Photonic crystal fibres

SMR 1829 - 8

Winter College on Fibre Optics, Fibre Lasers and Sensors

12 - 23 February 2007

Photonic crystal fibres

Jonathan Knight

University of Bath United Kingdom

1

Photonic crystal fibres

Jonathan Knight

University of Bath

United Kingdom

Overview of this lecture

2

Visible Near-IR Mid-IRUltravioletX-ray Far IR

1nm 0.5 m 1 m 5 m 50 m

Telecoms band

The photonic spectrum:

Wavelength

The -value

Wavevector = nk

Component of wavevector

parallel to fibre axis =

Fibre is invariant along

it’s length

In a homogeneous medium with refractive index n, the biggest

value can take is = nk, when it is a plane wave.

Once it is confined, we must have < nk

3

Conventional optical fiber

waveguides

nclad

k < < ncore

k

maxn

cladk

ncore

> nclad

nclad

Core index must be higher than that of cladding material to

get guided modes

Attenuation in standard fibres

Rayleigh

scattering

4

Group velocity and group index

Information actually propagates at the group

velocity vg…

g

dv

dk

Knowing vg we can define a group refractive

indexg

g

c dnn n

v d

c

n k

Group velocity dispersion

Another important parameter is the group-

velocity dispersion (GVD, D - variation of vg

with frequency) which determines how

pulses spread out (disperse) as they

propagate.

Units of D = ps/(nm.km)

5

Where does “dispersion” come

from

• Material dispersion

• Waveguide dispersion

• “structural” dispersion (in photonic

crystals)

Material dispersion – SiO2

0.6

0.8

1

1.2

1.4

1.6

1.8

0 2 4 6 8

Wavelength - m

Refr

active in

dex

SiO2

Electronic absorption

Latticevibrations

Point of

Inflection

1300nm

Optical

windowPoint of inflection

gives zero group-

velocity dispersion

(GVD) around

1300nm

wavelength

6

Group velocity dispersion

(GVD) of silica

-600

-500

-400

-300

-200

-100

0

100

0.5 0.7 0.9 1.1 1.3 1.5 1.7

Wavelength ( m)

GV

D p

s/n

m/k

m

Norm

aldis

pers

ion

Anomalous dispersion

Waveguide dispersion

• Mode index changes as mode shape changes

• Has a relatively small effect due to the small index contrast

• Consequently, only significant around the material zero-GVD wavelength

Computations for the fundamental mode in a circular

strand of glass index 1.5 surrounded by glass index 1.49

1.488

1.49

1.492

1.494

1.496

1.498

1.5

1.502

0 0.5 1 1.5 2

Wavelength/core radius

Mo

da

l in

de

x

Three zero points

7

Waveguide GVD

Can be used to, for

example, cancel the

material gvd at 1550nm

(which is normally

13ps/(nm.km))

Note that the waveguide

dispersion has a large

curvature-15

-10

-5

0

5

10

0 0.5 1 1.5 2


GV

D (p

s/(n

m.k

m)


8

Non-standard optical materials

1 m

“Effective index” in photonic

crystal fibres

Guiding core formed

by solid silica region

embedded in matrix

Just like a standard fibre…

But using a unique new

optical material

RI

9


Material systems +

fabrication technologies • Silica – ideal for stack and draw, tubes

available commercially

• Silicates – great for proof-of-principle experiments X.Feng et al., Opt. Express, 11 2225 (2003)

• Polymer: drilled/extruded preforms M. A. van Eijkelenborg, et al. Optics Express Vol. 9, No. 7, pp. 319-327 (2001).

• Tellurite and Chalcogenide glasses (extrusion, rotational casting, stacking)

• Chalcogenides and polymers (“rolling your own”)

Sydney OFTC mPOF group

B. Temelkuran et al, Nature 420, 650-653 (2002).

10

Silica fibre fabrication

Commercial tubes

Capillary tubes

Stack preform

Draw stack down

Jacket and draw to fibre

Length scale

1m

400m

1m

100m

1000km

Fibre fabrication

11

Forms of PCF

High numerical

aperture,multimode

Photonic bandgap

fiber with solid core Photonic bandgap

fiber with hollow core

Highly nonlinear fiber

with anomalous

dispersion

12


Define an effective index for the

“holey” material as neff = /k

Working at fixed frequency:

Bulk silica

nsilica

nair

propagating

evanescent

“Holey” silica

Low frequencies

“Holey” silica

High frequencies

Band

gaps

Dispersion!

