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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 23, Iss. 18 — Sep. 15, 1984
  • pp: 3236–3242

Strip gratings at a dielectric interface and application of Babinet’s principle

R. C. Compton, L. B. Whitbourn, and R. C. McPhedran  »View Author Affiliations


Applied Optics, Vol. 23, Issue 18, pp. 3236-3242 (1984)
http://dx.doi.org/10.1364/AO.23.003236


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Abstract

In this paper, we consider the transmission-line model used to calculate the transmittance of thin metallic strip gratings (at wavelengths longer than the grating period) to resolve a conflict of published expressions for the effect of a thick dielectric substrate on the equivalent circuit capacitance of capacitive gratings. By using rigorous diffraction theory we establish the correct expression and derive a modified form of Babinet’s principle for use with strip gratings on dielectric boundaries. It is found that the equivalent circuit capacitance of a strip grating on the boundary between media of refractive indices n1 and n2 is larger than its free-space value by a factor ( n 1 2 + n 2 2 ) / 2. The result is applicable in general to the capacitive part of the equivalent circuit of grid reflectors, which are widely used at submillimeter wavelengths. A useful set of rigorously calculated transmission curves for strip gratings is presented, and these are used to establish the range of validity of the transmission-line model.

© 1984 Optical Society of America

History
Original Manuscript: August 15, 1983
Published: September 15, 1984

Citation
R. C. Compton, L. B. Whitbourn, and R. C. McPhedran, "Strip gratings at a dielectric interface and application of Babinet’s principle," Appl. Opt. 23, 3236-3242 (1984)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-23-18-3236


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References

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  19. To derive the correct results it is necessary to go back to the results of Ulrich2 and make appropriate substitutions for the capacitive part of the equivalent circuit reactance of a mesh at a dielectric interface. The results in Table 3 of Ulrich’s paper are correct if Z0 is taken to be 2ω0 ln[csc(πa/g)] for inductive gratings and the reciprocal of this expression for capacitive gratings.
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