Abstract

A novel design, two-layer low-index trench fiber with parabolic-profile core, is proposed and investigated numerically in this paper. Based on scalar FD-BPM algorithm, the excellent performance over other types of structures and great potential in mode area enlargement are demonstrated. The effective mode area of our design (D = 100μm) is approximately 890 μm2. Both the high order mode (HOM) suppression and bending resistance of our design are better than that of Multi-Trench Fiber (MTF). The mode loss ratio and effective mode area are independent on the bending radius. Due to the circular symmetry of our proposed configuration design, the bending property is not varied with the changing of bending directions.

© 2014 Optical Society of America

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References

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  1. D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: current status and future perspectives [Invited],” J. Opt. Soc. Am. B 27(11), B63–B92 (2010).
    [CrossRef]
  2. S. C. Kumar, G. K. Samanta, K. Devi, S. Sanguinetti, and M. Ebrahim-Zadeh, “Single-frequency, high-power, continuous-wave fiber-laser-pumped Ti:sapphire laser,” Appl. Opt. 51(1), 15–20 (2012).
    [CrossRef] [PubMed]
  3. V. Gapontsev, V. Fomin, A. Ferin, and M. Abramov, “Diffraction limited ultra-high-power fiber lasers,” in Advanced Solid-State Photonics (Optical Society of America, 2010), p. AWA1.
  4. F. Kong, K. Saitoh, D. Mcclane, T. Hawkins, P. Foy, G. Gu, and L. Dong, “Mode area scaling with all-solid photonic bandgap fibers,” Opt. Express 20(24), 26363–26372 (2012).
    [CrossRef] [PubMed]
  5. J. P. Koplow, D. A. V. Kliner, and L. Goldberg, “Single-mode operation of a coiled multimode fiber amplifier,” Opt. Lett. 25(7), 442–444 (2000).
    [CrossRef] [PubMed]
  6. C.-H. Liu, G. Chang, N. Litchinitser, D. Guertin, N. Jacobsen, K. Tankala, and A. Galvanauskas, “Chirally coupled core fibers at 1550-nm and 1064-nm for effectively single-mode core size scaling,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies (Optical Society of America, Baltimore, Maryland, 2007), p. CTuBB3.
    [CrossRef]
  7. M. Devautour, P. Roy, and S. Février, “3-D modeling of modal competition in fiber laser: application to HOM suppression in multi-layered fiber,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference (Optical Society of America, Baltimore, Maryland, 2009), p. JWA54.
    [CrossRef]
  8. M. Napierała, T. Nasilowski, E. Bereś-Pawlik, P. Mergo, F. Berghmans, and H. Thienpont, “Large-mode-area photonic crystal fiber with double lattice constant structure and low bending loss,” Opt. Express 19(23), 22628–22636 (2011).
    [CrossRef] [PubMed]
  9. J. M. Fini, “Bend-resistant design of conventional and microstructure fibers with very large mode area,” Opt. Express 14(1), 69–81 (2006).
    [CrossRef] [PubMed]
  10. A. E. Siegman, “Gain-guided, index-antiguided fiber lasers,” J. Opt. Soc. Am. B 24(8), 1677–1682 (2007).