13

nsilica

nair

Air-filling fraction (%)

0 10 20 30 40 50 60 70 80

THE PLAYING THE PLAYING

FIELDFIELD

Mo

dal

index

Allow

edm

odes

No

modes

“honeycomb

bandgap” fibrenair

nsilica

“single-mode” fibre

Modes allowed

in all materials

Modes allowed in silica

Modes forbidden in air

Modes forbidden in silica

Modes forbidden in air

“High- ” fibre

“Air-guiding” fibre

1-dimensional model

Air holes

PCF

cladding

conventional

cladding

CoreCore

Fibre is single-mode for all wavelengths…or for all core sizes

14

“Effective index” view of

cladding index

Short wavelengths

Long wavelengths

But1

2 2 2( )core clad

DV n n

Normalised frequency:

conventional fibre

0

1

2

3

4

5

6

0.4 0.9 1.4 1.9

Wavelength (microns)

V

Useful range

• Fibre useful over a limited

range of frequencies

• Limited on long wavelength

edge by bend loss

• Limited on short

wavelength edge by 2nd

mode cutoff

15


Nonlinear optics

High nonlinear response (small core)

Strong waveguide dispersion

16

The importance of dispersion…

Dispersing a white-light

spectrum

Generating white light from a

laser source in a photonic crystal

fibre

Waveguide dispersion in a PCF

-250

-200

-150

-100

-50

0

50

100

0 1 2 3 4 5 6 7 8 9


GV

D (

ps/(

nm

.km

)

17

= 2 m, d

silica

“holey” silica

Sources of dispersion• Material dispersion of silica

• Waveguide dispersion

• Dispersion of the “holey” material

Index of the

“fundamental

space-filling mode”

1.2

1.25

1.3

1.35

1.4

1.45

1.5

0.5 1 1.5 2


Ind

ex

What can PCF do for nonlinear

optics?

Gro

up v

elo

city d

ispe

rsio

n (

ps/(

nm

.km

)

Wavelength (nm)

• Widely adjustable zero-GVD point

• Anomalous dispersion throughout

the visible and near-IR

• High nonlinear coefficient

• Large values of dispersion and slope

-200

-150

-100

-50

0

50

100

150

200

250

300

500 700 900 1100 1300 1500

Decreasing core size

Conventional fibre

PCF

Anomalous

dispersion

18

Sub-ns pulses• Typical pump Q-switched laser

source eg Nd:YAG microchip,

relatively narrow linewidth

• Pump close to zero-dispersion

wavelength

• Sidebands generated through

FWM/MI, at specific wavelengths,

as well as SRS peaks

• Ultimately, a temporally

incoherent supercontinuum

S. Coen, JOSA B 19 753 (2002)

J. D. Harvey, Opt. Lett. 28 2225 (2003)

W. J. Wadsworth, Opt. Express 12 299 (2004)

600 800 1000 1200 1400 1600 1800

Wavelength (nm)

Single-mode white light source

with a microchip laser

Nd: -based 1064nm microchip laser, sub-ns pulses,

7kHz rep rate, 30mW average power

19

Broadband single-mode white

light source

Applications: single-mode light source

Optical transmission –

nonlinear regime

Refractive index

“Self phase modulation”

Kerr

nonlinearity

20

Self-phase

modulation

(nonlinear)

“Anomalous”

dispersion fibre

(linear)

+

Soliton propagation

Magical energy for soliton

propagation

Linear dispersion and nonlinear self-phase modulation

are matched at just one peak power, which can be

found be matching the dispersion and nonlinear lengths

3

0 2 2

2

3.11

4

effDAP

cn

21

Soliton self-frequency shift

• Solitons are short pulses, and so must have a relatively broad spectral width

• The Raman gain spectrum, which peaks around 12THz, gives non-zero gain down towards zero frequency shift

• Consequently, a soliton can “pump itself” by SRS

• The long-wavelength edge experiences gain as it is pumped by the short-wavelength edge

• This leads to a continuous downshift of the soliton central frequency during propagation

0

Acts as

pumpExperiences

gain

Longer

Soliton propagation in a PCF

0

Short pulses Linear propagation,

Anomalous dispersion

Dispersed pulses

0

Short pulses Kerr nonlinear propagation,

Anomalous dispersionShort pulses

22

Autocorrelation signals of 100fs

pulses transmitted through 3.1m

of fiber at 1.35mW average

power.

Soliton effects at

850nm

Wavelength - 850nm

Dispersion - 50ps/nm/km

Core diameter - 2.1 m

Fundamental soliton energy 16pJ

Soliton length 1m

Autocorrelation width of

transmitted pulse as a function of

power.

W. J. Wadsworth et al, Electron. Lett. 36 53 (2000)

Average power - mW

0 1 2 3 4 5

Auto

corr

elat

ion w

idth

-fs

100

200

300

400

500

600

700

800

900

Delay (fs)

-500 0 500

auto

corr

ela

tor

sig

nal

Predicted fundamental

soliton energy

Soliton self-frequency shift from 850nm

840

860

880

900

920

940

960

0 0.5 1 1.5 2 2.5 3 3.5 4

Average output power (mW)

Ou

tpu

t w

av

elen

gth

Fiber length 6m, pulse length 200fs, rep rate 76MHz

23

General features of soliton propagation

in PCF with anomalous dispersion

-400

-300

-200

-100

0

100

200

300

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6


GV

D (

ps

.nm

-1.k

m-1

)

-400

-300

-200

-100

0

100

200

300

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6


GV

D (

ps

.nm

-1.k

m-1

)D

D=3 m

D=1 m

General features of soliton propagation in

PCF with anomalous dispersion

500 600 700 800 900 1000

Wavelength - nm

Incre

asin

g p

ow

er

Self-phase modulation

Pulse breakup,

self-frequency shifting solitons

Cherenkov radiation

Supercontinuum

formation

24

General features of soliton propagation in PCF with

negative dispersion slope

D

-400

-300

-200

-100

0

100

200

300

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6


GV

D (

ps

.nm

-1.k

m-1

)

-400

-300

-200

-100

0

100

200

300

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6


GV

D (

ps

.nm

-1.k

m-1

)

D=3 m

D=1 m

General features of solitons in

PCF with negative dispersion

slope

Incident pulse

breaks up into

several

fundamental

solitons with

different

energies

D. V. Skryabin et al. Science 301 1705 (2003)

As solitons approach

zero-dispersion

wavelength (dotted line)

they stop shifting and

shed radiation.

