Abstract

We demonstrate experimentally and theoretically that a nanoscale hollow channel placed centrally in the solid-glass core of a photonic crystal fiber strongly enhances the cylindrical birefringence (the modal index difference between radially and azimuthally polarized modes). Furthermore, it causes a large split in group velocity and group velocity dispersion. We show analytically that all three parameters can be varied over a wide range by tuning the diameters of the nanobore and the core.

© 2010 Optical Society of America

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References

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    [Crossref]
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2010 (3)

2009 (5)

2008 (2)

H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. P. Semprere, and P. St. J. Russell, “Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber,” Appl. Phys. Lett. 93, 111102 (2008).
[Crossref]

T. G. Euser, G. Whyte, M. Scharrer, J. S. Y. Chen, A. Abdolvand, J. Nold, C. F. Kaminski, and P. St. J. Russell, “Dynamic control of higher-order modes in hollow-core photonic crystal fibers,” Opt. Express 16, 17972–17981 (2008).
[Crossref] [PubMed]

2007 (1)

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz, and H. L. Fragnito, “Field enhancement within an optical fibre with a subwavelength air core,” Nat. Photon. 1, 115–118 (2007).
[Crossref]

2006 (2)

2004 (1)

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[Crossref] [PubMed]

1999 (1)

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D 32, 1455–1461 (1999).
[Crossref]

1998 (1)

1997 (1)

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[Crossref]

1996 (1)

1994 (1)

1984 (1)

1981 (1)

H.-T. Shang, “Chromatic dispersion measurement by white-light interferometry on metre-length single-mode optical fibres,” Electron. Lett. 17, 603–605 (1981).
[Crossref]

1978 (1)

Abdolvand, A.

Aiello, A.

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. St. J. Russell, and G. Leuchs, “Hybrid-entanglement in continuous variable systems,” http://arxiv.org/abs/1007.1322.

Andersen, U. L.

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. St. J. Russell, and G. Leuchs, “Hybrid-entanglement in continuous variable systems,” http://arxiv.org/abs/1007.1322.

Banzer, P.

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. St. J. Russell, and G. Leuchs, “Hybrid-entanglement in continuous variable systems,” http://arxiv.org/abs/1007.1322.

Barreiro, J. T.

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Remote preparation of single-photon “hybrid” entangled and vector-polarization states,” Phys. Rev. Lett. 105, 030407 (2010).
[Crossref] [PubMed]

Benabid, F.

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz, and H. L. Fragnito, “Field enhancement within an optical fibre with a subwavelength air core,” Nat. Photon. 1, 115–118 (2007).
[Crossref]

Biancalana, F.

Birks, T.

Chai, L.

Chen, J. S. Y.

Chen, W.

Cordeiro, C. M. B.

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz, and H. L. Fragnito, “Field enhancement within an optical fibre with a subwavelength air core,” Nat. Photon. 1, 115–118 (2007).
[Crossref]

Couny, F.

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz, and H. L. Fragnito, “Field enhancement within an optical fibre with a subwavelength air core,” Nat. Photon. 1, 115–118 (2007).
[Crossref]

Cruz, C. H. B.

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz, and H. L. Fragnito, “Field enhancement within an optical fibre with a subwavelength air core,” Nat. Photon. 1, 115–118 (2007).
[Crossref]

Da, N.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[Crossref] [PubMed]

Elser, D.

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. St. J. Russell, and G. Leuchs, “Hybrid-entanglement in continuous variable systems,” http://arxiv.org/abs/1007.1322.

Euser, T. G.

T. G. Euser, G. Whyte, M. Scharrer, J. S. Y. Chen, A. Abdolvand, J. Nold, C. F. Kaminski, and P. St. J. Russell, “Dynamic control of higher-order modes in hollow-core photonic crystal fibers,” Opt. Express 16, 17972–17981 (2008).
[Crossref] [PubMed]

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. St. J. Russell, and G. Leuchs, “Hybrid-entanglement in continuous variable systems,” http://arxiv.org/abs/1007.1322.

Fleming, J. W.

Förtsch, M.

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. St. J. Russell, and G. Leuchs, “Hybrid-entanglement in continuous variable systems,” http://arxiv.org/abs/1007.1322.

