Abstract

In this paper we study the impact of elliptically-deformed features such as cladding air-holes and elliptically-modulated cores, as ingredients for optimizing the coupling characteristics of dual-core fluorine-doped photonic crystal fiber (PCF) couplers. We provide a detailed numerical investigation by using a trial and error approach for optimizing the propagation characteristics of fluorine-doped PCF couplers. Typical characteristics of the newly proposed PCF coupler structure are: wavelength-flattened coupling characteristics between 0.7 μm and 1.6 μm wavelength range, coupling efficiency of 50±1 % from 0.9 μm to 1.6 μm, and a reasonably small coupling length of 1.3 cm. In addition we have elaborately derived the design parameters so that our proposed dual-core PCF coupler exhibits polarization-insensitive characteristics verified by using a full-vectorial beam propagation method. The proposed dual-core PCF can be effectively used as a 3-dB coupler, over a wide wavelength range.

© 2006 Optical Society of America

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    [CrossRef]
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2005 (5)

2004 (4)

2003 (2)

2002 (2)

K. Saitoh and M. Koshiba, "Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: Application to photonic crystal fibers," IEEE J. Quantum Electron. 38, 927-933 (2002).
[CrossRef]

F. Fogli, L. Saccomandi, P. Bassi, G. Bellanca, and S. Trillo, "Full vectorial BPM modeling of index-guiding photonic crystal fibers and couplers," Opt. Express 10, 54-59 (2002). http://opticsexpress.osa.org/abstract.cfm?URI=OPEX-10-1-54.
[PubMed]

2001 (3)

2000 (1)

B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, and A. H. Greenaway, "Experimental study of dual-core photonic crystal fiber," Electron. Lett. 36, 1358-1359 (2000).
[CrossRef]

1997 (1)

Argyros, A.

W. E. P. Padden, M. A. van Eijkelenborg, A. Argyros, and N. A. Issa, "Coupling in twin-core microstructured polymer optical fiber," Appl. Phys. Lett. 84, 1689-1691 (2004).
[CrossRef]

Arriaga, J.

Bang, O.

Bassi, P.

Bellanca, G.

Birks, T. A.

Bjarklev, A.

Broderick, N. G.R.

Cox, F.

Eggleton, B. J.

Eijkelenborg, M. A.

Fellew, M.

Finazzi, V.

Florous, N.

Fogli, F.

George, A. K.

Greenaway, A. H.

B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, and A. H. Greenaway, "Experimental study of dual-core photonic crystal fiber," Electron. Lett. 36, 1358-1359 (2000).
[CrossRef]

Henry, G.

Issa, N. A.

N. A. Issa, M. A. Eijkelenborg, M. Fellew, F. Cox, G. Henry, and C. J. Large, "Fabrication and study of microstructured optical fibers with elliptical holes," Opt. Lett. 29, 1336-1338 (2004).
[CrossRef] [PubMed]

W. E. P. Padden, M. A. van Eijkelenborg, A. Argyros, and N. A. Issa, "Coupling in twin-core microstructured polymer optical fiber," Appl. Phys. Lett. 84, 1689-1691 (2004).
[CrossRef]

Joly, N. Y.

Kakarantzas, G.

Kawanishi, S.

Knight, J. C.

Koshiba, M.

Kubota, H.

Kuhlmey, B. T.

Laegsgaard, J.

Large, C. J.

Leon-Saval, S. G.

Magi, E. C.

Mangan, B. J

Mangan, B. J.

B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, and A. H. Greenaway, "Experimental study of dual-core photonic crystal fiber," Electron. Lett. 36, 1358-1359 (2000).
[CrossRef]

McPhedran, R. C.

Monro, T. M.

Nguyen, H. C.

Osgood, R. M.

Padden, W. E. P.

W. E. P. Padden, M. A. van Eijkelenborg, A. Argyros, and N. A. Issa, "Coupling in twin-core microstructured polymer optical fiber," Appl. Phys. Lett. 84, 1689-1691 (2004).
[CrossRef]

Poletti, F.

