Abstract

The polarization properties of long-period gratings inscribed in highly birefringent photonic crystal fibers are investigated in the context of a multipole method analysis. It is demonstrated that by proper design such fibers may act as selective polarization elements, showing an ample separation of the resonance peaks corresponding to the two orthogonal polarization states. Furthermore, the infiltration of the fiber’s capillaries with an isotropic liquid may lead to extensive tuning of the resonant wavelengths. A tuning efficiency of up to 10nm°C is demonstrated in the case of a typical infiltrated birefringent photonic crystal fiber.

© 2008 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2007 (2)

2006 (7)

2005 (1)

2004 (3)

J. H. Lim, K. S. Lee, J. C. Kim, B. H. Lee, "Tunable fiber gratings fabricated in photonic crystal fiber by use of mechanical pressure," Opt. Lett. 29, 331-333 (2004).
[CrossRef] [PubMed]

H. Dobb, K. Kalli, and D. J. Webb, "Temperature-insensitive long period grating sensors in photonic crystal fiber," Electron. Lett. 40, 657-658 (2004).
[CrossRef]

M. Szpulak, J. Olszewski, T. Martynkien, W. Urbanczyk, and J. Wójcik, "Polarizing photonic crystal fibers with wide operation range," Opt. Commun. 239, 91-97 (2004).
[CrossRef]

2003 (6)

S. W. James and R. P. Tatam, "Optical fibre long-period grating sensors: characteristics and application," Meas. Sci. Technol. 14, R49-R61 (2003).
[CrossRef]

J. C. Knight, "Photonic crystal fibres," Nature 424, 847-851 (2003).
[CrossRef] [PubMed]

J. K. Bae, S. H. Kim, J. H. Kim, J. Bae, S. B. Lee, and J. M. Jeong, "Spectral shape tunable band-rejection filter using a long-period fiber grating with divided coil heaters," IEEE Photon. Technol. Lett. 15, 407-409 (2003).
[CrossRef]

K. P. Hansen, "Dispersion flattened hybrid-core nonlinear photonic crystal fiber," Opt. Express 11, 1503-1509 (2003).
[CrossRef] [PubMed]

N. A. Mortensen, J. R. Folkenberg, M. D. Nielsen, and K. P. Hansen, "Modal cutoff and the V parameter in photonic crystal fibers," Opt. Lett. 28, 1879-1881 (2003).
[CrossRef] [PubMed]

T. T. Larsen, A. Bjarklev, D. S. Hermann, and J. Broeng, "Optical devices based on liquid crystal photonic bandgap fibres," Opt. Express 11, 2589-2596 (2003).
[CrossRef] [PubMed]

2002 (6)

2001 (2)

2000 (3)

1999 (1)

1998 (3)

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Mettler, and A. M. Vengsarkar, "Long-period fibre grating fabrication with focused CO2 laser pulses," Electron. Lett. 34, 302-303 (1998).
[CrossRef]

J. R. Qian and H. F. Chen, "Gain flattening fibre filters using phase-shifted long period fibre gratings," Electron. Lett. 34, 1132-1133 (1998).
[CrossRef]

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. Russell, and J. P. de Sandro, "Large mode area photonic crystal fibre," Electron. Lett. 34, 1347-1348 (1998).
[CrossRef]

1997 (4)

A. S. Kurkov, M. Douay, O. Duhem, B. Leleu, J. F. Henninot, J. F. Bayon, and L. Rivoallan, "Long-period fibre gratings as a wavelength selective polarisation element," Electron. Lett. 33, 616-617 (1997).
[CrossRef]

B. Ortega, L. Dong, W. F. Liu, J. P. de Sandro, L. Reekie, S. I. Tsypina, V. N. Bagratashvili, and R. I. Laming, "High-performance optical fiber polarizers based on long-period gratings in birefringent optical fibers," IEEE Photon. Technol. Lett. 9, 1370-1372 (1997).
[CrossRef]

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, "Fiber grating sensors," J. Lightwave Technol. 15, 1442-1463 (1997).
[CrossRef]

T. A. Birks, J. C. Knight, and P. St. Russell, "Endlessly single-mode photonic crystal fiber," Opt. Lett. 22, 961-963 (1997).
[CrossRef] [PubMed]

1996 (1)

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, "Long-period fiber gratings as band-rejection filters," J. Lightwave Technol. 14, 58-65 (1996).
[CrossRef]

1979 (1)

1975 (1)

P. R. McIsaac, "Symmetry-induced modal characteristics of uniform waveguides--I: summary of results," IEEE Trans. Microwave Theory Tech. MTT-23, 421-429 (1975).
[CrossRef]

Appl. Opt. (1)

