Abstract

A method based on topology optimization is presented to design the cross section of hollow-core photonic bandgap fibers for minimizing energy loss by material absorption. The optical problem is modeled by the time-harmonic wave equation and solved with the finite element program Comsol Multiphysics. The optimization is based on continuous material interpolation functions between the refractive indices and is carried out by the method of moving asymptotes. An example illustrates the performance of the method where air and silica are redistributed around the core so that the overlap between the magnetic field distribution and the lossy silica material is reduced and the energy flow is increased 375% in the core. Simplified designs inspired from optimized geometry are presented, which will be easier to fabricate. The energy flow is increased up to almost 300% for these cases.

© 2009 Optical Society of America

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2009 (1)

O. Sigmund, “Manufacturing tolerant topology optimization,” Acta Mech. Sin. 25, 227-239 (2009).
[CrossRef]

2008 (4)

2007 (3)

R. Amezcua-Correa, N. G. R. Broderick, M. N. Petrovich, F. Poletti, and D. J. Richardson, “Design of 7 and 19 cells core air-guiding photonic crystal fibers for low-loss, wide bandwidth and dispersion controlled operation,” Opt. Express 15, 17577-17586 (2007).
[CrossRef] [PubMed]

R. Stainko and O. Sigmund, “Tailoring dispersion properties of photonic crystal waveguides by topology optimization,” Waves Random Complex Media 17, 477-489 (2007).
[CrossRef]

O. Sigmund, “Morphology-based black and white filters for topology optimization,” Struct. Multidiscip. Optim. 33, 401-424 (2007).
[CrossRef]

2006 (2)

L. H. Olesen, F. Okkels, and H. Bruus, “A high-level programming-language implementation of topology optimization applied to steady-state Navier-Stokes flow,” Int. J. Numer. Methods Eng. 65, 975-1001 (2006).
[CrossRef]

Y. Tsuji, K. Hirayama, T. Nomura, K. Sato, and S. Nishiwaki, “Design of optical circuit devices based on topology optimization,” IEEE Photonics Technol. Lett. 18, 850-852 (2006).
[CrossRef]

2005 (5)

J. S. Jensen and O. Sigmund, “Topology optimization of photonic crystal structures: a high bandwidth low loss T-junction waveguide,” J. Opt. Soc. Am. B 22, 1191-1198 (2005).
[CrossRef]

P. I. Borel, L. H. Frandsen, A. Harpøth, M. Kristensen, J. S. Jensen, and O. Sigmund, “Topology optimized broadband photonic crystal Y-splitter,” Electron. Lett. 41, 69-71 (2005).
[CrossRef]

P. J. Roberts, D. P. Williams, B. J. Mangan, H. Sabert, F. Couny, W. J. Wadsworth, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Realizing low loss air core photonic crystal fibers by exploiting an antiresonant core surround,” Opt. Express 13, 8277-8285 (2005).
[CrossRef] [PubMed]

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” Proc. SPIE 5686, 310-321 (2005).
[CrossRef]

P. J. Roberts, F. Couney, H. Sabert, B. J. Mangan, D. P. Williams, L. Farr, M. W. Mason, A. Tomlinson, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Ultimate low loss of hollow-core photonic crystal fibers,” Opt. Express 13, 236-244 (2005).
[CrossRef] [PubMed]

2004 (2)

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, “Designing air-core photonic-bandgap fibers free of surface modes,” IEEE J. Quantum Electron. 40, 551-556 (2004).
[CrossRef]

P. I. Borel, A. Harpøth, L. H. Frandsen, M. Kristensen, P. Shi, J. S. Jensen, and O. Sigmund, “Topology optimization and fabrication of photonic crystal structures,” Opt. Express 12, 1996-2001 (2004).
[CrossRef] [PubMed]

2003 (3)

O. Sigmund and J. S. Jensen, “Systematic design of phononic bandgap materials and structures by topology optimization,” Philos. Trans. R. Soc. London, Ser. A 361, 1001-1019 (2003).
[CrossRef]

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fiber,” Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

P. Russell, “Photonic crystal fibers,” Science 299, 358-362 (2003).
[CrossRef] [PubMed]

1999 (3)

