Floquet Theory for Discontinuously Supported Waveguides

<div>Periodic and semiperiodic solutions for Hill’s equation (<a href="https://static.hindawi.com/articles/mse/volume-2016/2651953/figures/#EEq4">5</a>) at <svg height="8.55521pt" id="M134" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -8.34882 37.1406 8.55521" width="37.1406pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M484 406C484 429 465 448 438 448C400 448 352 405 302 356L156 213L191 373C195 391 197 404 197 416C197 436 191 448 178 448C151 448 83 406 23 350L37 328C67 350 101 369 109 369C114 369 115 362 111 344L29 -5L34 -12C63 -5 86 -1 111 3C124 73 137 138 147 161C165 180 189 202 206 217C215 194 249 111 275 57C304 -1 319 -12 342 -12C368 -12 405 -5 471 92L454 115C427 80 395 55 384 55C374 55 364 58 341 106L262 274C282 296 367 378 414 378C427 378 440 370 444 367C449 363 454 362 462 368C476 379 484 395 484 406Z" id="g113-232"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="507" vert-adv-y="507"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,10.224,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,21.487,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,27.727,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z" id="g113-47"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="228" vert-adv-y="228"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,30.691,0)"><path d="M153 550H386L412 615L406 623H120L82 318C104 327 142 338 184 338C294 338 347 275 347 187C347 112 305 39 221 39C160 39 119 71 97 89C88 97 80 96 71 90C59 80 50 67 49 57C48 45 52 36 66 23C80 9 123 -12 169 -12C221 -11 288 15 342 59C403 109 431 165 431 225C431 308 366 395 238 395C212 395 165 379 127 364L153 550Z" id="g113-54"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g></svg>. The red and the blue dotted curves represent the solution of the first and the second of the conditions (<a href="https://static.hindawi.com/articles/mse/volume-2016/2651953/figures/#EEq10">16</a>), respectively.</div>

Modelling and Simulation in Engineering

Floquet Theory for Discontinuously Supported Waveguides

Figure 3