Transcript G030231-00 - DCC

White light Cavities
Stacy Wise, Guido Mueller,
David Reitze, D.B. Tanner,
University of Florida
LIGO-G030231-00-Z
California Institute of Technology
April 22nd 2003
Table of Content
• Motivation
• Long GW-wavelength limit
–
–
–
–
Michelson Interferometer
Cavity enhanced Michelson Interferometer
Signal Recycling
White Light Cavity (WLC)
• Realistic GW-detector
–
–
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Michelson Interferometer
Cavity enhanced MI
Signal recycling
WLC
• Outlook
Gravitational Waves:
 Generated by huge accelerated masses such
as accelerated black holes in a binary system
 Predicted by Einstein, never detected
 Amplitude is a relative
length change: h=dL/L
..
2G Q
h~
Q: Quadrupole Tensor
4
c r
Quadrupole waves:
• Stretch one direction
• Squeeze orthogonal direction
Interferometer is the
ideal tool to measure
gravitational waves:
But what type of sources do we expect to see ?
History of a big fat wedding
measure
masses
and
spins of
binary
system
Frequency increases over time
Maximum frequency: 2kHz
History of a big fat wedding
observe the dynamics:
spin flips and couplings…
Waveform unknown
History of a big fat wedding
detect normal
modes of
ringdown to
identify final
NS or BH.
Ringdown frequencies in NS: 1kHz – 20kHz
Advanced Configuration
Initial
LIGO
10-22
-22
10
h(f) / Hz1/2
Possible Sources:
• NS/NS mergers
out to 300 Mpc
• BH/BH mergers
• Normal modes
of NS (10 Mpc)
• Supernovae
•…
Optical noise
Int. thermal
Susp. thermal
Total noise
1023
-23
10
10-24
-24
10
10-25
1 Hz
-25
NS/NS mergers ?
10 Hz
100 Hz
• We see the inspiral !
• Probably the low frequency components of the
wedding night, not the entire show.
• And probably nothing from the ringdown.
10
0
10
1
2
10
10
f / Hz
NEED MORE BANDWIDTH !!!
3
10
1 kHz
LIGO I
 Simplified picture (low frequency limit nGW << FSR):
GW modulates phase of cavity internal field !
+W
Carrier
t = Lrt/c
E0(t) = EC + E+eiWt – E-e-iWt
-W
E1(t+t) = r1r2 ( EC + E+ eiWt – E- e-iWt )
+ ( EC
E2(t+2t) = (r1r2)
+ r 1r 2
+
…
2
+ E+ eiW(t+t) – E- e-iW(t+t)
)
( EC + E+ eiWt – E- e-iWt )
( EC e-iF + E+ eiW(t+t) – E- e-iW(t+t) )
( EC
+ E+eiW(t+2t)
– E-e-iW(t+2t) )
LIGO I
+W
Carrier
-W
Etot = ECS( r1r2)
+W
low frequency limit
nGW << FSR
-W
n
+ E+eiWt S ( r1r2) E+einWt - E-e-iWt S ( r1r2) E-e-inWt
n
(r1-r2) tMIEc
=
(1 – r1r2)
t1rMIE+e+iWt
+
Wt
i
(1 – r1r2e )
n
t1rMIE-e-iWt
(1 – r1r2e-iWt)
Gives LIGO I response: BW = Cavity Pol
LIGO II
+W
Carrier
-W
+W
-W
PM-sidebands:
Signal recycling changes
effective reflectivity of ITM
(similar to PR for carrier)
E+e+iWt
(1 – reffr2eiWt+F)
low frequency limit
nGW << FSR
reff eiF =
r1-rSeifSR
1-r1rSeifSR
E-e-iWt
(1 – reffr2e-iWt+F)
1. Shifts resonance (peak-) frequency
2. reff changes build up
3. reff changes bandwidth
IDEA: WLC
+W
fp
fn
Carrier
-W
Change reflectivity
of end mirror:
+W
low frequency limit
nGW << FSR
r2
r2e-iWt
-W
fp
fn
E+eiWt
(1 – r1r2)
E-e-iWt
(1 – r1r2)
1. Resonant at all frequency
2. Build up does not change BW
White light cavity
Basic Idea:
L(l) dL(l)
=
l
dl
Or
Make Cavity
longer for
longer wavelength
Unlimited Bandwidth
f(W) = Wt
L0(n) = - n0 dL
dn
How ?
or
L(l) dL(l)
=
l
dl
Several methods:
1. Atomic resonances (Wicht-paper)
Index of refraction in resonantly pumped two level
system (see lasing without inversion)
2. Angular Dispersion
a) Prisms (not dispersive enough ?)
b) Gratings
c) misaligned triangular cavities (tricky)
Original Idea published in: A. Wicht, K. Danzmann, M. Fleischhauer, M.O. Scully,
G. Mueller, R.-H. Rinkleff Opt. Comm. 134 (1997), pg 431-439
White light cavity
L0
New end
Mirror !
b
a
L0
Cavity length:
WLC requires:
with:
L(l) = L0 +
D [1+sina sinb(l)]
cosb(l)
L(l) ! dL(l) dL db
=
l
dl = db dl
dL = D
db cos2b
l
d
db
m
=
dl dcosb
Does this work ?
Is the dispersion in a grating large enough ?