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

S. E. Barkou, J. Broeng, and A. Bjarklev, “Silica-air photonic crystal fiber design that permits waveguiding by a true photonic bandgap effect,” Opt. Lett. 24, 46-48 (1999).
[CrossRef]

S. J. Cox and D. C. Dobson, “Maximizing band gaps in two-dimensional photonic crystals,” SIAM J. Appl. Math. 59, 2108-2120 (1999).
[CrossRef]

1996 (1)

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 699-702 (1996).
[CrossRef]

1995 (1)

T. A. Birks, P. J. Roberts, P. St. J. Russell, D. M. Atkin, and T. J. Shepherd, “Full 2-D photonic bandgaps in silica/air structures,” Electron. Lett. 31, 1941-1943 (1995).
[CrossRef]

1994 (1)

D. A. Tortorelli and P. Michaleris, “Design sensitivity analysis: overview and review,” Inverse Probl. Sci. Eng. 1, 71-105 (1994).
[CrossRef]

1988 (1)

M. P. Bendsøe and N. Kikuchi, “Generating optimal topologies in structural design using a homogenization method,” Comput. Methods Appl. Mech. Eng. 71, 197-224 (1988).
[CrossRef]

1987 (3)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

K. Svanberg, “The method of moving asymptotes--a new method for structural optimization,” Int. J. Numer. Methods Eng. 24, 359-373 (1987).
[CrossRef]

1977 (1)

Ahmad, R. U.

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” Proc. SPIE 5686, 310-321 (2005).
[CrossRef]

Allan, D. C.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fiber,” Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

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

Amezcua-Correa, R.

Anastassiou, C.

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” Proc. SPIE 5686, 310-321 (2005).
[CrossRef]

Atkin, D. M.

T. A. Birks, P. J. Roberts, P. St. J. Russell, D. M. Atkin, and T. J. Shepherd, “Full 2-D photonic bandgaps in silica/air structures,” Electron. Lett. 31, 1941-1943 (1995).
[CrossRef]

Barkou, S. E.

Bendsøe, M. P.

M. P. Bendsøe and N. Kikuchi, “Generating optimal topologies in structural design using a homogenization method,” Comput. Methods Appl. Mech. Eng. 71, 197-224 (1988).
[CrossRef]

M. P. Bendsøe and O. Sigmund, Topology Optimization, Theory, Methods and Applications (Springer, 2003).

Birks, T. A.

Bjarklev, A.

Borel, P. I.

P. I. Borel, L. H. Frandsen, A. Harpøth, M. Kristensen, J. S. Jensen, and O. Sigmund, “Topology optimized broadband photonic crystal Y-splitter,” Electron. Lett. 41, 69-71 (2005).
[CrossRef]

P. I. Borel, A. Harpøth, L. H. Frandsen, M. Kristensen, P. Shi, J. S. Jensen, and O. Sigmund, “Topology optimization and fabrication of photonic crystal structures,” Opt. Express 12, 1996-2001 (2004).
[CrossRef] [PubMed]

Borrelli, N. F.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fiber,” Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Brand, S.

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 699-702 (1996).
[CrossRef]

Broderick, N. G. R.

Broeng, J.

Bruus, H.

L. H. Olesen, F. Okkels, and H. Bruus, “A high-level programming-language implementation of topology optimization applied to steady-state Navier-Stokes flow,” Int. J. Numer. Methods Eng. 65, 975-1001 (2006).
[CrossRef]

Couney, F.

Couny, F.

Cox, S. J.

S. J. Cox and D. C. Dobson, “Maximizing band gaps in two-dimensional photonic crystals,” SIAM J. Appl. Math. 59, 2108-2120 (1999).
[CrossRef]

Cozens, J.

R. Syms and J. Cozens, Optical Guided Waves and Devices, 1st ed. (McGraw-Hill, 1992).

Cregan, R. F.

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

De La Rue, R. M.

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 699-702 (1996).
[CrossRef]

Devaiah, A. K.

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” Proc. SPIE 5686, 310-321 (2005).
[CrossRef]

Digonnet, M. J. F.

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, “Designing air-core photonic-bandgap fibers free of surface modes,” IEEE J. Quantum Electron. 40, 551-556 (2004).
[CrossRef]

Dobson, D. C.

