Diffractive Components for
Gravitational Wave Detectors
Stefanie Kroker
Institute of Applied Physics
Friedrich Schiller University Jena
02.03.2010
S. Kroker
Mirror
Cavity Couplers
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Outline
Introduction
2-Port Cavity Couplers
3-Port Cavity Couplers
Conclusion
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Grating Equation
-1 R
ni sin   n j sin   m / d
0R
Incident
Ray
1R
d… period
ni… refractive index medium of incidence
nj… refractive index propagation medium
of diffracted light
… angle of incidence
… diffraction angle
… wavelength
m=0,±1, ±2,…
1T
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-1 T 0 T
Born, Wolf: Principles of Optics
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Littrow Configuration
-1R
Second Order Littrow
Configuration
-2R
0R
Incident
Ray
0R
Incident
Ray
sin    / d
sin    / 2d
2-Port Cavity Coupler
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-1R
3-Port Cavity Coupler
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Cavity
Incident
Ray
-1R
0R
Incident
Ray
Mirror
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Cavity
-2R
Mirror
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-1R
0R
Mirrors
Resonant Waveguide
Grating
HR-Stack
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2-Port Cavity Coupler
Incident
Ray
-1R
Highly efficient reflection
grating in Littrow mount.
0R
Cavity
Desirable Properties:
R-1≈97%
R0 ≈3%
Mirror
T as low as possible!
highly efficient
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Resonant Waveguide Grating as Mirror
Low Index Material
High Index Material
nL
nH
Resonant Waveguide Grating
Normal incidence:
 / nH  d   / nL
Period upper grating 2 Period waveguide grating
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Optimized
for
diffraction
angle!
Typical Properties
Calculations:
R ≥ 97%
T ≈0.05%
At least achievable
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3-Port Cavity Coupler
Cavity
2nd order Littrow mount:
Incident
Ray
-2R
-1R
0R
sin    / d
Desireable properties:
R0≈95%
R-1≈5%
R-2, T as low as possible
Mirror
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Resonant Waveguide Grating as Mirror
Low Index Material
High Index Material
nL
nH
Waveguide Grating:
 / nH  d   / nL
=1550 nm :
d~600…700 nm
Period upper grating 3 Period waveguide grating
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Upper Grating 3 Ports: d≥
At least 3 diffraction
orders in grating
material!
Problem: Waveguide grating needs to be highly efficient
@ q0, ±q1
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Angular Tolerance of Silicon-Grating on SiO2
1,0
=1550 nm
0,9
Reflectivity
0,8
Waveguide Grating
0,7
dWG= 633 nm
0,6
0,5
Upper Grating
0,4
d3P=1899 nm
0,3
0,2
0
5
10
15
20
25
30
35
40
Angle of Incidence [°]
Diffraction Angle for m=±1 in SiO2
Need to increase
angular tolerance!
q1 ≈±34°
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Idea: Stack of Resonant Waveguide Gratings
Reflectivity
Stack RWG1RWG2
RWG 2
RWG 1
Angle of Incidence
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TM-Polarization
H ll Grating Grooves
Silicon
Silica
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1,0
0,9
0,8
Reflectivity
0,7
0,6
0,5
0,4
0,3
0,2
Lower Grating
Upper Grating
Stack
0,1
0,0
0
10
20
30
40
50
60
Angle of Incidence [°]
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70
80
90
TE-Polarization
E ll Grating Grooves
Silicon
Silica
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1,0
3-Port Grating:
R0≈94.3%
0,8
Reflectivity
R-1 ≈5.3%
R-2 ≈0.3%
0,6
T ≈0.016%
0,4
Lower Grating
Upper Grating
Stack
0,2
0,0
0
10
20
30
40
50
60
Angle of Incidence [°]
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70
80
90
Conclusion
- new concept for grating couplers: HR-Stacks replaced by
resonant waveguide gratings
- 2-port couplers: RWG optimized for diffraction angle of
upper grating
- 3-port couplers: angular tolerance of single RWG not
sufficient to provide low transmission,
stack of two or more RWGs can be used
(can also be used to decrease transmission
of 2-port couplers)
-technical implementation under investigation (T-shape
considered)
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Thank you very much
for your attention!
02.03.2010
S. Kroker