Abstract

Many inherent troubles from holey fiber technology are avoided according to leakage losses from the endlessly single-mode (ESM) property. The target-oriented design method (TODM) brings the potentialities of triple-clad fibers (TCFs) with arbitrarily available structure and performance into full play in transmission performance, because of the scalar wave equation combined with infinitesimal calculus of fiber performance. TCF with modified total internal reflection guidance optimized by TODM under the tolerance Δh16% has an ultrabroadband single-mode property similar to the ESM property of solid-core microstructured nonzero dispersion shifted fibers without tolerance and optimal structure to avoid higher-order modes and to reduce macro-bending loss.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996).
    [CrossRef]
  2. T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fibers,” Opt. Lett. 22, 961–963 (1997).
    [CrossRef]
  3. R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russel, P. J. Roberts, and D. C. Allen, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
    [CrossRef]
  4. J. C. Knight, “Photonic crystal fibers,” Nature 424, 847–851 (2003).
    [CrossRef]
  5. F. Poletti, E. R. N. Fokoua, M. N. Petrovich, N. V. Wheeler, N. K. Baddela, J. R. Hayes, and D. Richardson, “Hollow core photonic bandgap fibers for telecommunications: opportunities and potential issues,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2012), paper OTh1H3.
  6. J. Knight, “Microstructured optical fibers: making fibers better by leaving bits out,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OTuJ4.
  7. D. Ghosh, S. Roy, M. Pal, S. Bandyopadhyay, and S. Bhadra, “Modeling of microstructured nonzero dispersion shifted optical fibers with ultralow dispersion slope,” J. Opt. Soc. Am. B 26, 337–345 (2009).
    [CrossRef]
  8. F. Poletti, V. Finazzi, T. M. Monro, N. G. R. Broderick, V. Tse, and D. J. Richardson, “Inverse design and fabrication tolerances of ultra-flattened dispersion holey fibers,” Opt. Express 13, 3728–3736 (2005).
    [CrossRef]
  9. V. Rastogi and K. S. Chiang, “Holey optical fiber with circularly distributed by the radial effective-index method,” Opt. Lett. 28, 2449–2451 (2003).
    [CrossRef]
  10. P. R. Watekar, S. Ju, and W.-T. Han, “Near zero bending loss in a double-trenched bend insensitive optical fiber at 1550 nm,” Opt. Express 17, 20155–20166 (2009).
    [CrossRef]
  11. M.-J. Li, P. Tandon, D. C. Bookbinder, S. R. Bickham, M. A. McDermott, R. B. Desorcie, D. A. Nolan, J. J. Johnson, K. A. Lewis, and J. J. Englebert, “Ultra-low bending loss single-mode fiber for FTTH,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper PDP10.
  12. H. Etzkom and W. E. Heinlein, “Low-dispersion single-mode silica fiber with undoped core and three F-doped claddings,” Electron. Lett. 20, 423–424 (1984).
    [CrossRef]
  13. J. W. Fleming, “Material dispersion in lightguide glasses,” Electron. Lett. 14, 326–328 (1978).
    [CrossRef]
  14. H. Etzkorn and T. Heun, “Highly accurate numerical method for determination of propagation characteristics,” Opt. Quantum Electron. 18, 1–3 (1986).
    [CrossRef]
  15. S. Kawakami and S. Nishida, “Anomalous dispersion of new doubly clad optical fiber,” Electron. Lett. 10, 38–40 (1974).
    [CrossRef]
  16. B. J. Ainsile and C. R. Day, “Single mode fibers with modified dispersion characteristics,” J. Lightwave Technol. 4, 966–979 (1986).
    [CrossRef]
  17. P. L. Francois, F. Alard, J. F. Bayon, and B. Rose, “Multimode nature of quadruple-clad fibers,” Electron. Lett. 20, 37–38 (1984).
    [CrossRef]
  18. P. R. Watekar, S. Ju, and W. T. Han, “Single-mode optical fiber design with wide-band ultra low bending loss for FTTH application,” Opt. Express 16, 1180–1185 (2008).
    [CrossRef]

