Abstract

Since silica goes under the category of amorphous materials, it is difficult to investigate important processes such as second harmonic generation (SHG) in silica-based fibers. In this paper, we proposed a method for SHG relaying on cladding modes as pump modes. Cladding modes are introduced in optical fibers through tilted long period grating (T-LPG), where power of core mode is transferred into cladding modes. By functionalizing T-LPG with nonlinear coating, the interaction occurs between cladding modes and the coating material, consequently second harmonic signal (SHS) is generated with efficiency up to 0.14%.

© 2016 Optical Society of America

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References

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2015 (1)

2013 (4)

R. Wu, Y. Liu, N. Chen, F. Pang, and T. Wang, “Fabrication and sensing characteristics of tilted long-period fiber gratings,” Proc. SPIE 8561(85610), G1–G7 (2013).

J. Albert, L. Shao, and C. Caucheteur, “Tilted fiber Bragg grating sensors,” Laser Photonics Rev. 7(1), 83–108 (2013).
[Crossref]

W. Luo, W. Guo, F. Xu, and Y. Q. Lu, “Efficient surface second-harmonic generation in slot micro/nano-fibers,” Opt. Express 21(9), 11554–11561 (2013).
[Crossref] [PubMed]

T. Qi, S. Xiao, J. Shi, L. Yi, Z. Zhou, M. Bi, and W. Hu, “Cladding mode backward recoupling based displacement Sensor incorporating fiber up taper and Bragg grating,” IEEE Photonics J. 5(4), 7100608 (2013).
[Crossref]

2011 (2)

2009 (1)

2008 (1)

2007 (1)

Y. Xu, A. Wang, J. R. Heflin, and Z. Liu, “Proposal and analysis of a silica fiber with large and thermodynamically stable second order nonlinearity,” Appl. Phys. Lett. 90(211110), 1–3 (2007).

2006 (2)

J. Huang, Y. He, and Y. Lo, “Spectrum analysis for high-order cladding modes based on long-period fiber gratings,” Opt. Eng. 45(9), 095001 (2006).

J. R. Heflin, M. T. Guzy, P. J. Neyman, K. J. Gaskins, C. Brands, Z. Wang, H. W. Gibson, R. M. Davis, and K. E. Van Cott, “Efficient, thermally stable, second order nonlinear optical response in organic hybrid covalent/ionic self-assembled films,” Langmuir 22(13), 5723–5727 (2006).
[Crossref] [PubMed]

2000 (1)

1999 (2)

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286(5444), 1523–1528 (1999).
[Crossref] [PubMed]

S. Vasil’ev, E. Dianov, O. Medvedkov, V. Protopopov, D. Costantini, A. Iocco, H. Limberger, and R. Salathe, “Properties of the cladding modes of an optical fiber excited by refractive-index gratings,” Quantum Electron. 29(1), 65–68 (1999).
[Crossref]

1998 (1)

1997 (3)

1996 (2)

T. Erdogan and J. E. Sipe, “Tilted fiber phase gratings,” J. Opt. Soc. Am. A 13(2), 296–313 (1996).
[Crossref]

A. Vengsarkar, P. Lemaire, J. Judkins, V. Bhatia, T. Erdogan, and J. Sipe, “Long period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14(1), 58–65 (1996).
[Crossref]

1990 (1)

C. de Sterke and J. Sipe, “Coupled modes and the nonlinear Schrödinger equation,” Phys. Rev. A 42(1), 550–555 (1990).
[Crossref] [PubMed]

1989 (1)

1988 (1)

1987 (1)

1984 (1)

H. Ishio, J. Minowa, and K. Nosu, “Review and status of wavelength-division multiplexing technology and its application,” J. Lightwave Technol. 2(4), 448–463 (1984).
[Crossref]

Albert, J.

Andrejco, M. J.

Ashry, I.

Bhatia, V.

A. Vengsarkar, P. Lemaire, J. Judkins, V. Bhatia, T. Erdogan, and J. Sipe, “Long period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14(1), 58–65 (1996).
[Crossref]

Bi, M.

T. Qi, S. Xiao, J. Shi, L. Yi, Z. Zhou, M. Bi, and W. Hu, “Cladding mode backward recoupling based displacement Sensor incorporating fiber up taper and Bragg grating,” IEEE Photonics J. 5(4), 7100608 (2013).
[Crossref]

Blow, K. J.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286(5444), 1523–1528 (1999).
[Crossref] [PubMed]

Brands, C.

