Experimental Test of Reflectivity Formulas for Turbid Colloids: Beyond the Fresnel Reflection Amplitudes

Abstract

We compare light reflectivity measurements as a function of the angle of incidence for an interface between an optical glass and a turbid suspension of small particles, with theoretical predictions for the coherent reflectance calculated with different available theoretical models. The comparisons are made only in a small range of angles of incidence around the critical angle of the interface between the glass and the matrix of the colloidal suspensions. The experimental setup and its calibration procedure are discussed. We considered two Fresnel-based approximations and another two based on a multiple-scattering approach, and we present results for monodisperse latex colloidal suspensions of polymeric spherical particles in water with particle diameters of 120 and 520 nm, polydisperse titanium dioxide (rutile) particles suspensions in water with a most probable diameter of 404 nm, and suspensions of copper particles in water with diameters of 500 nm. The comparisons between experiment and theory are made without fitting any parameters.

Monitoring of temperature-mediated phase transitions of adipose tissue by combined optical coherence tomography and Abbe refractometry

“…Thus, in the current study, all the refractometric measurements were performed in the reflection mode. [58][59][60][61] The working principle of AR is based on the measurement of a critical angle. As it is shown in the inset of Fig.…”

Extinction Coefficient Modulation of MoO3 Films Doped with Plasmonic Nanoparticles: From an Effective Medium Theory Description

“…The k lz , where l = i, j is the z-component of the wavenumber and takes the form of k lz = k o n 2 l − n 2 1 sin 2 θ 1 , where k o = 2π/λ is the wave number in a vacuum and λ is the wavelength. To calculate the reflectance of the entire system, the composed formula of reflectance [42] is needed which is defined as,…”

“…The , where is the z -component of the wavenumber and takes the form of , where is the wave number in a vacuum and is the wavelength. To calculate the reflectance of the entire system, the composed formula of reflectance [ 42 ] is needed which is defined as, where d is the thickness of the thin film. To simulate the transmittance, the next expression is considered, where is the wavenumber in the effective medium, defined as where is the refractive index in each medium, is the angle of incidence, a is the radius of the particle, is the volume filling fraction, and is the forward-scattering amplitude of the NPs inside the matrix [ 44 ].…”

“…Finally, it will be shown that the modification of extinction coefficient depends strongly on these last two parameters. EMT is one of the most important theories for computing the optical properties of doped thin films combined with the transmittance and reflectance coefficients using the well-known Fresnel coefficients [ 42 , 43 ].…”

Optical Coherent Reflection from a Confined Colloidal Film: Modeling and Experiment

“…29 The vdH EMM can be used in some cases to predict the reflectivity from turbid colloids of particles comparable to the wavelength of light. 26,30 However, in ref 25, it was shown that although an effective index of refraction can be properly defined in case the size of the colloidal particles is comparable or even larger than the wavelength of incident radiation, it is not strictly legitimate to use it, in these cases, in the calculation of Fresnel's reflection and transmission coefficients. 23−25 The use of the MG model is only justified when the size of the colloidal particles is very small with respect to the wavelength of the incident radiation, whether their absorption is important or not.…”