2009

2008

2005

2003

1999

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russel, P. J. Roberts, and D. C. Allen, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
[CrossRef]

1997

1996

1986

B. J. Ainsile and C. R. Day, “Single mode fibers with modified dispersion characteristics,” J. Lightwave Technol. 4, 966–979 (1986).
[CrossRef]

H. Etzkorn and T. Heun, “Highly accurate numerical method for determination of propagation characteristics,” Opt. Quantum Electron. 18, 1–3 (1986).
[CrossRef]

1984

H. Etzkom and W. E. Heinlein, “Low-dispersion single-mode silica fiber with undoped core and three F-doped claddings,” Electron. Lett. 20, 423–424 (1984).
[CrossRef]

P. L. Francois, F. Alard, J. F. Bayon, and B. Rose, “Multimode nature of quadruple-clad fibers,” Electron. Lett. 20, 37–38 (1984).
[CrossRef]

1978

J. W. Fleming, “Material dispersion in lightguide glasses,” Electron. Lett. 14, 326–328 (1978).
[CrossRef]

1974

S. Kawakami and S. Nishida, “Anomalous dispersion of new doubly clad optical fiber,” Electron. Lett. 10, 38–40 (1974).
[CrossRef]

Ainsile, B. J.

B. J. Ainsile and C. R. Day, “Single mode fibers with modified dispersion characteristics,” J. Lightwave Technol. 4, 966–979 (1986).
[CrossRef]

Alard, F.

P. L. Francois, F. Alard, J. F. Bayon, and B. Rose, “Multimode nature of quadruple-clad fibers,” Electron. Lett. 20, 37–38 (1984).
[CrossRef]

Allen, D. C.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russel, P. J. Roberts, and D. C. Allen, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
[CrossRef]

Atkin, D. M.

Baddela, N. K.

F. Poletti, E. R. N. Fokoua, M. N. Petrovich, N. V. Wheeler, N. K. Baddela, J. R. Hayes, and D. Richardson, “Hollow core photonic bandgap fibers for telecommunications: opportunities and potential issues,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2012), paper OTh1H3.

Bandyopadhyay, S.

Bayon, J. F.

P. L. Francois, F. Alard, J. F. Bayon, and B. Rose, “Multimode nature of quadruple-clad fibers,” Electron. Lett. 20, 37–38 (1984).
[CrossRef]

Bhadra, S.

Bickham, S. R.

M.-J. Li, P. Tandon, D. C. Bookbinder, S. R. Bickham, M. A. McDermott, R. B. Desorcie, D. A. Nolan, J. J. Johnson, K. A. Lewis, and J. J. Englebert, “Ultra-low bending loss single-mode fiber for FTTH,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper PDP10.

Birks, T. A.

Bookbinder, D. C.

M.-J. Li, P. Tandon, D. C. Bookbinder, S. R. Bickham, M. A. McDermott, R. B. Desorcie, D. A. Nolan, J. J. Johnson, K. A. Lewis, and J. J. Englebert, “Ultra-low bending loss single-mode fiber for FTTH,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper PDP10.

Broderick, N. G. R.

Chiang, K. S.

Cregan, R. F.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russel, P. J. Roberts, and D. C. Allen, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
[CrossRef]

Day, C. R.

B. J. Ainsile and C. R. Day, “Single mode fibers with modified dispersion characteristics,” J. Lightwave Technol. 4, 966–979 (1986).
[CrossRef]

Desorcie, R. B.

M.-J. Li, P. Tandon, D. C. Bookbinder, S. R. Bickham, M. A. McDermott, R. B. Desorcie, D. A. Nolan, J. J. Johnson, K. A. Lewis, and J. J. Englebert, “Ultra-low bending loss single-mode fiber for FTTH,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper PDP10.

Englebert, J. J.

M.-J. Li, P. Tandon, D. C. Bookbinder, S. R. Bickham, M. A. McDermott, R. B. Desorcie, D. A. Nolan, J. J. Johnson, K. A. Lewis, and J. J. Englebert, “Ultra-low bending loss single-mode fiber for FTTH,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper PDP10.

Etzkom, H.