S. J. Cox and D. C. Dobson, “Maximizing band gaps in two-dimensional photonic crystals,” SIAM J. Appl. Math. 59, 2108-2120 (1999).
[CrossRef]

Dühring, M. B.

M. B. Dühring, J. S. Jensen, and O. Sigmund, “Acoustic design by topology optimization,” J. Sound Vib. 317, 557-575 (2008).
[CrossRef]

Fan, S.

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, “Designing air-core photonic-bandgap fibers free of surface modes,” IEEE J. Quantum Electron. 40, 551-556 (2004).
[CrossRef]

Farr, L.

Frandsen, L. H.

P. I. Borel, L. H. Frandsen, A. Harpøth, M. Kristensen, J. S. Jensen, and O. Sigmund, “Topology optimized broadband photonic crystal Y-splitter,” Electron. Lett. 41, 69-71 (2005).
[CrossRef]

P. I. Borel, A. Harpøth, L. H. Frandsen, M. Kristensen, P. Shi, J. S. Jensen, and O. Sigmund, “Topology optimization and fabrication of photonic crystal structures,” Opt. Express 12, 1996-2001 (2004).
[CrossRef] [PubMed]

Gallagher, M. T.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fiber,” Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Harpøth, A.

P. I. Borel, L. H. Frandsen, A. Harpøth, M. Kristensen, J. S. Jensen, and O. Sigmund, “Topology optimized broadband photonic crystal Y-splitter,” Electron. Lett. 41, 69-71 (2005).
[CrossRef]

P. I. Borel, A. Harpøth, L. H. Frandsen, M. Kristensen, P. Shi, J. S. Jensen, and O. Sigmund, “Topology optimization and fabrication of photonic crystal structures,” Opt. Express 12, 1996-2001 (2004).
[CrossRef] [PubMed]

Hirayama, K.

Y. Tsuji, K. Hirayama, T. Nomura, K. Sato, and S. Nishiwaki, “Design of optical circuit devices based on topology optimization,” IEEE Photonics Technol. Lett. 18, 850-852 (2006).
[CrossRef]

Hong, C.-S.

Hougaard, K.

O. Sigmund and K. Hougaard, “Geometrical properties of optimal photonic crystals,” Phys. Rev. Lett. 100, 153904 (2008).
[CrossRef] [PubMed]

Hu, J.

J. Hu and C. R. Menyuk, “Use of fingers in the core to reduce leakage loss in air-core photonic bandgap fibers,” in Proceedings of Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference (OFC/NFOEC), OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper OML6.
[PubMed]

Jacobs, S. A.

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” Proc. SPIE 5686, 310-321 (2005).
[CrossRef]

Jensen, J. S.

M. B. Dühring, J. S. Jensen, and O. Sigmund, “Acoustic design by topology optimization,” J. Sound Vib. 317, 557-575 (2008).
[CrossRef]

J. S. Jensen and O. Sigmund, “Topology optimization of photonic crystal structures: a high bandwidth low loss T-junction waveguide,” J. Opt. Soc. Am. B 22, 1191-1198 (2005).
[CrossRef]

P. I. Borel, L. H. Frandsen, A. Harpøth, M. Kristensen, J. S. Jensen, and O. Sigmund, “Topology optimized broadband photonic crystal Y-splitter,” Electron. Lett. 41, 69-71 (2005).
[CrossRef]

P. I. Borel, A. Harpøth, L. H. Frandsen, M. Kristensen, P. Shi, J. S. Jensen, and O. Sigmund, “Topology optimization and fabrication of photonic crystal structures,” Opt. Express 12, 1996-2001 (2004).
[CrossRef] [PubMed]

O. Sigmund and J. S. Jensen, “Systematic design of phononic bandgap materials and structures by topology optimization,” Philos. Trans. R. Soc. London, Ser. A 361, 1001-1019 (2003).
[CrossRef]

Joannopoulos, J. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals, Molding the Flow of Light, 2nd ed. (Princeton Univ. Press, 2008).

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

Johnson, S. G.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals, Molding the Flow of Light, 2nd ed. (Princeton Univ. Press, 2008).

Kikuchi, N.

