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Yung-fu Chen - One of the best experts on this subject based on the ideXlab platform.

  • High-power structured laser modes: direct generation of a vortex array.
    Optics letters, 2020
    Co-Authors: Yung-fu Chen, Y. C. Tseng, M. X. Hsieh, J. C. Tung, Ying Hui Hsieh, H. C. Liang, Kai-feng Huang
    Abstract:

    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.

  • Generating high-power asymmetrical Laguerre-Gaussian modes and exploring topological charges distribution.
    Optics express, 2018
    Co-Authors: Y. H. Hsieh, Kai-feng Huang, M. X. Hsieh, Yu Hsiang Lai, Yung-fu Chen
    Abstract:

    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.

  • Exploring vortex structures in orbital-angular-momentum beams generated from planar geometric modes with a mode converter
    Optics express, 2016
    Co-Authors: J. C. Tung, H. C. Liang, Kai-feng Huang, Yung-fu Chen
    Abstract:

    It is theoretically demonstrated that the planar geometric mode with a π/2 mode converter, so called the circularly geometric mode, can be solved from the Inhomogeneous Helmholtz Equation by considering the pump distribution on the lasing mode. Theoretical analysis clearly reveal that the vortex structures of circularly geometric modes are determined by the minimum order of transverse lasing modes, the total number of transverse lasing modes and the degenerate condition in the cavity. Moreover, we experimentally manifest that the circularly geometric mode can be generated from the selective pumped solid-state laser with an external π/2 mode converter. To explore the vortex structures of the generated geometric modes, the interference patterns are performed by an experimental apparatus consisting of a Mach-Zehnder interferometer. The good agreement between experimental observations and numerical calculations confirms the analysis of vortex structures is reliable.

  • Exploring the resonant vibration of thin plates: Reconstruction of Chladni patterns and determination of resonant wave numbers.
    The Journal of the Acoustical Society of America, 2015
    Co-Authors: P. H. Tuan, H. C. Liang, Kai-feng Huang, P. Y. Chiang, C. P. Wen, Yung-fu Chen
    Abstract:

    The Chladni nodal line patterns and resonant frequencies for a thin plate excited by an electronically controlled mechanical oscillator are experimentally measured. Experimental results reveal that the resonant frequencies can be fairly obtained by means of probing the variation of the effective impedance of the exciter with and without the thin plate. The influence of the extra mass from the central exciter is confirmed to be insignificant in measuring the resonant frequencies of the present system. In the theoretical aspect, the Inhomogeneous Helmholtz Equation is exploited to derive the response function as a function of the driving wave number for reconstructing experimental Chladni patterns. The resonant wave numbers are theoretically identified with the maximum coupling efficiency as well as the maximum entropy principle. Substituting the theoretical resonant wave numbers into the derived response function, all experimental Chladni patterns can be excellently reconstructed. More importantly, the dispersion relationship for the flexural wave of the vibrating plate can be determined with the experimental resonant frequencies and the theoretical resonant wave numbers. The determined dispersion relationship is confirmed to agree very well with the formula of the Kirchhoff-Love plate theory.

  • Exploring the distinction between experimental resonant modes and theoretical eigenmodes: From vibrating plates to laser cavities
    Physical review. E Statistical nonlinear and soft matter physics, 2014
    Co-Authors: P. H. Tuan, Kai-feng Huang, H. C. Liang, C. P. Wen, Yung-fu Chen
    Abstract:

    Experimentally resonant modes are commonly presumed to correspond to eigenmodes in the same bounded domain. However, the one-to-one correspondence between theoretical eigenmodes and experimental observations is never reached. Theoretically, eigenmodes in numerous classical and quantum systems are the solutions of the homogeneous Helmholtz Equation, whereas resonant modes should be solved from the Inhomogeneous Helmholtz Equation. In the present paper we employ the eigenmode expansion method to derive the wave functions for manifesting the distinction between eigenmodes and resonant modes. The derived wave functions are successfully used to reconstruct a variety of experimental results including Chladni figures generated from the vibrating plate, resonant patterns excited from microwave cavities, and lasing modes emitted from the vertical cavity.

Kai-feng Huang - One of the best experts on this subject based on the ideXlab platform.

  • High-power structured laser modes: direct generation of a vortex array.
    Optics letters, 2020
    Co-Authors: Yung-fu Chen, Y. C. Tseng, M. X. Hsieh, J. C. Tung, Ying Hui Hsieh, H. C. Liang, Kai-feng Huang
    Abstract:

    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.