Solitons self-frequency

shift due to Raman, with

rate depending on

soliton energy

25

Group-index matching

1.46

1.465

1.47

1.475

1.48

1.485

1.49

0.5 1 1.5 2 2.5

Wavelength (mm)

Ind

ex

Pure silica

Group-index matching

Pure silica

1.465

1.47

1.475

1.48

1.485

1.49

1.495

1.5

1.505

1.51

1.515

1.52

0.4 0.9 1.4 1.9 2.4

Wavelength microns

Gro

up

in

dex

5 m core PCF

26

See also N. Nishizawa and T. Goto, Opt. Lett. 27 152 (2002)

Anomalous gvdNormal gvd

Solitons are continually

self-frequency shifting

due to Raman

This means they are

always slowing down (as

ng increases)

1.475

1.477

1.479

1.481

1.483

1.485

1.487

1.489

0.5 0.7 0.9 1.1


Gro

up

In

de

x

These peaks are not

solitons, but are trapped

by the solitons at longer

wavelengths. They get

blue-shifted by FWM

interaction with the

solitons

Thus, blue-shifting will stop when group-index matching

becomes impossible!

Energy exchange between

colliding solitons

The experiment

Spectral

analysis

Femtosecond

pulses

PCF

27


colliding solitons

De

cre

asin

g d

ela

y

- Large delay – solitons don’t collide

Solitons collide at the end of fibre

- Collision moves towards input end


colliding solitons

“Energy exchange between colliding solitons in photonic crystal fibers”, F. Luan et al. to appear in Optics Express, 2006

• Delay is kept fixed at 1.5ps

• First pulse energy is varied

• Higher energy causes

faster SSFS

Similar

energies

Different

energies

28

Supercontinuum generated in Silica

PCF using 800nm pump pulses

Applications: Frequency metrology, optical coherence tomography


29

A single-mode laser (continuous

wave)

A laser running on two

longitudinal modes

Beat frequency = mode spacing

30

Mode-locked laser running on

fifteen longitudinal modes

Repetition rate = mode spacing

Mode-locked laser output

0 50 100

time (ns)

Time domain… Pulses spaced by 10ns…

31

0

0.2

0.4

0.6

0.8

1

1.2

400 600 800 1000 1200

Wavelength - nm

Pow

er

Mode-locked laser outputSpectral domain…

Gain profile of laser

Mode-locked laser outputSpectral domain…

800 800.0005 800.001 800.0015 800.002

Repetition rate=100MHz

Modes of

laser cavity

Wavelength - nm

32

• frequency spacing = repetition rate

of pump laser (measure or control

in time domain)

• Frequencies of interest can be

phase-locked to individual modes of

supercontinuum, to measure the

differences between them

• Measurements of absolute

frequencies can be made by

measuring 2f-f

frequency ruler

ten million steps in frequency

Supercontinuum is a frequency ruler

Work done by:Ted Hänsch, MPI Garching

John Hall, JILA

Optical coherence

tomographyMedical imaging technique, relying on low-coherence interferometry

Laser source

Remember that coherence length is inversely related to bandwidth.

33

Optical coherence

tomographyMedical imaging technique, relying on low-coherence interferometry

White light

source

OCTMedical imaging technique, relying on low-coherence interferometry

White light

source

Longitudinal spatial resolution fixed

by bandwidth of source

This is used to do a 2-dimensional scan of the eye, or even skin.

34

Reviews: J. C. Knight, Nature, 424, 847 (2003)

P. St. J. Russell, Science 299, 358 (2003)

Classic papers: Kaiser, P. & Astle, H. W., Low loss single material fibers made from pure fused silica. Bell Syst. Tech. Journ. 53 1021-1039 (1974)

Knight, J. C., Birks, T. A., Russell, P. St.J. and Atkin, D. M., All-silica single-mode optical fiber with photonic crystal cladding Opt. Lett. 21 1547-1549 (1996), errata 22 484 (1997)

Birks, T. A., Knight, J. C. and Russell, P. St.J., Endlessly single-mode photonic crystal fiber. Opt. Lett. 22 961-963 (1997)

Kumar, V. V. R. K. et al. Extruded soft glass photonic crystal fiber for ultrabroadsupercontinuum generation. Opt. Express 10 1520-1525 http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-25-1520 (2002)

Ranka, J. K., Windeler, R. S. and Stentz, A. J. Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800nm. Opt. Lett. 25 25-27 (2000)

