Miniprojets Laser noise

Miniprojets
•
Table optique, fonctionnement et applications
La majorité des expériences optiques sont installés sur des plateformes isolés
vibrationnellement. Différents types d'isolation avec des performances variées
existent. Comparez les solutions existantes quant à leurs performances et la facilité
de leur mise en oeuvre.
•
Instabilité de pointé d'un laser - causes et applications
Le faisceau de sortie d'un laser montre souvent des variations dans l'espace dus à
du bruit technique présent dans le fonctionnement de la cavité. Discuter les
différentes sources des ces instabilités, leurs ordres de grandeur ainsi que des
solutions actives et passives pour s'affranchir de cet effet.
•
Comptage de photons - fonctionnement et limites
En astronomie, en spectroscopie atomique et en biologie beaucoup de récepteurs
sont amenés à détecter des photons uniques. Quelles sont les différentes
approches techniques pour ces détecteurs? Discuter leurs performances en vue
des bruits limites.
IOL – 2007/08
Laser noise
Martina Knoop, CNRS/Université de Provence
IOL – 2007/08
1
References
•
Anthony E. Siegman, « Lasers », University Sceince Books, Mill Valley, California
1986
•
W. Demtröder, « Laser spectroscopy », Springer Verlag, Berlin
•
AL Schawlow and CH Townes, « Infrared and Optical Masers », Phys. Rev. 112,
1940 (1958)
•
H Haus, « Electromagnetic noise and Quantum optical Measurements », Springer,
Berlin 2000
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Noise contributions
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2
Laser noise
•
Two groups of origins
* quantum noise, in particular associated with spontaneous emission in the
gain medium
* technical noise, arising e.g. from excess noise of the pump source, from
vibrations of the laser cavity, or from temperature fluctuations
•
Laser noise is important for many applications. Some examples are:
* High precision optical measurements, e.g. in frequency metrology, precision
spectroscopy or interferometry, require low intensity and phase noise.
* The achievable data transmission rates of optical fiber communications
systems are usually limited by noise of lasers and amplifiers.
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Laser noise
Noise in cw lasers:
– frequency
– amplitude/intensity
– phase (linewidth), limits of temporal coherence
multimode laser : mode partition noise (few modes, higher-order transverse
modes)
in pulsed and mode-locked lasers
–
–
–
–
–
–
timing jitter
pulse energy
pulse duration
chirp
phase
supermode noise in harmonic mode locking
beam pointing fluctuations.
There may be coupling between the different parameters
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3
Laser noise analysis
Characterization of noise
•
•
•
•
colour
stationarity
statistical properties
periodicity
Measures
•
•
•
Intensity noise: measurements e.g. with photodiodes or photomultiplier tubes
Phase noise: beating with reference laser; heterodyne measurement with
unbalanced Mach-Zehnder interferometer
Timing jitter of mode-locked lasers: various measurement schemes exist - high
demands for low jitter levels!
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Quantum noise
•While the noise performance of electronic systems is often limited by thermal
noise, quantum-mechanical effects often set the limits for optical systems.
( high optical frequencies, the photon energy in the optical domain is much
higher than the thermal energy kBT at room temperature.)
In QM, the electric field of a light beam is described by quantum-mechanical
operators, and the outcome of optical measurements does not simply reflect the
expectations values of these operators, but is also subject to quantum
fluctuations.
Light with unusual quantum noise properties is called nonclassical light and
occurs e.g. in the form of squeezed light.
Quantum noise is often a limiting factor for the performance of optoelectronic
devices. However, it can occasionally be useful, e.g. in quantum cryptography.
vacuum fluctuations can get into the cavity e.g. through the output coupler mirror,
but also at any other location where optical losses occur.
