Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Holographic nature of three-wave mixing

Maria Bondani, Alessandra Andreoni

Published Sep 16, 2002• 18 citations
Publisher

Abstract

Three-wave interactions occurring in conditions of type I phase matching in a uniaxial crystal are considered in the general case of noncollinear wave propagation. It is demonstrated that, if one among the interacting fields at ${\ensuremath{\omega}}_{i}(i=1,2,3)$ is virtually unaffected in amplitude by the interaction, the remaining two fields at ${\ensuremath{\omega}}_{j}(j\ensuremath{\ne}i)$ are holographic replicas of each other, the constant field acting as the reference field in holography. Experiments are presented in which a holographic image of an object consisting in a pointlike light source is obtained by either up- or down-conversion for any choice of the object- and reference-field frequencies among ${\ensuremath{\omega}}_{1},$ ${\ensuremath{\omega}}_{2},$ and ${\ensuremath{\omega}}_{3}.$

DOI
10.1103/physreva.66.033805

Related papers

On the Possibility of Holographic Recording in the Absence of Coherence between a Reference Beam and a Beam Scattered by an Object

Rostislav M. Arkhipov, Mikhail V. Arkhipov, Nikolay N. Rosanov

For the holographic recording of the wave field of an object, a pattern created by the interference of the reference wave and the wave scattered by the object is used. Traditional holography requires mutual coherence of the reference and object-related beams. However, it has been shown in this work that the holographic recording of information concerning the object under study is possible without coherence between them, even by using radiation from different sources. Such recording can be carried out by employing subcycle or unipolar radiation pulses, when a resonant medium with a large phase memory time T 2 is used as the recording medium. In this case, the medium records the interference pattern formed by the subcycle or unipolar pulse reflected from the object and the polarization wave created by the same short pulse. Coherence is ensured by a polarization wave, which interacting with radiation reflected from the object induces a population grating in such a medium. This grating mimics the interference pattern in a similar holographic process with a monochromatic source having the wavelength equal to that corresponding to the resonant transition in the medium.

Journal of Experimental and Theoretical Physics Letters•May 1, 2020•37 citations

Properties of two interlinked χ^(2) interactions in noncollinear phase matching

Maria Bondani, Alessia Allevi, Emiliano Puddu +3 more

We present a compact experimental realization of the interaction among five field modes in a chi(2) nonlinear crystal. The classical evolution of the fields can be analytically described assuming that two of the fields play the role of nondepleted pumps. If one of the fields has a nonzero input amplitude, then the other two fields at the output are holographic replicas of the input signal.

Optics Letters•Jan 15, 2004•48 citations

Experimental observation of one-dimensional quantum holographic imaging

Xin-Bing Song, De-Qin Xu, Hai-Bo Wang +4 more

We report the experimental observation of quantum holographic imaging of one-dimensional object with entangled photon pairs, generated in a spontaneous parametric down-conversion process. The signal photons play both roles of “object wave” and “reference wave” in holography but are recorded by a point detector providing only encoding information, while the idler photons travel freely and are locally manipulated with spatial resolution. The holographic image is formed by the two-photon correlation measurement, although both the signal and idler beams are incoherent. Three types of quantum holography schemes are analyzed according to the detection regime of the signal photons.

arXiv:1301.6577•Applied Physics Letters•Sep 23, 2013•28 citations

Quantum holography with undetected light

Sebastian Töpfer, Marta Gilaberte Basset, Jorge Fuenzalida +3 more

Holography exploits the interference of a light field reflected/transmitted from an object with a reference beam to obtain a reconstruction of the spatial shape of the object. Classical holography techniques have been very successful in diverse areas such as microscopy, manufacturing technology, and basic science. However, detection constraints for wavelengths outside the visible range restrict the applications for imaging and sensing in general. For overcoming these detection limitations, we implement phase-shifting holography with nonclassical states of light, where we exploit quantum interference between two-photon probability amplitudes in a nonlinear interferometer. We demonstrate that it allows retrieving the spatial shape (amplitude and phase) of the photons transmitted/reflected from the object and thus obtaining an image of the object despite those photons are never detected. Moreover, there is no need to use a well-characterized reference beam, since the two-photon scheme already makes use of one of the photons as reference for holography.

