Abstract

We investigate the one-third harmonic generation (OTHG) in optical microfibers with power attenuation considered by analytically analyzing and numerically solving the coupled mode equations (CMEs). Both the strength and effective length of signal power growing in nonlinear media, which are extremely sensitive to the relative phase between the interaction waves, contribute to the final conversion efficiency. The relative phase and its evolution along the propagating direction play crucial roles in highly efficient OTHG. In order to obtain high conversion efficiency, the general expressions of optical threshold conditions are derived and discussed for choosing proper initial parameters. Numerically simulations are performed with both partial and absolute phase matching, which are corresponding to the microfibers with uniform and non-uniform diameters, respectively. Optimizations of relative phase and phase compensation are suggested by the simulations and provide significant enhancement of conversion efficiencies.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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2014 (1)

2013 (3)

2012 (3)

T. Lee, Y. Jung, C. A. Codemard, M. Ding, N. G. R. Broderick, and G. Brambilla, “Broadband third harmonic generation in tapered silica fibers,” Opt. Express 20(8), 8503–8511 (2012).

A. Coillet and P. Grelu, “Third-harmonic generation in optical microfibers: from silica experiments to highly nonlinear glass prospects,” Opt. Commun. 285(16), 3493–3497 (2012).
[Crossref]

A. Dot, A. Borne, B. Boulanger, K. Bencheikh, and J. A. Levenson, “Quantum theory analysis of triple photons generated by a χ(3)process,” Phys. Rev. A 85(2), 023809 (2012).
[Crossref]

2011 (3)

H. Cruz-Ramirez, R. Ramirez-Alarcon, M. Corona, K. Garay-Palmett, and A. B. U’Ren, “Spontaneous parametric processes in modern optics,” Opt. Photon. News 22(11), 36–41 (2011).
[Crossref]

M. Corona, K. Garay-Palmett, and A. B. U’Ren, “Third-order spontaneous parametric down-conversion in thin optical fibers as a photon-triplet source,” Phys. Rev. A 84(3), 033823 (2011).
[Crossref]

M. Corona, K. Garay-Palmett, and A. B. U’Ren, “Experimental proposal for the generation of entangled photon triplets by third-order spontaneous parametric downconversion in optical fibers,” Opt. Lett. 36(2), 190–192 (2011).
[Crossref] [PubMed]

2009 (1)

2007 (2)

V. Grubsky and J. Feinberg, “Phase-matched third-harmonic UV generation using low-order modes in a glass micro-fiber,” Opt. Commun. 274(2), 447–450 (2007).
[Crossref]

K. Bencheikh, F. Gravier, J. Douady, A. Levenson, and B. Boulanger, “Triple photons: a challenge in nonlinear and quantum optics,” C. R. Phys. 8(2), 206–220 (2007).
[Crossref]

2005 (1)

2004 (1)

Afshar V, S.

Bencheikh, K.

A. Dot, A. Borne, B. Boulanger, K. Bencheikh, and J. A. Levenson, “Quantum theory analysis of triple photons generated by a χ(3)process,” Phys. Rev. A 85(2), 023809 (2012).
[Crossref]

K. Bencheikh, F. Gravier, J. Douady, A. Levenson, and B. Boulanger, “Triple photons: a challenge in nonlinear and quantum optics,” C. R. Phys. 8(2), 206–220 (2007).
[Crossref]

Borne, A.

A. Dot, A. Borne, B. Boulanger, K. Bencheikh, and J. A. Levenson, “Quantum theory analysis of triple photons generated by a χ(3)process,” Phys. Rev. A 85(2), 023809 (2012).
[Crossref]

Boulanger, B.

A. Dot, A. Borne, B. Boulanger, K. Bencheikh, and J. A. Levenson, “Quantum theory analysis of triple photons generated by a χ(3)process,” Phys. Rev. A 85(2), 023809 (2012).
[Crossref]

K. Bencheikh, F. Gravier, J. Douady, A. Levenson, and B. Boulanger, “Triple photons: a challenge in nonlinear and quantum optics,” C. R. Phys. 8(2), 206–220 (2007).
[Crossref]

Brambilla, G.

Broderick, N. G.

Broderick, N. G. R.

Codemard, C. A.

Coillet, A.

A. Coillet and P. Grelu, “Third-harmonic generation in optical microfibers: from silica experiments to highly nonlinear glass prospects,” Opt. Commun. 285(16), 3493–3497 (2012).
[Crossref]

Corona, M.

M. Corona, K. Garay-Palmett, and A. B. U’Ren, “Experimental proposal for the generation of entangled photon triplets by third-order spontaneous parametric downconversion in optical fibers,” Opt. Lett. 36(2), 190–192 (2011).
[Crossref] [PubMed]

M. Corona, K. Garay-Palmett, and A. B. U’Ren, “Third-order spontaneous parametric down-conversion in thin optical fibers as a photon-triplet source,” Phys. Rev. A 84(3), 033823 (2011).
[Crossref]

H. Cruz-Ramirez, R. Ramirez-Alarcon, M. Corona, K. Garay-Palmett, and A. B. U’Ren, “Spontaneous parametric processes in modern optics,” Opt. Photon. News 22(11), 36–41 (2011).
[Crossref]

Cruz-Ramirez, H.

