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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 11 — May. 29, 2006
  • pp: 4861–4872
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Non-proximity resonant tunneling in multi-core photonic band gap fibers: An efficient mechanism for engineering highly-selective ultra-narrow band pass splitters

Nikolaos J. Florous, Kunimasa Saitoh, Tadashi Murao, Masanori Koshiba, and Maksim Skorobogatiy  »View Author Affiliations


Optics Express, Vol. 14, Issue 11, pp. 4861-4872 (2006)
http://dx.doi.org/10.1364/OE.14.004861


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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

1. Introduction

An important element in all-optical fiber communication systems and all-optical fiber measurements is apparently a wavelength-selective fiber device such as a fiber filter. A number of fabrication techniques have been used so far for realizing such devices [5

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]

]–[7

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]

]. The operational principle of conventional fiber filters typically involves in transferring energy over a coupling length between two distinct fiber cores coupled by proximity interaction. However in this case modes in closely separated individual cores are phase-matched at all wavelengths, thus making it difficult to engineer band pass filtering characteristics. It was recently shown that efficient band pass filters can be realized based on the resonant tunneling phenomenon [8

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

] in multi-core PCFs [9

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]

].

The composition of the present investigation will be as follows: in Section 2 we introduce the device concept and we give exact design guidelines for achieving the narrow bandpass filtering characteristics. Then in Section 3 we validate our design’s performance by showing various numerical simulations based on FEM numerical algorithms. In Section 4 we briefly address the possibility of realizing a polarization-independent splitter operating at a single wavelength, based on the prescribed MC-PBGF technology. A final conclusion will follow in Section 5 with some suggestions for future investigations.

2. Schematic representation and design guidelines for engineering MC-PBGF splitters

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. (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. (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.

3. Numerical results and device performance

Let n eff,1, n eff,2, and n eff,3 represent the effective refractive indices of the supermodes corresponding to the fields ϕ1, ϕ2, ϕ3, respectively, for each of the polarization states. Then assuming that initially all the energy is in the input core-A, this will correspond to the excitation of a supermode combination of the following type:

ϕ(z=0)=(ϕ1+ϕ2)2+ϕ3.
(1)

After propagation over a distance-z, this excitation pattern will evolve into:

ϕ(z)=(ϕ1exp(jβ1z)+ϕ2exp(jβ2z))2+ϕ3exp(jβ3z)
(2)

where βi=2πn eff,i0 (i=1, 2, 3) and λ0 is operating wavelength. If we design the PBGF so that the effective refractive indexes of its supermodes satisfy the condition:

neff,1neff,3=neff,3neff,2
(3)

or equivalently,

2neff,3neff,1neff,2=0,
(4)

complete power transfer from core A to core B or C can be achieved at the exact resonant wavelength λ0 by choosing mode propagation length z=Lc with

Lcx,y=λ02(neff,1x,yneff,3x,y)
(5)

Fig. 4. Qualitative representation of the 3 supermodes existing in the MC-PBGF splitter.
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. 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. 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.

To visualize the power splitting mechanism in our proposed PBGF splitter, in Fig. 7 we plot the coupling characteristics of the field distribution at different propagation distances, obtained by using a BPM [12

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]

]. Specifically Fig. 7 shows the snapshots of the electric field distribution, that is y-polarized mode (Ey ), for (a) λ1, y=1.339 µm, (b) λ2, y=1.357 µm, calculated at a distance of z=0 mm, (c) λ1, y=1.339 µm (d) λ2, y=1.357 µm, at a distance of z=1.0 mm, (e) λ1, y=1.339 µm, and (f) λ2, y =1.357 µm, at a distance of z=1.5 mm, (g) λ1, y=1.339 µm, and (h) λ2, y=1.357 µm, at a distance of z=2.0 mm, and finally for (i) λ1, y=1.339 µm, (j) λ2, y=1.357 µm, calculated at the coupling length of z=Lc =2.7 mm. We can clearly observe that at the coupling length of Lc =2.7 mm the two different wavelengths were splitted in the output cores B and C within a power decrement of 5 % from the targeted level of 100 %, associated with the slightly difference between the partial coupling lengths corresponding to the two different operating wavelengths.

4. Realization of polarization-insensitive PBGF splitters operating at a single wavelength

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

5. Conclusions

A generalized wavelength splitter based on the resonant tunneling effect in multi-core PBGFs with multiple integrated resonators in its profile, is proposed for future analysis in Fig. 11. The operational principle is exactly the same as that of the splitter in Fig. 1. By an appropriate choice of the design parameters the generalized wavelength splitter in Fig. 11 can perform a four-wavelength splitting operation within reasonably short coupling length, appropriate for the realization of multi-operational all-fiber devices. We believe that the inclusion of multiple integrated components in a single fiber for multifunctional purposes is a challenging problem and currently is an active research topic in our group.

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.

Acknowledgments

The authors would like to kindly acknowledge partial financial support of this project from the Postdoctoral Fellowship Program of the Japan Society for the Promotion of Science (JSPS).

References and links

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]

OCIS Codes
(060.2270) Fiber optics and optical communications : Fiber characterization
(060.2430) Fiber optics and optical communications : Fibers, single-mode

ToC Category:
Photonic Crystal Fibers

History
Original Manuscript: March 22, 2006
Revised Manuscript: May 1, 2006
Manuscript Accepted: May 10, 2006
Published: May 29, 2006

Citation
Nikolaos J. Florous, Kunimasa Saitoh, Tadashi Murao, Masanori Koshiba, and Maksim Skorobogatiy, "Non-proximity resonant tunneling in multi-core photonic band gap fibers: An efficient mechanism for engineering highly-selective ultra-narrow band pass splitters," Opt. Express 14, 4861-4872 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-11-4861


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References

  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]

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