H. Etzkom and W. E. Heinlein, “Low-dispersion single-mode silica fiber with undoped core and three F-doped claddings,” Electron. Lett. 20, 423–424 (1984).
[CrossRef]

Etzkorn, H.

H. Etzkorn and T. Heun, “Highly accurate numerical method for determination of propagation characteristics,” Opt. Quantum Electron. 18, 1–3 (1986).
[CrossRef]

Finazzi, V.

Fleming, J. W.

J. W. Fleming, “Material dispersion in lightguide glasses,” Electron. Lett. 14, 326–328 (1978).
[CrossRef]

Fokoua, E. R. N.

F. Poletti, E. R. N. Fokoua, M. N. Petrovich, N. V. Wheeler, N. K. Baddela, J. R. Hayes, and D. Richardson, “Hollow core photonic bandgap fibers for telecommunications: opportunities and potential issues,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2012), paper OTh1H3.

Francois, P. L.

P. L. Francois, F. Alard, J. F. Bayon, and B. Rose, “Multimode nature of quadruple-clad fibers,” Electron. Lett. 20, 37–38 (1984).
[CrossRef]

Ghosh, D.

Han, W. T.

Han, W.-T.

Hayes, J. R.

F. Poletti, E. R. N. Fokoua, M. N. Petrovich, N. V. Wheeler, N. K. Baddela, J. R. Hayes, and D. Richardson, “Hollow core photonic bandgap fibers for telecommunications: opportunities and potential issues,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2012), paper OTh1H3.

Heinlein, W. E.

H. Etzkom and W. E. Heinlein, “Low-dispersion single-mode silica fiber with undoped core and three F-doped claddings,” Electron. Lett. 20, 423–424 (1984).
[CrossRef]

Heun, T.

H. Etzkorn and T. Heun, “Highly accurate numerical method for determination of propagation characteristics,” Opt. Quantum Electron. 18, 1–3 (1986).
[CrossRef]

Johnson, J. J.

M.-J. Li, P. Tandon, D. C. Bookbinder, S. R. Bickham, M. A. McDermott, R. B. Desorcie, D. A. Nolan, J. J. Johnson, K. A. Lewis, and J. J. Englebert, “Ultra-low bending loss single-mode fiber for FTTH,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper PDP10.

Ju, S.

Kawakami, S.

S. Kawakami and S. Nishida, “Anomalous dispersion of new doubly clad optical fiber,” Electron. Lett. 10, 38–40 (1974).
[CrossRef]

Knight, J.

J. Knight, “Microstructured optical fibers: making fibers better by leaving bits out,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OTuJ4.

Knight, J. C.

J. C. Knight, “Photonic crystal fibers,” Nature 424, 847–851 (2003).
[CrossRef]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russel, P. J. Roberts, and D. C. Allen, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
[CrossRef]

T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fibers,” Opt. Lett. 22, 961–963 (1997).
[CrossRef]

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996).
[CrossRef]

Lewis, K. A.

M.-J. Li, P. Tandon, D. C. Bookbinder, S. R. Bickham, M. A. McDermott, R. B. Desorcie, D. A. Nolan, J. J. Johnson, K. A. Lewis, and J. J. Englebert, “Ultra-low bending loss single-mode fiber for FTTH,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper PDP10.

Li, M.-J.

M.-J. Li, P. Tandon, D. C. Bookbinder, S. R. Bickham, M. A. McDermott, R. B. Desorcie, D. A. Nolan, J. J. Johnson, K. A. Lewis, and J. J. Englebert, “Ultra-low bending loss single-mode fiber for FTTH,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper PDP10.

Mangan, B. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russel, P. J. Roberts, and D. C. Allen, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
[CrossRef]

McDermott, M. A.

M.-J. Li, P. Tandon, D. C. Bookbinder, S. R. Bickham, M. A. McDermott, R. B. Desorcie, D. A. Nolan, J. J. Johnson, K. A. Lewis, and J. J. Englebert, “Ultra-low bending loss single-mode fiber for FTTH,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper PDP10.

Monro, T. M.

Nishida, S.

S. Kawakami and S. Nishida, “Anomalous dispersion of new doubly clad optical fiber,” Electron. Lett. 10, 38–40 (1974).
[CrossRef]

Nolan, D. A.

