Abstract

The objective of the present investigation is to demonstrate the possibility of designing compact ultra-narrow band-pass filters based on the phenomenon of non-proximity resonant tunneling in multi-core photonic band gap fibers (PBGFs). The proposed PBGF consists of three identical air-cores separated by two defected air-holes which act as highly-selective resonators. With a fine adjustment of the design parameters associated with the resonant-air-holes, phase matching at two distinct wavelengths can be achieved, thus enabling very narrow-band resonant directional coupling between the input and the two output cores. The validation of the proposed design is ensured with an accurate PBGF analysis based on finite element modal and beam propagation algorithms. Typical characteristics of the proposed device over a single polarization are: reasonable short coupling length of 2.7 mm, dual bandpass transmission response at wavelengths of 1.339 and 1.357 µm, with corresponding full width at half maximum bandwidths of 1.2 nm and 1.1 nm respectively, and a relatively high transmission of 95% at the exact resonance wavelengths. The proposed ultra-narrow band-pass filter can be employed in various applications such as all-fiber bandpass/bandstop filtering and resonant sensors.

© 2006 Optical Society of America

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  1. P. St. J. Russell, "Photonic crystal fibers," Science 299, 358-362 (2003).
    [CrossRef] [PubMed]
  2. S. Kawanishi, T. Yamamoto, H. Kubota, M. Tanaka, and S. Yamaguchi, "Dispersion controlled and polarization maintaining photonic crystal fibers for high performance network systems," IEICE Trans. Electron. E87-C, 336-342 (2004).
  3. B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, and A. H. Greenaway, "Experimental study of dual-core photonic crystal fibre," Electron. Lett. 36, 1358-1359 (2000).
    [CrossRef]
  4. W. N. MacPherson, J. D. C. Jones, B. J. Mangan, J. C. Knight, and P. St. J. Russell, "Two-core photonic crystal fiber for Doppler difference velocimetry," Opt. Commun. 233, 375-380 (2003).
    [CrossRef]
  5. K. Kitayama and Y. Ishida, "Wavelength-selective coupling of two-core optical fiber: application and design," J. Opt. Soc. Am. A 2, 90-94 (1985).
    [CrossRef]
  6. R. Zengerle and O. G. Leminger, "Narrow-band wavelength-selective directional couplers made of dissimilar single-mode fibers," J. Lightwave Technol. LT-5, 1196-1198 (1987).
    [CrossRef]
  7. E. Eisenmann and E. Weidel, "Single-mode fused biconical couplers for wavelength division multiplexing with channel spacing between 100-300 nm," J. Lightwave Technol. LT-6, 113-119 (1988).
    [CrossRef]
  8. K. Thyagarajan, S.D. Seshadri, and A.K. Ghatak, "Waveguide polarizer based on resonant tunneling," J. Lightwave Technol. 9, 315-317 (1991).
    [CrossRef]
  9. K. Saitoh, N. Florous, M. Koshiba, and M. Skorobogatiy, "Design of narrow band-pass filters based on the resonant-tunneling phenomenon in multi-core photonic crystal fibers," Opt. Express 13, 10327-10335 (2005).
    [CrossRef] [PubMed]
  10. M. Skorobogatiy, K. Saitoh, and M. Koshiba, "Transverse light guides in microstructured optical fibers," Opt. Lett. 31, 314-316 (2006).
    [CrossRef] [PubMed]
  11. 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]
  12. 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]
  13. K. Saitoh and M. Koshiba, "Leakage loss and group velocity dispersion in air-core photonic bandgap fibers," Opt. Express 11, 3100-3109 (2003).
    [CrossRef] [PubMed]
  14. N. Florous, K. Saitoh, and M. Koshiba, "A novel approach for designing photonic crystal fiber splitters with polarization-independent propagation characteristics," Opt. Express 13, 7365-7373 (2005).
    [CrossRef] [PubMed]
  15. S. K. Varshney, N. Florous, K. Saitoh, and M. Koshiba, "The impact of elliptical deformations for optimizing the performance of dual-core fluorine-doped photonic crystal fiber couplers," Opt. Express 14, 1982-1995 (2006).
    [CrossRef] [PubMed]
  16. T. Tjugiarto, G. D. Peng, and P. L. Chu, "Bandpass filtering effect in tapered asymmetrical twin-core optical fibers," Electron. Lett. 29, 1077-1078 (1993).
    [CrossRef]
  17. B. Wu and P. L. Chu, "Narrow-bandpass filter with gain by use of twin-core rare-earth-doped fiber," Opt. Lett. 18, 1913-1915 (1993).
    [CrossRef] [PubMed]
  18. B. Ortega and L. Dong, "Accurate tuning of mismatched twin-core fiber filters," Opt. Lett. 23, 1277-1279 (1998).
    [CrossRef]

