Abstract

We present an efficient approach to design a high-channel-count multichannel fiber Bragg grating by assigning optimal sets of delay coefficients and constant phases to the corresponding channel responses. Based on approximate Fourier transform, the delay coefficients are chosen to separate all the single-channel gratings into several groups spatially in the grating structure, and the constant phases in each group are optimized to minimize the maximum index modulation to be approximately the square root of the maximum of the number of the channels in all groups times larger than that of the one-channel grating. Design examples demonstrate that the proposed method has advantages of low index modulation, low algorithmic complexity, and suitability for multichannel fiber Bragg grating designs with either identical or nonidentical spectral responses.

© 2012 Optical Society of America

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References

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  1. A. Othonos and K. Kalli, Fiber Bragg Gratings (Artech House, 1999).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  5. A. Arigiris, M. Konstantaki, A. Ikades, D. Chronis, P. Florias, K. Kallimani, and G. Pagiatakis, “Fabrication of high-reflectivity superimposed multiple-fiber Bragg gratings with unequal wavelength spacing,” Opt. Lett. 27, 1306–1308 (2002).
    [CrossRef]
  6. C. Wang, J. Azana, and L. R. Chen, “Efficient technique for increasing the channel density in multiwavelength sampled fiber Bragg grating filters,” IEEE Photon. Technol. Lett. 16, 1867–1869 (2004).
    [CrossRef]
  7. C. Wang, J. Azana, and L. R. Chen, “Spectral Talbot-like phenomena in one-dimensional photonic bandgap structures,” Opt. Lett. 29, 1590–1592 (2004).
    [CrossRef]
  8. L. R. Chen and J. Azaña, “Spectral Talbot phenomena in sampled arbitrarily chirped Bragg gratings,” Opt. Commun. 250, 302–308 (2005).
    [CrossRef]
  9. A. V. Buryak, K. Y. Kolossovski, and D. Y. Stepanov, “Optimization of refractive index sampling for multichannel fiber Bragg gratings,” IEEE J. Quantum Electron. 39, 91–98 (2003).
    [CrossRef]
  10. M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,” IEEE Photon. Technol. Lett. 10, 842–844 (1998).
    [CrossRef]
  11. J. E. Rothenberg, “Phase-only sampled 45 channel fiber Bragg grating written with a diffraction-compensated phase mask,” Opt. Lett. 31, 1199–1201 (2006).
    [CrossRef]
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    [CrossRef]
  14. K. Kolossovski, R. Sammut, A. Buryak, and D. Stepanov, “Three-step design optimization for multi-channel fibre Bragg gratings,” Opt. Express 11, 1029–1038 (2003).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  23. J. Bland-Hawthorn, A. Buryak, and K. Kolossovski, “Optimization algorithm for ultrabroadband multichannel aperiodic fiber Bragg grating filters,” J. Opt. Soc. Am. A 25, 153–158 (2008).
    [CrossRef]
  24. R. Feced, M. N. Zervas, and M. A. Muriel, “An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings,” IEEE J. Quantum Electron. 35, 1105–1115 (1999).
    [CrossRef]
  25. J. Skaar, L. Wang, and T. Erdogan, “On the synthesis of fiber Bragg grating by layer peeling,” IEEE J. Quantum Electron. 37, 165–173 (2001).
    [CrossRef]

2011 (2)

J. Bland-Hawthorn, S. C. Ellis, S. G. Leon-Saval, R. Haynes, M. M. Roth, H.-G. Löhmannsröben, A. J. Horton, J.-G. Cuby, T. A. Birks, J. S. Lawrence, P. Gillingham, S. D. Ryder, and C. Trinh, “A complex multi-notch astronomical filter to suppress the bright infrared sky,” Nat. Commun. 2, 581 (2011).
[CrossRef]

X. Chen, J. Hayashi, and H. Li, “Ultrahigh-channel-count fiber Bragg grating based on the triple sampling method,” Opt. Commun. 284, 1842–1846 (2011).
[CrossRef]

2010 (1)

2009 (3)

2008 (1)

2006 (3)

2005 (1)

L. R. Chen and J. Azaña, “Spectral Talbot phenomena in sampled arbitrarily chirped Bragg gratings,” Opt. Commun. 250, 302–308 (2005).
[CrossRef]

2004 (4)

2003 (4)

A. V. Buryak, K. Y. Kolossovski, and D. Y. Stepanov, “Optimization of refractive index sampling for multichannel fiber Bragg gratings,” IEEE J. Quantum Electron. 39, 91–98 (2003).
[CrossRef]