Needed dispersion
Grating dispersion
Working Point
Parameters
Final
Bandwidth
Bandwidth increased from 60 Hz to 36 MHz
Final Bandwidth
This is the optical line width, not the GW-response !
Not the Same !
White light cavity
Basic Idea:
L(l) dL(l)
=
l
dl
Or
Make Cavity
longer for
longer wavelength
Unlimited Bandwidth
But assumption
nGW<< c/L
not longer valid !
Michelson Interferometer
Response based on:
ds2 = 0
= c2dt2 + [1+h(t)]2dx2 + [1-h(t)]2dy2
• Propagation of GW: z-direction
• Polarization of GW: + (optimum)
Light travel time in X-arm seen by beam splitter:
h0 sin(Wt-kL)-sin(Wt)
Tx = L 1+
c
W
2
c dt = (1+0.5h0sin(Wt+kx))dx
Y-arm:
h0 sin(Wt-kL)-sin(Wt)
L
Ty =
1c
W
2
Phase difference at BS: Df = w(Tx-Ty)
Cavities
Cavity field at ITMx:
L: round trip length
wL/c = N2p
Carrier:
Ecav = it1r2Eineiwt S(r1r2)ne-iwtn
tn = (n+1)
Ecav = it1r2Ein
L + h0 sin(Wt-(n+1)kL)-sin(Wt)
c
2W
eiwt
1
1-r1r2
Sideband:
iwh0 e-iW/2FSR sinc(W/2FSR) -iWt
e
4FSR (1-r r )(1-r r eiW/FSR)
1 2
1 2
Sideband:
iwh0 e-iW/2FSR sinc(W/2FSR) iWt
e
4FSR (1-r r )(1-r r e-iW/FSR)
1 2
1 2
Cavities
Cavity field at ITMx:
Ecav = it1r2Eineiwt S(r1r2)ne-iwtn
tn = (n+1)
L + h0 sin(Wt-(n+1)kL)-sin(Wt)
c
2W
Interpretation:
iwh0
4FSR
sinc(W/2FSR) e-iW/2FSR
GW
1
(1-r1r2)
Carrier
build up
Signal recycling changes r1
1
(1-r1r2
eiW/FSR)
e-iWt
Signal build up
reffeiF (not r1)
White Light Cavity ?
Cavity field at ITMx:
Ecav = it1r2Eineiwt S(r1r2)ne-iwtn
tn = (n+1)L/c + ?
Work in progress …
Hope for:
Carrier:
r2
r2e-iW/FSR
Sideband:
Ecav = it1r2Ein
eiwt
1
1-r1r2
iwh0 e-iW/2FSR sinc(W/2FSR) -iWt
e
4FSR
(1-r r )(1-r r )
1 2
Sideband:
1 2
iwh0 e-iW/2FSR sinc(W/2FSR) iWt
e
4FSR
(1-r r )(1-r r )
1 2
1 2
White Light Cavity
Transfer function for optimum angle of incidence
and optimum polarization
?
All sky average will
average out the
sharp peaks.
Comments:
• Low frequency limit
should be OK.
• If Not, we should
check SR, too.
• Higher frequencies: ?
Compare with Adv. LIGO
Assume: 1MW in each arm cavity (infinite mirror masses):
5x10-23
Sh ~
T1/2
for a non recycled MI (T transmission of ITM)
Hz1/2
at DC
BW = T x FSR / 2p
Log T-1/2:
(~ Gain)
50
5
300
100
30
10
0.5
0.05
10 100 1k
10k
Log T[ppm]
10 100 1k
10k
SR: shifts to other frequencies, Gain, BW: replace T by Teff
Log T[ppm]
Scaling
5x10-23
Log T-1/2:
Sh ~
T1/2
BW = T x FSR / 2p
Hz1/2
(~ Gain)
50
5
300
100
30
10
0.5
0.05
10 100 1k
10k
Choices: want Sh ~ 5x10-25
want Sh ~ 5x10-24
Log T[ppm]
10 100 1k
10k
Log T[ppm]
BW ~ 0.5 Hz
BW ~ 50 Hz
Example for Grating: L = 10k ppm
(T = Losses = L)
L = 1k ppm
L = 100 ppm
Sh ~ 5x10-24, BW ~ MHz
Sh ~ 1.6x10-24, BW ~ MHz
Sh ~ 5x10-25, BW ~ MHz
(Pin = 10kW)
(Pin = 1kW)
(Pin = 100W)
Remarks
• WLC reduces shot noise limit above cavity pol.
• Quadrature components of the quantum noise are
uncoupled (no optical spring…).
• Radiation pressure noise will push on mirrors and
noise will depend on mass of mirrors.
• Losses in gratings need to be below ~200ppm for
grating, otherwise build up to low.
• Should be set up in an all reflective design.
• Nontransmissive materials for test masses possible:
Silicon
Outlook
•
•
•
•
Gratings with 97% losses from Uni Jena arrived
They produced already gratings with >99% efficiency
Stacy started to model gratings (preliminary: 99.6%)
Designed tabletop with expected optical linewidth
of 10GHz in 23cm cavity.
• GW-bandwith ? (need to study experimental setup)
RPN+thermal noise:
assumes equal masses
and same materials
in both cases.
All reflective optics
enables us to use new
materials (Silicon):
Larger masses,
better thermal properties
will reduce both noise
sources.