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Modes in Microstructured Optical Fibres

Modes in Microstructured Optical Fibres. Martijn de Sterke , Ross McPhedran, Peter Robinson, CUDOS and School of Physics, University of Sydney, Australia Boris Kuhlmey, Gilles Renversez, Daniel Maystre Institut Fresnel, Université Aix Marseille III, France. Outline.

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Modes in Microstructured Optical Fibres

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  1. Modes in Microstructured Optical Fibres Martijn de Sterke, Ross McPhedran, Peter Robinson, CUDOS and School of Physics, University of Sydney, Australia Boris Kuhlmey, Gilles Renversez, Daniel Maystre Institut Fresnel, Université Aix Marseille III, France

  2. Outline • Microstructured optical fibres (MOFs) • Modal cut-off in MOFS―what is issue? • Analysis MOF modes―Bloch transform • Modal cut-off of MOF modes • Second mode • Fundamental mode • Conclusion

  3. Conventional fibres: cladding, nJ Total internal reflection core nC>nJ MOFs and conventional fibres MOFs: Holes Silica matrix Core: - air hole - silica

  4. Conventional fibres: Cladding, nJ Total reflection Core, nC>nJ MOFs and conventional fibres MOFs:  Holes d Silica matrix Core: - air hole - silica

  5. Key MOF properties • “Endlessly single-modedness” (Birks et al, Opt. Lett. 22, 961 (1997)) • Unique dispersion

  6. MOFs and structural losses Finite number of rings  always losses

  7. Dilemma of Modes in MOFs (1) • Conventional fibre: number of modes is number of bound modes (without loss) • In a MOF, all modes have loss • Want: way to select small set of preferred MOF modes, to get a mode number

  8. Dilemma of Modes in MOFs (2) • The answer lies in the difference between bound modes and extended modes • Few bound modes: sensitive to core details, loss decreases exponentially with fibre size • Many extended modes: insensitive to core details, loss decreases algebraically with fibre size

  9. Properties of Modes in MOFs • Mode properties have been studied using the vector multipole method • This enables calculation of confinement loss accurately, down to very small levels • The form of modal fields is also calculated, and symmetry/degeneracy properties can be incorporated into the method JOSA B 19, 2322 & 2331 (2002)

  10. Bloch Transform • Bloch transform enables post processing of each mode to clarify structure better • Combine quantities Bn (describe field amplitude at each cylinder centred at cl) • Define: • If fields at all holes are in phase: peaks at k=0

  11. Bloch Transform: properties • Peaks at Bloch vectors associated with mode • Periodic in k-space (if holes on lattice) • Knowledge in first Brillouin zone suffices • Other properties as for Fourier transform • Heisenberg-like relation • Parseval-like relation

  12. Bloch Transform ky kx Bloch Transform: benefit • Understand and recognize modes |Sz| Max y Min x Real space Reciprocal space

  13. Extended modes : dependence on cladding shape |Sz| (real space) Bloch Transform (reciprocal lattice)

  14. Extended modes: weak dependence on core Centred Core Displaced Core No Core

  15. Defect modes |Sz| Bloch Transform

  16. Defect Modes: weak dependence on cladding shape

  17. Very strong losses! Defect Modes: strong dependence on defect ? Centred Core Displaced Core No Core

  18. Cutoff of second mode: from multimode to single mode • In modal cutoff studies, operate at λ=1.55 mm; follow modal changes as rescale period L and hole diameter d, keeping ratio constant.

  19. Cutoff of second mode: localisation transition Mode size 1 10-4 Loss Loss 10-8 10-12 l/L d/L=0.55, l=1.55mm

  20. 8 8 10 rings The transition sharpens Mode size 1 10-4 4 Loss Loss 10-8 10-12 l/L d/L=0.55, l=1.55mm

  21. Zero-width transition for infinite number of rings Number of rings Transition Width (on period)

  22. Without the cut-off moving Number of rings Cut-off wavlength (on period)

  23. Phase diagram of second mode monomode l/L “endlessly monomode” multimode d/L

  24. Cutoff of second mode: experimental verification From J. R. Folkenberg et al., Opt. Lett. 28, 1882 (2003).

  25. Fundamental mode transition? • Conventional fibres: no cut-off • W Fibres : cut-off possible, cut-off wavelength proportional to jacket size • MOF’s ?

  26. Hint of fundamental mode cut-off Loss d/L=0.3, l=1.55mm

  27. 3 3 3 3 3 4 4 4 4 8 5 5 5 6 6 Transition sharpens Loss d/L=0.3, l=1.55mm

  28. But keeps non-zero width Number of rings Transition width (on period)

  29. Cut-off Confined Extended (3) (3) (4) (4) (5) Transition of finite width: transition region Transition Q Loss l/L d/L=0.3, l=1.55mm

  30. Phase diagram and operating regimes Homogenisation

  31. Simple interpretation of second mode cut-off From Mortensen et al., Opt. Lett. 28, 1879 (2003)

  32. Conclusions • Both fundamental and second MOF modes exhibit transitions from extended to localized behaviour, but the way this happens differs • Number of MOF modes may be regarded as number of localized modes • MOF modes behave substantially differently than in conventional fibres only where they change from extended to localized

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