Phase shifts that accompany total internal reflection at a dielectric-dielectric interface

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 21, Issue 8, 2004, Pages 1559-1563

  Azzam, R M A ^a  

^a UNO College of Engineering   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DIELECTRIC MATERIALS; ELLIPSOMETRY; INTERFACES (MATERIALS); LIGHT POLARIZATION; MATRIX ALGEBRA; PHASE SHIFT; REFRACTIVE INDEX; TRANSPARENCY;

PLANAR INTERFACE; REFLECTION JONES MATRIX; TOTAL INTERNAL REFLECTION; TRANSPARENT MEDIA;

LIGHT REFLECTION;

EID: 4043057302     PISSN: 10847529     EISSN: None     Source Type: Journal    
DOI: 10.1364/JOSAA.21.001559     Document Type: Article

References (14)

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2. M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975).
3. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987).
4. R. M. A. Azzam, "Relations between amplitude reflectances and phase shifts of the p and s polarizations when electromagnetic radiation strikes interfaces between transparent media," Appl. Opt. 18, 1884-1886 (1979).
5. F. Abelès, "Un théoreme relatif à la réflexion métallique," C. R. Hebd. Seances Acad. Sci. 230, 1942-1943 (1950).
6. E. E. Hall, "The penetration of totally reflected light into the rarer medium," Phys. Rev. 15, 73-106 (1902).
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8. R. W. Astheimer, G. Falbel, and S. Minkowitz, "Infrared modulation by means of frustrated total internal reflection," Appl. Opt. 5, 87-91 (1966).
9. R. M. A. Azzam, "Contours of constant principal angle and constant principal azimuth in the complex ε plane," J. Opt. Soc. Am. 71, 1523-1528 (1981).
10. J. Bennett and H. E. Bennett, "Polarization," in Handbook of Optics, W. G. Driscoll and W. Vaughan, eds. (McGraw Hill, New York, 1978), Sect. 10.
11. For any N, Eq. (20) also has a trivial solution at φc, where all phase shifts are zero.
12. From Eq. (26) we also obtain cos2 φm = (N2 - 1)/(N2 + 1) = -cos(2φB), which provides a direct relation between the incidence angle of maximum TIR differential phase shift φm and the Brewster angle of external reflection φB.
13. From Eqs. (35) and (26) it is readily verified that sin2(Δφ)< sin2(90° - φm) = cos2 φm, so that Δφ = φm - φc < 90° - φm. This proves that φm is always closer to the critical angle than it is to grazing incidence (90°), consistent with Figs. 1 and 3.
14. Equation (40) can also be obtained by substituting (1 - ρ)2/(1 + ρ)2 = -tan2(Δ/2), when ρ = exp(jΔ), in Eq. (4.20a)