A flexible Bloch mode method for computing complex band structures and impedances of two-dimensional photonic crystals
Felix J. Lawrence, Lindsay C. Botten, Kokou B. Dossou, R. C. McPhedran, C. Martijn de Sterke
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9 pages, 4 figures. Source code available at https://launchpad.net/blochcode . The following article appeared in J. Appl. Phys. and may be found at http://link.aip.org/link/doi/10.1063/1.3674281 . Copyright 2011 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics
We present a flexible method that can calculate Bloch modes, complex band structures, and impedances of two-dimensional photonic crystals from scattering data produced by widely available numerical tools. The method generalizes previous work which relied on specialized multipole and FEM techniques underpinning transfer matrix methods. We describe the numerical technique for mode extraction, and apply it to calculate a complex band structure and to design two photonic crystal antireflection coatings. We do this for frequencies at which other methods fail, but which nevertheless are of significant practical interest.
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Edge states of photonic crystals have attracted much attention for the potential applications such as high transmission waveguide bends, spin dependent splitters and one-way photonic circuits. Here, we theoretically discuss and experimentally observe the deterministic edge states in checkerboard photonic crystals. Due to the self-complementarity of checkerboard photonic crystals, a common band gap is structurally protected between two photonic crystals with different unit cells. Deterministic edge states are found inside the common band gap by exploiting the Zak phase analysis and surface impe…
The density of Bloch electromagnetic states inside a one dimensional photonic crystal (1D PC) is formulated based on its dispersion relations. The formulation applied to any anisotropic medium with known dispersion relations and iso-frequency surfaces. Using a practical 1D PC parameters in the visible range, the density of Bloch states for different modes are calculated.
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We theoretically investigate the non-radiative heat transfer between two photonic crystals separated by a small gap in non-equilibrium thermal situation. We predict that the surface Bloch states coupling supported by these media can make heat exchanges larger than those measured at the same separation distance between two massive homogeneous materials made with the elementary components of photonic crystals. These results could find broad applications in near-field technologies.
Birefringent magnetophotonic crystals are found to exhibit degeneracy breaking for asymmetric contradirectional coupling in planar waveguides. Fundamental to high-order local normal mode coupling leads to partially overlapping gyrotropic bandgaps inside the Brillouin zone and partial suppression of Bloch mode propagation. A large magneto-optically active reorientation in polarization state is found for allowed Bloch modes at bandgap edges.
We investigate the propagation of electromagnetic waves in finite photonic band gap structures. We analyze the phenomenon of conduction and forbidden bands and we show that two regimes are to be distinguished with respect to the existence of a strong field near the interfaces. We precise the domain for which an effective medium theory is sounded.
We theoretically study light propagation in guided Bloch surface waves (BSWs) supported by photonic crystal ridges. We demonstrate that low propagation losses can be achieved just by a proper design of the multilayer to obtain photonic band gaps for both light polarizations. We present a design strategy based on a Fourier analysis that allows one to obtain intrinsic losses as low as 5 dB/km for a structure operating in the visible spectral range. These results clarify the limiting factors to light propagation in guided BSWs and represent a fundamental step towards the development of BSW-based …
We report on the first experimental observation of photonic Bloch oscillations and Zener tunneling in two-dimensional periodic systems. We study the propagation of an optical beam in a square photonic lattice superimposed on a refractive index ramp, and demonstrate the tunneling of light from the first to the higher-order transmission bands of the lattice bandgap spectrum, associated with the spectral dynamics inside the first Brillouin zone and corresponding oscillations of the primary beam.
An analysis is presented of frequency versus wave-vector dispersion in elliptically birefringent one-dimensional layered periodic structures. The presence of local normal mode polarization state variations from one layer to the next is found to lead to mode coupling and to affect the wave-vector dispersion and the character of the Bloch states of the system.
