Abstract

We analyze the transmission of a Single mode - Multimode -Multimode (SMm) fiber structure with the aim of exciting a single radial mode in the second multimode fiber. We show that by appropriate choice of the length of the central multimode fiber one can obtain > 90% of the total core power in a chosen mode. We also discuss methods of removing undesirable cladding and radiation modes and estimate tolerances for practical applications.

© 2014 Optical Society of America

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References

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  1. Y. Jeong, J. K. Sahu, D. N. Payne, and J. Nilsson, “Ytterbium-doped large-core fiber laser with 1.36 kw continuous-wave output power,” Opt. Express 126088–6092 (2004).
    [CrossRef] [PubMed]
  2. J. Limpert, O. Schmidt, J. Rothhardt, F. Rser, T. Schreiber, and A. Tnnermann, “Extended single-mode photonic crystal fiber lasers,” Opt. Express 14, 2715–2720 (2006).
    [CrossRef] [PubMed]
  3. J. P. Koplow, D. A. V. Kliner, and L. Goldberg, “Single-mode operation of a coiled multimode fiber amplifier,” Opt. Lett. 25, 442–444 (2000).
    [CrossRef]
  4. Y. Jeong, J. K. Sahu, D. B. S. Soh, C. A. Codemard, and J. Nilsson, “High-power tunable single-frequency single-mode erbium:ytterbium codoped large-core fiber master-oscillator power amplifier source,” Opt. Lett. 30, 2997–2999 (2005).
    [CrossRef] [PubMed]
  5. P. Wang, L. J. Cooper, J. K. Sahu, and W. A. Clarkson, “Efficient single-mode operation of a cladding pumped ytterbium-doped helical-core fiber laser,” Opt. Lett. 31, 226–228 (2006).
    [CrossRef] [PubMed]
  6. J. M. Sousa and O. G. Okhotnikov, “Multimode er-doped fiber for single-transverse-mode amplification,” Appl. Phys. Lett. 74, 1528–1530 (1999).
    [CrossRef]
  7. X. Zhu, A. Schlzgen, H. Li, L. Li, Q. Wang, S. Suzuki, V. L. Temyanko, J. V. Moloney, and N. Peyghambarian, “Single-transverse-mode output from a fiber laser based on multimode interference,” Opt. Lett. 33, 908–910 (2008).
    [CrossRef] [PubMed]
  8. X. Zhu, A. Schlzgen, H. Li, L. Li, L. Han, J. V. Moloney, and N. Peyghambarian, “Detailed investigation of self-imaging in large core multimode optical fibers for application in fiber lasers and amplifiers,” Opt. Express 16, 16632–16645 (2008).
    [PubMed]
  9. J. M. Fini and S. Ramachandran, “Natural bend-distortion immunity of higher-order-mode large-mode-area fibers,” Opt. Lett. 32, 748–750 (2007).
    [CrossRef] [PubMed]
  10. S. Ramachandran, J. W. Nicholson, S. Ghalmi, M. F. Yan, P. Wisk, E. Monberg, and F. V. Dimarcello, “Light propagation with ultralarge modal areas in optical fibers,” Opt. Lett. 31, 1797–1799 (2006).
    [CrossRef] [PubMed]
  11. Q. Wu, Y. Semenova, B. Yan, Y. Ma, P. Wang, C. Yu, and G. Farrell, “Fiber refractometer based on a fiber bragg grating and single mode - multimode - single mode fiber structure,” Opt. Lett. 36, 2197–2199 (2011).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  14. Q. Wang, G. Farrell, and W. Yan, “Investigation on single mode multimode singlemode fiber structure,” J. Light-wave Technol. 26, 512–519 (2008).
    [CrossRef]
  15. G. R. Hadley, “Wide-angle beam propagation using pade approximant operators,” Opt. Lett. 17, 1426–1428 (1992).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  19. D. Gloge, “Weakly guiding fibers,” Appl. Opt. 10, 2252–2258 (1971).
    [CrossRef] [PubMed]
  20. V. Sai, T. Kundu, C. Deshmukh, S. Titus, P. Kumar, and S. Mukherji, “Label-free fiber optic biosensor based on evanescent wave absorbance at 280nm,” Sens. Actuators, B 143, 724 (2010).
    [CrossRef]
  21. R. Bharadwaj, V. Sai, K. Thakare, A. Dhawangale, T. Kundu, S. Titus, P. K. Verma, and S. Mukherji, “Evanescent wave absorbance based fiber optic biosensor for label-free detection of e. coli at 280nm wavelength,” Biosens. Bioelectron. 26, 3367 (2011).
    [CrossRef]
  22. X. Li, S. Lin, J. Liang, Y. Zhang, H. Oigawa, and T. Ueda, “Fiber-optic temperature sensor based on difference of thermal expansion coefficient between fused silica and metallic materials,” IEEE Photon. J. 4, 155–162 (2012).
    [CrossRef]

