Browsing by Author "Hsieh, Y. H."

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Analytical representation for structured light generated by astigmatic transformation of Hermite-Gaussian beams
(2018-01-01)
Hsieh, Y. H.
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Tuan, P. H.
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Tung, J. C.
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Liang, H. C.
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Su, K. W.
Theoretical wave functions are analytically derived to formulate the propagation evolution of the Hermite-Gaussian (HG) beams transformed by single lens astigmatic mode converter with arbitrary angle. The derived wave functions are associated with the combination of the rotation transform and the antisymmetric fractional Fourier transform. The derived formula are validated by the mode conversions of high-order HG beams generated by an off-axis diode-pumped solid-state laser. In addition to validation, the creation and evolution of vortex structures in the transformed HG beams are numerically manifested. The present theoretical model can be applied not only to characterize the evolution of the transformed beams but to design the optical vortex beams with various forms.
Astigmatism inducing the degenerate effect in nearly hemispherical cavities: Generation of three-dimensional structured light
(2017-01-01)
Tung, J. C.
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Hsieh, Y. H.
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Liang, H. C.
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Su, K. W.
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Huang, K. F.
We originally perform an analytical form to explore the influence of the astigmatism on the degenerate effect in nearly hemispherical cavities. The frequency spectrum near hemispherical cavities clearly reveals that not only the difference of cavity lengths between each degeneracies but also frequency gaps have significant difference from non-hemispherical cavities. We further thoroughly demonstrate the laser experiment under the condition of nearly hemispherical cavities to confirm the theoretical exploration that the transverse topology of three-dimensional (3D) structured light in the degenerate cavities is well localized on the Lissajous curves.
Characterization and generation of high-power multi-axis vortex beams by using off-axis pumped degenerate cavities with external astigmatic mode converter
(2018-08-06)
Tuan, P. H.
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Hsieh, Y. H.
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Lai, Y. H.
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Huang, K. F.
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Chen, Y. F.
The generalized geometric mode with several high-order Hermite-Gaussian (HG) beams localized on ray periodic orbits in the degenerate resonator is generated by an off-axis pumped Nd: YVO4 laser, by performing beam transformation via an astigmatic mode converter, the generalized geometric modes are found that can be converted into the multi-axis vortex beams with the bundled-rings structures. Experimental results reveal that the generated multi-axis vortex beams can preserve quite stable beam structures even under high-power operation. Moreover, the radius of the bundled rings for the multi-axis vortex beams can be flexibly adjusted by the off-axis pumping to lead to vortex structures with easily controlled orbital angular momentum distribution. The good agreement between the experimental and theoretical results of propagation evolution for the astigmatic transformation of generalized geometric modes further verify the feasibility of using the proposed system to realize various high-powered, multi-center vortex beams with good reliability and predictability. (c) 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
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
Experimental and theoretical explorations for optimizing high-power geometric modes in diode-pumped solid-state lasers
(2018-07-01)
Hsieh, Y. H.
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Lai, Y. H.
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Tsou, C. H.
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Liang, H. C.
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Huang, K. F.
The variation of transverse patterns on the cavity length is experimentally explored by using an off-axis pumped Nd:YVO4 laser to identify the range of the length for generating geometric modes (GMs). Using the inhomogeneous Helmholtz equation, it is theoretically confirmed that the stable range of the cavity length for generating GMs can be significantly enlarged by decreasing the output reflectance. Furthermore, experimental results reveal that the cavity length for scaling up the output power of GMs must be shortened due to the thermal lensing effect in the gain medium. Considering the balance between the output efficiency and the stable range of the cavity length, the optimal output reflectance is verified to be approximately 80%. With the optimal output reflectance, the average output power of GMs can be up to 6.33 W at a pump power of 12 W.
Exploiting broad-area surface emitting lasers to manifest the path-length distributions of finite-potential quantum billiards
(2016-01-11)
Yu, Y. T.
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Tuan, P. H.
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Chang, K. C.
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Hsieh, Y. H.
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Huang, K. F.
Broad-area vertical-cavity surface-emitting lasers (VCSELs) with different cavity sizes are experimentally exploited to manifest the influence of the finite confinement strength on the path-length distribution of quantum billiards. The subthreshold emission spectra of VCSELs are measured to obtain the path-length distributions by using the Fourier transform. It is verified that the number of the resonant peaks in the path-length distribution decreases with decreasing the confinement strength. Theoretical analyses for finite-potential quantum billiards are numerically performed to confirm that the mesoscopic phenomena of quantum billiards with finite confinement strength can be analogously revealed by using broad-area VCSELs. (C) 2016 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
Extracting trajectory equations of classical periodic orbits from the quantum eigenmodes in two-dimensional integrable billiards
(2017-02-21)
Hsieh, Y. H.
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Yu, Y. T.
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Tuan, P. H.
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Tung, J. C.
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Huang, K. F.
The trajectory equations for classical periodic orbits in the equilateral-triangular and circular billiards are systematically extracted from quantum stationary coherent states. The relationship between the phase factors of quantum stationary coherent states and the initial positions of classical periodic orbits is analytically derived. In addition, the stationary coherent states with noncoprime parametric numbers are shown to correspond to the multiple periodic orbits, which cannot be explicable in the one-particle picture. The stationary coherent states are further verified to be linked to the resonant modes that are generally observed in the experimental wave system excited by a localized and unidirectional source. The excellent agreement between the resonant modes and the stationary coherent states not only manifests the importance of classical features in experimental systems but also paves the way to manipulate the mesoscopic wave functions localized on the periodic orbits for applications.
