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Journal articles on the topic 'Modes de Bloch'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 September 2024

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1

Maling, B., and R. V. Craster. "Whispering Bloch modes." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2191 (July 2016): 20160103. http://dx.doi.org/10.1098/rspa.2016.0103.

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We investigate eigenvalue problems for the planar Helmholtz equation in open systems with a high order of rotational symmetry. The resulting solutions have similarities with the whispering gallery modes exploited in photonic micro-resonators and elsewhere, but unlike these do not necessarily require a surrounding material boundary, with confinement instead resulting from the geometry of a series of inclusions arranged in a ring. The corresponding fields exhibit angular quasi-periodicity reminiscent of Bloch waves, and hence we refer to them as whispering Bloch modes (WBMs). We show that if the geometry of the system is slightly perturbed such that the rotational symmetry is broken, modes with asymmetric field patterns can be observed, resulting in field enhancement and other potentially desirable effects. We investigate the WBMs of two specific geometries first using expansion methods and then by applying a two-scale asymptotic scheme.

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2

Saito, Hikaru, Takumi Sannomiya, Naoki Yamamoto, Daichi Yoshimoto, Satoshi Hata, Yoshifumi Fujiyoshi, and Hiroki Kurata. "1pB_K2Electron beam spectroscopy for plasmonic Bloch modes." Microscopy 67, suppl_2 (October 26, 2018): i6. http://dx.doi.org/10.1093/jmicro/dfy047.

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3

Shchesnovich, V. S., and V. V. Konotop. "Nondecaying Bloch modes of a dissipative lattice." EPL (Europhysics Letters) 99, no. 6 (September 1, 2012): 60005. http://dx.doi.org/10.1209/0295-5075/99/60005.

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4

Träger, Denis, Robert Fischer, Dragomir N. Neshev, Andrey A. Sukhorukov, Cornelia Denz, Wieslaw Królikowski, and Yuri S. Kivshar. "Nonlinear Bloch modes in two-dimensional photonic lattices." Optics Express 14, no. 5 (2006): 1913. http://dx.doi.org/10.1364/oe.14.001913.

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5

Milord, L., E. Gerelli, C. Jamois, A. Harouri, C. Chevalier, P. Viktorovitch, X. Letartre, and T. Benyattou. "Engineering of slow Bloch modes for optical trapping." Applied Physics Letters 106, no. 12 (March 23, 2015): 121110. http://dx.doi.org/10.1063/1.4916612.

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6

Yang, Xiaosen, Yang Cao, and Yunjia Zhai. "Non-Hermitian Weyl semimetals: Non-Hermitian skin effect and non-Bloch bulk–boundary correspondence." Chinese Physics B 31, no. 1 (January 1, 2022): 010308. http://dx.doi.org/10.1088/1674-1056/ac3738.

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Abstract We investigate novel features of three-dimensional non-Hermitian Weyl semimetals, paying special attention to the unconventional bulk–boundary correspondence. We use the non-Bloch Chern numbers as the tool to obtain the topological phase diagram, which is also confirmed by the energy spectra from our numerical results. It is shown that, in sharp contrast to Hermitian systems, the conventional (Bloch) bulk–boundary correspondence breaks down in non-Hermitian topological semimetals, which is caused by the non-Hermitian skin effect. We establish the non-Bloch bulk–boundary correspondence for non-Hermitian Weyl semimetals: the topological edge modes are determined by the non-Bloch Chern number of the bulk bands. Moreover, these topological edge modes can manifest as the unidirectional edge motion, and their signatures are consistent with the non-Bloch bulk–boundary correspondence. Our work establishes the non-Bloch bulk–boundary correspondence for non-Hermitian topological semimetals.

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7

Deymier, Pierre A., Keith Runge, Alexander Khanikaev, and Andrea Alu. "Pseudo-spin polarized one-way elastic wave eigenstates in one-dimensional phononic superlattices." Journal of the Acoustical Society of America 155, no. 3_Supplement (March 1, 2024): A192. http://dx.doi.org/10.1121/10.0027268.

