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Parametric generation of broadband biphotons in a periodic sequence of thin crystals

E G Lariontsev

Published Feb 27, 2015• 1 citation

Abstract

Collinear parametric scattering of light under type-II phase matching is considered in a periodic sequence of nonlinear cells made of BBO crystals. The possibilities of reducing the duration of the wave packets of biphotons and increasing their intensity under monochromatic pumping are studied. The analysis is based on the account of dispersion of the refractive indices using Sellmeier equations. The obtained results allow one to conclude that at an appropriate choice of the crystal thicknesses and the number of cells, it is possible to significantly increase the flux of broadband biphotons and obtain extremely short quantum packets. It is shown that for sufficiently small thicknesses of individual crystals (layers), this system exhibits a fine structure in the spectrum of biphotons: with an increase in the number of cells (layers) the broadband spectrum is divided into a number of narrow bands and the number of these bands increases. When use is made of a nonlinear BBO crystal, this method allows one to obtain ultrashort packets of biphotons with duration . Compared with a different method of generation of broadband biphotons, which is based on the use of quasi-phase-matched periodically poled crystals, the method studied in this paper does not necessitate the need for the phase modulation of a biphoton to be converted into the amplitude modulation.

DOI: 10.1070/qe2015v045n02abeh015511

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Collinear parametric scattering of light under type-II phase matching is considered in a periodic sequence of nonlinear cells made of BBO crystals. The possibilities of reducing the duration of the wave packets of biphotons and increasing their intensity under monochromatic pumping are studied. The analysis is based on the account of dispersion of the refractive indices using Sellmeier equations. The obtained results allow one to conclude that at an appropriate choice of the crystal thicknesses and the number of cells, it is possible to significantly increase the flux of broadband biphotons and obtain extremely short quantum packets. It is shown that for sufficiently small thicknesses of individual crystals (layers), this system exhibits a fine structure in the spectrum of biphotons: with an increase in the number of cells (layers) the broadband spectrum is divided into a number of narrow bands and the number of these bands increases. When use is made of a nonlinear BBO crystal, this method allows one to obtain ultrashort packets of biphotons with duration . Compared with a different method of generation of broadband biphotons, which is based on the use of quasi-phase-matched periodically poled crystals, the method studied in this paper does not necessitate the need for the phase modulation of a biphoton to be converted into the amplitude modulation.

We study the theory of linearly chirped biphoton wave-packets produced in two basic quasi-phase-matching configurations: chirped photonic-like crystals and aperiodically poled crystals. The novelty is that these structures are considered as definite assembles of nonlinear layers that leads to detailed description of spontaneous parametric down-conversion (SPDC) processes through the discrete Gauss sums. We demonstrate that biphoton spectra for chirped photonic crystals involving a small number of layers consist from definite well-resolved spectral lines. We also discuss the forming of broadband spectra of signal (idler) waves in SPDC for both configurations as number of layers increases as well as in dependence of chirping parameters .

We propose and realize a method of high intensity generation of broadband biphotons and achieve its value up to 150 THz. The source is based on a thin BBO crystal with a thickness of 100 microns, in which spontaneous parametric down-conversion takes place. To compensate for the intensity decrease of the down-conversion caused by the small thickness of the crystal, it is placed inside the cavity of an Ar+ laser. In general, this experiment relates to the widely discussed problem of two-photon shaping in the frequency and/or angular domain.

The generation of biphoton wave packets with a broad spectrum owing to quasi-phase-matched spontaneous parametric down-conversion in a crystal with an aperiodic poling has been considered. Biphotons at the exit of such a sample are not Fourier limited; i.e., their correlation time is much larger than the inverse width of the spectrum. It has been shown that if the inverse grating vector varies linearly along the sample length, the generated biphoton wave packets can be compressed in time by transmitting two-photon light through an optical fiber.

The influence of disordering of quasi-phase-matched structures on the properties of biphoton fields generated by spontaneous parametric down-conversion in periodically poled crystals is studied in the general form, taking into consideration arbitrary one-dimensional spatial distribution of the crystal second-order susceptibility. It is shown that the spectral amplitudes of the biphoton wave function become complex and gain frequency- and angle-dependent phase shifts in the structures with unequal lengths of domains. Effects of the spectrum broadening and the phase shifting are expressed in terms of the crystal non-linear transfer function. Spectrum of the first-order correlation function is found to be strictly dependent on the transfer function module, but insensitive to the phase shifts. Availability of the phase shifts makes the second-order temporal correlation function of the broadened as-generated biphoton field to be almost the same as in case of a single-domain crystal. At the same time, possibility of strong temporal biphoton compression appears further if an additional phase-compensating element is placed after the aperiodically poled crystal.

In this paper, we have studied the process of monochromatic pump light in linearly chirped Periodically Poled [Formula: see text] (PPKTP) nonlinear crystal to generate single-cycle biphotons under Quasi-Phase-Matching (QPM) conditions through a Spontaneous Parametric Down-Conversion (SPDC). A detailed analysis of the phase mismatching function reveals that in PPKTP crystals, for the proper frequency range, the phase mismatching [Formula: see text] is stable and relatively close to 0 due to the relatively stable refractive index, and therefore has a good phase matching effect. Even when the chirp rate becomes small, it is able to produce single-cycle biphotons due to the near-perfect phase matching. Of course, as the chirp rate increases, the frequency response range becomes wider, the temporal width is narrower, and the number of cycles is smaller.