Non-dispersion boundary conditions of micro-optical element illuminated by broadband light source

Abstract

With the development of the microstructure fabrication process and the integration of micro-optical elements, diffractive micro-optical elements are widely used in broadband light sources, such as the integrated light guide plate (ILGP). And with the structural feature size of the ILGP decreasing from tens of microns to microns and even sub-microns, the diffraction dispersion phenomenon will inevitably become a prominent problem in research and design of non-dispersion elements. Nevertheless, under the broadband light source illumination, the analysis of the dispersion characteristic of diffraction spectrum of the microstructure array has not been reported in detail. Therefore a theoretical model of micro-optical element with a typical one-dimensional rectangular phase grating (RPG) and a widely used white LED source is established in this paper. The dispersion characteristic of the diffraction spectrum is studied, that is, with the increase of period of the RGP or the cone angle of incident beam, the dispersion of diffraction spectrum weakens. Dispersion parameter C and its formula are proposed, which can precisely measure the chromatic dispersion degree of the diffraction spectrum. Furthermore, the boundary criterion point of non-dispersion <i>C</i> = 0.3 is given explicitly. It is explored that no matter whether the cone angle of incident beam or the RPG period increases, the non-dispersion output light can be obtained only by matching the two parameters to make the dispersion parameter <i>C</i> less than 0.3. Then an RPG sample, of which the structural parameters are consistent with the designed ones, is fabricated by using micro-nano processing technology. By changing the cone angle of incident beam, the luminance and the chromaticity coordinates of the diffraction beam are tested. The analyses of the test results of the fabricated RPG sample show that the spectrum dispersion regularity is in accord with the theoretical analysis. The consistency verifies the correctness of dispersion parameter <i>C</i>, its formula and the non-dispersion boundary criterion point. The dispersion parameter <i>C</i> and non-dispersion boundary criterion point presented in this paper provide a guidance for analyzing the dispersion characteristics when the structural parameters of the integrated light guide plate and other broadband micro-optical element are designed.