Abstract

A fiber with a thin-metallic layer introduced between the central core and the cladding is proposed to lift the near-degeneracy of the modes TE01, TM01, and HE21. It can be used to obtain the pure mode TE01 as both the active and passive fibers. In the case of the active fiber, the fiber with the appropriate rare earth doping profile in the central core is presented as the gain medium of a fiber laser. The numerical results show that the pure mode TE01 (99.99%) can be obtained. In the case of the passive fiber, Gaussian light beams with suitable shift distance from the center core are coupled into the fiber. The results indicate that only the mode TE01 remains with the increasing propagation distance.

© 2013 Optical Society of America

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References

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2012 (1)

2011 (2)

M. P. Thirugnanasambandam, Y. Senatsky, and K. Ueda, “Generation of radially and azimuthally polarized beams in Yb:YAG laser with intra-cavity lens and birefringent crystal,” Opt. Express 19, 1905–1914 (2011).
[Crossref]

C. Wang, X. Wen, F. Zhang, and S. Jian, “Generation of radially polarized mode using an active cylindrically symmetric birefringence fiber,” Opt. Commun. 284, 1015–1018 (2011).
[Crossref]

2010 (3)

2009 (1)

2008 (1)

2007 (3)

2005 (1)

2002 (1)

1992 (1)

1991 (1)

C. R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 271–283 (1991).
[Crossref]

’t Hooft, G. W.

Aiello, A.

Bashkansky, M.

Biss, D. P.

D. P. Biss and T. G. Brown, “Gradient imaging with vortex beams,” in Frontiers in Optics 2004/Laser Science XXII/Diffractive Optics and Micro-Optics/Optical Fabrication and Testing, OSA Technical Digest (Optical Society of America, 2004), paper FTuG8.

Brown, T. G.

D. P. Biss and T. G. Brown, “Gradient imaging with vortex beams,” in Frontiers in Optics 2004/Laser Science XXII/Diffractive Optics and Micro-Optics/Optical Fabrication and Testing, OSA Technical Digest (Optical Society of America, 2004), paper FTuG8.

Chen, J.

Desurvire, E.

C. R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 271–283 (1991).
[Crossref]

Eliel, E. R.

Fatemi, F. K.

Feurer, T.

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys. A 86, 329–334 (2007).
[Crossref]

Fujisawa, T.

Giles, C. R.

C. R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 271–283 (1991).
[Crossref]

Gong, M.

Gu, C.

Han, X.

He, Y.

Hecht, E.

E. Hecht, Optics, 2nd ed. (Addison-Wesley, 1987), p. 102.

Heckenberg, N. R.

Jauregui, C.

C. Jocher, C. Jauregui, C. Voigtländer, F. Stutzki, S. Nolte, J. Limpert, and A. Tünnermann, “Fiber based modal filter for radially and azimuthally polarized beams,” in Lasers, Sources, and Related Photonic Devices, OSA Technical Digest (Optical Society of America, 2012), paper FW5C.3.

Jian, S.

C. Wang, X. Wen, F. Zhang, and S. Jian, “Generation of radially polarized mode using an active cylindrically symmetric birefringence fiber,” Opt. Commun. 284, 1015–1018 (2011).
[Crossref]

Jocher, C.

C. Jocher, C. Jauregui, C. Voigtländer, F. Stutzki, S. Nolte, J. Limpert, and A. Tünnermann, “Fiber based modal filter for radially and azimuthally polarized beams,” in Lasers, Sources, and Related Photonic Devices, OSA Technical Digest (Optical Society of America, 2012), paper FW5C.3.

Jureller, J. E.

Koshiba, M.

Lei, M.

Li, C.

Liao, S.

Limpert, J.

C. Jocher, C. Jauregui, C. Voigtländer, F. Stutzki, S. Nolte, J. Limpert, and A. Tünnermann, “Fiber based modal filter for radially and azimuthally polarized beams,” in Lasers, Sources, and Related Photonic Devices, OSA Technical Digest (Optical Society of America, 2012), paper FW5C.3.

Liu, Z.

Ma, P.

Ma, Y.

Meier, M.

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys. A 86, 329–334 (2007).
[Crossref]

Merano, M.

Ming, H.

Nieminen, T. A.

Nolte, S.

C. Jocher, C. Jauregui, C. Voigtländer, F. Stutzki, S. Nolte, J. Limpert, and A. Tünnermann, “Fiber based modal filter for radially and azimuthally polarized beams,” in Lasers, Sources, and Related Photonic Devices, OSA Technical Digest (Optical Society of America, 2012), paper FW5C.3.

