Abstract

The spectral spacing of the interference fringes formed by a pair of long-period fiber gratings was investigated. The variation of the fringe spacing was measured while the separation between the gratings was changed from 22 to 500 mm. When the grating separation was much longer than the length of the individual grating, the inverse of the fringe spacing became linearly proportional to the grating separation and to the differential effective group index of the fiber. In the third stop band of the grating pair, made along a dispersion-shifted fiber centered at 1.55 µm, the differential effective group index was calculated to be ∼6.4 × 10-3, which is approximately twice the differential effective index of the fiber. The discrepancy between the two indices was observed to decrease with the band order, a phenomenon that is explained by the first-order dispersion of the fiber. The measured interference fringes were not regularly spaced in the frequency domain, but regular spacing is required in wavelength-division multiplexing communication systems. Analysis of the second-order dispersion of the fiber and the grating-induced nonlinear phase shift within grating regions as the factors that induce chirping on the fringe spacing is presented.

© 1999 Optical Society of America

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References

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  1. E. M. Dianov, S. A. Vasiliev, A. S. Kurkov, O. I. Medvedkov, V. N. Protopopov, “In-fiber Mach–Zehnder interferometer based on a pair of long-period gratings,” in Proceedings of European Conference on Optical Communication (Interuniversity Microelectronics Center, Ghent, Belgium, 1996), pp. 65–68.
  2. L. Tallone, L. Boschis, L. Cognolato, E. Emelli, E. Riccardi, O. Rossotto, “Narrow-band rejection filters through fabrication of in-series long-period gratings,” in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. 175.
  3. D. S. Starodubov, V. Grubsky, A. Skorucak, J. Feinberg, J. X. Cai, K. M. Feng, A. E. Willner, “Novel fiber amplitude modulators for dynamic channel power equalization in WDM systems,” in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. PD8-1–PD8-4.
  4. X. J. Gu, “Wavelength-division multiplexing isolation fiber filter and light source using cascaded long-period fiber gratings,” Opt. Lett. 23, 509–510 (1998).
    [CrossRef]
  5. A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–64 (1996).
    [CrossRef]
  6. B. H. Lee, Y. Liu, S. B. Lee, S. S. Choi, J. N. Jang, “Displacements of the resonant peaks of a long-period fiber grating induced by a change of ambient refractive index,” Opt. Lett. 22, 1769–1771 (1997).
    [CrossRef]
  7. B. H. Lee, J. Nishii, “Bending sensitivity of in-series long-period fiber gratings,” Opt. Lett. 23, 1624–1626 (1998).
    [CrossRef]
  8. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley-Interscience, New York, 1984), pp. 177–185.
  9. M. J. Adams, An Introduction to Optical Waveguides (Wiley-Interscience, New York, 1980), Chap. 7.
  10. A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, P. J. Lemaire, N. S. Bergano, C. R. Davidson, “Long-period fiber-grating-based gain equalizers,” Opt. Lett. 21, 336–338 (1996).
    [CrossRef] [PubMed]
  11. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1293 (1997).
    [CrossRef]
  12. N. Kuwaki, M. Ohashi, C. Tanaka, N. Uesugi, S. Seikai, Y. Negishi, “Characteristics of dispersion-shifted dual shape core single-mode fibers,” J. Lightwave Technol. LT-5, 792–797 (1987).
    [CrossRef]
  13. G. Keiser, Optical Fiber Communications, 2 ed. (McGraw-Hill, New York, 1991), Chap. 3.
  14. B. H. Lee, J. Nishii, “Self-interference of a long-period fiber grating and its application as a temperature sensor,” Electron. Lett. 34, 2059–2060 (1998).
    [CrossRef]

1998 (3)

1997 (2)

1996 (2)

A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, P. J. Lemaire, N. S. Bergano, C. R. Davidson, “Long-period fiber-grating-based gain equalizers,” Opt. Lett. 21, 336–338 (1996).
[CrossRef] [PubMed]

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–64 (1996).
[CrossRef]

1987 (1)

N. Kuwaki, M. Ohashi, C. Tanaka, N. Uesugi, S. Seikai, Y. Negishi, “Characteristics of dispersion-shifted dual shape core single-mode fibers,” J. Lightwave Technol. LT-5, 792–797 (1987).
[CrossRef]

Adams, M. J.