H. Li, Y. Sheng, Y. Li, and J. E. Rothenberg, “Phased-only sampled fiber Bragg gratings for high channel counts chromatic dispersion compensation,” J. Lightwave Technol. 21, 2074–2083 (2003).
[CrossRef]

K. Kolossovski, R. Sammut, A. Buryak, and D. Stepanov, “Three-step design optimization for multi-channel fibre Bragg gratings,” Opt. Express 11, 1029–1038 (2003).
[CrossRef]

H. Li and Y. Sheng, “Direct design of multichannel fiber Bragg grating with discrete layer-peeling algorithm,” IEEE Photon. Technol. Lett. 15, 1252–1254 (2003).
[CrossRef]

2002 (1)

2001 (1)

J. Skaar, L. Wang, and T. Erdogan, “On the synthesis of fiber Bragg grating by layer peeling,” IEEE J. Quantum Electron. 37, 165–173 (2001).
[CrossRef]

1999 (1)

R. Feced, M. N. Zervas, and M. A. Muriel, “An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings,” IEEE J. Quantum Electron. 35, 1105–1115 (1999).
[CrossRef]

1998 (1)

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,” IEEE Photon. Technol. Lett. 10, 842–844 (1998).
[CrossRef]

1994 (1)

A. Othonos, X. Lee, and R. M. Measures, “Superimposed multiple Bragg gratings,” Electron. Lett. 30, 1972–1974 (1994).
[CrossRef]

Arigiris, A.

Azana, J.

C. Wang, J. Azana, and L. R. Chen, “Spectral Talbot-like phenomena in one-dimensional photonic bandgap structures,” Opt. Lett. 29, 1590–1592 (2004).
[CrossRef]

C. Wang, J. Azana, and L. R. Chen, “Efficient technique for increasing the channel density in multiwavelength sampled fiber Bragg grating filters,” IEEE Photon. Technol. Lett. 16, 1867–1869 (2004).
[CrossRef]

Azaña, J.

L. R. Chen and J. Azaña, “Spectral Talbot phenomena in sampled arbitrarily chirped Bragg gratings,” Opt. Commun. 250, 302–308 (2005).
[CrossRef]

Birks, T. A.

J. Bland-Hawthorn, S. C. Ellis, S. G. Leon-Saval, R. Haynes, M. M. Roth, H.-G. Löhmannsröben, A. J. Horton, J.-G. Cuby, T. A. Birks, J. S. Lawrence, P. Gillingham, S. D. Ryder, and C. Trinh, “A complex multi-notch astronomical filter to suppress the bright infrared sky,” Nat. Commun. 2, 581 (2011).
[CrossRef]

Bland-Hawthorn, J.

Buryak, A.

Buryak, A. V.

A. V. Buryak, K. Y. Kolossovski, and D. Y. Stepanov, “Optimization of refractive index sampling for multichannel fiber Bragg gratings,” IEEE J. Quantum Electron. 39, 91–98 (2003).
[CrossRef]

Chen, L. R.

L. R. Chen and J. Azaña, “Spectral Talbot phenomena in sampled arbitrarily chirped Bragg gratings,” Opt. Commun. 250, 302–308 (2005).
[CrossRef]

C. Wang, J. Azana, and L. R. Chen, “Efficient technique for increasing the channel density in multiwavelength sampled fiber Bragg grating filters,” IEEE Photon. Technol. Lett. 16, 1867–1869 (2004).
[CrossRef]

C. Wang, J. Azana, and L. R. Chen, “Spectral Talbot-like phenomena in one-dimensional photonic bandgap structures,” Opt. Lett. 29, 1590–1592 (2004).
[CrossRef]

Chen, X.

Chronis, D.

Cole, M. J.

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,” IEEE Photon. Technol. Lett. 10, 842–844 (1998).
[CrossRef]

Cuby, J.-G.

J. Bland-Hawthorn, S. C. Ellis, S. G. Leon-Saval, R. Haynes, M. M. Roth, H.-G. Löhmannsröben, A. J. Horton, J.-G. Cuby, T. A. Birks, J. S. Lawrence, P. Gillingham, S. D. Ryder, and C. Trinh, “A complex multi-notch astronomical filter to suppress the bright infrared sky,” Nat. Commun. 2, 581 (2011).
[CrossRef]

Durkin, M. K.

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,” IEEE Photon. Technol. Lett. 10, 842–844 (1998).
[CrossRef]

Edvell, G.

Ellis, S. C.