2006 (2)

2005 (2)

2004 (1)

S. Kawanishi, T. Yamamoto, H. Kubota, M. Tanaka, and S. Yamaguchi, "Dispersion controlled and polarization maintaining photonic crystal fibers for high performance network systems," IEICE Trans. Electron. E87-C, 336-342 (2004).

2003 (3)

W. N. MacPherson, J. D. C. Jones, B. J. Mangan, J. C. Knight, and P. St. J. Russell, "Two-core photonic crystal fiber for Doppler difference velocimetry," Opt. Commun. 233, 375-380 (2003).
[CrossRef]

P. St. J. Russell, "Photonic crystal fibers," Science 299, 358-362 (2003).
[CrossRef] [PubMed]

K. Saitoh and M. Koshiba, "Leakage loss and group velocity dispersion in air-core photonic bandgap fibers," Opt. Express 11, 3100-3109 (2003).
[CrossRef] [PubMed]

2002 (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]

2001 (1)

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 fibre," Electron. Lett. 36, 1358-1359 (2000).
[CrossRef]

1998 (1)

1993 (2)

B. Wu and P. L. Chu, "Narrow-bandpass filter with gain by use of twin-core rare-earth-doped fiber," Opt. Lett. 18, 1913-1915 (1993).
[CrossRef] [PubMed]

T. Tjugiarto, G. D. Peng, and P. L. Chu, "Bandpass filtering effect in tapered asymmetrical twin-core optical fibers," Electron. Lett. 29, 1077-1078 (1993).
[CrossRef]

1991 (1)

K. Thyagarajan, S.D. Seshadri, and A.K. Ghatak, "Waveguide polarizer based on resonant tunneling," J. Lightwave Technol. 9, 315-317 (1991).
[CrossRef]

1988 (1)

E. Eisenmann and E. Weidel, "Single-mode fused biconical couplers for wavelength division multiplexing with channel spacing between 100-300 nm," J. Lightwave Technol. LT-6, 113-119 (1988).
[CrossRef]

1987 (1)

R. Zengerle and O. G. Leminger, "Narrow-band wavelength-selective directional couplers made of dissimilar single-mode fibers," J. Lightwave Technol. LT-5, 1196-1198 (1987).
[CrossRef]

1985 (1)

Birks, T. A.

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

Chu, P. L.

B. Wu and P. L. Chu, "Narrow-bandpass filter with gain by use of twin-core rare-earth-doped fiber," Opt. Lett. 18, 1913-1915 (1993).
[CrossRef] [PubMed]

T. Tjugiarto, G. D. Peng, and P. L. Chu, "Bandpass filtering effect in tapered asymmetrical twin-core optical fibers," Electron. Lett. 29, 1077-1078 (1993).
[CrossRef]

Dong, L.

Eisenmann, E.

E. Eisenmann and E. Weidel, "Single-mode fused biconical couplers for wavelength division multiplexing with channel spacing between 100-300 nm," J. Lightwave Technol. LT-6, 113-119 (1988).
[CrossRef]

Florous, N.

Ghatak, A.K.

K. Thyagarajan, S.D. Seshadri, and A.K. Ghatak, "Waveguide polarizer based on resonant tunneling," J. Lightwave Technol. 9, 315-317 (1991).
[CrossRef]

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 fibre," Electron. Lett. 36, 1358-1359 (2000).
[CrossRef]

Ishida, Y.

Jones, J. D. C.