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We use a one-dimensional discrete binary elastic superlattice bridging continuous models of superlattices that showcase one-way propagation character and the discrete elastic Su-Schrieffer-Heeger model that does not. By considering Bloch wave solutions of the superlattice wave equation, we demonstrate conditions supporting elastic eigenmodes that do not satisfy translational invariance of Bloch waves over the entire Brillouin zone, unless their amplitude vanishes for some wave number. These modes are characterized by a pseudo-spin, and occur only on one side of the Brillouin zone for given spin, leading to spin-selective one-way wave propagation. We demonstrate how these features result from the interplay of translational invariance of Bloch waves, pseudo-spin, and a Fabry-Pérot resonance condition in the superlattice unit cell.

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8

Vandenbem, Cédric. "Electromagnetic surface waves of multilayer stacks: coupling between guided modes and Bloch modes." Optics Letters 33, no. 19 (September 30, 2008): 2260. http://dx.doi.org/10.1364/ol.33.002260.

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9

Smaâli, R., D. Felbacq, and G. Granet. "Bloch waves and non-propagating modes in photonic crystals." Physica E: Low-dimensional Systems and Nanostructures 18, no. 4 (June 2003): 443–51. http://dx.doi.org/10.1016/s1386-9477(03)00183-8.

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10

Gjonaj, B., J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk. "Optical Control of Plasmonic Bloch Modes on Periodic Nanostructures." Nano Letters 12, no. 2 (January 24, 2012): 546–50. http://dx.doi.org/10.1021/nl204071e.

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11

Yakimov, A. I., V. V. Kirienko, A. V. Dvurechenskii, and D. E. Utkin. "Manifestation of “Slow” Light in the Photocurrent Spectra of Ge/Si Quantum Dot Layers Combined with a Photonic Crystal." JETP Letters 118, no. 4 (August 2023): 244–48. http://dx.doi.org/10.1134/s0021364023602105.

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The spectral characteristics of the photocurrent in the near-infrared range in vertical Ge/Si p–i–n photodiodes with Ge quantum dots embedded in a two-dimensional photonic crystal are investigated. The interaction of the quantum dots with photonic Bloch modes leads to the resonant enhancement of the sensitivity of photodiodes. The dependences of the photocurrent on the angle of incidence of light are used to determine the dispersion relations of the Bloch modes. Regions in the dispersion characteristics where the group velocity of photons is close to zero are revealed. It is established that the maximum enhancement of the photocurrent relative to a photodiode without photonic crystal, which can be up to a factor of ~60, results from the interaction of quantum dots with “slow” Bloch modes.

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12

Deymier, Pierre A., Keith Runge, Alexander Khanikaev, and Andrea Alù. "Pseudo-Spin Polarized One-Way Elastic Wave Eigenstates in One-Dimensional Phononic Superlattices." Crystals 14, no. 1 (January 19, 2024): 92. http://dx.doi.org/10.3390/cryst14010092.

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We investigate a one-dimensional discrete binary elastic superlattice bridging continuous models of superlattices that showcase a one-way propagation character, as well as the discrete elastic Su–Schrieffer–Heeger model, which does not exhibit this character. By considering Bloch wave solutions of the superlattice wave equation, we demonstrate conditions supporting elastic eigenmodes that do not satisfy the translational invariance of Bloch waves over the entire Brillouin zone, unless their amplitude vanishes for a certain wave number. These modes are characterized by a pseudo-spin and occur only on one side of the Brillouin zone for a given spin, leading to spin-selective one-way wave propagation. We demonstrate how these features result from the interplay of the translational invariance of Bloch waves, pseudo-spins, and a Fabry–Pérot resonance condition in the superlattice unit cell.

