Abstract

Various simple anti-resonant, single cladding layer, hollow core fiber structures are examined. We show that the spacing between core and jacket glass and the shape of the support struts can be used to optimize confinement loss. We demonstrate the detrimental effect on confinement loss of thick nodes at the strut intersections and present a fabricated hexagram fiber that mitigates this effect in both straight and bent condition by presenting thin and radially elongated nodes. This fiber has loss comparable to published results for a first generation, multi-cladding ring, Kagome fiber with negative core curvature and has tolerable bend loss for many practical applications.

© 2015 Optical Society of America

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References

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  1. J. Tauer, F. Orban, H. Koer, A. B. Fedotov, I. V. Fedotov, V. P. Mitrokhin, A. M. Zheltikov, and E. Wintner, “High-throughput of single high-power laser pulses by hollow photonic band gap fibers,” Laser Phys. Lett. 4(6), 444–448 (2007).
    [Crossref]
  2. C. J. Hensley, M. A. Foster, B. Shim, and A. L. Gaeta, “Extremely high coupling and transmission of high-powered-femtosecond pulses in hollow-core photonic band-gap fiber,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies,” Technical Digest (CD) (Optical Society of America, 2008).
    [Crossref]
  3. E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43(4), 1783–1809 (1964).
    [Crossref]
  4. M. Miyagi and S. Nishida, “A proposal of low-loss leaky waveguide for submillimeter waves transmission,” IEEE Trans. Microw. Theory Tech. 28(4), 398–401 (1980).
    [Crossref]
  5. M. Miyagi, “Bending losses in hollow and dielectric tube leaky waveguides,” Appl. Opt. 20(7), 1221–1229 (1981).
    [Crossref] [PubMed]
  6. R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285(5433), 1537–1539 (1999).
    [Crossref] [PubMed]
  7. F. Poletti, M. N. Petrovich, and D. J. Richardson, “Hollow-core photonic bandgap fibers: technology and applications,” Nanophotonics 2(5-6), 315–340 (2013).
    [Crossref]
  8. Y. Jung, V. A. J. M. Sleiffer, N. Baddela, M. N. Petrovich, J. R. Hayes, N. V. Wheeler, D. R. Gray, E. Numkam Fokoua, J. P. Wooler, N. H.-L. Wong, F. Parmigiani, S. U. Alam, J. Surof, M. Kuschnerov, V. Veljanovski, H. De Waardt, F. Poletti, and D. J. Richardson, “First demonstration of a broadband 37-cell hollow core photonic bandgap fiber and its application to high capacity mode division multiplexing,” in Optical Fiber Communication Conference 2013, (Optical Society of America, 2013), paper PDP5A.3.
  9. F. Couny, F. Benabid, and P. S. Light, “Large-pitch kagome-structured hollow-core photonic crystal fiber,” Opt. Lett. 31(24), 3574–3576 (2006).
    [Crossref] [PubMed]
  10. Y. Y. Wang, N. V. Wheeler, F. Couny, P. J. Roberts, and F. Benabid, “Low loss broadband transmission in hypocycloid-core Kagome hollow-core photonic crystal fiber,” Opt. Lett. 36(5), 669–671 (2011).
    [Crossref] [PubMed]
  11. B. Debord, M. Alharbi, T. Bradley, C. Fourcade-Dutin, Y. Y. Wang, L. Vincetti, F. Gérôme, and F. Benabid, “Hypocycloid-shaped hollow-core photonic crystal fiber Part I: Arc curvature effect on confinement loss,” Opt. Express 21(23), 28597–28608 (2013).
    [Crossref] [PubMed]
  12. M. Alharbi, T. Bradley, B. Debord, C. Fourcade-Dutin, D. Ghosh, L. Vincetti, F. Gérôme, and F. Benabid, “Hypocycloid-shaped hollow-core photonic crystal fiber part II: Cladding effect on confinement and bend loss,” Opt. Express 21(23), 28609–28616 (2013).
    [Crossref] [PubMed]
  13. M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures,” Appl. Phys. Lett. 49(1), 13–15 (1986).
    [Crossref]
  14. S. Février, B. Beaudou, and P. Viale, “Understanding origin of loss in large pitch hollow-core photonic crystal fibers and their design simplification,” Opt. Express 18(5), 5142–5150 (2010).
    [Crossref] [PubMed]
  15. F. Gérôme, R. Jamier, J.-L. Auguste, G. Humbert, and J.-M. Blondy, “Simplified hollow-core photonic crystal fiber,” Opt. Lett. 35(8), 1157–1159 (2010).
    [Crossref] [PubMed]
  16. F. Yu, W. J. Wadsworth, and J. C. Knight, “Low loss silica hollow core fibers for 3-4 μm spectral region,” Opt. Express 20(10), 11153–11158 (2012).
    [Crossref] [PubMed]
  17. A. D. Pryamikov, A. S. Biriukov, A. F. Kosolapov, V. G. Plotnichenko, S. L. Semjonov, and E. M. Dianov, “Demonstration of a waveguide regime for a silica hollow--core microstructured optical fiber with a negative curvature of the core boundary in the spectral region > 3.5 μm,” Opt. Express 19(2), 1441–1448 (2011).
    [Crossref] [PubMed]
  18. A. N. Kolyadin, A. F. Kosolapov, A. D. Pryamikov, A. S. Biriukov, V. G. Plotnichenko, and E. M. Dianov, “Light transmission in negative curvature hollow core fiber in extremely high material loss region,” Opt. Express 21(8), 9514–9519 (2013).
    [Crossref] [PubMed]
  19. L. Vincetti and V. Setti, “Waveguiding mechanism in tube lattice fibers,” Opt. Express 18(22), 23133–23146 (2010).
    [Crossref] [PubMed]
  20. J. R. Hayes, F. Poletti, and D. J. Richardson, Reducing loss in practical single ring antiresonant hollow core fibers,” in CLEO/Europe and EQEC 2011 Conference Digest, (Optical Society of America, 2011), CJ2 2.
  21. F. Poletti, J. R. Hayes, and D. J. Richardson, “Low loss antiresonant hollow core fibers,” in Specialty Optical Fibers, (Optical Society of America, 2011), SOWB1.2.