W. N. MacPherson, J. D. C. Jones, B. J. Mangan, J. C. Knight, and P. St. J. Russell, "Two-core photonic crystal fiber for Doppler difference velocimetry," Opt. Commun. 233, 375-380 (2003).
[CrossRef]

Kawanishi, S.

S. Kawanishi, T. Yamamoto, H. Kubota, M. Tanaka, and S. Yamaguchi, "Dispersion controlled and polarization maintaining photonic crystal fibers for high performance network systems," IEICE Trans. Electron. E87-C, 336-342 (2004).

Kitayama, K.

Knight, J. C.

W. N. MacPherson, J. D. C. Jones, B. J. Mangan, J. C. Knight, and P. St. J. Russell, "Two-core photonic crystal fiber for Doppler difference velocimetry," Opt. Commun. 233, 375-380 (2003).
[CrossRef]

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

Koshiba, M.

Kubota, H.

S. Kawanishi, T. Yamamoto, H. Kubota, M. Tanaka, and S. Yamaguchi, "Dispersion controlled and polarization maintaining photonic crystal fibers for high performance network systems," IEICE Trans. Electron. E87-C, 336-342 (2004).

Leminger, O. G.

R. Zengerle and O. G. Leminger, "Narrow-band wavelength-selective directional couplers made of dissimilar single-mode fibers," J. Lightwave Technol. LT-5, 1196-1198 (1987).
[CrossRef]

MacPherson, W. N.

W. N. MacPherson, J. D. C. Jones, B. J. Mangan, J. C. Knight, and P. St. J. Russell, "Two-core photonic crystal fiber for Doppler difference velocimetry," Opt. Commun. 233, 375-380 (2003).
[CrossRef]

Mangan, B. J.

W. N. MacPherson, J. D. C. Jones, B. J. Mangan, J. C. Knight, and P. St. J. Russell, "Two-core photonic crystal fiber for Doppler difference velocimetry," Opt. Commun. 233, 375-380 (2003).
[CrossRef]

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

Ortega, B.

Peng, G. D.

T. Tjugiarto, G. D. Peng, and P. L. Chu, "Bandpass filtering effect in tapered asymmetrical twin-core optical fibers," Electron. Lett. 29, 1077-1078 (1993).
[CrossRef]

Russell, P. St. J.

P. St. J. Russell, "Photonic crystal fibers," Science 299, 358-362 (2003).
[CrossRef] [PubMed]

W. N. MacPherson, J. D. C. Jones, B. J. Mangan, J. C. Knight, and P. St. J. Russell, "Two-core photonic crystal fiber for Doppler difference velocimetry," Opt. Commun. 233, 375-380 (2003).
[CrossRef]

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

Saitoh, K.

Seshadri, S.D.

K. Thyagarajan, S.D. Seshadri, and A.K. Ghatak, "Waveguide polarizer based on resonant tunneling," J. Lightwave Technol. 9, 315-317 (1991).
[CrossRef]

Skorobogatiy, M.

Tanaka, M.

S. Kawanishi, T. Yamamoto, H. Kubota, M. Tanaka, and S. Yamaguchi, "Dispersion controlled and polarization maintaining photonic crystal fibers for high performance network systems," IEICE Trans. Electron. E87-C, 336-342 (2004).

Thyagarajan, K.

K. Thyagarajan, S.D. Seshadri, and A.K. Ghatak, "Waveguide polarizer based on resonant tunneling," J. Lightwave Technol. 9, 315-317 (1991).
[CrossRef]

Tjugiarto, T.

T. Tjugiarto, G. D. Peng, and P. L. Chu, "Bandpass filtering effect in tapered asymmetrical twin-core optical fibers," Electron. Lett. 29, 1077-1078 (1993).
[CrossRef]

Varshney, S. K.

Weidel, E.

E. Eisenmann and E. Weidel, "Single-mode fused biconical couplers for wavelength division multiplexing with channel spacing between 100-300 nm," J. Lightwave Technol. LT-6, 113-119 (1988).
[CrossRef]

Wu, B.

Yamaguchi, S.

S. Kawanishi, T. Yamamoto, H. Kubota, M. Tanaka, and S. Yamaguchi, "Dispersion controlled and polarization maintaining photonic crystal fibers for high performance network systems," IEICE Trans. Electron. E87-C, 336-342 (2004).