M. P. Bendsøe and N. Kikuchi, “Generating optimal topologies in structural design using a homogenization method,” Comput. Methods Appl. Mech. Eng. 71, 197-224 (1988).
[CrossRef]

Kim, H. K.

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, “Designing air-core photonic-bandgap fibers free of surface modes,” IEEE J. Quantum Electron. 40, 551-556 (2004).
[CrossRef]

Kino, G. S.

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, “Designing air-core photonic-bandgap fibers free of surface modes,” IEEE J. Quantum Electron. 40, 551-556 (2004).
[CrossRef]

Knight, J. C.

Koch, K. W.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fiber,” Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Kolodny, U.

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” Proc. SPIE 5686, 310-321 (2005).
[CrossRef]

Koshiba, M.

Koufman, J. A.

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” Proc. SPIE 5686, 310-321 (2005).
[CrossRef]

Krauss, T. F.

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 699-702 (1996).
[CrossRef]

Kristensen, M.

P. I. Borel, L. H. Frandsen, A. Harpøth, M. Kristensen, J. S. Jensen, and O. Sigmund, “Topology optimized broadband photonic crystal Y-splitter,” Electron. Lett. 41, 69-71 (2005).
[CrossRef]

P. I. Borel, A. Harpøth, L. H. Frandsen, M. Kristensen, P. Shi, J. S. Jensen, and O. Sigmund, “Topology optimization and fabrication of photonic crystal structures,” Opt. Express 12, 1996-2001 (2004).
[CrossRef] [PubMed]

Mangan, B. J.

Mason, M. W.

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals, Molding the Flow of Light, 2nd ed. (Princeton Univ. Press, 2008).

Menyuk, C. R.

J. Hu and C. R. Menyuk, “Use of fingers in the core to reduce leakage loss in air-core photonic bandgap fibers,” in Proceedings of Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference (OFC/NFOEC), OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper OML6.
[PubMed]

Michaleris, P.

D. A. Tortorelli and P. Michaleris, “Design sensitivity analysis: overview and review,” Inverse Probl. Sci. Eng. 1, 71-105 (1994).
[CrossRef]

Müller, D.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fiber,” Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Murao, T.

Nishiwaki, S.

Y. Tsuji, K. Hirayama, T. Nomura, K. Sato, and S. Nishiwaki, “Design of optical circuit devices based on topology optimization,” IEEE Photonics Technol. Lett. 18, 850-852 (2006).
[CrossRef]

Nomura, T.

Y. Tsuji, K. Hirayama, T. Nomura, K. Sato, and S. Nishiwaki, “Design of optical circuit devices based on topology optimization,” IEEE Photonics Technol. Lett. 18, 850-852 (2006).
[CrossRef]

Okkels, F.

L. H. Olesen, F. Okkels, and H. Bruus, “A high-level programming-language implementation of topology optimization applied to steady-state Navier-Stokes flow,” Int. J. Numer. Methods Eng. 65, 975-1001 (2006).
[CrossRef]

Olesen, L. H.

L. H. Olesen, F. Okkels, and H. Bruus, “A high-level programming-language implementation of topology optimization applied to steady-state Navier-Stokes flow,” Int. J. Numer. Methods Eng. 65, 975-1001 (2006).
[CrossRef]

Petrovich, M. N.

Poletti, F.

Richardson, D. J.

Riishede, J.

Roberts, P. J.

Russell, P.

P. Russell, “Photonic crystal fibers,” Science 299, 358-362 (2003).
[CrossRef] [PubMed]

Russell, P. St. J.

Sabert, H.

Saitoh, K.

Sato, K.

Y. Tsuji, K. Hirayama, T. Nomura, K. Sato, and S. Nishiwaki, “Design of optical circuit devices based on topology optimization,” IEEE Photonics Technol. Lett. 18, 850-852 (2006).
[CrossRef]

Shapira, G.

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” Proc. SPIE 5686, 310-321 (2005).
[CrossRef]

Shapshay, S. M.

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” Proc. SPIE 5686, 310-321 (2005).
[CrossRef]

Shepherd, T. J.

