By Martin Maldovan
Conceal -- Contents -- Preface -- advent -- conception -- 1 Structural Periodicity -- 1.1 Nonperiodic as opposed to Periodic buildings -- 1.2 Two-dimensional aspect Lattices -- 1.3 three-d element Lattices -- 1.4 Mathematical Description of Periodic buildings -- 1.5 Fourier sequence -- extra studying -- difficulties -- 2 Periodic features and constructions -- 2.1 creation -- 2.2 growing uncomplicated Periodic capabilities in Dimensions -- 2.3 developing uncomplicated Periodic capabilities in 3 Dimensions -- 2.4 mixture of easy Periodic services -- difficulties -- three Interference of Waves and Interference Lithography -- 3.1 Electromagnetic Waves -- 3.2 The Wave Equation -- 3.3 Electromagnetic airplane Waves -- 3.4 The Transverse personality of Electromagnetic aircraft Waves -- 3.5 Polarization -- 3.6 Electromagnetic strength -- 3.7 Interference of Electromagnetic airplane Waves -- 3.8 Interference Lithography -- extra examining -- difficulties -- four Periodic buildings and Interference Lithography -- 4.1 the relationship among the Interference of airplane Waves and Fourier sequence -- 4.2 uncomplicated Periodic buildings in Dimensions through Interference Lithography -- 4.3 easy Periodic constructions in 3 Dimensions through Interference Lithography -- additional examining -- difficulties -- Experimental -- five Fabrication of Periodic constructions -- 5.1 creation -- 5.2 gentle Beams -- 5.3 a number of Gratings and the Registration problem -- 5.4 Beam Configuration -- 5.5 development move: fabric systems and Photoresists -- 5.6 functional issues for Interference Lithography -- 5.7 ultimate comments -- additional studying -- purposes -- 6 Photonic Crystals -- 6.1 creation -- 6.2 One-dimensional Photonic Crystals -- 6.3 Two-dimensional Photonic Crystals -- 6.4 three-d Photonic Crystals -- extra examining -- difficulties -- 7 Phononic Crystals -- 7.1 creation -- 7.2 Phononic Crystals -- 7.3 One-dimensional Phononic Crystals -- 7.4 Two-dimensional Phononic Crystals -- 7.5 three-d Phononic Crystals -- extra interpreting -- difficulties -- eight Periodic mobile Solids -- 8.1 advent -- 8.2 One-dimensional Hookes legislation -- 8.3 the strain Tensor -- 8.4 the tension Tensor -- 8.5 StressStrain dating: The Generalized Hookes legislations -- 8.6 The Generalized Hookes legislations in Matrix Notation -- 8.7 The Elastic Constants of Cubic Crystals -- 8.8 Topological layout of Periodic mobile Solids -- 8.9 Finite point software to Calculate Linear Elastic Mechanical houses -- 8.10 Linear Elastic Mechanical homes of Periodic mobile Solids -- 8.11 Twelve-connected Stretch-dominated Periodic mobile Solids through Interference Lithography -- 8.12 Fabrication of an easy Cubic mobile sturdy through Interference Lithography -- 8.13 Plastic Deformation of Microframes -- additional examining -- nine extra functions -- 9.1 Controlling the Spontaneous Emission of sunshine -- 9.2 Localization of sunshine: Microcavities and Waveguides -- 9.3 Simultaneous Localization of sunshine and Sound in PhotonicPhononic Crystals: Novel AcousticOptical units -- 9.4 detrimental Refraction and Superlenses -- 9.5 Multifunctional Periodic constructions: greatest shipping of warmth and electrical energy -- 9.6 Microfluidics -- 9.7 Thermoelectric power -- additional studying -- Appendix A MATLAB application
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Additional resources for Periodic materials and interference lithography for photonics, phononics and mechanics
In this chapter, we use Fourier series expansions to systematically create periodic functions that represent two- and three-dimensional periodic structures. By making a few assumptions on the relative weights of the cosine and sine functions, we develop a method that allows us to create and classify periodic functions based on their Fourier series expansions. Periodic Materials and Interference Lithography. M. Maldovan and E. Thomas Copyright 2009 WILEY-VCH Verlag GmbH & Co. 1b) where n, m, and p are integer numbers, a, b, and c are the lengths of the edges of the unit cells, and a00 , anm , bnm and a000 , anmp , bnmp are the set of Fourier coefﬁcients corresponding to two- and three-dimensional periodic functions, respectively.
If f1 (x, y) + t > 0 → Material A, and if f1 (x, y) + t < 0 → Material B. 5, fA = 69%. 2 f 2 (x, y) and f 4 (x, y) Functions Analogously, in this section we obtain the formulas for the simple periodic functions f2 (x, y) and f4 (x, y) and graphically display the corresponding periodic structures. 4, respectively, where each simple periodic function is made of the sum of two cosine or sine terms. 4 into a single function for each case. 19) 37 38 2 Periodic Functions and Structures y y a a a x a (a) Fig.
The large cubes in solid lines deﬁne the conventional nonprimitive unit cells (which contain more than one lattice point), whereas the gray rhombs with six parallelogram faces deﬁne the primitive unit cells (which contain a single lattice point). When repeated in space, both the unit cells (nonprimitive and primitive) build up exactly the same lattice. The reason to use the conventional nonprimitive unit cell instead of the primitive unit cell is the fact that the former helps visualize the symmetric distribution of the points in the lattice.