Direct Determination of Photonic Stopband Topological Character: A Framework Based on Dispersion Measurements

IF 3.7 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY
Nitish Kumar Gupta, Sapireddy Srinivasu, Mukesh Kumar, Anjani Kumar Tiwari, Sudipta Sarkar Pal, Harshawardhan Wanare, S. Anantha Ramakrishna
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Abstract

Ascertainment of photonic stopband absolute topological character requires information regarding the Bloch eigenfunction spatial distribution. Consequently, the experimental investigations predominantly restrict themselves to the bulk-boundary correspondence principle and the ensuing emergence of topological surface state. Although capable of establishing the equivalence/inequivalence of bandgaps, the determination of their absolute topological identity remains out of its purview. The alternate method of reflection phase-based identification also provides only contentious improvements owing to the measurement complexities pertaining to the interferometric setups. To circumvent these limitations, the Kramers–Kronig amplitude-phase causality considerations are resorted to and an experimentally conducive method is proposed for bandgap topological character determination directly from the parametric reflectance measurements. Particularly, it is demonstrated that in case of 1D photonic crystals, polarization-resolved dispersion measurements suffice in qualitatively determining bandgaps’ absolute topological identities. By invoking the translational invariance of the investigated samples, a parameter “differential effective mass” is also defined, that encapsulates bandgaps’ topological identities and engenders an experimentally discernible bandgap classifier.

Abstract Image

直接确定光子止带拓扑特性:基于色散测量的框架
确定光子止带的绝对拓扑特性需要布洛赫特征函数空间分布的相关信息。因此,实验研究主要局限于体界对应原理和随之出现的拓扑表面态。虽然能够确定带隙的等价/不等价,但确定其绝对拓扑特性仍不在其研究范围之内。由于干涉装置的测量复杂性,基于反射相位的另一种识别方法也只能提供有争议的改进。为了规避这些限制,我们采用了克拉默-克罗尼格振幅-相位因果关系,并提出了一种有利于实验的方法,可直接通过参数反射测量确定带隙拓扑特性。特别是,研究证明,在一维光子晶体中,偏振分辨色散测量足以定性地确定带隙的绝对拓扑特性。通过引用所研究样品的平移不变性,还定义了一个参数 "差分有效质量",该参数包含了带隙的拓扑特性,并产生了一个实验可识别的带隙分类器。
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