Camacho Ryan M
Sandia National Laboratories, Albuquerque, NM 87123-1082, USA.
Opt Express. 2012 Sep 24;20(20):21977-91. doi: 10.1364/OE.20.021977.
A novel quantum mechanical formulation of the bi-photon wavefunction and spectra resulting from four-wave mixing is developed for azimuthally symmetric systems. Numerical calculations are performed verifying the use of the angular group velocity and angular group velocity dispersion in such systems, as opposed their commonly used linear counterparts. The dispersion profile and bi-photon spectra of two illustrative examples are given, emphasizing the physical origin of the effects leading to the conditions for angular momentum and energy conservation. A scheme is proposed in which widely spaced narrowband entangled photons may be produced through a four-wave mixing process in a chip-scale ring resonator. The entangled photon pairs are found to conserve energy and momentum in the four-wave mixing interaction, even though both photon modes lie in spectral regions of steep angular group velocity dispersion.
针对方位对称系统，开发了一种由四波混频产生的双光子波函数和光谱的新型量子力学公式。进行了数值计算，验证了此类系统中角群速度和角群速度色散的应用，这与常用的线性对应物不同。给出了两个示例的色散分布和双光子光谱，强调了导致角动量和能量守恒条件的效应的物理起源。提出了一种方案，其中可以通过芯片级环形谐振器中的四波混频过程产生间隔很宽的窄带纠缠光子。发现纠缠光子对在四波混频相互作用中守恒能量和动量，即使两个光子模式都位于角群速度色散陡峭的光谱区域。
