000129846 001__ 129846 000129846 005__ 20240112163659.0 000129846 0247_ $$2doi$$a10.1088/2040-8986/ab2bdf 000129846 0248_ $$2sideral$$a113064 000129846 037__ $$aART-2019-113064 000129846 041__ $$aeng 000129846 100__ $$0(orcid)0000-0003-3178-5253$$aTorcal-Milla, F.J.$$uUniversidad de Zaragoza 000129846 245__ $$aFar field diffraction of gratings with two roughness levels 000129846 260__ $$c2019 000129846 5060_ $$aAccess copy available to the general public$$fUnrestricted 000129846 5203_ $$aWe investigate the far field diffraction process produced by diffraction gratings with two roughness levels, such as steel tape gratings, which are used in environments where diffraction gratings made of glass are not possible. We obtain the analytical formulation describing the formation of diffraction orders in terms of the roughness parameters. Since roughness is stochastic, we use the mutual coherence function to propagate the field to the Fraunhofer regime. We conclude that diffraction orders exists when at least one correlation length of both roughness is larger than the period of the grating and the standard deviation on heights is around or larger than the illumination wavelength. Finally, we corroborate the analytical results with numerical simulations based on the fast Fourier transform, showing a high agreement. 000129846 536__ $$9info:eu-repo/grantAgreement/ES/DGA-FEDER/E44-17R$$9info:eu-repo/grantAgreement/ES/MINECO/DPI2016-75272-R 000129846 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/ 000129846 590__ $$a2.379$$b2019 000129846 591__ $$aOPTICS$$b40 / 97 = 0.412$$c2019$$dQ2$$eT2 000129846 592__ $$a1.167$$b2019 000129846 593__ $$aElectronic, Optical and Magnetic Materials$$c2019$$dQ1 000129846 593__ $$aAtomic and Molecular Physics, and Optics$$c2019$$dQ1 000129846 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000129846 700__ $$aSanchez-Brea, L.M. 000129846 7102_ $$12002$$2385$$aUniversidad de Zaragoza$$bDpto. Física Aplicada$$cÁrea Física Aplicada 000129846 773__ $$g21, 8 (2019), 085605 [6 pp]$$pJ. opt.$$tJournal of Optics (United Kingdom)$$x2040-8978 000129846 8564_ $$s4151874$$uhttps://zaguan.unizar.es/record/129846/files/texto_completo.pdf$$yPostprint 000129846 8564_ $$s1532983$$uhttps://zaguan.unizar.es/record/129846/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000129846 909CO $$ooai:zaguan.unizar.es:129846$$particulos$$pdriver 000129846 951__ $$a2024-01-12-14:07:48 000129846 980__ $$aARTICLE