Amooghorban Ehsan, Wubs Martijn
Faculty of Science, Department of Physics, Shahrekord University, P.O. Box 115, Shahrekord 88186-34141, Iran.
Nanotechnology Research Group, Shahrekord University, P.O. Box 115, Shahrekord 88186-34141, Iran.
Nanomaterials (Basel). 2023 Jan 10;13(2):291. doi: 10.3390/nano13020291.
The quantum optics of metamaterials starts with the question of whether the same effective-medium theories apply as in classical optics. In general, the answer is negative. For active plasmonics but also for some passive metamaterials, we show that an additional effective-medium parameter is indispensable besides the effective index, namely, the effective noise-photon distribution. Only with the extra parameter can one predict how well the quantumness of states of light is preserved in the metamaterial. The fact that the effective index alone is not always sufficient and that one additional effective parameter suffices in the quantum optics of metamaterials is both of fundamental and practical interest. Here, from a Lagrangian description of the quantum electrodynamics of media with both linear gain and loss, we compute the effective noise-photon distribution for quantum light propagation in arbitrary directions in layered metamaterials, thereby detailing and generalizing our previous work. The effective index with its direction and polarization dependence is the same as in classical effective-medium theories. As our main result, we derive both for passive and for active media how the value of the effective noise-photon distribution too depends on the polarization and propagation directions of the light. Interestingly, for -polarized light incident on passive metamaterials, the noise-photon distribution reduces to a thermal distribution, but for -polarized light it does not. We illustrate the robustness of our quantum optical effective-medium theory by accurate predictions both for power spectra and for balanced homodyne detection of output quantum states of the metamaterial.
经典光学中适用的有效介质理论在超材料中是否同样适用。一般来说，答案是否定的。对于有源等离子体激元以及一些无源超材料，我们表明，除了有效折射率外，一个额外的有效介质参数是不可或缺的，即有效噪声光子分布。只有借助这个额外参数，才能预测光量子态在超材料中的保持程度。仅有效折射率并不总是足够的，而在超材料的量子光学中一个额外的有效参数就足够了，这一事实既具有理论意义又具有实际意义。在此，我们从具有线性增益和损耗的介质的量子电动力学的拉格朗日描述出发，计算了分层超材料中量子光在任意方向传播时的有效噪声光子分布，从而详细阐述并推广了我们之前的工作。有效折射率及其方向和偏振依赖性与经典有效介质理论中的相同。作为我们的主要结果，我们推导了无源和有源介质中有效噪声光子分布的值如何也取决于光的偏振和传播方向。有趣的是，对于入射到无源超材料上的偏振光，噪声光子分布简化为热分布，但对于偏振光则不然。我们通过对超材料输出量子态的功率谱和平衡零差检测的准确预测，说明了我们的量子光学有效介质理论的稳健性。
