## Coupling characteristics of dual-core photonic crystal fiber couplers

Optics Express, Vol. 11, Issue 24, pp. 3188-3195 (2003)

http://dx.doi.org/10.1364/OE.11.003188

Acrobat PDF (136 KB)

### Abstract

Coupling characteristics of dual-core photonic crystal fiber (PCF) couplers are evaluated by using a vector finite element method and their application to a multiplexer-demultiplexer (MUX-DEMUX) based on PCF is investigated. The PCF couplers for 1.48/1.55-µm, 1.3/1.55-µm, 0.98/1.55-µm, and 0.85/1.55-µm wavelength MUX-DEMUX are designed and the beam propagation analysis of the proposed PCF couplers is performed. It is shown from numerical results that it is possible to realize significantly shorter MUX-DEMUX PCFs, compared to conventional optical fiber couplers.

© 2003 Optical Society of America

## 1. Introduction

1. J. Broeng, D. Mogilevstev, S.E. Barkou, and A. Bjarklev, “Photonic crystal fibers: A new class of optical waveguides,” Opt. Fiber Technol. **5**, 305–330 (1999). [CrossRef]

3. J.C. Knight, T.A. Birks, P.St.J. Russell, and D.M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. **21**, 1547–1549 (1996). [CrossRef] [PubMed]

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

5. J.C. Knight, J. Broeng, T.A. Birks, and P.St.J. Russell, “Photonic band gap guidance in optical fiber,” Science **282**, 1476–1478 (1998). [CrossRef] [PubMed]

6. R.F. Cregan, B.J. Mangan, J.C. Knight, T.A. Birks, P.St.J. Russell, P.J. Roberts, and D.C. Allan, “Single-mode photonic band gap guidance of light in air,” Science **285**, 1537–1539 (1999). [CrossRef] [PubMed]

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

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

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

8. N.G.R. Broderick, T.M. Monro, P.J. Bennett, and D.J. Richardson, “Nonlinearlity in holey optical fibers: Measurement and future opportunities,” Opt. Lett. **24**, 1395–1397 (1999). [CrossRef]

9. M.J. Gander, R. McBride, J.D.C. Jones, D. Mogilevtsev, T.A. Birks, J.C. Knight, and P.St.J. Russell, “Experimantal measurement of group velocity dispersion in photonic crystal fibre,” Electron. Lett. **35**, 63–64 (1999). [CrossRef]

10. B.J. Mangan, J.C. Knight, T.A. Birks, P.St.J. Russell, and A.H. Greenaway, “Experimental study of dualcore photonic crystal fibre,” Electron. Lett. **36**, 1358–1359 (2000). [CrossRef]

12. B.H. Lee, J.B. Eom, J. Kim, D.S. Moon, U.-C. Paek, and G.-H. Yang, “Photonic crystal fiber coupler,” Opt. Lett. **27**, 812–814 (2002). [CrossRef]

13. 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]

14. K. Saitoh, M. Koshiba, T. Hasegawa, and E. Sasaoka, “Chromatic dispersion control in photonic crystal fibers: application to ultra-flattend dispersion,” Opt. Express **11**, 843–852 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-8-843 [CrossRef] [PubMed]

15. K. Saitoh and M. Koshiba, “Full-vectorial finite element beam propagation method with perfectly matched layers for anisotropic optical waveguides,” J. Lightwave Technol. **19**, 405–413 (2001). [CrossRef]

## 2. Guided mode analysis

*t*(

_{i}*i*=1 to 4), the cross section of which is shown in Fig. 1, where

*x*and

*y*are the transverse directions,

*z*is the propagation direction, PML regions 1, 2 and 3, 4 are faced with the

*x*and

*y*directions, respectively, regions 5 to 8 correspond to the four corners, and

*W*and

_{x}*W*are the computational window sizes along the

_{y}*x*and

*y*directions, respectively.

13. 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]

16. F.L. Teixeira and W.C. Chew, “General closed-form pml constitutive tensors to match arbitrary bianisotropic and dispersive linear media,” IEEE Microwave Guided Wave Lett. **8**, 223–225 (1998). [CrossRef]

*k*

_{0}=2π/λ the free-space wavenumber, λ is the wavelength,

**denotes the electric field, and**

*E**n*is the refractive index. The PML parameters

*s*and

_{x}*s*are given in Table 1, where the values of

_{y}*s*(

_{i}*i*=1 to 4) are complex as

**in PML regions can be controlled by choosing the values of α**

*E*_{i}appropriately.