•S. Reynaud and A. Heidmann, "A semiclassical linear input output transformation for quantum
fluctuations", Opt. Commun. 71 (3-4), 209 (1989)
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4
Quantum noise
• Typical effects of this quantum noise are:
* some intensity noise (shot noise), phase noise, and a finite
linewidth even in the output of a (hypothetical) single-frequency
laser which is not subject to any technical noise such as mirror
vibrations
* unavoidable excess noise in optical amplifiers
* spontaneous emission of excited atoms or ions
* spontaneous Raman scattering
* parametric fluorescence
* partition noise occurring at beam splitters
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Fundamental limits (QNL)
Schawlow-Townes linewidth : linewidth of a single-frequency laser with
quantum noise only
Even before the first laser was experimentally demonstrated, A. L. Schawlow
and C. H. Townes calculated the fundamental (quantum) limit for the linewidth
of a laser. This lead to the famous Schawlow-Townes formula:
∆ν L =
πhν (∆ν c ) 2
Pout
with the photon energy hν, the cavity bandwidth ∆νc (full width at half
maximum), and the output power Pout. It has been assumed that there are no
parasitic cavity losses. (Compared with the original formula, a factor 4 has been removed
because of a different definition of the cavity bandwidth.)
References [1] A. L. Schawlow and C. H. Townes, "Infrared and optical masers", Phys. Rev. 112 (6), 1940 (1958)
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5
Fundamental limits (QNL)
A more general form of the equation is
∆ν Laser =
hνθltotToc
2
4πTrt Pout
Toc the output coupler transmission, ltot the total cavity losses (which may be larger than
Toc ), Trt the cavity round-trip time, and θ is the spontaneous emission factor which takes
into account increased spontaneous emission in three-level gain media.
The corresponding two-sided power spectral density of the phase noise is
SΦ ( f ) =
hνθltotToc −2
f
2
8π 2Trt Pout
This corresponds to white frequency noise with
Sν ( f ) =
hνθltotToc
2
8π 2Trt Pout
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Fundamental limits (QNL)
Carefully constructed solid state lasers can have very small linewidths in the
region of a few kHz, which is still significantly above their Schawlow-Townes
limit. The linewidth of semiconductor lasers is also normally much larger than
according to the formula; this is caused by amplitude-to-phase coupling
effects, quantified by the linewidth enhancement factor.
Example for Schwalow-Townes-linewidth
•
HeNe: 633 nm (5.1014 Hz), ∆νc= 1MHz, P=1mW : ∆νL =5.10-4 Hz
•
Ar+-laser : 6.1014 Hz, ∆νc= 3MHz, P=1W : ∆νL =5.10-5 Hz
Today, ∆νL = 10 kHz « easily », ∆νL = 1Hz with a lot of work
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6
Resonator noise
•
noise of a lossless resonator
•
noise of a lossy resonator
•
variation of round-trip time due to mirror fluctuations
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Intensity noise (amplitude noise)
Noise of the optical intensity or power of a laser beam
due to quantum noise (in laser gain and cavity losses) AND
technical noise (excess noise of pump source, vibrations of cavity mirrors,
thermal fluctutations in the gain medium
Intensity noise can be measured e.g. by recording the measured intensity as a
function of time (e.g. with a photodiode and an electronic spectrum analyzer)
Intensity noise can be quantified in the following ways:
* with an rms (root-mean-square) value (usually relative to the average power)
for a certain measurement bandwidth
* as a power spectral density S(f), usually of the power relative to the average
power ( relative intensity noise, RIN)
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7
Intensity noise
• in a semi-conductor: relaxation oscillations: photon and electron populations
reach equilibrium state on different time scales (different life times of the
injection carrier and the photon (three orders of magnitude)
• transient behaviour described by rate equations and the frequency
fr =
1
2 τ nτ p
⋅ {( I − I th ) / I th }
1/ 2
with τn and τp injection carrier and photon lifetime
Particularly for solid state lasers, noise is often strong around the relaxation oscillation
frequency and weak at frequencies well above this frequency. Semiconductor lasers
exhibit strongly damped relaxation oscillations, but with very high frequencies.