Richardson, D. J.

Russell, P. St. J.

Saccomandi, L.

Saitoh, K.

Sato, Y.

Smith, C. L.

Steel, M. J.

Tanaka, M.

Trillo, S.

Tse, V.

van Eijkelenborg, M. A.

W. E. P. Padden, M. A. van Eijkelenborg, A. Argyros, and N. A. Issa, "Coupling in twin-core microstructured polymer optical fiber," Appl. Phys. Lett. 84, 1689-1691 (2004).
[CrossRef]

Wadsworth, W. J.

Yamaguchi, S.

Yamamoto, T.

Yang, C.

Zhang, L.

Appl. Phys. Lett. (1)

W. E. P. Padden, M. A. van Eijkelenborg, A. Argyros, and N. A. Issa, "Coupling in twin-core microstructured polymer optical fiber," Appl. Phys. Lett. 84, 1689-1691 (2004).
[CrossRef]

Electron. Lett. (1)

B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, and A. H. Greenaway, "Experimental study of dual-core photonic crystal fiber," Electron. Lett. 36, 1358-1359 (2000).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. Saitoh and M. Koshiba, "Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: Application to photonic crystal fibers," IEEE J. Quantum Electron. 38, 927-933 (2002).
[CrossRef]

J. Lightwave Technol. (4)

Opt. Express (5)

Opt. Lett. (6)

Other (1)

A. Bjarklev, J. Broeng, and A. S. Bjarklev, Photonic Crystal Fibres, (Kulwer Academic Publishers, 2003).
[CrossRef]

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Figures (12)

Fig. 1.
Fig. 1.

Schematic representation of the proposed PCF structure. The air-holes in the cladding are arranged in a triangular configuration with lattice constant Λ, major diameters-2ry , and minor diameters-2rx . The dual fluorine-doped cores A and B have been perturbed to have elliptical shape with major diameters-2rdy , and minor diameters-2rdx , represented by red colors. The host material is pure silica. By a judicious choice of the geometrical parameters, this PCF coupler can exhibit wavelength-flattened coupling characteristics, insensitive to both x and y polarizations.

Fig. 2.
Fig. 2.

Variation of the effective mode area of the fundamental guided mode of the F-doped single-core PCF as a function of the wavelength-λ. Contrary to the effective area variation in standard single mode fibers as well as in usual undoped PCFs, we can observe that as the wavelength decreases the effective mode area increases, thus giving rise to the wavelength-flattened coupling characteristics.

Fig. 3.
Fig. 3.

Normalized coupling length Lc /Λ as a function of the normalized wavelength Λ/λ, for the F-doped dual-core PCF coupler. Solid curves correspond to x-polarization while dashed curves correspond to y-polarization. Red curves correspond to the results depicted from [4], black curves are associated with elliptically-deformed cladding air-holes having e = 1.4 with circular cores of ed = 1, while blue curves show the effect of the elliptical-deformation of the doped cores when the ellipticity becomes ed = 1.23. It is evident from these results that significant reduction of the coupling length can be achieved, by using elliptical features instead of circular.

Fig. 4.
Fig. 4.

Normalized coupling length Lc /Λ as a function of the normalized wavelength Λ/λ, for the F-doped dual core PCF coupler, and for two different sets of doping ellipticities that is: Set A (black and red curves), and Set B (blue and green curves). Solid curves correspond to x-polarization while dashed curves correspond to y-polarization. From these results becomes evident that by controlling the ellipticity of the doped regions we can succeed having optimum ultra-flat coupling characteristics (corresponding to blue curves) and additionally the total bandwidth was enlarged by a factor of 150 nm in comparison to the results in Ref. [4].

Fig. 5.
Fig. 5.