Electron. Lett. (5)

H. Dobb, K. Kalli, and D. J. Webb, "Temperature-insensitive long period grating sensors in photonic crystal fiber," Electron. Lett. 40, 657-658 (2004).
[CrossRef]

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Mettler, and A. M. Vengsarkar, "Long-period fibre grating fabrication with focused CO2 laser pulses," Electron. Lett. 34, 302-303 (1998).
[CrossRef]

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. Russell, and J. P. de Sandro, "Large mode area photonic crystal fibre," Electron. Lett. 34, 1347-1348 (1998).
[CrossRef]

J. R. Qian and H. F. Chen, "Gain flattening fibre filters using phase-shifted long period fibre gratings," Electron. Lett. 34, 1132-1133 (1998).
[CrossRef]

A. S. Kurkov, M. Douay, O. Duhem, B. Leleu, J. F. Henninot, J. F. Bayon, and L. Rivoallan, "Long-period fibre gratings as a wavelength selective polarisation element," Electron. Lett. 33, 616-617 (1997).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

B. Ortega, L. Dong, W. F. Liu, J. P. de Sandro, L. Reekie, S. I. Tsypina, V. N. Bagratashvili, and R. I. Laming, "High-performance optical fiber polarizers based on long-period gratings in birefringent optical fibers," IEEE Photon. Technol. Lett. 9, 1370-1372 (1997).
[CrossRef]

J. K. Bae, S. H. Kim, J. H. Kim, J. Bae, S. B. Lee, and J. M. Jeong, "Spectral shape tunable band-rejection filter using a long-period fiber grating with divided coil heaters," IEEE Photon. Technol. Lett. 15, 407-409 (2003).
[CrossRef]

P. S. Westbrook, B. J. Eggleton, R. S. Windeler, A. Hale, T. A. Strasser, and G. L. Burdge, "Cladding-mode resonances in hybrid polymer-silica microstructured optical fiber gratings," IEEE Photon. Technol. Lett. 12, 495-497 (2000).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

P. R. McIsaac, "Symmetry-induced modal characteristics of uniform waveguides--I: summary of results," IEEE Trans. Microwave Theory Tech. MTT-23, 421-429 (1975).
[CrossRef]

J. Lightwave Technol. (4)

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, "Fiber grating sensors," J. Lightwave Technol. 15, 1442-1463 (1997).
[CrossRef]

D. C. Zografopoulos, E. E. Kriezis, and T. D. Tsiboukis, "Tunable highly birefringent bandgap-guiding liquid-crystal microstructured fibers," J. Lightwave Technol. 44, 3427-3432 (2006).
[CrossRef]

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, "Long-period fiber gratings as band-rejection filters," J. Lightwave Technol. 14, 58-65 (1996).
[CrossRef]

B. J. Eggleton, P. S. Westbrook, C. A. White, C. Kerbage, R. S. Windeler, and G. L. Burdge, "Cladding-mode-resonances in air-silica microstructure optical fibers," J. Lightwave Technol. 18, 1084-1100 (2000).
[CrossRef]

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

J. Opt. Soc. Am. B (3)

Meas. Sci. Technol. (2)

S. W. James and R. P. Tatam, "Optical fibre long-period grating sensors: characteristics and application," Meas. Sci. Technol. 14, R49-R61 (2003).
[CrossRef]

T. R. Wolinski, K. Szaniawska, S. Ertman, P. Lesiak, A. W. Domanski, R. Dabrowski, E. Nowinowski-Kruszelnicki, and J. Wójcik, "Influence of temperature and electrical fields on propagation properties of photonic liquid-crystal fibers," Meas. Sci. Technol. 17, 985-991 (2006).
[CrossRef]

Nature (1)

J. C. Knight, "Photonic crystal fibres," Nature 424, 847-851 (2003).
[CrossRef] [PubMed]

Opt. Commun. (1)

M. Szpulak, J. Olszewski, T. Martynkien, W. Urbanczyk, and J. Wójcik, "Polarizing photonic crystal fibers with wide operation range," Opt. Commun. 239, 91-97 (2004).
[CrossRef]

Opt. Express (10)

B. T. Kuhlmey, R. C. McPhedran, C. M. de Sterke, P. A. Robinson, G. Renversez, and D. Maystre, "Microstructured optical fibers: where's the edge?" Opt. Express 10, 1285-1290 (2002).
[PubMed]

K. P. Hansen, "Dispersion flattened hybrid-core nonlinear photonic crystal fiber," Opt. Express 11, 1503-1509 (2003).
[CrossRef] [PubMed]