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13

Adams, Samuel D. M., Richard V. Craster, and Sebastien Guenneau. "Bloch waves in periodic multi-layered acoustic waveguides." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2098 (May 20, 2008): 2669–92. http://dx.doi.org/10.1098/rspa.2008.0065.

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The band spectrum and associated Floquet–Bloch eigensolutions, arising in acoustic and electromagnetic waveguides, which have periodic structure along the guide while remaining of finite width, are found. Homogeneous Dirichlet or Neumann conditions along the guide walls, or an alternation of them, are taken. Importantly, in some cases, a total stop band at zero frequency is identified providing space for low-frequency localized modes; geometric defects in the structured waveguide also create these modes. Numerical and asymptotic techniques identify dispersion curves and trapped modes. Some cases demonstrate maxima and minima of the spectral edges within the Brillouin zone and also allow for ultraslow light or sound. Imaging applications using anomalous dispersion to generate subwavelength resolution are possible and are demonstrated.

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14

Zhong, Yi, and Yun-Zhi Du. "New Localization Method of Abelian Gauge Fields on Bloch Branes." Universe 9, no. 10 (October 16, 2023): 450. http://dx.doi.org/10.3390/universe9100450.

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In this paper, we study the localization of the five-dimensional U(1) gauge field coupled with a background scalar potential on symmetric and asymmetric degenerate Bloch branes. By decomposing the U(1) gauge field AM into its vector part (A^M) and scalar components, we found that the Lagrangian of the five-dimensional U(1) gauge field can be rewritten as two independent parts: one for the vector field and the other for two scalar fields. Regarding the vector part, the effective potential exhibits a volcano-like shape with finite depth. We obtain a massless vector field on both types of Bloch branes and a set of massive KK resonances. For the scalar part, their massless modes are coupled with each other, while two sets of massive scalar KK modes are independent. Similar to the vector effective potential, the scalar potentials create infinite wells for both types of degenerate Bloch brane solutions. Therefore, there is only one independent massless scalar mode and two sets of massive scalar Kaluza–Klein resonances. Furthermore, we also observed that, for the two types of Bloch brane solutions, the asymmetric parameter c0 has different effects on the localization of scalar modes.

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15

Aladwani, Abdelaziz, Mostafa Nouh, and Mahmoud I. Hussein. "Efficient band-structure calculations of non-classically damped phononic materials by Bloch mode synthesis in state space." Journal of the Acoustical Society of America 151, no. 4 (April 2022): A177—A178. http://dx.doi.org/10.1121/10.0011020.

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Bloch mode synthesis (BMS) techniques enable efficient band-structure calculations of periodic media by forming reduced-order models of the unit cell. Rooted in the framework of the Craig-Bampton component mode synthesis methodology, these techniques decompose the unit cell into interior and boundary degrees-of-freedom that are nominally described, respectively, by sets of normal modes and constraint modes. In this paper, we generalize the BMS approach by state-space transformation to extend its applicability to generally damped periodic materials that violate the Caughey-O’Kelly condition for classical damping. In non-classically damped periodic models, the fixed-interface eigenvalue problem may, in general, produce a mixture of underdamped and overdamped modes. We examine two mode-selection schemes for the reduced order model and demonstrate the underlying accuracy-efficiency trade-offs when qualitatively distinct mixtures of underdamped and overdamped modes are incorporated. The proposed approach provides a highly effective computational tool for analysis of large models of phononic crystals and acoustic/elastic metamaterials with complex damping properties. This investigation does not only extend the applicability of BMS techniques to the most generally damped models of periodic media, it also advances our understanding of the nature of damping modes and the non-trivial manner by which they contribute to the wave propagation properties.

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16

Tewary, Vivek. "Combined effects of homogenization and singular perturbations: A bloch wave approach." Networks & Heterogeneous Media 16, no. 3 (2021): 427. http://dx.doi.org/10.3934/nhm.2021012.