17. M. Koshiba and Y. Tsuji, “Curvilinear hybrid edge/nodal elements with triangular shape for guided-wave problems,” J. Lightwave Technol. **18**, 737–743 (2000). [CrossRef]

*E*, a nodal element with six variables,

_{z}*E*

_{z1}to

*E*

_{z6}, is employed, while for the transverse fields,

*E*and

_{x}*E*, an edge element with eight variables,

_{y}*E*

_{t1}to

*E*

_{t8}, is employed, resulting in significantly fast convergence of solutions [17

17. M. Koshiba and Y. Tsuji, “Curvilinear hybrid edge/nodal elements with triangular shape for guided-wave problems,” J. Lightwave Technol. **18**, 737–743 (2000). [CrossRef]

*K*] and [

*M*] are the finite element matrices [13

13. 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]

*E*} is the discretized electric-field vector consisting of the edge and nodal variables.

## 3. Characteristics of PCF couplers

*d*is the hole diameter, and the background silica index is assumed to be 1.45. The separation between the centers of two cores, A and B, shown in Fig. 3(a) is √3λ and we call this PCF Type 1. On the other hand, the separation between the centers of A and B shown in Fig. 3(b) is 2λ and we call this PCF Type 2. Figure 4 shows the hole-pitch dependence of coupling length

*L*for the two PCF couplers shown in Fig. 3, where

*d*/Λ=0.5, operating wavelength λ=1.55 µm, and the red and the blue curves denote the coupling lengths for the

*x*-polarized and the

*y*-polarized modes, respectively. The coupling length

*L*is obtained by using the propagation constants of even mode β

_{e}and odd mode β

_{o}as

*d*/Λ=0.3, 0.5 0.7, and 0.9, where the operating wavelength λ=1.55 µm, the red and the blue curves denote the coupling lengths for the

*x*-polarized and the

*y*-polarized modes, respectively. The coupling lengths of couplers with smaller hole-pitch and smaller value of

*d*/λ becomes shorter. Moreover, the coupling length of

*x*-polarized mode is shorter than that of

*y*-polarized mode, because the two cores are placed in parallel to

*x*-axis and the coupling of

*x*-polarized mode is stronger than that of

*y*-polarized mode. Although, in order to obtain shorter coupling lengths, strong coupling between cores is necessary, too strong coupling causes lower extinction ratios. Therefore, in what follows, we consider PCF couplers using y-polarized mode. The structures shown in Fig. 3 exhibit relatively small difference between the coupling length for the

*x*- and

*y*-polarized modes. The difference can be enhanced by introducing structural birefringence into the cores. High birefringence can be obtained by adjusting the size of the air holes around the two core regions, which gives rise to an enhanced difference in the coupling lengths for the two polarization modes [18

18. L. Zhang and C. Yang, “Polarization splitter based on photonic crystal fibers,” Opt. Express **11**, 1015–1020 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-9-1015 [CrossRef] [PubMed]

*d*/Λ=0.7 and the operating wavelength λ is taken as a parameter. The coupling length increases with decreasing the operating wavelength. A PCF coupler can separate two wavelengths λ

_{1}and λ

_{2}, if it is in a bar-coupled state for one wavelength and a cross-coupled state for the other; i.e., the coupling length

*L*

_{λ1}at the wavelength λ

_{1}and the coupling length

*L*

_{λ2}at the wavelength λ

_{2}satisfy the relation

*d*/dependence of coupling length dependence of coupling length ratios

*L*

_{λ2}/

*L*

_{λ1}for couplers with hole-pitch dependence of coupling length=1.8, 2.0, and 2.2 µm. The one wavelength λ

_{1}is fixed at 1.55 µm and the another one λ

_{2}is 1.48 µm, 1.3 µm, 0.98 µm, and 0.85 µm. The wavelengths of 1.48 µm and 0.98 µm are used as pump lights in erbium-doped fiber amplifiers and the wavelength of 0.85 µm is used in short wavelength-range optical communication systems. Here, each coupler is called Coupler 1, 2, 3, or 4. From Fig. 7, we could say that the optimum coupling-length ratio is different for each coupler.

*L*

_{1.55}:

*L*

_{1}.48=9 : 10,

*L*

_{1.55}:

*L*

_{1.3}=2 : 3,

*L*

_{1.55}:

*L*

_{0.98}=1 : 2, and

*L*

_{1.55}:

*L*

_{0.85}=1: 4, respectively, and the fiber lengths are 2284 µm, 712 µm, 481 µm, and 1178 µm, respectively. The fiber lengths are much shorter than conventional optical fiber couplers. In conventional optical fiber couplers the two cores are separated by a long distance and the coupling between the modes of the two cores is week, and so the fiber coupler length becomes long. On the other hand, in dual-core PCF couplers investigated here the distance between the two cores is √3Λ (Λ ≅ 2 µm), and so very short coupling length can be realized.