Yamamoto, T.

S. Kawanishi, T. Yamamoto, H. Kubota, M. Tanaka, and S. Yamaguchi, "Dispersion controlled and polarization maintaining photonic crystal fibers for high performance network systems," IEICE Trans. Electron. E87-C, 336-342 (2004).

Zengerle, R.

R. Zengerle and O. G. Leminger, "Narrow-band wavelength-selective directional couplers made of dissimilar single-mode fibers," J. Lightwave Technol. LT-5, 1196-1198 (1987).
[CrossRef]

Electron. Lett. (2)

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

T. Tjugiarto, G. D. Peng, and P. L. Chu, "Bandpass filtering effect in tapered asymmetrical twin-core optical fibers," Electron. Lett. 29, 1077-1078 (1993).
[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]

IEICE Trans. Electron. (1)

S. Kawanishi, T. Yamamoto, H. Kubota, M. Tanaka, and S. Yamaguchi, "Dispersion controlled and polarization maintaining photonic crystal fibers for high performance network systems," IEICE Trans. Electron. E87-C, 336-342 (2004).

J. Lightwave Technol. (4)

R. Zengerle and O. G. Leminger, "Narrow-band wavelength-selective directional couplers made of dissimilar single-mode fibers," J. Lightwave Technol. LT-5, 1196-1198 (1987).
[CrossRef]

E. Eisenmann and E. Weidel, "Single-mode fused biconical couplers for wavelength division multiplexing with channel spacing between 100-300 nm," J. Lightwave Technol. LT-6, 113-119 (1988).
[CrossRef]

K. Thyagarajan, S.D. Seshadri, and A.K. Ghatak, "Waveguide polarizer based on resonant tunneling," J. Lightwave Technol. 9, 315-317 (1991).
[CrossRef]

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]

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

Opt. Commun. (1)

W. N. MacPherson, J. D. C. Jones, B. J. Mangan, J. C. Knight, and P. St. J. Russell, "Two-core photonic crystal fiber for Doppler difference velocimetry," Opt. Commun. 233, 375-380 (2003).
[CrossRef]

Opt. Express (4)

Opt. Lett. (3)

Science (1)

P. St. J. Russell, "Photonic crystal fibers," Science 299, 358-362 (2003).
[CrossRef] [PubMed]

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Figures (11)

Fig. 1.
Fig. 1.

Topology of a three-core PBGF splitter utilizing a non-proximity resonant tunneling coupling mechanism. The air-holes in the cladding are arranged in a triangular configuration with pitch constant Λ and air-hole diameters d. As an input core we consider the middle core-A, while B and C are the output cores. Two dissimilar transverse resonators with diameters d 1 (green colored) and d 2 (red colored) are then introduced by reducing (high index defects) the diameters of the air-holes in the middle of the line joining the cores. By a judicious choice of the design parameters this multi-core PBGF can act as an ultra-narrow dual band pass filter at a very short coupling length.

Fig. 2.
Fig. 2.

(a) Effective indexes of the x-polarized fundamental (solid blue curve) and the x-polarized excited resonant modes (red dashed curves) of the multi-core PBG fiber splitter, for fixed design parameters d/Λ=0.9, Λ=2 µm, and for several values of the normalized resonator’s diameter dr /Λ, ranged from 0.6 to 0.8, and (b) the evolution of the resonance wavelength as a function of the resonator’s normalized diameter dr /Λ. In this case the requirement that the resonance wavelength must lie within the PBG of the structure (between the grey boundaries), limits the normalized resonator’s diameter dr /Λ to vary from 0.62 up to 0.8.

Fig. 3.
Fig. 3.

(a) Effective indexes of the y-polarized fundamental (solid blue curve) and the y-polarized excited resonant modes (red dashed curves) of the multi-core PBG fiber splitter, for fixed design parameters d/Λ=0.9, Λ=2 µm, and for several values of the normalized resonator’s diameter dr /Λ, ranged from 0.1 to 0.85, and (b) the evolution of the resonance wavelength as a function of the resonator’s normalized diameter dr /Λ. Notice the remarkable insensitivity in the evolution of the resonant wavelength as a function of the resonator’s diameter in the range from 0.1 to 0.4 for the y-polarization. The PBG boundary is denoted within the grey strips.