T. A. Birks, P. J. Roberts, P. St. J. Russell, D. M. Atkin, and T. J. Shepherd, “Full 2-D photonic bandgaps in silica/air structures,” Electron. Lett. 31, 1941-1943 (1995).
[CrossRef]

Shi, P.

Shin, J.

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, “Designing air-core photonic-bandgap fibers free of surface modes,” IEEE J. Quantum Electron. 40, 551-556 (2004).
[CrossRef]

Shurgalin, M.

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” Proc. SPIE 5686, 310-321 (2005).
[CrossRef]

Sigmund, O.

O. Sigmund, “Manufacturing tolerant topology optimization,” Acta Mech. Sin. 25, 227-239 (2009).
[CrossRef]

O. Sigmund and K. Hougaard, “Geometrical properties of optimal photonic crystals,” Phys. Rev. Lett. 100, 153904 (2008).
[CrossRef] [PubMed]

M. B. Dühring, J. S. Jensen, and O. Sigmund, “Acoustic design by topology optimization,” J. Sound Vib. 317, 557-575 (2008).
[CrossRef]

J. Riishede and O. Sigmund, “Inverse design of dispersion compensating optical fiber using topology optimization,” J. Opt. Soc. Am. B 25, 88-97 (2008).
[CrossRef]

R. Stainko and O. Sigmund, “Tailoring dispersion properties of photonic crystal waveguides by topology optimization,” Waves Random Complex Media 17, 477-489 (2007).
[CrossRef]

O. Sigmund, “Morphology-based black and white filters for topology optimization,” Struct. Multidiscip. Optim. 33, 401-424 (2007).
[CrossRef]

P. I. Borel, L. H. Frandsen, A. Harpøth, M. Kristensen, J. S. Jensen, and O. Sigmund, “Topology optimized broadband photonic crystal Y-splitter,” Electron. Lett. 41, 69-71 (2005).
[CrossRef]

J. S. Jensen and O. Sigmund, “Topology optimization of photonic crystal structures: a high bandwidth low loss T-junction waveguide,” J. Opt. Soc. Am. B 22, 1191-1198 (2005).
[CrossRef]

P. I. Borel, A. Harpøth, L. H. Frandsen, M. Kristensen, P. Shi, J. S. Jensen, and O. Sigmund, “Topology optimization and fabrication of photonic crystal structures,” Opt. Express 12, 1996-2001 (2004).
[CrossRef] [PubMed]

O. Sigmund and J. S. Jensen, “Systematic design of phononic bandgap materials and structures by topology optimization,” Philos. Trans. R. Soc. London, Ser. A 361, 1001-1019 (2003).
[CrossRef]

M. P. Bendsøe and O. Sigmund, Topology Optimization, Theory, Methods and Applications (Springer, 2003).

Smith, C. M.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fiber,” Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Stainko, R.

R. Stainko and O. Sigmund, “Tailoring dispersion properties of photonic crystal waveguides by topology optimization,” Waves Random Complex Media 17, 477-489 (2007).
[CrossRef]

Svanberg, K.

K. Svanberg, “The method of moving asymptotes--a new method for structural optimization,” Int. J. Numer. Methods Eng. 24, 359-373 (1987).
[CrossRef]

Syms, R.

R. Syms and J. Cozens, Optical Guided Waves and Devices, 1st ed. (McGraw-Hill, 1992).

Temelkuran, B.

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” Proc. SPIE 5686, 310-321 (2005).
[CrossRef]

Tomlinson, A.

Torres, D.

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” Proc. SPIE 5686, 310-321 (2005).
[CrossRef]

Tortorelli, D. A.

D. A. Tortorelli and P. Michaleris, “Design sensitivity analysis: overview and review,” Inverse Probl. Sci. Eng. 1, 71-105 (1994).
[CrossRef]

Tsuji, Y.

Y. Tsuji, K. Hirayama, T. Nomura, K. Sato, and S. Nishiwaki, “Design of optical circuit devices based on topology optimization,” IEEE Photonics Technol. Lett. 18, 850-852 (2006).
[CrossRef]

Upadhyay, U. D.

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” Proc. SPIE 5686, 310-321 (2005).
[CrossRef]

Venkataraman, N.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fiber,” Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Wadsworth, W. J.

Wang, T.