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Intensity noise
Relative intensity noise (RIN)
(
RIN = ∆I p
2
− ∆I S
2
)/(I B )
2
p
with <∆Ip2> the mean square intensity noise current in the bandwidth B of a spectrum
analyser, <∆Is2> mean square shot noise in B, and Ip the detected current
Gain and intensity noise are often a consequence of pump noise (white
noise)
example: diode bars 20-30 dB above shot noise, singlemode diodes 10
dB
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8
Intensity noise
Intensity noise spectrum of a solid state laser. The noise level is given in decibels above
the shot noise limit. There is a peak at 74 kHz, resulting from relaxation oscillations.
Increased low-frequency noise is caused by excess noise of the pump source.
low-limit: shot noise. At least at high noise frequencies, well above the
relaxation oscillation frequency, this noise level is approached by many lasers.
However, for so-called squeezed states of light, the intensity noise can be
below the shot noise, at the cost of increased phase noise.
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Intensity noise
Intensity noise also depends on the operation conditions; in particular, it often
becomes weaker at high pump powers, where relaxation oscillations are
strongly damped.
Intensity noise also depends on
the operation conditions; in
particular, it often becomes
weaker at high pump powers,
where relaxation oscillations are
strongly damped.
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9
Intensity noise suppression
•
•
NOISE EATER
Definition: devices for reducing the intensity noise of optical beams by
automatically adjusted attenuation
•
A noise eater is a device made for reducing the intensity noise in a laser
beam. The principle of operation is that the optical power is reduced with an
electrically controllable attenuator (normally an electro-optic modulator), and
the control signal is derived from the input power ( feedforward scheme) or the
output power ( feedback scheme) as measured e.g. with a photodiode. This
allows to stabilize the laser power, i.e., to decrease intensity noise. The most
common approach is that based on an electronic feedback loop, e.g. of a PID
type. Proper design of the feedback electronics is vital to achieve a good noise
suppression.
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Laser TiSa doublé en fréquence
stabilisation en intensité
AOM
intensity [arb.u.]
λ/2
Glan prism
Invar cavity
F
1
t [ min ]
λ/4
≈ 1000
PDH lock
on TiSa control box
2
PM fiber
stabilisation en fréquence
10
Phase noise
Noise in oscillator systems characterized by
• long-term frequency stability: usually on min, h, given in ∆f/f (for a given
period/bandwidth (see next chapter)
•
and short-term frequency stability: random or periodic fluctuations over
periods less than a second
– due to quantum noise, in particular spontaneous emission of the gain medium into
the cavity modes, but also quantum noise associated with optical losses. In addition,
there can be technical noise influences, e.g. due to vibrations of the cavity mirrors
or to temperature fluctuations.
– leads to a finite linewidth of the laser output. The same applies to the
frequency components of the output of a mode-locked laser,
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Phase noise
The ideal oscillator :
V (t ) = V0 sin(ϖt )
the instantaneous output of
a fluctuating oscillator:
V (t ) = V0 [1 + A(t )]sin (ϖt + q (t ) )
q(t) discrete : spurious signal, discrete components
q(t) random : line broadening
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11
Phase noise - sources
•
dephasing in the laser amplifier medium
•
dephasing at the mirrors (δL)
δφ m =
2ϖ 0δL 2δL
=
c
λ
with ω0 the unmodulated laser oscillation frequency
•
axial phase shift: the Guoy effect (up to 2 Rayleigh ranges off the waist)
•
coupling of intensity noise to phase noise, e.g. via nonlinearities
•
build-up
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Phase noise
Phase noise can be quantified by the power spectral density of the
phase deviations. Phase noise is measured in the frequency
domain, and is expressed as a ratio of signal power to noise power
measured in a 1 Hz bandwidth at a given offset from the desired
signal. This power spectral density often diverges for zero frequency.
Example
A: flicker; B: 1/f; C: white/broadband noise
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12
Phase noise
•
The phase noise test characterizes the output spectral purity of an
oscillator by determining the ratio of desired energy being delivered by
the oscillator at the specified output frequency to the amount of
undesired energy being delivered at neighboring frequencies.
