This talk originates from a
performed in 2005 in the
frame of ESO’s OWL (then
a 100m telescope)
instrumentation, but which
is valid for all Extremely
Large Telescopes (ELTs).
6 November 2006 Liege Inst. d'Astrophysique 1
Main topics of the talk
1. The time domain
2. Quantum properties of (non-thermal) light
3. Intensity interferometry (HBTII)
4. Clocks and Detectors
5. Quanteye for 100m OWL
6. Aqueye, our Precursor for Asiago
7. The Photon Orbital Angular Momentum (light
For quantum optics activites in Padova see:
6 November 2006 Liege Inst. d'Astrophysique 2
1 - Time domain in astronomy
Astronomy expands by pushing parameter
. in wavelength
. in spatial resolution
Extremely High-Time Resolution Astrophysics?
Non-thermal processes and ‟Quantum‟ properties
Well below t 1x10-6 s, a “new” window to the
6 November 2006 Liege Inst. d'Astrophysique 3
From milliseconds All of astronomy
•Pulsars The giant pulses
oscillations observed from
•Lunar and stellar 0.4 to 8.8 GHz
•Milli-, micro-and with
•Photon-gas the brightest
effects pulses in the
•Photon emission The source must
•Coherent be smaller than
radiation bursts 1 meter in size!
•Photon quantum (Cordes et al.,
•Etc. 2004, Ap.J. 612,
Notice that atmospheric turbulence is poorly known at these very high frequencies.
6 November 2006 Liege Inst. d'Astrophysique 4
2 - Quantum optics in
astronomy - 1
• Photons are more complex than is generally appreciated.
• Classical astrophysics merges all radiation of a certain
wavelength into the quantity "intensity". When instead
treating radiation as a three-dimensional photon gas, other
effects also become significant, e.g. higher-order coherence
and the temporal correlation between photons.
• Glauber (1963a, 1963b, Nobel Prize 2005) showed that an
arbitrary state of light can be specified with a series of
coherence functions essentially describing one-, two-, three-,
etc. photon-correlations with respect to position r and time t.
• See also D.Dravins, ESO Messenger 78, 9 (1994).
6 November 2006 Liege Inst. d'Astrophysique 5
2 - Quantum optics in astronomy - 2
These quantum correlation effects are fully developed over
timescales equal to the inverse bandwidth of light. For
example, a 1 A bandpass filter in the visible gives a frequency
bandwidth of 1011 Hz, and the effects are then fully developed
on timescales of 10-11 seconds. Instrumentation with such
continuous resolutions is not yet available, but it is (hopefully)
possible to detect the effects, albeit with a decreased amplitude,
also at the more manageable 50 to 100 picosecond
The largest possible flux of photons is then necessary:
Extremely Large Telescopes are absolutely needed to bring
non-linear optics to astronomy.
Quantum optics and ELTs could thus become a
fundamentally new information channel to the Universe.
6 November 2006 Liege Inst. d'Astrophysique 6
First order correlation function - 1
The temporal coherence of light is quantified by the first order
(t ) (t )
g (1) ( )
whose modulus is also equal to the fringe visibility in the Michelson
I m ax I m in
g ( ) V ( )
I m ax I m in
Any realization of a photometer, spectrometer and phase interferometer
(Michelson, Mach-Zender) measures some properties of this first order
correlation function (see next slides).
6 November 2006 Liege Inst. d'Astrophysique 7
First order correlation function - 2
All classical optical instruments
measure properties of light that
can be deduced from the first-
order correlation function of
light, g(1), for two coordinates in
space r and time t. The different
classes are collected in this
E is the amplitude of the field,
< > denotes time average, and *
All such measurements can be ascribed to quantities of type E*E,
corresponding to intensity I, which in the quantum limit means observations
of individual photons or of statistical one-photon properties.
Thus classical measurements do not distinguish light sources with
identical G(1). Possible multi-photon phenomena in the photon stream
reaching the observer are not identified, not even in principle.
6 November 2006 Liege Inst. d'Astrophysique 8
First order correlation function - 3
• Therefore, conventional astronomical instruments
measure properties of light such as its intensity,
spectrum, polarization or first-order coherence.
