Stable Calculation of Optical Properties of Large Non-Periodic Dissipative Multilayered Systems
Luis Eduardo Puente-Díaz, Victor Castillo-Gallardo, Guillermo P. Ortiz, José Samuel Pérez-Huerta, Héctor Pérez-Aguilar, Vivechana Agarwal, W. Luis Mochán
The calculation of the transfer matrix for a large non-periodic multilayered system may become unstable in the presence of absorption. We discuss the origin of this instability and we explore two methods to overcome it: the use of a total matrix to solve for all the fields at all the interfaces simultaneously and an expansion in the Bloch-like modes of a periodic artificially repeated system. We apply both methods to obtain the reflectance spectra of multilayered chirped structures composed of nanostructured porous silicon (PS). Both methods yield reliable and numerically stable results. The former allows an analysis of the field within all layers while the latter is much more efficient computationally, allowing the design of novel structures and the optimization of their parameters. We compare numerical and experimental results across a wide spectral range from the infrared to the ultraviolet.
Nanostructures with one-dimensional periodicity, such as multilayered structures, are currently in the focus of active research in the context of hyperbolic metamaterials and photonic topological structures. An efficient way to describe the materials with subwavelength periodicity is based on the concept of effective material parameters, which can be rigorously derived incorporating both local and nonlocal responses. However, to provide any predictions relevant for applications, effective material parameters have to be supplemented by appropriate boundary conditions. In this work, we provide a…
Optical modes of a multilayered photonic structure with the twisted nematic liquid crystal as a defect layer have been investigated. The electroconvective flow in the nematic makes a spatially periodic structure in the form of abnormal rolls. Non-adiabatic propagation of polarized light in the defect layer causes unique features of the optical modes corresponding to the ordinary $o$-waves. The decay of these modes has been demonstrated with increasing voltage due to the effect of cross-polarization diffraction loss. The modes short-wave shift resulting from the contribution of the non-adiabati…
We present a formalism for studying the radiation-matter interaction in multilayered dielectric structures with active semiconductor quantum wells patterned with an in-plane periodic lattice. The theory is based on the diagonalization of the generalized Hopfield matrix, and it includes loss channels in a non-Hermitian formulation. Hybrid elementary excitations named photonic crystal polaritons arise in these systems, whose detailed dispersion and loss characteristics are shown to depend on material composition as well as on symmetry properties of the lattice. We show the generality of the appr…
For dielectric multilayered metamaterials, the effective-parameter representation is known to be insensitive to geometrical features occurring at deeply subwavelength scales. However, recent studies on periodic and aperiodically ordered geometries have shown the existence of certain critical parameter regimes where this conventional wisdom is upended, as the optical response of finite-size samples may depart considerably from the predictions of standard effective-medium theory. In these regimes, characterized by a mixed evanescent/propagating light transport, different classes of spatial (dis)…
Using the transfer matrix method we examine the parametric behavior of the transmittance of TE and TM electromagnetic plane waves propagating in frequency range which are far from the absorption bands of a periodic multilayered system. We focus on the dependence of the transmittance on the frequency and angle of incidence of the electromagnetic wave for the case in which the periodic structure comprises alternating material-metamaterial layers of various permittivities and permeabilities. A specific example of high transmittance at any angle of incidence in the visible region of the spectrum i…
The paper is devoted to the dynamics of dissipative gap solitons in the periodically corrugated optical waveguides whose spectrum of linear excitations contains a mode that can be referred to as a quasi-Bound State in the Continuum. These systems can support a large variety of stable bright and dark dissipative solitons that can interact with each other and with the inhomogeneities of the pump. One of the focus points of this work is the influence of slow variations of the pump on the behavior of the solitons. It is shown that for the fixed sets of parameters the effect of pump inhomogeneities…
Time crystals are periodic states exhibiting spontaneous symmetry breaking in either time-independent or periodically forced quantum many-body systems. Spontaneous modification of discrete time translation symmetry in a periodically driven physical system can create a discrete time crystal (DTC). DTCs constitute a state of matter with properties such as temporal rigid long-range order and coherence which are inherently desirable for quantum computing and quantum information processing. Despite their appeal, experimental demonstrations of DTCs are scarce and hence many significant aspects of th…
We theoretically and experimentally investigate the formation of dissipative coherent structures in Kerr nonlinear optical microresonators, whose integrated dispersion exceeds the free-spectral range. We demonstrate that the presence of any periodic modulation along the resonator's circumference, such as periodically varying dispersion, can excite higher-order comb structures. We explore the outcomes of coherent microcomb generation in both cases of anomalous and normal dispersion. We are able to access this regime in microresonators via the high peak power of synchronous pulse-driving. For so…
The resonant mode approximation of the scattering matrix is considered for calculating the optical properties of multilayered periodic structures within the formalism of the Fourier-modal method for two diffraction thresholds in close proximity of the spectral-angular range of interest. The developed approximation opens up possibilities for the fast calculation of the scattering matrix of these structures when describing the integral characteristics of spectra and dispersion curves containing high-Q resonances, such as bound states in the continuum.
Single solitons are a special limit of more general waveforms commonly referred to as cnoidal waves or Turing rolls. We theoretically and computationally investigate the stability and accessibility of cnoidal waves in microresonators. We show that they are robust and, in contrast to single solitons, can be easily and deterministically accessed in most cases. Their bandwidth can be comparable to single solitons, in which limit they are effectively a periodic train of solitons and correspond to a frequency comb with increased power. We comprehensively explore the three-dimensional parameter spac…