arXiv:2106.04904•Science Advances•Jan 14, 2022•114 citations

Holographic Grids

Walter Schempp

The holographic transform H is thought of as the sesquilinear mapping which assigns to the elements of the tensor product vector space L2(R) @ L2(R) the matrix coefficient function of the linear Schrodinger representation of the three-dimensional real Heisenberg nil-potent Lie group. - It is the purpose of the present paper to study the quantum mechanical approach to optical holography including optical phase conjugation, electron holography, and computerized tomographic methods in high resolution imaging radar, for instance synthetic-aperture imaging radar like side-looking airborne SAR, and space shuttle SAR. The aspect common to these techniques is the geometric encoding of the two-wave mixing u @ v by the interference pattern H(u,v;.,.) in the holographic plane R @ R performed simultaneously for the amplitude and the phase by the holographic transform H.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Oct 25, 1988•6 citations

Overview of optical phase conjugation

B. Ya. Zel’dovich

Summary form only given. In this tallk I will try to supplement what I learned in the field. Here are the topics to be touched on. The order is not historical, but serves a tutorial purpose. 1. Time reversibility (TR) of optical wave propagation. 2. Mathematical description of TR in terms of complex amplitudes and complex conjugate amplitudes. 3. Static holography by real and conjugate images. 4.Static holography: illumination by counterpropagating reference waves at the recording and reconstruction stages. 5. Dynamic holography/four-wave mixing for phase conjugation (R. Hellwarth, A. Yariv, Yariv-Pepper instability. 6. Delayed and hidden holograms, photon echoes, electro-acoustic echoes. 7. Two-photon coherence, fast nonlinearities and three-wave mixing via X(2) nonlinearity. 8. Yet unrealized: Bragg (periodic domain). Time-domain phase conjugation: reversal of chirp and compensation of the dispersion spread in fibers. 10. Why a laser may (and may not) oscillate at a single transverse mode: discrimination of gain/loss. 11. Phase conjugation via stimulated Brillouin scattering (V.V. Ragulsky; V.V. Shkunov). 12. Brillouin-enhanced four-wave mixing for phase conjugation, ten to the tenth power amplification of the image (G.A. Pasmanik). 13. Photorefractive crystals: nonlinear response at low intensity at a cost of long build-up time. 14. Double phase conjugation 15. Feinberg's cat and cat conjugator.

