Diffractive shaping of excimer laser beams

Abstract

We address the problem of shaping the intensity distribution of a highly directional partially coherent field, such as an excimer laser beam, by means of diffractive optics. Our theoretical analysis is based on modelling the multi-transverse-mode laser beam as a Gaussian Schell-model beam. It is shown numerically that a periodic element, which is unsuitable for the shaping of a coherent laser beam, works well with an excimer laser beam because of its partial spatial coherence. The conversion of an approximately Gaussian excimer laser beam into a flat-top beam in the Fourier plane of a lens is demonstrated with a diffractive beam shaper fabricated as a multilevel profile in SiOl by electron-beam lithography and proportional reactive-ion etching.     

Internally excited acoustic resonator for photoacoustic trace detection

The quantum-cascade laser can be used as an infrared source for a small portable photoacoustic trace gas detector. The device that we describe uses a quantum-cascade laser without collimating optics mounted inside an acoustic resonator. The laser is positioned in the center of a longitudinal resonator at a pressure antinode and emits radiation along the length of the resonator exciting an axially symmetric longitudinal acoustic mode of an open-ended cylindrical resonator. Experiments are reported with an 8-microm, quasi-cw-modulated, room-temperature laser used to detect N2O.     

Laser-mode selection by a combination of biprism-like reflectors with narrow amplitude masks

In recent work the laser mode selectivity induced separately by a biprism-like reflector and by an absorbing strip was investigated by numerical analysis. It was shown that each of these elements in an otherwise conventional resonator was suitable to cause the laser to oscillate preferentially on the first odd mode that contains a line singularity, which is a useful dark beam (i.e., a laser beam with a dark central region) for high-resolution metrological applications. We study the combined effect of these two mode-selecting elements and show that the unified analysis leads to much better performance than could be expected from a simple superposition of the performance with each element alone. The results indicate that the mode selectivity can be enhanced by at least a factor of 3 compared with that of laser resonators with biprism-like reflectors alone. Thus a laser equipped with such a combined element will oscillate on a pure first-order mode with high power efficiency. Moreover, calculations show that the resultant dark beam, focused for metrological applications, has a significantly improved shape compared with the dark beam obtained by external modulation of a fundamental Gaussian beam.     

Performance of Nd:YAG lasers in coupled generalized self-filtering and positive-branch unstable resonators

A new optical resonator based on the combination of a generalized self-filtering unstable resonator (GSFUR) and a positive-branch unstable resonator (PBUR) in a three-mirror scheme is reported. It is shown both theoretically and experimentally that a nearly diffraction-limited Gaussian-output laser beam with a large mode volume can be obtained with this cavity design. The laser cavity is particularly interesting for use in high-threshold pumped gain media and eliminates some disadvantages of the SFUR and GSFUR designs. This resonator, with an effective magnification of -6.16, was applied to a pulsed Nd:YAG laser in free-running and in Q-switched modes of operation. The output energy was ~70 mJ, 5.5 times greater than when a single GSFUR design was used. The output beam had a pulse duration of ~30 ns in the Q-switched mode of operation and a beam divergence of 0.26 mrad. The required relations for the GSFUR-PBUR optical design and the output energy were derived and verified experimentally.     

Dynamical stable cavity of side-pumped thin-disk laser with slanted sides

In this article, we use the results of finite-element analysis (FEA) of temperature distribution, deformation, and stress to provide a full three-dimensional simulation of a dynamically stable cavity by propagating wavefront into hot, thermally deformed Yb:YAG/YAG thin-disk laser, using the fast Fourier transform (FFT) split-step beam propagation method (BPM). The wave optics computation therefore delivers realistic results for important features of a laser-like intensity, phase profile, and resonator eigenvalues and higher order-eigenmodes of the laser beam.     

Mode properties of off-axis one-sided hybrid resonator for novel high average power dual-slab laser

A novel dual-slab laser with off-axis one-sided hybrid resonator is presented. The mode properties of the hybrid resonator are calculated using a fast Fourier transform method (FFT). The influence of wavefront distoration on the output beam quality is considered. Results indicate that the novel dual-slab laser is better than the normal dual-slab laser with off-axis one-sided hybrid resonator.     

Implementation of intra-cavity beam shaping technique to enhance pump efficiency

In this work we propose an implementation of a new intra-cavity beam shaping technique to vary the intensity distribution of the fundamental mode in a resonator cavity while maintaining a constant intensity distribution at the output. This method can be useful for fitting a transversal intensity profile of the required mode with a pump beam profile in the region of the active medium to increase mode discrimination.     