Udem, T., Holzwarth, R. and Hänsch, T. W. Optical frequency metrology. Nature 416 233-237 (2002)

Povazay, B. et al. Submicrometer axial resolution optical coherence tomography. Opt. Lett. 27 1800-1802 (2002)

Topical work: B. Zsigri et al., Demonstration of broadcast, transmission and wavelength conversion functionalities using photonic crystal fibers. IEEE Photon. Technol. Lett. 18 2290 (2006)

J. H. Rothwell et al. Photonic sensing based on variation of propagation properties of photonic crystal fibers. Optics Express 14 12445 (2006)

H. Hasegawa et al. 10Gb/s transmission over 5km at 850nm using single-mode photonic crystal fiber, single-mode VCSEL and Si-APD. IEICE Electronics Express

E. F. Chilcce et al., Tellurite photonic crystal fiber made by a stack-and-draw technique. Journ. Non-Crystalline Solids 352 3423 (2006)

Selected reading

Bandgap fibres

35

Overview of this section

Light in identical coupled fibres

2i

2i

36

What if the fibres are different?

1

2

Guided mode indices

1.456

1.458

1.46

1.462

1.464

1.466

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Wavelength - nm

Eff

ec

tiv

e I

nd

ex

Cladding index

First core index

Second core index

37

Guided mode indices

1.456

1.458

1.46

1.462

1.464

1.466

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Wavelength - nm

Eff

ecti

ve I

nd

ex

Cladding index

First core index

Second core index

Mode crossings coupling

Eff

ective

in

de

x

Multi-core fibre

Single mode core

X X

SMFSMF

“Loss” of this device would be

strongly wavelength dependent!

Low loss away from the mode

coincidences

High loss (depending on number

of cores) near the coincidences

38

Guided mode indices

Cladding index

Mode indices must be down here!1.456

1.458

1.46

1.462

1.464

1.466

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Wavelength - nm

Eff

ecti

ve I

nd

ex

Index of core mode would have to be below cladding index

1.445

1.45

1.455

1.46

1.465

500 1000 1500 2000

Wavelength (nm)

Eff

ecti

ve in

dex

Guided modes in a standard fibre

Core index 1.46

Cladding index 1.45

Core diameter 7 m

39

1.448

1.4485

1.449

1.4495

1.45

1.4505

1.451

1.4515

1.452

600 1100 1600

Wavelength (nm)

Eff

ecti

ve in

dex

Density of

states:

periodic array

of cores

Guided

modes of a

single core

Guided modes and band gaps

Demonstrations of “simple”

bandgap fibres

• Liquid-filled holey glass fibre1

• Two different glasses in an all-solid fibre2

• Doped and undoped silica in an all-solid fibre3

• Liquid-crystal based PBG fibre devices4

1. J. Jasapara et al OFC 2002 519 (2002).

2. F. Luan et al, Opt. Lett. 29 2369 (2004)

3. A. Argyros et al, Opt. Express 13 309 (2005)

4. T. Larsen et al, Opt. Express 11 2589 (2003)

40

Fabricating a simple photonic

bandgap fibre

Two commercial glasses –

SF6 and LLF1, indices

1.54 and 1.79“All-solid photonic bandgap fiber”, F. Luan et al, Opt. Lett. 29 2369 (2004)

“Simple” bandgap fiber

“All-solid photonic bandgap fiber”, F. Luan et al, Opt. Lett. 29 2369 (2004)

(light = high index)

41

“Simple” bandgap fiber

“All-solid photonic bandgap fiber”, F. Luan et al, Opt. Lett. 29 2369 (2004)

-85

-75

-65

-55

-45

-35

0.25 0.35 0.45 0.55 0.65

5006007008001000

Frequency (1015 Hz)

Wavelength (nm)

Tra

nsm

itte

d s

igna

l (d

B)

(residual pump for supercontinuum)

Dispersion in a PBG fibre

Bandgap - mode is well

confined to low-index

region

Mode

spreads

out

Mode

spreads

out

Gro

up

in

de

x

Dispersion 0

Dispersion

normal

Dispersion

anomalous

Wavelength

42

Resultant group-velocity dispersion

Dispersion 0

Dispersion

normal

Dispersion

anomalous

Wavelength

Gro

up

velo

city

dis

pe

rsio

n

Bandgap

Waveguide GVD

Remember…waveguide

dispersion arises because

core size is fixed while

wavelength changes…

-15

-10

-5

0

5

10

0 0.5 1 1.5 2


GV

D (p

s/(n

m.k

m)

Bandgap fibres operate in this regime, so

waveguide dispersion is always anomalous

43

Effect of waveguide dispersion

Dispersion 0

Dispersion

normal

Dispersion

anomalous

Wavelength

Gro

up

ve

locity d

isp

ers

ion

+ material dispersion

Bend loss

• Cladding density of

states (DOS) plot

• Fundamental core

guided mode shown in

yellow

• Even and odd

bandgaps suffer

different bend loss

• Varying ‘depth’ , n

44

Cladding

modes LPl,m

• Decay rate determines

how strongly the rod

modes couple

• For l=0 modes does

not decay, strongly

coupled

• For l=1 does decay,

weakly coupled

Evolution of the ring

band gaps

45

THE RING FIBRE

Comparison of rods

and rings

16 14 12 10 8 16 14 12

-50

-40

-30

-20

-10

0

600 800 1000 1200 1400 1600

wavelength (nm)

tra

ns

mit

ted

sig

na

l(d

B)