J. R. Heflin, M. T. Guzy, P. J. Neyman, K. J. Gaskins, C. Brands, Z. Wang, H. W. Gibson, R. M. Davis, and K. E. Van Cott, “Efficient, thermally stable, second order nonlinear optical response in organic hybrid covalent/ionic self-assembled films,” Langmuir 22(13), 5723–5727 (2006).
[Crossref] [PubMed]

Campagnola, P. J.

P. J. Campagnola and C.-Y. Dong, “Second harmonic generation microscopy: principles and applications to disease diagnosis,” Laser Photonics Rev. 5(1), 13–26 (2011).
[Crossref]

Caucheteur, C.

J. Albert, L. Shao, and C. Caucheteur, “Tilted fiber Bragg grating sensors,” Laser Photonics Rev. 7(1), 83–108 (2013).
[Crossref]

Chen, N.

R. Wu, Y. Liu, N. Chen, F. Pang, and T. Wang, “Fabrication and sensing characteristics of tilted long-period fiber gratings,” Proc. SPIE 8561(85610), G1–G7 (2013).

Cheung, C.

Costantini, D.

S. Vasil’ev, E. Dianov, O. Medvedkov, V. Protopopov, D. Costantini, A. Iocco, H. Limberger, and R. Salathe, “Properties of the cladding modes of an optical fiber excited by refractive-index gratings,” Quantum Electron. 29(1), 65–68 (1999).
[Crossref]

Cotter, D.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286(5444), 1523–1528 (1999).
[Crossref] [PubMed]

Daengngam, C.

Davis, R. M.

J. R. Heflin, M. T. Guzy, P. J. Neyman, K. J. Gaskins, C. Brands, Z. Wang, H. W. Gibson, R. M. Davis, and K. E. Van Cott, “Efficient, thermally stable, second order nonlinear optical response in organic hybrid covalent/ionic self-assembled films,” Langmuir 22(13), 5723–5727 (2006).
[Crossref] [PubMed]

de Sterke, C.

C. de Sterke and J. Sipe, “Coupled modes and the nonlinear Schrödinger equation,” Phys. Rev. A 42(1), 550–555 (1990).
[Crossref] [PubMed]

Dianov, E.

S. Vasil’ev, E. Dianov, O. Medvedkov, V. Protopopov, D. Costantini, A. Iocco, H. Limberger, and R. Salathe, “Properties of the cladding modes of an optical fiber excited by refractive-index gratings,” Quantum Electron. 29(1), 65–68 (1999).
[Crossref]

Dong, C.-Y.

P. J. Campagnola and C.-Y. Dong, “Second harmonic generation microscopy: principles and applications to disease diagnosis,” Laser Photonics Rev. 5(1), 13–26 (2011).
[Crossref]

Dong, L.

Ellis, A. D.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286(5444), 1523–1528 (1999).
[Crossref] [PubMed]

Erdogan, T.

Gambling, W.

Gaskins, K. J.

J. R. Heflin, M. T. Guzy, P. J. Neyman, K. J. Gaskins, C. Brands, Z. Wang, H. W. Gibson, R. M. Davis, and K. E. Van Cott, “Efficient, thermally stable, second order nonlinear optical response in organic hybrid covalent/ionic self-assembled films,” Langmuir 22(13), 5723–5727 (2006).
[Crossref] [PubMed]

Gibson, H. W.

J. R. Heflin, M. T. Guzy, P. J. Neyman, K. J. Gaskins, C. Brands, Z. Wang, H. W. Gibson, R. M. Davis, and K. E. Van Cott, “Efficient, thermally stable, second order nonlinear optical response in organic hybrid covalent/ionic self-assembled films,” Langmuir 22(13), 5723–5727 (2006).
[Crossref] [PubMed]

Guo, T.

Guo, W.

Guzy, M. T.

J. R. Heflin, M. T. Guzy, P. J. Neyman, K. J. Gaskins, C. Brands, Z. Wang, H. W. Gibson, R. M. Davis, and K. E. Van Cott, “Efficient, thermally stable, second order nonlinear optical response in organic hybrid covalent/ionic self-assembled films,” Langmuir 22(13), 5723–5727 (2006).
[Crossref] [PubMed]

He, Y.