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<p style='text-indent:20px;'>In this work, we study Bloch wave homogenization of periodically heterogeneous media with fourth order singular perturbations. We recover different homogenization regimes depending on the relative strength of the singular perturbation and length scale of the periodic heterogeneity. The homogenized tensor is obtained in terms of the first Bloch eigenvalue. The higher Bloch modes do not contribute to the homogenization limit. The main difficulty is the presence of two parameters which requires us to obtain uniform bounds on the Bloch spectral data in various regimes of the parameter.</p>

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17

Yuan, Shaohua, Chaowei Sui, Jiyong Kang, and Chenglong Jia. "Electric readout of Bloch sphere spanned by twisted magnon modes." Applied Physics Letters 120, no. 13 (March 28, 2022): 132402. http://dx.doi.org/10.1063/5.0085775.

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We present a magnonic type of Bloch sphere based on twisted spin-wave (magnon) eigenmodes with opposite intrinsic orbital angular momentum, which is topology-protected and damping-resistant. Taking advantage of the release of the chiral degeneracy of magnons by dynamic dipolar interactions and/or interfacial Dzyaloshinskii–Moriya interactions in ferromagnetic nanodisks, we show how these magnonic “qubit” states can be precisely launched and electrically detected through combined spin pumping and inverse spin Hall effect. The experimental feasibility is verified using full-edged numerical micromagnetic simulations for FeB nanodisks. Our investigations demonstrate the potential of twisted spin waves for magnonic information encoding in a flexible and realizable approach.

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18

Zheligovsky, V. A., and R. A. Chertovskih. "On Kinematic Generation of the Magnetic Modes of Bloch Type." Izvestiya, Physics of the Solid Earth 56, no. 1 (January 2020): 103–16. http://dx.doi.org/10.1134/s1069351320010152.

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19

Huisman, S. R., G. Ctistis, S. Stobbe, J. L. Herek, P. Lodahl, W. L. Vos, and P. W. H. Pinkse. "Extraction of optical Bloch modes in a photonic-crystal waveguide." Journal of Applied Physics 111, no. 3 (February 2012): 033108. http://dx.doi.org/10.1063/1.3682105.

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20

Tausch, Johannes. "Computing Floquet–Bloch modes in biperiodic slabs with boundary elements." Journal of Computational and Applied Mathematics 254 (December 2013): 192–203. http://dx.doi.org/10.1016/j.cam.2013.03.008.

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21

Maes, Björn, Peter Bienstman, and Roel Baets. "Bloch modes and self-localized waveguides in nonlinear photonic crystals." Journal of the Optical Society of America B 22, no. 3 (March 1, 2005): 613. http://dx.doi.org/10.1364/josab.22.000613.

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22

Zang, Leyun, Myeong Soo Kang, Miroslav Kolesik, Michael Scharrer, and Philip Russell. "Dispersion of photonic Bloch modes in periodically twisted birefringent media." Journal of the Optical Society of America B 27, no. 9 (August 12, 2010): 1742. http://dx.doi.org/10.1364/josab.27.001742.

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23

Baghbadorani, Hajar Kaviani, Daniele Aurelio, Jamal Barvestani, and Marco Liscidini. "Guided modes in photonic crystal slabs supporting Bloch surface waves." Journal of the Optical Society of America B 35, no. 4 (March 15, 2018): 805. http://dx.doi.org/10.1364/josab.35.000805.

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24

Liu, Sheng, Yi Hu, Peng Zhang, Xuetao Gan, Cibo Lou, Daohong Song, Jianlin Zhao, Jingjun Xu, and Zhigang Chen. "Tunable self-shifting Bloch modes in anisotropic hexagonal photonic lattices." Optics Letters 37, no. 12 (June 4, 2012): 2184. http://dx.doi.org/10.1364/ol.37.002184.

