General analytical solution for the electromagnetic grating diffraction problem.

Implementing the modal method in the electromagnetic grating diffraction problem delivered by the curvilinear coordinate transformation yields a general analytical solution to the 1D grating diffraction problem in a form of a T-matrix. Simultaneously it is shown that the validity of the Rayleigh expansion is defined by the validity of the modal expansion in a transformed medium delivered by the coordinate transformation.

Fano-like resonance emerging from magnetic and electric plasmon mode coupling in small arrays of gold particles.

In this work we theoretically and experimentally analyze the resonant behavior of individual 3 × 3 gold particle oligomers illuminated under normal and oblique incidence. While this structure hosts both dipolar and quadrupolar electric and magnetic delocalized modes, only dipolar electric and quadrupolar magnetic modes remain at normal incidence. These modes couple into a strongly asymmetric spectral response typical of a Fano-like resonance. In the basis of the coupled mode theory, an analytical representation of the optical extinction in terms of singular functions is used to identify the hybrid modes emerging from the electric and magnetic mode coupling and to interpret the asymmetric line profiles. Especially, we demonstrate that the characteristic Fano line shape results from the spectral interference of a broad hybrid mode with a sharp one. This structure presents a special feature in which the electric field intensity is confined on different lines of the oligomer depending on the illumination wavelength relative to the Fano dip. This Fano-type resonance is experimentally observed performing extinction cross section measurements on arrays of gold nano-disks. The vanishing of the Fano dip when increasing the incidence angle is also experimentally observed in accordance with numerical simulations.

Efficient curvilinear coordinate method for grating diffraction simulation.

The article presents a new method for rigorous simulation of the light diffraction on one-dimensional gratings. The method is capable to solve metal-dielectric structures in linear time and consumed memory with respect to structure complexity. Exceptional performance and convergence for metal gratings are achieved by implementing a curvilinear coordinate transformation into the generalized source method previously developed for dielectric gratings.

Azimuthally polarized laser mode generation by multilayer mirror with wideband grating-induced TM leakage in the TE stopband.

A new intracavity laser polarization-mode selection scheme relying upon a TE/TM diffractive dichroism principle in a grating multilayer mirror is proposed and demonstrated. The grating diffracts the first orders between the TE and TM band edges of the angular spectra of the laser mirror inducing a leakage of the TM polarization into the mirror substrate through the multilayer stack whereas TE diffraction into the substrate is forbidden. This mechanism is non-resonant, thus relatively wide-band. Applied with a circular-line grating in the 1.0 µm - 1.1 µm wavelength range, this mirror filters out the radially polarization mode and causes the emission of the azimuthally polarized mode. An original amorphous silicon grating technology was developed and the optical function demonstrated in a Nd:YAG laser.

Fourier modal method for relief gratings with oblique boundary conditions.

Oblique boundary conditions are introduced in the Fourier modal method at each slice of the staircase decomposition of an arbitrary profile of a dielectric corrugation grating. The precision and convergence improvement are demonstrated by comparison with reference methods.

Numerical demonstration of the validity of the Rayleigh hypothesis.

The Rayleigh hypothesis and the related method of diffraction analysis are revisited. It is shown that the Rayleigh method can be applied to deep grating modeling without numerical problems and that it gives any desired accuracy whatever the groove depth. This proves the validity of the Rayleigh hypothesis and rehabilitates the Rayleigh method.

Bridging pole and coupled wave formalisms for grating waveguide resonance analysis and design synthesis.

The algebraic polar expression of resonant reflection from a grating waveguide excited by a free space wave is formulated in terms of the physically meaningful phenomenological parameters of the coupled wave formalism. The reflection coefficient is simply represented as a circle in the complex plane which sheds light on the behaviour of the modulus and phase of anomalous reflection. Analytical expressions are derived for the phenomenological parameters that can now be calculated from optogeometrical quantities which are simple to measure. The relevance and usefulness of bridging the two formalisms is shown in the example of the design of an evanescent wave biosensor.