Beams of the Future
Coating Noise - An important problem in GW detectors
Mihai Bondarescu,
Oleg Kogan, Yanbei Chen,
Andrew Lundgreen, Ruxandra Bondarescu, David Tsang
A Caltech - AEI - Cornell Collaboration
http://theory.caltech.edu/~mihai
[email protected]
Overview
• Coating Thermal Noise is the dominant noise source in Advanced
LIGO’s highest sensitivity frequency range.
• Previous Work
» MESA
» Baseline Gaussian
• Our results » reduction in coating noise compared to Mesa
– 12% at nearly no cost
– 28% at a reasonable cost
– 60% in an ideal world where cost is irrelevant
» Side benefits
– Substrate Noise is also lowered dramatically
– Diffraction loss higher in higher modes
Mihai Bondarescu
http://theory.caltech.edu/~mihai
[email protected]
Advanced LIGO design
Mihai Bondarescu
http://theory.caltech.edu/~mihai
[email protected]
Arm Cavities - Current Status
• Circulating power over 830 kw
» Radiation pressure : ~3*10-3 N
» Compare to 9-12 kw and ~ 3-4* 10-5 N in initial LIGO
• Gaussian Beams - Baseline Design
» High thermal noise
» Nearly Flat Spherical Mirrors ( r= 53.7 km)
– To be changed to nearly concentric
• Hyperboloidal beams
» Mesa
» Finite Mirror Effects
• Conical Beams
» Lowest noise
Mihai Bondarescu
http://theory.caltech.edu/~mihai
[email protected]
Noise in LIGO
Coating Thermal
Noise is the leading
noise source in
Advanced LIGO at
100 Hz
It can be reduced.
Mihai Bondarescu
http://theory.caltech.edu/~mihai
[email protected]
Hyperboloidal Beams
• Composed of minimal Gaussians
propagating on generators of coaxial
hyperboloids parametrized by a twist
angle  and falling on the mirror
inside a disk of radius D.
=0 Original Mesa
= No Tilt Instability
=/2 Minimal Gaussian
=0.91  Has Coating Thermal Noise
12% Lower than Mesa when finite mirror
effects are taken into account
» 28 % Coating Noise Reduction Possible
by reshaping the mirror to conform to the
finite cavity eigenbeam phasefront
»
»
»
»
Mihai Bondarescu
http://theory.caltech.edu/~mihai
[email protected]
Mirror Construction
• Classically, a Mesa mirror is
the innermost 17 cm of the
phasefront of the infinite
theoretical beam.
• The mirror is finite
• Phasefront of the finite
beam fails to match the
mirror surface.
• Shaping the mirror to match
the phasefront of the finite
beam dramatically
decreases diffraction.
Mihai Bondarescu
http://theory.caltech.edu/~mihai
[email protected]
Finite Mirror Effects
•
•
•
•
Mirror is finite. Normally, this
leads to higher diffraction loss
compared to clipping
approximation.
In a few cases, this can be
used to our advantage to
reduce coating thermal noise
[compared to Mesa] by
12% - =0.91  hyperboloidal
beam. No mirror reshaping
28% - by shaping the mirror
to match the phasefront of the
eigenbeam supported by
finite mirrors.
Mihai Bondarescu
http://theory.caltech.edu/~mihai
[email protected]
Finite Mirror Effects
• 28% Coating Noise
Reduction
» Power Distribution
remains Mesa
» Mirror remains close
to Mexican Hat
» A factor of 30
reduction in diffraction
loss depends on the
fine structure and
correct positioning of
the mirror.
Mihai Bondarescu
http://theory.caltech.edu/~mihai
[email protected]
Finite Mirror Effects
• 28% Coating Noise
Reduction
» Power Distribution
remains Mesa
» Mirror remains close
to Mexican Hat
» A factor of 30
reduction in diffraction
loss depends on the
fine structure and
correct positioning of
the mirror.
Mihai Bondarescu
http://theory.caltech.edu/~mihai
[email protected]
Thermal Noise Minimization
Lowering the thermal noise at all costs
Observing Diffraction Loss and Normalization constraints
Mihai Bondarescu
http://theory.caltech.edu/~mihai
[email protected]
Gauss-Laguerre Basis
• For minimization to be
possible, we need a
coordinate system in the
space of LIGO beams
• Gauss-Laguerre basis
In the center of the cavity
» Orthonormal
» Complete
• Used to analytically analyze
hyperboloidal beams in gr-qc
0602074 (Galdi, Castaldi,
Pierro, Pinto, Agresti,
D’Ambrosio, De Salvo )
For all real U, A’s can be real
Mihai Bondarescu
http://theory.caltech.edu/~mihai
[email protected]
Gauss-Laguerre
• For minimization to be
possible, we need a
coordinate system in the
space of LIGO beams
• Gauss-Laguerre basis
» Orthonormal
» Complete
• Used to analytically analyze
hyperboloidal beams in gr-qc
0602074 (Galdi, Castaldi,
Pierro, Pinto, Agresti,
D’Ambrosio, De Salvo )
Mihai Bondarescu
http://theory.caltech.edu/~mihai
[email protected]
Coating Thermal Noise
Minimization Process
• Coating Thermal Noise
R
N ~  p(r ) rdr ~
2
0

R
i , j , k ,l  0
0
*
*
A
A
A
A

(
r
,
z
)

(
r
,
z
)

(
r
,
z
)

j
l (r , z0 )rdr
 i j k l i 0
0
k
0
p |U |2
• Constraints
» Normalization

1   p(r )rdr 
0


 A A   (r , z )
i , j 0
i
j
i
0
*
j
(r , z0 )rdr
0
» Constant Diffraction Loss
10
6

  p(r )rdr 
R


 A A   (r , z )
i , j 0
i
j
i
0
*
j
(r , z0 )rdr
R
Mihai Bondarescu
http://theory.caltech.edu/~mihai
[email protected]
The Conical Beam
10
Thermal Noise
Conical
Mesa
Gaussian
8
6
4
2
0
Substrate Brownian
Substrate Thermoelastic
Coating
Mihai Bondarescu
http://theory.caltech.edu/~mihai
[email protected]
Mirror Height [ ≈ 1.06µm]
Light Intensity
12
Summary
• We show that, compared to MESA, coating thermal noise can be
further lowered by
» 12% at no cost
» 28% at a reasonable cost
» 60% in an ideal world where cost is irrelevant
• Additional Benefits
» Substrate Thermal Noise Lowered dramatically
» Diffraction loss increases for higher order modes
Mihai Bondarescu
http://theory.caltech.edu/~mihai
[email protected]
JOBS WANTED!!
Mihai Bondarescu
http://theory.caltech.edu/~mihai
[email protected]