2012

C. L. Linslal, P. M. S. Mohan, A. Halder, and T. K. Gangopadhyay, “Eigenvalue equation and core-mode cutoff of weakly guiding tapered fiber as three layer optical waveguide and used as biochemical sensor,” Appl. Opt. 51, 3445–3452 (2012).
[CrossRef] [PubMed]

X. Li, S. Lin, J. Liang, Y. Zhang, H. Oigawa, and T. Ueda, “Fiber-optic temperature sensor based on difference of thermal expansion coefficient between fused silica and metallic materials,” IEEE Photon. J. 4, 155–162 (2012).
[CrossRef]

2011

R. Bharadwaj, V. Sai, K. Thakare, A. Dhawangale, T. Kundu, S. Titus, P. K. Verma, and S. Mukherji, “Evanescent wave absorbance based fiber optic biosensor for label-free detection of e. coli at 280nm wavelength,” Biosens. Bioelectron. 26, 3367 (2011).
[CrossRef]

Q. Wu, Y. Semenova, B. Yan, Y. Ma, P. Wang, C. Yu, and G. Farrell, “Fiber refractometer based on a fiber bragg grating and single mode - multimode - single mode fiber structure,” Opt. Lett. 36, 2197–2199 (2011).
[CrossRef] [PubMed]

2010

V. Sai, T. Kundu, C. Deshmukh, S. Titus, P. Kumar, and S. Mukherji, “Label-free fiber optic biosensor based on evanescent wave absorbance at 280nm,” Sens. Actuators, B 143, 724 (2010).
[CrossRef]

2009

X. Zhu, A. Schulzgen, H. Li, L. Li, V. L. Temyanko, J. V. Moloney, and N. Peyghambarian, “High-power fiber lasers and amplifiers based on multimode interference,” IEEE J. Sel. Top. Quantum Electron. 15, 71–78 (2009).
[CrossRef]

2008

2007

2006

2005

2004

2000

1999

J. M. Sousa and O. G. Okhotnikov, “Multimode er-doped fiber for single-transverse-mode amplification,” Appl. Phys. Lett. 74, 1528–1530 (1999).
[CrossRef]

1992

1971

Bharadwaj, R.

R. Bharadwaj, V. Sai, K. Thakare, A. Dhawangale, T. Kundu, S. Titus, P. K. Verma, and S. Mukherji, “Evanescent wave absorbance based fiber optic biosensor for label-free detection of e. coli at 280nm wavelength,” Biosens. Bioelectron. 26, 3367 (2011).
[CrossRef]

Clarkson, W. A.

Codemard, C. A.

Cooper, L. J.

Deshmukh, C.

V. Sai, T. Kundu, C. Deshmukh, S. Titus, P. Kumar, and S. Mukherji, “Label-free fiber optic biosensor based on evanescent wave absorbance at 280nm,” Sens. Actuators, B 143, 724 (2010).
[CrossRef]

Dhawangale, A.