M. J. Adams, An Introduction to Optical Waveguides (Wiley-Interscience, New York, 1980), Chap. 7.

Bergano, N. S.

Bhatia, V.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–64 (1996).
[CrossRef]

Boschis, L.

L. Tallone, L. Boschis, L. Cognolato, E. Emelli, E. Riccardi, O. Rossotto, “Narrow-band rejection filters through fabrication of in-series long-period gratings,” in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. 175.

Cai, J. X.

D. S. Starodubov, V. Grubsky, A. Skorucak, J. Feinberg, J. X. Cai, K. M. Feng, A. E. Willner, “Novel fiber amplitude modulators for dynamic channel power equalization in WDM systems,” in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. PD8-1–PD8-4.

Choi, S. S.

Cognolato, L.

L. Tallone, L. Boschis, L. Cognolato, E. Emelli, E. Riccardi, O. Rossotto, “Narrow-band rejection filters through fabrication of in-series long-period gratings,” in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. 175.

Davidson, C. R.

Dianov, E. M.

E. M. Dianov, S. A. Vasiliev, A. S. Kurkov, O. I. Medvedkov, V. N. Protopopov, “In-fiber Mach–Zehnder interferometer based on a pair of long-period gratings,” in Proceedings of European Conference on Optical Communication (Interuniversity Microelectronics Center, Ghent, Belgium, 1996), pp. 65–68.

Emelli, E.

L. Tallone, L. Boschis, L. Cognolato, E. Emelli, E. Riccardi, O. Rossotto, “Narrow-band rejection filters through fabrication of in-series long-period gratings,” in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. 175.

Erdogan, T.

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1293 (1997).
[CrossRef]

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–64 (1996).
[CrossRef]

Feinberg, J.

D. S. Starodubov, V. Grubsky, A. Skorucak, J. Feinberg, J. X. Cai, K. M. Feng, A. E. Willner, “Novel fiber amplitude modulators for dynamic channel power equalization in WDM systems,” in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. PD8-1–PD8-4.

Feng, K. M.

D. S. Starodubov, V. Grubsky, A. Skorucak, J. Feinberg, J. X. Cai, K. M. Feng, A. E. Willner, “Novel fiber amplitude modulators for dynamic channel power equalization in WDM systems,” in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. PD8-1–PD8-4.

Grubsky, V.

D. S. Starodubov, V. Grubsky, A. Skorucak, J. Feinberg, J. X. Cai, K. M. Feng, A. E. Willner, “Novel fiber amplitude modulators for dynamic channel power equalization in WDM systems,” in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. PD8-1–PD8-4.

Gu, X. J.

Jang, J. N.

Judkins, J. B.

A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, P. J. Lemaire, N. S. Bergano, C. R. Davidson, “Long-period fiber-grating-based gain equalizers,” Opt. Lett. 21, 336–338 (1996).
[CrossRef] [PubMed]

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–64 (1996).
[CrossRef]

Keiser, G.

G. Keiser, Optical Fiber Communications, 2 ed. (McGraw-Hill, New York, 1991), Chap. 3.

Kurkov, A. S.

E. M. Dianov, S. A. Vasiliev, A. S. Kurkov, O. I. Medvedkov, V. N. Protopopov, “In-fiber Mach–Zehnder interferometer based on a pair of long-period gratings,” in Proceedings of European Conference on Optical Communication (Interuniversity Microelectronics Center, Ghent, Belgium, 1996), pp. 65–68.

Kuwaki, N.

N. Kuwaki, M. Ohashi, C. Tanaka, N. Uesugi, S. Seikai, Y. Negishi, “Characteristics of dispersion-shifted dual shape core single-mode fibers,” J. Lightwave Technol. LT-5, 792–797 (1987).
[CrossRef]

Lee, B. H.

