Martijn de Sterke, Ross McPhedran,

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
MOFs and conventional fibres
MOFs
Holes
Silica matrix
Core - air hole - silica
4
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
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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)
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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 k0

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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 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)
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Extended modes weak dependence on core

Centred Core
Displaced Core
No Core
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Defect modes

Sz
Bloch Transform
16
Defect Modes weak dependence on cladding shape

17
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 ?1.55 mm
  follow modal changes as rescale period L and hole
  diameter d, keeping ratio constant.

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Cutoff of second mode localisation transition

Mode size
1
10-4
Loss
Loss
10-8
10-12
l/L
d/L0.55, l1.55mm
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The transition sharpens

Mode size
1
10-4
4
Loss
Loss
10-8
10-12
l/L
d/L0.55, l1.55mm
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)
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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
• MOFs ?

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Hint of fundamental mode cut-off

Loss
d/L0.3, l1.55mm
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Transition sharpens

Loss
d/L0.3, l1.55mm
28
But keeps non-zero width

Number of rings
Transition width (on period)
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Transition of finite width transition region

Transition
Q
Loss
l/L
d/L0.3, l1.55mm
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Phase diagram and operating regimes

Homogenisation
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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