R. Bharadwaj, V. Sai, K. Thakare, A. Dhawangale, T. Kundu, S. Titus, P. K. Verma, and S. Mukherji, “Evanescent wave absorbance based fiber optic biosensor for label-free detection of e. coli at 280nm wavelength,” Biosens. Bioelectron. 26, 3367 (2011).
[CrossRef]

Dimarcello, F. V.

Farrell, G.

Fini, J. M.

Gangopadhyay, T. K.

Ghalmi, S.

Gloge, D.

Goldberg, L.

Gulyaev, Y. V.

O. V. Ivanov, S. A. Nikitov, and Y. V. Gulyaev, “Cladding modes of optical fibers: properties and applications,” Phys. Usp. 49, 167–191 (2006).
[CrossRef]

Hadley, G. R.

Halder, A.

Han, L.

Ivanov, O. V.

O. V. Ivanov, S. A. Nikitov, and Y. V. Gulyaev, “Cladding modes of optical fibers: properties and applications,” Phys. Usp. 49, 167–191 (2006).
[CrossRef]

Jeong, Y.

Kliner, D. A. V.

Koplow, J. P.

Kumar, P.

V. Sai, T. Kundu, C. Deshmukh, S. Titus, P. Kumar, and S. Mukherji, “Label-free fiber optic biosensor based on evanescent wave absorbance at 280nm,” Sens. Actuators, B 143, 724 (2010).
[CrossRef]

Kundu, T.

R. Bharadwaj, V. Sai, K. Thakare, A. Dhawangale, T. Kundu, S. Titus, P. K. Verma, and S. Mukherji, “Evanescent wave absorbance based fiber optic biosensor for label-free detection of e. coli at 280nm wavelength,” Biosens. Bioelectron. 26, 3367 (2011).
[CrossRef]

V. Sai, T. Kundu, C. Deshmukh, S. Titus, P. Kumar, and S. Mukherji, “Label-free fiber optic biosensor based on evanescent wave absorbance at 280nm,” Sens. Actuators, B 143, 724 (2010).
[CrossRef]

Li, H.

Li, L.

Li, X.

X. Li, S. Lin, J. Liang, Y. Zhang, H. Oigawa, and T. Ueda, “Fiber-optic temperature sensor based on difference of thermal expansion coefficient between fused silica and metallic materials,” IEEE Photon. J. 4, 155–162 (2012).
[CrossRef]

Liang, J.

X. Li, S. Lin, J. Liang, Y. Zhang, H. Oigawa, and T. Ueda, “Fiber-optic temperature sensor based on difference of thermal expansion coefficient between fused silica and metallic materials,” IEEE Photon. J. 4, 155–162 (2012).
[CrossRef]

Limpert, J.

Lin, S.

X. Li, S. Lin, J. Liang, Y. Zhang, H. Oigawa, and T. Ueda, “Fiber-optic temperature sensor based on difference of thermal expansion coefficient between fused silica and metallic materials,” IEEE Photon. J. 4, 155–162 (2012).
[CrossRef]

Linslal, C. L.

Ma, Y.

Mohan, P. M. S.

Moloney, J. V.

Monberg, E.

Monzn-Hernndez, D.

Mukherji, S.

R. Bharadwaj, V. Sai, K. Thakare, A. Dhawangale, T. Kundu, S. Titus, P. K. Verma, and S. Mukherji, “Evanescent wave absorbance based fiber optic biosensor for label-free detection of e. coli at 280nm wavelength,” Biosens. Bioelectron. 26, 3367 (2011).
[CrossRef]

V. Sai, T. Kundu, C. Deshmukh, S. Titus, P. Kumar, and S. Mukherji, “Label-free fiber optic biosensor based on evanescent wave absorbance at 280nm,” Sens. Actuators, B 143, 724 (2010).
[CrossRef]

Nicholson, J. W.