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25

Möller, Björn M., Mikhail V. Artemyev, and Ulrike Woggon. "Bloch modes and group velocity delay in coupled resonator chains." physica status solidi (a) 204, no. 11 (November 2007): 3636–46. http://dx.doi.org/10.1002/pssa.200776410.

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26

Bagheriasl, Mohammad, and Guido Valerio. "Bloch Analysis of Electromagnetic Waves in Twist-Symmetric Lines." Symmetry 11, no. 5 (May 3, 2019): 620. http://dx.doi.org/10.3390/sym11050620.

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We discuss here under which conditions a periodic line with a twist-symmetric shape can be replaced by an equivalent non-twist symmetric structure having the same dispersive behavior. To this aim, we explain the effect of twist symmetry in terms of coupling among adjacent cells through higher-order waveguide modes. We use several waveguide modes to accurately derive the dispersion diagram of a line through a multimodal transmission matrix. With this method, we can calculate both the phase and attenuation constants of Bloch modes, both in shielded and open structures. In addition, we use the higher symmetry of these structures to further reduce the computational cost by restricting the analysis to a subunit cell of the structure instead of the entire unit cell. We confirm the validity of our analysis by comparing our results with those of a commercial software.

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27

Ge, Daohan, Yujie Zhou, Mengcheng Lv, Jiakang Shi, Abubakar A. Babangida, Liqiang Zhang, and Shining Zhu. "High-sensitivity Bloch surface wave sensor with Fano resonance in grating-coupled multilayer structures." Chinese Physics B 31, no. 4 (March 1, 2022): 044102. http://dx.doi.org/10.1088/1674-1056/ac2e60.

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A new type of device consisting of a lithium niobate film coupled with a distributed Bragg reflector (DBR) was theoretically proposed to explore and release Bloch surface waves for applications in sensing and detection. The film and grating made of lithium niobate (LiNbO3) were placed on both sides of the DBR and a concentrated electromagnetic field was formed at the film layer. By adjusting the spatial incidence angle of the incident light, two detection and analysis modes were obtained, including surface diffraction detection and guided Bloch detection. Surface diffraction detection was used to detect the gas molecule concentrations, while guided Bloch detection was applied for the concentration detection of biomolecule-modulated biological solutions. According to the drift of the Fano curve, the average sensor sensitivities from the analysis of the two modes were 1560 °/RIU and 1161 °/RIU, and the maximum detection sensitivity reached 2320 °/RIU and 2200 °/RIU, respectively. This study revealed the potential application of LiNbO3 as a tunable material when combined with DBR to construct a new type of biosensor, which offered broad application prospects in Bloch surface wave biosensors.

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28

Dias, Bernardo, José M. M. M. de Almeida, and Luís C. C. Coelho. "Photonic Crystal Design for Bloch Surface Wave Sensing." Journal of Physics: Conference Series 2407, no. 1 (December 1, 2022): 012015. http://dx.doi.org/10.1088/1742-6596/2407/1/012015.

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Abstract Bloch Surface Waves (BSW) consist of electromagnetic modes generated at the interface between a photonic crystal and an isotropic dielectric. This type of surface mode displays sharp resonances and high sensitivity to external refractive index variations, and thus appears to be an ideal candidate for usage in optical sensors. Nevertheless, design and optimization of photonic crystals is not a trivial task and constitutes an ongoing field of research. The sensitivity of BSW in both refractometric and adsorption sensing is calculated analytically using first-order perturbation theory for TE modes, allowing the understanding of how several physical parameters of the photonic crystal influence the sensitivity. Preliminary experimental results are presented, which aim to use the analytical calculations to allow for both refractometric and adsorption sensing in a single photonic crystal structure.

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29

Kupersztych, J., and M. Raynaud. "Collective surface modes in small spherical metallic systems within the Bloch-Jensen hydrodynamical model." Journal of Physics: Condensed Matter 6, no. 49 (December 5, 1994): 10669–82. http://dx.doi.org/10.1088/0953-8984/6/49/010.