Oh, E.

Park, D.

Park, S.

Peng, F.

Romano, V.

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys. A 86, 329–334 (2007).
[Crossref]

Rubinsztein-Dunlop, H.

Scherer, N. F.

Senatsky, Y.

Sibbett, W.

Stutzki, F.

C. Jocher, C. Jauregui, C. Voigtländer, F. Stutzki, S. Nolte, J. Limpert, and A. Tünnermann, “Fiber based modal filter for radially and azimuthally polarized beams,” in Lasers, Sources, and Related Photonic Devices, OSA Technical Digest (Optical Society of America, 2012), paper FW5C.3.

Su, R.

Thirugnanasambandam, M. P.

Toussaint, K. C.

Tünnermann, A.

C. Jocher, C. Jauregui, C. Voigtländer, F. Stutzki, S. Nolte, J. Limpert, and A. Tünnermann, “Fiber based modal filter for radially and azimuthally polarized beams,” in Lasers, Sources, and Related Photonic Devices, OSA Technical Digest (Optical Society of America, 2012), paper FW5C.3.

Ueda, K.

van Exter, M. P.

Voigtländer, C.

C. Jocher, C. Jauregui, C. Voigtländer, F. Stutzki, S. Nolte, J. Limpert, and A. Tünnermann, “Fiber based modal filter for radially and azimuthally polarized beams,” in Lasers, Sources, and Related Photonic Devices, OSA Technical Digest (Optical Society of America, 2012), paper FW5C.3.

Wang, A.

Wang, C.

C. Wang, X. Wen, F. Zhang, and S. Jian, “Generation of radially polarized mode using an active cylindrically symmetric birefringence fiber,” Opt. Commun. 284, 1015–1018 (2011).
[Crossref]

Wang, X.

Wen, X.

C. Wang, X. Wen, F. Zhang, and S. Jian, “Generation of radially polarized mode using an active cylindrically symmetric birefringence fiber,” Opt. Commun. 284, 1015–1018 (2011).
[Crossref]

Woerdman, J. P.

Xu, K.

Xu, L.

Yan, P.

Yan, S.

Yang, Y.

Yao, B.

Yuan, Y.

Zhang, F.

C. Wang, X. Wen, F. Zhang, and S. Jian, “Generation of radially polarized mode using an active cylindrically symmetric birefringence fiber,” Opt. Commun. 284, 1015–1018 (2011).
[Crossref]

Zhang, H.

Zhao, W.

Zheng, R.

Zhou, P.

Zhu, X.

Appl. Phys. A (1)

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys. A 86, 329–334 (2007).
[Crossref]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

C. Wang, X. Wen, F. Zhang, and S. Jian, “Generation of radially polarized mode using an active cylindrically symmetric birefringence fiber,” Opt. Commun. 284, 1015–1018 (2011).
[Crossref]

Opt. Express (5)

Opt. Lett. (4)

Other (4)

http://refractiveindex.info .

E. Hecht, Optics, 2nd ed. (Addison-Wesley, 1987), p. 102.

C. Jocher, C. Jauregui, C. Voigtländer, F. Stutzki, S. Nolte, J. Limpert, and A. Tünnermann, “Fiber based modal filter for radially and azimuthally polarized beams,” in Lasers, Sources, and Related Photonic Devices, OSA Technical Digest (Optical Society of America, 2012), paper FW5C.3.

D. P. Biss and T. G. Brown, “Gradient imaging with vortex beams,” in Frontiers in Optics 2004/Laser Science XXII/Diffractive Optics and Micro-Optics/Optical Fabrication and Testing, OSA Technical Digest (Optical Society of America, 2004), paper FTuG8.

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Figures (21)

Fig. 1.
Fig. 1.

Cross section of the designed fiber.

Fig. 2.
Fig. 2.

Intensity patterns of the modes (a), (b) HE11, (c) TE01, (d) HE21o, (e) HE21e, and (f) TM01. Arrows show their polarizations.

Fig. 3.
Fig. 3.

Dependencies of Re(neff) for (a) the modes TE01, TM01, HE21, and HE11, and (b) Δ1 and Δ2 on the gold layer thickness, where r1=10μm, n1=1.453, n2=1.45, and nm=0.5511.5i at the wavelength of 1.55 μm.

Fig. 4.
Fig. 4.

Dependencies of the confinement losses for the modes TE01, TM01, HE21, and HE11 on gold layer thickness, where r1=10μm, n1=1.453, n2=1.45, and nm=0.5511.5i at the wavelength of 1.55 μm.

Fig. 5.
Fig. 5.