Nikitov, S. A.

O. V. Ivanov, S. A. Nikitov, and Y. V. Gulyaev, “Cladding modes of optical fibers: properties and applications,” Phys. Usp. 49, 167–191 (2006).
[CrossRef]

Nilsson, J.

Oigawa, H.

X. Li, S. Lin, J. Liang, Y. Zhang, H. Oigawa, and T. Ueda, “Fiber-optic temperature sensor based on difference of thermal expansion coefficient between fused silica and metallic materials,” IEEE Photon. J. 4, 155–162 (2012).
[CrossRef]

Okhotnikov, O. G.

J. M. Sousa and O. G. Okhotnikov, “Multimode er-doped fiber for single-transverse-mode amplification,” Appl. Phys. Lett. 74, 1528–1530 (1999).
[CrossRef]

Payne, D. N.

Peyghambarian, N.

Ramachandran, S.

Rothhardt, J.

Rser, F.

Sahu, J. K.

Sai, V.

R. Bharadwaj, V. Sai, K. Thakare, A. Dhawangale, T. Kundu, S. Titus, P. K. Verma, and S. Mukherji, “Evanescent wave absorbance based fiber optic biosensor for label-free detection of e. coli at 280nm wavelength,” Biosens. Bioelectron. 26, 3367 (2011).
[CrossRef]

V. Sai, T. Kundu, C. Deshmukh, S. Titus, P. Kumar, and S. Mukherji, “Label-free fiber optic biosensor based on evanescent wave absorbance at 280nm,” Sens. Actuators, B 143, 724 (2010).
[CrossRef]

Schlzgen, A.

Schmidt, O.

Schreiber, T.

Schulzgen, A.

X. Zhu, A. Schulzgen, H. Li, L. Li, V. L. Temyanko, J. V. Moloney, and N. Peyghambarian, “High-power fiber lasers and amplifiers based on multimode interference,” IEEE J. Sel. Top. Quantum Electron. 15, 71–78 (2009).
[CrossRef]

Semenova, Y.

Soh, D. B. S.

Sousa, J. M.

J. M. Sousa and O. G. Okhotnikov, “Multimode er-doped fiber for single-transverse-mode amplification,” Appl. Phys. Lett. 74, 1528–1530 (1999).
[CrossRef]

Suzuki, S.

Temyanko, V. L.

X. Zhu, A. Schulzgen, H. Li, L. Li, V. L. Temyanko, J. V. Moloney, and N. Peyghambarian, “High-power fiber lasers and amplifiers based on multimode interference,” IEEE J. Sel. Top. Quantum Electron. 15, 71–78 (2009).
[CrossRef]

X. Zhu, A. Schlzgen, H. Li, L. Li, Q. Wang, S. Suzuki, V. L. Temyanko, J. V. Moloney, and N. Peyghambarian, “Single-transverse-mode output from a fiber laser based on multimode interference,” Opt. Lett. 33, 908–910 (2008).
[CrossRef] [PubMed]

Thakare, K.

R. Bharadwaj, V. Sai, K. Thakare, A. Dhawangale, T. Kundu, S. Titus, P. K. Verma, and S. Mukherji, “Evanescent wave absorbance based fiber optic biosensor for label-free detection of e. coli at 280nm wavelength,” Biosens. Bioelectron. 26, 3367 (2011).
[CrossRef]

Titus, S.

R. Bharadwaj, V. Sai, K. Thakare, A. Dhawangale, T. Kundu, S. Titus, P. K. Verma, and S. Mukherji, “Evanescent wave absorbance based fiber optic biosensor for label-free detection of e. coli at 280nm wavelength,” Biosens. Bioelectron. 26, 3367 (2011).
[CrossRef]

V. Sai, T. Kundu, C. Deshmukh, S. Titus, P. Kumar, and S. Mukherji, “Label-free fiber optic biosensor based on evanescent wave absorbance at 280nm,” Sens. Actuators, B 143, 724 (2010).
[CrossRef]

Tnnermann, A.