However, such properties are generally insufficient,
even in principle, to determine the physical conditions
under which light has been created (e.g. thermal
processes versus stimulated emission), or subsequent
• Yet, different types of light may have quantum-
statistical differences regarding collective multi-photon
properties in the photon gas. Such properties are known
for light from laboratory sources and might ultimately
become experimentally measurable also for astronomical
6 November 2006 Liege Inst. d'Astrophysique 9
A drastic example
6 November 2006 Liege Inst. d'Astrophysique 10
Second order correlation function - 1
The description of collective multi-photon phenomena in a photon gas
requires a quantum-mechanical treatment since photons have integer
spin, and therefore constitute a boson fluid with properties different from
a fluid of classical distinguishable particles. The second order correlation
describes the correlation of intensity between two coordinates in space r
and time t.
With respect to time, the second order correlation function is defined by:
I (t ) I (t )
g ( 2)
( ) g ( 2 ) ( )
I (t ) 2
For any classical wave the degree of coherence should always be less
than g(2)(0) . This result is contradicted for quantum states of light.
6 November 2006 Liege Inst. d'Astrophysique 11
Second Order correlation function - 3
In thermodynamic equilibrium, photons occupy the energy levels
according to Bose-Einstein (BE) distribution.
However, away from equilibrium, photons may deviate from BE. For
example, in the laboratory, one can observe how the physical nature of the
photon gas gradually changes from chaotic (g(2) = 2) to ordered (g(2)= 1)
when a laser is "turned on“, and the emission gradually changes from
spontaneous to stimulated.
Therefore, by measuring g(2) and knowing the laser parameters involved, it
is possible to deduce the atomic energy level populations, which is an
example of an astrophysically important parameter (non-LTE departure
coefficient) which cannot be directly observed with classical measurements
of one-photon properties.
To determine whether one individual photon is due to spontaneous or
stimulated emission requires the study of statistical properties of the boson
6 November 2006 Liege Inst. d'Astrophysique 12
Second Order correlation function - 4
measured in two-photon
experiments. All such
measurements can be
ascribed to quantities of
type I*I, i.e. intensity
multiplied by itself, which
in the quantum limit
means observations of
pairs of photons, or of
In the Hanbury Brown Twiss intensity interferometer (HBTII) this is measured for r1 r2
but t1 = t2: <I(0,0) I(r,0)>, thus deducing angular sizes of stars, reminiscent of a classical
For r1 = r2 but t1 t2 we instead have an intensity-correlation spectrometer, which
measures <I (0,0) I (0,t)>, determining the spectral width of e.g. scattered laser light.
6 November 2006 Liege Inst. d'Astrophysique 13
For a source with g(2)
2, neither an intensity
interferometer nor an
spectrometer will yield
correct results. Additional
required to fully extract
the information content
Many different quantum states of optical fields exist, not only those mentioned above which can be
given classical analogs, but also e.g. photon antibunching with g(2) = 0, which is a purely quantum-
mechanical state. This implies that neighboring photons "avoid" one another in space and time.
While such properties are normal for fermions (e.g. electrons), which obey the Pauli exclusion
principle, ensembles of bosons (e.g. photons) show such properties only in special situations. An
antibunching tendency implies that the detection of a photon at a given time is followed by a
decreased probability to detect another immediately afterward.
6 November 2006 Liege Inst. d'Astrophysique 14
Photon Arrival Times
R. Loudon The
of Light (2000)
0 is the typical
time scale, e.g.
6 November 2006 Liege Inst. d'Astrophysique 15
Photon statistics, antibunching,
quantum optical spectroscopy
Photon Statistics Laser and Fluorescence Identical
Gaussian Sources H.Kimble, Spectral Lines
F.T.Arecchi, M.Dagenais, May Differ In
Phys.Rev.Lett. 15, 912 L.Mandel Photon
(1965) Phys.Rev.Lett. 39, Statistics
6 November 2006 Liege Inst. d'Astrophysique 16
A laboratory example
The different statistical properties of thermal and laser laboratory
Adapted from D.Dravins, H.O.Hagerbo, L.Lindegren, E.Mezey,
B.Nilsson: SPIE 2198, 289 , 1994)
6 November 2006 Liege Inst. d'Astrophysique 17
Advantages of very large telescopes
Telescope diameter Intensity <I> Second-order Fourth-order photon
correlation <I2> statistics <I4>
3.6 m 1 1 1
8.2 m 5 27 720
4 x 8.2 m 21 430 185,000
50 m 193 37,000 1,385,000,000
100 m 770 595,000 355,000,000,000
6 November 2006 Liege Inst. d'Astrophysique 18
Cosmic Lasers in Action
A (too) early paper on optical astronomical laser :
D.H. Menzel, : Laser Action in Non-Lte Atmospheres, in
Spectrum Formation in Stars with Steady-State Extended
Atmospheres, Proceedings of IAU Colloq. 2, 1969 in
Munich, Germany. Edited by H. G. Groth and P. Wellmann,
National Bureau of Standards Special Publication 332.