This ratio is usually expressed as a series of power measurements
performed at various offset frequencies from the carrier, The power
measurements are normalized to a 1 Hz bandwidth basis and
expressed with respect to the carrier power level.
This is the standard measure of phase fluctuations described in NIST
Technical Note 1337.
•
Phase noise is directly related to frequency noise, as the instantaneous
frequency is basically the temporal derivative of the phase.
(→ measurements)
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Frequency/phase noise
Spectral densities for
frequency and phase:
Sy ( f ) =
1
ν 02
S ∆ν ( f ) =
f2
ν 02
Sφ ( f )
Spectral density composed of different
noise components:
+2
Sy ( f ) =
hα f α
∑
α
= −2
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13
Frequency noise
Frequency noise is noise of the instantaneous frequency of an oscillating
signal. The instantaneous frequency is defined as
ν (t ) =
1 dϕ
2π dt
The power spectral density of frequency noise is directly related to that of the
phase noise:
Sν ( f ) = f 2 Sϕ ( f )
This means that e.g. white frequency noise corresponds to phase noise with a
power spectral density proportional to 1/f2. (example: a single-frequency laser
which is only subject to quantum noise and exhibits the Schawlow-Townes linewidth)
Numerical processing of frequency noise rather than phase noise can
have technical advantages in certain situations.
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Frequency noise - measurement
•
heterodyning
ω1 and ω2 in a nonlinear device
(ω1 + ω2 ) and (ω1 - ω2) (beat frequency)
– mixing of two (or more) frequencies
producing
•
heterodyne detection
– detection by non-linear mixing with radiation of a reference frequency (local
oscillator).
– signal and ref are superimposed at the mixer (PD, nonlinear amplitude response
>a part of the output is prop to the square of the input),
– Let the electric field of the received signal be
Esig cos(ϖ sig + ϕ )
– and that of the local oscillator be
ELO cos(ϖ LO )
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14
Frequency noise - heterodyning
•
For simplicity, assume that the output of the detector I is proportional to the
square of the amplitude:
I ∝ ( Esig cos(ϖ sig t + ϕ ) + E LO cos(ϖ LO t )) 2
2
2
= E sig (1 / 2)(1 + cos( 2ϖ sig t + 2ϕ )) + E LO (1 / 2)(1 + cos( 2ϖ LO t ))
[
]
+ Esig E LO cos((ϖ sig + ϖ LO )t + ϕ ) + cos((ϖ sig − ϖ LO )t + ϕ )
•
The output has high frequency (2ωsig and 2ωLO) and constant components. In
heterodyne detection, the high frequency components and usually the constant
components are filtered out, leaving the two intermediate (beat) frequencies at
ωsig + ωLO and ωsig − ωLO. The amplitude of these last components is
proportional to the amplitude of the signal radiation. With appropriate signal
analysis the phase of the signal can be recovered as well.
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Frequency noise - homodyning
•
same principle as heterodyning, but frequency from the same source.
one part is the local oscillator, the other (perturbed) part is the signal
•
insensitive to laser frequency fluctuations
•
•
self-heterodyning
reference and signal coming from the same source, one part is shifted in
frequency (to avoid noise at origin)
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15
Laser noise - reduction
•
Laser noise can be reduced in many ways. Basically one has the following
options:
* reducing quantum noise e.g. by increasing the intracavity power level and by
minimizing losses
* reducing technical noise influences (e.g. by building a stable laser cavity, by
temperature stabilization of the setup, or by using a low-noise pump source)
* optimizing laser parameters so that the laser reacts less strongly to noise
influences
* using active or passive stabilization schemes
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Phase locked loop
A PLL holds the relative phase of the two oscillators at quadrature which is usually
the best point for converting small phase variations into voltage variations.
time constant is set long enough to preserve the slowest phase variations of
interest.
The components of a PLL that contribute to the loop gain include:
•
The phase detector (PD) and charge pump (CP).