Ueda, T.

X. Li, S. Lin, J. Liang, Y. Zhang, H. Oigawa, and T. Ueda, “Fiber-optic temperature sensor based on difference of thermal expansion coefficient between fused silica and metallic materials,” IEEE Photon. J. 4, 155–162 (2012).
[CrossRef]

Verma, P. K.

R. Bharadwaj, V. Sai, K. Thakare, A. Dhawangale, T. Kundu, S. Titus, P. K. Verma, and S. Mukherji, “Evanescent wave absorbance based fiber optic biosensor for label-free detection of e. coli at 280nm wavelength,” Biosens. Bioelectron. 26, 3367 (2011).
[CrossRef]

Villatoro, J.

Wang, P.

Wang, Q.

Wisk, P.

Wu, Q.

Yan, B.

Yan, M. F.

Yan, W.

Q. Wang, G. Farrell, and W. Yan, “Investigation on single mode multimode singlemode fiber structure,” J. Light-wave Technol. 26, 512–519 (2008).
[CrossRef]

Yu, C.

Zhang, Y.

X. Li, S. Lin, J. Liang, Y. Zhang, H. Oigawa, and T. Ueda, “Fiber-optic temperature sensor based on difference of thermal expansion coefficient between fused silica and metallic materials,” IEEE Photon. J. 4, 155–162 (2012).
[CrossRef]

Zhu, X.

Appl. Opt.

Appl. Phys. Lett.

J. M. Sousa and O. G. Okhotnikov, “Multimode er-doped fiber for single-transverse-mode amplification,” Appl. Phys. Lett. 74, 1528–1530 (1999).
[CrossRef]

Biosens. Bioelectron.

R. Bharadwaj, V. Sai, K. Thakare, A. Dhawangale, T. Kundu, S. Titus, P. K. Verma, and S. Mukherji, “Evanescent wave absorbance based fiber optic biosensor for label-free detection of e. coli at 280nm wavelength,” Biosens. Bioelectron. 26, 3367 (2011).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

X. Zhu, A. Schulzgen, H. Li, L. Li, V. L. Temyanko, J. V. Moloney, and N. Peyghambarian, “High-power fiber lasers and amplifiers based on multimode interference,” IEEE J. Sel. Top. Quantum Electron. 15, 71–78 (2009).
[CrossRef]

IEEE Photon. J.

X. Li, S. Lin, J. Liang, Y. Zhang, H. Oigawa, and T. Ueda, “Fiber-optic temperature sensor based on difference of thermal expansion coefficient between fused silica and metallic materials,” IEEE Photon. J. 4, 155–162 (2012).
[CrossRef]

J. Light-wave Technol.

Q. Wang, G. Farrell, and W. Yan, “Investigation on single mode multimode singlemode fiber structure,” J. Light-wave Technol. 26, 512–519 (2008).
[CrossRef]

J. Lightwave Technol.

Opt. Express

Opt. Lett.

J. M. Fini and S. Ramachandran, “Natural bend-distortion immunity of higher-order-mode large-mode-area fibers,” Opt. Lett. 32, 748–750 (2007).
[CrossRef] [PubMed]

S. Ramachandran, J. W. Nicholson, S. Ghalmi, M. F. Yan, P. Wisk, E. Monberg, and F. V. Dimarcello, “Light propagation with ultralarge modal areas in optical fibers,” Opt. Lett. 31, 1797–1799 (2006).
[CrossRef] [PubMed]

Q. Wu, Y. Semenova, B. Yan, Y. Ma, P. Wang, C. Yu, and G. Farrell, “Fiber refractometer based on a fiber bragg grating and single mode - multimode - single mode fiber structure,” Opt. Lett. 36, 2197–2199 (2011).
[CrossRef] [PubMed]