Lee, S. B.

Lemaire, P. J.

A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, P. J. Lemaire, N. S. Bergano, C. R. Davidson, “Long-period fiber-grating-based gain equalizers,” Opt. Lett. 21, 336–338 (1996).
[CrossRef] [PubMed]

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–64 (1996).
[CrossRef]

Liu, Y.

Medvedkov, O. I.

E. M. Dianov, S. A. Vasiliev, A. S. Kurkov, O. I. Medvedkov, V. N. Protopopov, “In-fiber Mach–Zehnder interferometer based on a pair of long-period gratings,” in Proceedings of European Conference on Optical Communication (Interuniversity Microelectronics Center, Ghent, Belgium, 1996), pp. 65–68.

Negishi, Y.

N. Kuwaki, M. Ohashi, C. Tanaka, N. Uesugi, S. Seikai, Y. Negishi, “Characteristics of dispersion-shifted dual shape core single-mode fibers,” J. Lightwave Technol. LT-5, 792–797 (1987).
[CrossRef]

Nishii, J.

B. H. Lee, J. Nishii, “Self-interference of a long-period fiber grating and its application as a temperature sensor,” Electron. Lett. 34, 2059–2060 (1998).
[CrossRef]

B. H. Lee, J. Nishii, “Bending sensitivity of in-series long-period fiber gratings,” Opt. Lett. 23, 1624–1626 (1998).
[CrossRef]

Ohashi, M.

N. Kuwaki, M. Ohashi, C. Tanaka, N. Uesugi, S. Seikai, Y. Negishi, “Characteristics of dispersion-shifted dual shape core single-mode fibers,” J. Lightwave Technol. LT-5, 792–797 (1987).
[CrossRef]

Pedrazzani, J. R.

Protopopov, V. N.

E. M. Dianov, S. A. Vasiliev, A. S. Kurkov, O. I. Medvedkov, V. N. Protopopov, “In-fiber Mach–Zehnder interferometer based on a pair of long-period gratings,” in Proceedings of European Conference on Optical Communication (Interuniversity Microelectronics Center, Ghent, Belgium, 1996), pp. 65–68.

Riccardi, E.

L. Tallone, L. Boschis, L. Cognolato, E. Emelli, E. Riccardi, O. Rossotto, “Narrow-band rejection filters through fabrication of in-series long-period gratings,” in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. 175.

Rossotto, O.

L. Tallone, L. Boschis, L. Cognolato, E. Emelli, E. Riccardi, O. Rossotto, “Narrow-band rejection filters through fabrication of in-series long-period gratings,” in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. 175.

Seikai, S.

N. Kuwaki, M. Ohashi, C. Tanaka, N. Uesugi, S. Seikai, Y. Negishi, “Characteristics of dispersion-shifted dual shape core single-mode fibers,” J. Lightwave Technol. LT-5, 792–797 (1987).
[CrossRef]

Sipe, J. E.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–64 (1996).
[CrossRef]

Skorucak, A.

D. S. Starodubov, V. Grubsky, A. Skorucak, J. Feinberg, J. X. Cai, K. M. Feng, A. E. Willner, “Novel fiber amplitude modulators for dynamic channel power equalization in WDM systems,” in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. PD8-1–PD8-4.

Starodubov, D. S.

D. S. Starodubov, V. Grubsky, A. Skorucak, J. Feinberg, J. X. Cai, K. M. Feng, A. E. Willner, “Novel fiber amplitude modulators for dynamic channel power equalization in WDM systems,” in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. PD8-1–PD8-4.

Tallone, L.

L. Tallone, L. Boschis, L. Cognolato, E. Emelli, E. Riccardi, O. Rossotto, “Narrow-band rejection filters through fabrication of in-series long-period gratings,” in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. 175.

Tanaka, C.

