PUMA publications for /tag/Interference%20diffraction_grating%20diffractionSat Jun 03 15:24:54 CEST 2023Opt. Expressjun1219392--19403Simple spatially resolved period measurement of chirped pulse compression gratings312023myown chirp diffraction peer interference diffraction_grating from:florianbienert We present an easy-to-implement and low-cost setup for the precise measurement of the period chirp of diffraction gratings offering a resolution of 15 pm and reasonable scan speeds of 2 seconds per measurement point. The principle of the measurement is illustrated on the example of two different pulse compression gratings, one fabricated by laser interference lithography (LIL) and the other by scanning beam interference lithography (SBIL). A period chirp of 0.22 pm/mm2 at a nominal period of 610 nm was measured for the grating fabricated with LIL, whereas no chirp was observed for the grating fabricated by SBIL, which had a nominal period of 586.2 nm.Mon Feb 13 10:25:03 CET 2023Opt. Expressfeb45334--5346General mathematical model for the period chirp in interference lithography312023chirp diffraction diffraction_grating interference myown peer We present a general analytical model for the calculation of the spatial distribution of the grating period, enabling the unification of all configurations of classical laser interference lithography (LIL) and scanning-beam interference lithography (SBIL) into one formalism. This is possible due to the consideration of Gaussian beams instead of point sources which allow for the accurate description of not only the laser\&\#x2019;s far-field but also its near-field. The proposed model enables the calculation of the grating period, the inclination and the slant of the grating lines on arbitrarily shaped substrates, originating from the interference of arbitrarily orientated and positioned Gaussian beams.Mon Feb 13 10:24:21 CET 2023Opt. Expressfeb45334--5346General mathematical model for the period chirp in interference lithography312023myown chirp period Interference diffraction Laser-Interference-Lithography diffraction_grating shaping from:florianbienert mathematical Beam peer Laser beams gratings interference model Gaussian Holographic Scanning-Beam-Interference-Lithography We present a general analytical model for the calculation of the spatial distribution of the grating period, enabling the unification of all configurations of classical laser interference lithography (LIL) and scanning-beam interference lithography (SBIL) into one formalism. This is possible due to the consideration of Gaussian beams instead of point sources which allow for the accurate description of not only the laser\&\#x2019;s far-field but also its near-field. The proposed model enables the calculation of the grating period, the inclination and the slant of the grating lines on arbitrarily shaped substrates, originating from the interference of arbitrarily orientated and positioned Gaussian beams.Thu Jun 09 10:04:50 CEST 2022Optics Expressjun1322410Theoretical investigation on the elimination of the period chirp by deliberate substrate deformations302022LIL algorithm chirp diffraction diffraction_grating grating interference interference_lithography myown peer therory We present a theoretical investigation on the approach of deliberately bending the substrate during the exposure within laser interference lithography to compensate for the period chirp. It is shown that the yet undiscovered function of the surface geometry, necessary to achieve the zero-chirp case (i.e. having a perfectly constant period over the whole substrate) is determined by a first-order differential equation. As the direct analytical solution of this differential equation is difficult, a numerical approach is developed, based on the optimization of pre-defined functions towards the unknown analytical solution of the differential equation by means of a Nelder-Mead simplex algorithm. By applying this method to a concrete example, we show that an off-center placement of the substrate with respect to the point sources is advantageous both in terms of achievable period and substrate curvature and that a fourth-order polynomial can greatly satisfy the differential equation leading to a root-mean-square deviation of only 1.4 pm with respect to the targeted period of 610 nm.Thu Jun 09 10:04:50 CEST 2022Optics Expressjun1322410Theoretical investigation on the elimination of the period chirp by deliberate substrate deformations302022myown chirp diffraction diffraction_grating interference_lithography LIL from:florianbienert grating peer interference therory algorithm We present a theoretical investigation on the approach of deliberately bending the substrate during the exposure within laser interference lithography to compensate for the period chirp. It is shown that the yet undiscovered function of the surface geometry, necessary to achieve the zero-chirp case (i.e. having a perfectly constant period over the whole substrate) is determined by a first-order differential equation. As the direct analytical solution of this differential equation is difficult, a numerical approach is developed, based on the optimization of pre-defined functions towards the unknown analytical solution of the differential equation by means of a Nelder-Mead simplex algorithm. By applying this method to a concrete example, we show that an off-center placement of the substrate with respect to the point sources is advantageous both in terms of achievable period and substrate curvature and that a fourth-order polynomial can greatly satisfy the differential equation leading to a root-mean-square deviation of only 1.4 pm with respect to the targeted period of 610 nm.Thu Mar 17 14:03:13 CET 2022Appl. Opt.mar92313--2326Comprehensive theoretical analysis of the period chirp in laser interference lithography612022chirp period Interference diffraction_grating Laser_beam ltihography interference_lithography from:florianbienert ifsw Diffraction grating We present a theoretical investigation on laser interference lithography used for the exposure of linear gratings. The focus is on the geometry of the arising interference lines on the substrate, in particular on their period and orientation, depending on the illumination geometry as determined by the setup. The common approach with point sources emitting spherical wavefronts is considered for the illumination. Three different cases are discussed, namely the interference between two point sources with either two convex, two concave or mixed, i.e., convex and concave wavefronts. General equations focusing mainly on the calculation of the period and the orientation of the grating lines are derived for each of the three exposure cases considering arbitrarily positioned point sources and arbitrarily shaped substrates. Additionally, the interference of symmetrically positioned point sources illuminating plane substrates is investigated, as these boundary conditions significantly simplify the derived equations.Thu Mar 17 13:51:15 CET 2022Appl. Opt.mar92313--2326Comprehensive theoretical analysis of the period chirp in laser interference lithography612022Diffraction Interference Laser_beam chirp diffraction_grating grating ifsw interference_lithography ltihography period We present a theoretical investigation on laser interference lithography used for the exposure of linear gratings. The focus is on the geometry of the arising interference lines on the substrate, in particular on their period and orientation, depending on the illumination geometry as determined by the setup. The common approach with point sources emitting spherical wavefronts is considered for the illumination. Three different cases are discussed, namely the interference between two point sources with either two convex, two concave or mixed, i.e., convex and concave wavefronts. General equations focusing mainly on the calculation of the period and the orientation of the grating lines are derived for each of the three exposure cases considering arbitrarily positioned point sources and arbitrarily shaped substrates. Additionally, the interference of symmetrically positioned point sources illuminating plane substrates is investigated, as these boundary conditions significantly simplify the derived equations.Interference diffraction_grating diffractionCommunity for tag(s) Interference diffraction_grating diffraction