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arXiv:1412.5192 · Nature Communications

Giant narrowband twin-beam generation along the pump-energy propagation direction

Angela M. Pérez, Kirill Yu. Spasibko, Polina R. Sharapova, Olga V. Tikhonova, Gerd Leuchs, Maria V. Chekhova

Published Jul 17, 2015• 28 citations
arXivHTMLPDF

Abstract

Walk-off effects, originating from the difference between the group and phase velocities, limit the efficiency of nonlinear optical interactions. While transverse walk-off can be eliminated by proper medium engineering, longitudinal walk-off is harder to avoid. In particular, ultrafast twin-beam generation via pulsed parametric down-conversion and four-wave mixing is only possible in short crystals or fibres. Here we show that in high-gain parametric down-conversion, one can overcome the destructive role of both effects and even turn them into useful tools for shaping the emission. In our experiment, one of the twin beams is emitted along the pump Poynting vector or its group velocity matches that of the pump. The result is markedly enhanced generation of both twin beams, with the simultaneous narrowing of angular and frequency spectrum. The effect will enable efficient generation of ultrafast twin photons and beams in cavities, waveguides and whispering-gallery mode resonators.

DOI
10.1038/ncomms8707

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Walk-off effects, originating from the difference between the group and phase velocities, limit the efficiency of nonlinear optical interactions. While transverse walk-off can be eliminated by proper medium engineering, longitudinal walk-off is harder to avoid. In particular, ultrafast twin-beam generation via pulsed parametric down-conversion and four-wave mixing is only possible in short crystals or fibres. Here we show that in high-gain parametric down-conversion, one can overcome the destructive role of both effects and even turn them into useful tools for shaping the emission. In our experiment, one of the twin beams is emitted along the pump Poynting vector or its group velocity matches that of the pump. The result is markedly enhanced generation of both twin beams, with the simultaneous narrowing of angular and frequency spectrum. The effect will enable efficient generation of ultrafast twin photons and beams in cavities, waveguides and whispering-gallery mode resonators.
The shape and propagation velocities of pulsed twin beams generated in the process of parametric light down-conversion have been theoretically studied in the case where the delays caused by the dispersion of group velocities exceed the length of a pump pulse. It has been shown that the effective group velocity of the scattered pulse is determined by the arithmetic mean of the group velocities at the scattered radiation and pump frequencies. The scattering matrix elements for the large parametric gain have been numerically found. It has been shown that mixing of the spectral components of scattered radiation can cause a significant narrowing of the twin beam pulses. Finally, for the case of generation of broadband twin beams sequentially in two crystals with an aperiodic domain structure, it has been shown that the visibility of the three-frequency interference decreases as the pump pulse lags behind the scattered radiation pulses.
We suggest a novel optical parametric generator (OPG) in which one of the downconverted beams is spontaneously generated along the Poynting vector of the pump beam. In this configuration, the generation takes advantage of the walk-off of the extraordinary pump, rather than being degraded by it. As a result, the generated signal and idler beams are bright due to a high conversion efficiency, spatially nearly single mode due to the preferred direction of the Poynting vector, tunable over a wide range of wavelengths and broadband. The two beams are also correlated in frequency and in the photon number per pulse. Furthermore, due to their thermal statistics, these beams can be used as a pump to efficiently generate other nonlinear processes.
We suggest a novel optical parametric generator (OPG) in which one of the downconverted beams is spontaneously generated along the Poynting vector of the pump beam. In this configuration, the generation takes advantage of the walk-off of the extraordinary pump, rather than being degraded by it. As a result, the generated signal and idler beams are bright due to a high conversion efficiency, spatially nearly single mode due to the preferred direction of the Poynting vector, tunable over a wide range of wavelengths and broadband. The two beams are also correlated in frequency and in the photon number per pulse. Furthermore, due to their thermal statistics, these beams can be used as a pump to efficiently generate other nonlinear processes. (C) 2016 Optical Society of America
Uniaxial anisotropy in nonlinear birefringent crystals limits the efficiency of nonlinear optical interactions and breaks the spatial symmetry of light generated in the parametric down-conversion (PDC) process. Therefore, this effect is usually undesirable and must be compensated for. However, high gain may be used to overcome the destructive role of anisotropy in order to generate bright two-mode correlated twin-beams. In this work, we provide a rigorous theoretical description of the spatial properties of bright squeezed light in the presence of strong anisotropy. We investigate a single crystal and a system of two crystals with an air gap (corresponding to a nonlinear SU(1,1) interferometer) and demonstrate the generation of bright correlated twin-beams in such configurations at high gain due to anisotropy. We explore the mode structure of the generated light and show how anisotropy, together with crystal spacing, can be used for radiation shaping.
We provide an efficient method for the calculation of high-gain, twin-beam generation in waveguides derived from a canonical treatment of Maxwell's equations. Equations of motion are derived that naturally accommodate photon generation via spontaneous parametric down-conversion (SPDC) or spontaneous four-wave mixing and, also, include the effects both of self-phase modulation of the pump and of cross-phase modulation of the twin beams by the pump. The equations we solve involve fields that evolve in space and are labeled by a frequency. We provide a proof that these fields satisfy bona fide commutation relations and that in the distant past and future they reduce to standard time-evolving Heisenberg operators. Having solved for the input-output relations of these Heisenberg operators we also show how to construct the ket describing the quantum state of the twin beams. Finally, we consider the example of high-gain SPDC in a waveguide with a flat nonlinearity profile, for which our approach provides an explicit solution that requires only a single matrix exponentiation.
nonlinear grating. A peculiar feature of this resonant configuration is that the two pumps simultaneously generate photon pairs over an entire branch of modes, via quasi-phase matching with both fundamental vectors of the reciprocal lattice of the nonlinearity. The parametric gain of these modes depends thus coherently on the sum of the two pump amplitudes and can be controlled by varying their relative intensities and phases. We find that a significant enhancement of the source conversion efficiency, comparable to that of one-dimensionally poled crystals, can be achieved by a dual symmetric pump. We also show how the four-mode coupling arising among shared modes at resonance can be tailored by changing the dual pump parameters.