  • Generating high-power asymmetrical Laguerre-Gaussian modes and exploring topological charges distribution.
    Optics express, 2018
    Co-Authors: Y. H. Hsieh, Kai-feng Huang, M. X. Hsieh, Yu Hsiang Lai, Yung-fu Chen
    Abstract:

    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.

  • Exploring vortex structures in orbital-angular-momentum beams generated from planar geometric modes with a mode converter
    Optics express, 2016
    Co-Authors: J. C. Tung, H. C. Liang, Kai-feng Huang, Yung-fu Chen
    Abstract:

    It is theoretically demonstrated that the planar geometric mode with a π/2 mode converter, so called the circularly geometric mode, can be solved from the Inhomogeneous Helmholtz Equation by considering the pump distribution on the lasing mode. Theoretical analysis clearly reveal that the vortex structures of circularly geometric modes are determined by the minimum order of transverse lasing modes, the total number of transverse lasing modes and the degenerate condition in the cavity. Moreover, we experimentally manifest that the circularly geometric mode can be generated from the selective pumped solid-state laser with an external π/2 mode converter. To explore the vortex structures of the generated geometric modes, the interference patterns are performed by an experimental apparatus consisting of a Mach-Zehnder interferometer. The good agreement between experimental observations and numerical calculations confirms the analysis of vortex structures is reliable.

  • Exploring the resonant vibration of thin plates: Reconstruction of Chladni patterns and determination of resonant wave numbers.
    The Journal of the Acoustical Society of America, 2015
    Co-Authors: P. H. Tuan, H. C. Liang, Kai-feng Huang, P. Y. Chiang, C. P. Wen, Yung-fu Chen
    Abstract:

    The Chladni nodal line patterns and resonant frequencies for a thin plate excited by an electronically controlled mechanical oscillator are experimentally measured. Experimental results reveal that the resonant frequencies can be fairly obtained by means of probing the variation of the effective impedance of the exciter with and without the thin plate. The influence of the extra mass from the central exciter is confirmed to be insignificant in measuring the resonant frequencies of the present system. In the theoretical aspect, the Inhomogeneous Helmholtz Equation is exploited to derive the response function as a function of the driving wave number for reconstructing experimental Chladni patterns. The resonant wave numbers are theoretically identified with the maximum coupling efficiency as well as the maximum entropy principle. Substituting the theoretical resonant wave numbers into the derived response function, all experimental Chladni patterns can be excellently reconstructed. More importantly, the dispersion relationship for the flexural wave of the vibrating plate can be determined with the experimental resonant frequencies and the theoretical resonant wave numbers. The determined dispersion relationship is confirmed to agree very well with the formula of the Kirchhoff-Love plate theory.

  • Exploring the distinction between experimental resonant modes and theoretical eigenmodes: From vibrating plates to laser cavities
    Physical review. E Statistical nonlinear and soft matter physics, 2014
    Co-Authors: P. H. Tuan, Kai-feng Huang, H. C. Liang, C. P. Wen, Yung-fu Chen
    Abstract:

    Experimentally resonant modes are commonly presumed to correspond to eigenmodes in the same bounded domain. However, the one-to-one correspondence between theoretical eigenmodes and experimental observations is never reached. Theoretically, eigenmodes in numerous classical and quantum systems are the solutions of the homogeneous Helmholtz Equation, whereas resonant modes should be solved from the Inhomogeneous Helmholtz Equation. In the present paper we employ the eigenmode expansion method to derive the wave functions for manifesting the distinction between eigenmodes and resonant modes. The derived wave functions are successfully used to reconstruct a variety of experimental results including Chladni figures generated from the vibrating plate, resonant patterns excited from microwave cavities, and lasing modes emitted from the vertical cavity.

H. C. Liang - One of the best experts on this subject based on the ideXlab platform.

  • High-power structured laser modes: direct generation of a vortex array.
    Optics letters, 2020
    Co-Authors: Yung-fu Chen, Y. C. Tseng, M. X. Hsieh, J. C. Tung, Ying Hui Hsieh, H. C. Liang, Kai-feng Huang
    Abstract:

    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.

