We study the possibility to obtain structural colors through the use of supersymmetric transformations in optics such as the Darboux transform. Structural colors were originally discovered by studying the interference of light with natural photonics structures giving rise to vivid and spectacular tonalities. They differ fundamentally from ordinary colors based on light absorption at particular wavelengths, as they result from light interference only. To treat interference analytically, we make use of the Darboux transform to define materials with continuously varying spatial distributions of the refractive index that are exactly solvable for the electric field. Consequently, it is possible to calculate analytically the Transfer Matrix linked to the definition of the transmission and reflection coefficients. Interestingly, by using gain, anomalous transmission/ reflection (i.e. larger than one) can be obtained, the physical system being open towards the external environment (the system is using external energy in order to increase both transmission and reflection). The generated active optical cavity can thus be used to amplify the incoming light in the desired spectral-angular region. The calculated refractive index distributions can be realized in practice as 1D multi-layered structures corresponding to optical filters in the visible.
We apply the supersymmetric Darboux transformation to the optical Helmoltz wave equation to generate analytically complex-valued PT-symmetric potentials (physically a graded refractive index dielectric). PT-symmetry is then spontaneously broken controlling the amplitude of the imaginary part of the refractive index distribution. Consequently a resonance is detectable which is related to a singularity of the S matrix, responsible for extraordinary high transmission and reflection peaks in the scattering spectra. We demonstrate how controlling the resonance we can achieve different amplification rates up to four orders of magnitude at the exact singular point. Total transmission and very high reflection can be also obtained. All the visible portion of the spectrum can be spanned by enlarging the spatial width of the potential. All these potentials can be unified in a single device with the capability to dynamically control the imaginary part of the refractive index, thus defining a tunable dynamical optical filter behaving as a perfect amplifier, a transparent barrier or a high efficiency mirror with the main dimension of few hundreds of nanometers.
We develop a model of full-field optical coherence tomography (FF-OCT) that includes a description of partial temporal and spatial coherence, together with a mean-field scattering theory going beyond the Born approximation. Based on explicit expressions of the FF-OCT signal, we discuss essential features of FF-OCT imaging, such as the influence of partial coherence on the decay of the signal with depth that is captured by the model. We derive the conditions under which the spatially averaged signal exhibits a pure exponential decay with depth, providing a clear frame for the use of the Beer-Lambert law for quantitative measurements of the extinction length in scattering media.
We apply first order perturbation theory to the scalar radiative transport equation for the temporal field autocorrelation function to study DCT and SCOT sensitivity to changes in the Brownian motion of the constituent scattering particles.
In an effort to address Monte Carlo (MC) light prorogation shortcomings in terms of computational burden and light polarization-sensitivity, we report an efficient GPU-based MC for modeling polarized light in scattering medium.
Numerous methods consider the temporal field autocorrelation function in order to study the dynamical properties of a medium, e.g. diffuse correlation tomography (DCT) [1] and speckle contrast optical tomography (SCOT) [5]. In this paper, we calculate the field correlation function in the transport regime as the solution to the correlation transport equation (CTE) introduced in [1]. We show how perturbation theory can be applied to the CTE in order to calculate the sensitivity kernel relating the variation of the local Brownian motion of particles to the typical data. The Green’s function of the standard radiative transport equation (RTE) can be used to construct the sensitivity kernel in the first Born approximation where the correlation time is considered to be the small parameter. We stress that the sensitivity kernel is defined for every point within the scattering medium. The sensitivity kernel is then the Jacobian matrix required in DCT or SCOT in order to perform the image reconstruction [5]. Eventually, we demonstrate how the use of the CTE, instead of the correlation diffusion approximation, is increasing the resolution of reconstructed images of dynamical parts of a scattering medium.
We apply first order perturbation theory and reciprocity to the scalar radiative transport equation for the temporal field auto-correlation function to study its sensitivity to changes in the Brownian motion of the constituent scattering particles.
We describe a reciprocity relation for polarized radiative transport between arbitrarily positioned sources and detectors separated by a scattering medium. Applications to polarized Diffuse Optical Tomography are shown which allow for efficient computation of the sensitivity kernel.
We demonstrate numerically the increased resolution of the image of a pure
absorber as recorded by a scanning system composed of aligned source-detector when only
polarization-preserving photons are selected.
A novel numerical technique is presented to calculate the T-matrix for a single particle through the use of the volume integral equation for electromagnetic scattering. It is based on the method called Coupled Dipole Approximation (CDA), see O. J. F. Martin et al.1. The basic procedure includes the parallel use of the Lippmann-Schwinger and the Dyson equations to iteratively solve for the T-matrix and the Green’s function dyadic respectively. The boundary conditions of the particle are thus automatically satisfied. The method can be used for the evaluation of the optical properties (e.g. Müller matrix) of anisotropic, inhomogeneous and asymmetric particles, both in far and near field, giving as output the T-matrix, which depends only on the scatterer itself and is independent from the polarization and direction of the incoming field. Estimation of the accuracy of the method is provided through comparison with the analytical spherical case (Mie theory) as well as non-spherical cubic ice particles.
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