    [CrossRef]
  11. L. A. Dong, J. Li, H. A. McKay, L. B. Fu, and B. K. Thomas, “Large effective mode area optical fibers for high power lasers,” Proc. SPIE 7195, 71950N (2009).
    [CrossRef]
  12. D. Jain, C. Baskiotis, and J. K. Sahu, “Mode area scaling with multi-trench rod-type fibers,” Opt. Express 21(2), 1448–1455 (2013).
    [CrossRef] [PubMed]
  13. D. Jain, C. Baskiotis, and J. K. Sahu, “Bending performance of large mode area multi-trench fibers,” Opt. Express 21(22), 26663–26670 (2013).
    [CrossRef] [PubMed]
  14. A. Abeeluck, N. Litchinitser, C. Headley, and B. Eggleton, “Analysis of spectral characteristics of photonic bandgap waveguides,” Opt. Express 10(23), 1320–1333 (2002).
    [CrossRef] [PubMed]
  15. J. Van Roey, J. van derDonk, and P. E. Lagasse, “Beam-propagation method: analysis and assessment,” J. Opt. Soc. Am. 71(7), 803–810 (1981).
    [CrossRef]
  16. Y. Chung and N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron. 26(8), 1335–1339 (1990).
    [CrossRef]
  17. L. Dong, H. A. McKay, A. Marcinkevicius, L. Fu, J. Li, B. K. Thomas, and M. E. Fermann, “Extending effective area of fundamental mode in optical fibers,” J. Lightwave Technol. 27(11), 1565–1570 (2009).
    [CrossRef]
  18. G. C. Gu, F. T. Kong, T. W. Hawkins, P. Foy, K. X. Wei, B. Samson, and L. Dong, “Impact of fiber outer boundaries on leaky mode losses in leakage channel fibers,” Opt. Express 21(20), 24039–24048 (2013).
    [CrossRef] [PubMed]
  19. D. Marcuse, “Influence of curvature on the losses of doubly clad fibers,” Appl. Opt. 21(23), 4208–4213 (1982).
    [CrossRef] [PubMed]
  20. J. Fini, “Design of solid and microstructure fibers for suppression of higher-order modes,” Opt. Express 13(9), 3477–3490 (2005).
    [CrossRef] [PubMed]
  21. R. Zuitlin, Y. Shamir, Y. Sintov, and M. Shtaif, “Modeling the evolution of spatial beam parameters in parabolic index fibers,” Opt. Lett. 37(17), 3636–3638 (2012).
    [CrossRef] [PubMed]
  22. M.-J. Li, X. Chen, A. Liu, S. Gray, J. Wang, D. T. Walton, and L. A. Zenteno, “Limit of effective area for single-mode operation in step-index large mode area laser fibers,” J. Lightwave Technol. 27(15), 3010–3016 (2009).
    [CrossRef]
  23. Y. Jeong, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, L. M. B. Hickey, and P. W. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500 W,” IEEE J. Sel. Top. Quantum Electron. 13(3), 546–551 (2007).
    [CrossRef]
  24. Y. Jeong, J. Sahu, D. Payne, and J. Nilsson, “Ytterbium-doped large-core fiber laser with 1.36 kW continuous-wave output power,” Opt. Express 12(25), 6088–6092 (2004).
    [CrossRef] [PubMed]
  25. Y. Jeong, A. J. Boyland, J. K. Sahu, S. Chung, J. Nilsson, and D. N. Payne, “Multi-kilowatt single-mode ytterbium-doped large-core fiber laser,” J. Opt. Soc. Korea. 13(4), 416–422 (2009).
    [CrossRef]
  26. J. M. Fini, “Design of large-mode-area amplifier fibers resistant to bend-induced distortion,” J. Opt. Soc. Am. B 24(8), 1669–1676 (2007).
    [CrossRef]