M.-J. Li, P. Tandon, D. C. Bookbinder, S. R. Bickham, M. A. McDermott, R. B. Desorcie, D. A. Nolan, J. J. Johnson, K. A. Lewis, and J. J. Englebert, “Ultra-low bending loss single-mode fiber for FTTH,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper PDP10.

Pal, M.

Petrovich, M. N.

F. Poletti, E. R. N. Fokoua, M. N. Petrovich, N. V. Wheeler, N. K. Baddela, J. R. Hayes, and D. Richardson, “Hollow core photonic bandgap fibers for telecommunications: opportunities and potential issues,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2012), paper OTh1H3.

Poletti, F.

F. Poletti, V. Finazzi, T. M. Monro, N. G. R. Broderick, V. Tse, and D. J. Richardson, “Inverse design and fabrication tolerances of ultra-flattened dispersion holey fibers,” Opt. Express 13, 3728–3736 (2005).
[CrossRef]

F. Poletti, E. R. N. Fokoua, M. N. Petrovich, N. V. Wheeler, N. K. Baddela, J. R. Hayes, and D. Richardson, “Hollow core photonic bandgap fibers for telecommunications: opportunities and potential issues,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2012), paper OTh1H3.

Rastogi, V.

Richardson, D.

F. Poletti, E. R. N. Fokoua, M. N. Petrovich, N. V. Wheeler, N. K. Baddela, J. R. Hayes, and D. Richardson, “Hollow core photonic bandgap fibers for telecommunications: opportunities and potential issues,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2012), paper OTh1H3.

Richardson, D. J.

Roberts, P. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russel, P. J. Roberts, and D. C. Allen, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
[CrossRef]

Rose, B.

P. L. Francois, F. Alard, J. F. Bayon, and B. Rose, “Multimode nature of quadruple-clad fibers,” Electron. Lett. 20, 37–38 (1984).
[CrossRef]

Roy, S.

Russel, P. St. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russel, P. J. Roberts, and D. C. Allen, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
[CrossRef]

Russell, P. St. J.

Tandon, P.

M.-J. Li, P. Tandon, D. C. Bookbinder, S. R. Bickham, M. A. McDermott, R. B. Desorcie, D. A. Nolan, J. J. Johnson, K. A. Lewis, and J. J. Englebert, “Ultra-low bending loss single-mode fiber for FTTH,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper PDP10.

Tse, V.

Watekar, P. R.

Wheeler, N. V.

F. Poletti, E. R. N. Fokoua, M. N. Petrovich, N. V. Wheeler, N. K. Baddela, J. R. Hayes, and D. Richardson, “Hollow core photonic bandgap fibers for telecommunications: opportunities and potential issues,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2012), paper OTh1H3.

Electron. Lett.

H. Etzkom and W. E. Heinlein, “Low-dispersion single-mode silica fiber with undoped core and three F-doped claddings,” Electron. Lett. 20, 423–424 (1984).
[CrossRef]

J. W. Fleming, “Material dispersion in lightguide glasses,” Electron. Lett. 14, 326–328 (1978).
[CrossRef]

S. Kawakami and S. Nishida, “Anomalous dispersion of new doubly clad optical fiber,” Electron. Lett. 10, 38–40 (1974).
[CrossRef]

P. L. Francois, F. Alard, J. F. Bayon, and B. Rose, “Multimode nature of quadruple-clad fibers,” Electron. Lett. 20, 37–38 (1984).
[CrossRef]

J. Lightwave Technol.

B. J. Ainsile and C. R. Day, “Single mode fibers with modified dispersion characteristics,” J. Lightwave Technol. 4, 966–979 (1986).
[CrossRef]

J. Opt. Soc. Am. B

Nature

J. C. Knight, “Photonic crystal fibers,” Nature 424, 847–851 (2003).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Quantum Electron.

