Longitudinal and transverse displacements of a bounded microwave beam at total internal reflection*

Cowan, James J.; Aničin, B. A.

doi:10.1364/josa.67.001307

Cited by 104 publications

(37 citation statements)

References 10 publications

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“…1 confirmed Artmann's prediction for incidence far enough from the critical region [3,5,[7][8][9][10].…”

Section: Introductionsupporting

confidence: 69%

“…In an interesting paper dated 1986 [21], Cheng and Tang compared the Horowitz-Tamir formula with experimental data [8]. The Horowitz-Tamir formula as well the formula presented in this paper do not contain any axial corrections.…”

Section: Discussionmentioning

confidence: 79%

“…Notwithstanding the great interest in the literature [11][12][13][14][15] (for clear and detailed reviews on the GH shift see Refs. [16,17]), the divergence problem of the Artmann formula was often overcome by using numerical calculations [14,18,19] to fit the experimental curves [7][8][9][10]. An analytical formula for the amplification of the GH shift at critical angle was recently proposed [14] but it is only valid for incidence at critical angles and does not explain the maximum obtained by numerical calculation for angles greater than the critical one.…”

Section: Introductionmentioning

confidence: 99%

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Closed-form expression for the Goos-Hänchen lateral displacement

Araújo

Maia

2016

Phys. Rev. A

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Abstract. The Artmann formula provides an accurate determination of the Goos-Hänchen 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-Hänchen 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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“…1 confirmed Artmann's prediction for incidence far enough from the critical region [3,5,[7][8][9][10].…”

Section: Introductionsupporting

confidence: 69%

Section: Discussionmentioning

confidence: 79%

Section: Introductionmentioning

confidence: 99%

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Closed-form expression for the Goos-Hänchen lateral displacement

Araújo

Maia

2016

Phys. Rev. A

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“…1(d), it is clear that, increasing σ s leads to the weakening of the effect of spatial coherence on the GH shift. It should be pointed out that, for a coherent beam, the effect of beam width has been investigated in the very early literature [18,23] and has also been experimental demonstrated [21,28]. Therefore it is expected that the beam width has also an effect on the GH shift for PCFs.…”

mentioning

confidence: 97%

Goos-Hänchen Shifts of Partially Coherent Light Fields

2013

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We investigate the Goos-Hänchen (GH) shifts of partially coherent fields (PCFs) by using the theory of coherence. We derive a formal expression for the GH shifts of PCFs in terms of Mercer's expansion, and then clearly demonstrate the dependence of the GH shift of each mode of PCFs on spatial coherence and beam width. We discuss the effect of spatial coherence on the resultant GH shifts, especially for the cases near the critical angles, such as totally reflection angle.PACS numbers: 42.50. Ar, 42.25.Gy, 42.30.Jf Goos-Hänchen (GH) Shift refers to a tiny (lateral) displacement, from the path expected from geometrical optics, upon total reflection [1]. This effect has been extended into other fields that involve the coherent-wave phenomena, such as neutron waves [2,3], electron waves [4,5], and spin waves [6]. It was explained by Artmann [7] that the different transverse wave vectors of a light beam undergo different phase changes and sum of these waves form a reflected beam with a lateral shift. Recently, it was shown [8] that the GH shift is the sum of Renard's conventional energy flux plus a self-interference shift. The self-interference shift originates from the interference between the incident and the reflected beams. Furthermore, it was discovered that the classical Fresnel formulas for laws of refraction and reflection of light are not applicable to partially coherent light [9]. These explanations indicate that the interference or coherence of light is very important to the GH shift.In 2008, we numerically showed the effect of spatial coherence on the change of the GH shift near the critical angles [10]. Later, an experiment [11] showed the large difference between the measured GH shift of a partially coherent LED light and the theoretical result of a coherent light. However, the very recent investigations [12][13][14][15][16] have raised an important issue "whether the spatial coherence of the partially coherent fields (PCFs) influences the GH shifts?" Although the exact numerical results, calculated from our previous theory [10], are in good agreement with the experimental data [13,14,16], it is necessary to reconsider this issue thoroughly and bring to light the role of spatial coherence on the GH shift.In this Letter, we use the exact theory of coherence to investigate the GH shift of PCFs. First we derive a formal expression to calculate the GH shift of PCFs in terms of the mode expansion of PCFs. Based on this expression, we explain the physical mechanism about the dependence of the GH shift on the spatial coherence and the beam width. Finally, we suggest a proposal for showing the new effect of the spatial coherence on the practical GH shift below the critical angles.First we derive the GH shift of PCFs based on the coherence theory [17]. For the two-dimensional PCFs, one usually uses the cross-spectral density (CSD), W (x 1 , z 1 ; x 2 , z 2 , ν), to describe its propagation, where (x 1 , z 1 ) and (x 2 , z 2 ) are the coordinates of the two points in the fields, and ν is the frequency of light....

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“…This phenomenon has been widely analyzed both theoretically [3][4][5][6][7][8][9] and experimentally [1,[10][11][12][13][14]. The investigation on the GH shift has been extended to other areas of physics, such as acoustics, quantum mechanics and plasma physics [15].…”

mentioning

confidence: 99%

Negative and positive lateral shift of a light beam reflected from a grounded slab

et al. 2006

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We consider the lateral shift of a light beam reflecting from a dielectric slab backed by a metal. It is found that the lateral shift of the reflected beam can be negative while the intensity of reflected beam is almost equal to the incident one under a certain condition. The explanation for the negativity of the lateral shift is given in terms of the interference of the reflected waves from the two interfaces. It is also shown that the lateral shift can be enhanced or suppressed under some other conditions. The numerical calculation on the lateral shift for a realistic Gaussian-shaped beam confirms our theoretical prediction.

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Longitudinal and transverse displacements of a bounded microwave beam at total internal reflection*

Cited by 104 publications

References 10 publications

Closed-form expression for the Goos-Hänchen lateral displacement

Closed-form expression for the Goos-Hänchen lateral displacement

Goos-Hänchen Shifts of Partially Coherent Light Fields

Negative and positive lateral shift of a light beam reflected from a grounded slab

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