Photonic-Crystal Fibers Photonic Crystals: Periodic Surprises in Electromagnetism A Long and Winding Road

Photonic Crystals:
Periodic Surprises in Electromagnetism
Steven G. Johnson
MIT
A Long and Winding Road
Photonic-Crystal Fibers
1/31/02 INSPEC
literature search:
14810 hits
458604 hits
87652 hits
Bloch’s theorem is more important
than Maxwell’s equations ;^)
Optical Fibers Today
(not to scale)
losses ~ 0.2 dB/km
more complex profiles
to tune dispersion
“high” index
doped-silica core
n ~ 1.46
silica cladding
n ~ 1.45
(amplifiers every
50–100km)
“LP01”
confined mode
field diameter ~ 8µm
protective
polymer
sheath
[ R. Ramaswami & K. N. Sivarajan, Optical Networks: A Practical Perspective ]
but this is
~ as good as
it gets…
The Glass Ceiling: Limits of Silica
Loss: amplifiers every 50–100km
…limited by Rayleigh scattering (molecular entropy)
…cannot use “exotic” wavelengths like 10.6µm
Nonlinearities: after ~100km, cause dispersion, crosstalk, power limits
(limited by mode area ~ single-mode, bending loss)
also cannot be made (very) large for compact nonlinear devices
Radical modifications to dispersion, polarization effects?
…tunability is limited by low index contrast
Long Distances
High Bit-Rates
Compact Devices
Dense Wavelength Multiplexing (DWDM)
Breaking the Glass Ceiling:
Hollow-core Bandgap Fibers
Bragg fiber
1000x better
loss/nonlinear limits
[ Yeh et al., 1978 ]
(from density)
1d
crystal
+ omnidirectional
= OmniGuides
2d
crystal
Photonic Crystal
(You can also
put stuff in here …)
PCF
[ Knight et al., 1998 ]
Breaking the Glass Ceiling:
Hollow-core Bandgap Fibers
Bragg fiber
[ Yeh et al., 1978 ]
[ figs courtesy
Y. Fink et al., MIT ]
white/grey
= chalco/polymer
+ omnidirectional
= OmniGuides
silica
[ R. F. Cregan
et al.,
Science 285,
1537 (1999) ]
5µm
PCF
[ Knight et al., 1998 ]
Breaking the Glass Ceiling:
Hollow-core Bandgap Fibers
Guiding @ 10.6µm
[ figs courtesy
Y. Fink et al., MIT ]
(high-power CO2 lasers)
loss < 1 dB/m
white/grey
= chalco/polymer
(material loss ~ 104 dB/m)
[ Temelkuran et al.,
Nature 420, 650 (2002) ]
silica
[ R. F. Cregan
et al.,
Science 285,
1537 (1999) ]
5µm
Guiding @ 1.55µm
loss ~ 13dB/km
[ Smith, et al.,
Nature 424, 657 (2003) ]
OFC 2004: 1.7dB/km
BlazePhotonics
Breaking the Glass Ceiling II:
Solid-core Holey Fibers
solid core
holey cladding forms
effective
low-index material
Can have much higher contrast
than doped silica…
strong confinement = enhanced
nonlinearities, birefringence, …
[ J. C. Knight et al., Opt. Lett. 21, 1547 (1996) ]
Breaking the Glass Ceiling II:
Solid-core Holey Fibers
endlessly
single-mode
[ T. A. Birks et al.,
Opt. Lett. 22,
961 (1997) ]
polarization
-maintaining
[ K. Suzuki,
Opt. Express 9,
676 (2001) ]
nonlinear fibers
[ Wadsworth et al.,
JOSA B 19,
2148 (2002) ]
low-contrast
linear fiber
(large area)
[ J. C. Knight et al.,
Elec. Lett. 34,
1347 (1998) ]
Omnidirectional Bragg Mirrors
a 1d crystal can reflect light from
all angles and polarizations
[ Winn, Fink et al. (1998) ]
…it behaves
like a metal
(but at any wavelength)
perfect metal
OmniGuide Fibers
omnidirectional mirrors
c.f. Photonic Bandgap Fibers
& Devices Group @ MIT
(also a Cambridge MA
start-up: www.omni-guide.com)
[ S. G. Johnson et al., Opt. Express 9, 748 (2001) ]
Hollow Metal Waveguides, Reborn
G
are
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needed
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decom
toand
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pressor
athis picture.
G
are
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decom
e™
toand
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pressor
athis picture.
metal waveguide modes
OmniGuide fiber gaps
frequency w
G
are
Qraphics
uickTim
needed
decom
e™
toand
see
pressor
athis picture.
1970’s microwave tubes
@ Bell Labs
wavenumber b
wavenumber b
Hollow Metal Waveguides, Reborn
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pressor
athis picture.
G
are
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needed
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e™
toand
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pressor
athis picture.
metal waveguide modes
OmniGuide fiber modes
frequency w
G
are
Qraphics
uickTim
needed
decom
e™
toand
see
pressor
athis picture.
1970’s microwave tubes
@ Bell Labs
wavenumber b
wavenumber b
modes are directly analogous to those in hollow metal waveguide
An Old Friend: the TE01 mode
lowest-loss mode,
just as in metal
E
(near) node at interface
= strong confinement
= low losses
from metal:
optimal R ~ 10l
R
Here, use R=13µm for l=1.55µm … n=4.6/1.6 (any omnidirectional is similar)
TE01 vs. PMD
non-degenerate mode, so
cannot be split
i.e. immune
to birefringence
i.e. PMD is zero
E
Let’s Get Quantitative
…but what about
the cladding?
Gas can have
low loss
& nonlinearity
…some field
penetrates!
& may need to use
very “bad” material
to get high index contrast
Let’s Get Quantitative
Absorption (& Rayleigh Scattering)
= small imaginary De
Nonlinearity
= small De ~ |E|2
Acircularity, bending, roughness, …
= small perturbations
Hard to compute directly
… use Perturbation Theory
Perturbation Theory
Given solution for ideal system
compute approximate effect
of small changes
…solves hard problems starting with easy problems
& provides (semi) analytical insight
Perturbation Theory
for Hermitian eigenproblems
Oˆ u  u u
Du & D u for small DOˆ
given eigenvectors/values:
…find change
Solution:
DOˆ
(1)
(2 )
Du  0  Du  Du  
expand as power series in
Du
(1)
u DOˆ u