N. Kuwaki, M. Ohashi, C. Tanaka, N. Uesugi, S. Seikai, Y. Negishi, “Characteristics of dispersion-shifted dual shape core single-mode fibers,” J. Lightwave Technol. LT-5, 792–797 (1987).
[CrossRef]

Uesugi, N.

N. Kuwaki, M. Ohashi, C. Tanaka, N. Uesugi, S. Seikai, Y. Negishi, “Characteristics of dispersion-shifted dual shape core single-mode fibers,” J. Lightwave Technol. LT-5, 792–797 (1987).
[CrossRef]

Vasiliev, S. A.

E. M. Dianov, S. A. Vasiliev, A. S. Kurkov, O. I. Medvedkov, V. N. Protopopov, “In-fiber Mach–Zehnder interferometer based on a pair of long-period gratings,” in Proceedings of European Conference on Optical Communication (Interuniversity Microelectronics Center, Ghent, Belgium, 1996), pp. 65–68.

Vengsarkar, A. M.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–64 (1996).
[CrossRef]

A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, P. J. Lemaire, N. S. Bergano, C. R. Davidson, “Long-period fiber-grating-based gain equalizers,” Opt. Lett. 21, 336–338 (1996).
[CrossRef] [PubMed]

Willner, A. E.

D. S. Starodubov, V. Grubsky, A. Skorucak, J. Feinberg, J. X. Cai, K. M. Feng, A. E. Willner, “Novel fiber amplitude modulators for dynamic channel power equalization in WDM systems,” in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. PD8-1–PD8-4.

Yariv, A.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley-Interscience, New York, 1984), pp. 177–185.

Yeh, P.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley-Interscience, New York, 1984), pp. 177–185.

Electron. Lett. (1)

B. H. Lee, J. Nishii, “Self-interference of a long-period fiber grating and its application as a temperature sensor,” Electron. Lett. 34, 2059–2060 (1998).
[CrossRef]

J. Lightwave Technol. (3)

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1293 (1997).
[CrossRef]

N. Kuwaki, M. Ohashi, C. Tanaka, N. Uesugi, S. Seikai, Y. Negishi, “Characteristics of dispersion-shifted dual shape core single-mode fibers,” J. Lightwave Technol. LT-5, 792–797 (1987).
[CrossRef]

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–64 (1996).
[CrossRef]

Opt. Lett. (4)

Other (6)

E. M. Dianov, S. A. Vasiliev, A. S. Kurkov, O. I. Medvedkov, V. N. Protopopov, “In-fiber Mach–Zehnder interferometer based on a pair of long-period gratings,” in Proceedings of European Conference on Optical Communication (Interuniversity Microelectronics Center, Ghent, Belgium, 1996), pp. 65–68.

L. Tallone, L. Boschis, L. Cognolato, E. Emelli, E. Riccardi, O. Rossotto, “Narrow-band rejection filters through fabrication of in-series long-period gratings,” in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. 175.

D. S. Starodubov, V. Grubsky, A. Skorucak, J. Feinberg, J. X. Cai, K. M. Feng, A. E. Willner, “Novel fiber amplitude modulators for dynamic channel power equalization in WDM systems,” in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. PD8-1–PD8-4.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley-Interscience, New York, 1984), pp. 177–185.

M. J. Adams, An Introduction to Optical Waveguides (Wiley-Interscience, New York, 1980), Chap. 7.

G. Keiser, Optical Fiber Communications, 2 ed. (McGraw-Hill, New York, 1991), Chap. 3.

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Figures (12)

Fig. 1
Fig. 1

Interference fringe of a LPG pair with 500-mm separation. Each LPG has a 20-mm length, and the fringe in the third stop band is plotted. The fringe spacing is ∼0.75 nm.

Fig. 2
Fig. 2

Interference fringe of a LPG pair with 500-mm separation. Each LPG has a 20-mm length, and the fringe in the second stop band is plotted. The fringe spacing is ∼0.62 nm.

Fig. 3
Fig. 3

Interference fringe of a LPG pair with 300-mm separation. Each LPG has a 20-mm length, and the fringe in the third stop band is plotted. The fringe spacing is ∼1.24 nm.

