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arXiv:2303.17074

Partial coherence and coherence length in StimPDC

Gustavo Henrique dos Santos, Raphael César de Souza Pimenta, Rafael M. Gomes, Stephen Patrick Walborn, P. H. Souto Ribeiro

Published Mar 30, 2023• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2303.17074

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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.
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) 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.
Coherence properties of the down-converted beams generated in spontaneous parametric down-conversion are investigated in detail using an iCCD camera. Experimental results are compared with those from a theoretical model developed for pulsed pumping with a Gaussian transverse profile. The results allow us to tailor the shape of correlation area of the signal and idler photons using pump-field and crystal parameters. As an example, splitting of a correlation area caused by a two-peak pump-field spectrum is experimentally studied.
Using a multidimensional Gaussian approximation of the wave function for the signal and idler light generated by spontaneous parametric down-conversion, we derive analytical expressions for the second-order coherence function and the fourth-order coherence function (which is proportional to the signal-idler photon coincidence rate). The magnitudes of these functions are expressed as products of Gaussian functions of the azimuthal angles, the polar angles, and the time delay. Their widths determine six parameters: the coherence angles and coherence time, and the entanglement angles and entanglement time. We show how these parameters are governed by the pump-beam waist, the pump spectral width, and the crystal length. We thereby derive relations analogous to the van Cittert--Zernike theorem and the Siegert relation for thermal light. We show that the normalized photon coincidence rate decreases sharply as the signal and idler apertures become mismatched or misaligned. We experimentally confirm this latter prediction by using parametrically down-converted light obtained from a LiIO3{\mathrm{LiIO}}_{3}LiIO3​ crystal pumped by Kr+{\mathrm{Kr}}^{+}Kr+-ion laser radiation at 413 nm. \textcopyright{}1996 The American Physical Society.
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.
The correlation properties of the pump field in spontaneous parametric down-conversion are crucial in determining the degree of entanglement of generated signal and idler photons. We find theoretically that continuous-variable entanglement of the transverse positions and momenta of these photons can be achieved only if the coherence of the pump beam is sufficiently high. The positions of signal and idler photons are found to be correlated, even for an incoherent pump. However, the momenta of the signal and idler photons are not anti-correlated, even though transverse momentum is conserved.