uu
(1)
& D u  0  D u 
(first-order is usually enough)
Perturbation Theory
for electromagnetism
Dw
ˆ H
c H D

2w H H
2
(1)
w  De E

2
2 e E
Db
(1)
 Dw / vg
(1)
2
…e.g. absorption
gives
imaginary Dw
= decay!
dw
vg 
db
Suppressing Cladding Losses
G
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needed
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decom
toand
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pressor
athis picture.
G
are
Qraphics
uickTim
needed
decom
e™
toand
see
pressor
athis picture.
G
are
Qraphics
uickTim
needed
e™
decom
toand
see
pressor
athis picture.
-2
1x1
0
G
are
Qraphics
uickTim
needed
decom
e™
toand
see
pressor
athis picture.
Bu
lk C
l add
i ngLoss
es:
ModeLoss
es
11
EH
-3
/
1x1
0
La
r ge
G
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decom
toand
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pressor
athis picture.
dif er e
nt ialoss
TE
str ong
ly su
ppr e
ssed
01
claddin
g los
-4
!
1x1
0
TE
01
( like oh
m iclosse
s)
1x1
0
-5
1.2
1.6
2
l
(µm )
2.4
2.8
G
are
Qraphics
uickTim
needed
decom
e™
toand
see
pressor
athis picture.
Suppressing Cladding Nonlinearity
G
are
Qraphics
uickTim
needed
decom
e™
toand
see
pressor
athis picture.
*
G
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decom
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toand
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pressor
athis pictur
-6
1x1
0
Cladding N
onl ineari t y:
ModeNonli nea
ri t y
/
1x1
0
Wil be
-7 are
G
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needed
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e™
toand
see
pressor
athis picture.
do
m ina
t edby
no
nlinea
r it yof a
ir
TE
01
-8
~1
0, 00
0 t imesweaker
1x1
0
no
nlinea
r it yt hansilica
(including
factor of 10 in area)
1x1
0
* “nonlinearity” = Db(1) / P
-9
1.2
1.6
2
l
(µm )
2.4
2.8
G
are
Qraphics
uickTim
needed
e™
decom
toand
see
pressor
athis picture.
Absorption & Nonlinearity Scaling
G
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Qraphics
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decom
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toand
see
pressor
athis picture.
-2
1x10
-3
J
J
1x10
J
J
J
3
G
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pressor
athis picture.
cla dding absorpt i o
n ~1/ R
J
J
-4
1x10
J
J J
J J J
J J J
J J J J
J JJJ
( li ke m eta l o
hm ic l o
ss! )
-5
1x10
B
-6
1x10
-7
B
B
B
B
B
B
B B
B B
B B
BB
BB
BB
BB
BB
B
cla dding n
onl ineari t y~ 1/R
1x10
-8
1x10
-9
1x10
3
core radius (µm)
10
13
5
G
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Qraphics
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decom
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toand
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pressor
athis picture.
Radiation Leakage Loss (17 layers)
G
Qre
raphics
uickTim
needed
decom
e™
toand
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pressor
athis picture.
5
1x10
4
leakage loss (dB/km)
1x10
mo
