RESUMEN
We systematically studied the relation between the conditional auto-correlation function (CACF) and cross-correlation function (CCF) of biphotons or pairs of single photons. The biphotons were generated from a heated atomic vapor via the spontaneous four-wave mixing (SFWM) process. In practical usage, one single photon of a pair is utilized as the heralding photon, and another is employed as the heralded photon. Motivated by the data of CACF of the heralded photons versus CCF, we proposed a universal formula to predict the CACF. The derived formula was based on general theory and is also valid for the biphoton generation process of spontaneous parametric down-conversion (SPDC). With the formula, we utilized the experimentally determined parameters to predict CACFs, which can well agree with the measured CACFs. The proposed formula enables one to quantitatively know the CACF of heralded single photons without the measurement of Hanbury-Brown-Twiss-type three-fold coincidence count. This study provides a better understanding of biphoton generation using the SFWM or SPDC process. Our work demonstrates a valuable tool for analyzing a vital property of how the heralded photons are close to Fock-state single photons.
RESUMEN
Guiding mid-infrared (mid-IR) signals provide wide-ranging applications including chemical sensing, thermal imaging, and optical waveguiding. To manipulate mid-IR signals on photonic chips, it is critical to build a waveguide that provides both sub-diffraction field confinement and low loss. We present a mid-IR waveguide made up of a multilayer graphene/hexagonal boron nitride (hBN) stacking (MLGhS) and a high-refractive index nanowire. The guided mode of the proposed waveguide structure is formed by coupling the fundamental volume plasmon polariton with the fundamental hyperbolic phonon polariton in hBN, and is then modulated by a high-index nanowire. Interestingly, we found that the effective index, propagation length, and mode area of the guided mode vary as the dependences of N-1, N, and N3/2, where N is the number of graphene layers. In addition, an anomalous result, which reveals Lp and Am monotonously decrease as Fermi energy increases that is not observed in conventional graphene plasmon waveguides, occurs in the present structure. The modal properties are analyzed by altering geometry effects and material parameters, and by crossing the upper Reststrahlen band of hBN from the wavevector k = 1,300 to 1,500 cm-1. Furthermore, crosstalk between adjacent waveguides are investigated to assess the degree of integration. The proposed idea not only provides a potential approach for designing tunable and large-area photonic integrated circuits, but it also has the potential to be extended to other 2D materials such as silicone, germanene, and stanene.