J. Huang, Y. He, and Y. Lo, “Spectrum analysis for high-order cladding modes based on long-period fiber gratings,” Opt. Eng. 45(9), 095001 (2006).

Heflin, J. R.

C. Daengngam, I. Kandas, I. Ashry, A. Wang, J. R. Heflin, and Y. Xu, “Fabrication and characterization of periodically patterned silica fiber structures for enhanced second-order nonlinearity,” Opt. Express 23(6), 8113–8127 (2015).
[Crossref] [PubMed]

C. Daengngam, M. Hofmann, Z. Liu, A. Wang, J. R. Heflin, and Y. Xu, “Demonstration of a cylindrically symmetric second-order nonlinear fiber with self-assembled organic surface layers,” Opt. Express 19(11), 10326–10335 (2011).
[Crossref] [PubMed]

Y. Xu, A. Wang, J. R. Heflin, and Z. Liu, “Proposal and analysis of a silica fiber with large and thermodynamically stable second order nonlinearity,” Appl. Phys. Lett. 90(211110), 1–3 (2007).

J. R. Heflin, M. T. Guzy, P. J. Neyman, K. J. Gaskins, C. Brands, Z. Wang, H. W. Gibson, R. M. Davis, and K. E. Van Cott, “Efficient, thermally stable, second order nonlinear optical response in organic hybrid covalent/ionic self-assembled films,” Langmuir 22(13), 5723–5727 (2006).
[Crossref] [PubMed]

Hill, K.

K. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15(8), 1263–1276 (1997).
[Crossref]

Hofmann, M.

Hu, W.

T. Qi, S. Xiao, J. Shi, L. Yi, Z. Zhou, M. Bi, and W. Hu, “Cladding mode backward recoupling based displacement Sensor incorporating fiber up taper and Bragg grating,” IEEE Photonics J. 5(4), 7100608 (2013).
[Crossref]

Huang, J.

J. Huang, Y. He, and Y. Lo, “Spectrum analysis for high-order cladding modes based on long-period fiber gratings,” Opt. Eng. 45(9), 095001 (2006).

Iocco, A.

S. Vasil’ev, E. Dianov, O. Medvedkov, V. Protopopov, D. Costantini, A. Iocco, H. Limberger, and R. Salathe, “Properties of the cladding modes of an optical fiber excited by refractive-index gratings,” Quantum Electron. 29(1), 65–68 (1999).
[Crossref]

Ishio, H.

H. Ishio, J. Minowa, and K. Nosu, “Review and status of wavelength-division multiplexing technology and its application,” J. Lightwave Technol. 2(4), 448–463 (1984).
[Crossref]

James, S.

Judkins, J.

A. Vengsarkar, P. Lemaire, J. Judkins, V. Bhatia, T. Erdogan, and J. Sipe, “Long period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14(1), 58–65 (1996).
[Crossref]

Kandas, I.

Kelly, A. E.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286(5444), 1523–1528 (1999).
[Crossref] [PubMed]

Krug, P. A.

Lee, K. S.

Lemaire, P.

A. Vengsarkar, P. Lemaire, J. Judkins, V. Bhatia, T. Erdogan, and J. Sipe, “Long period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14(1), 58–65 (1996).
[Crossref]

Limberger, H.

S. Vasil’ev, E. Dianov, O. Medvedkov, V. Protopopov, D. Costantini, A. Iocco, H. Limberger, and R. Salathe, “Properties of the cladding modes of an optical fiber excited by refractive-index gratings,” Quantum Electron. 29(1), 65–68 (1999).
[Crossref]

Liu, Y.

R. Wu, Y. Liu, N. Chen, F. Pang, and T. Wang, “Fabrication and sensing characteristics of tilted long-period fiber gratings,” Proc. SPIE 8561(85610), G1–G7 (2013).

Liu, Z.

C. Daengngam, M. Hofmann, Z. Liu, A. Wang, J. R. Heflin, and Y. Xu, “Demonstration of a cylindrically symmetric second-order nonlinear fiber with self-assembled organic surface layers,” Opt. Express 19(11), 10326–10335 (2011).
[Crossref] [PubMed]

Y. Xu, A. Wang, J. R. Heflin, and Z. Liu, “Proposal and analysis of a silica fiber with large and thermodynamically stable second order nonlinearity,” Appl. Phys. Lett. 90(211110), 1–3 (2007).