Fragnito, H. L.

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz, and H. L. Fragnito, “Field enhancement within an optical fibre with a subwavelength air core,” Nat. Photon. 1, 115–118 (2007).
[Crossref]

Gabriel, C.

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. St. J. Russell, and G. Leuchs, “Hybrid-entanglement in continuous variable systems,” http://arxiv.org/abs/1007.1322.

Gaeta, A. L.

A. Ishaaya, C. J. Hensley, B. Shim, S. Schrauth, K. W. Koch, and A. L. Gaeta, “Highly-efficient coupling of linearly- and radially-polarized femtosecond pulses in hollow-core photonic band-gap fibers,” Opt. Express 17, 18630–18637 (2009).
[Crossref]

A. A. Ishaaya, B. Shim, C. J. Hensley, S. Schrauth, A. L. Gaeta, and K. W. Koch, “Efficient excitation of polarization vortices in a photonic bandgap fiber with ultrashort laser pulses,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest Series (CD) (Optical Society of America, 2008), paper CThV3.
[PubMed]

Granzow, N.

Hayashi, T.

He, J.

T. Lan, J. He, and C. Tien, “Versatile excitation of localized surface plasmon polaritons via spatially modulated polarized focus,” in Quantum Electronics and Laser Science Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2010), paper QMD5.

Hell, S. W.

Hensley, C. J.

A. Ishaaya, C. J. Hensley, B. Shim, S. Schrauth, K. W. Koch, and A. L. Gaeta, “Highly-efficient coupling of linearly- and radially-polarized femtosecond pulses in hollow-core photonic band-gap fibers,” Opt. Express 17, 18630–18637 (2009).
[Crossref]

A. A. Ishaaya, B. Shim, C. J. Hensley, S. Schrauth, A. L. Gaeta, and K. W. Koch, “Efficient excitation of polarization vortices in a photonic bandgap fiber with ultrashort laser pulses,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest Series (CD) (Optical Society of America, 2008), paper CThV3.
[PubMed]

Hirano, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[Crossref]

Hu, M. L.

Ishaaya, A.

Ishaaya, A. A.

A. A. Ishaaya, B. Shim, C. J. Hensley, S. Schrauth, A. L. Gaeta, and K. W. Koch, “Efficient excitation of polarization vortices in a photonic bandgap fiber with ultrashort laser pulses,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest Series (CD) (Optical Society of America, 2008), paper CThV3.
[PubMed]

Joly, N.

Joly, N. Y.

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. St. J. Russell, and G. Leuchs, “Hybrid-entanglement in continuous variable systems,” http://arxiv.org/abs/1007.1322.

Kaminski, C. F.

Knight, J.

Knight, J. C.

V. Pureur, J. C. Knight, and B. T. Kuhlmey, “Higher order guided mode propagation in solid-core photonic bandgap fibers,” Opt. Express 18, 8906–8915 (2010).
[Crossref] [PubMed]

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz, and H. L. Fragnito, “Field enhancement within an optical fibre with a subwavelength air core,” Nat. Photon. 1, 115–118 (2007).
[Crossref]

Koch, K. W.

A. Ishaaya, C. J. Hensley, B. Shim, S. Schrauth, K. W. Koch, and A. L. Gaeta, “Highly-efficient coupling of linearly- and radially-polarized femtosecond pulses in hollow-core photonic band-gap fibers,” Opt. Express 17, 18630–18637 (2009).
[Crossref]

A. A. Ishaaya, B. Shim, C. J. Hensley, S. Schrauth, A. L. Gaeta, and K. W. Koch, “Efficient excitation of polarization vortices in a photonic bandgap fiber with ultrashort laser pulses,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest Series (CD) (Optical Society of America, 2008), paper CThV3.
[PubMed]

Kristensen, P.

Kuga, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[Crossref]

Kuhlmey, B. T.

Kwiat, P. G.

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Remote preparation of single-photon “hybrid” entangled and vector-polarization states,” Phys. Rev. Lett. 105, 030407 (2010).
[Crossref] [PubMed]

Lan, T.

T. Lan, J. He, and C. Tien, “Versatile excitation of localized surface plasmon polaritons via spatially modulated polarized focus,” in Quantum Electronics and Laser Science Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2010), paper QMD5.

