Raymond Reinisch

Optimization of surface-plasmon-enhanced magneto-optical effects

Kretschmann prism couplers, including magneto-optical media such as Co, Fe, and Ni, allow enhancement of the magneto-optical response, such as conversion of light polarization, thanks to the resonant excitation of surface plasmons. Since these media have high losses, they support overdamped surface plasmons. A way to get high-quality surface-plasmon resonance is to use noble-metal/ferromagnetic-metal multilayer thin films. The question that arises is, which surface-plasmon resonance leads to the largest enhancement: is it the overdamped or the high-quality one? We show that the best optimization not only depends on the orientation of the magnetic field but also on the magneto-optical coefficients. The most effective enhancer of the magneto-optical effects is the high-quality surface plasmons for the transverse orientation and may be the overdamped surface plasmons for the polar and longitudinal ones. This applies when the noble metal is gold and the magneto-optical medium is cobalt.

Coupled-mode formalism and linear theory of diffraction for a simplified analysis of second harmonic generation at grating couplers

Abstract We present a new approach to study second harmonic generation at grating couplers where we take full advantage of the fact that, in this type of second harmonic generation, there is a resonant excitation of normal modes of the grating coupler (guided wave or surface plasmon). Therefore the analysis reported here is developed in the framework of the coupled-mode formalism. This allows us to show that the associated diffraction phenomenon, which occurs in nonlinear optics, can be handled using the linear theory of diffraction. The resulting simplicity, which arises from the simultaneous use of the coupled-mode and linear diffraction theories, allows an easy physical insight in the process of second harmonic generation at grating couplers. Proceeding along these lines, we derive not only the guided wave amplitude but also that of the radiated diffracted orders at the second harmonic frequency.

Grating and prism couplers: radiation pattern and m-line

Abstract Prism or grating couplers are known to exhibit m-lines in the far-field and zeros in the near-field. Despite the fact that a lot of papers have been devoted to these couplers, there is some confusion concerning the possible link between the m-line and zero: is the former a consequence of the latter? One of the objects of this paper is to clarify this point. It is the opportunity to consider, in addition to the near-field and far-field patterns, the question of the intermediate region constituted by the Fresnel zone and to give a criterium of the far-field pattern.

Second-harmonic generation by counterpropagating surface plasmons at a silver diffraction grating

We report an experimental study of second-harmonic generation at a silver diffraction grating when counterpropagating surface plasmons are excited with a single pump beam. In the surface plasmon minigap, no second-harmonic light is observed in the specular direction, whereas a strong signal is detected in the direction normal to the mean plane of the grating.

M-line spectroscopy for nonlinear characterization of polymeric waveguides

Nonlinear M-line spectroscopy is based on the analysis of the nonlinear change in the shape of the dark line associated with the excitation of guided waves. This is an easy technique for the determination of Kerr properties of thin films, which can constitute optical waveguides. Full spatiotemporal nonlinear modeling tools have been developed recently for nonlinear waveguide couplers, which are used for the determination of the complex nonlinear coefficient of organic polymers.

Grating-enhanced second-harmonic generation in polymer waveguides: role of losses

A numerical study of second-harmonic (SH) generation in a corrugated polymer waveguide is performed with a rigorous electromagnetic theory. Comparison with experiment reveals the role of losses inside the waveguide-small losses do not significantly affect the nonresonant response and reduce the resonant enhancement of SH generation. High losses can lead to the opposite effect-instead of enhancement, dips in the SH efficiency are observed in the vicinity of guided-wave excitation. The peculiarities of the angular dependencies of SH generation are explained from the phenomenological point of view, and the role of phase matching is discussed.

Symmetry relations for reflection and transmission coefficients of magneto-optic systems

In magneto-optic systems, Kerr and Faraday effects bring into play reflection and transmission matrices. Considering planar multilayer systems, we show that the elements of the reflection and transmission matrices obey general and simple relations valid whatever the geometry of the magneto-optic device may be.

Bistability of second harmonic generation in optical waveguides with depletion of the pump field

The paper is concerned with second harmonic generation in optical resonators like prism or grating couplers when the depletion of the pump field is strong enough so that is can no longer be neglected. This means that we have to take into account the feedback between the signal field at 2(omega) circular frequency and the pump field at (omega) . Two different approaches are developed. The first one is a rigorous electromagnetic analysis based on the numerical integration of nonlinear Maxwell equations at both (omega) and 2(omega) frequencies, incorporated in a root-finding procedure to take the depletion into account. The second is based on a couple mode analysis which leads to a set of coupled mode equations governing the amplitudes of the pump and second harmonic frequency fields. These methods allow to predict that second- harmonic generation in prism or grating couplers can lead to optical bistability. Contrary to the Kerr-like bistability, this new type of bistability occurs not only at one side of the resonance maximum but on both sides provided the absolute value of the offset in the incident angle is above a threshold. The two approaches give numerical results in very good agreement. The coupled mode theory provides analytical predictions of the threshold value and brings physical insight on this new effect.

Electromagnetic resonances and phase matching in guided-wave nonlinear optics

This paper is concerned with the interplay between electromagnetic resonances and the phase-matching condition in guided-wave nonlinear optics. Several examples are given: quasi phase-matched second-harmonic generation using a grating with a subwavelength periodicity, cascaded optical bistability, Kerr-type distributed couplers under pulse illumination with duration of the order of the cavity build-up time or shorter, surface plasmon-enhanced stimulated Raman scattering at a grating overcoated by a few monolayers of a Raman active medium.

Electromagnetic study of second harmonic generation by a corrugated waveguide

When an incident plane wave with circular frequency (omega) falls on a grating coated by a layer of nonlinear material, it generates a nonlinear polarization PNL(2(omega) ) which acts as a source term and produces a second harmonic (SH) field called signal. The excitation of an electromagnetic resonance like surface plasmon or a guided wave increases the local field and thus the signal. The problem is to be able to compute and optimize the latter. We have developed a new theory which uses a coordinate transformation mapping the grating profile onto a plane. This simplifies the boundary conditions but complicates the propagation equation. Taking advantage of the psuedoperiodicity of the problem, the Fourier harmonics of the field are solution of a set of first order differential equations with constant coefficients. The resolution of this system via eigenvalue and eigenvector technique avoid numerical instabilities and lead to accurate results which agree perfectly with those found via the Rayleigh method or by the Differential method, when they work. A phenomenological approach is then developed to explain the unusual shape of the resonance lines at 2(omega) , which is based on the poles and zeros of the scattering operator S at (omega) and 2(omega) . It is shown that S(2(omega) ) presents 3 complex poles with 3 associated complex zeros. Their knowledge, plus the nonlinear reflectivity of the plane device allows predicting all the possible shapes of the 2(omega) signal as a function of angle of incidence. The phenomenological study explains an experimental result, found a few years ago, that if 2(omega) lies inside the absorption band of the guiding material instead of the transparent region, the enhanced second harmonic generation (SHG) is changed into a reduced one. It means that in the case phase matching can lead to a minimum instead of maximum. An algorithm is then proposed to maximize the signal intensity; with polyurethane as a guiding material a conversion factor of up to 40% is found when incident power is equal to 40 kW.