Lo, Y.

J. Huang, Y. He, and Y. Lo, “Spectrum analysis for high-order cladding modes based on long-period fiber gratings,” Opt. Eng. 45(9), 095001 (2006).

Lu, Y. Q.

Luo, W.

Manning, R. J.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286(5444), 1523–1528 (1999).
[Crossref] [PubMed]

Medvedkov, O.

S. Vasil’ev, E. Dianov, O. Medvedkov, V. Protopopov, D. Costantini, A. Iocco, H. Limberger, and R. Salathe, “Properties of the cladding modes of an optical fiber excited by refractive-index gratings,” Quantum Electron. 29(1), 65–68 (1999).
[Crossref]

Meltz, G.

K. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15(8), 1263–1276 (1997).
[Crossref]

Minowa, J.

H. Ishio, J. Minowa, and K. Nosu, “Review and status of wavelength-division multiplexing technology and its application,” J. Lightwave Technol. 2(4), 448–463 (1984).
[Crossref]

Nesset, D.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286(5444), 1523–1528 (1999).
[Crossref] [PubMed]

Neyman, P. J.

J. R. Heflin, M. T. Guzy, P. J. Neyman, K. J. Gaskins, C. Brands, Z. Wang, H. W. Gibson, R. M. Davis, and K. E. Van Cott, “Efficient, thermally stable, second order nonlinear optical response in organic hybrid covalent/ionic self-assembled films,” Langmuir 22(13), 5723–5727 (2006).
[Crossref] [PubMed]

Nosu, K.

H. Ishio, J. Minowa, and K. Nosu, “Review and status of wavelength-division multiplexing technology and its application,” J. Lightwave Technol. 2(4), 448–463 (1984).
[Crossref]

Ortega, B.

Pang, F.

R. Wu, Y. Liu, N. Chen, F. Pang, and T. Wang, “Fabrication and sensing characteristics of tilted long-period fiber gratings,” Proc. SPIE 8561(85610), G1–G7 (2013).

Payne, D.

Phillips, I. D.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286(5444), 1523–1528 (1999).
[Crossref] [PubMed]

Poustie, A. J.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286(5444), 1523–1528 (1999).
[Crossref] [PubMed]

Protopopov, V.

S. Vasil’ev, E. Dianov, O. Medvedkov, V. Protopopov, D. Costantini, A. Iocco, H. Limberger, and R. Salathe, “Properties of the cladding modes of an optical fiber excited by refractive-index gratings,” Quantum Electron. 29(1), 65–68 (1999).
[Crossref]

Qi, T.

T. Qi, S. Xiao, J. Shi, L. Yi, Z. Zhou, M. Bi, and W. Hu, “Cladding mode backward recoupling based displacement Sensor incorporating fiber up taper and Bragg grating,” IEEE Photonics J. 5(4), 7100608 (2013).
[Crossref]

Reekie, L.

Rogers, D. C.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286(5444), 1523–1528 (1999).
[Crossref] [PubMed]

Saifi, M. A.

Salathe, R.

S. Vasil’ev, E. Dianov, O. Medvedkov, V. Protopopov, D. Costantini, A. Iocco, H. Limberger, and R. Salathe, “Properties of the cladding modes of an optical fiber excited by refractive-index gratings,” Quantum Electron. 29(1), 65–68 (1999).
[Crossref]

Shao, L.

Shi, J.

T. Qi, S. Xiao, J. Shi, L. Yi, Z. Zhou, M. Bi, and W. Hu, “Cladding mode backward recoupling based displacement Sensor incorporating fiber up taper and Bragg grating,” IEEE Photonics J. 5(4), 7100608 (2013).
[Crossref]

Sipe, J.

A. Vengsarkar, P. Lemaire, J. Judkins, V. Bhatia, T. Erdogan, and J. Sipe, “Long period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14(1), 58–65 (1996).
[Crossref]

C. de Sterke and J. Sipe, “Coupled modes and the nonlinear Schrödinger equation,” Phys. Rev. A 42(1), 550–555 (1990).
[Crossref] [PubMed]

Sipe, J. E.

