Suppression of light propagation in a medium made of randomly arranged dielectric spheres

📝 Abstract

Light propagation in a medium made of densely packed dielectric spheres is investigated by using a rigorous diffraction theory. It is shown that a substantial suppression of the local density of states occurs in spectral domains where the single constituents exhibit Mie resonances. The local density of states decreases exponentially at the pertinent frequencies with a linearly increasing spatial extension of the aggregated spheres. It is shown that a self-sustaining random arrangement of core-shell spheres shows the same fundamental characteristics. Such approach offers a path towards easy to fabricate photonic materials with omnidirectional gaps that may find use in various applications.

💡 Analysis

Light propagation in a medium made of densely packed dielectric spheres is investigated by using a rigorous diffraction theory. It is shown that a substantial suppression of the local density of states occurs in spectral domains where the single constituents exhibit Mie resonances. The local density of states decreases exponentially at the pertinent frequencies with a linearly increasing spatial extension of the aggregated spheres. It is shown that a self-sustaining random arrangement of core-shell spheres shows the same fundamental characteristics. Such approach offers a path towards easy to fabricate photonic materials with omnidirectional gaps that may find use in various applications.

📄 Content

Suppression of light propagation in a medium made of randomly arranged dielectric spheres Carsten Rockstuhl∗and Falk Lederer Institute of Solid State Theory and Optics, Friedrich-Schiller-Universit¨at, Max-Wien-Platz 1, D-07743 Jena, Germany Light propagation in a medium made of densely packed dielectric spheres is investigated by using a rigorous diffraction theory. It is shown that a substantial suppression of the local density of states occurs in spectral domains where the single constituents exhibit Mie resonances. The local density of states decreases exponentially at the pertinent frequencies with a linearly increasing spatial extension of the aggregated spheres. It is shown that a self-sustaining random arrangement of core- shell spheres shows the same fundamental characteristics. Such approach offers a path towards easy to fabricate photonic materials with omnidirectional gaps that may find use in various applications. In the past several years light propagation in random media composed of discrete scattering objects has attracted a considerable deal of interest. It derives its fascination not only from numerous potential applications such as, e.g., the random laser [1, 2], but also because it challenges our fundamental understanding of light propagation. Most notably, the effect of light localization attracted considerable attention [3]. Light localization can be understood as a synonym for the occurrence of a complete photonic band gap where spectral components of light within the photonic band gap must not propagate within the medium because Maxwell’s equations provide only evanescent wave solutions. By placing a source that emits light at a frequency within the gap inside such material, the light transport offthe the source is suppressed. It remains localized. Light localization in one-dimensional structures may be easily achieved by, e.g., introducing a defect into a sequence of dielectric layers arranged to form a Bragg stack. In two-dimensional media made of infinitely extended cylinders of high permittivity this localization was feasible by exploiting scattering resonances of sufficient strength [4, 5]. As a signature of localization one may use the exponential decay of the local density of states (LDOS) at a point inside the medium with increasing size of the system. A significant suppression of the LDOS in a finite system may be interpreted as a sign of the appearance of a complete band gap, although it does not constitute a rigorous proof. Because scattering resonances also affect the formation of a gap for a periodic arrangement of the cylinders, a complementary computation of the photonic band structure proved that the band gaps occurs indeed in the same spectral domain as the reduced LDOS [5]. In three-dimensional systems, made of spheres [6], this possibility of light localization is controversially discussed as in experiments absorption may potentially shade localization effects [7]. To investigate theoretically the possibility of a suppression of light propagation, one may take advantage of an analytical approach [8]. But as the structure involves a high index contrast and a size of the scatterers that is comparable to the wavelength, usually the problem requires a rigorous solution of Maxwell’s equations [9, 10]. Using a super cell approach rigorous computations of the photonic density of states can be performed. For an amorphous photonic material consisting of a continuous-random-network a complete photonic band gap has been identified recently [11]. This work has shown that appropriate short-range order might also permit for light localization, in addition to the well-known suppression of light propagation in periodic media due to Bragg resonances [12]. However, most experimental investigations of light propagation in 3D random media [13] employed sufficiently dense packed high permittivity spheres. This is mainly due to their easy fabrication procedure that relies on colloidal chemistry. The excitation of Mie resonances in these spheres is usually regarded as the primary reason for suppressing propagation [14, 15]. To theoretically verify the effects associated with light localization, various efforts were under- taken in the past. In Ref. 16 the density of states was computed for small clusters of spheres using a generalized Mie theory. In Ref. 17 scattering effects depending on the cluster size were studied for low index contrast using the superposition T-matrix method. A large scale finite-difference time-domain (FDTD) method was also used to trace light propagation in ensembles of spheres with a strongly varying size [18]. In this work we focus on investigating the LDOS of large clusters made of randomly arranged identical high permittivity spheres. For this purpose we use the FDTD method [19]. It is shown that the LDOS decays exponentially with increasing size of the cluster in certain frequency intervals indicating a significant reduction of light transport velocity. The spectral positions of

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