Partially coherent transmittance of dielectric lamellae

Grossman, Erich N.; McDonald, Donald G.

doi:10.1117/12.199887

Cited by 24 publications

(18 citation statements)

References 11 publications

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“…In this limit, the transmission and reflection responses can be characterized by treating the optical parameters as a power law (Halpern et al 1986). More generally, the scattered light in a plane-parallel sample of homogenous material are partially-coherent and can be treated by the approach described in Grossman & McDonald (1995).…”

Section: Modeling and Analysismentioning

confidence: 99%

Optical Properties of Iron Silicates in the Infrared to Millimeter as a Function of Wavelength and Temperature

Richey¹,

Kinzer²,

Cataldo³

et al. 2013

ApJ

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The Optical Properties of Astronomical Silicates with Infrared Techniques (OPASI-T) program utilizes multiple instruments to provide spectral data over a wide range of temperature and wavelengths. Experimental methods include Vector Network Analyzer (VNA) and Fourier Transform Spectroscopy (FTS) transmission, and reflection/scattering measurements. From this data, we can determine the optical parameters for the index of refraction, n, and the absorption coefficient, k. The analysis of the laboratory transmittance data for each sample type is based upon different mathematical models, which are applied to each data set according to their degree of coherence. Presented here are results from iron silicate dust grain analogs, in several sample preparations and at temperatures ranging from 5-300 K, across the infrared and millimeter portion of the spectrum (from 2.5-10,000 µm or 4,000-1 cm −1 ).

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Section: Modeling and Analysismentioning

confidence: 99%

Optical Properties of Iron Silicates in the Infrared to Millimeter as a Function of Wavelength and Temperature

Richey¹,

Kinzer²,

Cataldo³

et al. 2013

ApJ

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“…The best fit is obtained by minimizing the value of SEE in Eq. (13). The uncertainty of the fitted thickness d and rms roughness σ are estimated by varying dor σ from the best-fit value until the SEE is 0.01 greater than the smallest SEE.…”

Section: Resultsmentioning

confidence: 99%

Partially Coherent Spectral Transmittance of Dielectric Thin Films with Rough Surfaces

Lee

Khuu

Zhang

2005

Journal of Thermophysics and Heat Transfer

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The effects of scattering and partial coherence on the transmittance of thin films with rough surfaces are investigated. For the rough side, the rms roughness is between 0.3 and 0.7 µm, whereas the autocorrelation length ranges from 1 to 36 µm. Scalar scattering theory (SST) is used to account for the scattering losses in the specular direction due to surface roughness, and then the calculated transmittance is spectrally averaged over the coherence spectral width. The spectral averaging method takes into consideration the effect of partial coherence. A Fouriertransform infrared spectrometer measures the near-normal transmittance in the midinfrared region from 2-to 20-µm wavelengths. Comparison of the calculated transmittance with that of the measured transmittance shows that the combination of SST with spectral averaging can correctly predict the measured fringe contrast and fringe flipping, whereas SST alone does not result in quantitative agreement with the experiments. A coherence function is introduced to characterize the degree of coherence as a function of wave number for samples with or without a rough surface. Furthermore, it is shown that SST is not applicable to surfaces whose autocorrelation length is greater than the wavelength of the incident radiation. Nomenclature d = thickness, m i = √ −1 k = imaginary part of the complex refractive index n = real part of the complex refractive index R = reflectance r = Fresnel reflection coefficient S = scattering factor T = transmittancē T = spectrally averaged transmittance t = Fresnel transmission coefficient β = phase shift, rad ν = free spectral range, m −1 δν = coherence spectral width, m −1 θ = polar angle, rad λ = wavelength of the incident radiation in vacuum, m ν = wave number, m −1 σ = rms roughness, m τ = internal transmissivity = fringe contrast φ = coherence function Subscripts coh = coherent p = p polarization r = reflection s = s polarization t = transmission

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“…Figure 10 (b) also shows the same analysis using our implemented fringe method discussed above. We find an absorption in the region of the transverse-optical (TO) phonon c. 18.5 [22] [15] and a corresponding rapid variation in the refractive index. Similarly, a longbaseline variation in the absorption due to the phonon band is matched by a consistent variation in the real part of the refractive index.…”

Section: Application To Silicon Optical Flatsmentioning

confidence: 99%

Metrology of complex refractive index for solids in the terahertz regime using frequency domain spectroscopy

Chick¹,

Murdin²,

Matmon³

et al. 2018

Metrologia

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Frequency domain spectroscopy allows an experimenter to establish optical properties of solids in a wide frequency band including the technically challenging 10 region, and in other bands enables metrological comparison between competing techniques. We advance a method for extracting the optical properties of high-index solids using only transmission-mode frequency domain spectroscopy of plane-parallel Fabry-Perot optical flats. We show that different data processing techniques yield different kinds of systematic error, and that some commonly used techniques have inherent systematic errors which are underappreciated. We use model datasets to cross-compare algorithms in isolation from experimental errors, and propose a new algorithm which has qualitatively different systematic errors to its competitors. We show that our proposal is more robust to experimental non-idealities such as noise or apodization, and extract the complex refractive index spectrum of crystalline silicon as a practical example. Finally, we advance the idea that algorithms are complementary rather than competitive, and should be used together as part of a toolbox for better metrology.

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Partially coherent transmittance of dielectric lamellae

Cited by 24 publications

References 11 publications

Optical Properties of Iron Silicates in the Infrared to Millimeter as a Function of Wavelength and Temperature

Optical Properties of Iron Silicates in the Infrared to Millimeter as a Function of Wavelength and Temperature

Partially Coherent Spectral Transmittance of Dielectric Thin Films with Rough Surfaces

Metrology of complex refractive index for solids in the terahertz regime using frequency domain spectroscopy

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