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” Proc. SPIE 5686, 310-321 (2005).
[CrossRef]

Wang, Z.

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” Proc. SPIE 5686, 310-321 (2005).
[CrossRef]

Weisberg, O.

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” Proc. SPIE 5686, 310-321 (2005).
[CrossRef]

West, J. A.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fiber,” Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Williams, D. P.

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals, Molding the Flow of Light, 2nd ed. (Princeton Univ. Press, 2008).

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

Yariv, A.

Yeh, P.

Acta Mech. Sin. (1)

O. Sigmund, “Manufacturing tolerant topology optimization,” Acta Mech. Sin. 25, 227-239 (2009).
[CrossRef]

Comput. Methods Appl. Mech. Eng. (1)

M. P. Bendsøe and N. Kikuchi, “Generating optimal topologies in structural design using a homogenization method,” Comput. Methods Appl. Mech. Eng. 71, 197-224 (1988).
[CrossRef]

Electron. Lett. (2)

T. A. Birks, P. J. Roberts, P. St. J. Russell, D. M. Atkin, and T. J. Shepherd, “Full 2-D photonic bandgaps in silica/air structures,” Electron. Lett. 31, 1941-1943 (1995).
[CrossRef]

P. I. Borel, L. H. Frandsen, A. Harpøth, M. Kristensen, J. S. Jensen, and O. Sigmund, “Topology optimized broadband photonic crystal Y-splitter,” Electron. Lett. 41, 69-71 (2005).
[CrossRef]

IEEE J. Quantum Electron. (1)

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, “Designing air-core photonic-bandgap fibers free of surface modes,” IEEE J. Quantum Electron. 40, 551-556 (2004).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

Y. Tsuji, K. Hirayama, T. Nomura, K. Sato, and S. Nishiwaki, “Design of optical circuit devices based on topology optimization,” IEEE Photonics Technol. Lett. 18, 850-852 (2006).
[CrossRef]

Int. J. Numer. Methods Eng. (2)

L. H. Olesen, F. Okkels, and H. Bruus, “A high-level programming-language implementation of topology optimization applied to steady-state Navier-Stokes flow,” Int. J. Numer. Methods Eng. 65, 975-1001 (2006).
[CrossRef]

K. Svanberg, “The method of moving asymptotes--a new method for structural optimization,” Int. J. Numer. Methods Eng. 24, 359-373 (1987).
[CrossRef]

Inverse Probl. Sci. Eng. (1)

D. A. Tortorelli and P. Michaleris, “Design sensitivity analysis: overview and review,” Inverse Probl. Sci. Eng. 1, 71-105 (1994).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (2)

J. Sound Vib. (1)

M. B. Dühring, J. S. Jensen, and O. Sigmund, “Acoustic design by topology optimization,” J. Sound Vib. 317, 557-575 (2008).
[CrossRef]

Nature (2)

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fiber,” Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 699-702 (1996).
[CrossRef]

Opt. Express (4)

Opt. Lett. (1)

Philos. Trans. R. Soc. London, Ser. A (1)

O. Sigmund and J. S. Jensen, “Systematic design of phononic bandgap materials and structures by topology optimization,” Philos. Trans. R. Soc. London, Ser. A 361, 1001-1019 (2003).
[CrossRef]

Phys. Rev. Lett. (3)

O. Sigmund and K. Hougaard, “Geometrical properties of optimal photonic crystals,” Phys. Rev. Lett. 100, 153904 (2008).
[CrossRef] [PubMed]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

Proc. SPIE (1)

D. Torres, O. Weisberg, G. Shapira, C. Anastassiou, B. Temelkuran, M. Shurgalin, S. A. Jacobs, R. U. Ahmad, T. Wang, U. Kolodny, S. M. Shapshay, Z. Wang, A. K. Devaiah, U. D. Upadhyay, and J. A. Koufman, “OmniGuide photonic bandgap fibers for flexible delivery of CO2 laser energy for laryngeal and airway surgery,” Proc. SPIE 5686, 310-321 (2005).
[CrossRef]

Science (2)

P. Russell, “Photonic crystal fibers,” Science 299, 358-362 (2003).
[CrossRef] [PubMed]

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

SIAM J. Appl. Math. (1)