Abstract: The radiative transfer equation is written in
microscopic form, and from some simplifications on the
ratio of occupation numbers for upper and lower level, a
laser action is suggested.
Two (more recent) review papers:
M.Elitzur: Masers in the Sky, Scientific American, 272,
No.2, 52 (Feb. 1995), for radio masers
C. H. Townes, Astronomical masers and lasers, in Quantum
Electron., 1997, 27 (12), 1031-1034
6 November 2006 Liege Inst. d'Astrophysique 19
An overall vision of astrophysical lasers
Letokhov, V. S.
Quant. Electr. 32,
1065 (2002) =
32, 1065 (2002)
Masers and lasers in the active medium particle-density vs. dimension diagram.
6 November 2006 Liege Inst. d'Astrophysique 20
Laser emission in Eta Car -1
Observations with HST have identified a gas cloud that acts as a
natural ultraviolet laser, near Eta Carinae. The interstellar laser may
result from Eta Carinae's violently chaotic eruptions, in which it blasts
parts of itself out into space, like an interstellar geyser.
6 November 2006 Liege Inst. d'Astrophysique 21
Laser Emission in Eta Carinae - 2
See the Papers:
S. Johansson, V.S. Letokhov:
- Possibility of Measuring the Width of Narrow Fe II
Astrophysical Laser Lines in the Vicinity of Eta Carinae by
means of Brown-Twiss-Townes Heterodyne Correlation
- Astrophysical laser operating in the OI 8446-Å line in the
Weigelt blobs of η Carinae, MNRAS, Volume 364, Issue 1, pp.
6 November 2006 Liege Inst. d'Astrophysique 22
3 - The HBT Intensity Interferometer
The crucially important laboratory
work by Hanbury Brown, Twiss and
Purcell was performed around 1955.
It really was at the basis of the
previous considerations (see Glauber
Subsequently (1965), they built a
large optical intensity interferometer
at Narrabri, Australia. Each 'mirror'
was a mosaic of 252 small hexagonal
mirrors, 38 cm.
The composite mirrors were approximately of paraboloidal shape, but great optical
accuracy was not sought, since it was only required that the starlight be directed onto the
The light-gathering power of the 6.5 m diameter mirrors, the detectors, electronics etc.
allowed the Narrabri interferometer to operate down to magnitude +2.0
See the book by R. Hanbury Brown, 1974
6 November 2006 Liege Inst. d'Astrophysique 23
The HBTII correlator
The two 'mirrors' directed the starlight to two
photomultipliers (RCA Type 8575, photocathode 42
mm diameter, stellar image about 25 mm). The
starlight was filtered through a narrow-band
The most-used filter was 443 nm ± 5 nm.
The photocurrent is sent to a wide-band amplifier, then
through a phase-reversing switch, and then through a
wide-band filter that passes 10-110 MHz. The signals
from the two photomultipliers then are multiplied in
the correlator in that frequency range.
This bandwidth excludes seeing frequencies, thus
eliminating their effects.
In the jargon of the first slides, we would today consider the HBTII as the first
astronomical instrument capable to measure the second order correlation coefficient in
the photon strem.
6 November 2006 Liege Inst. d'Astrophysique 24
The mirrors were mounted on two carriages that ran on a circular railway of 188 m
diameter. A central cabin containing the controls and electronics was connected to the
carriages by TV-type coaxial cables from a tower.
The separation of the mirrors could be varied from 10 m up to 188 m. The mirrors
rotated on three axes to follow the star. The available baseline distances permitted
measurements of angular diameters from 0.011" to 0.0006".
The electrical bandwidth (100 MHz) implies that the paths from the photomultipliers to
the correlator must be equal to about 1 ns (30 cm in length) to avoid loss of correlation
due to temporal coherence: it is much easier to equalize electrical transmission lines that
optical paths (in the Michelson stellar interferometer, the paths must be equal to 1 or
6 November 2006 Liege Inst. d'Astrophysique 25
The filtered starlight is a quasi-monochromatic signal, in which the
closely-spaced frequency components can be considered to beat against
one another to create fluctuations in intensity. The accompanying
fluctuations in phase were lost (notice, this loss of phase information is
not necessarily true, see the recent papers by Ofir and Ribak, MNRAS
The normalized correlation is proportional to |γ|2, the square of the fringe
visibility in the Michelson case. Although the phase information was
gone, the magnitude of the degree of coherence was still there, allowing
the measurement of diameters (and possibly of limb-darkening if higher
S/N ratio could have been reached in the second lobe).