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30

LINTON, C. M., and M. McIVER. "The existence of Rayleigh–Bloch surface waves." Journal of Fluid Mechanics 470 (October 31, 2002): 85–90. http://dx.doi.org/10.1017/s0022112002002227.

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Rayleigh–Bloch surface waves arise in many physical contexts including water waves and acoustics. They represent disturbances travelling along an infinite periodic structure. In the absence of any existence results, a number of authors have previously computed such modes for certain specific geometries. Here we prove that such waves can exist in the absence of any incident wave forcing for a wide class of structures.

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31

Sobucki, K., M. Krawczyk, O. Tartakivska, and P. Graczyk. "Magnon spectrum of Bloch hopfion beyond ferromagnetic resonance." APL Materials 10, no. 9 (September 1, 2022): 091103. http://dx.doi.org/10.1063/5.0100484.

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With the development of new nanofabrication technologies and measurement techniques, the interest of researchers is moving toward 3D structures and 3D magnetization textures. Special attention is paid to the topological magnetization textures, particularly hopfions. In this paper, we investigate the magnetization dynamics of the hopfion through the numerical solution of the eigenvalue problem. We show that the spectrum of spin-wave modes of the hopfion is much richer than those attainable in ferromagnetic resonance experiments or time-domain simulations reported so far. We identified four groups of modes that differ in the character of oscillations (clockwise or counter-clockwise rotation sense), the position of an average amplitude localization along the radial direction, and different oscillations in the vertical cross section. The knowledge of the full spin-wave spectrum shall help in hopfion identification, understanding of the interaction between spin waves and hopfion dynamics as well as the development of the potential of hopfion in spintronic and magnonic applications.

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32

Couny, F., F. Benabid, P. J. Roberts, M. T. Burnett, and S. A. Maier. "Identification of Bloch-modes in hollow-core photonic crystal fiber cladding." Optics Express 15, no. 2 (January 22, 2007): 325. http://dx.doi.org/10.1364/oe.15.000325.

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33

Blau, Yoav, Noam Berman, and Jacob Scheuer. "Optimal excitation of the Bloch modes of coupled resonator optical waveguides." Optical Engineering 53, no. 10 (September 8, 2014): 102712. http://dx.doi.org/10.1117/1.oe.53.10.102712.

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34

Ansari, Abbas Sheikh, and Behzad Rejaei. "Extraction of effective constitutive parameters of artificial media using Bloch modes." Journal of the Optical Society of America B 36, no. 11 (November 1, 2019): 3226. http://dx.doi.org/10.1364/josab.36.003226.

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35

Kuhlmey, Boris T., Ross C. McPhedran, and C. Martijn de Sterke. "Bloch method for the analysis of modes in microstructured optical fibers." Optics Express 12, no. 8 (2004): 1769. http://dx.doi.org/10.1364/opex.12.001769.

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36

Gralak, Boris, Stefan Enoch, and Gérard Tayeb. "From scattering or impedance matrices to Bloch modes of photonic crystals." Journal of the Optical Society of America A 19, no. 8 (August 1, 2002): 1547. http://dx.doi.org/10.1364/josaa.19.001547.

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37

Lu, Zhongjie, A. Cesmelioglu, J. J. W. Van der Vegt, and Yan Xu. "Discontinuous Galerkin Approximations for Computing Electromagnetic Bloch Modes in Photonic Crystals." Journal of Scientific Computing 70, no. 2 (August 23, 2016): 922–64. http://dx.doi.org/10.1007/s10915-016-0270-1.

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38

Kitahara, Hideaki, Takeshi Kawaguchi, Junichi Miyashita, Ryoko Shimada, and Mitsuo Wada Takeda. "Strongly Localized Singular Bloch Modes Created in Dual-Periodic Microstrip Lines." Journal of the Physical Society of Japan 73, no. 2 (February 15, 2004): 296–99. http://dx.doi.org/10.1143/jpsj.73.296.