J. P. Koplow, D. A. V. Kliner, and L. Goldberg, “Single-mode operation of a coiled multimode fiber amplifier,” Opt. Lett. 25, 442–444 (2000).
[CrossRef]

Y. Jeong, J. K. Sahu, D. B. S. Soh, C. A. Codemard, and J. Nilsson, “High-power tunable single-frequency single-mode erbium:ytterbium codoped large-core fiber master-oscillator power amplifier source,” Opt. Lett. 30, 2997–2999 (2005).
[CrossRef] [PubMed]

P. Wang, L. J. Cooper, J. K. Sahu, and W. A. Clarkson, “Efficient single-mode operation of a cladding pumped ytterbium-doped helical-core fiber laser,” Opt. Lett. 31, 226–228 (2006).
[CrossRef] [PubMed]

X. Zhu, A. Schlzgen, H. Li, L. Li, Q. Wang, S. Suzuki, V. L. Temyanko, J. V. Moloney, and N. Peyghambarian, “Single-transverse-mode output from a fiber laser based on multimode interference,” Opt. Lett. 33, 908–910 (2008).
[CrossRef] [PubMed]

G. R. Hadley, “Wide-angle beam propagation using pade approximant operators,” Opt. Lett. 17, 1426–1428 (1992).
[CrossRef] [PubMed]

Phys. Usp.

O. V. Ivanov, S. A. Nikitov, and Y. V. Gulyaev, “Cladding modes of optical fibers: properties and applications,” Phys. Usp. 49, 167–191 (2006).
[CrossRef]

Sens. Actuators, B

V. Sai, T. Kundu, C. Deshmukh, S. Titus, P. Kumar, and S. Mukherji, “Label-free fiber optic biosensor based on evanescent wave absorbance at 280nm,” Sens. Actuators, B 143, 724 (2010).
[CrossRef]

Other

Introduction to Fiber Optics (Cambridge University, 2011).

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Figures (13)

Fig. 1
Fig. 1

Single mode - Multimode - Multimode (SMm) fiber structure (not to scale).

Fig. 2
Fig. 2

Power coupled to LP0,1, LP0,2 and LP0,7 modes of MMF2 for various lengths of MMF1 using two analyses. Core diameters of MMF1 and MMF2 are 50μm and 105μm, respectively.

Fig. 3
Fig. 3

Fraction of the power coupled to core (∑m |bm|2, solid blue line) and cladding modes (∑k |dk|2, dotted red line) of MMF2 as a function of the length of MMF1. Total power coupled to MMF2 (∑m |bm|2 + ∑k |dk|2, dotted black line) is also shown.

Fig. 4
Fig. 4

Power coupling coefficients for the radial modes of a 50μm core MMF2 for different lengths of MMF1 (105μm core) with corresponding normalized radial launch field. Dimensions of x-axis in inset is in μm.

Fig. 5
Fig. 5

(a) Propagation of field in SMm structure with MMF1 core diameter and length of 99μm and 10881μm, respectively. MMF2 core diameter is 30μm. Cladding diameter of MMF1 and MMF2 are 125μm. MMF2 is surrounded by a medium with RI of 1.4272. This excites LP0,2 mode in MMF2. White line shows the refractive index discontinuities in the structure. R is the length in radial direction. (b) Power that would couple to the LP0,2 mode of a 30μm core fiber, as a fraction of local propagating power (dashed blue line) and input power (solid green line) for various lengths (z) in the structure. For z > 10881μm, this defines the propagating power in LP0,2 mode of MMF2. Total power propagating in the structure is also shown (dot-dashed black line).

Fig. 6
Fig. 6

Normalized radial power profile of LP0,9 and LP0,10 modes of 64μm core diameter fiber. LP0,10 is near to cut-off and carry a large fraction of power in cladding. Inset shows the decaying fields of LP0,9 and LP0,10 modes in the cladding region.