6 November 2006 Liege Inst. d'Astrophysique 26
Results of HBTII
Measurements were finally made on 30 or so stars of spectral types B0
to F5 (the sensitivity increases very rapidly with the temperature of the
Measurements could not be made on Betelgeuse, since the mirrors could
not be brought closer than 10 m apart, and the 6.5 m mirrors would
themselves resolve the star, reducing the correlation to zero.
CHANGE OF CORRELATION WITH BASELINE (a) Beta Cru (B0 IV); (b) Alpha Eri (B5 IV); (c) Alpha Car (F0 II)
6 November 2006 Liege Inst. d'Astrophysique 27
The HBTII sensitivity is expressed by:
S / N Kinstr (QE) AreaTelescope T Electr.BW f (m) g (sky)
independent on the optical BW and weakly
dependent on the optical quality- Being a
second order effect it is intrinsically very
low: the original HBT limit was around the
6th mag in one week of integration!
The figure shows the expected gain over the
original HBT realization with modern
detectors (QE 0.4 instead of 0.2) and time
tagging capabilities (100 ps instead of 100
MHz), and precursors like VLTs, LBT,
MAGIC, and finally with the 100 m OWL.
The curves refer to 1, 2 and 3 hours of
6 November 2006 Liege Inst. d'Astrophysique 28
Future of HBTII with ELTs?
In my opinion, the interest in HBTII will survive in the ELTs
I wish to recall the following points:
1- ease of adjusting the time delays of the channels to equality
within few centimeters (electronic instead of optical
2 - immunity to seeing: adaptive optics is not required
4 - blue sensitivity, with the possibility to utilize the large
body of data from Michelson-type interferometers and to
supplement their data with observations in this spectral
6 November 2006 Liege Inst. d'Astrophysique 29
Very Long Baseline Optical Intensity
The most exciting development of the HBT interferometer is the an
Intensity Interferometry with two distant telescopes, therefore an optical
No optical link is indeed needed,
only time tagging to better than
say 100 ps and proper account
of atmospheric refraction and
The concept could be tested
immediately with two or all
telescopes of the ESO VLT
and/or with the two apertures
of the LBT!
LBT would provide essential (almost) zero-delay information.
MAGIC I+II on the Roque is also a very attractive possibility.
6 November 2006 Liege Inst. d'Astrophysique 30
4 - Clocks and Detectors
A few words now about clocks and detectors.
There is a substantial difference, which applies
both to clocks and to detectors, between the
astronomical applications and other applications
such as nuclear physics, laser ranging, laboratory
correlation spectroscopy etc:
we require a continuous functioning, no room for
signal gating, coincidences, integrations etc.
The photons from the celestial source will arrive
when they want!
6 November 2006 Liege Inst. d'Astrophysique 31
Time Distribution among two distant
• The existing GPS and probably also the future Galileo
fall short of the needed precision (say 100 ps or better).
• The problem of distributing a very precise and
extremely well synchronized time among distant
observers is bound to become easier and easier in the
• VLBI indeed is not the only science requiring this
accurate time: terrestrial and interplanetary
communications will act as a most powerful driver .
6 November 2006 Liege Inst. d'Astrophysique 32
An example of very accurate time
distribution – feasible today
Only one master
needed on the
(courtesy of Carlo
6 November 2006 Liege Inst. d'Astrophysique 33
Far Future: Distribution of entangled photons
QIPS: Weinfurter, Zeilinger,
Rarity, Barbieri. ESA
6 November 2006 Liege Inst. d'Astrophysique 34
The Harrison Project
In the frame of a
large contract with
System managed by
Torino Time, we
funding with the
6 November 2006 Liege Inst. d'Astrophysique 35
Inside Quanteye, we performed a market survey for detectors
suitable for High-Time-Resolution Astrophysics & Quantum Optic,
such as PMTs, Streak Cameras, Hybrid Photo Detectors, Avalanche
Photodiodes etc. and available in 2004-2005.
