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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1987
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10847529_v4_n5_p834_Depine http://hdl.handle.net/20.500.12110/paper_10847529_v4_n5_p834_Depine |
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paper:paper_10847529_v4_n5_p834_Depine |
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paper:paper_10847529_v4_n5_p834_Depine2023-06-08T16:06:02Z 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 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. 1987 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10847529_v4_n5_p834_Depine http://hdl.handle.net/20.500.12110/paper_10847529_v4_n5_p834_Depine |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
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. |
| title |
Comparison between the differential and integral methods used to solve the grating problem in the HH∥ase |
| spellingShingle |
Comparison between the differential and integral methods used to solve the grating problem in the HH∥ase |
| title_short |
Comparison between the differential and integral methods used to solve the grating problem in the HH∥ase |
| title_full |
Comparison between the differential and integral methods used to solve the grating problem in the HH∥ase |
| title_fullStr |
Comparison between the differential and integral methods used to solve the grating problem in the HH∥ase |
| title_full_unstemmed |
Comparison between the differential and integral methods used to solve the grating problem in the HH∥ase |
| title_sort |
comparison between the differential and integral methods used to solve the grating problem in the hh∥ase |
| publishDate |
1987 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10847529_v4_n5_p834_Depine http://hdl.handle.net/20.500.12110/paper_10847529_v4_n5_p834_Depine |
| _version_ |
1768544424516648960 |