K. Suzuki, H. Kubota, S. Kawanishi, M. Tanaka, and M. Fujita, "Optical properties of a low-loss polarization-maintaining photonic crystal fiber," Opt. Express 9, 676-680 (2001).
[CrossRef] [PubMed]

A. Ferrando, E. Silvestre, P. Andrés, J. J. Miret, and M. V. Andres, "Designing the properties of dispersion-flattened photonic crystal fibers," Opt. Express 9, 687-697 (2001).
[CrossRef] [PubMed]

L. Rindorf, J. B. Jensen, M. Dufva, L. H. Pedersen, P. E. Høiby, and O. Bang, "Photonic crystal fiber long-period gratings for biochemical sensing," Opt. Express 14, 8224-8231 (2006).
[CrossRef] [PubMed]

D. C. Zografopoulos, E. E. Kriezis, and T. D. Tsiboukis, "Photonic crystal-liquid crystal fibers for single-polarization or high-birefringence guidance," Opt. Express 14, 914-925 (2006).
[CrossRef] [PubMed]

W. H. Reeves, J. C. Knight, P. St. Russell, and P. J. Roberts, "Demonstration of ultra-flattened dispersion in photonic crystal fibers," Opt. Express 10, 609-613 (2002).
[PubMed]

T. T. Larsen, A. Bjarklev, D. S. Hermann, and J. Broeng, "Optical devices based on liquid crystal photonic bandgap fibres," Opt. Express 11, 2589-2596 (2003).
[CrossRef] [PubMed]

R. Zhang, J. Teipel, and H. Giessen, "Theoretical design of a liquid-core photonic crystal fiber for supercontinuum generation," Opt. Express 14, 6800-6812 (2006).
[CrossRef] [PubMed]

D. Noordegraaf, L. Scolari, J. Lægsgaard, L. Rindorf, and T. T. Alkeskjold, "Electrically and mechanically induced long period gratings in liquid crystal photonic bandgap fibers," Opt. Express 15, 7901-7912 (2007).
[CrossRef] [PubMed]

Opt. Lett. (9)

J. H. Lim, K. S. Lee, J. C. Kim, B. H. Lee, "Tunable fiber gratings fabricated in photonic crystal fiber by use of mechanical pressure," Opt. Lett. 29, 331-333 (2004).
[CrossRef] [PubMed]

G. Renversez, F. Bordas, and B. T. Kuhlmey, "Second mode transition in microstructured optical fibers: determination of the critical geometrical parameter and study of the matrix refractive index and effects of cladding size," Opt. Lett. 30, 1264-1267 (2005).
[CrossRef] [PubMed]

P. Steinvurzel, E. D. Moore, E. C. Magi, and B. J. Eggleton, "Tuning properties of long period gratings in photonic bandgap fibers," Opt. Lett. 31, 2103-2105 (2006).
[CrossRef] [PubMed]

Y. P. Wang, L. M. Xiao, D. N. Wang, and W. Jin, "In-fiber polarizer based on a long-period fiber grating written on photonic crystal fiber," Opt. Lett. 32, 1035-1037 (2007).
[CrossRef] [PubMed]

C. Kerbage, P. Steinvurzel, P. Reyes, P. S. Westbrook, R. S. Windeler, A. Hale, and B. J. Eggleton, "Highly tunable birefringent microstructured optical fiber," Opt. Lett. 27, 842-844 (2002).
[CrossRef]

G. Kakarantzas, T. A. Birks, and P. St. Russell, "Structural long-period gratings in photonic crystal fibers," Opt. Lett. 27, 1013-1015 (2002).
[CrossRef]

N. A. Mortensen, J. R. Folkenberg, M. D. Nielsen, and K. P. Hansen, "Modal cutoff and the V parameter in photonic crystal fibers," Opt. Lett. 28, 1879-1881 (2003).
[CrossRef] [PubMed]

T. A. Birks, J. C. Knight, and P. St. Russell, "Endlessly single-mode photonic crystal fiber," Opt. Lett. 22, 961-963 (1997).
[CrossRef] [PubMed]

B. J. Eggleton, P. S. Westbrook, R. S. Windeler, S. Spalter, and T. A. Strasser, "Grating resonances in air-silica microstructured optical fibers," Opt. Lett. 24, 1460-1462 (1999).
[CrossRef]

Other (4)

CUDOS Microstructured Optical Fiber Utilities package, http://www.physics.usyd.edu.au/cudos/mofsoftware.

PM-1550-01, Polarisation Maintaining PCF by Blaze Photonics, http://blazephotonics.com.

Cargille Labs, http://cargille.com.