2013 (3)

2012 (3)

2011 (1)

2010 (1)

2009 (4)

L. A. Dong, J. Li, H. A. McKay, L. B. Fu, and B. K. Thomas, “Large effective mode area optical fibers for high power lasers,” Proc. SPIE 7195, 71950N (2009).
[CrossRef]

L. Dong, H. A. McKay, A. Marcinkevicius, L. Fu, J. Li, B. K. Thomas, and M. E. Fermann, “Extending effective area of fundamental mode in optical fibers,” J. Lightwave Technol. 27(11), 1565–1570 (2009).
[CrossRef]

M.-J. Li, X. Chen, A. Liu, S. Gray, J. Wang, D. T. Walton, and L. A. Zenteno, “Limit of effective area for single-mode operation in step-index large mode area laser fibers,” J. Lightwave Technol. 27(15), 3010–3016 (2009).
[CrossRef]

Y. Jeong, A. J. Boyland, J. K. Sahu, S. Chung, J. Nilsson, and D. N. Payne, “Multi-kilowatt single-mode ytterbium-doped large-core fiber laser,” J. Opt. Soc. Korea. 13(4), 416–422 (2009).
[CrossRef]

2007 (3)

J. M. Fini, “Design of large-mode-area amplifier fibers resistant to bend-induced distortion,” J. Opt. Soc. Am. B 24(8), 1669–1676 (2007).
[CrossRef]

Y. Jeong, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, L. M. B. Hickey, and P. W. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500 W,” IEEE J. Sel. Top. Quantum Electron. 13(3), 546–551 (2007).
[CrossRef]

A. E. Siegman, “Gain-guided, index-antiguided fiber lasers,” J. Opt. Soc. Am. B 24(8), 1677–1682 (2007).
[CrossRef]

2006 (1)

2005 (1)

2004 (1)

2002 (1)

2000 (1)

1990 (1)

Y. Chung and N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron. 26(8), 1335–1339 (1990).
[CrossRef]

1982 (1)

1981 (1)

Abeeluck, A.

Baskiotis, C.

Beres-Pawlik, E.

Berghmans, F.

Boyland, A. J.

Y. Jeong, A. J. Boyland, J. K. Sahu, S. Chung, J. Nilsson, and D. N. Payne, “Multi-kilowatt single-mode ytterbium-doped large-core fiber laser,” J. Opt. Soc. Korea. 13(4), 416–422 (2009).
[CrossRef]

Chen, X.

Chung, S.

Y. Jeong, A. J. Boyland, J. K. Sahu, S. Chung, J. Nilsson, and D. N. Payne, “Multi-kilowatt single-mode ytterbium-doped large-core fiber laser,” J. Opt. Soc. Korea. 13(4), 416–422 (2009).
[CrossRef]

Chung, Y.

Y. Chung and N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron. 26(8), 1335–1339 (1990).
[CrossRef]

Clarkson, W. A.

Dagli, N.

Y. Chung and N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron. 26(8), 1335–1339 (1990).
[CrossRef]

Devi, K.

Dong, L.

Dong, L. A.

L. A. Dong, J. Li, H. A. McKay, L. B. Fu, and B. K. Thomas, “Large effective mode area optical fibers for high power lasers,” Proc. SPIE 7195, 71950N (2009).
[CrossRef]

Ebrahim-Zadeh, M.

Eggleton, B.

Fermann, M. E.

Fini, J.

Fini, J. M.

Foy, P.

Fu, L.

Fu, L. B.

L. A. Dong, J. Li, H. A. McKay, L. B. Fu, and B. K. Thomas, “Large effective mode area optical fibers for high power lasers,” Proc. SPIE 7195, 71950N (2009).
[CrossRef]

Goldberg, L.

Gray, S.

Gu, G.

Gu, G. C.

Hawkins, T.

Hawkins, T. W.

Headley, C.

Hickey, L. M. B.

Y. Jeong, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, L. M. B. Hickey, and P. W. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500 W,” IEEE J. Sel. Top. Quantum Electron. 13(3), 546–551 (2007).
[CrossRef]

Horley, R.

Y. Jeong, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, L. M. B. Hickey, and P. W. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500 W,” IEEE J. Sel. Top. Quantum Electron. 13(3), 546–551 (2007).
[CrossRef]

Jain, D.

Jeong, Y.

Y. Jeong, A. J. Boyland, J. K. Sahu, S. Chung, J. Nilsson, and D. N. Payne, “Multi-kilowatt single-mode ytterbium-doped large-core fiber laser,” J. Opt. Soc. Korea. 13(4), 416–422 (2009).
[CrossRef]

Y. Jeong, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, L. M. B. Hickey, and P. W. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500 W,” IEEE J. Sel. Top. Quantum Electron. 13(3), 546–551 (2007).
[CrossRef]

Y. Jeong, J. Sahu, D. Payne, and J. Nilsson, “Ytterbium-doped large-core fiber laser with 1.36 kW continuous-wave output power,” Opt. Express 12(25), 6088–6092 (2004).
[CrossRef] [PubMed]

Kliner, D. A. V.

Kong, F.

Kong, F. T.

Koplow, J. P.

Kumar, S. C.