2013 (4)

2012 (1)

2011 (2)

2010 (3)

2007 (1)

J. Tauer, F. Orban, H. Koer, A. B. Fedotov, I. V. Fedotov, V. P. Mitrokhin, A. M. Zheltikov, and E. Wintner, “High-throughput of single high-power laser pulses by hollow photonic band gap fibers,” Laser Phys. Lett. 4(6), 444–448 (2007).
[Crossref]

2006 (1)

1999 (1)

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285(5433), 1537–1539 (1999).
[Crossref] [PubMed]

1986 (1)

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures,” Appl. Phys. Lett. 49(1), 13–15 (1986).
[Crossref]

1981 (1)

1980 (1)

M. Miyagi and S. Nishida, “A proposal of low-loss leaky waveguide for submillimeter waves transmission,” IEEE Trans. Microw. Theory Tech. 28(4), 398–401 (1980).
[Crossref]

1964 (1)

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43(4), 1783–1809 (1964).
[Crossref]

Alharbi, M.

Allan, D. C.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285(5433), 1537–1539 (1999).
[Crossref] [PubMed]

Auguste, J.-L.

Beaudou, B.

Benabid, F.

Biriukov, A. S.

Birks, T. A.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285(5433), 1537–1539 (1999).
[Crossref] [PubMed]

Blondy, J.-M.

Bradley, T.

Couny, F.

Cregan, R. F.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285(5433), 1537–1539 (1999).
[Crossref] [PubMed]

Debord, B.

Dianov, E. M.

Duguay, M. A.

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures,” Appl. Phys. Lett. 49(1), 13–15 (1986).
[Crossref]

Fedotov, A. B.

J. Tauer, F. Orban, H. Koer, A. B. Fedotov, I. V. Fedotov, V. P. Mitrokhin, A. M. Zheltikov, and E. Wintner, “High-throughput of single high-power laser pulses by hollow photonic band gap fibers,” Laser Phys. Lett. 4(6), 444–448 (2007).
[Crossref]

Fedotov, I. V.

J. Tauer, F. Orban, H. Koer, A. B. Fedotov, I. V. Fedotov, V. P. Mitrokhin, A. M. Zheltikov, and E. Wintner, “High-throughput of single high-power laser pulses by hollow photonic band gap fibers,” Laser Phys. Lett. 4(6), 444–448 (2007).
[Crossref]

Février, S.

Fourcade-Dutin, C.

Gérôme, F.

Ghosh, D.

Humbert, G.

Jamier, R.

Knight, J. C.

F. Yu, W. J. Wadsworth, and J. C. Knight, “Low loss silica hollow core fibers for 3-4 μm spectral region,” Opt. Express 20(10), 11153–11158 (2012).
[Crossref] [PubMed]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285(5433), 1537–1539 (1999).
[Crossref] [PubMed]

Koch, T. L.