-50

-40

-30

-20

-10

0

450 550 650 750 850 950 1050

wavelength (nm)

tra

nsm

itte

dsig

na

l(d

B)

16 14 12 10 8 16 14 12

-50

-40

-30

-20

-10

0

600 800 1000 1200 1400 1600

wavelength (nm)

tra

ns

mit

ted

sig

na

l(d

B)

-50

-40

-30

-20

-10

0

450 550 650 750 850 950 1050

wavelength (nm)

tra

nsm

itte

dsig

na

l(d

B)

46

“Pencil” fibre

How to make an air-guide

High index rods

Air

core

Air

47

How to make an air-guide

High index rods

Air

Band gaps in a silica/air

photonic crystal

6 8 10 12 14 16 18 20

k pitch

0.6

0.8

1

1.2

1.4

ffe

n

Edge of computational window

No modes

Band gap

Effective index of cladding material

Outside computational window

6 8 10 12 14 16 18 20

k×pitch

neff

1.4

1.2

1

0.8

0.6

48

How to fabricate a hollow-core

fibre

A round core can be

formed by:

Omitting 1 unit cell (too

small)

Omitting 7 cells

Omitting 19 cells

Omitting 37 cells…

etc.

Working hollow-core fiber…

R. F. Cregan et al, Science 285 1537 (1999)

C. M. Smith et al, Nature 424 657 (2003)

49

Modelled Fabricated

Air mode guided

in a band gap

Hollow-core fiber

1000 1100 12000

40

120

80

Wavelength (nm)

Att

enuat

ion (

dB

/km

)

= 3 m

FF > 90%…with 7-cell defect

50

Near field patterns – 60m length

Linear color map

Higher-order modes – 1

meter length

Linear color map

51

Hollow-core fiber

What determines minimum

attenuation?

• Light is scattered out of

fundamental mode, into (core-

) guided or (cladding-)

propagating modes

• Scattering is due to small-

scale irregularities/roughness

on glass surface

Hollow-core fiber guiding green

light

52

Band gap is visible!

input

output

Band

gap

Band gap is visible!

output

Band

gap

53

Measure the scattering as

a function of

Computed

and observed

bandgaps

F. Couny et al, Opt. Express, 13 558 (2005)

54

Hollow-core fiber

1000 1100 12000

40

120

80

Wavelength (nm)

Att

enuat

ion (

dB

/km

)

= 3 m

FF > 90%…with 7-cell defect

900 950 1000 1050 1100 1150 1200

-6

-5

-4

-3

-2

-1

0

Tra

nsm

itte

d s

pectr

um

(dB

)

Wavelength (nm)

Loss peaks in transmitted

spectrum

Low loss window

Extent of band gap

Surface

mode

crossings

55

Two classes of core-guided modes

Frequency

Mo

de

Ind

ex

Guided air modes

Guided air mode

Computed

and observed

bandgaps

F. Couny et al, Opt. Express, 13 558 (2005)

-48

-43

-38

-33

-28

3.88 3.93 3.98 4.03 4.08 4.13

k/ m-1

Tra

nsm

itte

d i

nte

nsit

y (

dB

)

56

900 950 1000 1050 1100 1150 1200

-6

-5

-4

-3

-2

-1

0

Tra

nsm

itte

d s

pectr

um

(d

B)

Wavelength (nm)

Loss peaks in

transmitted

spectrum: short fibre

900 910 920 930 940 950 960 970 980 990 1000

-10

-8

-6

-4

-2

0

Tra

nsm

itte

d s

pectr

um

(dB

)

Wavelength (nm)

• Loss peaks

correspond to anti-

crossings with

surface modes

• Actual bandgap is

wider than low-loss

region

Attenuation in hollow-core fibres

Lowest reported attenuation: 1.2dB/km

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

0 10 20 30 40

Hole diamet er - m

Capillary

"guidance"

Conventional fiber

-3dB length is mm

-3dB length is 10’s km

1.2dB/km

7-cell core

design

19-cell core

57

Low-loss fibres: larger core

• Attenuation is due to

scattering from glass

• Larger cores reduce

overlap of mode with glass

• Overlap remains sensitive

to core surroundings

• In particular, core wall

thickness must be carefully

chosen

Fiber with 19-cell hollow core

Mode profile in a 19-cell hollow

core

-40

-30

-20

-10

0

-30.0 -20.0 -10.0 0.0 10.0 20.0 30.0

Position [ m]

No

rma

lise

d in

tensity [

dB

]

Cladding decay

9.5 dB/

Fraction of light in

core : 98.4%

cladding holes : 1%

glass : 0.6%

log scale, 40 dB range

P. J. Roberts et al, Opt. Express 13 236 (2005)

58

Attenuation in a large-core fibre

• Attenuation is due to glass

• Larger cores reduce

overlap of mode with glass

• Overlap is sensitive to

core surroundings

• But larger core perimeters

support a higher density of

surface modes…

0

5

10

15

20

25

30

1500 1550 1600 1650

Wavelength (nm)

Att

enuat

ion (

dB

/km

)

What limits the attenuation?

