Theory of refraction and reflection with partially coherent electromagnetic beams

Lahiri, Mayukh; Wolf, Emil

doi:10.1103/physreva.86.043815

Cited by 13 publications

(8 citation statements)

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“…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.…”

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confidence: 99%

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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Goos-Hänchen Shifts of Partially Coherent Light Fields

2013

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“…6) have been studied in great detail. Recently, a theory of refraction and reflection of partially coherent electromagnetic beams has been developed [3]. This theory suggests that spatial coherence of a beam may also change on refraction and on reflection.…”

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Change in spatial coherence of light on refraction and on reflection

Lahiri

Wolf

2013

J. Opt. Soc. Am. A

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“…Hence, each plane wave component has a different angle of refraction and also the Fresnel coefficients have different values for each of them. When the two media are nonabsorbing (approximately) and when the angle of incidence is smaller than the critical angle, the mathematical treatment of negative refraction of a partially coherent electromagnetic beam is almost the same as that developed for the case of usual (positive) refraction [6], except one now needs to use the fact that both n 2 and θ t are negative and to apply the modified Fresnel formulas (3), instead of the usual Fresnel formulas, for each plane wave component present in the beam. Following this procedure, one can obtain an expression for the CSDM of the transmitted beam at the interface (analogous expression for positive refraction is given by Eq.…”

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“…However, they are not applicable to partially coherent electromagnetic beams. Recently, a theory of refraction of partially coherent beams has been formulated for positive refractive index materials [6]. In this Letter, we discuss how the theory can be generalized to negative refraction, and show that negative refraction can produce change in spatial coherence properties of a partially coherent beam.…”

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“…Following this procedure, one can obtain an expression for the CSDM of the transmitted beam at the interface (analogous expression for positive refraction is given by Eq. (30) of [6]) and can calculate the degree of spatial coherence of the beam. We now apply this formulation to illustrate that negative refraction of a partially coherent electromagnetic beam can produce change in the spatial coherence properties of the beam.…”

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