Fig. 4.
Fig. 4.

Qualitative representation of the 3 supermodes existing in the MC-PBGF splitter.

Fig. 5.
Fig. 5.

Coupling length (mm) as a function of the normalized resonator’s diameter dr /Λ, for (a) x-polarization and (b) y-polarization. Observe the remarkable linear evolution of the curve in the case of x-polarization and the asymptotic behavior as the normalized diameter tends to lower values, for the y-polarization.

Fig. 6.
Fig. 6.

Dual band-pass filtering characteristics for y-polarization of the three-core PBG fiber splitter, at the two resonant wavelengths of λ1=1.339 µm and λ2=1.357 µm, with corresponding full width at half maximum (FWHM) bandwidths of 1.2 nm and 1.1 nm, respectively. The transmission peak at the exact resonance wavelengths is about 95 % a result that indicates the slightly difference between the partial coupling lengths at the two different wavelengths.

Fig. 7.
Fig. 7.

The left hand column represents the snapshots of the electric field distribution, that is y-polarization (Ey ), in the multi-core PBGF splitter, at λ1, y =1.339 µm, and the right hand column represents the snapshots of the electric field distribution, that is y-polarization (Ey ), at λ2, y =1.357 µm. Successive rows correspond to distances of z=0 mm, z=1.0 mm, z=1.5 mm, z=2.0 mm, and finally at the coupling length of z=Lc =2.7 mm. We can clearly see that at the coupling length of Lc =2.7 mm, almost complete power transfer can be achieved from the input core-A to the output cores B and C at wavelengths of λ1, y =1.339 µm and λ2, y =1.357 µm, respectively with a transmission level of about 95 % due to the slightly difference in the values of the exact coupling lengths at the two different wavelengths.

Fig. 8.
Fig. 8.

Evolution of the resonance wavelengths, as a function of the resonator’s normalized diameter dr /Λ, for x-polarization (blue curve) and y-polarization (red curve). The two curves cross each other at a point corresponding to resonance wavelength of λres=1.325 µm and normalized resonator’s diameter dr /Λ=0.75. Thus by fixing both resonators’ diameters at the prescribed value, polarization-independent propagation characteristics can be realized at a single wavelength of λres=1.325 µm.

Fig. 9.
Fig. 9.

Dual-core PBGF splitter with an embedded resonator in its profile, for achieving polarization-independent propagation characteristics.

Fig. 10.
Fig. 10.

Normalized power distribution in the MC-PBGF splitter for x-polarization (blue curve) and y-polarization (red curve) at operating wavelength of λres=1.325 µm, and for (a) input core-A, (b) output core-B. The coupling length for polarization-independent operation was confirmed by the BPM analysis to be Lc =22.3 mm. Thus by fixing the MC-PBGF splitter’s length at the prescribed value, the structure operates as a dual-core coupler, with a transmittivity of more than 90 %, independent of the polarization state.

Fig. 11.
Fig. 11.

Topology of the proposed five-core PBGF splitter utilizing a non-proximity resonant tunneling coupling mechanism. As an input core we consider the central core-A, while B, C, D and E are the output cores. Four dissimilar transverse resonators with diameters d 1 (yellow colored), d 2 (green colored), d3 (teal colored), and d 4 (red colored) are introduced by reducing (high index defects) the diameters of the air-holes across the lines joining the cores. By a judicious choice of the design parameters this multicore PBGF can perform an ultra-narrow bandpass filtering operation at four distinct wavelengths with a reasonably short coupling length.

Equations (5)

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ϕ ( z = 0 ) = ( ϕ 1 + ϕ 2 ) 2 + ϕ 3 .
ϕ ( z ) = ( ϕ 1 exp ( j β 1 z ) + ϕ 2 exp ( j β 2 z ) ) 2 + ϕ 3 exp ( j β 3 z )
n eff , 1 n eff , 3 = n eff , 3 n eff , 2
2 n eff , 3 n eff , 1 n eff , 2 = 0 ,
L c x , y = λ 0 2 ( n eff , 1 x , y n eff , 3 x , y )

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