  • Exploring vortex structures in orbital-angular-momentum beams generated from planar geometric modes with a mode converter
    Optics express, 2016
    Co-Authors: J. C. Tung, H. C. Liang, Kai-feng Huang, Yung-fu Chen
    Abstract:

    It is theoretically demonstrated that the planar geometric mode with a π/2 mode converter, so called the circularly geometric mode, can be solved from the Inhomogeneous Helmholtz Equation by considering the pump distribution on the lasing mode. Theoretical analysis clearly reveal that the vortex structures of circularly geometric modes are determined by the minimum order of transverse lasing modes, the total number of transverse lasing modes and the degenerate condition in the cavity. Moreover, we experimentally manifest that the circularly geometric mode can be generated from the selective pumped solid-state laser with an external π/2 mode converter. To explore the vortex structures of the generated geometric modes, the interference patterns are performed by an experimental apparatus consisting of a Mach-Zehnder interferometer. The good agreement between experimental observations and numerical calculations confirms the analysis of vortex structures is reliable.

  • Exploring the resonant vibration of thin plates: Reconstruction of Chladni patterns and determination of resonant wave numbers.
    The Journal of the Acoustical Society of America, 2015
    Co-Authors: P. H. Tuan, H. C. Liang, Kai-feng Huang, P. Y. Chiang, C. P. Wen, Yung-fu Chen
    Abstract:

    The Chladni nodal line patterns and resonant frequencies for a thin plate excited by an electronically controlled mechanical oscillator are experimentally measured. Experimental results reveal that the resonant frequencies can be fairly obtained by means of probing the variation of the effective impedance of the exciter with and without the thin plate. The influence of the extra mass from the central exciter is confirmed to be insignificant in measuring the resonant frequencies of the present system. In the theoretical aspect, the Inhomogeneous Helmholtz Equation is exploited to derive the response function as a function of the driving wave number for reconstructing experimental Chladni patterns. The resonant wave numbers are theoretically identified with the maximum coupling efficiency as well as the maximum entropy principle. Substituting the theoretical resonant wave numbers into the derived response function, all experimental Chladni patterns can be excellently reconstructed. More importantly, the dispersion relationship for the flexural wave of the vibrating plate can be determined with the experimental resonant frequencies and the theoretical resonant wave numbers. The determined dispersion relationship is confirmed to agree very well with the formula of the Kirchhoff-Love plate theory.

  • Exploring the distinction between experimental resonant modes and theoretical eigenmodes: From vibrating plates to laser cavities
    Physical review. E Statistical nonlinear and soft matter physics, 2014
    Co-Authors: P. H. Tuan, Kai-feng Huang, H. C. Liang, C. P. Wen, Yung-fu Chen
    Abstract:

    Experimentally resonant modes are commonly presumed to correspond to eigenmodes in the same bounded domain. However, the one-to-one correspondence between theoretical eigenmodes and experimental observations is never reached. Theoretically, eigenmodes in numerous classical and quantum systems are the solutions of the homogeneous Helmholtz Equation, whereas resonant modes should be solved from the Inhomogeneous Helmholtz Equation. In the present paper we employ the eigenmode expansion method to derive the wave functions for manifesting the distinction between eigenmodes and resonant modes. The derived wave functions are successfully used to reconstruct a variety of experimental results including Chladni figures generated from the vibrating plate, resonant patterns excited from microwave cavities, and lasing modes emitted from the vertical cavity.

  • Exploring the effect of fractional degeneracy and the emergence of ray-wave duality in solid-state lasers with off-axis pumping
    Physical Review A, 2013
    Co-Authors: Yung-fu Chen, J. C. Tung, H. C. Liang, P. Y. Chiang, Kai-feng Huang
    Abstract:

    We employ the Inhomogeneous Helmholtz Equation to explore the influence of the fractional degeneracy and the pump distribution on the resonant lasing mode. Theoretical analyses clearly reveal the relationship between the fractional degeneracy and the emergence of the ray-wave duality. Furthermore, we perform thorough laser experiments to confirm the theoretical exploration that the resonant modes near the degenerate cavities are well localized on the ray trajectories under the condition of the off-axis pumping. We also exploit the derived wave functions to calculate the resonant strengths that can noticeably manifest the enhancements of the output powers in the degenerate cavities.

J. C. Tung - One of the best experts on this subject based on the ideXlab platform.

  • High-power structured laser modes: direct generation of a vortex array.
    Optics letters, 2020
    Co-Authors: Yung-fu Chen, Y. C. Tseng, M. X. Hsieh, J. C. Tung, Ying Hui Hsieh, H. C. Liang, Kai-feng Huang
    Abstract:

    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.

