Neutron reflection from condensed matter, the Goos–Hänchen effect and coherence

Ignatovich, V. K.

doi:10.1016/j.physleta.2003.12.026

Cited by 67 publications

(44 citation statements)

References 12 publications

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“…(3) is not unique. This is correct, although in most cases [3][4][5][6] the various expressions given are equal to our Eq. (3) as long as the perpendicular component of the wave vector is not much smaller than the critical wave vector.…”

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confidence: 56%

“…Indeed, it was his detailed work [3] that motivated us to measure the GH shift for neutrons. Ignatovich argues that our Eq.…”

mentioning

confidence: 99%

“…In Ref. [3] Ignatovich derived identical expressions for the GH shift starting from completely different concepts, ranging from a distribution of plane waves to a Gaussian beam to a wave packet description. Ignatovich claims, ''It is well known that the GH shift occurs when a particle is totally reflected.''…”

mentioning

confidence: 99%

“…Ignatovich [3] writes the following in his derivation of the GH shift: ''This distance can be called the GH shift, but a spatial displacement can be well defined only for finite size beams. In case of infinite plane waves we can talk only about the phase shift.''…”

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confidence: 56%

“…Indeed, it was his detailed work [3] that motivated us to measure the GH shift for neutrons. Ignatovich argues that our Eq.…”

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confidence: 99%

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“…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.…”

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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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2010

Handbook of Neutron Optics

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Neutron reflection from condensed matter, the Goos–Hänchen effect and coherence

Abstract: The Goos-Hänchen (G-H) effect for neutron reflection from condensed matter is considered. An experiment to quantify the effect is proposed. The relation of G-H shift to the neutron coherence length is considered.

Cited by 67 publications

References 12 publications

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Goos-Hänchen Shifts of Partially Coherent Light Fields

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