心臓病診療プラクティス 16. 心不全を癒す

A quantum optical model involving a plasmonic nanostructure (PN) is proposed for controlling the diffraction efficiency of an electromagnetically induced grating in a four-level quantum system. By tuning the distance between the PN and the four-level quantum system, diffraction efficiency can be adjusted and energy can be transferred from zero order to higher orders. Moreover, due to the presence of the PN, the medium becomes phase-dependent and therefore, phase control of grating can be possible by changing the relative phase of the applied fields.

Phase-dependent electromagnetically induced grating in a four-level quantum system near a plasmonic nanostructure

By using a weak measurement technique, we investigated the interplay between the angular and lateral Goos-Haenchen shift of a focused He-Ne laser beam for incidence near the critical angle. We verified that this interplay dramatically affects the composite Goos-Haenchen shift of the propagated beam. The experimental results confirm theoretical predictions that recently appeared in the literature.

Weak measurement og the composite Goo-Haenchen shift in the critical region

The Artmann formula provides an accurate determination of the Goos-H\"anchen lateral displacement in terms of the light wavelength, refractive index, and incidence angle. In the total reflection region, this formula is widely used in the literature and confirmed by experiments. Nevertheless, for incidence at critical angle, it tends to infinity and numerical calculations are needed to reproduce the experimental data. In this paper, we overcome the divergence problem at critical angle and find, for Gaussian beams, a closed formula in terms of modified Bessel functions of the first kind. The formula is in excellent agreement with numerical calculations and reproduces, for incidence angles greater than critical ones, the Artmann formula. The closed form also allows one to understand how the breaking of symmetry in the angular distribution is responsible for the difference between measurements done by considering the maximum and the mean value of the beam intensity. The results obtained in this study clearly show the Goos-H\"anchen lateral displacement dependence on the angular distribution shape of the incoming beam. Finally, we also present a brief comparison with experimental data and other analytical formulas found in the literature.

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Closed-form expression for the Goos-Hänchen lateral displacement

By using a weak measurement technique, we investigated the interplay between the angular and the lateral Goos–Hanchen shift of a focused He–Ne laser beam for incidence near the critical angle. We verified that this interplay dramatically affects the composite Goos–Hanchen shift of the propagated beam. The experimental results confirm theoretical predictions that recently appeared in the literature.

Weak measurement of the composite Goos-Hänchen shift in the critical region.

We show under which conditions optical Gaussian beams, propagating throughout an homogeneous dielectric right angle prism, present an asymmetric Goos–Hanchen (GH) effect. This asymmetric behavior is seen for incidence at critical angles and happens in the propagation direction of the outgoing beam. The asymmetric GH effect can also be seen as an amplification of the standard GH shift. Due to the fact that it only depends on the ratio between the wavelength and the minimal waist size of the incoming Gaussian beam, it can also be used to determine one of these parameters. Multiple-peak interference is an additional phenomenon seen in the presence of such asymmetric effects.

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The asymmetric Goos-Hänchen effect

We use the stationary phase method to determine the paths of optical beams that propagate through a dielectric block. In the presence of partial internal reflection, we recover the geometrical result obtained by using Snell's law. For total internal reflection, the stationary phase method overreaches Snell's law, predicting the Goos-Hanchen shift.

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The use of the stationary phase method as a mathematical tool to determine the path of optical beams

A detailed analysis of the propagation of laser Gaussian beams at critical angles shows under which conditions it is possible to maximize the breaking of symmetry in the angular distribution and for which values of the laser wavelength and beam waist it is possible to find an analytic formula for the maximal angular deviation from the optical path predicted by the Snell law. For beam propagation through $N$ dielectric blocks and for a maximal breaking of symmetry, a closed expression for the Goos-H\"anchen shift is obtained. The multiple-peak phenomenon clearly represents additional evidence of the breaking of symmetry in the angular distribution of optical beams. Finally, the laser wavelength and beam-waist conditions to produce focal effects in the outgoing beam are also briefly discussed.

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Maximal breaking of symmetry at critical angles and a closed-form expression for angular deviations of the Snell law

We propose a scheme for inducing a blazed transmission grating in a four-level, $N$-type atomic medium under electromagnetically induced transparency (EIT). The blazed grating relies on the giant Kerr nonlinearity that the atomic medium exhibits under EIT. The grating is created using an intensity mask in one of the driving optical fields and only weak fields with intensities below saturation level are involved. Diffraction efficiencies of a resonant probe beam close to $100%$ are predicted.

Electromagnetically induced blazed grating at low light levels

We show in which conditions optical gaussian beams, propagating throughout an homogeneous dielectric right angle prism, present an asymmetric Goos-Hanchen (GH) effect. This asymmetric behavior is seen for incidence at critical angles and happens in the propagation direction of the outgoing beam. The asymmetric GH effect can be also seen as an amplification of the standard GH shift. Due to the fact that it only depends on the ratio between the wavelength and the minimal waist size of the incoming gaussian beam, it can be also used to determine one of these parameters. Multiple peaks interference is an additional phenomenon seen in the presence of such asymmetric effects.

Silvânia A. Carvalho

Papers

The asymmetric Goos-Hänchen effect

The use of the stationary phase method as a mathematical tool to determine the path of optical beams

Maximal breaking of symmetry at critical angles and a closed-form expression for angular deviations of the Snell law

Electromagnetically induced blazed grating at low light levels

The asymmetric Goos-H\"anchen effect