• Scattering by roughness at the silica/air surfaces is very strong, because of the massive dipole moment

• Such roughness is probably intrinsic, due to frozen-in and thermally-excited capillary waves. These result in the observed scattering

1

10

100

1000

10000

100000

30 50 70 90 110 130 150

angle in silica deg.

Scatt

ere

d s

ign

al

P. J. Roberts, Opt. Express 13 236 (2005)

Angular distribution of

scattered light

59

What can be done to reduce

scattering?

• Obvious – reduce overlap of the guided mode with

the core walls!!

Core

Core wall

Cladding

Core wall must be

made anti-resonant

as well!

24 1t

nCore wall thickness must be

Wavelength dependence of

attenuation

1

10

100

1000

10000

400 500 630 780 1000 1260 1580 2000

Wavelength [nm]

7-cell fibre

19-cell fibre

-3

60

0.01

0.10

1.00

10.00

MINIMUM ATTENUATION

WAVELENGTHA

ttenuation [dB

/km

]

Wavelength [nm]

B=50 m

1820 2220

IR = A exp(-B/ )

1540

PCF, light in

glass 1%-3All silica

1.7 dB/km

HC fiber

1/ scale

20dB

Comparison of 7-cell and 19-cell

HC designs

0

5

10

15

20

25

30

1500 1520 1540 1560 1580 1600 1620 1640 1660 1680 17001500 1550 1600 1650 1700

Wavelength (nm) Wavelength (nm)

Attenuation (

dB

/km

)

Attenuation (

dB

/km

)

Wavelength (nm)

61

1

10

100

1000

2.5 3.0 3.5

Wavelength ( m)

Att

enu

atio

n (

dB

m-1

)

Attenuation of bulk silica

Mid-Infrared beam delivery

using a silica fibre

• Hollow-core fibre for

the mid-IR

• 43 m core, 8 m

pitch, 160 m OD

62

Mid-Infrared beam delivery

using a silica fibre

J. Shephard et al, Opt. Express 13 7139 (2005)

Silica-based fibre with just 1/50th

the attenuation of bulk silica

2700 2800 2900 3000 3100 3200 3300 3400 35000.0

5.0x10-7

1.0x10-6

1.5x10-6

2.0x10-6

Sig

nal / n

A

Wavelength / nm

3080nm

< 1dB/m

Reviews: J. C. Knight, Nature, 424, 847 (2003)

P. St. J. Russell, Science 299, 358 (2003)

Classic papers: J. C. Knight et al. “Photonic bandgap guidance in optical fibers” Science 282, 1476 (1998)

R. F. Cregan et al. “Single-mode photonic bandgap guidance of light in air”, Science 285, 1537 (1999)

N. M. Litchinitser et al., “Antiresonant reflecting photonic crystal optical waveguides,” Opt. Lett. 27, 1592 (2002).

D. G. Ouzounov et al. “Generation of megawatt optical solitons in hollow-core photonic bandgapfibers” Science 301, 1702 (2003)

Topical work: R. Amezcua-Correa et al. “Optimizing the usable bandwidth and loss through core design in realistic hollow-core photonic bandgap fibers” Opt. Express 14, 7974 (2006)

J. Atai et al. “Stability and collisions of gap solitons in a model of a hollow optical fiber“ Opt. Commun. 265, 342 (2006)

C. K. Nielsen et al. “A 158 fs 5.3 nJ fiber-laser system at 1 m using photonic bandgap fibers for dispersion control and pulse compression” Opt. Express 14, 6063 (2006)

J. M. Stone et al., “An improved photonic bandgap fiber based on an array of rings“ Opt. Express 14,6291 (2006)

C. Peucheret, “Demodulation of DPSK signals up to 40 Gb/s using a highly birefringent photonic bandgap fiber” IEEE Photon. Technol. Lett. 18 1392 (2006)

A. Wang et al. “Three-level neodymium fiber laser incorporating photonic bandgap fiber“ Opt. Lett. 31 1388 (2006)

G. Bouwmans et al. “Fabrication and characterization of an all-solid 2D photonic bandgap fiber with a low-loss region (< 20 dB/km) around 1550 nm” Opt. Express 13 8452-8459 (2005)

Selected background reading

63

Photonic crystal fibres:

