Modeling of the general astigmatic Gaussian beam and its propagation through 3D optical systems

High power UV lasers employing elliptically focusing enhancement cavities

Continuous wave UV lasers have a plethora of applications in many fields, among others, laser spectroscopy, atom trapping, and other related areas. We present a high power continuous wave UV laser system based on twofold second harmonic generation of IR radiation for cooling bunched relativistic ion beams and laser spectroscopy with an output power exceeding 2.4 W in the UV range. Laser operation in the UV regime is often limited by degradation of β-barium borate (BBO) due to two-photon absorption (TPA). We were able to overcome this issue with a novel design of an elliptically focusing enhancement cavity employing commercially available BBO as the nonlinear medium. Building on previous results, we implemented a novel elliptically focusing enhancement cavity featuring an extreme waist ratio of w0,sag/w0,tan = 27.5 at the center of the BBO crystal, aiming to further reduce the peak intensity. This paper details the results as well as our advanced locking scheme for the enhancement cavities for both second harmonic generation steps.

femtoPro: virtual-reality interactive training simulator of an ultrafast laser laboratory

The huge field of optics and photonics research and development is in constant demand of well-trained experts. However, it is challenging to teach efficiently the setup process of complicated optical experiments due to limited hardware availability and eye-safety concerns, in particular, in the case of femtosecond lasers. We have developed an interactive simulation of an ultrafast laser laboratory ("femtoPro") for teaching and training, implementing physical models for the calculation and visualization of Gaussian laser beam propagation, ultrashort optical pulses, their modulation by typical optical elements, and linear as well as nonlinear light-matter interaction. This facilitates the setup and simulated measurement procedure, in virtual reality (VR) and at real-time speeds, of various typical optical arrangements and spectroscopy schemes such as telescopes, interferometers, or pulse characterization. femtoPro can be employed to supplement academic teaching in connection with regular courses in optics or spectroscopy, to train future scientists and engineers in the field of (ultrafast) optics in practical skills, to communicate to other researchers how to set up and align a particular experiment, to "test-build" and simulate new designs of optical setups, to simulate ultrafast spectroscopy data, to offer practical exercises to high-school students, and to reach out to the general public.

Primary aberration optimization for double-plane symmetric beam shaping systems using a pair of curved reference surfaces

The geometric aberration of centered refracting double-plane symmetric optical systems (DPSOS) is investigated. For DPSOS with different defocus values in the tangential plane and the sagittal plane (astigmatic wavefront), a pair of curved reference surfaces which vanishes the quadratic terms of the optical path difference (OPD) between a general ray and a reference ray are deduced. With the curved reference surfaces, the primary (fourth-order) wave aberration function for DPSOS is calculated and analyzed, which can be used for beam shaping designs with astigmatic input wavefront, such as slab lasers and semiconductor lasers. Further, the proposed curved reference surfaces can be applied to analyze the aberrations of general DPSOS.

Conservation of extremal ellipticity and analytical expressions for astigmatism and asymmetry in Gaussian beam transformations

A Gaussian beam with initial astigmatism, waist, and M² asymmetry propagates through a simple optical system consisting of a single thin, aberration-free lens. We derive simple analytical expressions for the asymmetry, astigmatism, and ellipticity of the beam after the lens, and show that the maximal ellipticity of the beam is a conserved quantity that is solely dependent on these input parameters. This appears to still hold for general astigmatic Gaussian beams. Our simple, analytical results conveniently determine the trade-off between astigmatism and asymmetry of a laser for a given output maximum ellipticity requirement pre- or post-lenses.

Measurement of M²-Curve for Asymmetric Beams by Self-Referencing Interferometer Wavefront Sensor

For asymmetric laser beams, the values of beam quality factor Mx2 and My2 are inconsistent if one selects a different coordinate system or measures beam quality with different experimental conditionals, even when analyzing the same beam. To overcome this non-uniqueness, a new beam quality characterization method named as M²-curve is developed. The M²-curve not only contains the beam quality factor Mx2 and My2 in the x-direction and y-direction, respectively; but also introduces a curve of Mxα2 versus rotation angle α of coordinate axis. Moreover, we also present a real-time measurement method to demonstrate beam propagation factor M²-curve with a modified self-referencing Mach-Zehnder interferometer based-wavefront sensor (henceforth SRI-WFS). The feasibility of the proposed method is demonstrated with the theoretical analysis and experiment in multimode beams. The experimental results showed that the proposed measurement method is simple, fast, and a single-shot measurement procedure without movable parts.

Analysis of non-linearity in differential wavefront sensing technique

An analytical model of a differential wavefront sensing (DWS) technique based on Gaussian Beam propagation has been derived. Compared with the result of the interference signals detected by quadrant photodiode, which is calculated by using the numerical method, the analytical model has been verified. Both the analytical model and numerical simulation show milli-radians level non-linearity effect of DWS detection. In addition, the beam clipping has strong influence on the non-linearity of DWS. The larger the beam clipping is, the smaller the non-linearity is. However, the beam walking effect hardly has influence on DWS. Thus, it can be ignored in laser interferometer.