Variations of (a) Δ1 and (b) Δ2 with δ for different metallic layers at 1.55 μm.

Fig. 6.
Fig. 6.

Variations of the confinement losses for the modes (a) TE01, (b) TM01, (c) HE21, and (d) HE11 with δ for different metallic layers at 1.55 μm.

Fig. 7.
Fig. 7.

Δ1 and Δ2 versus wavelength.

Fig. 8.
Fig. 8.

Dependencies of the confinement losses for the modes TE01, TM01, HE21, and HE11 on the wavelength.

Fig. 9.
Fig. 9.

Reflection of the electric field with (a) perpendicular and (b) parallel polarization, where k⃗ is the wave vector and E⃗ is the electric field.

Fig. 10.
Fig. 10.

DepthGH of the gold and central core interface for perpendicular and parallel polarizations.

Fig. 11.
Fig. 11.

η for the modes TE01 and TM01 as a function of the gold layer thickness.

Fig. 12.
Fig. 12.

Schematic illustration of the fiber laser.

Fig. 13.
Fig. 13.

Cross section of the central core. The blue region corresponds to the doped region.

Fig. 14.
Fig. 14.

Output laser power versus pump power for the fiber laser.

Fig. 15.
Fig. 15.

Factor Q and the output laser power of the mode TE01 versus Γ with bidirectional pumping scheme, where each pump power is 4 W.

Fig. 16.
Fig. 16.

Electric field profiles of the x- (Ex) and y-polarized (Ey) components for the mode TE01. The white arrows show the direction of the electric field.

Fig. 17.
Fig. 17.

Schematic illustration of the central core with a Gaussian laser beam coupled, where d is the distance that the center of the Gaussian laser beam is away from the center of the core. The white arrow shows the polarization of the Gaussian laser beam.

Fig. 18.
Fig. 18.

Variations of the reference refractive index along the propagation distance with d of 3, 5, 7, and 10 μm. The inset figures show the corresponding intensity distributions at the propagation distance of 5 mm.

Fig. 19.
Fig. 19.

Electric field distributions at the propagation distance of (a) 0.1 mm, (b) 5 mm, (c) 10 mm, and (d) 15 mm with d of 7 μm. The orientation and length of the arrows indicate the polarization direction and amplitude of the electric field vector, respectively. The inset figures show the corresponding intensity distribution.

Fig. 20.
Fig. 20.

Schematic illustration of the central core with the x- and y-polarized beams with antisymmetric field distributions as the initial laser source. d is the offset distance between the centers of the core and the Gaussian beam. The white arrows show the polarization of the Gaussian laser beams.

Fig. 21.
Fig. 21.

Electric field distributions at the propagation distance of (a) 0.1 mm, (b) 4 mm, (c) 10 mm, and (d) 12 mm with d of 7 μm in the case of two pairs of antisymmetric Gaussian laser beams. The orientation and length of the arrows indicate the polarization direction and amplitude of the electric field vector, respectively. The inset figures show corresponding intensity distribution.

Tables (2)

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Table 1. Refractive Indices for Different Metals at 1.55 μm

Tables Icon

Table 2. Parameters Used in Simulations

Equations (12)

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Lossconfinement=20ln(10)2πλIm(neff)dB/m.
rTE01=ErE=cosθn2sin2θcosθ+n2sin2θ,
rTM01=ErE=n2cosθ+n2sin2θn2cosθ+n2sin2θ,
DisplacementGH=λ2πdδ(θ)dθ,
DepthGH=|DisplacementGH|/2tan(θ).
ηi=02π0r112Re(E⃗i×H⃗i*·e⃗z)rdrdφ02π012Re(E⃗i×H⃗i*·e⃗z)rdrdφi=TE01,TM01.
N2kN1k=[Pp+(z)+Pp(z)]σapΓpkhvpAk+i[Psi+(z)+Psi(z)]σasΓsikhvsAk[Pp+(z)+Pp(z)]σepΓpkhvpAk+1τ+i[Psi+(z)+Psi(z)]σesΓsikhvsAk,
±dPp±(z)dz=kΓpk[σepN2k(z)σapN1k]Pp±(z)αpPp±(z),
±dPsi±(z)dz=kΓsik[σesN2k(z)σasN1k]Psi±(z)αsiPsi±(z),
E⃗y=e⃗y200·exp[(xd)2+y2ω02],
E⃗x=e⃗x200·{exp[x2+(yd)2ω02]+exp[x2+(y+d)2ω02]},
E⃗y=e⃗y200·{exp[(xd)2+y2ω02]exp[(x+d)2+y2ω02]},

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