The third part

More applications

Things to do with photonic crystal

fibres …

• High power lasers

• Modelocked lasers

• Pulse and beam delivery and

manipulation

• Others

64

PCF fibre laser

PCF in a fibre laser

PCF with a fibre laser

PCF fibre laser

• Very high numerical aperture for cladding

• Leads to relatively small inner cladding

diameters

• As a result, large ratio core/cladding

•…and short pump absorption length

65

Inner cladding NA

Pure

silica“Holey”

silica

??Refr

active index

Outer cladding is made of slab

waveguides

0

0.2

0.4

0.6

0.8

1

-6 -4 -2 0 2 4 6

Distance x /w

Inte

nsi

ty

0.1

0.2

0.3

Effective index is just

of slab waveguide modes

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Nu

me

rica

l A

pe

rtu

re

w /

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

effnk

w/ ratio

66

Example: Limpert et al

J. Limpert et al, Opt. Express 13 1055 (2005)

• Yb3+-doped core diameter 35 m

• Inner cladding diameter 120 m

• Numerical aperture 0.6

• Fibre length 48 cm

• Pumped from one end

• Output power up to 120W

• 74% slope efficiency

PCF in a fibre laser…

• Want to make use of some special

property of the fibre, without completely

replacing existing gain medium

• Examples are dispersion

characteristics, spectral transmission

67

Mode-locked fibre lasers

• For mode-locked operation, want total

round-trip dispersion to be close to zero.

This is usually achieved by having

opposite signs of dispersion in different

parts of the cavity loop

• Mode-locking mechanisms are many,

but some of the most popular are

nonlinear polarisation evolution, SESAM

Reminder about GVD

In plain silica: GVD is anomalous at wavelengths longer than 1300nm, and

normal at shorter wavelengths

In conventional fibres: GVD is always normal at wavelengths shorter than

1300nm. It can be normal at longer wavelengths too through fibre design.

However, it is usually anomalous at wavelengths around 1550nm

In solid-core PCF: GVD can be anomalous at any wavelength longer than

about 500nm, through fibre design.

In photonic bandgap fibres: GVD is normal on the short-wavelength side of

each transmission window, and anomalous on the long-wavelength side

68

Example: modelocked fibre

lasers

#1 – solid core fibre

H. Lim et al, Optics Express 10 1497 (2002)

• Yb-based soliton fiber laser

• Uses PCF for anomalous dispersion

around 1 m wavelength

• Yb-doped fibre allows nonlinear

polarisation evolution, PCF in

principle maintains polarisation

• Mode-locking initiated by AOM, but

runs stably thereafter

• Still some excitation of perpendicular

fibre mode, limits performance

Example: modelocked fibre

lasers

#2 – hollow core fibre

• Sigma-type cavity

• Consists of a PM loop and a linear

part for NPE

69

Intracavity filter for 3-level fibre

laser

PumpUsual 4-level

transition (1.06 m)

Desired 3-level

transition (910 m)

Neodymium energy levels

808 n

m

4I9/2

4I11/2

4I13/2

4I15/2

4F3/2

4F5/2

Intra-cavity filter for 3-level

laserNeed: strong suppression at 1.06 m

Low attenuation at 808 nm


low-loss splices to gain fibre

One widely-used solution: use a W-index fiber

(which has a fundamental-mode cut-off).

Works reasonably well, but cannot provide a strong

and sharp discrimination.

70

Intra-cavity filter for 3-level

laser

600 800 1000 1200 1400

-30

-25

-20

-15

-10

-5

0

fiber length: 10 cmInsert

lo

ss (

dB

)

Wavelength (nm)

Pump

808 nm

3-level

transition

4-level

transition

Need: strong suppression at 1.06 m



low-loss splices to gain fibre

3-level neodymium fiber laser

Nd fiber SMF 1060 BGF

Splice 1 2

Fresnel

Reflection

R~4%

M2

>95% Reflectivity

Pump

850 900 950 1000 1050 1100 1150 1200-90

-80

-70

-60

-50

-40

-30

-20

-10

0

10

Rela

tive in

ten

sit

y (

dB

)

Wavelength (nm)

0 200 400 600 8000

50

100

150

200

250

slope efficiency: 32%

Outp

utpow

er(m

w)

Launched pump power(mw)

71

Effect of intra-cavity PBGFR

ela

tive inte

nsity –

dB

scale

No PBGF

PBGF 1

PBGF 2

Wavelength (nm)

PCF with a fibre laser

• Either for beam delivery, or for beam

transformations

– Examples: high-power femtosecond pulse

delivery, high power transmission, pulse

compression, supercontinuum

generation…

72

Linear use of HC dispersion…

C.J.S. de Matos

et al., Opt. Lett.,

30 436 (2005)

20kW peak

power

C. Billet et al., Optics Express,

13 3236 (2005)

For CPA recompression…

and parabolic pulse compression…

Group velocity dispersion at

800nm wavelength

1.00

1.01

1.02

1.03

1.04

1.05

1.06

1.07

730 750 770 790 810 830 850

Wavelength (nm)

Gro

up

in

de

x

-1500

-1000

-500

0

500

1000

1500

D (p

s.n

m-1.k

m-1)

0.2

0.4

0.6

740 780 820 860Wavelength(nm)

Att

en

ua

tio

n(d

B/m

)

Dispersion

Group index

Soliton regime

73

Beam control

Amplified

TiSapph

system

Pulse

analysis

5m fibre

60nJ – minimum output pulse

length < 300fs after 5m of fibre

Delivering short pulses at 800nm

wavelength

Nonlinear response 1000 times less than standard fibres!!

