Comparison between the differential and integral methods used to solve the grating problem in the HH∥ase
The usual differential method for solving the grating problem in the H∥ case is shown to be unable to predict the efficiencies of blazed gratings in a reliable manner. Its predictions are compared with those obtained using the integral method developed by Maystre, a reliable method that has shown it...
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| Formato: | Capítulo de libro |
| Lenguaje: | Inglés |
| Publicado: |
1987
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| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
| Aporte de: | Registro referencial: Solicitar el recurso aquí |
| Sumario: | The usual differential method for solving the grating problem in the H∥ case is shown to be unable to predict the efficiencies of blazed gratings in a reliable manner. Its predictions are compared with those obtained using the integral method developed by Maystre, a reliable method that has shown its validity over a wide range of applications. The efficiencies of sinusoidal gratings as a function of angle of incidence are calculated by both methods for two values of the groove-height-to-period ratio. For 0.05 (low modulations) both formalisms yield similar results, but for 0.2 only a qualitative agreement is observed. The differential method is shown to involve an approximation valid only for low-modulated surfaces, a fact that accounts for the observed discrepancies. As a self-consistency test, the fulfillment of the electromagnetic boundary conditions is checked by calculating the jumps of the field components, which should be continuous at the grating surface. © 1987 Optical Society of America. |
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| Bibliografía: | Cerutti-Maori, G., Petit, R., Cadilhac, M., Etude numerique du champ diffracte par un reseau (1969) C. R. Acad. Sci. (Paris), 268 B, pp. 1060-1063 Neviere, N., Vincent, P., Petit, R., Sur la theorie du reseau conducteur et ses applications a l'optique (1974) Nouv. Rev. Opt, 5, pp. 65-77 Vincent, P., Differential methods (1980) Electromagnetic Theory of Gratings, 22, p. 101. , of Topics in Current Physics, R. Petit, ed., (Springer-Verlag, Berlin) Depine, R.A., Simon, J.M., Diffraction grating efficiencies: An exact differential algorithm valid for high conductivities (1983) Opt. Acta, 30, pp. 1273-1286 Simon, J.M., Depine, R.A., Diffraction grating efficiencies: Differential methods for H|| case (1984) Optik, 67, pp. 145-153 Maystre, D., A new general integral theory for dielectric coated gratings (1978) J. Opt. Soc. Am, 68, pp. 490-495 Maystre, D., Integral methods (1980) Electromagnetic Theory of Gratings, 22, p. 63. , of Topics in Current Physics, R. Petit, ed., (Springer-Verlag, Berlin) Maystre, D., Neviere, M., Petit, R., Experimental verifications and applications of the theory (1980) Electromagnetic Theory of Gratings, 22, p. 159. , of Topics in Current Physics, R. Petit, ed., (Springer-Verlag, Berlin) |
| ISSN: | 10847529 |
| DOI: | 10.1364/JOSAA.4.000834 |