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures,” Appl. Phys. Lett. 49(1), 13–15 (1986).
[Crossref]

Koer, H.

J. Tauer, F. Orban, H. Koer, A. B. Fedotov, I. V. Fedotov, V. P. Mitrokhin, A. M. Zheltikov, and E. Wintner, “High-throughput of single high-power laser pulses by hollow photonic band gap fibers,” Laser Phys. Lett. 4(6), 444–448 (2007).
[Crossref]

Kokubun, Y.

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures,” Appl. Phys. Lett. 49(1), 13–15 (1986).
[Crossref]

Kolyadin, A. N.

Kosolapov, A. F.

Light, P. S.

Mangan, B. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285(5433), 1537–1539 (1999).
[Crossref] [PubMed]

Marcatili, E. A. J.

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43(4), 1783–1809 (1964).
[Crossref]

Mitrokhin, V. P.

J. Tauer, F. Orban, H. Koer, A. B. Fedotov, I. V. Fedotov, V. P. Mitrokhin, A. M. Zheltikov, and E. Wintner, “High-throughput of single high-power laser pulses by hollow photonic band gap fibers,” Laser Phys. Lett. 4(6), 444–448 (2007).
[Crossref]

Miyagi, M.

M. Miyagi, “Bending losses in hollow and dielectric tube leaky waveguides,” Appl. Opt. 20(7), 1221–1229 (1981).
[Crossref] [PubMed]

M. Miyagi and S. Nishida, “A proposal of low-loss leaky waveguide for submillimeter waves transmission,” IEEE Trans. Microw. Theory Tech. 28(4), 398–401 (1980).
[Crossref]

Nishida, S.

M. Miyagi and S. Nishida, “A proposal of low-loss leaky waveguide for submillimeter waves transmission,” IEEE Trans. Microw. Theory Tech. 28(4), 398–401 (1980).
[Crossref]

Orban, F.

J. Tauer, F. Orban, H. Koer, A. B. Fedotov, I. V. Fedotov, V. P. Mitrokhin, A. M. Zheltikov, and E. Wintner, “High-throughput of single high-power laser pulses by hollow photonic band gap fibers,” Laser Phys. Lett. 4(6), 444–448 (2007).
[Crossref]

Petrovich, M. N.

F. Poletti, M. N. Petrovich, and D. J. Richardson, “Hollow-core photonic bandgap fibers: technology and applications,” Nanophotonics 2(5-6), 315–340 (2013).
[Crossref]

Pfeiffer, L.

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures,” Appl. Phys. Lett. 49(1), 13–15 (1986).
[Crossref]

Plotnichenko, V. G.

Poletti, F.

F. Poletti, M. N. Petrovich, and D. J. Richardson, “Hollow-core photonic bandgap fibers: technology and applications,” Nanophotonics 2(5-6), 315–340 (2013).
[Crossref]

Pryamikov, A. D.

Richardson, D. J.

F. Poletti, M. N. Petrovich, and D. J. Richardson, “Hollow-core photonic bandgap fibers: technology and applications,” Nanophotonics 2(5-6), 315–340 (2013).
[Crossref]

Roberts, P. J.

Y. Y. Wang, N. V. Wheeler, F. Couny, P. J. Roberts, and F. Benabid, “Low loss broadband transmission in hypocycloid-core Kagome hollow-core photonic crystal fiber,” Opt. Lett. 36(5), 669–671 (2011).
[Crossref] [PubMed]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285(5433), 1537–1539 (1999).
[Crossref] [PubMed]

Russell, P. S.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285(5433), 1537–1539 (1999).
[Crossref] [PubMed]

Schmeltzer, R. A.

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43(4), 1783–1809 (1964).
[Crossref]

Semjonov, S. L.

Setti, V.

Tauer, J.

J. Tauer, F. Orban, H. Koer, A. B. Fedotov, I. V. Fedotov, V. P. Mitrokhin, A. M. Zheltikov, and E. Wintner, “High-throughput of single high-power laser pulses by hollow photonic band gap fibers,” Laser Phys. Lett. 4(6), 444–448 (2007).
[Crossref]

Viale, P.

Vincetti, L.

Wadsworth, W. J.

Wang, Y. Y.

Wheeler, N. V.

Wintner, E.

J. Tauer, F. Orban, H. Koer, A. B. Fedotov, I. V. Fedotov, V. P. Mitrokhin, A. M. Zheltikov, and E. Wintner, “High-throughput of single high-power laser pulses by hollow photonic band gap fibers,” Laser Phys. Lett. 4(6), 444–448 (2007).
[Crossref]

Yu, F.

