Total internal reflection diffraction grating in conical mounting
Introduction
During the last three decade surface relief diffraction gratings became an integral part of many modern optical systems and devices including imaging systems [1], [2], array illuminators [3], pulse shapers [4], and beam splitters and deflectors [5], [6]. Some of the investigations were extended to include surface relief diffraction gratings that also involve total internal reflection (TIR) in the substrate on which the gratings are recorded. These included theoretical investigations of surface relief dielectric gratings in classical (Littrow) mounting [7] as well as subsequent experimental investigations [8]. In such classical mounting, the grating vector and all diffraction orders lie in the plane of incidence.
In this paper, we investigate surface relief TIR diffraction gratings in conical mounting, where the plane of incidence does not contain the grating vector, and determine the relevant conditions and parameters for such gratings. These are then used to design and experimentally record surface relief TIR diffraction gratings in conical mounting that have high diffraction efficiency and where the diffraction angle into the first order is equal to that of the incidence angle, so the diffracted light continues to propagate by TIR. Such gratings in conical mounting can be exploited in planar optics configurations [9], [10].
Section snippets
Basic conditions for TIR diffraction gratings in conical mounting
A typical three-dimensional conical diffraction geometry for TIR diffraction gratings is schematically presented in Fig. 1. The surface relief TIR diffraction grating is recorded on a transparent substrate of refractive index nsub that is surrounded with a material (typically air) of refractive index nsup, where nsub > nsup. A linearly polarized monochromatic light beam, propagating inside the substrate, is obliquely incident onto the TIR diffraction grating at the polar angle θinc and azimuthal
Design and optimization procedures
Using Eqs. (4), (5), we calculated the minimum and maximum TIR diffraction grating periods Λmin and Λmax as a function of the polar incidence angle θinc for three selected azimuthal incidence angles ϕinc. For these calculations we assumed a sinusoidal surface relief diffraction grating formed on a glass substrate with refractive index nsub = 1.52, free-space wavelength of incident light as λ = 0.6328 μm, and the selected three azimuthal incidence angles were ϕinc = 30°, 45°, 60°. The calculated
Experimental procedure and results
To experimentally verify our calculated results, we found it convenient to resort to optical configuration comprised of two laterally displaced nearly sinusoidal surface relief gratings, arranged as shown schematically in Fig. 5. One merely served to couple an incident light into the substrate and direct it towards the TIR diffraction grating. The gratings were obtained by recording the interference pattern of two plane waves, that were derived from an Argon laser of wavelength λ = 0.3630 μm, in
Concluding remarks
We determined the main conditions and parameters for obtaining TIR diffraction gratings in conical mounting. These include the needed grating periods, azimuthal and polar incidence angles, and grating depths that also lead to high first order diffraction efficiency. The calculated and experimental results clearly demonstrate that it is indeed possible to control the angular orientation of light propagating inside the substrate, and achieve high diffraction efficiency from TIR diffraction
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