•
The loop filter, with a transfer function of Z(s)
•
The voltage-controlled oscillator (VCO), with a sensitivity of KV / s
•
The feedback divider, 1 / N IOL – 2007/08
16
Noise reduction - frequency
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Noise reduction - frequency
Frequency stabilisation can be done by actively controlling the laseroutput of a Fabry-Perot cavity to an
amount of reflected intensity.
Disadvantage is that, in this case, output intensity changes cause the same signal as frequency
instabilities.
Solution: Modulate the signal, make a derivative of the profile and create an error signal around a zero
offset.
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17
Noise reduction - frequency
Pound-Drever-Hall
Modulating the carrier signal sin(ϖ) with a sin(Ω) of the Pockels cell/EOM creates two sidebands
sin(ϖ+Ω’) and sin(ϖ-Ω’).
Multiplying this with the original sin(Ω) term in the mixer yields two terms: cos(Ω+Ω’) and cos(Ω-Ω’).
cos(Ω-Ω’) is a DC signal and is transmitted through the low pass filter.
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Pound-Drever-Hall stabilisation
AOM
Optical
Isolator
Ti:Sapph
AOM
Cavity
EOM
Local
Osc.
PD
Servo
Amp.
Phase
Shift
amplitude [V]
0.04
0.02
Low-Pass
Filter
0.00
Mixer
-0.02
40 MHz
∆ν
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18
Timing jitter
• Fluctuations of the temporal positions of pulses
•
Pulse trains, generated e.g. in mode-locked lasers, exhibit some deviations of
the temporal pulse positions from those in a perfectly periodic pulse train. This
phenomenon is called timing jitter and is important for many applications, e.g.
for long-range optical fiber communications or for optical sampling
measurements.
The considered timing errors can be of different kinds:
• the deviations between the temporal pulse positions and those of perfectly
regular clock ticks
• the deviations between the temporal pulse positions and those of the ticks of a
real (noisy) oscillator (e.g. the electronic oscillator which drives the modulator
of an actively mode-locked laser)
• the deviations of the pulse-to-pulse spacing from the average pulse period
(→ pulse-to-pulse jitter or cycle jitter)
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Timing jitter
Timing errors may be quantified in different ways:
• with an rms (root-mean-square) value for a certain measurement bandwidth
•
• as a power spectral density, either of the timing deviation or of the timing
phase
•
Timing jitter is related to phase noise in the optical frequency components of
the pulse train. In the absence of technical noise, it is limited by quantum
noise, but in most cases it is dominated by vibrations and drifts of the laser
cavity.
The timing jitter of mode-locked lasers can be very small – in some cases
significantly smaller than that of high quality electronic oscillators. This
applies particularly to short time scales, where a laser can be used as a
very precise timing reference (as a kind of flywheel).
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19
Gordon-Haus jitter
Timing jitter originating from fluctuations of the center frequency
fluctuations of the center frequency of the optical pulses are coupled to the timing
via group velocity dispersion: a change of center frequency translates into a
change of group velocity, which will subsequently affect the pulse timing
Gordon-Haus effect (J. P. Gordon and H. A. Haus, "Random walk of coherently
amplified solitons in optical fiber transmission", Opt. Lett. 11, 665 (1986)[.
Study
Noise in a fiber-optic link with periodically spaced fiber amplifiers to keep the
pulse energy within a narrow range. The amplifiers, which were implicitly assumed
to have a wavelength-independent gain, introduce quantum noise which shifts the
optical center frequency by a random amount.
In many subsequent amplifiers, the center frequency (and with it the group
velocity) of each pulse undergoes a random walk, without any correlation between
the center frequency changes of different pulses.
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Gordon-Haus jitter
Subsequently, the timing deviations of the pulses accumulate more and more. A
central result is that the variance of the timing errors grows
in proportion to the fiber losses per unit length,
in proportion to the third power of the transmission distance,
and inversely proportional to the square root of the optical energy per pulse.