H. Cruz-Ramirez, R. Ramirez-Alarcon, M. Corona, K. Garay-Palmett, and A. B. U’Ren, “Spontaneous parametric processes in modern optics,” Opt. Photon. News 22(11), 36–41 (2011).
[Crossref]

Ding, M.

Dot, A.

A. Dot, A. Borne, B. Boulanger, K. Bencheikh, and J. A. Levenson, “Quantum theory analysis of triple photons generated by a χ(3)process,” Phys. Rev. A 85(2), 023809 (2012).
[Crossref]

Douady, J.

K. Bencheikh, F. Gravier, J. Douady, A. Levenson, and B. Boulanger, “Triple photons: a challenge in nonlinear and quantum optics,” C. R. Phys. 8(2), 206–220 (2007).
[Crossref]

Feinberg, J.

V. Grubsky and J. Feinberg, “Phase-matched third-harmonic UV generation using low-order modes in a glass micro-fiber,” Opt. Commun. 274(2), 447–450 (2007).
[Crossref]

Garay-Palmett, K.

M. Corona, K. Garay-Palmett, and A. B. U’Ren, “Experimental proposal for the generation of entangled photon triplets by third-order spontaneous parametric downconversion in optical fibers,” Opt. Lett. 36(2), 190–192 (2011).
[Crossref] [PubMed]

M. Corona, K. Garay-Palmett, and A. B. U’Ren, “Third-order spontaneous parametric down-conversion in thin optical fibers as a photon-triplet source,” Phys. Rev. A 84(3), 033823 (2011).
[Crossref]

H. Cruz-Ramirez, R. Ramirez-Alarcon, M. Corona, K. Garay-Palmett, and A. B. U’Ren, “Spontaneous parametric processes in modern optics,” Opt. Photon. News 22(11), 36–41 (2011).
[Crossref]

Gravier, F.

K. Bencheikh, F. Gravier, J. Douady, A. Levenson, and B. Boulanger, “Triple photons: a challenge in nonlinear and quantum optics,” C. R. Phys. 8(2), 206–220 (2007).
[Crossref]

Grelu, P.

A. Coillet and P. Grelu, “Third-harmonic generation in optical microfibers: from silica experiments to highly nonlinear glass prospects,” Opt. Commun. 285(16), 3493–3497 (2012).
[Crossref]

Grubsky, V.

V. Grubsky and J. Feinberg, “Phase-matched third-harmonic UV generation using low-order modes in a glass micro-fiber,” Opt. Commun. 274(2), 447–450 (2007).
[Crossref]

V. Grubsky and A. Savchenko, “Glass micro-fibers for efficient third harmonic generation,” Opt. Express 13(18), 6798–6806 (2005).
[Crossref] [PubMed]

Huang, T.

Jung, Y.

Lam, H. Q.

Lee, T.

Levenson, A.

K. Bencheikh, F. Gravier, J. Douady, A. Levenson, and B. Boulanger, “Triple photons: a challenge in nonlinear and quantum optics,” C. R. Phys. 8(2), 206–220 (2007).
[Crossref]

Levenson, J. A.

A. Dot, A. Borne, B. Boulanger, K. Bencheikh, and J. A. Levenson, “Quantum theory analysis of triple photons generated by a χ(3)process,” Phys. Rev. A 85(2), 023809 (2012).
[Crossref]

Lohe, M. A.

Lou, J.

Mazur, E.

Monro, T. M.

Perry, S. P.

Ping, S.

Ramirez-Alarcon, R.

H. Cruz-Ramirez, R. Ramirez-Alarcon, M. Corona, K. Garay-Palmett, and A. B. U’Ren, “Spontaneous parametric processes in modern optics,” Opt. Photon. News 22(11), 36–41 (2011).
[Crossref]

Savchenko, A.

Shao, X.

Sun, Y.

Tong, L.

U’Ren, A. B.

M. Corona, K. Garay-Palmett, and A. B. U’Ren, “Experimental proposal for the generation of entangled photon triplets by third-order spontaneous parametric downconversion in optical fibers,” Opt. Lett. 36(2), 190–192 (2011).
[Crossref] [PubMed]

H. Cruz-Ramirez, R. Ramirez-Alarcon, M. Corona, K. Garay-Palmett, and A. B. U’Ren, “Spontaneous parametric processes in modern optics,” Opt. Photon. News 22(11), 36–41 (2011).
[Crossref]

M. Corona, K. Garay-Palmett, and A. B. U’Ren, “Third-order spontaneous parametric down-conversion in thin optical fibers as a photon-triplet source,” Phys. Rev. A 84(3), 033823 (2011).
[Crossref]

Wu, Z.

Zhang, J.