J. Bland-Hawthorn, S. C. Ellis, S. G. Leon-Saval, R. Haynes, M. M. Roth, H.-G. Löhmannsröben, A. J. Horton, J.-G. Cuby, T. A. Birks, J. S. Lawrence, P. Gillingham, S. D. Ryder, and C. Trinh, “A complex multi-notch astronomical filter to suppress the bright infrared sky,” Nat. Commun. 2, 581 (2011).
[CrossRef]

Englund, M.

Erdogan, T.

J. Skaar, L. Wang, and T. Erdogan, “On the synthesis of fiber Bragg grating by layer peeling,” IEEE J. Quantum Electron. 37, 165–173 (2001).
[CrossRef]

Feced, R.

R. Feced, M. N. Zervas, and M. A. Muriel, “An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings,” IEEE J. Quantum Electron. 35, 1105–1115 (1999).
[CrossRef]

Florias, P.

Gillingham, P.

J. Bland-Hawthorn, S. C. Ellis, S. G. Leon-Saval, R. Haynes, M. M. Roth, H.-G. Löhmannsröben, A. J. Horton, J.-G. Cuby, T. A. Birks, J. S. Lawrence, P. Gillingham, S. D. Ryder, and C. Trinh, “A complex multi-notch astronomical filter to suppress the bright infrared sky,” Nat. Commun. 2, 581 (2011).
[CrossRef]

Gong, Y.

Hayashi, J.

Haynes, R.

J. Bland-Hawthorn, S. C. Ellis, S. G. Leon-Saval, R. Haynes, M. M. Roth, H.-G. Löhmannsröben, A. J. Horton, J.-G. Cuby, T. A. Birks, J. S. Lawrence, P. Gillingham, S. D. Ryder, and C. Trinh, “A complex multi-notch astronomical filter to suppress the bright infrared sky,” Nat. Commun. 2, 581 (2011).
[CrossRef]

Horton, A. J.

J. Bland-Hawthorn, S. C. Ellis, S. G. Leon-Saval, R. Haynes, M. M. Roth, H.-G. Löhmannsröben, A. J. Horton, J.-G. Cuby, T. A. Birks, J. S. Lawrence, P. Gillingham, S. D. Ryder, and C. Trinh, “A complex multi-notch astronomical filter to suppress the bright infrared sky,” Nat. Commun. 2, 581 (2011).
[CrossRef]

Hu, X.

Ibsen, M.

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,” IEEE Photon. Technol. Lett. 10, 842–844 (1998).
[CrossRef]

Ikades, A.

Kalli, K.

A. Othonos and K. Kalli, Fiber Bragg Gratings (Artech House, 1999).

Kallimani, K.

Kao, Y.

Kolossovski, K.

Kolossovski, K. Y.

A. V. Buryak, K. Y. Kolossovski, and D. Y. Stepanov, “Optimization of refractive index sampling for multichannel fiber Bragg gratings,” IEEE J. Quantum Electron. 39, 91–98 (2003).
[CrossRef]

Konstantaki, M.

Kumagai, T.

Laming, R. I.

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,” IEEE Photon. Technol. Lett. 10, 842–844 (1998).
[CrossRef]

Lawrence, J. S.

J. Bland-Hawthorn, S. C. Ellis, S. G. Leon-Saval, R. Haynes, M. M. Roth, H.-G. Löhmannsröben, A. J. Horton, J.-G. Cuby, T. A. Birks, J. S. Lawrence, P. Gillingham, S. D. Ryder, and C. Trinh, “A complex multi-notch astronomical filter to suppress the bright infrared sky,” Nat. Commun. 2, 581 (2011).
[CrossRef]

Lee, C.

Lee, R.

Lee, X.

A. Othonos, X. Lee, and R. M. Measures, “Superimposed multiple Bragg gratings,” Electron. Lett. 30, 1972–1974 (1994).
[CrossRef]

Leon-Saval, S. G.

J. Bland-Hawthorn, S. C. Ellis, S. G. Leon-Saval, R. Haynes, M. M. Roth, H.-G. Löhmannsröben, A. J. Horton, J.-G. Cuby, T. A. Birks, J. S. Lawrence, P. Gillingham, S. D. Ryder, and C. Trinh, “A complex multi-notch astronomical filter to suppress the bright infrared sky,” Nat. Commun. 2, 581 (2011).
[CrossRef]

Li, H.

Li, M.

Li, Y.

Lin, A.

Liu, X.

Löhmannsröben, H.-G.

J. Bland-Hawthorn, S. C. Ellis, S. G. Leon-Saval, R. Haynes, M. M. Roth, H.-G. Löhmannsröben, A. J. Horton, J.-G. Cuby, T. A. Birks, J. S. Lawrence, P. Gillingham, S. D. Ryder, and C. Trinh, “A complex multi-notch astronomical filter to suppress the bright infrared sky,” Nat. Commun. 2, 581 (2011).
[CrossRef]

Measures, R. M.