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39

Saba, Matthias, and Gerd Schröder-Turk. "Bloch Modes and Evanescent Modes of Photonic Crystals: Weak Form Solutions Based on Accurate Interface Triangulation." Crystals 5, no. 1 (January 5, 2015): 14–44. http://dx.doi.org/10.3390/cryst5010014.

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40

Marcucci, Niccolò, Giorgio Zambito, Maria Caterina Giordano, Francesco Buatier de Mongeot, and Emiliano Descrovi. "Controlling resonant surface modes by arbitrary light induced optical anisotropies." EPJ Web of Conferences 266 (2022): 05008. http://dx.doi.org/10.1051/epjconf/202226605008.

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In this work the sensitivity of Bloch Surface Waves to laser-induced anisotropy of azo-polymeric thin layers is expe rimentally shown . The nanoscale reshaping of the films via thermal-Scanning Probe Lithography allows to couple light to circular photonic nanocavities, tailoring on-demand resonant BSW confined within the nanocavity.

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41

Kanj, Ali, Alexander F. Vakakis, and Sameh Tawfick. "Buckling-induced transmission switching in phononic waveguides." Journal of the Acoustical Society of America 154, no. 3 (September 1, 2023): 1640–59. http://dx.doi.org/10.1121/10.0020831.

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On-chip phononic circuits tailor the transmission of elastic waves and couple to electronics and photonics to enable new signal manipulation capabilities. Phononic circuits rely on waveguides that transmit elastic waves within desired frequency passbands, which are typically designed based on the Bloch modes of the constitutive unit cell of the waveguide, assuming periodicity. Acoustic microelectromechanical system waveguides composed of coupled drumhead resonators offer megahertz operation frequencies for applications in acoustic switching. Here, we construct a reduced-order model (ROM) to demonstrate the mechanism of transmission switching in coupled drumhead-resonator waveguides. The ROM considers the mechanics of buckling under the effect of temperature variation. Each unit cell has two degrees of freedom: translation to capture the symmetric bending modes and angular motion to capture the asymmetric bending modes of the membranes. We show that thermoelastic buckling induces a phase transition triggered by temperature variation, causing the localization of the first-passband modes, similar to Anderson localization caused by disorders. The proposed ROM is essential to understanding these phenomena since Bloch mode analysis fails for weakly disordered (<5%) finite waveguides due to the disorder amplification caused by the thermoelastic buckling. The illustrated transmission control can be extended to two-dimensional circuits in the future.

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42

Forati, Ebrahim. "Density of Bloch states inside a one dimensional photonic crystal." Physica Scripta 97, no. 4 (March 17, 2022): 045814. http://dx.doi.org/10.1088/1402-4896/ac5bbc.

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Abstract The density of Bloch modes inside a one dimensional photonic crystal (1D PC) is formulated based on its dispersion relations. This density function has applications in thermal emission inside a 1D PC, as well as controlling the dynamics of active materials embedded in them. After deriving the formulations, a practical 1D PC parameters in the visible range are used to calculate the density of transverse electric and transverse magnetic modes. Compared to the alternative methods such as using Dyadic Greens functions, this method is less complex and is exact. The method applies to any anisotropic medium for which the dispersion equations are available, analytically.

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43

Colquitt, D. J., R. V. Craster, T. Antonakakis, and S. Guenneau. "Rayleigh–Bloch waves along elastic diffraction gratings." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2173 (January 2015): 20140465. http://dx.doi.org/10.1098/rspa.2014.0465.

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Rayleigh–Bloch (RB) waves in elasticity, in contrast to those in scalar wave systems, appear to have had little attention. Despite the importance of RB waves in applications, their connections to trapped modes and the ubiquitous nature of diffraction gratings, there has been no investigation of whether such waves occur within elastic diffraction gratings for the in-plane vector elastic system. We identify boundary conditions that support such waves and numerical simulations confirm their presence. An asymptotic technique is also developed to generate effective medium homogenized equations for the grating that allows us to replace the detailed microstructure by a continuum representation. Further numerical simulations confirm that the asymptotic scheme captures the essential features of these waves.

