Nonlinear Mixing of Two Laser Beams and THz Plasmons Generation in Graphene Coated Optical Fibre

Graphene is a most suitable material for Terahertz (THz) radiation generation. An efficient mechanism of THz surface plasmons (THz SPs) generation in graphene coated optical fibre by nonlinear mixing of two laser beams is proposed. The graphene coated fiber supports THz SPs with plasmon resonance in the THz regime and controllable by thickness of graphene and radius of optical fibre. The laser beams exert a difference frequency ponderomotive force on the electrons of the graphene. This ponderomotive force induces a nonlinear current in graphene which driving the difference frequency THz SPs. The normalized amplitude of THz SPs decreases with frequency as the nonlinear coupling gets weaker. The efficiency of the device is around 0.01% at a laser intensity of 3x1014 W/cm2. This scheme will be useful making the compact THz radiation source and THz plasmon sensor.

Nonlinear Mixing Characteristics of Reflectance Spectra of Typical Mineral Pigments

Hyperspectral technology has been used to identify pigments that adhere to the surfaces of polychrome artifacts. However, the colors are often produced by the mixing of pigments, which requires that the spectral characteristics of the pigment mixtures be considered before pigment unmixing is conducted. Therefore, we proposed an experimental approach to investigate the nonlinear degree of spectral reflectance, using several mixing models, and to evaluate their performances in the study of typical mineral pigments. First, five mineral pigments of azurite, malachite, cinnabar, orpiment, and calcite were selected to form five groups of samples, according to their different mass ratios. Second, a fully constrained least squares algorithm based on the linear model and three algorithms based on the nonlinear model were employed to calculate the proportion of each pigment in the mixtures. We evaluated the abundance accuracy as well as the similarity between the measured and reconstructed spectra produced by those mixing models. Third, we conducted pigment unmixing on a Chinese painting to verify the applicability of the nonlinear model. Fourth, continuum removal was also introduced to test the nonlinearity of mineral pigment mixing. Finally, the results indicated that the spectral mixing of different mineral pigments was more in line with the nonlinear mixing model. The spectral nonlinearity of mixed pigments was higher near to the wavelength corresponding to their colors. Meanwhile, the nonlinearity increased with the wavelength increases in the shortwave infrared bands.

Hyperspectral Unmixing Based on Constrained Bilinear or Linear-Quadratic Matrix Factorization

Unsupervised hyperspectral unmixing methods aim to extract endmember spectra and infer the proportion of each of these spectra in each observed pixel when considering linear mixtures. However, the interaction between sunlight and the Earth’s surface is often very complex, so that observed spectra are then composed of nonlinear mixing terms. This nonlinearity is generally bilinear or linear quadratic. In this work, unsupervised hyperspectral unmixing methods, designed for the bilinear and linear-quadratic mixing models, are proposed. These methods are based on bilinear or linear-quadratic matrix factorization with non-negativity constraints. Two types of algorithms are considered. The first ones only use the projection of the gradient, and are therefore linked to an optimal manual choice of their learning rates, which remains the limitation of these algorithms. The second developed algorithms, which overcome the above drawback, employ multiplicative projective update rules with automatically chosen learning rates. In addition, the endmember proportions estimation, with three alternative approaches, constitutes another contribution of this work. Besides, the reduction of the number of manipulated variables in the optimization processes is also an originality of the proposed methods. Experiments based on realistic synthetic hyperspectral data, generated according to the two considered nonlinear mixing models, and also on two real hyperspectral images, are carried out to evaluate the performance of the proposed approaches. The obtained results show that the best proposed approaches yield a much better performance than various tested literature methods.

Hyperspectral Nonlinear Unmixing by Using Plug-and-Play Prior for Abundance Maps

Spectral unmixing (SU) aims at decomposing the mixed pixel into basic components, called endmembers with corresponding abundance fractions. Linear mixing model (LMM) and nonlinear mixing models (NLMMs) are two main classes to solve the SU. This paper proposes a new nonlinear unmixing method base on general bilinear model, which is one of the NLMMs. Since retrieving the endmembers’ abundances represents an ill-posed inverse problem, prior knowledge of abundances has been investigated by conceiving regularizations techniques (e.g., sparsity, total variation, group sparsity, and low rankness), so to enhance the ability to restrict the solution space and thus to achieve reliable estimates. All the regularizations mentioned above can be interpreted as denoising of abundance maps. In this paper, instead of investing effort in designing more powerful regularizations of abundances, we use plug-and-play prior technique, that is to use directly a state-of-the-art denoiser, which is conceived to exploit the spatial correlation of abundance maps and nonlinear interaction maps. The numerical results in simulated data and real hyperspectral dataset show that the proposed method can improve the estimation of abundances dramatically compared with state-of-the-art nonlinear unmixing methods.