TY - JOUR
T1 - Reflectivity calculated for a three-dimensional silicon photonic band gap crystal with finite support
AU - Devashish, D.
AU - Hasan, Shakeeb B.
AU - van der Vegt, J.J.W.
AU - Vos, Willem L.
PY - 2017/4/26
Y1 - 2017/4/26
N2 - We study numerically the reflectivity of three-dimensional (3D) photonic crystals with a complete 3D photonic band gap. We employ the finite element method to study crystals with the cubic diamondlike inverse woodpile structure. The high-index backbone has a dielectric function similar to silicon. We study crystals with a range of thicknesses up to ten unit cells (L≤10c). The crystals are surrounded by vacuum, and have a finite support as in experiments. The polarization-resolved reflectivity spectra reveal Fabry-Pérot fringes related to standing waves in the finite crystal, as well as broad stop bands with nearly 100% reflectivity, even for thin crystals. The frequency ranges of the stop bands change little with angle of incidence, which is plausible since the stop bands are part of the 3D band gap. Moreover, this result supports the previous assertion that intense reflection peaks measured with a large numerical aperture provide a faithful signature of the 3D photonic band gap. For p-polarized waves, we observe an intriguing hybridization between the Fabry-Pérot resonances and the Brewster angle that remains to be observed in experiments. From the strong reflectivity peaks, it is inferred that the maximum reflectivity observed in experiments is not limited by finite size. The frequency ranges of the stop bands agree very well with stop gaps in the photonic band structure that pertain to infinite and perfect crystals. The angle-dependent reflectivity spectra provide an improved interpretation of the reflectivity measurements performed with a certain numerical aperture and a new insight in the crystal structure, namely unequal pore radii in X and Z directions. The Bragg attenuation lengths LB are found to be smaller by a factor 6 to 9 than earlier estimates that are based on the width of the stop band. Hence, crystals with a thickness of 12 unit cells studied in experiments are in the thick crystal limit (LLB). Our reflectivity calculations suggest that the 3D silicon photonic band gap crystals are interesting candidates for back reflectors in a solar cell in order to enhance the photovoltaic efficiency.
AB - We study numerically the reflectivity of three-dimensional (3D) photonic crystals with a complete 3D photonic band gap. We employ the finite element method to study crystals with the cubic diamondlike inverse woodpile structure. The high-index backbone has a dielectric function similar to silicon. We study crystals with a range of thicknesses up to ten unit cells (L≤10c). The crystals are surrounded by vacuum, and have a finite support as in experiments. The polarization-resolved reflectivity spectra reveal Fabry-Pérot fringes related to standing waves in the finite crystal, as well as broad stop bands with nearly 100% reflectivity, even for thin crystals. The frequency ranges of the stop bands change little with angle of incidence, which is plausible since the stop bands are part of the 3D band gap. Moreover, this result supports the previous assertion that intense reflection peaks measured with a large numerical aperture provide a faithful signature of the 3D photonic band gap. For p-polarized waves, we observe an intriguing hybridization between the Fabry-Pérot resonances and the Brewster angle that remains to be observed in experiments. From the strong reflectivity peaks, it is inferred that the maximum reflectivity observed in experiments is not limited by finite size. The frequency ranges of the stop bands agree very well with stop gaps in the photonic band structure that pertain to infinite and perfect crystals. The angle-dependent reflectivity spectra provide an improved interpretation of the reflectivity measurements performed with a certain numerical aperture and a new insight in the crystal structure, namely unequal pore radii in X and Z directions. The Bragg attenuation lengths LB are found to be smaller by a factor 6 to 9 than earlier estimates that are based on the width of the stop band. Hence, crystals with a thickness of 12 unit cells studied in experiments are in the thick crystal limit (LLB). Our reflectivity calculations suggest that the 3D silicon photonic band gap crystals are interesting candidates for back reflectors in a solar cell in order to enhance the photovoltaic efficiency.
UR - http://www.scopus.com/inward/record.url?scp=85018337348&partnerID=8YFLogxK
U2 - 10.1103/PhysRevB.95.155141
DO - 10.1103/PhysRevB.95.155141
M3 - Article
AN - SCOPUS:85018337348
VL - 95
JO - Physical review B: Covering condensed matter and materials physics
JF - Physical review B: Covering condensed matter and materials physics
SN - 2469-9950
IS - 15
M1 - 155141
ER -