desar e“l ea
ky”
3
1x10
Finite #layers:
1x10
loss
dec
r eas
es
2Qraphics
are
G
uickTim
needed
e™
decom
toand
see
pressor
athis picture.
1
1x10
exp
onen
t ialy
wit hnumber of layers
0
1x10
-1
1x10
3
( ~1/ R
-2
)
1x10
-3
1x10
1x10
-4
1.2
1.6
2
l
(µm )
2.4
2.8
ther Losses
Acircularity & Bending
main effect is coupling to lossier modes,
but can be ~ 0.01 dB/km with enough (~50) layers
tricky
Surface Roughness
suppressed like absorption
Acircularity & Perturbation Theory
(or any shifting-boundary problem)
De = e1 – e2
e2
e1
De = e2 – e1
… just plug De’s into
perturbation formulas?
FAILS for high index contrast!
beware field discontinuity…
fortunately, a simple correction exists
[ S. G. Johnson et al.,
PRE 65, 066611 (2002) ]
Acircularity & Perturbation Theory
(or any shifting-boundary problem)
De = e1 – e2
e2
De = e2 – e1
e1
(continuous field components)
Dh
Dw
(1)


w surf.
2

1
2
2
Dh De E||  D D 


e
eE
2
[ S. G. Johnson et al.,
PRE 65, 066611 (2002) ]
Yes, but how do you make it?
[ figs courtesy Y. Fink et al., MIT ]
1
find compatible materials
3
(many new possibilities)
2
Make pre-form
(“scale model”)
chalcogenide glass, n ~ 2.8
+ polymer (or oxide), n ~ 1.5
fiber drawing
Fiber Draw Tower @ MIT
building 13, constructed 2000–2001
~6 meter
(20 feet)
research
tower
[ figs courtesy Y. Fink et al., MIT ]
A Drawn Bandgap Fiber
[ figs courtesy Y. Fink et al., MIT ]
• Photonic crystal structural
uniformity, adhesion,
physical durability through
large temperature excursions
white/grey
= chalco/polymer
Band Gap Guidance
Wavevector
Transmission
window can be
shifted by scaling
(different draw speed)
original (blue)
& shifted (red)
transmission:
Transmission (arb. u.)
1.2
0.8
0.4
0.0
10000
[ figs courtesy Y. Fink et al., MIT ]
8000
6000
4000
-1
Wavenumber (cm )
2000
High-Power Transmission
at 10.6µm (no previous dielectric waveguide)
Polymer losses @10.6µm ~ 50,000dB/m…
…waveguide losses ~ 1dB/m
Log. of Trans. (arb. u.)
-3.0
Transmission (arb. u.)
8
6
4
-3.5
[ B. Temelkuran et al.,
Nature 420, 650 (2002) ]
-4.0
slope = -0.95 dB/m
R2 = 0.99
-4.5
2.5
3.0
3.5
Length (meters)
4.0
2
cool movie
0
5
5
6
6
7
7
8
8
9
9 10 10
10 11 11
11 12 12
12
Wavelength(m)
(m)
Wavelength
[ figs courtesy Y. Fink et al., MIT ]
Enough about MIT already…
2d-periodic Photonic-Crystal Fibers
[R. F. Cregan et al., Science 285, 1537 (1999) ]
G
are
Qraphics
uickTim
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decom
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toand
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pressor
athis picture.
air holes
Not guided via
2d TE bandgap:
a
0.6
EEJ J J J J J J EE
E
E
E
JE
J JEJEJ JEE
J
JEE
J
JJ
E
J
E
J
E
J
J
J
J
J
E
J
E
E
JJ
J E
E
J
E
E
J
E
JJ
0.5 J J J J J J J J J EEEEEE
J JJJJJ
JJ JJ J
J
J JJJJ JJJ
J
0.4 J J J J
JJJ
J
JJ
JJ
JJ
J
JJ
JJ
0.3
EE
J J JEJEJEJEJEE
E
JE
J
J
J
EEE
J J J J EE
EJ J J J J J J J J
J
EJ
JE
EJ
0.2
JE
EJ
JE
EJ
JE
J TMbands
E
J
0.1
J
E
E
J
TEbands
J
E
E
J
J
J
J
E
0E