The technology is rapidly advancing, especially under the push of
telecommunications, in particular of quantum cryptography.
We selected for that study, and for the precursor for Asiago a Single
Photon Avalanche Photodiode (SPAD) produced in Italy by MPD.
Other products are now available, from SENS-L in Ireland, id-
Quantique in Suisse, The Czeck Technical University in Prage,
the Max-Planck-Institute for Solid State in Munich, etc.
6 November 2006 Liege Inst. d'Astrophysique 36
MPD SPADs Our detector is the
(SPAD) from MPD,
by Prof. S. Cova in
Milano, and used
already in several
AdOpt devices in Italy
(LBT) and at ESO.
One advantage is the
low cost. The active
area is 50
Cons: devices have been
no CCD- type array, 70 nsecond dead time acquired.
6 November 2006 Liege Inst. d'Astrophysique 37
5 - QuantEYE for the 100m OWL - 1
The baseline solution of focal reducer plus 10x10 lenslet array. The focus of
each lenset is brought to a distributed array of 10x10 SPADs.
The filters are inserted in the parallel beam. A number of very narrow ( 1 A)
bandpass filters, 4 linear polarizers, a number of broad band filters (e.g. BVRI)
Quanteye thus behaves as a fixed-aperture, non-imaging photometer.
The 10x10 outputs are stored in separate memories and can be analyzed in a
variety of modes.
6 November 2006 Liege Inst. d'Astrophysique 38
The electronics of Quanteye
The arrival time of each
photon is acquired and stored.
An on-line correlator allows
real time control of the
observation. An asynchronous
post processing guarantees
data integrity for future
The huge amount of data can be handled by
present-day technology. For example, a run of
1 minute at 1 GHz produces 3 TBytes per
head; existing hard drives of 300 GBytes for
each of the 25 lines insure two such runs
before reading out the data.
6 November 2006 Liege Inst. d'Astrophysique 39
The overall design of Quanteye
Two reading heads (one fixed on the optical axis, one moving over the
scientific field to point a reference star), a real time cross-correlator, a
large storage unit, and a clock (e.g. a Hydrogen Maser unit).
6 November 2006 Liege Inst. d'Astrophysique 40
The photometric capabilities of Quanteye
Quantum Optics mode: full 100m OWL aperture, 6 mirrors, no integration
allowed, 1 A wide filter, SPAD QE = 0.4 at 540 nm, 1 linear polarizer, dark = 100
c/s correspondent to V = 13.9
V T(2) T(3) T(2), T(3) = indicative time
needed to detect deviations from
10.0 0.02 s 140 s Poisson distribution of 2 or 3
12.5 1.63 s (39 h) simultaneous photons. The
Table is a vivid illustration that
15.0 163 s Quantum Astronomy needs the
17.5 4.5 h largest possible collector!
In a more conventional broad band High Time Resolution Astrophysics,
Quanteye would be the fastest photometer, with an exceptionally high
dynamic range (more than 25 mag, from the 5th to the 30th). It could also
reproduce 10x10 telescopes observing the star in 10x10 colors,
polarization states, etc
6 November 2006 Liege Inst. d'Astrophysique 41
6 - AQUEYE
Aqueye (the Asiago
Quantum Eye) is being
built for the 182 cm
Copernicus Telescope at
Cima Ekar as a proof-
with very limited
Aqueye will act as a
photometer with a FoV
of 3” (slightly worse than
the average seeing).
6 November 2006 Liege Inst. d'Astrophysique 42
We are making the best use of the
exisiting AFOSC imaging
spectrograph, which already provides
an intermediate pupil.
6 November 2006 Liege Inst. d'Astrophysique 43
The optical design of Aqueye - 1
The pupil is sub-divided in 4 sub-
The lenses are low cost commercial
The pyramid is custum built.
6 November 2006 Liege Inst. d'Astrophysique 44
The optical design of Aqueye - 2
Optical performances are very
good at all wavelengths from
420 to 750 nm.
6 November 2006 Liege Inst. d'Astrophysique 45
The Mechanical Design of Aqueye
One can use the filters of AFOSC, or insert 4 different filters and
polarizers in the parallel section of each beam after the pyramid.
6 November 2006 Liege Inst. d'Astrophysique 46
Electronics with commercial boards
The selected commercial boards are
used in nuclear physics applications.