C. R. Phys. (1)

K. Bencheikh, F. Gravier, J. Douady, A. Levenson, and B. Boulanger, “Triple photons: a challenge in nonlinear and quantum optics,” C. R. Phys. 8(2), 206–220 (2007).
[Crossref]

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

Opt. Commun. (2)

V. Grubsky and J. Feinberg, “Phase-matched third-harmonic UV generation using low-order modes in a glass micro-fiber,” Opt. Commun. 274(2), 447–450 (2007).
[Crossref]

A. Coillet and P. Grelu, “Third-harmonic generation in optical microfibers: from silica experiments to highly nonlinear glass prospects,” Opt. Commun. 285(16), 3493–3497 (2012).
[Crossref]

Opt. Express (5)

Opt. Lett. (2)

Opt. Photon. News (1)

H. Cruz-Ramirez, R. Ramirez-Alarcon, M. Corona, K. Garay-Palmett, and A. B. U’Ren, “Spontaneous parametric processes in modern optics,” Opt. Photon. News 22(11), 36–41 (2011).
[Crossref]

Phys. Rev. A (2)

A. Dot, A. Borne, B. Boulanger, K. Bencheikh, and J. A. Levenson, “Quantum theory analysis of triple photons generated by a χ(3)process,” Phys. Rev. A 85(2), 023809 (2012).
[Crossref]

M. Corona, K. Garay-Palmett, and A. B. U’Ren, “Third-order spontaneous parametric down-conversion in thin optical fibers as a photon-triplet source,” Phys. Rev. A 84(3), 033823 (2011).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1 Relative phase distribution for THG and OTHG.
Fig. 2
Fig. 2 (a) Relative phase, (b) sine value of relative phase and (c) gain coefficient as a function of propagating length for 6 different initial relative phases with nonlinear phase modulation compensated at the beginning; (d) maximum gain coefficient and its corresponding effective interaction length as a function of initial relative phase.
Fig. 3
Fig. 3 (a) Relative phase, (b) sine value of relative phase and (c) gain coefficient as a function of propagating length for 6 different modal phase mismatches with initial relative phase fixed at -π/2; (d) maximum gain coefficient and its corresponding effective interaction length as a function of modal phase mismatch δβ .
Fig. 4
Fig. 4 (a) Relative phase, (b) sine value of relative phase and (c) gain coefficient as a function of propagating length for 3 sets of different initial condition; (d) modal phase mismatch as a function of propagating length in non-uniform microfibers.

Equations (28)

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A 1 z = α 1 A 1 +i γ 0 [ ( J 1 | A 1 | 2 +2 J 2 | A 3 | 2 ) A 1 + J 3 ( A 1 * ) 2 A 3 e iδβz ]
A 3 z = α 3 A 3 +i γ 0 [ ( 6 J 2 | A 1 | 2 +3 J 5 | A 3 | 2 ) A 3 + J 3 * A 1 3 e iδβz ]
d ρ 1 dz = α 1 ρ 1 γ 0 J 3 ρ 1 2 ρ 3 sinθ
d ρ 3 dz = α 3 ρ 3 + γ 0 J 3 ρ 1 3 sinθ
dθ dz =δβ+z dδβ dz +K( ρ 1 , ρ 3 ,θ )
K( ρ 1 , ρ 3 ,θ )= γ 0 [ 3( 2 J 2 J 1 ) ρ 1 2 +3( J 5 2 J 2 ) ρ 3 2 +( ρ 1 3 ρ 3 1 3 ρ 1 ρ 3 ) J 3 cosθ ]
d P t dz =2b P t α 1 2( 1b ) P t α 3
db dz =2b( b1 )( α 1 α 3 )2 γ 0 J 3 b P t b b 2 sinθ
dθ dz =δβ+z dδβ dz +K( b, P t ,θ )
K( b, P t ,θ )= P t γ 0 [ b( 4 J 2 J 1 J 5 )+3( J 5 2 J 2 )+( 4b3 ) b 1b J 3 cosθ ]
d P t dz =2 P t α
db dz =2 γ 0 J 3 P t ( 0 )b b b 2 e 2αz sinθ
db dz =2 γ 0 J 3 P t ( 0 )b b b 2 e 2αz
dδβ dz = 1 z [ δβ+K( b, P t ) ]
K( b, P t )= P t (0) e 2αz γ 0 [ b( 4 J 2 J 1 J 5 )+3( J 5 2 J 2 ) ]
dθ dz =δβ+K( b, P t ,θ )
d P s dz =2αb P t 2 γ 0 J 3 b P t 2 b b 2 sinθ
P t > α γ 0 J 3 b b 2 sinθ
b b 2 > α γ 0 J 3 P t sinθ
sinθ< α γ 0 J 3 P t b b 2
g( z )=10 log 10 b( z )P( z ) b( 0 )P( 0 ) =10 log 10 b( z ) b( 0 ) 8.68αz
J 1 =0.97μ m 2 , J 2 =1.46μ m 2 , J 3 =0.39μ m 2 , J 5 =3.96μ m 2
θ( z ) | z=0 =π/2 ±Δθ,Δθ0
( dθ dz ) | z=0 =0, ( dθ dz ) | z>0 <0
θ( z ) | z=0 =π/2
dθ dz { >0,0<z<l =0,z=l <0,z>l
θ( z )=π/2
dθ( z ) dz =0

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