Equivalent Refractive Index of Multilayer-Type Photonic Crystals
Method of calculating the equivalent refractive index of multilayer-type photonic crystals is proposed. The equivalent index here refers to the Herpin's index which has been conventionally utilized for the design of antireflective (AR) coatings on flat multilayer filters. The index is directly...
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| Published in: | Japanese Journal of Applied Physics Vol. 49; no. 9; pp. 092001 - 092001-5 |
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| Main Author: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
The Japan Society of Applied Physics
01-09-2010
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| Online Access: | Get full text |
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| Summary: | Method of calculating the equivalent refractive index of multilayer-type photonic crystals is proposed. The equivalent index here refers to the Herpin's index which has been conventionally utilized for the design of antireflective (AR) coatings on flat multilayer filters. The index is directly connected to the Fresnel reflection coefficient between the ambient media and photonic crystals. The procedure of calculating the equivalent index of autocloning-type photonic crystals, which consists of multilayer of zigzag cross section, is described. Difference between the indices of photonic crystals and flat multilayer is also discussed. |
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| Bibliography: | Schematic view of an autocloning-type multilayer photonic crystal (MLPhC). Schematic view of the space for computation of reflection spectra. BBC and PML stand for Bloch boundary condition and perfectly matched layers, respectively. Example of the trajectories of complex reflectivity of the electric field for TE modes. (a) Reflectivity at the launching/monitoring position. (b) Reflectivity at the surface of MLPhC, calculated using eq. ( ). PB and SB stand for passband and stopband, respectively. Real (upper) and imaginary (lower) part of the complex reflectivity of TE modes at the surface of MLPhC. SB stands for stopband. Envelope function $r_{\text{env}}(\lambda)$ (thick solid line), obtained by picking up $\mathop{\mathrm{Re}}[r(\lambda)]$ (thin dotted line) at the wavelengths where $\mathop{\mathrm{Im}}[r(\lambda)]=0$. Calculated equivalent index of flat multilayer (dotted lines) and MLPhC (solid lines) having layer structure of (H/2--L--H/2) N . Upper and lower plots correspond to TE and TM modes, respectively (Note that the curves of flat structure are identical for both figures). Calculated equivalent index of flat multilayer (dotted lines) and MLPhC (solid lines) having layer structure of (L/2--H--L/2) N . Upper and lower plots correspond to TE and TM modes, respectively. Equivalent index for various horizontal lattice constant ($\Lambda$) of MLPhC. Layer structure is (H/2--L--H/2) N . |
| ISSN: | 0021-4922 1347-4065 |
| DOI: | 10.1143/JJAP.49.092001 |