Fig. 4
Fig. 4

Variation of the fringe spacing inversely plotted as a function of grating separation. The fringe in the higher-order band has the wider spacing. The fringe at the longer grating separation has the narrower spacing. The curves are linear curves that connect the axis origin and the data points of the 500-mm LPG pair.

Fig. 5
Fig. 5

Variation of the fringe spacing in the third stop band with respect to inverse grating separation. Dotted curve, the linear curve of Fig. 4, which fitted well at a long grating separation. Solid curve, the best-fitting curve, including the phase shift induced by the grating itself.

Fig. 6
Fig. 6

Phase shift within a LPG plotted as a function of detuning in phase. Solid curve, κd = 1/8π; dashed–dotted curve, κd = 1/4π; dotted curve, κd = 3/8π. The phase shift is getting nonlinear with increasing grating strength.

Fig. 7
Fig. 7

Grating-induced phase-shift-correction factor g plotted as a function of detuning in phase. Solid curve, κd = 1/8π; the dashed–dotted curve, κd = 1/4π, dotted curve, κd = 3/8π.

Fig. 8
Fig. 8

Interference fringe of a LPG pair with its simulated envelope curves. The grating separation was 300 mm. The envelope curves were calculated from coupled-mode equations.

Fig. 9
Fig. 9

Skew effect on the ideal fringe of a LPG pair with 300-mm separation. Solid curve, the interference fringe simulated with a constant fringe spacing of 1.235 nm and with α = 0.9. Dotted curve, a sinusoidal curve with the same periodicity.

Fig. 10
Fig. 10

Skew effect on the ideal fringe of a LPG pair with 100-mm separation. Solid curve, the interference fringe simulated with a constant fringe spacing of 3.62 nm and with no power loss in the cladding mode. Dotted curve, a sinusoidal curve with the same periodicity. Compared with those of the sinusoidal curve, the minimum peaks of the fringe moved a bit toward the band center, especially near the band edges.

Fig. 11
Fig. 11

Comparison of the measured fringe spectrum and the simulated spectrum. Solid curve, the measured spectrum of the LPG pair with 300-mm separation. Dotted curve, the spectrum simulated to have uniform spacing in the frequency domain.

Fig. 12
Fig. 12

Comparison of the measured fringe spectrum and the simulated spectrum. Solid curve, the measured spectrum of the LPG pair with 300-mm separation. Dotted curve, the spectrum simulated including the grating-induced phase shift and the dispersion of the fiber modes.

Tables (1)

Tables Icon

Table 1 Variation of Differential Effective Group Index in a LPG Pair with 500-mm Grating Separation

Equations (23)

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

Ψ=Φinλ, d-βoutcoreλ-βoutcladλL-d,
S=2πddλ Φinλ, d-ddλβoutcoreλ-βoutcladλL-d.
Φin=-βincoreλ-βincladλd,
S=λ2Δmind+ΔmoutL-d,
ΔmΔneff-λ ddλ Δneff,
Δneffneffcore-neffclad.
Sλ2ΔmoutL.
Φin=2 argcos sd-i Δβ2ssin sd,
gΔβd, κdddλ Φin-ddλΔβd=-dΦindΔβd.
S=Sapprox1-dLgΔminΔmout-1,
T±α×R2,
R1-T=κκ*ssin sd2.
Δβd=-2πλ2 Δmindδλ.
Tpair=|T expiΨ-αR|2=T2+α2R2-2αTR cosΨ,
Ψ=2πS0λ-λ0,
Δf=cΔmL,
Ψ=Ψλ-2πλ ΔneffL.
ΔΨΨλ-Ψλ0=2πLλλ0λΔneffλ0-λ0Δneffλ.
ΔΨ=2πΔmλ0Lλλ0 Δλ 1+12ΔmΔmλ Δλ.
δλ=12ΔmΔmλλ-λ02.
dΔmdλ=cDcore-Dclad,
δλ=ελ-λ02,
εc2ΔmDcore-Dclad.

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