Conference on Lasers and Electro-Optics•Jan 1, 1998•0 citations
Three-wave interactions occurring in conditions of type I phase matching in a uniaxial crystal are considered in the general case of noncollinear wave propagation. It is demonstrated that, if one among the interacting fields at \ensuremathωi(i=1,2,3){\ensuremath{\omega}}_{i}(i=1,2,3)\ensuremathωi​(i=1,2,3) is virtually unaffected in amplitude by the interaction, the remaining two fields at \ensuremathωj(j\ensuremath≠i){\ensuremath{\omega}}_{j}(j\ensuremath{\ne}i)\ensuremathωj​(j\ensuremath=i) are holographic replicas of each other, the constant field acting as the reference field in holography. Experiments are presented in which a holographic image of an object consisting in a pointlike light source is obtained by either up- or down-conversion for any choice of the object- and reference-field frequencies among \ensuremathω1,{\ensuremath{\omega}}_{1},\ensuremathω1​, \ensuremathω2,{\ensuremath{\omega}}_{2},\ensuremathω2​, and \ensuremathω3.{\ensuremath{\omega}}_{3}.\ensuremathω3​.
For the holographic recording of the wave field of an object, a pattern created by the interference of the reference wave and the wave scattered by the object is used. Traditional holography requires mutual coherence of the reference and object-related beams. However, it has been shown in this work that the holographic recording of information concerning the object under study is possible without coherence between them, even by using radiation from different sources. Such recording can be carried out by employing subcycle or unipolar radiation pulses, when a resonant medium with a large phase memory time T 2 is used as the recording medium. In this case, the medium records the interference pattern formed by the subcycle or unipolar pulse reflected from the object and the polarization wave created by the same short pulse. Coherence is ensured by a polarization wave, which interacting with radiation reflected from the object induces a population grating in such a medium. This grating mimics the interference pattern in a similar holographic process with a monochromatic source having the wavelength equal to that corresponding to the resonant transition in the medium.
We report the experimental observation of quantum holographic imaging of one-dimensional object with entangled photon pairs, generated in a spontaneous parametric down-conversion process. The signal photons play both roles of “object wave” and “reference wave” in holography but are recorded by a point detector providing only encoding information, while the idler photons travel freely and are locally manipulated with spatial resolution. The holographic image is formed by the two-photon correlation measurement, although both the signal and idler beams are incoherent. Three types of quantum holography schemes are analyzed according to the detection regime of the signal photons.
Holography exploits the interference of a light field reflected/transmitted from an object with a reference beam to obtain a reconstruction of the spatial shape of the object. Classical holography techniques have been very successful in diverse areas such as microscopy, manufacturing technology, and basic science. However, detection constraints for wavelengths outside the visible range restrict the applications for imaging and sensing in general. For overcoming these detection limitations, we implement phase-shifting holography with nonclassical states of light, where we exploit quantum interference between two-photon probability amplitudes in a nonlinear interferometer. We demonstrate that it allows retrieving the spatial shape (amplitude and phase) of the photons transmitted/reflected from the object and thus obtaining an image of the object despite those photons are never detected. Moreover, there is no need to use a well-characterized reference beam, since the two-photon scheme already makes use of one of the photons as reference for holography.
The holographic transform H is thought of as the sesquilinear mapping which assigns to the elements of the tensor product vector space L2(R) @ L2(R) the matrix coefficient function of the linear Schrodinger representation of the three-dimensional real Heisenberg nil-potent Lie group. - It is the purpose of the present paper to study the quantum mechanical approach to optical holography including optical phase conjugation, electron holography, and computerized tomographic methods in high resolution imaging radar, for instance synthetic-aperture imaging radar like side-looking airborne SAR, and space shuttle SAR. The aspect common to these techniques is the geometric encoding of the two-wave mixing u @ v by the interference pattern H(u,v;.,.) in the holographic plane R @ R performed simultaneously for the amplitude and the phase by the holographic transform H.
Summary form only given. In this tallk I will try to supplement what I learned in the field. Here are the topics to be touched on. The order is not historical, but serves a tutorial purpose. 1. Time reversibility (TR) of optical wave propagation. 2. Mathematical description of TR in terms of complex amplitudes and complex conjugate amplitudes. 3. Static holography by real and conjugate images. 4.Static holography: illumination by counterpropagating reference waves at the recording and reconstruction stages. 5. Dynamic holography/four-wave mixing for phase conjugation (R. Hellwarth, A. Yariv, Yariv-Pepper instability. 6. Delayed and hidden holograms, photon echoes, electro-acoustic echoes. 7. Two-photon coherence, fast nonlinearities and three-wave mixing via X(2) nonlinearity. 8. Yet unrealized: Bragg (periodic domain). Time-domain phase conjugation: reversal of chirp and compensation of the dispersion spread in fibers. 10. Why a laser may (and may not) oscillate at a single transverse mode: discrimination of gain/loss. 11. Phase conjugation via stimulated Brillouin scattering (V.V. Ragulsky; V.V. Shkunov). 12. Brillouin-enhanced four-wave mixing for phase conjugation, ten to the tenth power amplification of the image (G.A. Pasmanik). 13. Photorefractive crystals: nonlinear response at low intensity at a cost of long build-up time. 14. Double phase conjugation 15. Feinberg's cat and cat conjugator.