ANNALS OF OPTICS - XXV ENFMC - 2002
Patterns in optical parametric oscillators:
transverse multimode operation
Marcelo Martinelli *, Sara Ducci, Sylvain Gigan, Nicolas Treps, Agnès Maître, and Claude Fabre
*Instituto de Física da USP - São Paulo, SP, Brazil
Laboratoire Kastler Brossel, Université Pierre et Marie Curie- Paris, France
mmartine@usp.br
Abstract
Optical Parametric Oscillators have been used as a source of quantum states of light, like
squeezed vacuum, twin beams, and quadrature squeezed light by cascaded χ(3). On the other hand,
it has been shown that spatial effects on squeezed light can only be achieved by transverse
multimode combinations of quantum fields. We describe the latest results on the generation of
transverse multimode beams and the study of noise distribution in transverse degenerate OPOs,
presenting multimode twin beams in confocal configuration.
Nonclassical states of light have been widely studied for the last decades. As an example of these states, we can
mention the intensity noise fluctuations reduced below the shot noise limit, the generation of intense beams with
noise compressed in one quadrature, squeezed vacuum fluctuations in the output of sub-threshold OPOs, and
twin beams generation with correlated intensity fluctuations. A comprehensive description of these
measurements can be seen in ref.[1]. Most of time one deals with a bright beam, or vacuum fluctuations that are
measured in homodyne detection with the help of a coherent TEM00 beam.
Generally the transverse section of the beam is completely integrated on the detection process, the light being
focused on the detector to avoid loss of information that would reduce the nonclassical effect of the
measurement. Blocking part of the beam or measuring the noise fluctuation in a small region of the single
transverse mode squeezed beam wavefront would reduce the noise compression, just like the attenuation of the
beam by a neutral density filter.
On the other hand, multitransverse nonclassical states can present quantum correlation between different points
of the beam wavefront or local squeezing. This is characterized by the noise reduction even if we sample only a
small region of the beam. As shown in ref. [2], the single transverse mode squeezed state cannot be used to go
beyond the shot noise limit in the resolution of optical images. This problem appears also in the measurement of
small displacements by light beams [3], where these multitransverse squeezed modes can improve the final
resolution.
Multimode generation of squeezed light has already been observed in laser diodes [4]. Optical Parametric
Oscillators operating in cavities with degenerate transverse modes are very promising for the generation of these
multitransverse nonclassical states. Many theoretical works in the subject have discussed the generation of
spatial squeezing in plane cavity OPO [5], quasi-planar cavity [6], or confocal cavity pumped by a plane wave
[7]. It was shown that in this configuration we can have multitransverse mode squeezed vacuum, which can be
measured by any axially symmetrical local oscillator.
Here we present the study of pattern formation in type-I phase matching, degenerate OPO, showing the images
of the system near the concentric limit. The noise distribution in type-II phase matching concentric OPO is also
shown. Finally, we demonstrate the transverse multimode behavior of twin beams generated by a confocal OPO
working with a KTP crystal.
Concentric, type I OPO:
Non- uniform spatial distribution of noise can be expected in transverse degenerate cavity OPO, like the
concentric case. Since the effective cavity length of the cavity depend on the refractive index [8], a type II cavity
cannot be triply concentric, and multimode operation is allowed in only one of the longitudinal modes (signal or
idler). In this situation, increasing threshold and diffuse structures where shown near the concentric limit [9].
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ANNALS OF OPTICS - XXV ENFMC - 2002
On the other hand, type I OPO have parallel polarized signal and idler beams, so the triply concentric cavity can
be obtained. Using a LiNbO3 crystal inserted in a near-concentric cavity made by two concave mirrors (R=20
mm), we observed the pattern formation (Figure 1) in the output beam of a 532 nm pumped OPO. This is a first
condition for transverse distribution of noise, and the pattern formation in a 0.2 mm range near the concentric
limit with low threshold (12 mW) gives a comfortable condition for the system operation.
(a)
(b)
(c)
Figure 1: Structures formed in the output beam of a type I OPO. a) Gaussian output, 0.23
mm below the concentric limit; b) pattern formation, 0.21 mm below the concentric limit;
c) pattern formation, 0,02 mm below the concentric limit.
Confocal, type II OPO:
This system was shown to be a rich source of patterns in the output [10]. We demonstrate the multimode
character of the twin beams generated using an unbalanced detection system for the noise measurement. This
system is shown in figure 2. Fields Ê1 and Ê2, incident in two photodetectors, are attenuated by two adjustable
apertures in front of each beam. If we know the transmittance of the beam through these stops, we can
compensate the attenuation in the measured intensity by electronic amplification of the photocurrent.
In this case, correcting the intensity fluctuations and subtracting the added vacuum fluctuations by the beam
attenuation, we can recover the original value of the noise compression in twin beams.
N CORR =
2
∆2 î out
G 1 î1 + G 2 î 2
+1−
2
G 1 î1 + G 2 î 2
G 1 î1 + G 2 î 2
(
, with ∆2 i out = G 1 δî1 + G 2 δî 2
)
2
Of course, this assumption is valid only if the attenuation process makes a random elimination of the photons in
the incident beam. That is true for neutral density attenuators or a pair of single mode incident beams. For
multimode squeezed beams, the correction returns a different value from the twin beam measurement obtained
with the apertures removed.
Ê1
^i
1
G1
T1
Ê2
^i
out
T2
^i
2
G2
Gi=1/Ti
Figure 2: Unbalanced system for multimode twin beam detection.
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ANNALS OF OPTICS - XXV ENFMC - 2002
The result shown in figure 3 for twin beams in a confocal cavity are made attenuating separately each
one of the twin beams. While the attenuation in signal doesn’t affect much the measured corrected
noise, the attenuation in the idler deviates the corrected noise from the measured 82% normalized
noise of the twin beams, showing clearly the multimode behavior of the squeezed light.
Signal
Idler
Corrected Noise - NCORR
1.2
Near Field
Far Field
1.0
Signal
0.8
0.0
Idler.
0.2
0.4
0.6
0.8
1.0
Transmittance - T
Figure 3: Left: Measurement of the corrected noise as a function of an iris transmittance in
signal and idler beams in the confocal regime. Right: Far field and near field images of the
output beams.
Conclusions
We demonstrate the pattern formation in type I concentric OPO, which can be a source of multimode squeezed
light. Confocal cavity OPOs are shown as sources of multimode twin beams, and a experimental criteria for the
transverse multimode squeezing in demonstrated.
Acknowledgements
M. M. would like to thank FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo) and CAPES
(Comissão de Aperfeiçoamento do Ensino Superior) for funding.
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