Therefore: Dominant source of jitter for long-haul data transmission.
Effective suppression by use of regularly spaced optical filters, or simply amplifiers
with limited gain bandwidth, in order to eliminate this unbounded drift.
The term Gordon-Haus effect is nowadays often used in a rather general way –
basically always when center frequency fluctuations couple to the timing via
chromatic dispersion.
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20
Squeezing
Nonclassical states of light with noise below the standard quantum limit in one
quadrature component
In quantum optics there is a quantum uncertainty, and any measurement of the complex
amplitude of the light field can deliver different values within an uncertainty region.
Moreover, there is an uncertainty relation for the quadrature components of the light field,
saying that the product of the uncertainties in both components is at least some quantity
times Planck's constant.
Glauber's coherent states have circularly symmetric uncertainty regions, so that the uncertainty relation
dictates some minimum noise amplitudes e.g. for the amplitude and phase. A further reduction e.g. of
amplitude noise is possible only by "squeezing" the uncertainty region, reducing its width in the
amplitude direction while increasing it in the orthogonal direction, so that the phase uncertainty is
increased..
amplitude-squeezing
phase-squeezing
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Squeezing
Squeezed light can be generated
from light in a coherent state or vacuum state by using certain optical
nonlinear interactions.
Examples
• an optical parametric amplifier with a vacuum input can generate a squeezed
vacuum with a reduction of the noise of one quadrature components by the order
of 10 dB.
• frequency doubling,
• the Kerr nonlinearity in optical fibers also allows to generate amplitude-squeezed
light.
• semiconductor lasers can generate amplitude-squeezed light when operated
with a carefully stabilized pump current.
• squeezing can also arise from atom-light interactions.
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21
Exemple: VIRGO
Fabry-Perot cavity to detect gravitational wave h = 2
δL
L
~ 3.10 − 23 / Hz
Présentation de François Bondu 2006
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The VIRGO collaboration
• 12 laboratories CNRS (France) and INFN (Italy),
including European Gravitational Observatory, Cascina, Italy
F.Acernese6, P.Amico10, M.Alshourbagy11, S.Aoudia7, S.Avino6, D.Babusci4, G.Ballardin2, F.Barone6, L.Barsotti11,
M.Barsuglia8, F.Beauville1, M.-A.Bizouard8, C.Boccara9, F.Bondu7, L.Bosi10, C.Bradaschia11, S.Braccini11, S.Birindelli11,
A.Brillet7, V.Brisson8, L.Brocco12, D.Buskulic1, E.Calloni6, E.Campagna3, F.Cavalier8, R.Cavalieri2, G.Cella11,
E.Chassande-Mottin7, C.Corda11,
A.-C.Clapson8, F.Cleva7, J.-P.Coulon7, E.Cuoco2, V.Dattilo2, M.Davier8, R.De Rosa6, L.Di Fiore6, A.Di Virgilio11,
B.Dujardin7, A.Eleuteri6, D.Enard2, I.Ferrante11, F.Fidecaro11, I.Fiori11, R.Flaminio1,2, J.-D.Fournier7, O.Francois2,
S.Frasca12, F.Frasconi2;11, A.Freise2, L.Gammaitoni10, A.Gennai11, A.Giazotto11, G.Giordano4, L.Giordano6, R.Gouaty1,
D.Grosjean1, G.Guidi3, S.Hebri2, H.Heitmann7, P.Hello8, L.Holloway2, S. Karkar1, S.Kreckelbergh8, P.La Penna2,
N.Letendre1, M.Lorenzini3, V.Loriette9, M.Loupias2, G.Losurdo3, J.-M.Mackowski5, E.Majorana12, C.N.Man7, M.