H. Etzkorn and T. Heun, “Highly accurate numerical method for determination of propagation characteristics,” Opt. Quantum Electron. 18, 1–3 (1986).
[CrossRef]

Science

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russel, P. J. Roberts, and D. C. Allen, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
[CrossRef]

Other

F. Poletti, E. R. N. Fokoua, M. N. Petrovich, N. V. Wheeler, N. K. Baddela, J. R. Hayes, and D. Richardson, “Hollow core photonic bandgap fibers for telecommunications: opportunities and potential issues,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2012), paper OTh1H3.

J. Knight, “Microstructured optical fibers: making fibers better by leaving bits out,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OTuJ4.

M.-J. Li, P. Tandon, D. C. Bookbinder, S. R. Bickham, M. A. McDermott, R. B. Desorcie, D. A. Nolan, J. J. Johnson, K. A. Lewis, and J. J. Englebert, “Ultra-low bending loss single-mode fiber for FTTH,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper PDP10.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1.
Fig. 1.

Dispersion characteristics of a triple-clad DFF.

Fig. 2.
Fig. 2.

Evolution of dispersion characteristics of TCF with S0 in 1300–1800 nm, when p1=0.621, p2=1, and Aeff=60±1μm2.

Fig. 3.
Fig. 3.

Evolution of dispersion characteristics of TCF having the optimal S0 with p1 in 1310–1800 nm, when p2=1.0 and Aeff=60±0.4μm2.

Fig. 4.
Fig. 4.

Evolution of dispersion characteristics of TCF having the optimal S0 with p1 in 1310–1800 nm, when p2=1.0 and Aeff=70±0.4μm2.

Fig. 5.
Fig. 5.

Evolution of dispersion characteristics of TCF having the optimal S0 with p1 in 1460–1700 nm, when p2=1.0 and Aeff=70±0.4μm2.

Fig. 6.
Fig. 6.

Evolution of dispersion characteristics of TCF having the optimal S0 with p1 in 1400–1800 nm, when p2=1.0 and Aeff=70±0.4μm2.

Fig. 7.
Fig. 7.

Evolution of Fc01 with wavelength for the CF with p1=0.2 and p2=1.0 when TCF with p1=0.2 and p2=1.0 when Δh1=30%.

Fig. 8.
Fig. 8.

Evolution of Fc01 with wavelength for the TCF with p1=1.413 and p2=1 when Δh1=1%.

Tables (5)

Tables Icon

Table 1. Dispersion Characteristics in ps/(km×nm) at nm

Tables Icon

Table 2. λc01 and λc11 of the First Type of TCF when Δh130%

Tables Icon

Table 3. λc01 and λc11 of the Second Type of TCF when Δh15%

Tables Icon

Table 4. λc01 and λc11 of the Third Type of TCF when Δh16%

Tables Icon

Table 5. Calculated MBL of Some DFFa

Equations (11)

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

VSMF=2πaλnco2ncl2,
VPCF=2πΛλnFM2(λ)nFSM2(λ).
Δco=nco2ncl22nco2,Δ1=n12ncl22nco2,Δ2=n22ncl22nco2.
h1=r1aa,h2=r2r1a,p1=Δ1Δco,p2=Δ2Δco,x1=a,x2=h1,x3=h2,x4=Δco,x5=p1,x6=p2.
Fm(r)=Jm(rk2n02β2),(0,a)A1[Km(rβ2k2n12)+C1Im(rβ2k2n12)],(a,r1)A2[Jm(rk2n22β2)+C2Ym(rk2n22β2)],(r1,r2)A3Km(rβ2k2n32),(r2,),
D=1cddλ{kβ0n(r)[n(r)λdn(r)dλ]F02(r)rdr0F02(r)rdr},
Aeff=2π(0F02(r)rdr)20F04(r)rdr.
αmacro=10ln10(πV816aRbW3)exp(4RbΔW33aV2)[0(1g)F0rdr]20F02r2rdr,
g=n(r)2nmin2nmax2nmin2,V=kanmax2nmin2,W=aβ2(knmin)2,Δ=nmax2nmin22nmax2,
λc11=2πanco2ncl2Vc,
[y1x1y1x2y1x3y1xmy2x1y2x2y2x3y2xmynx1ynx2ynx3ynxm][Δx1Δx2Δxm]=[Δy1Δy2Δyn],

Metrics