Application of Heisenberg uncertainty relation for the optimal modeling of surface diffraction.

The modeling of the scattering of a plane wave at a rough aperiodic surface-as well as its diffraction by a microstructured surface-is possible only by limiting the infinite surface to a window of finite width D. We show that the scattering spectrum at infinity in the Fraunhofer zone can be obtained from the diffraction modeling of a grating of period D whose surface profile coincides with the aperiodic surface in this window. This is justified by adopting the corpuscular representation of light and resorting to Heisenberg's uncertainty relation applied to the photon's canonically conjugate variables momentum and position. This approach gives a deep and comprehensive representation of scattering phenomena, and also the limit of what can be meaningfully calculated and measured. Numerical examples of grating profiles demonstrate that results obtained under the widely used Beckmann-Kirchoff approximation are matched. The described approach can solve scattering problems that usual methods cannot, or face difficulties, such as when there is significant roughness with respect to the wavelength.

In-line femtosecond common-path interferometer in reflection mode.

An innovative method to perform femtosecond time-resolved interferometry in reflection mode is proposed. The experiment consists in the combined use of a pump-probe setup and of a fully passive in-line femtosecond common-path interferometer. The originality of this interferometer relies on the use of a single birefringent crystal first to generate a pair of phase-locked pulses and second to recombine them to interfere. As predicted by analytical modeling, this interferometer measures the temporal derivative of the ultrafast changes of the complex optical reflection coefficient of the sample. Working conditions are illustrated through picosecond opto-acoustic experiments on a thin film.

Reformulation of the coordinate transformation method through the concept of adaptive spatial resolution. Application to trapezoidal gratings.

We reformulate the coordinate transformation method for profiles represented by parametric equations. Numerically, the eigenvalue problem is solved by expanding both the electromagnetic field and the periodic coefficients of Maxwell's equations into Fourier series. For trapezoidal gratings, it is shown that the convergence of the method is closely related to the representation of the profile. A proper choice of the representation permits handling profiles that previously had been out of reach owing to their sharp edges. From a practical point of view, we are now able to analyze gratings with two vertical facets by using the coordinate transformation method.

Rigorous and efficient grating-analysis method made easy for optical engineers.

The coordinate-transformation-based differential method of Chandezon et al. [J. Opt. (Paris) 11, 235 (1980); J. Opt. Soc. Am. 72, 839 (1982)] (the C method) is one of the simplest and most versatile methods for modeling surface-relief gratings. However, to date it has been used by only a small number of people, probably because, traditionally, elementary tensor theory is used to formulate the method. We reformulate the C method without using any knowledge of tensor, thus, we hope, making the C method more accessible to optical engineers.