Two recursive and numerically stable matrix algorithms for modeling layered diffraction gratings, the S-matrix algorithm and the R-matrix algorithm, are systematically presented in a form that is independent of the underlying grating models, geometries, and mountings. Many implementation variants of the algorithms are also presented. Their physical interpretations are given, and their numerical stabilities and efficiencies are discussed in detail. The single most important criterion for achieving unconditional numerical stability with both algorithms is to avoid the exponentially growing functions in every step of the matrix recursion. From the viewpoint of numerical efficiency, the S-matrix algorithm is generally preferred to the R-matrix algorithm, but exceptional cases are noted.

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Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings

We show that short-pulse laser-induced classical ripples on dielectrics, semiconductors, and conductors exhibit a prominent "non-classical" characteristic-in normal incidence the periods are definitely smaller than laser wavelengths, which indicates that the simplified scattering model should be revised. Taking into account the surface plasmons (SPs), we consider that the ripples result from the initial direct SP-laser interference and the subsequent grating-assisted SP-laser coupling. With the model, the period-decreasing phenomenon originates in the admixture of the field-distribution effect and the grating-coupling effect. Further, we propose an approach for obtaining the dielectric constant, electron density, and electron collision time of the high-excited surface. With the derived parameters, the numerical simulations are in good agreement with the experimental results. On the other hand, our results confirm that the surface irradiated by short-pulse laser with damage-threshold fluence should behave metallic, no matter for metal, semiconductor, or dielectric, and the short-pulse laser-induced subwavelength structures should be ascribed to a phenomenon of nano-optics.

Origin of laser-induced near-subwavelength ripples: interference between surface plasmons and incident laser

Most photovoltaic (solar) cells are made from crystalline silicon (c-Si), which has an indirect band gap. This gives rise to weak absorption of one-third of usable solar photons. Therefore, improved light trapping schemes are needed, particularly for c-Si thin film solar cells. Here, a photonic crystal-based light-trapping approach is analyzed and compared to previous approaches. For a solar cell made of a 2 µm thin film of c-Si and a 6 bilayer distributed Bragg reflector (DBR) in the back, power generation can be enhanced by a relative amount of 24.0% by adding a 1D grating, 26.3% by replacing the DBR with a six-period triangular photonic crystal made of air holes in silicon, 31.3% by a DBR plus 2D grating, and 26.5% by replacing it with an eight-period inverse opal photonic crystal.

Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals

We use a rigorous electromagnetic approach to develop a light-trapping theory, which reveals that the standard limit developed by Yablonovitch can be substantially surpassed in nanophotonic regimes, opening new avenues for highly efficient solar cells

/pdf/fundamental-limit-of-nanophotonic-light-trapping-in-solar-18kh2cgxx1.pdf

Fundamental limit of nanophotonic light-trapping in solar cells

Optical surfaces coated with a thin layer to improve light transmission are ubiquitous in everyday optical applications as well as in industrial and scientific instruments. Discovered first in 1817 by Fraunhofer, the coating of lenses became standard practice in the 1930s. In spite of intensive research, broad-band antireflection coatings are still limited by the lack of materials with low refractive indices. A method based on the phase separation of a macromolecular liquid to generate nanoporous polymer films is demonstrated that creates surfaces with high optical transmission.

https://science.sciencemag.org/content/sci/283/5401/520.full.pdf

Nanophase-Separated Polymer Films as High-Performance Antireflection Coatings

Diffractive optical structures for increasing the efficiency of crystalline silicon solar cells are discussed. As a consequence of the indirect band gap, light absorption becomes very ineffective near the band edge. This can be remedied by use of optimized diffraction gratings that lead to light trapping. We present blazed gratings that increase the optically effective cell thickness by approximately a factor of 5. In addition we present a wideband antireflection structure for glass that consists of a diffraction grating with a dielectric overcoat, which leads to an average reflection of less than 0.6% in the wavelength range between 300 and 2100 nm.

Claus Heine

Papers

Submicrometer gratings for solar energy applications.