  • Exploring vortex structures in orbital-angular-momentum beams generated from planar geometric modes with a mode converter
    Optics express, 2016
    Co-Authors: J. C. Tung, H. C. Liang, Kai-feng Huang, Yung-fu Chen
    Abstract:

    It is theoretically demonstrated that the planar geometric mode with a π/2 mode converter, so called the circularly geometric mode, can be solved from the Inhomogeneous Helmholtz Equation by considering the pump distribution on the lasing mode. Theoretical analysis clearly reveal that the vortex structures of circularly geometric modes are determined by the minimum order of transverse lasing modes, the total number of transverse lasing modes and the degenerate condition in the cavity. Moreover, we experimentally manifest that the circularly geometric mode can be generated from the selective pumped solid-state laser with an external π/2 mode converter. To explore the vortex structures of the generated geometric modes, the interference patterns are performed by an experimental apparatus consisting of a Mach-Zehnder interferometer. The good agreement between experimental observations and numerical calculations confirms the analysis of vortex structures is reliable.

  • Exploring the effect of fractional degeneracy and the emergence of ray-wave duality in solid-state lasers with off-axis pumping
    Physical Review A, 2013
    Co-Authors: Yung-fu Chen, J. C. Tung, H. C. Liang, P. Y. Chiang, Kai-feng Huang
    Abstract:

    We employ the Inhomogeneous Helmholtz Equation to explore the influence of the fractional degeneracy and the pump distribution on the resonant lasing mode. Theoretical analyses clearly reveal the relationship between the fractional degeneracy and the emergence of the ray-wave duality. Furthermore, we perform thorough laser experiments to confirm the theoretical exploration that the resonant modes near the degenerate cavities are well localized on the ray trajectories under the condition of the off-axis pumping. We also exploit the derived wave functions to calculate the resonant strengths that can noticeably manifest the enhancements of the output powers in the degenerate cavities.

Changhwan Jang - One of the best experts on this subject based on the ideXlab platform.

  • Inhomogeneous Helmholtz Equation for Water Waves on Variable Depth
    2016
    Co-Authors: Hyoseob Kim, Changhwan Jang
    Abstract:

    Abstract − The Inhomogeneous Helmholtz Equation is introduced for variable water depth and potential func-tion and separation of variables are introduced for the derivation. Only harmonic wave motions are considered. The governing Equation composed of the potential function for irrotational flow is directly applied to the still water level, and the Inhomogeneous Helmholtz Equation for variable water depth is obtained. By introducing the wave amplitude and wave phase gradient the governing Equation with complex potential function is trans-formed into two Equations of real variables. The transformed Equations are the first and second-order ordinary differential Equations, respectively, and can be solved in a forward marching manner when proper boundary val-ues are supplied, i.e. the wave amplitude, the wave amplitude gradient, and the wave phase gradient at a side boundary. Simple spatially-centered finite difference numerical schemes are adopted to solve the present set of Equations. The Equation set is applied to two test cases, Booij’s inclined plane slope profile, and Bragg’s wavy bed profile. The present Equations set is satisfactorily verified against other theories including the full linear Equation, Massel’s modified mild-slope Equation, and Berkhoff’s mild-slope Equation etc

  • Inhomogeneous Helmholtz Equation for water waves on variable depth
    Journal of the Korean Society for Marine Environment & Energy, 2010
    Co-Authors: Hyoseob Kim, Changhwan Jang
    Abstract:

    Abstract − The Inhomogeneous Helmholtz Equation is introduced for variable water depth and potential func-tion and separation of variables are introduced for the derivation. Only harmonic wave motions are considered.The governing Equation composed of the potential function for irrotational flow is directly applied to the stillwater level, and the Inhomogeneous Helmholtz Equation for variable water depth is obtained. By introducingthe wave amplitude and wave phase gradient the governing Equation with complex potential function is trans-formed into two Equations of real variables. The transformed Equations are the first and second-order ordinarydifferential Equations, respectively, and can be solved in a forward marching manner when proper boundary val-ues are supplied, i.e. the wave amplitude, the wave amplitude gradient, and the wave phase gradient at a sideboundary. Simple spatially-centered finite difference numerical schemes are adopted to solve the present set ofEquations. The Equation set is applied to two test cases, Booij’s inclined plane slope profile, and Bragg’s wavybed profile. The present Equations set is satisfactorily verified against other theories including the full linearEquation, Massel’s modified mild-slope Equation, and Berkhoff’s mild-slope Equation etc.Keywords: Inhomogeneous Helmholtz Equation(비균질 Helmholtz 방정식), variable water depth(변동 수심),separation of variables(변수 분리), complex potential function(복합 포텐셜 함수), spatially-centered finitedifference numerical scheme(중앙차분 수치기법 )