Bending of Lloyd's mirror to eliminate the period chirp in the fabrication of diffraction gratings.

We present a new technique to prevent the detrimental period chirp that appears in optical gratings fabricated by laser interference lithography (LIL). The idea is to bend the Lloyd's mirror in the lithographic setup to eliminate the period chirp already at the step of the grating's exposure. A new mathematical model was developed to describe the required bending geometry of the mirror. It is shown that this geometry can be described by multiple cross-sections of the mirror, each obtained by the solution of an implicit first-order differential equation. The proposed approach is illustrated on the basis of a concrete example. By slightly bending the Lloyd's mirror (by ≈ 3.5 mm of maximum deflection over an area of 142 mm × 215 mm) the period chirp of the exposed grating can be eliminated completely.

Detrimental effects of period-chirped gratings in pulse compressors.

We present a comprehensive simulative and experimental investigation of how period-chirped pulse compression gratings affect the compressed pulses. A specifically developed ray-tracing tool was used for the simulative investigations. It is shown that the chirp creates a characteristic spatio-spectral error pattern, which leads to a degradation of the beam quality and an increase of the pulse duration. The experimental investigations, for which both a narrow-bandwidth continuous-wave and a pulsed laser beam were guided through a Treacy-compressor comprised of period-chirped gratings, confirm the simulation results and present methods on how to identify the chirp's characteristic error pattern in practice.

Simple spatially resolved period measurement of chirped pulse compression gratings.

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.

General mathematical model for the period chirp in 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'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.

Quantitative investigation on a period variation reduction method for the fabrication of large-area gratings using two-spherical-beam laser interference lithography.

Gratings produced by two-spherical-beam Laser Interference Lithography (LIL) will have a nonuniform period, and the associated period variation is larger with the increase of the substrate size. This work quantitatively investigates a noninvasive method for improving the period variation on 4-inch silicon wafers. By temporarily deforming the flexible silicon wafer using a customized concave vacuum chuck [J. Vac. Sci. Technol. B19(6), 2347 (2001)10.1116/1.1421558], we show that the fabricated gratings will have improved period uniformity, with the period variation reduced by 86% at the 1000 nm central grating period setting. This process is a simple and efficient way to achieve linear gratings without altering the LIL configuration with two spherical beams. We present experimental results on the impact of a concave vacuum chuck on the chirp reduction at different grating period settings. Then, we compare two different LIL configurations with different wavelength sources concerning their influence on the efficiency of period variation reduction. Finally, the flatness of the 4-inch silicon wafers due to the temporary bending process is verified using optical profilometry measurements.

Experimental analysis on CPA-free thin-disk multipass amplifiers operated in a helium-rich atmosphere.

We present an experimental investigation on the benefits of helium as an atmospheric gas in CPA-free thin-disk multipass amplifiers (TDMPAs) for the amplification to average powers exceeding 1 kW and pulse peak powers reaching 5 GW. Both the performance of the amplifier and the properties of the amplified sub-400 fs laser pulses centred at a wavelength of 1030 nm are compared for different helium concentrations in air, outlining and quantifying the benefits of a helium-rich atmosphere. The amplification of 100 µJ pulses in an atmosphere with 60% helium instead of air led to a maximum increase in efficiency from 24% to 29%. This translated into an increase of average output power and pulse energy of 34 W (i.e +19%) and 0.34 mJ (i.e. +19%) respectively. At the same time an improvement of the beam quality from M2 = 1.18 to M2 = 1.14 was achieved. For the amplification of 10 µJ pulses to over 1 kW of average power an atmosphere with 33% helium led to an improved beam pointing stability by a factor of 2. Moreover, the beam propagation factor M2 improved by 0.1, and the power stability improved by approximately 10%.

Theoretical investigation on the elimination of the period chirp by deliberate substrate deformations.

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.

Comprehensive theoretical analysis of the period chirp in laser interference lithography.

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.

Ultrafast green thin-disk laser exceeding 1.4 kW of average power.

We present an ultrafast laser with a near-diffraction-limited beam quality delivering more than 1.4 kW of average power in the visible spectral range. The laser is based on second harmonic generation in a lithium triborate crystal of a Yb:YAG thin-disk multipass amplifier emitting more than 2 kW of average power in the infrared.