Separated Schmidt modes in the angular spectrum of biphotons

Introducing angular dispersion into a pulsed field associates each frequency with a particular angle with respect to the propagation axis. A perennial yet implicit assumption is that the propagation angle is differentiable with respect to the frequency. Recent work on space–time wave packets has shown that the existence of a frequency at which the derivative of the propagation angle does not exist—which we refer to as non-differentiable angular dispersion—allows for the optical field to exhibit unique and useful characteristics that are unattainable by endowing optical fields with conventional angular dispersion. Because these novel, to the best of our knowledge, features are retained in principle even when the specific non-differentiable frequency is not part of the selected spectrum, the question arises as to the impact of the proximity of the spectrum to this frequency. We show here that operating in the vicinity of the non-differentiable frequency is imperative to reduce the deleterious impact of (1) errors in implementing the angular-dispersion profile and (2) the spectral uncertainty intrinsic to finite-energy wave packets in any realistic system. Non-differential angular dispersion can then be viewed as a resource—quantified by a Schmidt number—that is maximized in the vicinity of the non-differentiable frequency. These results will be useful in designing novel phase-matching of nonlinear interactions in dispersive media.

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SPONTANNOE PARAMETRIChESKOE RASSEYaNIE V DVUOSNYKh NELINEYNO-OPTIChESKIKh KRISTALLAKh: OSOBENNOSTI SOSTOYaNIYa POLYaRIZATsII IZLUChENIYa

Frolovtsev,

Magnitskiy

2024

Žurnal èksperimentalʹnoj i teoretičeskoj fiziki

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Separated Schmidt modes in the angular spectrum of biphotons

Cited by 4 publications

References 45 publications

On the Improvement of the Degree of Polarization Entanglement in the Double-Crystal Scheme of Spontaneous Parametric Down-Conversion

On the Improvement of the Degree of Polarization Entanglement in the Double-Crystal Scheme of Spontaneous Parametric Down-Conversion

Non-differentiable angular dispersion as an optical resource

SPONTANNOE PARAMETRIChESKOE RASSEYaNIE V DVUOSNYKh NELINEYNO-OPTIChESKIKh KRISTALLAKh: OSOBENNOSTI SOSTOYaNIYa POLYaRIZATsII IZLUChENIYa

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