Dispersion Properties of Surface Waves Decaying in Red-Shifted and Blue-Shifted Gaps in Photonic Hypercrystals

<div>The plot of tangential <svg height="9.25202pt" id="M99" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -5.96091 10.1794 9.25202" width="10.1794pt" 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="M387 375C387 402 357 448 257 448C172 448 82 404 82 326C82 289 108 255 156 241V239C85 223 23 181 23 116C23 39 89 -12 182 -12C265 -12 336 31 378 91L361 114C320 73 269 47 216 47C157 47 115 82 115 137C115 191 160 219 218 219C243 219 262 218 272 217L304 259L302 266C295 265 281 264 255 264C195 264 163 294 163 335C163 377 200 416 249 416C293 416 321 389 329 342C331 332 335 329 341 329C355 329 387 352 387 375Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.005,3.132)"><path d="M487 458L455 460C436 434 425 433 397 433C331 433 279 437 225 437C103 437 52 374 24 338L49 312C100 363 152 379 229 374C210 308 184 213 163 117C158 94 156 74 156 58C156 6 180 -12 211 -12C261 -12 313 27 348 68L332 99C307 76 285 64 267 64C252 64 236 86 250 148L301 373C320 373 344 369 364 369C399 369 435 370 450 372C458 386 470 411 487 458Z"></path></g></svg> (blue) and normal <svg height="9.25202pt" id="M100" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -5.96091 10.2982 9.25202" width="10.2982pt" 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="M387 375C387 402 357 448 257 448C172 448 82 404 82 326C82 289 108 255 156 241V239C85 223 23 181 23 116C23 39 89 -12 182 -12C265 -12 336 31 378 91L361 114C320 73 269 47 216 47C157 47 115 82 115 137C115 191 160 219 218 219C243 219 262 218 272 217L304 259L302 266C295 265 281 264 255 264C195 264 163 294 163 335C163 377 200 416 249 416C293 416 321 389 329 342C331 332 335 329 341 329C355 329 387 352 387 375Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.005,3.132)"><path d="M504 89L488 119C453 85 428 69 416 69C408 69 405 75 412 102L462 304C492 438 460 451 436 451S388 441 356 423C311 397 229 336 170 256H168L189 340C208 418 200 451 177 451C144 451 82 413 24 352L40 322C65 345 98 369 108 369C114 369 119 363 112 335L28 -3L36 -12C54 -3 83 4 112 10C125 73 138 122 153 174C205 258 328 382 376 382C395 382 399 369 384 305L330 93C312 25 323 -12 351 -12C378 -12 439 21 504 89Z"></path></g></svg> (brown) components of dielectric constant for HMM versus de-dimensional frequency <span class="nowrap"><svg height="8.8423pt" id="M101" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 12.8091 8.8423" width="12.8091pt" 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="M962 650H739L732 622L760 619C812 613 819 604 798 552C760 457 671 267 606 131H604L511 638H480L237 131H233L183 554C177 607 183 614 226 619L248 622L257 650H24L17 622C88 615 92 611 103 524L173 -11H203L450 491H453L543 -11H575L839 529C882 609 886 613 953 622L962 650Z"></path></g></svg>.</span></div>

Advances in Condensed Matter Physics

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Figure 2

Figure 2: Dispersion Properties of Surface Waves Decaying in Red-Shifted and Blue-Shifted Gaps in Photonic Hypercrystals 