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Wang, Zhanwen, Jingwei Wang, Lida Liu, and Yuntian Chen. "Rotational Bloch Boundary Conditions and the Finite-Element Implementation in Photonic Devices." Photonics 10, no. 6 (June 16, 2023): 691. http://dx.doi.org/10.3390/photonics10060691.

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This article described the implementation of rotational Bloch boundary conditions in photonic devices using the finite element method (FEM). For the electromagnetic analysis of periodic structures, FEM and Bloch boundary conditions are now widely used. The vast majority of recent research, however, focused on applying Bloch boundary conditions to periodic optical systems with translational symmetry. Our research focused on a flexible numerical method that may be applied to the mode analysis of any photonic device with discrete rotational symmetry. By including the Bloch rotational boundary conditions into FEM, we were able to limit the computational domain to the original one periodic unit, thus enhancing computational speed and decreasing memory consumption. When combined with the finite-element method, rotational Bloch boundary conditions will give a potent tool for the mode analysis of photonic devices with complicated structures and rotational symmetry. In the meantime, the degenerated modes we calculated were consistent with group theory. Overall, this study expands the numerical tools of studying rotational photonic devices, and has useful applications in the study and design of optical fibers, sensors, and other photonic devices.

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Dobson, David C., and Joseph E. Pasciak. "Analysis of an Algorithm for Computing Electromagnetic Bloch Modes Using Nedelec Spaces." Computational Methods in Applied Mathematics 1, no. 2 (2001): 138–53. http://dx.doi.org/10.2478/cmam-2001-0010.

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AbstractThe problem of approximating the band structure of electromagnetic Bloch modes in a three-dimensional periodic medium is studied. We analyze a mixed finite element approximation technique based on a variation of Nedelec edge elements. The usual conditions for convergence of the static problem are first verified. Subsequently, convergence of approximate eigenvalues to those of the continuous system is proved.

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Fountaine, Katherine T., William S. Whitney, and Harry A. Atwater. "Resonant absorption in semiconductor nanowires and nanowire arrays: Relating leaky waveguide modes to Bloch photonic crystal modes." Journal of Applied Physics 116, no. 15 (October 21, 2014): 153106. http://dx.doi.org/10.1063/1.4898758.

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Pechstedt, R. D., P. St J. Russell, T. A. Birks, and F. D. Lloyd-Lucas. "Selective coupling of fiber modes with use of surface-guided Bloch modes supported by dielectric multilayer stacks." Journal of the Optical Society of America A 12, no. 12 (December 1, 1995): 2655. http://dx.doi.org/10.1364/josaa.12.002655.

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Tang, Xi, Haoqi Luo, Junxue Chen, Ramachandram Badugu, Pei Wang, Joseph R. Lakowicz, and Douguo Zhang. "Converting the guided modes of Bloch surface waves with the surface pattern." Journal of the Optical Society of America B 38, no. 5 (April 16, 2021): 1579. http://dx.doi.org/10.1364/josab.418106.

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Enoch, S., G. Tayeb, and D. Maystre. "Dispersion Diagrams of Bloch Modes Applied to the Design of Directive Sources." Progress In Electromagnetics Research 41 (2003): 61–81. http://dx.doi.org/10.2528/pier02010803.

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Zhang, Peng, Cibo Lou, Sheng Liu, Jianlin Zhao, Jingjun Xu, and Zhigang Chen. "Tuning of Bloch modes, diffraction, and refraction by two-dimensional lattice reconfiguration." Optics Letters 35, no. 6 (March 15, 2010): 892. http://dx.doi.org/10.1364/ol.35.000892.

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