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-peak-power structured lights in selectively pumped passively Q-switched lasers with astigmatic mode transformations
(2017-12-01)
Chang, C. C.
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Hsieh, Y. H.
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Lee, C. Y.
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Sung, C. L.
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Tuan, P. H.
Various high-order Hermite-Gaussian (HG) modes with high repetition rates and high peak powers are systematically generated by designing the cavity configuration to satisfy the criterion of the passive Q-switching. For the HG(m,0) modes with the order m = 1-9, the pulse repetition rate can exceed 100 kHz with peak power higher than 0.3 kW. For the HG(m,m) modes with the order m = 1-10, the pulse repetition rate can be up to 37 kHz with peak power higher than 0.35 kW. Furthermore, the high-order HG beams is transformed by using an astigmatic mode converter to generate various structured lights with optical vortices. Experimental patterns of the transformed high-order HG beams in the propagation are theoretically analyzed and the phase structures are numerically manifested.
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
Generating laser transverse modes analogous to quantum Green's functions of two-dimensional harmonic oscillators
(2017-12-01)
Tung, J. C.
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Hsieh, Y. H.
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Omatsu, T.
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Huang, K. F.
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Chen, Y. F.
We theoretically analyzed the relationship between quantum Green's functions of two-dimensional harmonic oscillators and radial-order Laguerre - Gaussian laser modes of spherical resonators. By using a nearly hemispherical resonator and a tight focusing in the end-pumped solid-state laser, we successfully generated various laser transverse modes analogous to quantum Green's functions. We further experimentally and numerically verified that the transverse order associated with quantum Green's functions is noticeably raised with increasing the pump power induced by the thermal effect. More importantly, the high lasing efficiency and the salient structure enable the present laser source to be used in exploring the light -matter interaction. (C) 2017 Chinese Laser Press
Generation and characterization of burst modes in passively mode-locked lasers with internal Fabry-Perot cavities
(2020-01-01)
Li, S. C.
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Huang, T. L.
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Hsieh, Y. H.
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Liang, H. C.
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Huang, K. F.
The generation of burst pulses in a multi-pass passively mode-locked laser is systematically explored. We exploit intracavity mirrors with different thicknesses to serve as reflected Fabry-Perot (RFP) cavities in laser resonators. Using a RFP cavity with the thinnest optical thickness, we can generate picosecond optical burst pulses with the highest intra-burst pulse rate of 33.12 GHz. The maximum output power of 2.6 W is obtained at an incident pump power of 11.9 W. We further develop an analytical model which considers the RFP effects to manifest the first-order autocorrelation and spectral behaviors in experiments. The agreement between theoretical analyses and experimental explorations provides the feasibility to flexibly manipulate the burst modes in practical applications. (C) 2019 Optical Society of America
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
Laser wave-packet representation to unify eigenmodes and geometric modes in spherical cavities
(2019-06-01)
Chen, Y. F.
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Li, S. C.
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Hsieh, Y. H.
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Tung, J. C.
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Liang, H. C.
In terms of the Gaussian beam parameter and Gouy phase, the parametric equations for geometric rays of periodic orbits in spherical resonators are originally generalized as the real parts of polar forms. The derived polar forms are employed to create an analytical wave-packet representation for unifying the ray and wave. The developed wave-packet representation can concurrently manifest the geometric modes and eigenmodes in the degenerate and nondegenerate cavities. Complete comparisons with experimental data are made not only to verify the derived wave-packet representation, but also to disclose the transition from the eigenmodes to geometric modes by increasing the transverse order in a degenerate cavity. (c) 2019 Optical Society of America.
Manifesting the connection between topological structures of quantum stationary coherent states and bundles of classical Lissajous orbits
(2018-05-01)
Chen, Y. F.
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Hsieh, Y. H.
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Tung, J. C.
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Liang, H. C.
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Huang, K. F.
Quantum stationary coherent states with spatial intensities localized on Lissajous orbits are theoretically explored by taking the inverse Fourier transform of the time-dependent coherent state. It is analytically verified that the stationary coherent state can be expressed as an integral of the Gaussian wave packet over the classical periodic orbit. With the derived integral, the phase singularities of the stationary coherent state can be precisely manifested from low-order to extremely high-order states. It is found that the phase singularities near the cross-point of the Lissajous orbits are generally arranged as rhombic vortex arrays. Finally, the stationary coherent states can be used as a basis to manifest the connection between topological structures of quantum eigenstates and bundles of classical Lissajous orbits. Copyright (C) EPLA, 2018
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
Self-assembled perovskite-spinel heterostructure on a highly distorted substrate
(2013-03-18)
Zhu, Y. M.
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Ke, D.
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Yu, R.
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Hsieh, Y. H.
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Liu, H. J.
The pattern configuration and interface structure in epitaxial BiFeO3-CoFe2O4 heterostructures grown on (010) pc NdGaO3 substrates have been investigated systematically by transmission electron microscopy and chemical analysis. The crystal orientation of CoFe2O4 variants was tuned to [111](CFO), while BiFeO3 kept [010](pc) matching the substrate. Triangular prism-shaped CoFe2O4 embedded in the BiFeO3 matrix grew as an equilibrium island mode with {111}(CFO) as its surfaces and interfaces. Two types of BiFeO3-CoFe2O4 orientation relationships were determined as (001)[010](BFO)//(0-22)[111](CFO) and (101)[010](BFO)//(similar to 220)[111](CFO). The results reveal that the dominant factors controlling the growth orientation of the present vertical heterostructures are surface energy anisotropy and atomic structure continuity. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4796037]