A. Bjarklev, J. Broeng, and A. S. Bjarklev, Photonic Crystal Fibers (Kluwer, 2003).
[CrossRef]

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Figures (12)

Fig. 1
Fig. 1

Structural layout of the highly birefringent PCF under study: lattice pitch Λ, capillary radius r, defect radius r d , and refractive indices of the infinite glass matrix and holes n g and n h , respectively.

Fig. 2
Fig. 2

(a) Dispersion curves and (b) losses for the fundamental and the target cladding mode of the fiber shown in Fig. 1 for a symmetrical cladding ( r = r d = 0.2 Λ ) and for n g = 1.45 , n h = 1 . Both modes are double degenerate (x and y polarized).

Fig. 3
Fig. 3

Modal optical power profiles (Poynting vector) for (a) the fundamental and (b) the target cladding mode of the fiber shown in Fig. 1 at Λ λ = 2 , r d = r = 0.2 Λ , n g = 1.45 , and n h = 1 . The fundamental mode is well confined in the fiber’s core, while the power of the cladding mode is split between the core and the region between the first two rings of cylinders of the periodic cladding.

Fig. 4
Fig. 4

Birefringence curves for the fundamental mode of the fiber shown in Fig. 1 for values of the defect radius ranging from r d = 0.25 Λ to r d = 0.5 Λ . The cladding capillary radius is set to r = 0.2 Λ , the fiberglass is silica n g = 1.45 , and the capillaries are not infiltrated ( n h = 1 ) . Birefringence values of more than 10 3 are predicted in a broad wavelength window.

Fig. 5
Fig. 5

Coupling coefficients between the x-polarized (diamonds) and y-polarized (circles) fundamental mode and the first 27 cladding modes supported by the fiber. Coupling is maximized between pairs of modes with both the same polarization and the same class of symmetry. Inset, effective indices of the cladding modes.

Fig. 6
Fig. 6

Electric field intensity profiles for the y-polarized fundamental and target cladding modes of the fiber shown at Fig. 1 for Λ = 4.4 μ m , λ = 1.55 μ m , n h = 1 , r = 0.2 Λ and r d = 0.5 Λ : (a) E y component of the fundamental mode, (b) E y component of the target cladding mode. Silica dispersion has been taken into account.

Fig. 7
Fig. 7

Sensitivity of the y-resonance wavelength over the grating pitch value Λ LPG y . The average slope of the sensitivity curve is approximately 10 nm μ m .

Fig. 8
Fig. 8

Modal dispersion curves for both polarizations of the fundamental mode and the first six cladding modes ( m = 1 , , 6 with respect to Fig. 5) in the wavelength window 1 μ m < λ < 2 μ m .

Fig. 9
Fig. 9

Dependence of the effective index of the x-polarized fundamental mode on the variation of the infiltrated liquid’s refractive index n h . Higher values of n h lead to an increase of the modal effective index.

Fig. 10
Fig. 10

Tuning of the resonant wavelengths for the liquid-infiltrated LPG-PCF under study, as extracted after the calculation of the two-dimensional test function maps f ct i ( λ , n h ) : (a) Tuning curves corresponding to X coupling (x-core mode with m = 3 cladding mode) and (b) to Y coupling (y-core mode with m = 4 cladding mode). Extensive tuning performance (up to > 10 nm ° C ) is predicted for both X and Y coupling. The tuning curves may be adjusted by properly selecting the period Λ LPG of the grating.

Fig. 11
Fig. 11

Loss coefficient for the x-polarized mode of a PCF (Fig. 1) with Λ = 4.4 μ m , n h = 1.3 , r d = 0.5 Λ for different values of the cladding hole radius r.

Fig. 12
Fig. 12

Resonant wavelength tuning curves of the LPG-PCF of Fig. 1 corresponding to the x-polarized mode for r = 0.25 Λ (other parameters as in Fig. 10).

Tables (1)

Tables Icon

Table 1 LPG Resonances between the Core and the First Six Cladding Modes ( m = 1 , , 6 ) in the Wavelength Window 1 μ m < λ < 2 μ m

Equations (7)

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α ( dB m ) = 8.686 ( 2 π λ ) Im { n eff } .
E core ( x , y ) · E core * ( x , y ) d x d y = E clad , m ( x , y ) · E clad , m * ( x , y ) d x d y = 1 ,
κ ( m ) = core E core ( x , y ) · E clad , m * ( x , y ) d x d y
( n eff fund , i n eff clad , i ) Λ LPG = λ res ,
Δ n x Λ LPG = λ 0 ,
f ct i ( λ ) = [ n eff fund , i ( λ ) n eff , m clad , i ( λ ) ] Λ LPG i λ
f ct i ( λ , n h ) = [ n eff fund , i ( λ , n h ) n eff clad , i ( λ , n h ) ] Λ LPG λ

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