Strong in-plane birefringence of spatially nanostructured silicon

Ковалев, Д. И.; Polisski, G.; Diener, J.; Heckler, H.; Künzner, N.; Timoshenko, V. Yu.; Koch, F.

doi:10.1063/1.1343476

Cited by 101 publications

(54 citation statements)

References 12 publications

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“…This preferential pore alignment has an important implication for the optical properties of the layers [3]. Etched Si layers electrochemically formed on p-type Si (110) wafers reveal strong in-plane birefringence [1,2,3]. Birefringent etched Si layers demonstrate properties of a uniaxial negative crystal whose optical axis lies along the [001] in-plane crystallographic direction [4].…”

Section: Introductionmentioning

confidence: 99%

“…Recently it has been indicated that nanostructuring of Si by porousification of low-symmetry Si (110) surfaces or by formation of micrometer sized Si periodic structures is an appropriate technique for producing birefringent Si-based material [2]. The reduced symmetry of the dielectric function of etched Si layers originates from the selective pore dispersion in equivalent [100] crystallographic directions.…”

Section: Introductionmentioning

confidence: 99%

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Optical properties of photo-electrochemical etching of anisotropic silicon (110)

Amirhoseiny

Hassan

2012

IEICE Electron. Express

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Photo-electrochemical etched Si layers were prepared on n-type (110) oriented silicon wafer. SEM results shows groove structure for etched Si (110). The photoluminescence (PL), Fourier transformed infrared (FTIR) absorption and Raman spectroscopy of etched Si (110) as a function of etching time was studied. All samples showed a PL peak in the visible spectral and the intensity of the PL peak increases with rising of the etching time. It is also found that the Raman peak of the etched Si samples is red shifted and its intensity significantly decreases as the etching time increases.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optical properties of photo-electrochemical etching of anisotropic silicon (110)

Amirhoseiny

Hassan

2012

IEICE Electron. Express

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“…Besides, if H 1 = 0 then from (31), (30) and (22) we have that electric field keeps its components E 3 and E 2 . Combining (22) with (31) we obtained:…”

Section: Transverse Electric (Te) and Transverse Magnetic (Tm) Wavesmentioning

confidence: 99%

“…Transverse electric wave means E 3 = 0, then from (30)-(31) we have component H 1 = 0 and from (22) that E 2 = 0. On the other hand, if E 1 = 0 then from (33) and (32) we have that magnetic field keeps its components H 3 and H 2 .…”

Section: Transverse Electric (Te) and Transverse Magnetic (Tm) Wavesmentioning

confidence: 99%

“…The layers material of this structure consist of anisotropic mesoporous silicon exhibiting optical birefringence given by an artificial in-plane uniaxial symmetry [22]. The analyzed FabryPerot microcavity structure is made up of two Bragg mirrors (each formed by 12 pairs of alternating mesoporous silicon layers with two different refractive indices and an optical thickness equal to λ 0 /4) separated by a microcavity layer with an optical thickness equal to λ 0 /2.…”

Section: The Anisotropic Layered Systemmentioning

confidence: 99%

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Sturm-Liouville Matrix Equation for the Study of Electromagnetic-Waves Propagation in Layered Anisotropic Media

Pernas-Salomón¹,

Pérez‐Álvarez²

2014

PIER M

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Abstract-We obtain a Sturm-Lioville matrix equation of motion (SLME) for the study of electromagnetic wave propagation in layered anisotropic structures. Conducting media were taken into account so that ohmic loss is considered. This equation can be treated using a 4 × 4 associated transfer matrix (T) in layered anisotropic structures, where the tensors: permittivity, permeability and the electric conductivity have a piecewise dependence on the coordinate perpendicular to the layered structure. We use the SLME eigenfunctions and eigenvalues to analyze qualitatively the numerical instability (Ωd problem) which potentially affects practical applications of the transfer matrix method. By means of the SLME coefficients we show analytically that T determinant value can be used to keep a check on the numerical accuracy of calculations. We derive equations to analyze wave propagation in linear layered isotropic structures. The SLME approach is applied on two typical layered structures to verify theoretical predictions and experimental results.

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Nanocolumnar Metamaterial Platforms: Scaling Rules for Structural Parameters Revealed from Optical Anisotropy

Kilic,

Traouli,

Hilfiker

et al. 2024

Advanced Optical Materials

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Nanostructures represent a frontier where meticulous attention to the control and assessment of structural dimensions becomes a linchpin for their seamless integration into diverse technological applications. However, determining the critical dimensions and optical properties of nanostructures with precision still remains a challenging task. In this study, by using an integrative and comprehensive methodical series of studies, the evolution of the depolarization factors in the anisotropic Bruggeman effective medium approximation (AB‐EMA) is investigated. It is found that these anisotropic factors are extremely sensitive to the changes in critical dimensions of the nanostructure platforms. In order to perform a systematic characterization of these parameters, spatially coherent, highly‐ordered slanted nanocolumns are fabricated from zirconia, silicon, titanium, and permalloy on silicon substrates with varying column lengths using glancing angle deposition (GLAD). In tandem, broad‐spectral range Mueller matrix spectroscopic ellipsometry data, spanning from the near‐infrared to the vacuum UV (0.72–6.5 eV), is analyzed with a best‐match model approach based on the anisotropic Bruggeman effective medium theory. The anisotropic optical properties, including complex dielectric function, birefringence, and dichroism, are thereby extracted. Most notably, the research unveils a generalized, material‐independent inverse relationship between depolarization factors and column length. It is envisioned that the presented scaling rules will permit accurate prediction of optical properties of nanocolumnar thin films improving their integration and optimization for optoelectronic and photonic device applications. As an outlook, the highly porous nature and extreme birefringence properties of the fabricated columnar metamaterial platforms are further explored in the detection of nanoparticles from the cross‐polarized integrated spectral color variations.

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Strong in-plane birefringence of spatially nanostructured silicon

Cited by 101 publications

References 12 publications

Optical properties of photo-electrochemical etching of anisotropic silicon (110)

Optical properties of photo-electrochemical etching of anisotropic silicon (110)

Sturm-Liouville Matrix Equation for the Study of Electromagnetic-Waves Propagation in Layered Anisotropic Media

Nanocolumnar Metamaterial Platforms: Scaling Rules for Structural Parameters Revealed from Optical Anisotropy

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