The Quantum Well of One-Dimensional Photonic Crystals

<div>The quantum transmissivity of 1D PCs with <svg height="11.6791pt" id="M128" style="vertical-align:-3.29112pt" version="1.1" viewbox="-0.0498162 -8.38798 48.1377 11.6791" width="48.1377pt" 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="M495 86L479 114C446 82 419 66 409 66C401 66 401 72 406 97C420 166 436 231 453 297C489 435 454 448 428 448C406 448 384 439 354 422C305 394 222 327 161 247H159L183 345C200 415 194 448 173 448C143 448 82 410 23 351L38 325C64 349 95 371 105 371C111 371 116 365 109 336L25 -4L31 -12C50 -4 77 3 107 9C119 69 132 122 145 168C197 254 321 381 370 381C387 381 393 374 378 305L329 95C309 17 320 -12 345 -12C372 -12 430 19 495 86Z" id="g113-111"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="502" vert-adv-y="502"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.461,3.132)"><path d="M460 334C460 396 434 451 378 451C330 451 241 408 148 300H146L237 679C241 697 241 710 232 710C213 710 153 684 67 675L66 646H95C141 646 145 642 134 595L39 170C23 97 31 54 46 33C64 8 100 -12 137 -12C178 -12 234 3 298 43C391 101 460 222 460 334ZM371 320C371 204 316 89 248 51C230 41 208 37 192 37C143 37 102 72 119 166C124 194 129 215 135 235C202 323 298 392 335 392C353 392 371 372 371 320Z" id="g50-99"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="478" vert-adv-y="478"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,14.957,0)"><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,-0.013,26.22,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z" id="g121-48"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,32.46,0)"><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,-0.013,35.424,0)"><path d="M456 178V225H360V632H320C217 496 115 347 20 206V178H280V106C280 40 276 34 189 27V0H445V27C364 34 360 39 360 106V178H456ZM280 225H82C149 335 214 431 278 520H280V225Z" id="g121-50"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,41.664,0)"><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="g121-51"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g></svg>. (a) The structure is <svg height="14.0501pt" id="M129" style="vertical-align:-2.268101pt" version="1.1" viewbox="-0.0498162 -11.782 57.6311 14.0501" width="57.6311pt" 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="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path d="M578 512C578 619 494 650 387 650H140L134 622C219 615 223 609 210 542L127 119C112 40 104 34 23 28L17 0H235C317 0 387 7 444 33C515 65 564 122 564 195C564 289 495 335 412 352V354C505 373 578 422 578 512ZM486 510C486 422 423 367 314 367H257L294 565C299 591 305 602 315 608C324 614 339 617 362 617C421 617 486 595 486 510ZM466 200C466 100 393 35 296 35C222 35 198 51 212 127L250 333H303C388 333 466 303 466 200Z" id="g113-67"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="601" vert-adv-y="601"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,11.92,0)"><path d="M578 512C578 619 494 650 387 650H140L134 622C219 615 223 609 210 542L127 119C112 40 104 34 23 28L17 0H235C317 0 387 7 444 33C515 65 564 122 564 195C564 289 495 335 412 352V354C505 373 578 422 578 512ZM486 510C486 422 423 367 314 367H257L294 565C299 591 305 602 315 608C324 614 339 617 362 617C421 617 486 595 486 510ZM466 200C466 100 393 35 296 35C222 35 198 51 212 127L250 333H303C388 333 466 303 466 200Z" id="g113-67"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="601" vert-adv-y="601"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,19.081,0)"><path d="M686 28C612 35 607 44 591 112C563 234 541 360 519 489L489 666L457 658L147 121C100 40 89 36 24 28L17 0H240L250 28C168 34 159 41 190 101L262 237H482C495 180 503 137 510 91C517 47 514 35 441 28L433 0H677L686 28ZM475 280H285L429 541H431L475 280Z" id="g113-66"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="703" vert-adv-y="703"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,28.215,0)"><path d="M578 512C578 619 494 650 387 650H140L134 622C219 615 223 609 210 542L127 119C112 40 104 34 23 28L17 0H235C317 0 387 7 444 33C515 65 564 122 564 195C564 289 495 335 412 352V354C505 373 578 422 578 512ZM486 510C486 422 423 367 314 367H257L294 565C299 591 305 602 315 608C324 614 339 617 362 617C421 617 486 595 486 510ZM466 200C466 100 393 35 296 35C222 35 198 51 212 127L250 333H303C388 333 466 303 466 200Z" id="g113-67"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="601" vert-adv-y="601"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,35.637,0)"><path d="M578 512C578 619 494 650 387 650H140L134 