Mantovani11, F. Marchesoni10, F.Marion1, J. Marque2, F.Martelli3, A.Masserot1, M.Mazzoni3, L.Milano6, C. Moins2,
J.Moreau9, N.Morgado5, B.Mours1, A. Pai12, C.Palomba12, F.Paoletti2;11, S. Pardi6, A.Pasqualetti2, R.Passaquieti11,
D.Passuello11, B.Perniola3, F. Piergiovanni3, L.Pinard5, R.Poggiani11, M.Punturo10, P.Puppo12, K.Qipiani6, P.Rapagnani12,
V.Reita9, A.Remillieux5, F.Ricci12, I.Ricciardi6, P.Ruggi2, G.Russo6, S.Solimeno6, A.Spallicci7, R.Stanga3, R.Taddei2,
M.Tonelli11, A.Toncelli11, E.Tournefier1, F.Travasso10, G.Vajente11, D.Verkindt1, F.Vetrano3, A.Viceré3, J.-Y.Vinet7,
H.Vocca10, M.Yvert1, Z.Zhang2
1CNRS, Laboratoire d'Annecy-le-Vieux de physique des particules, Annecy-le-Vieux, France
2European Gravitational Observatory (EGO), Cascina (Pi) Italia
3INFN, Sezione di Firenze/Urbino, Sesto Fiorentino, and/or Università di Firenze, and/or Università di Urbino, Italia
4 INFN, Laboratori Nazionali di Frascati, Frascati (Rm), Italia
5CNRS, LMA, Villeurbanne, Lyon, France
6INFN, sezione di Napoli and/or Università di Napoli "Federico II" Complesso Universitario di Monte S.Angelo, Italia and/or Università di Salerno,
Fisciano (Sa), Italia
7 Departement Artemis - Observatoire Cote d'Azur, BP 42209, 06304 Nice , Cedex 4, France
8CNRS, Laboratoire de l'Accélérateur Linéaire (LAL), IN2P3/CNRS-Univ. De Paris-Sud, Orsay , France
9CNRS, ESPCI, Paris, France
– 2007/08
10INFN Sezione di Perugia and/or Università di Perugia,IOL
Perugia,
Italia
11INFN, Sezione di Pisa and/or Università di Pisa, Pisa, Italia
12INFN, Sezione di Roma and/or Università "La Sapienza", Roma, Italia
22
I. Virgo design and status
Design
Astrophysical performances
spectral resolution
reliability
horizon
II. Laser system
Injected laser
Mode Cleaning
Frequency stabilization
II. Optical performances
Mirror metrology
Optical simulation
Actual performances
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VIRGO optical design
δL
~ 3.10−23 / Hz
L
Input
Michelson
Suspended
Output
<<Mode
Mode
configuration
mirrors
Cleaner
Cleaner>>
cancel
to filter
attoshot
dark
filter
seismic
output
fringe
outnoise
mode
input
+ servo
beam
loop
jitter
to cancel
and select
lasermode
frequency noise
Long
Recycling
arms
mirror
to
divide
totoreduce
mirror
and
suspension
noise
thermal
noise
Fabry-Perot cavity to detect gravitational wave
h=2
L=3 km
L=144m
Slave laser
Master
laser
I. Design and Status
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23
Spectral resolution
Control noises
I. Design and Status
Reduced power
IOL – 2007/08
VIRGO design spectral resolution
Main sources of noise limiting the VIRGO design spectral resolution
Shot noise
1
Seismic noise
Thermal noise
Shot noise
IOL – 2007/08
24
Injected laser
Main Beam Path
Master laser, 1W, Innolight
F.I.
F.I.
E.O.
F.I.
II. Laser system
Slave laser, 22W, LZH
IOL – 2007/08
II. Laser system
1/sqrt(Hz)
dP/P
IN-LOOP
Power stabilization
IOL – 2007/08
25
OUT OF LOOP
Noise performances
II. Laser system
IOL – 2007/08
OUT OF LOOP
Frequency stabilization – Noise upper limit
Electronic noise
II. Laser system
IOL – 2007/08
26
IN LOOP
Frequency stabilization – Noise upper limit
II. Laser system
IOL – 2007/08
Mirror Suspensions
The
rma
lN
oise
Measured
Upper Limit
IOL – 2007/08
27