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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

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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

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MOFs:

Holes

Silica matrix

Core: - air hole- silica

cladding, nJConventional fibres:

core nC >nJ

Total internal reflection

MOFs and conventional fibres

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Cladding, nJConventional fibres:

Core, nC >nJ Total reflection

MOFs:

d

Holes

Silica matrix

Core: - air hole- silica

MOFs and conventional fibres

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Key MOF properties

• “Endlessly single-modedness” (Birks et al, Opt. Lett. 22, 961 (1997))

• Unique dispersion

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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

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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

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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 k=0

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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

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Bloch Transform: benefit

• Understand and recognize modes

x

y

|Sz|

kx

ky

Bloch TransformMax

Min

Real space Reciprocal space

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Extended modes : dependence on cladding shape

|Sz| (real space)

Bloch Transform (reciprocal lattice)

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Centred Core Displaced Core No Core

Extended modes: weak dependence on core

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Defect modes|Sz| Bloch Transform

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Defect Modes: weak dependence on cladding shape

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Centred Core Displaced Core No Core

Defect Modes: strong dependence on defect

?

Very strong losses!

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Cutoff of second mode: from multimode to single mode

• In modal cutoff studies, operate at λ=1.55 m; follow modal changes as rescale period and hole diameter d, keeping ratio constant.

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Cutoff of second mode: localisation transition

Mode size

Loss

1

10-4

10-8

10-12

Los

s

d/=0.55, m

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8

10 rings

8

The transition sharpens

Mode size

Loss

1

10-4

10-8

10-12

Los

s

d/=0.55, m

4

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Zero-width transition for infinite number of rings

Number of ringsT

rans

ition

Wid

th (

on p

erio

d)

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Without the cut-off moving

Cut

-off

wav

leng

th (

on p

erio

d)Number of rings

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Phase diagram of second mode

multimode

monomode

“end

less

ly m

onom

ode”

d

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Cutoff of second mode: experimental verification

From J. R. Folkenberg et al., Opt. Lett. 28, 1882 (2003).

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Fundamental mode transition?

• Conventional fibres: no cut-off

• W Fibres : cut-off possible, cut-off wavelength proportional to jacket size

• MOF’s ?

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Hint of fundamental mode cut-off

d/=0.3, m

Los

s

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334

34

5

34

5 63

4 8

5 6

Transition sharpens

d/=0.3, m

Los

s

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But keeps non-zero width

Number of ringsT

rans

itio

n w

idth

(on

per

iod)

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Transition of finite width: transition region

d/=0.3, m

Los

s

QConfined Extended

Cut-off

Transition

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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)

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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