622C219 615 223 609 210 542L127 119C112 40 104 34 23 28L17 0H235C317 0 387 7 444 33C515 65 564 122 564 195C564 289 495 335 412 352V354C505 373 578 422 578 512ZM486 510C486 422 423 367 314 367H257L294 565C299 591 305 602 315 608C324 614 339 617 362 617C421 617 486 595 486 510ZM466 200C466 100 393 35 296 35C222 35 198 51 212 127L250 333H303C388 333 466 303 466 200Z" id="g113-67"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="601" vert-adv-y="601"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,43.45,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,47.965,-5.996)"><path d="M389 0V32C297 37 291 46 291 118V635C234 612 176 595 109 583V556L161 554C203 551 207 548 207 497V118C207 46 201 37 110 32V0H389Z" id="g58-47"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,52.397,-5.996)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 317 408 376 408 465C408 569 328 635 237 635C178 635 131 610 100 575L42 494L67 471C94 511 138 565 205 565C277 565 321 518 321 435C321 348 259 269 195 195C146 136 89 82 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g58-48"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg>; (b) the structure is <svg height="14.0501pt" id="M130" style="vertical-align:-2.268101pt" version="1.1" viewbox="-0.0498162 -11.782 61.4306 14.0501" width="61.4306pt" 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="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path d="M578 512C578 619 494 650 387 650H140L134 622C219 615 223 609 210 542L127 119C112 40 104 34 23 28L17 0H235C317 0 387 7 444 33C515 65 564 122 564 195C564 289 495 335 412 352V354C505 373 578 422 578 512ZM486 510C486 422 423 367 314 367H257L294 565C299 591 305 602 315 608C324 614 339 617 362 617C421 617 486 595 486 510ZM466 200C466 100 393 35 296 35C222 35 198 51 212 127L250 333H303C388 333 466 303 466 200Z" id="g113-67"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="601" vert-adv-y="601"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,11.659,0)"><path d="M686 28C612 35 607 44 591 112C563 234 541 360 519 489L489 666L457 658L147 121C100 40 89 36 24 28L17 0H240L250 28C168 34 159 41 190 101L262 237H482C495 180 503 137 510 91C517 47 514 35 441 28L433 0H677L686 28ZM475 280H285L429 541H431L475 280Z" id="g113-66"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="703" vert-adv-y="703"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,20.794,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,25.308,-5.996)"><path d="M141 347C170 480 264 541 327 570C364 587 403 598 436 605L429 641C389 634 339 622 300 609C192 569 37 458 37 239C37 86 126 -12 245 -12C367 -12 454 89 454 210C454 314 379 397 272 397C252 397 231 391 208 380L141 347ZM231 338C323 338 366 257 366 174C366 107 339 27 263 27C180 27 129 123 129 244C129 268 130 291 135 310C158 323 192 338 231 338Z" id="g58-52"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,30.255,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,34.753,0)"><path d="M686 28C612 35 607 44 591 112C563 234 541 360 519 489L489 666L457 658L147 121C100 40 89 36 24 28L17 0H240L250 28C168 34 159 41 190 101L262 237H482C495 180 503 137 510 91C517 47 514 35 441 28L433 0H677L686 28ZM475 280H285L429 541H431L475 280Z" id="g113-66"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="703" vert-adv-y="703"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,43.888,0)"><path d="M578 512C578 619 494 650 387 650H140L134 622C219 615 223 609 210 542L127 119C112 40 104 34 23 28L17 0H235C317 0 387 7 444 33C515 65 564 122 564 195C564 289 495 335 412 352V354C505 373 578 422 578 512ZM486 510C486 422 423 367 314 367H257L294 565C299 591 305 602 315 608C324 614 339 617 362 617C421 617 486 595 486 510ZM466 200C466 100 393 35 296 35C222 35 198 51 212 127L250 333H303C388 333 466 303 466 200Z" id="g113-67"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="601" vert-adv-y="601"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,51.701,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,56.216,-5.996)"><path d="M141 347C170 480 264 541 327 570C364 587 403 598 436 605L429 641C389 634 339 622 300 609C192 569 37 458 37 239C37 86 126 -12 245 -12C367 -12 454 89 454 210C454 314 379 397 272 397C252 397 231 391 208 380L141 347ZM231 338C323 338 366 257 366 174C366 107 339 27 263 27C180 27 129 123 129 244C129 268 130 291 135 310C158 323 192 338 231 338Z" id="g58-52"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg>.</div>

Advances in Condensed Matter Physics

The Quantum Well of One-Dimensional Photonic Crystals

Figure 2