Zheltikov, A. M.

J. Tauer, F. Orban, H. Koer, A. B. Fedotov, I. V. Fedotov, V. P. Mitrokhin, A. M. Zheltikov, and E. Wintner, “High-throughput of single high-power laser pulses by hollow photonic band gap fibers,” Laser Phys. Lett. 4(6), 444–448 (2007).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures,” Appl. Phys. Lett. 49(1), 13–15 (1986).
[Crossref]

Bell Syst. Tech. J. (1)

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43(4), 1783–1809 (1964).
[Crossref]

IEEE Trans. Microw. Theory Tech. (1)

M. Miyagi and S. Nishida, “A proposal of low-loss leaky waveguide for submillimeter waves transmission,” IEEE Trans. Microw. Theory Tech. 28(4), 398–401 (1980).
[Crossref]

Laser Phys. Lett. (1)

J. Tauer, F. Orban, H. Koer, A. B. Fedotov, I. V. Fedotov, V. P. Mitrokhin, A. M. Zheltikov, and E. Wintner, “High-throughput of single high-power laser pulses by hollow photonic band gap fibers,” Laser Phys. Lett. 4(6), 444–448 (2007).
[Crossref]

Nanophotonics (1)

F. Poletti, M. N. Petrovich, and D. J. Richardson, “Hollow-core photonic bandgap fibers: technology and applications,” Nanophotonics 2(5-6), 315–340 (2013).
[Crossref]

Opt. Express (7)

S. Février, B. Beaudou, and P. Viale, “Understanding origin of loss in large pitch hollow-core photonic crystal fibers and their design simplification,” Opt. Express 18(5), 5142–5150 (2010).
[Crossref] [PubMed]

F. Yu, W. J. Wadsworth, and J. C. Knight, “Low loss silica hollow core fibers for 3-4 μm spectral region,” Opt. Express 20(10), 11153–11158 (2012).
[Crossref] [PubMed]

A. N. Kolyadin, A. F. Kosolapov, A. D. Pryamikov, A. S. Biriukov, V. G. Plotnichenko, and E. M. Dianov, “Light transmission in negative curvature hollow core fiber in extremely high material loss region,” Opt. Express 21(8), 9514–9519 (2013).
[Crossref] [PubMed]

B. Debord, M. Alharbi, T. Bradley, C. Fourcade-Dutin, Y. Y. Wang, L. Vincetti, F. Gérôme, and F. Benabid, “Hypocycloid-shaped hollow-core photonic crystal fiber Part I: Arc curvature effect on confinement loss,” Opt. Express 21(23), 28597–28608 (2013).
[Crossref] [PubMed]

M. Alharbi, T. Bradley, B. Debord, C. Fourcade-Dutin, D. Ghosh, L. Vincetti, F. Gérôme, and F. Benabid, “Hypocycloid-shaped hollow-core photonic crystal fiber part II: Cladding effect on confinement and bend loss,” Opt. Express 21(23), 28609–28616 (2013).
[Crossref] [PubMed]

L. Vincetti and V. Setti, “Waveguiding mechanism in tube lattice fibers,” Opt. Express 18(22), 23133–23146 (2010).
[Crossref] [PubMed]

A. D. Pryamikov, A. S. Biriukov, A. F. Kosolapov, V. G. Plotnichenko, S. L. Semjonov, and E. M. Dianov, “Demonstration of a waveguide regime for a silica hollow--core microstructured optical fiber with a negative curvature of the core boundary in the spectral region > 3.5 μm,” Opt. Express 19(2), 1441–1448 (2011).
[Crossref] [PubMed]

Opt. Lett. (3)

Science (1)

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285(5433), 1537–1539 (1999).
[Crossref] [PubMed]

Other (4)

C. J. Hensley, M. A. Foster, B. Shim, and A. L. Gaeta, “Extremely high coupling and transmission of high-powered-femtosecond pulses in hollow-core photonic band-gap fiber,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies,” Technical Digest (CD) (Optical Society of America, 2008).
[Crossref]

Y. Jung, V. A. J. M. Sleiffer, N. Baddela, M. N. Petrovich, J. R. Hayes, N. V. Wheeler, D. R. Gray, E. Numkam Fokoua, J. P. Wooler, N. H.-L. Wong, F. Parmigiani, S. U. Alam, J. Surof, M. Kuschnerov, V. Veljanovski, H. De Waardt, F. Poletti, and D. J. Richardson, “First demonstration of a broadband 37-cell hollow core photonic bandgap fiber and its application to high capacity mode division multiplexing,” in Optical Fiber Communication Conference 2013, (Optical Society of America, 2013), paper PDP5A.3.

