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Volumn 28, Issue 3, 2011, Pages 391-400

Partial spatial coherence and partial polarizationin random evanescent fields on lossless interfaces

Author keywords

[No Author keywords available]

Indexed keywords

ELECTROMAGNETISM; LIGHT; NANOPHOTONICS; NEAR FIELD SCANNING OPTICAL MICROSCOPY; REFRACTIVE INDEX; THREE DIMENSIONAL;

EID: 79952334615     PISSN: 10847529     EISSN: 15208532     Source Type: Journal    
DOI: 10.1364/JOSAA.28.000391     Document Type: Article
Times cited : (21)

References (26)
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    • The form of the Fresnel coefficient for p polarization given in Eq. (13) is valid only for an evanescent wave. For propagating waves, the factor √2ñ2γ2 + 1 is absent in the numerator. However, the factor follows directly from the boundary conditions, if the (complex) vector p̂2 related to the evanescent wave is normalized to unity. For example, in [19,20], the square-root factor is missing since in those treatments p̂2 is not normalized; more precisely, p̂*2 · p̂2 ≠ 1 but instead p̂2 · p̂2 = 1. The form of t p given in Eq. (13) preserves the physical meaning of the Fresnel coefficients as the ratio of the complex amplitudes on the opposite sides of the surface. See also [23].
    • The form of the Fresnel coefficient for p polarization given in Eq. (13) is valid only for an evanescent wave. For propagating waves, the factor √2ñ2γ2 + 1 is absent in the numerator. However, the factor follows directly from the boundary conditions, if the (complex) vector p̂2 related to the evanescent wave is normalized to unity. For example, in [19,20], the square-root factor is missing since in those treatments p̂2 is not normalized; more precisely, p̂*2 · p̂2 ≠ 1 but instead p̂2 · p̂2 = 1. The form of t p given in Eq. (13) preserves the physical meaning of the Fresnel coefficients as the ratio of the complex amplitudes on the opposite sides of the surface. See also [23].
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    • The p-polarized amplitude of the evanescent wave looks different from that given in [19,20], but it is the same. The variances in the appearance originate from the differences in the Fresnel coefficients for the p-polarized light. However, for the Fresnel coefficient in Eq. (13), the energy density of the p-polarized evanescent wave is of the intuitive form given in Eq. (22). For the evanescent wave of [19,20], the energy density contains an additional factor, wp = |tp|2|Ep| 2(2ñ2γ2 + 1. See also [21] above
    • The p-polarized amplitude of the evanescent wave looks different from that given in [19,20], but it is the same. The variances in the appearance originate from the differences in the Fresnel coefficients for the p-polarized light. However, for the Fresnel coefficient in Eq. (13), the energy density of the p-polarized evanescent wave is of the intuitive form given in Eq. (22). For the evanescent wave of [19,20], the energy density contains an additional factor, wp = |tp|2|Ep| 2(2ñ2γ2 + 1. See also [21] above.


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