M

K
silica
(usually)
b wavenumber breaks mirror plane,
so no pure TE/TM polarizations
PCF: Holey Silica Cladding
r = 0.1a
w (2πc/a)
light cone
b (2π/a)
2r
n=1.46
a
PCF: Holey Silica Cladding
r = 0.17717a
w (2πc/a)
light cone
b (2π/a)
2r
n=1.46
a
PCF: Holey Silica Cladding
r = 0.22973a
w (2πc/a)
light cone
b (2π/a)
2r
n=1.46
a
PCF: Holey Silica Cladding
r = 0.30912a
w (2πc/a)
light cone
b (2π/a)
2r
n=1.46
a
PCF: Holey Silica Cladding
r = 0.34197a
w (2πc/a)
light cone
b (2π/a)
2r
n=1.46
a
PCF: Holey Silica Cladding
r = 0.37193a
w (2πc/a)
light cone
b (2π/a)
2r
n=1.46
a
PCF: Holey Silica Cladding
r = 0.4a
w (2πc/a)
light cone
b (2π/a)
2r
n=1.46
a
PCF: Holey Silica Cladding
r = 0.42557a
w (2πc/a)
light cone
b (2π/a)
2r
n=1.46
a
PCF: Holey Silica Cladding
n=1.46
2r
a
r = 0.45a
light cone
w (2πc/a)
gap-guided modes
go here
index-guided modes
go here
b (2π/a)
PCF: Holey Silica Cladding
r = 0.45a
light cone
2r
n=1.46
a
above air line:
w (2πc/a)
guiding in air core
is possible
[ figs: West et al,
Opt. Express 12 (8), 1485 (2004) ]
b (2π/a)
below air line: surface states of air core
PCF Projected Bands
[ J. Broeng et al., Opt. Lett. 25, 96 (2000) ]
w (2πc/a)
2.4
2.0
band gap
“fingers”
appear!
1.6
1.2
0.8
1.11 1.27
bulk
crystal
continuum
1.43 1.59
1.75
1.91
b (2π/a)
2.07 2.23 2.39
PCF Guided Mode(s)
[ J. Broeng et al., Opt. Lett. 25, 96 (2000) ]
2.4
fundamental & 2nd order
w (2πc/a)
guided modes
2.0
fundamental
air-guided
mode
1.6
1.2
0.8
1.11 1.27
bulk
crystal
continuum
1.43 1.59
1.75
1.91
b (2π/a)
2.07 2.23 2.39
Experimental Air-guiding PCF
Fabrication (e.g.)
silica glass tube (cm’s)
(outer
cladding)
~50 µm
fiber
draw
~1 mm
fuse &
draw
Experimental Air-guiding PCF
[ R. F. Cregan et al., Science 285, 1537 (1999) ]
10µm
5µm
Experimental Air-guiding PCF
[ R. F. Cregan et al., Science 285, 1537 (1999) ]
transmitted intensity
after ~ 3cm
w (c/a) (not 2πc/a)
State-of-the-art air-guiding losses
[Mangan, et al., OFC 2004 PDP24 ]
hollow (air) core (covers 19 holes)
guided field profile:
(flux density)
3.9µm
1.7dB/km
BlazePhotonics
over ~ 800m @1.57µm
State-of-the-art air-guiding losses
larger core =
less field penetrates
cladding
ergo,
roughness etc.
produce lower loss
13dB/km
1.7dB/km
Corning
BlazePhotonics
over ~ 100m @1.5µm
over ~ 800m @1.57µm
[ Smith, et al., Nature 424, 657 (2003) ]
[ Mangan, et al., OFC 2004 PDP24 ]
State-of-the-art air-guiding losses
larger core = more surface states crossing guided mode
100nm
20nm
13dB/km
1.7dB/km
Corning
BlazePhotonics
over ~ 100m @1.5µm