Lagasse, P. E.

Li, J.

L. Dong, H. A. McKay, A. Marcinkevicius, L. Fu, J. Li, B. K. Thomas, and M. E. Fermann, “Extending effective area of fundamental mode in optical fibers,” J. Lightwave Technol. 27(11), 1565–1570 (2009).
[CrossRef]

L. A. Dong, J. Li, H. A. McKay, L. B. Fu, and B. K. Thomas, “Large effective mode area optical fibers for high power lasers,” Proc. SPIE 7195, 71950N (2009).
[CrossRef]

Li, M.-J.

Litchinitser, N.

Liu, A.

Marcinkevicius, A.

Marcuse, D.

Mcclane, D.

McKay, H. A.

L. A. Dong, J. Li, H. A. McKay, L. B. Fu, and B. K. Thomas, “Large effective mode area optical fibers for high power lasers,” Proc. SPIE 7195, 71950N (2009).
[CrossRef]

L. Dong, H. A. McKay, A. Marcinkevicius, L. Fu, J. Li, B. K. Thomas, and M. E. Fermann, “Extending effective area of fundamental mode in optical fibers,” J. Lightwave Technol. 27(11), 1565–1570 (2009).
[CrossRef]

Mergo, P.

Napierala, M.

Nasilowski, T.

Nilsson, J.

D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: current status and future perspectives [Invited],” J. Opt. Soc. Am. B 27(11), B63–B92 (2010).
[CrossRef]

Y. Jeong, A. J. Boyland, J. K. Sahu, S. Chung, J. Nilsson, and D. N. Payne, “Multi-kilowatt single-mode ytterbium-doped large-core fiber laser,” J. Opt. Soc. Korea. 13(4), 416–422 (2009).
[CrossRef]

Y. Jeong, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, L. M. B. Hickey, and P. W. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500 W,” IEEE J. Sel. Top. Quantum Electron. 13(3), 546–551 (2007).
[CrossRef]

Y. Jeong, J. Sahu, D. Payne, and J. Nilsson, “Ytterbium-doped large-core fiber laser with 1.36 kW continuous-wave output power,” Opt. Express 12(25), 6088–6092 (2004).
[CrossRef] [PubMed]

Payne, D.

Payne, D. N.

Y. Jeong, A. J. Boyland, J. K. Sahu, S. Chung, J. Nilsson, and D. N. Payne, “Multi-kilowatt single-mode ytterbium-doped large-core fiber laser,” J. Opt. Soc. Korea. 13(4), 416–422 (2009).
[CrossRef]

Y. Jeong, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, L. M. B. Hickey, and P. W. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500 W,” IEEE J. Sel. Top. Quantum Electron. 13(3), 546–551 (2007).
[CrossRef]

Richardson, D. J.

Sahu, J.

Sahu, J. K.

D. Jain, C. Baskiotis, and J. K. Sahu, “Bending performance of large mode area multi-trench fibers,” Opt. Express 21(22), 26663–26670 (2013).
[CrossRef] [PubMed]

D. Jain, C. Baskiotis, and J. K. Sahu, “Mode area scaling with multi-trench rod-type fibers,” Opt. Express 21(2), 1448–1455 (2013).
[CrossRef] [PubMed]

Y. Jeong, A. J. Boyland, J. K. Sahu, S. Chung, J. Nilsson, and D. N. Payne, “Multi-kilowatt single-mode ytterbium-doped large-core fiber laser,” J. Opt. Soc. Korea. 13(4), 416–422 (2009).
[CrossRef]

Y. Jeong, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, L. M. B. Hickey, and P. W. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500 W,” IEEE J. Sel. Top. Quantum Electron. 13(3), 546–551 (2007).
[CrossRef]

Saitoh, K.

Samanta, G. K.

Samson, B.

Sanguinetti, S.

Shamir, Y.

Shtaif, M.

Siegman, A. E.

Sintov, Y.

Thienpont, H.

Thomas, B. K.