J. R. Hayes, F. Poletti, and D. J. Richardson, Reducing loss in practical single ring antiresonant hollow core fibers,” in CLEO/Europe and EQEC 2011 Conference Digest, (Optical Society of America, 2011), CJ2 2.

F. Poletti, J. R. Hayes, and D. J. Richardson, “Low loss antiresonant hollow core fibers,” in Specialty Optical Fibers, (Optical Society of America, 2011), SOWB1.2.

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Figures (9)

Fig. 1
Fig. 1 (a) Calculated confinement loss of various circularly symmetric glass-air structures: capillary fiber, tubular fiber in air and jacketed tubular fibers with optimised and non-optimized jacket separation. The curves refer to the fibers shown in the inset, where air regions are shown in white, the core radius is 15 μm and core tube thickness is 0.42 μm. (b) Calculated confinement loss vs radius r for capillary (circles), tubular (diamonds) and optimized jacketed tubular fiber (squares).
Fig. 2
Fig. 2 Calculated loss at three wavelengths vs normalized air gap (z/r) for the structure shown in the insert.
Fig. 3
Fig. 3 FEM calculations of the confinement loss of two fiber structures (S1 blue, S2 black) that may be fabricated from a stack of 6 capillaries, a 2 layer Kagome structure (S3 orange) and an optimized, jacketed tubular tube introduced in the previous section (red: FEM simulation; black dashed: semi-analytic matrix method). All fibers have the same core inradius r = 15 µm and thickness of the core surround t = 0.42 µm.
Fig. 4
Fig. 4 Calculated confinement loss for hexagram fibers without thickened nodes (black curve) and with two sizes of thickened nodes (green and blue curves). The loss of a jacketed tubular fiber with optimised jacket separation is shown by the red curve. All fibers have r = 15 µm t = 0.42 µm as in Fig. 3.
Fig. 5
Fig. 5 Measured loss for two fibers (top and bottom) with azimuthally elongated nodes compared to calculated confinement loss for a reference jacketed tubular fiber having the same dimensions r,t in each case. Electron micrographs of the hexagram region of each fiber and a higher magnification image of a node are also shown on the left. The mode image (top insert) was obtained from 2.1m of fibre over the spectrum below 1.1 µm
Fig. 6
Fig. 6 Outline of the fabrication process (a) A stack of 6 capillaries. (b)An optical micrograph of a cane produced from the stack. (c) A cane is inserted inside a jacket tube and the cane is pressurized during fiber draw as described in the text. (d) Electron micrograph of a hexagram fiber with tilted nodes.
Fig. 7
Fig. 7 (a) Measured loss of hexagram fiber with azimuthal nodes (black curve), hexagram fiber with non-optimized tilted nodes (blue curve), 2r ~54 µm, t~0.31 µm at bend radius 20 cm and calculated confinement loss for a jacketed tubular fiber (dashed curve) having the same r,t . (b) Bend loss relative to R = 20cm of the hexagram fiber with azimuthal nodes for bend radii from 10cm to 4cm.
Fig. 8
Fig. 8 (a) Measured loss of hexagram fiber (solid curve) with tilted nodes, 2r ~50 µm, t~0.31 µm at bend radius 20 cm and calculated confinement loss for a jacketed tubular fiber (dashed curve) having the same r,t . The mode image (insert) was obtained from fiber length ~13m. (b) Bend loss relative to R = 20cm of same fiber for bend radii from 10cm to 4cm.
Fig. 9
Fig. 9 Comparison between the calculated loss of fibers having radially aligned sharp intersections (red curve) and rounded radially aligned nodes (green curve). Both have 2r = 50 µm, t~0.31 µm. Measured loss of the fabricated fiber is shown by the blue curve. The inserts to the right of the graph are electron micrographs for the fabricated fiber and drawings for the simulated fibers at a different scale.

Equations (4)

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α(r,R,λ) k 1 ( λ 2 r 3 )+ k 2 ( r 3 λ 2 1 R 2 )
α min (r,R,λ) w 1 ( λ 3 r 4 )+ w 2 ( r 2 λ 1 R 2 )
λ m = 2t m n 2 1
z opt = λ 4 1 n eff 2 π 2 J 01 r0.65r

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