15. K. Saitoh and M. Koshiba, “Full-vectorial finite element beam propagation method with perfectly matched layers for anisotropic optical waveguides,” J. Lightwave Technol. **19**, 405–413 (2001). [CrossRef]

_{1}and λ

_{2}. The

*y*-polarized fundamental modes at λ

_{1}and λ

_{2}are inputted into the core A in Fig. 3(a) and the beam propagation analysis is performed. Figure 8 shows the normalized power variation along the propagation distance in the bar port. In Couplers 1 to 4, the separation of two wavelengths of λ

_{1}and λ

_{2}is achieved at the propagation distance of 2284 µm, 712 µm, 481 µm, and 1178 µm, respectively. These results are in good agreement with the coupling lengths estimated by using (5), and Couplers 1 to 4 operate as MUX/DEMUX for 1.48/1.55-µm, 1.3/1.55-µm, 0.98/1.55-µm, and 0.85/1.55-µm wavelength, respectively. In Coupler 3, the field confinement is weak because of smaller value of

*d*/Λ, and so, the extinction ratio of this coupler is lower, compared to the other couplers.

## 4. Conclusion

## References

1. | J. Broeng, D. Mogilevstev, S.E. Barkou, and A. Bjarklev, “Photonic crystal fibers: A new class of optical waveguides,” Opt. Fiber Technol. |

2. | T.A. Birks, J.C. Knight, B.J. Mangan, and P.St.J. Russell, “Photonic crystal fibers: An endless variety,” IEICE Trans. Electron. |

3. | J.C. Knight, T.A. Birks, P.St.J. Russell, and D.M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. |

4. | T.A. Birks, J.C. Knight, and P.St.J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. |

5. | J.C. Knight, J. Broeng, T.A. Birks, and P.St.J. Russell, “Photonic band gap guidance in optical fiber,” Science |

6. | R.F. Cregan, B.J. Mangan, J.C. Knight, T.A. Birks, P.St.J. Russell, P.J. Roberts, and D.C. Allan, “Single-mode photonic band gap guidance of light in air,” Science |

7. | J.C. Knight, T.A. Birks, R.F. Cregan, P.St.J. Russell, and J.-P. de Sandro, “Large mode area photonic crystal fiber,” Electron. Lett. |

8. | N.G.R. Broderick, T.M. Monro, P.J. Bennett, and D.J. Richardson, “Nonlinearlity in holey optical fibers: Measurement and future opportunities,” Opt. Lett. |

9. | M.J. Gander, R. McBride, J.D.C. Jones, D. Mogilevtsev, T.A. Birks, J.C. Knight, and P.St.J. Russell, “Experimantal measurement of group velocity dispersion in photonic crystal fibre,” Electron. Lett. |

10. | B.J. Mangan, J.C. Knight, T.A. Birks, P.St.J. Russell, and A.H. Greenaway, “Experimental study of dualcore photonic crystal fibre,” Electron. Lett. |

11. | 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 |

12. | B.H. Lee, J.B. Eom, J. Kim, D.S. Moon, U.-C. Paek, and G.-H. Yang, “Photonic crystal fiber coupler,” Opt. Lett. |

13. | 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. |

14. | K. Saitoh, M. Koshiba, T. Hasegawa, and E. Sasaoka, “Chromatic dispersion control in photonic crystal fibers: application to ultra-flattend dispersion,” Opt. Express |

15. | K. Saitoh and M. Koshiba, “Full-vectorial finite element beam propagation method with perfectly matched layers for anisotropic optical waveguides,” J. Lightwave Technol. |

16. | F.L. Teixeira and W.C. Chew, “General closed-form pml constitutive tensors to match arbitrary bianisotropic and dispersive linear media,” IEEE Microwave Guided Wave Lett. |

17. | M. Koshiba and Y. Tsuji, “Curvilinear hybrid edge/nodal elements with triangular shape for guided-wave problems,” J. Lightwave Technol. |

18. | L. Zhang and C. Yang, “Polarization splitter based on photonic crystal fibers,” Opt. Express |

**OCIS Codes**

(060.1810) Fiber optics and optical communications : Buffers, couplers, routers, switches, and multiplexers

(060.2270) Fiber optics and optical communications : Fiber characterization

(060.2280) Fiber optics and optical communications : Fiber design and fabrication