L. A. Dong, J. Li, H. A. McKay, L. B. Fu, and B. K. Thomas, “Large effective mode area optical fibers for high power lasers,” Proc. SPIE 7195, 71950N (2009).
[CrossRef]

L. Dong, H. A. McKay, A. Marcinkevicius, L. Fu, J. Li, B. K. Thomas, and M. E. Fermann, “Extending effective area of fundamental mode in optical fibers,” J. Lightwave Technol. 27(11), 1565–1570 (2009).
[CrossRef]

Turner, P. W.

Y. Jeong, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, L. M. B. Hickey, and P. W. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500 W,” IEEE J. Sel. Top. Quantum Electron. 13(3), 546–551 (2007).
[CrossRef]

van derDonk, J.

Van Roey, J.

Walton, D. T.

Wang, J.

Wei, K. X.

Zenteno, L. A.

Zuitlin, R.

Appl. Opt. (2)

IEEE J. Quantum Electron. (1)

Y. Chung and N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron. 26(8), 1335–1339 (1990).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

Y. Jeong, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, L. M. B. Hickey, and P. W. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500 W,” IEEE J. Sel. Top. Quantum Electron. 13(3), 546–551 (2007).
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (3)

J. Opt. Soc. Korea. (1)

Y. Jeong, A. J. Boyland, J. K. Sahu, S. Chung, J. Nilsson, and D. N. Payne, “Multi-kilowatt single-mode ytterbium-doped large-core fiber laser,” J. Opt. Soc. Korea. 13(4), 416–422 (2009).
[CrossRef]

Opt. Express (9)

Y. Jeong, J. Sahu, D. Payne, and J. Nilsson, “Ytterbium-doped large-core fiber laser with 1.36 kW continuous-wave output power,” Opt. Express 12(25), 6088–6092 (2004).
[CrossRef] [PubMed]

J. Fini, “Design of solid and microstructure fibers for suppression of higher-order modes,” Opt. Express 13(9), 3477–3490 (2005).
[CrossRef] [PubMed]

D. Jain, C. Baskiotis, and J. K. Sahu, “Mode area scaling with multi-trench rod-type fibers,” Opt. Express 21(2), 1448–1455 (2013).
[CrossRef] [PubMed]

D. Jain, C. Baskiotis, and J. K. Sahu, “Bending performance of large mode area multi-trench fibers,” Opt. Express 21(22), 26663–26670 (2013).
[CrossRef] [PubMed]

A. Abeeluck, N. Litchinitser, C. Headley, and B. Eggleton, “Analysis of spectral characteristics of photonic bandgap waveguides,” Opt. Express 10(23), 1320–1333 (2002).
[CrossRef] [PubMed]

G. C. Gu, F. T. Kong, T. W. Hawkins, P. Foy, K. X. Wei, B. Samson, and L. Dong, “Impact of fiber outer boundaries on leaky mode losses in leakage channel fibers,” Opt. Express 21(20), 24039–24048 (2013).
[CrossRef] [PubMed]

M. Napierała, T. Nasilowski, E. Bereś-Pawlik, P. Mergo, F. Berghmans, and H. Thienpont, “Large-mode-area photonic crystal fiber with double lattice constant structure and low bending loss,” Opt. Express 19(23), 22628–22636 (2011).
[CrossRef] [PubMed]

J. M. Fini, “Bend-resistant design of conventional and microstructure fibers with very large mode area,” Opt. Express 14(1), 69–81 (2006).
[CrossRef] [PubMed]

F. Kong, K. Saitoh, D. Mcclane, T. Hawkins, P. Foy, G. Gu, and L. Dong, “Mode area scaling with all-solid photonic bandgap fibers,” Opt. Express 20(24), 26363–26372 (2012).
[CrossRef] [PubMed]

Opt. Lett. (2)

Proc. SPIE (1)

L. A. Dong, J. Li, H. A. McKay, L. B. Fu, and B. K. Thomas, “Large effective mode area optical fibers for high power lasers,” Proc. SPIE 7195, 71950N (2009).
[CrossRef]

Other (3)

