Reflectivity of 1D photonic crystals: A comparison of computational schemes with experimental results

Pérez-Huerta, J.S.; Ariza-Flores, D.; Castro-García, R.; Mochán, W. Luis; Ortiz, Guillermo P.; Agarwal, Vivechana

doi:10.1142/s0217979218501369

Cited by 14 publications

(6 citation statements)

References 22 publications

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“…[25,34] Moreover, the obtained results were compared with those of a simulation method that predicts the behavior of the reflection spectrum of the photonic crystal when it is decorated or not with polyNI-PAM spheres (Figure S1). The simulation is based on the well-known transfer matrix method [35,36] and the Bruggeman equation, [37][38][39] which is used to reproduce the optical behavior of a porous silicon matrix. The geometric model displayed in Figure 4 is proposed for simulating the effect of polyNIPAM on the optical behavior of the photonic crystals.…”

Section: Optical Response Of Hybrid Sensormentioning

confidence: 99%

Stimuli‐responsive hydrogel microgels on porous silicon one‐dimensional photonic crystals: Tapping the full potential for optical sensor applications

Valadez,

Flores,

Pacholski

2023

Nano Select

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Porous silicon 1D photonic crystals, namely rugate filters, are covered with a loosely packed hexagonally ordered array of stimuli‐responsive hydrogel microgels, and the optical properties of the resulting hybrid sensor are thoroughly investigated. For this purpose, both rugate filters with and without hydrogel microgel on top are immersed in ethanol/water mixtures possessing different compositions and NaCl solutions. Reflectance spectra of all samples are taken and analyzed concerning the spectral positions and reflectance intensity of the strong peak related to the photonic crystal rugate peak as well as the side bands resulting from Fabry–Pérot interference at the interfaces bordering the porous silicon. For the latter analysis, a Fourier transform is applied to the side bands for calculating the effective optical thickness (EOT). Thereby it can be shown that the spectral position of both the rugate peak and the EOT peak is best suited for monitoring refractive index changes in the immersion medium whereas the swelling and collapse of the stimuli‐responsive hydrogel microgel can be only detected by variations in the amplitude of the rugate peak and the EOT peak. These results are confirmed by simulations using a simple geometrical model and shall serve as guide for developing tailor‐made optical sensors.

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Section: Optical Response Of Hybrid Sensormentioning

confidence: 99%

Stimuli‐responsive hydrogel microgels on porous silicon one‐dimensional photonic crystals: Tapping the full potential for optical sensor applications

Valadez,

Flores,

Pacholski

2023

Nano Select

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“…where is Bloch's vector and the transfer matrix of a single period of thickness [28,48,49]. Thus, whenever Total number of stacked sub-mirrors, thickness , overlap between consecutive PBG and average reflectance ⟨ ⟩ for optimized structures designed with a number of periods per sub-mirror (first block) or a number of periods for those sub-mirrors tuned to wavelengths ≥ 800 nm (second block, see text), for different values of .…”

Section: Photonic Structure With Sub-mirrors Stackingmentioning

confidence: 99%

Optimization of wide-band quasi-omnidirectional 1-D photonic structures

Castillo-Gallardo,

Puente-Díaz,

Ariza-Flores

et al. 2021

Preprint

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We have designed, optimized, fabricated and characterized highly reflective quasi-omnidirectional (angular range of 0 − 60 • ) multilayered structures with a wide spectral range. Two techniques, chirping (a continuous change in thicknesses) and stacking of Bragg-type sub-structures, have been used to enhance the reflectance with minimum thickness for a given pair of refractive indices. Numerical calculations were carried out employing the transfer matrix method and we optimized the design parameters to obtain maximal reflectance averaged over different spectral ranges for all angles. We fabricated some of the optimized structures with porous silicon dielectric multilayers with low refractive contrast and compared their measured optical properties with the calculations. Two chirped structures with thicknesses 21.6 m and 60.4 m, resulting in quasi omnidirectional mirrors with bandwidths of 360 nm and 1800 nm, centered at 1160 nm and 1925 nm respectively have been shown. In addition, we fabricated a stacked sub-Bragg mirror structure with a quasi omnidirectional bandwidth of 1800 nm (centered at 1850 nm) and a thickness of 41.5 m, which is almost two third (in thickness) of the chirped structure. Thus, our techniques allowed us to obtain relatively thin quasi-omnidirectional mirrors with wide bands over different wavelength ranges. Our analysis techniques can be used for the optimization of the reflectance not only in multilayered PS systems with different refractive index contrasts but also for systems with other types of materials with low refractive index contrast. The present study could also be useful for obtaining omnidirectional dielectric mirrors in large spectral regions using different materials, flat focusing reflectors, thermal regulators, or, if defects are included, as filters or remote chemical/biosensors with a wide angular independent response.

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“…Several equivalent formulations have been proposed to obtain M [39,40,41]. Within a homogeneous nonmagnetic layer α characterized by a dielectric function α and refractive index n α = √ α , the field is in general the sum of upward (+) and downward (−) going plane waves, with wavevector components k ± α = ±k α along z given by the dispersion relation…”

Section: Flat Interfacesmentioning

confidence: 99%

Rough 1D Photonic Crystals: a transfer matrix approach

Ortiz¹,

Ricci²,

Toranzos³

et al. 2020

Preprint

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Interfacial roughness is prevalent in 1D photonic crystals and other layered structures, but is not generally accounted for in their design nor the analysis of their optical properties due to a lack of simple theoretical approaches. We present a transfer matrix formalism to incorporate the effects of interfacial roughness in the optical properties of stratified systems such as 1D photonic crystals and apply it to calculate the optical response of some nanoporous anodic alumina and porous silicon structures. We have validated our formalism by comparing our results to some experiments.

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Reflectivity of 1D photonic crystals: A comparison of computational schemes with experimental results

Cited by 14 publications

References 22 publications

Stimuli‐responsive hydrogel microgels on porous silicon one‐dimensional photonic crystals: Tapping the full potential for optical sensor applications

Stimuli‐responsive hydrogel microgels on porous silicon one‐dimensional photonic crystals: Tapping the full potential for optical sensor applications

Optimization of wide-band quasi-omnidirectional 1-D photonic structures

Rough 1D Photonic Crystals: a transfer matrix approach

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