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arXiv:2507.14673 · Physical Review A

Tailoring spatial modes produced by stimulated parametric down-conversion

Aarón A. Aguilar-Cardoso, Cheng Li, Tobey J. B. Luck, Manuel F. Ferrer-Garcia, Jeremy Upham, Jeff S. Lundeen, Robert W. Boyd

Published Oct 6, 2025• 5 citations
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Abstract

We theoretically study and experimentally demonstrate controlled generation of spatial modes of light via stimulated parametric down-conversion (StimPDC) by transferring the spatial structure of a pump beam to the stimulated idler beam. We show how the beam characteristics of the stimulated beam depend on both the pump and seed beam's characteristics, enabling experimental control over size and propagation behavior. We also show how to control and improve the fidelity of different spatial modes and demonstrate that the angular basis ensures uniform fidelity across modes generated with StimPDC.

DOI
10.1103/g22l-cgr1

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arXiv:quant-ph/0104064•Physical Review Letters•Sep 10, 2001•28 citations
We theoretically study and experimentally demonstrate controlled generation of spatial modes of light via stimulated parametric down-conversion (StimPDC) by transferring the spatial structure of a pump beam to the stimulated idler beam. We show how the beam characteristics of the stimulated beam depend on both the pump and seed beam's characteristics, enabling experimental control over size and propagation behavior. We also show how to control and improve the fidelity of different spatial modes and demonstrate that the angular basis ensures uniform fidelity across modes generated with StimPDC.
Stimulated parametric down-conversion (StimPDC) is the seeded version of the process that underlies much of photonic quantum information. Replacing the vacuum at one input port with a coherent seed leaves the interaction Hamiltonian, the phase-matching function and the two-photon amplitude unchanged, while raising the output to levels accessible with ordinary classical detectors. This review treats the transverse spatial physics of that process. We show that a single relation, in which the idler amplitude is the pointwise product of the pump field with the complex conjugate of the seed, organizes results usually presented separately: the image and coherence transfer experiments of the 1990s; phase conjugation and its use for wavefront correction; the conservation and conjugation of orbital angular momentum, together with the generation of radial modes and geometric intensity patterns; and the processing of vector vortex beams carrying spatially varying polarization. We then consider StimPDC as an instrument rather than as an object of study, covering stimulated emission tomography, the experimental realization of Klyshko's advanced-wave picture, and the transfer of partial coherence, including the conservation of the twist phase of twisted Gaussian Schell-model beams. We close with the quantum regime, reached when the seed approaches the single-photon level or the idler is used as a herald, and with an assessment of open problems and prospective applications.
In parametric down conversion, a nonlinear crystal is pumped by a laser and spontaneous emission takes place in signal and idler modes according to the phase matching conditions. A seed laser can stimulate the emission in the signal beam if there is mode overlap between them. This also enhances the emission in the idler beam, affecting its coherence properties. While the degree of coherence of the idler field as a function of the seed power has already been studied, the transverse coherence length has not yet been properly investigated. The transverse coherence length is a key parameter of optical beams that determines the beam divergence, for example. Here, we present a theoretical and experimental investigation of the transverse coherence length in stimulated down conversion. In addition, we make a connection between stimulated down conversion and partially coherent sources like the Gaussian Schell model beams, and show that in general the idler field cannot be described with this model.
Stimulated parametric down-conversion (StimPDC) produces an idler beam that exhibits a phase conjugate of the spatial structure of the classical seed beam. Extending this effect to the single-photon regime can, in principle, enable the control of the orbital angular momentum of single photons. However, its experimental implementation remains challenging due to the lower photon flux of realistic single-photon sources compared to a classical pump beam, which causes the StimPDC process to occur less frequently compared to its spontaneous counterpart. To overcome this, we propose a cascaded parametric down-conversion scheme, in which the signal photon from a spontaneously down-converted pair seeds the StimPDC process, while the idler photon heralds the seed's presence. This configuration uses coincidence detection to effectively post-select for stimulated events among the background of spontaneous contributions. We show that phase conjugation at the single-photon level manifests as a bias towards equal orbital angular momentum between the heralding idler and the stimulated idler. Our results offer a practical route to manipulate single-photon correlations in the orbital angular momentum degree of freedom and could have implications for applications such as free-space quantum communication and quantum-enhanced sensing.
The ability to manipulate the orbital angular momentum (OAM) of a single photon is of vital importance to photonic quantum technologies. A particularly relevant operation is the phase conjugation of OAM. One can in principle achieve this using stimulated parametric down-conversion (StimPDC), which produces an idler beam that exhibits a phase conjugate of the seed beam’s spatial structure. However, implementing StimPDC for single-photon OAM phase conjugation remains challenging. This is because the photon flux of realistic single-photon sources is low compared to that of a classical pump beam, which causes the StimPDC process to occur less frequently compared to its spontaneous counterpart. To overcome this, we propose a cascaded parametric down-conversion scheme, in which the signal photon from a spontaneously down-converted pair seeds the StimPDC process, while the idler photon heralds the seed’s presence. This configuration uses coincidence detection to effectively post-select for stimulated events among the background of spontaneous contributions. We show that single-photon OAM phase conjugation manifests as a bias toward equal OAM between the heralding idler and the stimulated idler. Our results offer a practical route to manipulate single-photon correlations in the OAM degree of freedom and could have implications for applications such as free-space quantum communication and quantum-enhanced sensing.