Tam, H. Y.

Tatam, R.

Terhune, R.

Topliss, S.

Tsao, C.

Van Cott, K. E.

J. R. Heflin, M. T. Guzy, P. J. Neyman, K. J. Gaskins, C. Brands, Z. Wang, H. W. Gibson, R. M. Davis, and K. E. Van Cott, “Efficient, thermally stable, second order nonlinear optical response in organic hybrid covalent/ionic self-assembled films,” Langmuir 22(13), 5723–5727 (2006).
[Crossref] [PubMed]

Vasil’ev, S.

S. Vasil’ev, E. Dianov, O. Medvedkov, V. Protopopov, D. Costantini, A. Iocco, H. Limberger, and R. Salathe, “Properties of the cladding modes of an optical fiber excited by refractive-index gratings,” Quantum Electron. 29(1), 65–68 (1999).
[Crossref]

Vengsarkar, A.

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Xiao, S.

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Figures (7)

Fig. 1
Fig. 1 Schematic representation of coupling through T-LPG coated with organic nonlinear molecules and the generated SHS.
Fig. 2
Fig. 2 Possible cladding radii for which the intermodal phase matching condition is satisfied, at the intersections (green crosses) between   n eff cl for modes with azimuthal order lpump = 2 (Blue curves) and   n eff cl for modes with azimuthal order lSHS = 4 (Red curves).
Fig. 3
Fig. 3 Possible cladding radii for which the intermodal phase matching condition is satisfied, at the intersections (green crosses) between blue curves and red curves. SRI takes values of 1, 1.33 and 1.4.
Fig. 4
Fig. 4 Power of pump mode as a function of: (a) wavelength, λ and (b) longitudinal distance, Z.
Fig. 5
Fig. 5 Power of the generated SHS mode,  H E 4,3 cl,2ω as a function of: (a) wavelength, λ and (b) longitudinal distance, Z, for SRI = 1, 1.33 and 1.4. Zooming for the small values is clarified to the right.
Fig. 6
Fig. 6 Radial components of electric fields versus radial distance for: (a) pump mode  H E 2,1 cl,ω , and (b) SHS mode,  H E 4,3 cl,2ω with different SRI values.
Fig. 7
Fig. 7 Possible cladding radii for which the intermodal phase matching condition is satisfied, at the intersections (green crosses) between modes with azimuthal order lpump = 1 (Blue curves) and modes with azimuthal order lSHS = 2 (Red curves).

Tables (4)

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Table 1 T-LPG parameters that maximize the mode conversion from core to cladding.

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Table 2 LPG parameters that maximize the mode conversion from core to cladding.

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Table 3 SHG efficiency through LPG and T-LPG.

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Table 4 Comparison between the proposed model and the previous work.

Equations (9)

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d A 1,1 co ( Z ) dZ = i  A 1,1 co ( Z )   f 1,11,1  coco  + i  l,m A l,m cl  ( Z ) g + 1,1l, m  cocl   e i2 δ 1,1l,m Z
d A l,m cl ( Z ) dZ = i  A l,m cl ( Z )   f l,ml,m clcl    + i  A 1,1 co ( Z )    g 1,1l, m  cocl    e +i2  δ 1,1l,m  Z  
d A SHS cl, 2ω ( Z ) dZ = i2ω 4  v g (2ω) | A pump cl, ω ( Z ) | 2 χ eff ( 2 ) e iΔβZ
Δβ= 2 β pump cl β SHS cl
χ eff ( 2 ) = 0 2π dϕ a 2 a 2 +δ rdr  χ rrr ( 2 ) E SHS cl * ( r,ϕ ) ( E pump cl ( r,ϕ ) ) 2
χ eff ( 2 ) = 0 2π dϕ a 2 a 2+δ rdr  χ rrr ( 2 ) E SHS cl ( r ) ( E pump cl ( r ) ) 2 e i(2 l pump l SHS )ϕ
A SHS cl, 2ω = 0 L i2ω 4  υ g (2ω) | A pump cl, ω ( Z ) | 2 χ eff ( 2 ) e iΔβZ   dZ
P= | A | 2 P o
η total = P SHS cl, 2ω (L) P 1,1 co (0) = |   A SHS cl, 2ω (L) A 1,1 co (0) | 2

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