Angular selective light transmission characteristics of a grating optical filter **

The grating optical filters are investigated to determine the degree of impact of the geometric grating parameters on the angular characteristics of the light transmission. The filter consists of a plane-parallel transparent substrate with thin-layer gratings on two surfaces. The gratings are formed by alternating transmitting and absorption bands. The relative position of two gratings provides angular selectivity of the light transmission. A graphic-analytical method is developed to determine the angular characteristic of the filter light transmission in the form of the dependence of the light transmission coefficient on the beams incidence angle. The effect of a filter characteristic angle (this angle determines a shift of the gratings on the input and output surfaces), fringe spacing (fringe spacing on each grating is equal to the total width of two adjacent alternating bands), and fringe ratio (relation of the fringe spacing of the input and output gratings) on the angular characteristics of the light transmission. The filter characteristics in the areas of decreasing and increasing transmittance are equidistant, linear, and symmetrical with respect to the characteristic angles of the filters in the range of the incidence angles from 0° up to 60°. At large incidence angles, equidistance, linearity, and symmetry of the characteristics are violated. The obtained regularities should be considered when determining the geometrical parameters of the filters satisfying the required for the specified glazed construction and the preset angular characteristics of the light transmission. It is advisable to apply the filter in the areas where the light transmission control is needed at the change of the beams incidence angle due to the movement of a light source and/or a glazed object relative to each other, especially in architectural glazing.

оптический фильтр, решетка с чередующимися полосами, графоаналитический расчет, угловая характеристика светопропускания, optical filter, grating with alternating bands, graphic-analytical calculation, angular characteristic of light transmission

1. Macleod, H.-A. Thin-Film Optical Filters. 4th ed. Boca Raton : CRC Press, 2012, 800 p.

2. Liu, R., et al. Microporous phase-separated films of polymer blends for enhanced outcoupling of light from OLEDs. Optics Express, 2011, vol. 19, pp. A1272–A1280.

3. Yanzhong, C., et al. Structured lens formed by a 2D square hole array in a metallic film. Optics Letters, 2008, vol. 33, pp. 753–755.

4. Fehrembach, A.-L., Maystre, D., Sentenac, A. Phenomenological theory of filtering by resonant dielectric gratings. The Journal of the Optical Society of America, 2002, vol. A 19, no. 6, pp. 1136–1144.

5. Wang, Z., et al. Plasmonic critical angle in optical transmission through subwavelength metallic gratings. Optics Letters, 2011, vol. 36, no. 23, pp. 4584–4586.

6. Jiang, S., et al. Multi-channel and sharp angular spatial filters based on one-dimensional photonic crystals. Chinese Optics Letters, 2006, vol. 4, no. 10, pp. 605–607.

7. Nakagawa, W., et al. Wide-field-of-view narrow-band spectral filters based on photonic crystal nanocavities. Optics Letters, 2011, vol. 27, no. 3, pp. 191–193.

8. Simovski, C.R. O material'nykh parametrakh metamaterialov. [Material parameters of metamaterials: a review).] Optics and Spectroscopy, 2009, vol. 107, no. 5, pp. 766–793 (in Russian).

9. Mazilu, M., Miller, A., Donchev, V.T. Modular Method for Calculation of Transmission and Reflection in Multilayered Structures. Applied Optics, 2001, vol. 40, pp. 6670–6676.

10. Li, Z.-B., et al. Periodic dielectric bars assisted enhanced transmission and directional light emission from a single subwavelength slit. Optics Letters, 2006, vol. 14, pp. 8037–8042.

11. Zakirullin, R.S. Sposob regulirovaniya napravlennogo svetopropuskaniya: patent 2509324 Ros. Federatsiya: 6 G02B 5/20, E06B 9/24, G02B 1/10. [Method of regulation for directional light: RF Patent no. 2509324: 6 G02B 5/20, E06B 9/24, G02B 1/10/] RF Patent, 2012 (in Russian).

12. Zakirullin, R.S. Sposob uglovogo selektivnogo regulirovaniya napravlennogo svetopropuskaniya. [Method of angular selective regulation for directional light.] Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2013, no. 3 (85), pp. 17–22 (in Russian).

13. Zakirullin, R.S. Selektivnoe regulirovanie napravlennogo svetopropuskaniya po uglam padeniya luchey. [Selective beam incidence angle control over directional light transmission.] Technical Physics, 2012, vol. 82, no. 10, pp. 134–136 (in Russian).

14. Zakirullin, R.S. Raschet parametrov opticheskogo fil'tra s uglovym selektivnym svetopropuskaniem. [Parameters calculation of optical filter with angular selective light transmission.] Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2013, no. 5 (87), pp. 54–58 (in Russian).

15. Zakirullin, R. S. Grating optical filter for pre-adapted angular selective regulation of directional light transmission. 8th Iberoamerican Optics Meeting and 1th Latin American Meeting on Optics, Lasers and Applications. Proc. SPIE, 2013, vol. 8785, p. 15.

16. Zakirullin, R.S. Intellektual'noe okno kak opticheskiy fil'tr s uglovym selektivnym svetopropuskaniem. [Intelligent window as an optical filter with angular selective transmission.] Scientific Herald of the Voronezh State University of Architecture and Civil Engineering. Construction and Architecture, 2014, iss. 1 (33), pp. 11–19 (in Russian).

17. Zakirullin, R.S. Opticheskiy fil'tr s uglovoy selektivnost'yu svetopropuskaniya. [Optical filter with angular selectivity of light transmission.] Journal of Optical technology, 2013, vol. 80, iss. 8, pp. 16–24 (in Russian).