S. J. Cox and D. C. Dobson, “Maximizing band gaps in two-dimensional photonic crystals,” SIAM J. Appl. Math. 59, 2108-2120 (1999).
[CrossRef]

Struct. Multidiscip. Optim. (1)

O. Sigmund, “Morphology-based black and white filters for topology optimization,” Struct. Multidiscip. Optim. 33, 401-424 (2007).
[CrossRef]

Waves Random Complex Media (1)

R. Stainko and O. Sigmund, “Tailoring dispersion properties of photonic crystal waveguides by topology optimization,” Waves Random Complex Media 17, 477-489 (2007).
[CrossRef]

Other (6)

www.rsoftdesign.com.

COMSOL Reference Manual for COMSOL 3.5. COMSOL AB, Stockholm, www.comsol.se.

J. Hu and C. R. Menyuk, “Use of fingers in the core to reduce leakage loss in air-core photonic bandgap fibers,” in Proceedings of Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference (OFC/NFOEC), OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper OML6.
[PubMed]

M. P. Bendsøe and O. Sigmund, Topology Optimization, Theory, Methods and Applications (Springer, 2003).

R. Syms and J. Cozens, Optical Guided Waves and Devices, 1st ed. (McGraw-Hill, 1992).

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals, Molding the Flow of Light, 2nd ed. (Princeton Univ. Press, 2008).

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Figures (6)

Fig. 1
Fig. 1

Geometry of the photonic crystal fiber used in the optimization. Black indicates silica and white is air. The design domain is Ω d , and Ω c is the core region where the objective function is optimized.

Fig. 2
Fig. 2

Logarithm to the normalized objective function Φ Φ init as function of the optical wavelength λ 0 is indicated both for the initial design with different values of the absorption coefficient α s and for the optimized design with α s = 0.0001 .

Fig. 3
Fig. 3

Logarithm to the normalized objective function Φ Φ init as function of the number of iterations in the optimization. The four irregularities indicate the updating of α s .

Fig. 4
Fig. 4

Center region of the HC-PCF where black indicates silica and white is air. (a),(b) The contour lines show the distribution of the normalized energy measure from the objective function Φ Φ max in the initial and the optimized design, respectively. (c),(d) The normalized time average power flow P P max in the x 3 direction is indicated by the contour lines for the initial and the optimized design, respectively.

Fig. 5
Fig. 5

Geometry of the center region of the HC-PCF where black is silica and white is air. The contour lines indicate the normalized absolute value of the magnetic field | H 1 | | H 1 , max | . (a) Initial design. (b) Optimized design.

Fig. 6
Fig. 6

Four simplified geometries of the HC-PCF inspired from the optimized design. Black is silica and white is air. The contour lines show the distribution of the energy measure from the normalized objective function Φ Φ max .

Tables (1)

Tables Icon

Table 1 Increase of Objective Function Φ and Time-average Power flow P in the x 3 Direction for Optimized Design and Four Simplified Designs Compared to Values for Initial Design

Equations (12)

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

H p , ν ( x 1 , x 2 , x 3 ) = H p , ν ( x 1 , x 2 ) e i β ν x 3 ,
e i j k x j ( n 2 e k l p H p x l ) k 0 2 H i = 0 ,
H j ( r ) = n = 1 N H j , n φ j , n ( r ) .
j = 1 3 S k j H j = f k ,
n ( ξ ) = n a + ξ ( n s n a ) .
max ξ log ( Φ ) = log Ω c j = 1 2 | H j ( r , ξ ( r ) ) | 2 d r ,
subject to 0 ξ ( r ) 1 r Ω d .
ξ ( r ) = n = 1 N d ξ n φ 4 , n ( r ) .
d Φ d ξ = Φ ξ + k = 1 3 ( Φ H k R H k R ξ + Φ H k I H k I ξ ) .
j = 1 3 S k j λ j = ( Φ H k R i Φ H k I ) T ,
Φ H k , n R i Φ H k , n I = Ω c ( 2 H k R i 2 H k I ) φ k , n d r .
d Φ d ξ = Φ ξ + k = 1 3 R ( λ k T j = 1 3 S k j ξ H j ) .

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