A. Othonos, X. Lee, and R. M. Measures, “Superimposed multiple Bragg gratings,” Electron. Lett. 30, 1972–1974 (1994).
[CrossRef]

Muriel, M. A.

R. Feced, M. N. Zervas, and M. A. Muriel, “An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings,” IEEE J. Quantum Electron. 35, 1105–1115 (1999).
[CrossRef]

Ogusu, K.

Othonos, A.

A. Othonos, X. Lee, and R. M. Measures, “Superimposed multiple Bragg gratings,” Electron. Lett. 30, 1972–1974 (1994).
[CrossRef]

A. Othonos and K. Kalli, Fiber Bragg Gratings (Artech House, 1999).

Pagiatakis, G.

Roth, M. M.

J. Bland-Hawthorn, S. C. Ellis, S. G. Leon-Saval, R. Haynes, M. M. Roth, H.-G. Löhmannsröben, A. J. Horton, J.-G. Cuby, T. A. Birks, J. S. Lawrence, P. Gillingham, S. D. Ryder, and C. Trinh, “A complex multi-notch astronomical filter to suppress the bright infrared sky,” Nat. Commun. 2, 581 (2011).
[CrossRef]

Rothenberg, J. E.

Ryder, S. D.

J. Bland-Hawthorn, S. C. Ellis, S. G. Leon-Saval, R. Haynes, M. M. Roth, H.-G. Löhmannsröben, A. J. Horton, J.-G. Cuby, T. A. Birks, J. S. Lawrence, P. Gillingham, S. D. Ryder, and C. Trinh, “A complex multi-notch astronomical filter to suppress the bright infrared sky,” Nat. Commun. 2, 581 (2011).
[CrossRef]

Sammut, R.

Sheng, Y.

Skaar, J.

J. Skaar, L. Wang, and T. Erdogan, “On the synthesis of fiber Bragg grating by layer peeling,” IEEE J. Quantum Electron. 37, 165–173 (2001).
[CrossRef]

Steblina, V.

Stepanov, D.

Stepanov, D. Y.

A. V. Buryak, K. Y. Kolossovski, and D. Y. Stepanov, “Optimization of refractive index sampling for multichannel fiber Bragg gratings,” IEEE J. Quantum Electron. 39, 91–98 (2003).
[CrossRef]

Trinh, C.

J. Bland-Hawthorn, S. C. Ellis, S. G. Leon-Saval, R. Haynes, M. M. Roth, H.-G. Löhmannsröben, A. J. Horton, J.-G. Cuby, T. A. Birks, J. S. Lawrence, P. Gillingham, S. D. Ryder, and C. Trinh, “A complex multi-notch astronomical filter to suppress the bright infrared sky,” Nat. Commun. 2, 581 (2011).
[CrossRef]

Wang, C.

C. Wang, J. Azana, and L. R. Chen, “Efficient technique for increasing the channel density in multiwavelength sampled fiber Bragg grating filters,” IEEE Photon. Technol. Lett. 16, 1867–1869 (2004).
[CrossRef]

C. Wang, J. Azana, and L. R. Chen, “Spectral Talbot-like phenomena in one-dimensional photonic bandgap structures,” Opt. Lett. 29, 1590–1592 (2004).
[CrossRef]

Wang, L.

Zervas, M. N.

R. Feced, M. N. Zervas, and M. A. Muriel, “An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings,” IEEE J. Quantum Electron. 35, 1105–1115 (1999).
[CrossRef]

Zhao, W.

Appl. Opt. (1)

Electron. Lett. (1)

A. Othonos, X. Lee, and R. M. Measures, “Superimposed multiple Bragg gratings,” Electron. Lett. 30, 1972–1974 (1994).
[CrossRef]

IEEE J. Quantum Electron. (3)

A. V. Buryak, K. Y. Kolossovski, and D. Y. Stepanov, “Optimization of refractive index sampling for multichannel fiber Bragg gratings,” IEEE J. Quantum Electron. 39, 91–98 (2003).
[CrossRef]

R. Feced, M. N. Zervas, and M. A. Muriel, “An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings,” IEEE J. Quantum Electron. 35, 1105–1115 (1999).
[CrossRef]

J. Skaar, L. Wang, and T. Erdogan, “On the synthesis of fiber Bragg grating by layer peeling,” IEEE J. Quantum Electron. 37, 165–173 (2001).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,” IEEE Photon. Technol. Lett. 10, 842–844 (1998).
[CrossRef]

