Browsing by Author "Hsieh, M. X."

Now showing 1 - 9 of 9

Characterizing the topological charges distribution of the elliptical beams with vortex lattices
(2020-01-01)
Hsieh, Y. H.
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Lai, Y. H.
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Hsieh, M. X.
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Chen, Y. F.
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電子物理學系
A new numerical approach is proposed to analyze the topological charges distribution of elliptical beams with vortex lattices generated from the astigmatic transformations of Hermite-Gaussian beams. The birth and death of the topological charges for elliptical beams are thoroughly verified by continuously changing the astigmatic strength. The theoretical explorations are exploited to make a complete comparison with experimental measurements which are obtained from an off-axis pumped solid-state laser with an external astigmatic mode converter and a Mach-Zehnder interferometer. The good agreement between the theoretical and experimental results provides the feasibility to flexibly manipulate the topological charges of vortex lattices in further applications. (C) 2019 Optical Society of America
Exploring elliptical vortex beams with the spatial damping effect
(2019-02-15)
Chen, Y. F.
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Hsieh, M. X.
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Lai, Y. H.
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Hsieh, Y. H.
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Tu, C. W.
A general integral formula is analytically derived to represent the wave function of elliptical vortex modes. The derived formula can be straightforwardly employed to take account of spatial damping to explore vortex structure. Spatial damping is found to cause the central degenerate singularity of the circular vortex mode to be split into several singularities with different topological charges. For the non-circular vortex beam, the influence of spatial damping on the distribution of singularities is not significant. Theoretical analyses are confirmed to agree very well with the experimental measurements. (C) 2019 Optical Society of America
Generalized wave-packet formulation with ray-wave connections for geometric modes in degenerate astigmatic laser resonators
(2019-11-01)
Chen, Y. F.
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Tung, J. C.
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Hsieh, M. X.
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Hsieh, Y. H.
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Liang, H. C.
The parametric equations for periodic rays in degenerate astigmatic laser resonators are derived in a generalized way. The derived parametric equations clearly reveal the formation of Lissajous geometric modes with phase variation along the propagation. Using the representation of a quantum coherent state, a generalized wave-packet formula is derived to connect with the periodic rays of geometric modes. The derived wave-packet formula is not only validated through comparing with various experimental patterns, but also is directly exploited to manifest the spatial asymmetries of Lissajous lasing modes due to a highly transmissive output coupler. (C) 2019 Optical Society of America
Generating high-power asymmetrical Laguerre-Gaussian modes and exploring topological charges distribution
(2018-11-26)
Hsieh, Y. H.
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Lai, Y. H.
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Hsieh, M. X.
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Huang, K. F.
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Chen, Y. F.
We employ an off-axis pumped Nd:YVO4 laser and control the reflectance of output coupler to directly generate asymmetrical Hermite-Gaussian (HG) modes with various transverse orders. By using an astigmatic mode converter, the generated asymmetrical HG modes are straightforwardly transformed into asymmetrical Laguerre-Gaussian (LG) modes with a crescent-like shape. The average output power of all the crescent-shaped LG modes can exceed 1W at the pump power of 4W. Furthermore, experimental results are theoretically verified by resonant modes derived from the inhomogeneous Helmholtz equation with the localized source distribution. Theoretical resonant modes are also used to explore the dependence of the phase structures of LG modes on the system loss. As the loss increases, it is found that the singularities at the origin will be rearranged and new singularities are formed in the outside region with average orbital angular momentum remaining unchanged. (C) 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
High-power structured laser modes: direct generation of a vortex array
(2020-07-15)
Chen, Y. F.
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Ke, H. T.
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Tseng, Y. C.
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Hsieh, M. X.
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Tung, J. C.
The frequency degeneracy induced by the astigmatism in a nearly hemispherical cavity is originally exploited to generate vortex array laser modes with the output power up to 300 mW. The inhomogeneous Helmholtz equation is employed to derive the wave function for manifesting the characteristics of the lasing modes. The theoretical wave function explicitly reveals the role of the Gouy phase in the formation of vortex arrays. Numerical analyses are further performed to confirm that the thermal lensing effect in the laser crystal assists the lasing transverse order to increase with increasing pump power. It is believed that the high efficiency enables the present laser modes to be useful in the applications of structured vortex beams. (C) 2020 Optical Society of America
High-power structured laser modes: manifestation of quantum Green's function
(2020-08-15)
Chen, Y. F.
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Tseng, Y. C.
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Ke, H. T.
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Hsieh, M. X.
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Tung, J. C.
The distributions of resonant frequencies in an astigmatic cavity are theoretically confirmed to be analogously equivalent to the quantum energy structures of two-dimensional commensurate harmonic oscillators. In the first part [Opt. Lett. 45, 4096 (2020)] of this two-part series study, the lasing modes were verified to reveal a variety of vortex array structures. Here, in the second part of this two-part series study, the lasing modes are confirmed to agree very well with the quantum Green's functions that correspond to a bundle of Lissajous figures in the high-order regime. (C) 2020 Optical Society of America
Integral-based parallel algorithm for the fast generation of the Zernike polynomials
(2020-01-20)
Hsieh, Y. H.
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Yu, Y. T.
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Lai, Y. H.
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Hsieh, M. X.
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Chen, Y. F.
The integral representation of the Zernike radial functions is well approximated by applying the Riemann sums with a surprisingly rapid convergence. The errors of the Riemann sums are found to averagely be not exceed 3 x 10(-14), 3.3 x 10(-14), and 1.8 x 10(-13) for the radial order up to 30, 50, and 100, respectively. Moreover, a parallel algorithm based on the Riemann sums is proposed to directly generate a set of radial functions. With the aid of the graphics processing units (GPUs), the algorithm shows an acceleration ratio up to 200-fold over the traditional CPU computation. The fast generation for a set of Zernike radial polynomials is expected to be valuable in further applications, such as the aberration analysis and the pattern recognition. (C) 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Origin of continuous curves and dotted spots in laser transverse modes with geometric structures
(2019-12-15)
Chen, Y. F.
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Tung, J. C.
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Hsieh, M. X.
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Hsieh, Y. H.
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Liang, H. C.
The transverse structures of geometric modes in degenerate laser resonators with large astigmatism are systematically investigated by starting from the Gaussian wave packet formulation with ray-wave connections. The overlapping degree D between Gaussian wave packets is derived as an analytic expression that manifests the critical overlapping with D = 1. The transverse patterns are confirmed to display a structure of continuous curves or dotted spots, depending on D > 1 or D < 1, respectively. A thorough comparison between experimental results and numerical calculations is performed to validate the theoretical analysis. (C) 2019 Optical Society of America
Wave representation for asymmetric elliptic vortex beams generated from the astigmatic mode converter
(2019-04-15)
Chen, Y. F.
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Lai, Y. H.
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Hsieh, M. X.
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Hsieh, Y. H.
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Tu, C. W.
An analytical wave representation is derived to express the asymmetric elliptic vortex beams generated by using an astigmatic mode converter to transform the asymmetric Hermite-Gaussian modes. The effect of the spatial asymmetry on the elliptic vortex beam can be straight forwardly considered in the analytical wave representation. A detailed comparison with experimental intensity patterns and phase structures is made. The good agreement between experimental results and theoretical analyses confirms the characterization and generation of the asymmetric elliptic vortex beams. (C) 2019 Optical Society of America