Max output rate = 10 Mhz
Typical rate = 100 Khz
SPAD precision = 30 ps 0
2 TDC PXI o VME
CAEN PC Controller
Optionally: DATA BUS
SPAD 3 External ref. (input)
10 Mhz clock (output)
Under Clock External
In the frame
6 November 2006 Liege Inst. d'Astrophysique 47
The detector system on the bench
From right to left:
Two SPADs connected to the VME-TDC unit, the dedicated PC, the
1 TeraByte storage unit, the PC screen
6 November 2006 Liege Inst. d'Astrophysique 48
QuantEYE (and even
Aqueye) would generate
polarization) data strings.
Quantum algorithms could
prove advantageous over
especially if the quantum
computer materializes in
the near future. This
computational task is one
our planned activities inside
the Engineering Dept..
6 November 2006 Liege Inst. d'Astrophysique 49
Expected photometric capabilities of Aqueye for HTRA
1.82 m aperture divided in 4 channels, 2 mirrors+pyramid+ 4 lenses + 200
A filter at 50% transmission, no polarizer. SPAD: QE = 0.45 a 550 nm,
dark = 50 c/s = V 16.0 star, V = 19 mag/(arcsec)2 star, FoV 3 arcsec Vsky
= 17.3. Vega (V=0) at Zenith: 800 phcm-2s-1 A-1.
This table shows the
V Counts/s Average time performances for eanch
between 2 counts individual SPAD. Given
that the dead time is 70 ns,
0 1.31x108 7.6 ns the linear regime starts at V
5 1.31x106 0.76 s = 2.5, and ends around the
16th dark counts
10 1.31x104 0.76 ms dominate). By conbning the
15 1.31x102 76 ms 4 channels with proper
20 1.31x100 0.76 s statistical analysis we could
do certainly better.
6 November 2006 Liege Inst. d'Astrophysique 50
What can be observed with Aqueye?
The 182 cm telescope is too small to detect quantum effects, however
we can try very high time resolution photometry on different
astrophysical problems, starting of course with the mighty Crab pulsar.
Skinakas Observatory 1.3 m Stroboscopic observations by
telescope; OPTIMA (MPE) + Andrej Cadez with the Vega
QVANTOS Mark II (Lund) telescope (70 cm) in Lubiana.
6 November 2006 Liege Inst. d'Astrophysique 51
Lunar and KBO Occultations
Theoretical model of an A0-V star occultation by a Kuiper Belt Object
6 November 2006 Liege Inst. d'Astrophysique 52
The Crab pulsar from Asiago and Slovenia
Skinakas Observatory 1.3 m
telescope; OPTIMA (MPE) +
QVANTOS Mark II (Lund).
Stroboscopic observations by A. Cadez
with the Vega telescope (70 cm) near
6 November 2006 Liege Inst. d'Astrophysique 53
By determining the absolute
transit time over several years
one could detect the presence
of Earth-like planets.
Adapted from (Matthew J.
Holman and Norman W. Murray,
The Use of Transit Timing to
SCIENCE, 25 FEBRUARY 2005
VOL 307, 1288)
I have chosen this example to remind that UTC is a discontinuous time,
and that at the 10 picosecond level everything is difficult.
6 November 2006 Liege Inst. d'Astrophysique 54
D.Dravins, L. Lindegren, E.Mezey & A.T.Young, ATMOSPHERIC
INTENSITY SCINTILLATION OF STARS. I. Statistical
Distributions and Temporal Properties PASP 109, 173-207 (1997),
and 2 more papers.
6 November 2006 Liege Inst. d'Astrophysique 55
6 - Photon Orbital Angular Momentum - 1
Photons have spin angular momentum ± ћ along their
direction of propagation.
However, any electromagnetic field containing a
phase term exp( i ℓ φ ) (e. g. Laguerre-Gaussian and
Bessel modes) also carries a quantity of OAM,
because the Poynting vector and the linear
momentum density of these beams have an azimuthal
component ℓ . The carried POAM is equal to ℓ ħ per
(L. Allen et al. Phys. Rev. A 45, 8185 (1992)).
Beams having as much as ℓ = 300 ћ OAM have been
realized in the laboratory.
6 November 2006 Liege Inst. d'Astrophysique 56
Wavefront Intensity Phase
POAM - 2
The wavefront has an helical shape
composed by ℓ lobes disposed around
the propagation axis z. A phase
singularity called optical vortex is
nested inside the wavefront, along
the axis z.
