids 284, 198–202 (2001).
[CrossRef]

Kobliska, R. J.

R. J. Kobliska and S. A. Solin, “Temperature dependence of the Raman spectrum and the depolarization spectrum of amorphous As2S3,” Phys. Rev. B 8, 756–768 (1973).
[CrossRef]

Kuhlmey, B. T.

Laegsgaard, J.

Lamont, M.

M. Pelusi, F. Luan, T. Vo, M. Lamont, S. Madden, and D. Bulla, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nat. Photonics 3, 139–143 (2009).
[CrossRef]

Lamont, M. R.

Lamont, M. R. E.

Lee, J. H.

J. H. Lee, J. van Howe, C. Xu, and X. Liu, “Soliton self-frequency shift: Experimental demonstrations and applications,” IEEE J. Sel. Top. Quantum Electron. 14, 713–723 (2008).
[CrossRef]

Liu, X.

J. H. Lee, J. van Howe, C. Xu, and X. Liu, “Soliton self-frequency shift: Experimental demonstrations and applications,” IEEE J. Sel. Top. Quantum Electron. 14, 713–723 (2008).
[CrossRef]

C. Xu and X. Liu, “Photonic analog-to-digital converter using soliton self-frequency shift and interleaving spectral filters,” Opt. Lett. 28, 986–988 (2003).
[CrossRef] [PubMed]

Luan, F.

Luther-Davies, B.

Madden, S.

J. Van Erps, F. Luan, M. Pelusi, T. Iredale, S. Madden, D.-Y. Choi, D. Bulla, B. Luther-Davies, H. Thienpont, and B. Eggleton, “High-resolution optical sampling of 640-Gb/s data using four-wave mixing in dispersion engineered highly nonlinear As2S3 planar waveguides,” J. Lightwave Technol. 28, 209–215 (2010).
[CrossRef]

R. Pant, C. Xiong, S. Madden, B. L. Davies, and B. J. Eggleton, “Investigation of all-optical analog-to-digital quantization using a chalcogenide waveguide: A step towards on-chip analog-to-digital conversion,” Opt. Commun. 283, 2258–2262 (2010).
[CrossRef]

M. Pelusi, F. Luan, T. Vo, M. Lamont, S. Madden, and D. Bulla, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nat. Photonics 3, 139–143 (2009).
[CrossRef]

M. R. Lamont, B. Luther-Davies, D.-Y. Choi, S. Madden, and B. J. Eggleton, “Supercontinuum generation in dispersion engineered highly nonlinear γ = 10/W/m) As2S3 chalcogenide planar waveguide,” Opt. Express 16, 14938–14944 (2008).
[CrossRef] [PubMed]

Magi, E.

Mägi, E. C.

Menyuk, C. R.

Mitschke, F. M.

Mollenauer, L. F.

Osellame, R.

Pant, R.

R. Pant, C. Xiong, S. Madden, B. L. Davies, and B. J. Eggleton, “Investigation of all-optical analog-to-digital quantization using a chalcogenide waveguide: A step towards on-chip analog-to-digital conversion,” Opt. Commun. 283, 2258–2262 (2010).
[CrossRef]

A. C. Judge, O. Bang, B. J. Eggleton, B. T. Kuhlmey, E. C. Mägi, R. Pant, and C. M. de Sterke, “Optimization of the soliton self-frequency shift in a tapered photonic crystal fiber,” J. Opt. Soc. Am. B 26, 2064–2071 (2009).
[CrossRef]

Pelusi, M.

Psaila, N. D.

Roelens, M. A. F.

Sanghera, J. S.

Santos, L. F.

V. K. Tikhomirov, L. F. Santos, R. M. Almeida, A. Jha, J. Kobelke, and M. Scheffler, “On the origin of the boson peak in the raman scattering spectrum of As2S3 glass,” J. Non-Cryst. Solids 284, 198–202 (2001).
[CrossRef]

Scheffler, M.

V. K. Tikhomirov, L. F. Santos, R. M. Almeida, A. Jha, J. Kobelke, and M. Scheffler, “On the origin of the boson peak in the raman scattering spectrum of As2S3 glass,” J. Non-Cryst. Solids 284, 198–202 (2001).
[CrossRef]

Shaw, L. B.

Shen, S.

Shurgalin, M.

J. Gopinath, M. Soljačić, E. Ippen, V. Fuflyigin, W. King, and M. Shurgalin, “Third order nonlinearities in Ge-As-Se-based glasses for telecommunications applications,” J. Appl. Phys. 96, 6931 (2004).