**ToC Category:**

Research Papers

**History**

Original Manuscript: September 17, 2003

Revised Manuscript: November 4, 2003

Published: December 1, 2003

**Citation**

Kunimasa Saitoh, Yuichiro Sato, and Masanori Koshiba, "Coupling characteristics of dual-core photonic crystal fiber couplers," Opt. Express **11**, 3188-3195 (2003)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-24-3188

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### References

- J. Broeng, D. Mogilevstev, S.E. Barkou, and A. Bjarklev, �??Photonic crystal fibers: A new class of optical waveguides,�?? Opt. Fiber Technol. 5, 305-330 (1999). [CrossRef]
- T.A. Birks, J.C. Knight, B.J. Mangan, and P.St.J. Russell, �??Photonic crystal fibers: An endless variety,�?? IEICE Trans. Electron. E84-C, 585-592 (2001).
- J.C. Knight, T.A. Birks, P.St.J. Russell, and D.M. Atkin, �??All-silica single-mode optical fiber with photonic crystal cladding,�?? Opt. Lett. 21, 1547-1549 (1996). [CrossRef] [PubMed]
- T.A. Birks, J.C. Knight, and P.St.J. Russell, �??Endlessly single-mode photonic crystal fiber,�?? Opt. Lett. 22, 961-963 (1997). [CrossRef] [PubMed]
- J.C. Knight, J. Broeng, T.A. Birks, and P.St.J. Russell, �??Photonic band gap guidance in optical fiber,�?? Science 282, 1476-1478 (1998). [CrossRef] [PubMed]
- R.F. Cregan, B.J. Mangan, J.C. Knight, T.A. Birks, P.St.J. Russell, P.J. Roberts, and D.C. Allan, �??Singlemode photonic band gap guidance of light in air,�?? Science 285, 1537-1539 (1999). [CrossRef] [PubMed]
- J.C. Knight, T.A. Birks, R.F. Cregan, P.St.J. Russell, and J.-P. de Sandro, �??Large mode area photonic crystal fiber,�?? Electron. Lett. 34, 1347-1348 (1998). [CrossRef]
- N.G.R. Broderick, T.M. Monro, P.J. Bennett, and D.J. Richardson, �??Nonlinearlity in holey optical fibers: Measurement and future opportunities,�?? Opt. Lett. 24, 1395-1397 (1999). [CrossRef]
- M.J. Gander, R. McBride, J.D.C. Jones, D. Mogilevtsev, T.A. Birks, J.C. Knight, and P.St.J. Russell, "Experimantal measurement of group velocity dispersion in photonic crystal fibre,�?? Electron. Lett. 35, 63-64 (1999). [CrossRef]
- B.J. Mangan, J.C. Knight, T.A. Birks, P.St.J. Russell, and A.H. Greenaway, �??Experimental study of dualcore photonic crystal fibre,�?? Electron. Lett. 36, 1358-1359 (2000). [CrossRef]
- F. Fogli, L. Saccomandi, P. Bassi, G. Bellanca, and S. Trillo, �??Full vectorial BPM modeling of indexguiding photonic crystal fibers and couplers,�?? Opt. Express 10, 54-59 (2002), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-1-54">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-1-54</a> [CrossRef] [PubMed]
- B.H. Lee, J.B. Eom, J. Kim, D.S. Moon, U.-C. Paek, and G.-H. Yang, �??Photonic crystal fiber coupler,�?? Opt. Lett. 27, 812-814 (2002). [CrossRef]
- 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]
- K. Saitoh, M. Koshiba, T. Hasegawa, and E. Sasaoka, �??Chromatic dispersion control in photonic crystal fibers: application to ultra-flattend dispersion,�?? Opt. Express 11, 843-852 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-8-843">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-8-843</a> [CrossRef] [PubMed]
- K. Saitoh and M. Koshiba, �??Full-vectorial finite element beam propagation method with perfectly matched layers for anisotropic optical waveguides,�?? J. Lightwave Technol. 19, 405-413 (2001). [CrossRef]
- F.L. Teixeira and W.C. Chew, �??General closed-form pml constitutive tensors to match arbitrary bianisotropic and dispersive linear media,�?? IEEE Microwave Guided Wave Lett. 8, 223-225 (1998). [CrossRef]
- M. Koshiba and Y. Tsuji, �??Curvilinear hybrid edge/nodal elements with triangular shape for guided-wave problems,�?? J. Lightwave Technol. 18, 737-743 (2000). [CrossRef]
- L. Zhang and C. Yang, �??Polarization splitter based on photonic crystal fibers,�?? Opt. Express 11, 1015-1020 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-9-1015">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-9-1015</a> [CrossRef] [PubMed]

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