We perform phase-sensitive near-field scanning optical microscopy on photonic-crystal waveguides. The observed intricate field patterns are analyzed by spatial Fourier transformations, revealing several guided TE- and TM-like modes. Using the reconstruction algorithm proposed by Ha, et al. (Opt. Lett. 34 (2009)), we decompose the measured two-dimensional field pattern in a superposition of propagating Bloch modes. This opens new possibilities to study specific modes in near-field measurements. We apply the method to study the transverse behavior of a guided TE-like mode, where the mode extends…
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Floquet-Bloch lattices are systems in which wave packets are subjet to periodic modulations both in time and space, showing rich dynamics. While this type of lattices is difficult to implement in solid-state physics, optical systems have provided excellent platforms to probe their physics: among other effects, they have revealed genuine phenomena such as the anomalous Floquet topological insulator and the funnelling of light into localised interface modes. Despite the crucial importance of the band dispersion in the photon dynamics and the topological properties of the lattice, the direct expe…
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Light propagation in periodic environments is often associated with a number of interesting and potentially useful processes. If a crystalline optical potential is also linearly ramped, light can undergo periodic Bloch oscillations, a direct outcome of localized Wannier-Stark states and their equidistant eigenvalue spectrum. Even though these effects have been extensively explored in conservative settings, this is by no means the case in non-Hermitian photonic lattices encompassing both amplification and attenuation. Quite recently, Bloch oscillations have been predicted in parity-time-symmetr…
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Versatile manipulation of nano- and microobjects underlies the optomechanics and a variety of its applications in biology, medicine, and lab-on-a-chip platforms. For flexible tailoring optical forces, as well as for extraordinary optomechanical effects, additional degrees of freedom should be introduced into the system. Here, we demonstrate that photonic crystals provide a flexible platform for nanoparticles optical manipulation due to both Bloch surface waves (BSWs) and the complex character of the reflection coefficient paving a way for complex optomechanical interactions control. We demonst…
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Based on a perturbative approach, we propose a simple and efficient method to engineer topological edge states in two dimensional magnetic photonic crystals. The topological edge states in the microstructures can be constructed and varied by altering the parameters of the microstructure according to the fieldenergy distributions of the Bloch states at the related Bloch wave vectors. The validity of the proposed method has been demonstrated by exact numerical calculations through three concrete examples. Our method makes the topological edge states 'designable'.
Bloch oscillations, the oscillatory motion of a quantum particle in a periodic potential, are one of the most fascinating effects of coherent quantum transport. Originally studied in the context of electrons in crystals, Bloch oscillations manifest the wave nature of matter and are found in a wide variety of different physical systems. Here we report on the first experimental observation of fractional Bloch oscillations, using a photonic lattice as a model system of a two-particle extended Bose-Hubbard Hamiltonian. In our photonic simulator, the dynamics of two correlated particles hopping on …
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Photonic crystals are periodic structures which prevent light propagation along one or more directions in certain frequency intervals. Their band spectrum is usually analyzed using Floquet-Bloch decomposition. This spectrum is located on the real axis, and it enters the complex plane when absorption and dispersion is considered in the dielectric permittivity of material constituents. Here, we review fundamental definition and properties of dispersion law and group velocity in photonic crystals and we illustrate them with numerical examples.
We propose a practical and efficient solution for the coupling of light from integrated single-mode waveguides to supercollimating planar photonic crystals on conventional silicon-on-insulator platforms. The device consists of a rib waveguide, designed to sustain spatially extended single-modes and matched to a supercollimating photonic crystal, which has been truncated at its boundary to improve impedance matching between the two photonic components. Three-dimensional simulations show transmission efficiencies up to 96 % and reflections below 0.2 % at wavelengths close to 1.55 microns. This a…
Edge modes of a finite-size woodpile can appear within a complete bandgap on an <010> edge. The mode area is as small as 0.066 squared half-in-vacuum-wavelengths, and the propagation loss is small. The field maxima occur at a dielectric-vacuum interface, like at a metal-dielectric interface for surface plasmon modes. The edge mode is a subwavelength-scale 2D light localization mode in non-metallic materials. Analysis of two-mode co-directional coupling between identical surface Bloch modes suggests that a large photonic crystal or surface designing would be needed for suppressing the evanescen…