Fig. 7
Fig. 7

Propagation of the field in SMm structure for excitation of LP0,10 mode in MMF2. Core diameters of MMF1 and MMF2 are 128μm and 64μm. RI of the medium outside MMF1 is 1.0 (air) and MMF2 is 1.4272. Cladding diameter of MMF2 in (a) is 150μm leading to leakage of power into the outer medium and in (b) is 250μm leading to propagation of the mode in the core.

Fig. 8
Fig. 8

Propagation of field in SMm structure for excitation of LP0,10 mode in MMF2. Core diameters of MMF1 and MMF2 are 128μm and 64μm with cladding diameter of 150μm. RI of the medium outside MMF1 is 1.0 (air). (a) shows the propagation of LP0,10 mode in MMF2 with outer medium RI of 1.4270. (b) shows the propagation of LP0,10 mode with outer medium RI of 1.0 (air). In this case, cladding modes are removed by exposing 5 cm of length of MMF2 (31641μm – 81641μm) to an outside medium with an RI value equal to that of the cladding.

Fig. 9
Fig. 9

Scheme to use SMm structure in high power fiber lasers and amplifiers.

Fig. 10
Fig. 10

BeamProp simulation of the scheme presented in Fig. 9. Core diameter of MMF1 and MMF2 are 176μm and 50μm, respectively with cladding diameter of 200μm. MMF1 length is 31941μm. (a) When the medium outside MMF2 is air, power from MMF1 is coupled to both the core and cladding region of MMF2. Index matching liquid is applied from 5 cm – 11 cm, to radiate away this power in the cladding modes. White line shows the refractive index discontinuities in the structure. R is the length in radial direction. (b) Power that would couple to the LP0,3 mode of a 50μm core termination fiber, as a fraction of the local propagating power (dashed line) and the input power (solid line) for various lengths (z) along the structure. For z > 31941μm, this defines the propagating power in LP0,3 mode of MMF2. Total power propagating in the structure is also shown (dot-dashed line).

Fig. 11
Fig. 11

Change in γ factor with change in length of MMF1 for the cases listed in table 1.

Fig. 12
Fig. 12

Change in γ factor with change in length of MMF1 for the lower order modes (LP0,2 and LP0,3) presented in table 2.

Fig. 13
Fig. 13

Change in γ factor with change in length of MMF1 for the higher order modes (LP0,10LP0,23) presented in table 2.

Tables (3)

Tables Icon

Table 1 Fraction of power in each mode of MMF2 for different lengths and core diameters of MMF1. LP0,1 and LP0,2 modes are selected in MMF2.

Tables Icon

Table 2 Selected lower and higher order radial core modes of large core diameter MMF2 for different lengths and core diameters of MMF1.

Tables Icon

Table 3 Length of MMF1 required to excite near single LP0,n mode with finite cladding diameter and outside medium as air.

Equations (13)

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

R = i N 1 j N 2 | n i n j n i + n j | 2 N 1 N 2
c ε o n 2 A | ψ | 2 d A = 1
Φ s = n c n Ψ n
c n = A Φ s Ψ n d A A Ψ n 2 d A
c n = n n n s c n
c n = A ϕ s A ϕ s 2 d A ψ n A ψ n 2 d A d A
n c n Ψ n exp ( i β n l ) = m b m Ψ m + k d k Ψ k + p ( β ) Ψ β d β
b m = n c n exp ( i β n l ) A Ψ n Ψ m d A A Ψ m 2 d A
b m = n α m n s c n a m n exp ( i β n l )
a m n = A ψ n A ψ n 2 d A ψ m A ψ m 2 d A d A
T ( d B ) = 10 log 10 ( m | b m | 2 )
γ n = | b n | 2 m | b m | 2 > 0.9
A = P clad P α L 2.303

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