H. Li and Y. Sheng, “Direct design of multichannel fiber Bragg grating with discrete layer-peeling algorithm,” IEEE Photon. Technol. Lett. 15, 1252–1254 (2003).
[CrossRef]

C. Wang, J. Azana, and L. R. Chen, “Efficient technique for increasing the channel density in multiwavelength sampled fiber Bragg grating filters,” IEEE Photon. Technol. Lett. 16, 1867–1869 (2004).
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Nat. Commun. (1)

J. Bland-Hawthorn, S. C. Ellis, S. G. Leon-Saval, R. Haynes, M. M. Roth, H.-G. Löhmannsröben, A. J. Horton, J.-G. Cuby, T. A. Birks, J. S. Lawrence, P. Gillingham, S. D. Ryder, and C. Trinh, “A complex multi-notch astronomical filter to suppress the bright infrared sky,” Nat. Commun. 2, 581 (2011).
[CrossRef]

Opt. Commun. (2)

L. R. Chen and J. Azaña, “Spectral Talbot phenomena in sampled arbitrarily chirped Bragg gratings,” Opt. Commun. 250, 302–308 (2005).
[CrossRef]

X. Chen, J. Hayashi, and H. Li, “Ultrahigh-channel-count fiber Bragg grating based on the triple sampling method,” Opt. Commun. 284, 1842–1846 (2011).
[CrossRef]

Opt. Express (6)

Opt. Lett. (3)

Other (1)

A. Othonos and K. Kalli, Fiber Bragg Gratings (Artech House, 1999).

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Figures (8)

Fig. 1.
Fig. 1.

Proposed approach to design a multichannel grating structure.

Fig. 2.
Fig. 2.

Index modulation of a one-channel FBG for the 112 channel dispersion-free FBG with the bandwidth of 50 GHz and the channel spacing of 100 GHz.

Fig. 3.
Fig. 3.

(a) Reconstructed index modulation of the 112 channel dispersion-free FBG filter. The insets show the details of Δn at both the edges and the center of the grating; (b) The calculated reflection spectrum of the grating with this design. The insets show the details of reflection (solid curve) and group delay (dashed curve) spectra for the channels at the center wavelengths of 1531.9, 1576.2, and 1624.0 nm.

Fig. 4.
Fig. 4.

(a) Reconstructed index modulation of the 112 channel dispersion-free FBG filter with max(Mi)=5. The insets show the details of Δn at the both edges and center of the grating; (b) The calculated reflection spectrum of the grating with this design. The insets show the details of reflection (solid curve) and group delay (dashed curve) spectra for the channels at the center wavelengths of 1531.9, 1576.2, and 1624.0 nm.

Fig. 5.
Fig. 5.

Index modulation of a one-channel FBG for dispersion compensation.

Fig. 6.
Fig. 6.

(a) Reconstructed index modulation of the 112 channel dispersion-compensated FBG filter. The insets show the details of Δn at the both edges and center of the grating; (b) The calculated reflection spectrum of the grating with this design. The insets show the details of reflection (solid curve) and group delay (dashed curve) spectra for the channels at the center wavelengths of 1531.9, 1576.2, and 1624.0 nm.

Fig. 7.
Fig. 7.

(a) Reconstructed index modulation of the 112 channel FBG filter with simultaneous dispersion and dispersion slope compensations. The insets show the details of Δn at the both edges and center of the grating; (b) The calculated reflection spectrum of the grating with this design. The insets show the details of reflection (solid curve) and group delay (dashed curve) spectra for the channels at the center wavelengths of 1531.9, 1576.2, and 1624.0 nm.

Fig. 8.
Fig. 8.

Effect of index modulation variations in the designed FBG filters. (a) Reflection and (b) group delay spectra for the channels with their center wavelengths of 1531.9, 1576.2, and 1624.0 nm as the perturbation factor σ are 15% (solid curve with circle marker), 5% (dashed curve), 0% (solid curve), 5% (dotted curve), and 15% (dash-dotted curve), respectively.

Equations (7)

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

r(δ)=m=1Nrm(δδm)ejφmej(δδm)cτm,
q(z)F1[r(δ)]=m=1Nqm(zzm)ejϕm,
Δn(z)ejθ(z)=λ0q(z)/jπ,
qg,i=m=M1+M2++Mi1+1M1+M2++Mi1+Miqm(zzi)ejϕm.
rm(δ)=Rexp(ln2(δ/δPB)8),
D2(l)=D2+lD3Δλl=N/2+1,,1,0,1,N/2,
Δn=Δn(1+σ).

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