Propagation of a partially coherent beam from an unstable resonator through turbulent atmosphere

The influence of atmospheric turbulence on the propagation of a partially coherent beam from an unstable resonator was studied numerically. The resonant mode of the unstable resonator is obtained by iterative calculation using the Huygens–Fresnel formula. Also, using the extended Huygens–Fresnel integral, the intensity distribution of a propagating laser beam is calculated for different conditions. The influence of turbulence on the profile of partially coherent beams of an unstable resonator is studied. The effects of geometrical parameters of the resonator on the far-field beam profile are investigated. The results show that an unstable resonator with higher magnification has a superior far-field beam profile under partial coherency and turbulence conditions.     

正支共焦非稳激光谐振腔的数值模拟

谐振腔内像差对光束质量的影响十分明显，直接导致激光器的输出功率及光束质量的下降。对理想状态以及受相位倾斜、像散像差扰动后的正支共焦非稳腔进行了数值模拟分析。计算机仿真结果表明，采用数值迭代分析法可以很好地对正支共焦非稳腔的模式特性进行研究，从而为自动调腔或采用自适应光学技术对谐振腔内像差进行自动补偿提供了理论基础。     

Characterizing output beams for lasers that use high-magnification unstable resonators.

Laser beams generated from high-magnification on-axis unstable resonators by use of hard-edged optics typically have a doughnut-shaped distribution in the near field (i.e., a flat-top profile with a hole in the middle for an axially coupled beam). We derive analytical expressions describing this distribution by using the flattened Gaussian beams concept. The superposition of two flattened Gaussian beams whose flatness and steepness of edges are controlled by defined parameters (i.e., the beam width and the order) is used to analyze the output beam intensity along the propagation axis. Finally, experimental measurements of beam propagation from a copper-vapor laser fitted with a high-magnification unstable resonator show excellent agreement with theoretical predictions.     

Theory of 1- N-way phase-locked resonators

A 1-N-way resonator based on beam splitting and beam combining effects in rectangular cross-sectional multimode waveguides was recently proposed. Such a resonator structure offers a valuable way in which N low-power laser elements may be combined in a coherent fashion. We examine the case of passive 1-N-way resonators. We develop a theory of these 1-N-way structures to show that there is only one possible mode of these resonators. The theory is used to give a scaling law for the design tolerances of the beam splitting and beam combining region of the resonator.     

Multifunctional gratings for surface-emitting lasers: design and implementation

We experimentally demonstrate the use of two different multifunctional grating couplers in surface-emitting lasers for improved beam quality and advanced beam profiles. The lasers used for the demonstration are grating-based unstable resonator lasers, each with a grating coupler for surface emission and beam shaping. The new design method, described in detail, allows for simultaneous optimization of arbitrary feedback and outcoupling characteristics of the grating coupler. The first coupler is designed to reduce feedback to the resonator that would otherwise disturb the operation of the laser and lower the beam quality and to produce an output beam focused to four spots. The second coupler is designed to provide the feedback needed to support the unstable resonator, eliminating one feedback grating, and simultaneously focus the output beam to a single spot. As far as we know, this is the first time such multifunctional couplers are used in grating-coupled surface-emitting lasers. The couplers provide near-diffraction-limited spots that are a considerable improvement compared with previous lasers with no feedback control in the couplers.     

Ti:sapphire laser cavity mode and pump-laser mode calculations

Comprehensive calculations of the cavity mode size throughout a Ti:sapphire laser, made with the ABCD Gaussian beam formalism are reported. These calculations show that the beam is not collimated, in general, in what are normally referred to as the collimated arms of the laser cavity. Additionally, the mode size and volume (in the gain medium) of the argon-ion laser, which is used to pump the Ti:sapphire laser optically, are evaluated for different focusing geometries, and graphs that can be used to select suitable mode-matching optics are produced. It is concluded that an appropriate strategy for mode matching the pump beam to the Ti:sapphire laser mode is to use a zoom telescope to tailor the collimated pump-laser beam diameter to an optimum value. Finally, comparisons of the pump-laser mode and the Ti:sapphire laser mode are presented for selected pumping geometries.     

