Photonic crystal fibres.
Transcript of 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
Wavelength/core radius
GV
D (p
s/(n
m.k
m)
Overview of this lecture
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
Overview of this lecture
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
Overview of this lecture
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
Overview of this lecture
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
Wavelength/core radius
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
Wavelength (microns)
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
Wavelength (microns)
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
Wavelength (microns)
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
Wavelength (microns)
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
Wavelength (microns)
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
Wavelength (microns)
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
Energy exchange between
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
Energy exchange between
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
Overview of this lecture
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
Wavelength/core radius
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 attenuation at 910 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 attenuation at 808 nm
Low attenuation at 910 nm
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