Lee, H. W.

H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. P. Semprere, and P. St. J. Russell, “Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber,” Appl. Phys. Lett. 93, 111102 (2008).
[Crossref]

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[Crossref] [PubMed]

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. St. J. Russell, and G. Leuchs, “Hybrid-entanglement in continuous variable systems,” http://arxiv.org/abs/1007.1322.

Li, G.

Li, J.

Li, R.

Li, X.

Li, Y. F.

Lin, D.

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory(Chapman and Hall, 1983).

Maier, S. A.

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz, and H. L. Fragnito, “Field enhancement within an optical fibre with a subwavelength air core,” Nat. Photon. 1, 115–118 (2007).
[Crossref]

Marom, E.

Marquardt, C.

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, C. Marquardt, P. St. J. Russell, and G. Leuchs, “Hybrid-entanglement in continuous variable systems,” http://arxiv.org/abs/1007.1322.

Michihata, M.

Nesterov, A. V.

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D 32, 1455–1461 (1999).
[Crossref]

Niziev, V. G.

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D 32, 1455–1461 (1999).
[Crossref]

Nold, J.

Peng, M.

Pureur, V.

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[Crossref] [PubMed]

Ramachandran, S.

Russell, P. St. J.

Sasada, H.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[Crossref]

Schadt, M.

Scharrer, M.

Schmidt, M. A.

M. A. Schmidt, N. Granzow, N. Da, M. Peng, L. Wondraczek, and P. St. J. Russell, “All-solid bandgap guiding in tellurite-filled silica photonic crystal fibers,” Opt. Lett. 34, 1946–1948 (2009).
[Crossref] [PubMed]

H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. P. Semprere, and P. St. J. Russell, “Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber,” Appl. Phys. Lett. 93, 111102 (2008).
[Crossref]

Schrauth, S.

A. Ishaaya, C. J. Hensley, B. Shim, S. Schrauth, K. W. Koch, and A. L. Gaeta, “Highly-efficient coupling of linearly- and radially-polarized femtosecond pulses in hollow-core photonic band-gap fibers,” Opt. Express 17, 18630–18637 (2009).
[Crossref]

A. A. Ishaaya, B. Shim, C. J. Hensley, S. Schrauth, A. L. Gaeta, and K. W. Koch, “Efficient excitation of polarization vortices in a photonic bandgap fiber with ultrashort laser pulses,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest Series (CD) (Optical Society of America, 2008), paper CThV3.
[PubMed]

Semprere, L. P.

H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. P. Semprere, and P. St. J. Russell, “Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber,” Appl. Phys. Lett. 93, 111102 (2008).
[Crossref]

Serebryannikov, E. E.

Shang, H.-T.

H.-T. Shang, “Chromatic dispersion measurement by white-light interferometry on metre-length single-mode optical fibres,” Electron. Lett. 17, 603–605 (1981).
[Crossref]

Shim, B.

A. Ishaaya, C. J. Hensley, B. Shim, S. Schrauth, K. W. Koch, and A. L. Gaeta, “Highly-efficient coupling of linearly- and radially-polarized femtosecond pulses in hollow-core photonic band-gap fibers,” Opt. Express 17, 18630–18637 (2009).
[Crossref]

A. A. Ishaaya, B. Shim, C. J. Hensley, S. Schrauth, A. L. Gaeta, and K. W. Koch, “Efficient excitation of polarization vortices in a photonic bandgap fiber with ultrashort laser pulses,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest Series (CD) (Optical Society of America, 2008), paper CThV3.
[PubMed]

Shimizu, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[Crossref]

Shiokawa, N.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[Crossref]

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory(Chapman and Hall, 1983).

Song, Y. J.

Stalder, M.

Takaya, Y.

Tien, C.

T. Lan, J. He, and C. Tien, “Versatile excitation of localized surface plasmon polaritons via spatially modulated polarized focus,” in Quantum Electronics and Laser Science Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2010), paper QMD5.

Torii, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997).
[Crossref]

Tyagi, H. K.

H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. P. Semprere, and P. St. J. Russell, “Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber,” Appl. Phys. Lett. 93, 111102 (2008).
[Crossref]

Ueda, K.

Wadsworth, W.