High cw power using an external cavity for spectral beam combining of diode laser-bar emission

In extension to known concepts of wavelength-multiplexing diode laser arrays, a new external cavity is presented. The setup simultaneously improves the beam quality of each single emitter of a standard 25 emitter broad-area stripe laser bar and spectrally superimposes the 25 beams into one. By using this external resonator in an "off-axis" arrangement, beam qualities of Mslow2<14 and Mfast2<3 with optical powers in excess of 10 W in cw operation are obtained.     

Complete spatial characterization of a pulsed doughnut-type beam by use of spherical optics and a cylindrical lens.

A complete spatial characterization (in second-order moments) of a doughnut-type beam from a pulsed transversely excited atmospheric CO2 laser is described. It includes the measurement of the orbital angular momentum carried by the beam. The key element in the characterization is the use of a cylindrical lens in addition to the usual spherical optics. Internal features of the beam that would have remained hidden if only spherical optics were employed were revealed by use of the cylindrical lens. The experimental results are compared and agree with a theoretical Laguerre-Gauss mode beam.     

Properties of a phase-conjugate etalon mirror and its application to laser resonator spatial-mode control

The concept of a phase-conjugate etalon mirror consisting of one flat and one aspheric surface is introduced. This new element can be used as an end mirror of a conventional resonator to promote spatial-mode selection and mode shaping. A phase-conjugate etalon designed for the fundamental Gaussian mode is experimentally implemented and tested with a single-mode He-Ne laser.     

Annular resonator with a Cassegrain configuration

An advanced annular resonator is studied both theoretically and experimentally. This resonator has a Cassegrain mirror configuration and is designed to extract circular and high-quality beams from annular gain media. We carried out beam propagation in this resonator, calculating the intensity distributions of the laser beam. We also proved the performance experimentally by applying the resonator to a CO2 laser. The operation of the new resonator is demonstrated successfully. The quality of the output beam is in good agreement with theoretical calculations of laser output power of 20 W.     

Optical Resonators

The open resonator is a new device in physical optics which has been extensively investigated in recent years. Important applications have been described in laser technique and in microwave technique. Theory and experimental results are briefly reviewed, with emphasis on physical conceptions rather than on mathematical details. Plane parallel Fabry-Perot resonators, spherical mirror resonators and flat-roof resonators are described, along with the closely related beam waveguides.     

Numerical simulation of a laser resonator with an in-phase doughnut-like output beam

A numerical model of the toric concave mirror laser resonator is founded by using the eigenvector method. Numerical calculation shows that an in-phase doughnut-like beam mode with high beam quality can be obtained in this resonator, whose diffraction loss is the lowest, and whose intensity distribution covers the whole resonator mirror. Systematical simulations indicate that, different from the spherical stable resonator, the effects of Fresnel number of the resonator and curvature radius of the toric concave total reflector on output beam quality is not very obvious. Under the condition of curvature radius of 15 m, the M ² factor of the output beam of this resonator with a large range of Fresnel number from 6.2 to 12.6 is from 1.3 to 1.9. Furthermore, the diffraction loss is close to 1.0% or less than 1.0%. Under the condition of Fresnel number of 7.07, the M ² factor of the output beam of this resonator with curvature radius from 6 to 30 m is from 1.60 to 1.24, and the diffraction loss is close to 1.0% or less than 1.0%.     

Efficient analytic model to optimum design laser resonator and optical coupling system of diode-end-pumped solid-state lasers: influence of gain medium length and pump beam M2 factor

A comprehensive analytical model for optimization longitudinal pumping of ideal four-level lasers is presented for accurate analysis by removing limiting assumptions on active length and pump-beam radius in the gain medium. By taking into account the circular-symmetric Gaussian pump beam including the M2 factor, an analytical formula for the root mean square of the pump beam in the active medium is developed to relate properties of the gain medium and pump beam to the requirement on efficient optimum design. Under the condition of minimum root mean square of pump-beam radius inside the active medium, the key parameters of the optimum optical coupling system have been analytically derived. Using these parameters, optimum mode size and maximum output efficiency are derived as a function of the gain medium length, absorption coefficient, pump-beam M2 factor, and input power. Dependence of the obtained parameters on the gain medium length, absorption coefficient, pump-beam M2 factor, and input power has been investigated. The results of this theory are found to be more comprehensive than the previous theoretical investigations. The present model provides a straightforward procedure to design the optimum laser resonator and the coupling optics for maximizing the output.