Three-periodic 1D photonic crystals for designing the photonic optical devices operating in the infrared regime

Abstract

We investigate theoretically and numerically one-dimensional three-periodic photonic crystals of the structure <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">[</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">S</mml:mi> <mml:mi mathvariant="normal">i</mml:mi> <mml:mi mathvariant="normal">O</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">T</mml:mi> <mml:mi mathvariant="normal">i</mml:mi> <mml:mi mathvariant="normal">O</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> <mml:msup> <mml:mo stretchy="false">)</mml:mo> <mml:mi>N</mml:mi> </mml:msup> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">A</mml:mi> <mml:mi mathvariant="normal">l</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">O</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">Z</mml:mi> <mml:mi mathvariant="normal">r</mml:mi> <mml:mi mathvariant="normal">O</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> <mml:msup> <mml:mo stretchy="false">)</mml:mo> <mml:mi>M</mml:mi> </mml:msup> </mml:mrow> <mml:msup> <mml:mo stretchy="false">]</mml:mo> <mml:mi>K</mml:mi> </mml:msup> </mml:mrow> </mml:math> , formed by dielectric oxides <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">S</mml:mi> <mml:mi mathvariant="normal">i</mml:mi> <mml:mi mathvariant="normal">O</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">T</mml:mi> <mml:mi mathvariant="normal">i</mml:mi> <mml:mi mathvariant="normal">O</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">A</mml:mi> <mml:mi mathvariant="normal">l</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">O</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msub> </mml:math> , and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">Z</mml:mi> <mml:mi mathvariant="normal">r</mml:mi> <mml:mi mathvariant="normal">O</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> </mml:math> ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>N</mml:mi> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>M</mml:mi> </mml:math> are the number of subperiods, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>K</mml:mi> </mml:math> is the number of superperiods). We study the transmission spectra, energy and power fluxes of TE- and TM-polarized electromagnetic waves for a photonic crystal, characterized by the sharp PBG edges, and narrow and pronounced peaks of defect modes. The angular distance (difference in the incidence angles) between the transmission peaks of different polarizations is shown to be about 1.5°, which is 5 times more than in the ternary photonic crystals. The results can be useful for designing highly efficient optical devices operating in the infrared regime on the side-surface of the photonic crystal, such as polarization-sensitive couplers and angle sensors for optical fiber systems.

Topics & Concepts