Photons, i.e. the basic energy quanta of monochromatic waves, are highly non-localized and occupy all available space in one dimension. This non-local property can complicate the modelling of the quantized electromagnetic field in the presence of optical elements that are local objects. Therefore, in this paper, we take an alternative approach and quantize the electromagnetic field in position space. Taking into account the negative- and the positive-frequency solutions of Maxwell's equations, we construct annihilation operators for highly localized field excitations with bosonic commutator relations. These provide natural building blocks of wave packets of light and enable us to construct locally acting interaction Hamiltonians for two-sided semi-transparent mirrors.

光子，即单色波的基本能量量子，是高度非定域的，在一维中占据所有可用空间。在存在作为局部物体的光学元件的情况下，这种非局部特性会使量化电磁场的建模复杂化。因此，在本文中，我们采用另一种方法对位置空间中的电磁场进行量化。考虑到麦克斯韦方程组的负频解和正频解，我们构造了具有玻色换向器关系的高度局域化场激发的湮灭算子。这些提供了光波包的自然构建块，并使我们能够为双面半透明镜构建局部作用的相互作用哈密顿量。