Sinkin, O.

Skryabin, D. V.

A. V. Gorbach and D. V. Skryabin, “Theory of radiation trapping by the accelerating solitons in optical fibers,” Phys. Rev. A 76, 053803 (2007).
[CrossRef]

Solin, S. A.

R. J. Kobliska and S. A. Solin, “Temperature dependence of the Raman spectrum and the depolarization spectrum of amorphous As2S3,” Phys. Rev. B 8, 756–768 (1973).
[CrossRef]

Soljacic, M.

J. Gopinath, M. Soljačić, E. Ippen, V. Fuflyigin, W. King, and M. Shurgalin, “Third order nonlinearities in Ge-As-Se-based glasses for telecommunications applications,” J. Appl. Phys. 96, 6931 (2004).

Stolen, R. H.

Thienpont, H.

Thomson, R. R.

Tikhomirov, V. K.

V. K. Tikhomirov, L. F. Santos, R. M. Almeida, A. Jha, J. Kobelke, and M. Scheffler, “On the origin of the boson peak in the raman scattering spectrum of As2S3 glass,” J. Non-Cryst. Solids 284, 198–202 (2001).
[CrossRef]

Tomlinson, W. J.

Tuniz, A.

Van Erps, J.

van Howe, J.

J. H. Lee, J. van Howe, C. Xu, and X. Liu, “Soliton self-frequency shift: Experimental demonstrations and applications,” IEEE J. Sel. Top. Quantum Electron. 14, 713–723 (2008).
[CrossRef]

Vo, T.

M. Pelusi, F. Luan, T. Vo, M. Lamont, S. Madden, and D. Bulla, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nat. Photonics 3, 139–143 (2009).
[CrossRef]

Voronin, A. A.

Weber, H.

P. Beaud, W. Hodel, B. Zysset, and H. Weber, “Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single–mode optical fiber,” IEEE J. Quantum Electron. 23, 1938–1946 (1987).
[CrossRef]

Wood, D.

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[CrossRef]

Xiong, C.

R. Pant, C. Xiong, S. Madden, B. L. Davies, and B. J. Eggleton, “Investigation of all-optical analog-to-digital quantization using a chalcogenide waveguide: A step towards on-chip analog-to-digital conversion,” Opt. Commun. 283, 2258–2262 (2010).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

(a) Raman spectra and (b) spectral response functions R for bulk samples of As2S3 (solid blue lines) and silica (broken red lines).

Fig. 2.
Fig. 2.

Light guiding properties of As2S3 rib waveguide TM mode with predominantly vertically (y) polarized electric field: (a) normalised vertical electric field (Ey ) profile, (b) GVD, and (c) effective mode area. The base of the chalcogenide layer in (a) lies at y = 0.

Fig. 3.
Fig. 3.

(a) Spectrogram of final pulse and (b) spectral evolution of initial sech pulse with N = 3.9 propagated along a 20 cm ridge waveguide. The colour dB scale is the same for both subfigures.

Equations (11)

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+ i ω n n 2 c n eff 1 2 ( ω ) A eff 1 4 ( ω ) d δ 2 π d δ 2 π
× h ˜ ( δ ) G ˜ ( z , δ δ ) G ˜ ( z , δ δ ) G ˜ * ( z , δ ) ,
G ˜ ( z , δ ) = F ˜ ( z , δ ) n eff 1 2 ( ω ) A eff 1 4 ( ω ) ,
h ( t ) = ( 1 f R ) δ ( t ) + 2 3 f R h R ( t ) ,
d ω ¯ dz = β 2 T s 3 f R 1 f R R ( T s ) ,
R ( T s ) = π 2 T s 4 6 0 d ω 2 π α R ( ω ) ω 3 sinh 2 ( π T s ω 2 ) .
γ ( ω ) = ω n n 2 ( 1 f R ) c n eff 2 ( ω ) A eff ( ω ) .
T s ( ω ¯ ) = 2 β 2 ( ω ¯ ) γ ( ω ¯ ) E ( ω ¯ ) .
T s ( ω ¯ ) = 2 β 2 ( ω ¯ ) ω ¯ 0 γ ( ω ¯ ) E 0 ( ω ¯ ) ,
d ω ¯ d ζ = f R T s R ( T s ) ,
f R = ( 2.90 γ α R ( ω peak ) L eff ) 1 dg R dP 0 ,

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