Lateral shift of the transmitted light beam through a left-handed slab

It is reported that when a light beam travels through a slab of left-handed medium in the air, the lateral shift of the transmitted beam can be negative as well as positive. The necessary condition for the lateral shift to be positive is given. The validity of the stationary-phase approach is demonstrated by numerical simulations for a Gaussian-shaped beam. A restriction to the slab's thickness is provided that is necessary for the beam to retain its profile in the traveling. It is shown that the lateral shift of the reflected beam is equal to that of the transmitted beam in the symmetric configuration.Comment: 14 pages, 4 figure

Goos-Haenchen induced vector eigenmodes in a dome cavity

We demonstrate numerically calculated electromagnetic eigenmodes of a 3D dome cavity resonator that owe their shape and character entirely to the Goos-Haenchen effect. The V-shaped modes, which have purely TE or TM polarization, are well described by a 2D billiard map with the Goos-Haenchen shift included. A phase space plot of this augmented billiard map reveals a saddle-node bifurcation; the stable periodic orbit that is created in the bifurcation corresponds to the numerically calculated eigenmode, dictating the angle of its "V". A transition from a fundamental Gaussian to a TM V mode has been observed as the cavity is lengthened to become nearly hemispherical.Comment: 4 pages, 4 figure

Unified theory for Goos-H\"{a}nchen and Imbert-Fedorov effects

A unified theory is advanced to describe both the lateral Goos-H\"{a}nchen (GH) effect and the transverse Imbert-Fedorov (IF) effect, through representing the vector angular spectrum of a 3-dimensional light beam in terms of a 2-form angular spectrum consisting of its 2 orthogonal polarized components. From this theory, the quantization characteristics of the GH and IF displacements are obtained, and the Artmann formula for the GH displacement is derived. It is found that the eigenstates of the GH displacement are the 2 orthogonal linear polarizations in this 2-form representation, and the eigenstates of the IF displacement are the 2 orthogonal circular polarizations. The theoretical predictions are found to be in agreement with recent experimental results.Comment: 15 pages, 3 figure

Goos-H\"anchen shifts in frustrated total internal reflection studied with wave packet propagation

We have investigated that the Goos-H\"anchen (GH) shifts in frustrated total internal reflection (FTIR) studied with wave packet propagation. In the first-order approximation of the transmission coefficient, the GH shift is exactly the expression given by stationary phase method, thus saturates an asymptotic constant in two different ways depending on the angle of incidence. Taking account into the second-order approximation, the GH shift always depends on the width of the air gap due to the modification of the beam width. It is further shown that the GH shift with second-order correction increases with decreasing the beam width at the small incidence angles, while for the large incidence angles it reveals a strong decrease with decreasing the beam width. These phenomena offers the better understanding of the tunneling delay time in FTIR.Comment: 4 pages, 3 figure

Fresnel laws at curved dielectric interfaces of microresonators

We discuss curvature corrections to Fresnel's laws for the reflection and transmission of light at a non-planar refractive-index boundary. The reflection coefficients are obtained from the resonances of a dielectric disk within a sequential-reflection model. The Goos-H\"anchen effect for curved light fronts at a planar interface can be adapted to provide a qualitative and quantitative extension of the ray model which explains the observed deviations from Fresnel's laws.Comment: submitted to Phys. Rev.

Kaspar Schott’s “encyclopedia of all mathematical sciences”

In 1661, Kaspar Schott published his comprehensive textbook “Cursus mathematicus” in Würzburg for the first time, his “Encyclopedia of all mathematical sciences”. It was so successful that it was published again in 1674 and 1677. In its 28 books, Schott gave an introduction for beginners in 22 mathematical disciplines by means of 533 figures and numerous tables. He wanted to avoid the shortness and the unintelligibility of his predecessors Alsted and Hérigone. He cited or recommended far more than hundred authors, among them Protestants like Michael Stifel and Johannes Kepler, but also Catholics like Nicolaus Copernicus. The paper gives a survey of this work and explains especially interesting aspects: The dedication to the German emperor Leopold I., Athanasius Kircher’s letter of recommendation as well as Schott’s classification of sciences, explanations regarding geometry, astronomy, and algebra

Control of Goos-Hanchen shift of a light beam via a coherent driving field

We present a proposal to manipulate the Goos-Hanchen shift of a light beam via a coherent control field, which is injected into a cavity configuration containing the two-level atomic medium. It is found that the lateral shifts of the reflected and transmitted probe beams can be easily controlled by adjusting the intensity and detuning of the control field. Using this scheme, the lateral shift at the fixed incident angle can be enhanced (positive or negative) under the suitable conditions on the control field, without changing the structure of the cavity.Comment: 12 pages, 5 figure

Goos-Haenchen shift and localization of optical modes in deformed microcavities

Recently, an interesting phenomenon of spatial localization of optical modes along periodic ray trajectories near avoided resonance crossings has been observed [J. Wiersig, Phys. Rev. Lett. 97, 253901 (2006)]. For the case of a microdisk cavity with elliptical cross section we use the Husimi function to analyse this localization in phase space. Moreover, we present a semiclassical explanation of this phenomenon in terms of the Goos-Haenchen shift which works very well even deep in the wave regime. This semiclassical correction to the ray dynamics modifies the phase space structure such that modes can localize either on stable islands or along unstable periodic ray trajectories.Comment: 9 pages, 14 figures in reduced qualit

Technoscientia est Potentia?: Contemplative, interventionist, constructionist and creationist idea(l)s in (techno)science

Within the realm of nano-, bio-, info- and cogno- (or NBIC) technosciences, the ‘power to change the world’ is often invoked. One could dismiss such formulations as ‘purely rhetorical’, interpret them as rhetorical and self-fulfilling or view them as an adequate depiction of one of the fundamental characteristics of technoscience. In the latter case, a very specific nexus between science and technology, or, the epistemic and the constructionist realm is envisioned. The following paper focuses on this nexus drawing on theoretical conceptions as well as empirical material. It presents an overview of different technoscientific ways to ‘change the world’—via contemplation and representation, intervention and control, engineering, construction and creation. It further argues that the hybrid character of technoscience makes it difficult (if not impossible) to separate knowledge production from real world interventions and challenges current science and technology policy approaches in fundamental ways