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Design and optimization of an achromatic photonic crystal bend

Jasmin Smajic, Christian Hafner, and Daniel Erni

Open Access Open Access

Abstract

We perform a simple sensitivity analysis of a W1 waveguide bend in a photonic crystal (PhC) where we use the information obtained to optimize the PhC bend’s frequency response. Within a single optimization step we already achieve very low power reflection coefficients over almost the entire frequency range of the photonic bandgap (PBG), i.e., an achromatic bend. A further analysis shows that there is a single critical rod in the optimized bend structure that exhibits an extraordinary high sensitivity at a given frequency. Hence power reflection becomes tunable from 0% up to 100% involving only small changes in the critical rod’s properties. This opens the door to novel topologies for compact switches and sensor applications.

©2003 Optical Society of America

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Supplementary Material (7)

Media 1: MOV (402 KB)     
Media 2: MOV (410 KB)     
Media 3: MOV (391 KB)     
Media 4: MOV (393 KB)     
Media 5: MOV (387 KB)     
Media 6: MOV (239 KB)     
Media 7: MOV (397 KB)     

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Figures (6)
Fig. 1.
Fig. 1. (Movie file for the light propagation 401 KB) Scheme of the PhC 90° W1 waveguide bend (left). As will be discussed in section 3 two sets of rods are selected, characterized a potential increase (+) or decrease (-) of the rod’s radius. The performance of this initial bend is given by the spectral response of the reflectance R and transmittance T (right). The light propagation is depicted as the magnitude of the Poynting field (movie, right inset).

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Fig. 2.
Fig. 2. Sensitivity analysis of the power reflectivity R concerning only a restricted area of the PhC bend structure: The variations ΔR are assigned to each rod while decreasing the corresponding rod’s radius Δr=- 10% (left) and for an increase of the rod’s radius Δr=+10% (right), both at a frequency of ω·a/(2·π·c)=0.42. The background color indicates zero variation ΔR=0.

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Fig. 3.
Fig. 3. The frequency response of the modified bend after a ±10% radius variation of the seleced rods (left). The corresponding Poynting field is given in the inset (movie for the light propagation, 410 KB). The frequency response after a ±13.27% radius variation shows two small maxima for R (right). The corresponding Poynting fields for both maxima are given in the insets (movie for the first maximum 391 KB, on left; movie for the second maximum 394 KB, on right).

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Fig. 4.
Fig. 4. Sensitivity analysis regarding the first maximum of R (at ω·a/(2·π·c)=0.367) for a negative radius variation Δr=- 2% (left), and for a positive radius variation Δr=+2% (right).

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Fig. 5.
Fig. 5. Sensitivity analysis regarding the second maximum of R (at ω·a/(2·π·c)=0.417) for a negative radius variation Δr=- 2% (left), and for a positive radius variation Δr=+2% (right).

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Fig. 6.
Fig. 6. The frequency response for the predicted - 30% radius variation of the critical rod. The Poynting field for three different operating points is depicted in the insets (light propagation movies for the first 387 KB, second 240 KB, and third 397 KB operating point).

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