Wang, C. Y.

Wei, T. C.

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Remote preparation of single-photon “hybrid” entangled and vector-polarization states,” Phys. Rev. Lett. 105, 030407 (2010).
[Crossref] [PubMed]

Whyte, G.

Wichmann, J.

Wiederhecker, G. S.

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Figures (9)

Fig. 1
Fig. 1 Optical microscope images of (a) the first and (b) the second cane. The diameter of the hole in the core was reduced from 96 µm to 16 µm . (c) SEM of the cladding microstructure of the fused silica nanobore PCF. (d) SEM of the fiber core. The core has diameter 930 nm with a 180 nm wide nanobore located in its center.
Fig. 2
Fig. 2 (a) Experimental setup: light from a PCF-based SC source passes through a polarizer (P1) and a polarization converter [20] that converts the polarization state to either radial or azimuthal. This beam is coupled into a Mach–Zehnder interferometer. One arm includes 41 cm of the nanobore PCF shown in Figs. 1c, 1d. The fiber arm and reference arm are recombined, pass a grating monochromator (GM) and the interference signal is measured by detector (D). A CCD camera and a polarizer (P2) are used to analyze the polarization state of the beam exiting the fiber. (b) Operating principle of the polarization converter using a liquid-crystal cell with alignment layers linearly rubbed on one side and circularly on the other side (from [20]).
Fig. 3
Fig. 3 (a)–(f) Normalized Poynting vector profiles at λ = 820 nm for radially (top row) and azimuthally (bottom row) polarized modes obtained by imaging a 2.1 × 2.1 μm 2 region of the near field at the fiber end face onto a CCD camera. (c)–(f) Poynting vector profiles measured for orthogonal orientations of the polarizer (P2) (linear gray scale identical in each image). (g), (h) Vector plots of the measured electric field orientations in (a) and (b).
Fig. 4
Fig. 4 (top panel) Experimentally determined relative group delay of azimuthal and radial modes as a function of wavelength; (lower panel) measured (symbols) and calculated (curves) GVD of the azimuthal (black), radial (red), and HE 21 modes (blue). The shaded area indicates anomalous dispersion. The solid curves are the results of FE simulations, and the dashed curves are based on the analytical step-index model. (inset) Detail of the region where the effective phase indices of the radial and HE 21 modes match.
Fig. 5
Fig. 5 (a)–(c) FE calculations of the normalized modal Poynting vector profiles at λ = 820 nm for radial (top row) and azimuthal (middle row) modes and the HE 21 higher-order mode (bottom row). All three modes show a doughnut-shaped profile. (d)–(i) Simulated profiles for orthogonal positions of the linear polarizer (P2). (j)–(l) Vector electric field distributions.
Fig. 6
Fig. 6 Spectral dependence of cylindrical birefringence B c for different nanobore radii a. Core radius and air-filling fraction are 540 nm and 0.84. Inset shows the phase indices of the azimuthal (solid curves) and radial (dashed curves) modes for a = 0 (black) and 250 nm (green).
Fig. 7
Fig. 7 Calculated cylindrical birefringence versus normalized frequency for different values of the ratio a / b (step-index model). Core radius and air-filling fraction are 540 nm and 0.84. The silica refractive index is kept constant at n s = 1.45 . The low frequency edge of each curve (near b / λ = 0.4 ) corresponds to the cut-off frequency of the radial mode.
Fig. 8
Fig. 8 Calculated GVD curves for radial and azimuthal modes (step-index model). Core radius and air-filling fraction are 540 nm and 0.84. Data are plotted for three different values of a.
Fig. 9
Fig. 9 Calculated relative change of the second (long wavelength) ZDW ( λ ZDW ) as function of nanobore radius for the azimuthal (black) and radial (red) modes (step-index model). Curves have been normalized to the value of λ ZDW at a = 0 . Inset shows the absolute values of λ ZDW . Core radius and air-filling fraction are 540 nm and 0.84. For a < 153 nm (dashed line), λ ZDW for the azimuthal mode decreases by a maximum of 2% ( 17 nm ), while λ ZDW for the radial mode decreases by a maximum of 14% ( 100 nm ).

Equations (1)

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n cl F + ( 1 F ) n s 2

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