Dispersion Topological Darkness at Multiple Wavelengths and Polarization States

Abstract

waveguides [5] and slow light systems [6] that are insensitive to imperfections. Therefore, it is generally believed that topological effects promise to result in robust and unique designs and functionalities for future photonic systems. "Topological darkness" is a phenomenon described in the 2D optical-constant space (i.e., refractive index, n, and extinction coefficient, k) using the geometric topological concept. [7,8] To distinguish it from other topological photonic structures designed in wave-vector spaces, [3,4] we will refer to it as dispersion topological darkness (DTD) in this article.Perfect/complete suppression of reflection, as one of the prerequisites to enhance the absorption, was explored extensively using various structures. [9,10] It is in principle achievable in several ideal optical systems under given incident angles, polarization states, and wavelengths [e.g., Brewster angle, [11] prism coupled surface plasmon resonance (SPR) system, [12] coherent absorption system, [13,14] and parity-time metamaterial systems [15,16] , complete suppression of reflection is still challenging due to inhomogeneity, disorder or irregularities of samples, and fabrication errors (e.g., inevitable surface roughness). In particular, if the transmission of a structure is further entirely suppressed, along with the complete suppression of reflection in previously reported DTD phenomena, the perfect/ complete absorption can be guaranteed.According to the Fresnel reflection coefficient for a simple three-layered structure (constructed by a top nanopatterned thin-film with engineerable optical constants, a central lossless spacer layer and a bottom mirror to prevent transmission, see the inset in Figure 1a), a zero reflection line divides the finite optical constant (i.e., n and k) 2D space into two regions (see the solid red curve in Figure 1a). If two endpoints of the dispersion curve for a given top nanopatterned thin film locate in these two regions in this closed finite space (see the blue dotted line in Figure 1a), respectively, Jordan theorem [17] secures at least one intersection point between the zero reflection line and the dispersion curve of the top thin film. Therefore, the condition for zero reflection can always be topologically protected within this closed finite space, which is so called "topological darkness." [7,8] This concept is only related to the effective dispersion Complete suppression of reflection is in principle achievable in ideal optical systems with unique optical features including complete light absorption, abrupt phase change, etc. However, conventional optical systems have an extremely tight tolerance on fabrication errors or inherent roughness of thin films or patterns. Therefore, it is difficult to realize the perfect reflectionless condition in practice. To overcome this challenge, a "topological darkness" concept with mild restrictions to the film quality is proposed using periodic metallic patterns and self-assembled core-shell particles. Due to the topological effect, the robust ...

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