Normalized coupling length Lc /Λ as a function of the normalized wavelength Λ/λ, for the F-doped dual-core PCF coupler, for different incremental index differences between the doped-cores and the host material (pure silica). It is clear that by increasing the index difference the coupling length decreases while at the same time the flatness improves drastically. There is a value of the index difference where the optimum flatness occurs. This optimum value has been estimated to be Δ = 0.004 (blue curves).

Fig. 6.
Fig. 6.

Normalized coupling length Lc /Λ as a function of the normalized wavelength Λ/λ, for the F-doped dual-core PCF coupler, for a ±2 % tolerance of the pitch constant. From these results we can see that indeed the variation of the coupling length seems sensitive to possible variations of the pitch constant. Additionally we confirm that the optimum value of the pitch constant for achieving the best flatness is Λ = 12 μm.

Fig. 7.
Fig. 7.

Impact of the variation of the cladding’s air-holes ellipticity-e to the normalized coupling length Lc /Λ, as a function of the normalized wavelength Λ/λ for the F-doped dual-core PCF coupler. Solid curves correspond to x-polarization while dashed curves to y-polarization. The tolerance was chosen as ±2 % around its nominal value of e = 1.4.

Fig. 8.
Fig. 8.

Influence of the ellipticity tolerance of ±1 % and ±2 % around its nominal value of e = 1.4 of the central air-hole (i.e. the air-hole which separates the two cores), for x-polarization (solid curves), and y-polarization (dashed curves). It is evident that when the ellipticity increases the coupling length increases while the flatness becomes poor. As a conclusion the central air-hole ellipticity should be the same with the ellipticity of the air-holes in the cladding.

Fig. 9.
Fig. 9.

Normalized power variation inside the dual-core PCF coupler as a function of the propagation distance at wavelength of 1.55 μm, for (a) x-polarization, (b) y-polarization and for core-A (blue curve), core-B (red curve). The coupling lengths have been confirmed by the BPM analysis to be Lc = 12.68 mm for the x-polarized mode andLc = 13.07 mm for the y-polarized mode. The slightly difference between the two partial coupling lengths comes from the orientation of the two cores across the x-axis.

Fig. 10.
Fig. 10.

Normalized power variation inside the dual-core PCF coupler as a function of the operating wavelength in the dual-core PCF coupler calculated at fixed coupling length ofLc = 13 mm, for (a) x-polarization and (b) y-polarization. The blue curve corresponds to the output power in core-A, while the red curve corresponds to core-B. The main conclusion from these results is that the coupling efficiency varies by a fraction of ± 1 % in the wavelength range from 0.9 μm up to 1.6 μm, around the expected value of 0.5 corresponding to the operation of a 3-dB coupler.

Fig. 11.
Fig. 11.

Snapshots of the electric field distribution, at a fixed wavelength of λ = 1.55 μm in the proposed polarization-insensitive dual-core F-doped PCF coupler calculated by the BPM analysis, for (a) x-polarized mode (Ex ) and (b) y-polarized mode (Ey ) at distance of z = 0 mm, (c) x-polarized mode (Ex ) and (d) y-polarized mode (Ey ) at a distance of 4 mm, (e) x-polarized mode (Ex ), and (f) y-polarized mode (Ey ) at a distance of 8 mm, and (g) x-polarized mode (Ex ), and (h) y-polarized mode (Ey ) at a distance of 13 mm. At the coupling length ofLc = 13 mm the power was splitted in the two cores within a difference of ± 1 %. Thus the device effectively acts as a polarization-insensitive 3-dB coupler.

Fig. 12.
Fig. 12.

Variation of splice loss as a function of the wavelength for x-polarization (blue solid curve) and y-polarization (red dotted curve). It can be clearly seen that the splice loss decreases as wavelength increases. Note that the splice loss is almost identical for both x and y-polarizations a fact that indicate the polarization insensitivity of the proposed design.

Equations (1)

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L c x , y = λ 2 ( n e x , y n o x , y )

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