Closed-form expression for the Goos-Hänchen lateral displacement

@article{Arajo2016ClosedformEF,
  title={Closed-form expression for the Goos-H{\"a}nchen lateral displacement},
  author={Manoel P. Ara{\'u}jo and Stefano De Leo and Gabriel Gulak Maia},
  journal={Physical Review A},
  year={2016},
  volume={93},
  pages={023801}
}
The Artmann formula provides an accurate determination of the Goos-Hanchen lateral displacement in terms of the light wavelength, refractive index and in- cidence angle. In the total reflection region, this formula is widely used in the literature and confirmed by exper- iments. 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… 

Figures from this paper

Angular deviations: from a cubic equation to a universal closed formula to determine the peak position of reflected and (upper) transmitted beams
A deviations and lateral displacements are optical effects widely investigated in literature. In this paper, by using the Taylor expansion of the Fresnel coefficients, we obtain an analytic
Oscillatory behavior of light in the composite Goos-Hänchen shift
For incidence in the critical region, the propagation of gaussian lasers through triangular dielectric blocks is characterized by the joint action of angular deviations and lateral displacements.
Direct calculation of the strong Goos–Hänchen effect of a Gaussian light beam due to the excitation of surface plasmon polaritons in the Otto configuration
We study theoretically the influence of the surface plasmon excitation on the Goos-H\"{a}nchen lateral shift of a $p$-polarized Gaussian beam incident obliquely on a dielectric-metal bilayer in the
Direct measurement of the composite Goos-Hänchen shift of an optical beam.
TLDR
The experimental results confirm recent theoretical predictions about the composite Goos-Hänchen shift, including the observation of negative shifts of the beam's intensity peak.
Incidence Angles Maximizing the Goos–Hänchen Shift in Seismic Data Analysis
In the solid/liquid and liquid/solid scenarios, for the cases in which the P and S reflected waves are represented by complex amplitudes, we give the closed formulas for the Goos–Hänchen phase from
Goos–Hänchen induced normal moveout correction for wide-angle reflections
The Goos–Hänchen (GH) lateral shift has been theoretically simulated and observed in lab. GH lateral shift introduces additional traveltime and distance when the incidence angles are larger than the
Lateral shifts and angular deviations of Gaussian optical beams reflected by and transmitted through dielectric blocks: a tutorial review
ABSTRACT In this work, we summarize the current state of understanding of lateral displacement and angular deviations of an optical beam propagating through dielectric blocks. In part I, the
Experimental evidence of laser power oscillations induced by the relative Fresnel (Goos–Hänchen) phase
The amplification of the relative Fresnel (Goos-Haenchen) phase by an appropriate number of total internal reflections and the choice of favorable incidence angles allow to observe full oscillations
Optimizing Weak Measurements to Detect Angular Deviations
We analyze and compare the angular deviations for an optical beam reflected by and transmitted through a dielectric triangular prism. The analytic expressions derived for the angular deviations hold
...
...

References

SHOWING 1-10 OF 26 REFERENCES
Lateral Displacement of a Light Beam at a Dielectric Interface
The lateral (Goos–Hanchen) shift of a gaussian light beam incident from a denser medium upon the interface to a rarer medium is investigated by means of a rigorous integral representation comprising
Goos–Hänchen effect around and off the critical angle
A general expression for the Goos–Hanchen lateral shift of a Gaussian wave beam, applicable for incident angle θ equal to, near, or larger than the critical angle θc, is obtained. It yields finite
Numerical Study of Goos-hänchen Shift on the Surface of Anisotropic Left-Handed Materials
The Goos-Hänchen shift on the surface when an optical beam is obliquely incident from one isotropic right-handed material (RHM) into another biaxial anisotropic left-handed material (BALHM) is
Goos–Hänchen and Imbert–Fedorov beam shifts: an overview
We consider reflection and transmission of polarized paraxial light beams at a plane dielectric interface. The field transformations taking into account a finite beam width are described based on the
Numerical study of the displacement of a three-dimensional Gaussian beam transmitted at total internal reflection. Near-field applications
TLDR
A theoretical model of this proposed scan tunneling optical microscope experiment is presented to obtain a numerical estimation of theitudinal and transverse shifts of a light beam at total internal reflection to verify the validity of the formalism and the feasibility of the near-field observation of these shifts.
The frequency crossover for the Goos–Hänchen shift
For total reflection, the Goos–Hänchen (GH) shift is proportional to the wavelength of the laser beam. At critical angles, such a shift is instead proportional to the square root of the product of
Axial dependence of optical weak measurements in the critical region
The interference between optical beams of different polarizations plays a fundamental role in reproducing the optical analog of the electron spin weak measurement. The extraordinary point in optical
Goos-Hänchen shifts of partially coherent light fields.
TLDR
It is shown that both the spatial coherence and the beam width have an important effect on the GH shift, especially near the critical angles (such as totally reflection angle).
An angular spectrum representation approach to the Goos-Hänchen shift
The reflection of a beam of light at a plane interface is treated using the angular spectrum representation. The Goos-Hanchen shift is found to be proportional to the first derivative of the phase of
The asymmetric Goos-Hänchen effect
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
...
...