For helically phased beams, the phase
singularity on the axis dictates zero
intensity there: the cross−sectional
intensity pattern of all such beams
has an annular character that
persists no matter how tightly the
M. Padgett, J. Courtial,
L. Allen, Phys.Today beam is focused.
May 2004, p.25
6 November 2006 Liege Inst. d'Astrophysique 57
Cosmic Sources with POAM??
In astrophysics, POAM could be induced by (M. Harwit ApJ,
597, 1266, 2003):
• interstellar media with density discontinuities on wide
scales (edges of shocked domains) might induce POAM on
a maser beam.
• intense beams from pointlike sources such as pulsars or
Kerr black holes,
• the blackbody radiation of the cosmic microwave
• SETI. A very clever population could artificially
generate photons with PAOM (and also entanglement).
Considerable theoretical effort is needed to elucidate these
6 November 2006 Liege Inst. d'Astrophysique 58
Photon Orbital Angular Momentum -3
So our idea was:
Can POAM be used for nulling the „normal‟ light
from a star on the optical axis of the telescope
(as with a coronagraph), and then provide a
different way to help the discovery of faint
objects close to a bright source (e.g. extrasolar
6 November 2006 Liege Inst. d'Astrophysique 59
How POAM can be generated in the lab
ℓ = -1 ℓ = +1
The generation of beams
carrying OAM proceeds thanks
to the insertion in the optical
path of a phase modifying
N=1 device which imprints a certain
vorticity on the incident beam.
One of such devices is the fork
hologram. If the hologram
presents N dislocations, then at
the m-th diffraction order it
imposes a OAM value equal to N
m ħ (A. Vaziri et al. J. Opt. B 4,
S47 (2002)). A l = 1 fork
hologram was kindly lent us by
Prof. A. Zeilinger (Vienna
6 November 2006 Liege Inst. d'Astrophysique 60
When the axis of the incoming beam is not centered with the
hologram‟s dislocation, the intensity distribution of the output beam
has generally a non-symmetric pattern. The wavefront of the output
beam contains an off-axis optical vortex and the carried OAM may
have a non-integer value. Also focused (non-Gaussian) and tilted
beams are not described by a single L-G mode (L. E. Helseth Opt. Comm.
229, 85 (2004) and M. V. Vasnetsov et al. New J. Phys. 7, 46 (2005)).
When we observe two distinct sources having different positions with
respect to the center of the hologram, the superposition of their L-G
modes will draw a complicated non-symmetric pattern. So we can detect
the presence of a very close companion by analyzing the deviations
observed from the L-G modes expected from a single source centered
with the hologram.
6 November 2006 Liege Inst. d'Astrophysique 61
Sub-Rayleigh and coronagraphy
Therefore, POAM could find applications to astronomical
Swartzlander (Opt. Lett. 26, 497 (2001)) proposed to peer
into the darkness of an optical vortex to enhance the
contrast of a faint source placed very close to a star (below
the Rayleigh limit).
Foo et al. (Opt. Lett. 30, 3308 (2005)) proposed to place in the
first focal plane of a Lyot coronagraph a phase mask that
generates a ℓ = 2 optical vortex.
In laboratory test of this coronagraphic setup (J. H. Lee et al.
Phys. Rev. Lett. 97, 053901 (2006)), two close laser sources
with intensity contrast of 95% were clearly resolved.
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Our sub-Rayleigh experiment
limit (α /D)
We (seeTamburini et al. Phys. Rev. Lett. 97, 163903, 2006)
demonstrated the possibility to achieve sub-Rayleigh
separability of monochromatic and white light sources
with non-integer optical vortex generated by a ℓ = 1
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The achieved resolution
The achieved angular resolution corresponds
approximately to 40% of the Rayleigh criterium.
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A first experiment at the telescope
In a first campaign of observations in 2005, we tested the ℓ =
1 fork-hologram at the f/16 Cassegrain focus of the 122 cm
telescope of Asiago. We observed a double star with a fast
CCD camera (frame rate of 0.07 seconds), to freeze the seeing
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The first star Ras Algethi (α Her, not spatially filtered)
OVs generated by the
double system 4”.7
(dark centers of the L-
Bad seeing gave rise to severe problems, in particular we were
not able to obtain clear “doughnut” patterns from the star. We
are now improving on this preliminary apparatus, planning for
further observations in a near future. At any rate, we think we
have demonstrated the potential interest of the technique,
especially for telescopes equipped with adaptive optics
devices, and in space.
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