over ~ 800m @1.57µm
[ Smith, et al., Nature 424, 657 (2003) ]
[ Mangan, et al., OFC 2004 PDP24 ]
Index-Guiding PCF & microstructured fiber:
Holey Fibers
solid core
holey cladding forms
effective
low-index material
Can have much higher contrast
than doped silica…
strong confinement = enhanced
nonlinearities, birefringence, …
[ J. C. Knight et al., Opt. Lett. 21, 1547 (1996) ]
Holey Projected Bands, Batman!
w (c/a) (not 2πc/a)
(Schematic)
band gaps
are
unused
bulk
crystal
continuum
guided band
lies below
“crystal light line”
b (a–1)
Guided Mode in a Solid Core
G
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Qraphics
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toand
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pressor
athis picture.
small computation: only lowest-w band!
(~ one minute, planewave)
0.12
1.46 – bc/w = 1.46 – neff
holey PCF light cone
flux density
0.1
0.08
0.06
fundamental
mode
0.04
(two polarizations)
2r
0.02
0
0.3
endlessly single mode: Dneff decreases with l
0.4
0.5
0.6
0.7
0.8
l/a
0.9
1
1.1
1.2
n=1.46
a
r = 0.3a
Holey Fiber PMF
(Polarization-Maintaining Fiber)
birefringence B = Dbc/w
= 0.0014
(10 times B of silica PMF)
Loss = 1.3 dB/km @ 1.55µm
over 1.5km
no longer degenerate with
Can operate in a single polarization, PMD = 0
(also, known polarization at output)
[ K. Suzuki, Opt. Express 9, 676 (2001) ]
Nonlinear Holey Fibers:
Supercontinuum Generation
(enhanced by strong confinement + unusual dispersion)
e.g. 400–1600nm “white” light:
from 850nm ~200 fs pulses (4 nJ)
[ W. J. Wadsworth et al., J. Opt. Soc. Am. B 19, 2148 (2002) ]
Endlessly Single-Mode
[ T. A. Birks et al., Opt. Lett. 22, 961 (1997) ]
at higher w
(smaller l),
the light is more
concentrated in silica
…so the effective
index contrast is less
…and the fiber can stay
single mode for all l!
http://www.bath.ac.uk/physics/groups/opto
Low Contrast Holey Fibers
[ J. C. Knight et al., Elec. Lett. 34, 1347 (1998) ]
The holes can also form an
effective low-contrast medium
i.e. light is only affected slightly
by small, widely-spaced holes
This yields
large-area, single-mode
fibers (low nonlinearities)
…but bending loss is worse
~ 10 times standard fiber mode diameter
Holey Fiber Losses
Best reported results:
0.28 dB/km @1.55µm
[ Tajima, ECOC 2003 ]
G
are
Qraphics
uickTim
needed
decom
e™
toand
see
pressor
athis picture.
TheThe
Upshot
Upshot:
Potential new regimes for fiber operation,
even using very poor materials.
The Story of Photonic Crystals
Finding Materials –> Finding Structures