Able to deliver short pulses at 800nm through a fibre!!

0

500

1000

1500

2000

2500

3000

0 50 100 150

Output pulse energy (nJ)

Deco

nvo

lved

au

toco

rrela

tio

n len

gth

(fs)

Soliton self-frequency shift in

hollow-core

0

0.2

0.4

0.6

0.8

1

770 780 790 800 810 820 830

Wavelength (nm)

Inte

ns

ity

(n

orm

ali

ze

d)

input

20 nJ

40 nJ

60nJ

80nJ

100nJ

120nJ

Origin of SSFS is Raman

response of gas in core, with

lower and much narrower

gain than in silica.

(See D. G. Ouzounov et al.,

Science 301 1702 (2003))

74

Pulse compression

• In the normal dispersion regime, femtosecond pulse

propagation is dominated by self-phase modulation

• This can be used to compress pulses…

McConnell et al., Appl. Phys. B 78 557 (2004). See also Schenkel et al, JOSA B 22 687 (2005)

250fs pulses Nonlinear fibre

Grating

compensatorAutocorrelator

25fs pulses

Pulse compression in hollow-core

fibre

D. Ouzounov et al. Opt. Express 13, 6153 (2005)

• Use Xe to avoid SSFS (no Raman)

• Use elevated pressures to increase n2

• Use high powers to be well above

fundamental soliton energy

• Peak power is several MW

• Using 120fs pulses, compression is

limited by higher-order dispersion

• Using ps input pulses, much higher

compression ratios would be possible

75

Spectral compression

M. Rusu et al., Appl. Phys. Lett. 89, 091118 (2006)

• Nonlinear spectral compression uses

self phase modulation to compress

pulses

• Remember, in a Kerr medium with

positive n2, the leading edge of the pulse

is red-shifted. So a chirped pulse with

blue components at the front and red

components at the back will be spectrally

compressed

• This can lead to transform-limited longer

pulses

“Adiabatic” soliton compression

3

0 2

2

1.762

eff

sol

DA

cn E

Tse et al.,Opt. Lett. 31 3504 (2006)

Soliton length

Soliton energy

DispersionNonlinear

effective

area In a tapered fibre…assuming

no losses, energy remains

fixed…assuming area

remains fixed, if D gets

smaller, soliton length gets

smaller too!

This is “adiabatic” soliton

compression

76

“Conventional” PCF-based supercontinuum generation…

W. J. Wadsworth et al. Opt. Express 12 299 (2004)

• Pump at or close to the zero-GVD

wavelength (in this example,

1.06 m)

• Supercontinuum spreads through

sequential processes to longer and

shorter wavelengths

• Blue/uv extent is limited by phase

matching, group index matching etc.

Tapered fibre supercontinuum

generation

Solution: let the fibre evolve with

the spectrum…

• Fibre is tapered so that zero-GVD

wavelength changes along the

length

• At input end, chosen to match to

pump wavelength,

• As higher frequencies are

generated along the fibre length,

the zero-gvd wavelength evolves

to continue efficient nonlinear

generation

• Taper length depends on pump

source and attenuation

D = 5 m

D = 1 m

10

-20

m

A. Kudlinski et al., Opt. Express 14, 5715-5722 (2006)

77

Gas-phase fibre optics

F. Benabid et al, Nature 434 488 (2005)

HC-smf

splice

All-fibre

gas cell

Suitable for absorption-based

frequency standards, Raman

convertors, laser-atom interactions,

gas-based lasers?…

Current work: D. Ouzounov et al. “Soliton pulse compression in photonic bandgap fibers” Opt. Express 13,6153 (2005)

G. McConnell et al., “Ultra-short pulse compression using photonic crystal fibre” Appl. Phys. B 78 557 (2004).

B. Schenkel et al. “Pulse compression with supercontinuum generation in microstructure fibers“ JOSA B 22, 687 (2005)

A. Wang et al., “ "Three-level neodymium fiber laser incorporating photonic bandgap fiber," Opt. Lett. 31, 1388-1390 (2006)

Tse et al., “Pulse compression at 1.06 m in dispersion-decreasing holey fibers” Opt. Lett. 31 3504 (2006)

F. Benabid et al.,

M. Rusu et al., "All-fiber picosecond laser source based on nonlinear spectral compression," Appl. Phys. Lett. 89, 091118 (2006).

J. Limpert et al., "High-power picosecond fiber amplifier based on nonlinear spectral compression," Opt. Lett. 30, 714-716 (2005).

C.J.S. de Matos et al., “20-kW peak power all-fiber 1.57-µm source based on compression in air-core photonic bandgap fiber, its frequency doubling, and broadband generation from 430 to 1450 nm” Opt. Lett., 30 436 (2005)

C. Billet et al., “Intermediate asymptotic evolution and photonic bandgap fiber compression of optical similaritons around 1550 nm ” Optics Express, 13 3236 (2005)

F. Benabid et al, Nature 434 488 (2005)

A. Kudlinski et al., Opt. Express 14, 5715-5722 (2006)

Selected background reading

Documents

Photonic crystal fibres