Photon-matter interactions

自量子力学早期以来，人们一直认为光子在普通粒子中是独一无二的，因为它没有带对易分量的位置算符。 1999年，我与威廉·贝利斯（William Baylis）合作构建了这样一个光子位置算符，后来发现存在一个完整的光子位置算符家族，取决于光子总角动量的方向和大小。 尽管实验学家每天都在“计数”光子，但并没有精确的方法来计算光子数密度。 部分原因是人们认为没有光子位置算符，在这个意义上说，一个存在的电子，它通常被认为是光子能量密度的知识是足够的。 然而，在非线性过程和激光理论的实用书籍中，光子能量密度和数密度都被考虑。 我目前的研究包括光子局域化，角动量和数密度的调查和应用这些概念的超快激光脉冲和光束的聚焦。在与皇后大学的Marc Dignam的合作中，我还致力于描述光脉冲在半导体纳米结构中产生的激发（称为激子）。 用激子来描述这些系统与实验者使用的物理图像很接近，并且比基于自由电子和空穴的描述更适用于数值计算。 当用两个光脉冲激发时，这些激子产生偏振光栅，该偏振光栅将激子散射成波矢量，该波矢量给出四波混频，并且通常给出通常测量的n波混频信号。 然而，仍然有逻辑上的困难与激子基础的使用和泡利不相容原理的实施。 我在这方面的持续研究将是解决这些问题。

Since the early days of quantum mechanics it has been thought that the photon is unique amongst common particles in having no position operator with commuting components.  In 1999 I constructed such a photon position operator and, in collaboration with William Baylis, later found that there is a whole family of photon position operators depending on the direction and magnitude of the photon's total angular momentum.   In spite of the fact that photons are "counted" every day by experimentalists, there was no precise way to calculate photon number density.  In part because of the perception that there is no photon position operator in that sense that one exists for the electron, it is commonly thought that knowledge of photon energy density is sufficient.  However, in practical books on nonlinear processes and laser theory both photon energy density and number density are considered.  My current research includes an investigation of photon localizability, angular momentum and number density and the application of these concepts to ultrafast laser pulses and focusing of optical beams. In collaboration with Marc Dignam at Queens University I am also working on the description of excitations (called excitons) created in semiconductor nanostructures by optical pulses.  The description of these systems in terms of excitons is close to the physical picture used by experimentalists, and is more practical for numerical calculations than a description based on free electrons and holes.  When excited with two optical pulses, these excitons produce a polarization grating that scatters the excitons into wave vectors that give the four-wave mixing and, in general, the n-wave mixing signals that are commonly measured.  However, there are still logical difficulties with use of the exciton basis and with implementation of the Pauli exclusion principle.  My on-going research in this area will be on the resolution of these issues.