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![Page 1: Hollow core planar waveguides and multilayers Prof. M. Skorobogatiy, review for the course ‘Introduction to Photonic Crystals’ École Polytechnique de Montréal.](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649d0e5503460f949e42f0/html5/thumbnails/1.jpg)
Hollow core planar waveguides and multilayers
Prof. M. Skorobogatiy, review for the course
‘Introduction to Photonic Crystals’
École Polytechnique de Montréal
Montréal, QC, Canada
![Page 2: Hollow core planar waveguides and multilayers Prof. M. Skorobogatiy, review for the course ‘Introduction to Photonic Crystals’ École Polytechnique de Montréal.](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649d0e5503460f949e42f0/html5/thumbnails/2.jpg)
2
~D
T
R
I=1
R2
R3
R4
T
D2/
D
T T
21
10 2
( ) / (1 ) (1 )
10log ( ( ) / ) [ / ]
bounce
L LL D
o
o
I L I T T
TLoss I L I dB m
L D
TIR silica fiber D=10m =1.55m, loss=0.2dB/km
T=10-6-10-5
Hollow core planar waveguide, scaling relations
REFLECTOR
![Page 3: Hollow core planar waveguides and multilayers Prof. M. Skorobogatiy, review for the course ‘Introduction to Photonic Crystals’ École Polytechnique de Montréal.](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649d0e5503460f949e42f0/html5/thumbnails/3.jpg)
3 Metallic reflectors
Simplest mirrors present thin layers of metals such as aluminum deposited on glass substrates. Choice of metals will determine reflection characteristics of a mirror.
• Aluminum is the cheapest and least expensive material with a coefficient of reflection of 88%-92% in the visible.
• More expensive is silver with reflectivity of 95%-99% even in the IR, while less than 90% in the blue and UV.
• Most expensive is gold with an excellent reflectivity of 98%-99% in the IR, while poor reflectivity below 550 nm.
Metallic Reflector
Omnidirectional reflection, high material loss in the IR
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4 Losses of hollow metallic waveguides
D=100m; =1-10m; T=10-2
Losses=1-10 dB/m
T
R
I=1
D
REFLECTOR
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5
1
1
90o0 tan-1(nh/nl)
p-pols-pol2
h l
h l
n n
n n
Reflectance
Contraste d’indice s’augmente
Conventional Dielectric Mirrors
Very low material absorption loss, strong dependence of
reflection characteristics on the light polarization
SiO2-air0.04
AsSe-air0.22
nl
nh
Contraste d’indice s’augmente
Dielectric reflectors
Dielectric mirrors are characterised by very low absorption losses, but their reflection characteristics are strongly dependent of the angle of radiation incidence and polarization. For the s-polarized light reflectivity increases monotonically with an increase of an angle of incidence. However, for a p-polarised light reflectivity goes through zero at a so called Brewster angle.
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6 Losses of hollow dielectric waveguides
2,
2 3
5 10[ / ] [ / ]
ln(10) ln(10)
4;
TE TMTE
c c r c
c r rTE TM TE TM TE
cr c c
TLoss dB m Loss dB m
n D Dn
nT T T Loss Loss
cn
D=100m; =1-10m;
nc=1; nr=1.5
LossesTE=0.04-4 dB/cm
T
R
I=1
D
REFLECTOR
~Drn
cn
![Page 7: Hollow core planar waveguides and multilayers Prof. M. Skorobogatiy, review for the course ‘Introduction to Photonic Crystals’ École Polytechnique de Montréal.](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649d0e5503460f949e42f0/html5/thumbnails/7.jpg)
7 ARROW waveguides
=1.55mm
LossesTE=0.2 dB/cm
![Page 8: Hollow core planar waveguides and multilayers Prof. M. Skorobogatiy, review for the course ‘Introduction to Photonic Crystals’ École Polytechnique de Montréal.](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649d0e5503460f949e42f0/html5/thumbnails/8.jpg)
8 ARROW multilayer waveguides
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9
D. Yin et al. 14 June 2004 / Vol. 12, No. 12 / OPTICS EXPRESS 2710
dc~3.7m
12m
Capillary1 layer
2 layers3 layers
Sensor applications - putting the light where the analyte (gas) is
Planar antiresonant reflecting optical (ARROW) waveguides, SiN/SiO2 (2.1/1.46)
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Omnidirectional reflectorsOR
high index contrast multilayers
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11
6 9 1 2 1 50
5 0
1 0 0
0
5 0
1 0 0
0
5 0
1 0 0
0
5 0
1 0 0
0
5 0
1 0 0
normal
450 s
450 p
800 p
800 s
Wavelength (microns)
Te / polystyrene
normal=0o
=90o
Ep
Es
Omnidirectional Dielectric Mirrors
Reflection for all angles of incidence and polarizations
Multilayer dielectric reflectors
Omnidirectional reflection - for any incoming polarization and any angle of incidence radiation is completely reflected in a certain frequency band.
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12 Omnidirectional dielectric reflectors
normal=0o
=90o
Ep
Es
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13
normal=0o
=90o
Ep
Es
Omnidirectional dielectric reflectors
cω = β/n
cncω = β/n
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14
normal=0o
=90o
Ep
Es
Omnidirectional dielectric reflectors
cω = β/n
cn
cω = β/n
When cladding index nc is increased beyond a critical value, omnidirectional reflectivity is lost.
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Omnidirectional reflectorsSURPRIZE !!!
low index contrast multilayers
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16 All-polymer multilayers
nl
nh
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17 Giant birefringence polymer multilayers
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18 Giant birefringence polymer guides