C.-H. Liu, G. Chang, N. Litchinitser, D. Guertin, N. Jacobsen, K. Tankala, and A. Galvanauskas, “Chirally coupled core fibers at 1550-nm and 1064-nm for effectively single-mode core size scaling,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies (Optical Society of America, Baltimore, Maryland, 2007), p. CTuBB3.
[CrossRef]

M. Devautour, P. Roy, and S. Février, “3-D modeling of modal competition in fiber laser: application to HOM suppression in multi-layered fiber,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference (Optical Society of America, Baltimore, Maryland, 2009), p. JWA54.
[CrossRef]

V. Gapontsev, V. Fomin, A. Ferin, and M. Abramov, “Diffraction limited ultra-high-power fiber lasers,” in Advanced Solid-State Photonics (Optical Society of America, 2010), p. AWA1.

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Figures (8)

Fig. 1
Fig. 1

(a) The cross section of the MTF structure. (b) The refractive index profiles of the unbent (blue) and bent (red) MTF and the notations in this paper, where D is the core diameter, t is the thickness of the low-index rings (trenches), d is the thickness of the high-index rings, and Δn is the refractive index difference between the core and the trenches.

Fig. 2
Fig. 2

(a) The leakage loss of the LP01 and HOMs and loss ratio between the low-loss HOM and LP01 in the range of the thickness d (4-38μm) in the unbent MTF. (b) The total loss of LP01 and HOMs and loss ratio between the low-loss HOM and LP01, including the leakage and bending loss, in the bent MTF. (c) and (d) The effective index of the corresponding core modes and first leaky cladding mode in the unbent MTF and in the bent MTF, respectively.

Fig. 3
Fig. 3

(a) The index profiles of unbent (blue) and bent (red) parabolic-profile fiber and parameters, where core diameter is D, and index difference of the top of the parabolic profile and cladding is Δn. (b), (c) and (d) are total loss of LP01 and the low-loss HOM in the unbent and bent parabolic-profile fiber with core diameter D = 50μm, 75μm and 100μm, respectively, and the yellow areas are where total loss of the low-loss HOM are about 10dB/m.

Fig. 4
Fig. 4

(a) the cross section of two trench fiber with parabolic-profile core. (b) The index profiles of this unbent (blue) and bent (red) design and the parameters in this paper, where D stands for core diameter, Δn for index difference of trenches and cladding, d for the thickness of the high-index rings, t1 for the thickness of the inner low-index trench and t2 for the thickness of the outside low-index trench.

Fig. 5
Fig. 5

(a) The leakage loss of LP01 and HOMs and loss ratio between the low-loss HOM and LP01 in our unbent design. (b) The total loss of LP01 and HOMs and loss ratio between the low-loss HOM and LP01 in our bent design. (c) and (d) The effective index of core modes and the first leaky cladding mode in our unbent design and in our bent design, respectively.

Fig. 6
Fig. 6

(a) The leakage loss of LP01 and low-loss HOM and loss ratio between the low-loss HOM and LP01 in the unbent two trench fiber with parabolic-profile core with D = 100μm, t1 = 1μm, t2 = 3μm, Δn = 0.0012. (b) The total loss of LP01 and low-loss HOM and loss ratio between the low-loss HOM and LP01 in this bent design with bending radius R = 0.25m.

Fig. 7
Fig. 7

The influence of the bending radius and the thickness (d) of the high-index ring on the total loss of the low-loss HOM and LP01 in our bent design (D = 100μm, t1 = 1μm, t2 = 3μm and Δn = 0.0012), and the influence of the bending radius on the total loss of the low-loss HOM and LP01 in the parabolic-profile fiber (D = 100μm and Δn = 0.0012).

Fig. 8
Fig. 8

(a) The influence of the bending radius on the effective mode area of LP01 in the bent MTF (D = 50μm) and our bent design (D = 100μm). (b) The LP01 surface profiles of the unbent (top left) and bent (top right) MTF (D = 50μm), our unbent (bottom left) and bent (bottom right) design (D = 100μm), where bending radius is 0.25m. The 50μm-diameter central regions are marked by red circles.

Equations (1)

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n eff =n 1+2 x R n(1+ x R )

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