Journals Articles Conferences News About CLP
Submit a paper Email Alert
Search
Search
Articles
Journals
News
Advanced Search
Top Searches
2D MaterialsTransformation opticsQuantum PhotonicsSmall lasersSemiconductor UV PhotonicsSupersymmetric microring laser arrays

Photonics Research, Volume. 5, Issue 6, 733(2017)

Generating laser transverse modes analogous to quantum Green’s functions of two-dimensional harmonic oscillators

J. C. Tung1,2, Y. H. Hsieh3, T. Omatsu1,2, K. F. Huang3, and Y. F. Chen3、*
Author Affiliations
  • 1Graduate School of Engineering, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan
  • 2Molecular Chirality Research Center, Chiba University, 1-33, Yayoi-cho, Inage-ku, Chiba 263-8522, Japan
  • 3Department of Electrophysics, National Chiao Tung University, 1001 Ta-Hsueh Rd., Hsinchu 30010, Taiwan
    • show less
    Full TextGet PDF
    Figures&Tables (8)
    Equations (16)
    References (50)
    Cited By (13)
    Tools
    Paper Information
    Topics

    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.

    Keywords
    diode-pumpedsolid-stateLaser beam characterizationLasers

    4. CONCLUSIONS

    In summary, we have theoretically explored the pattern formation of quantum Green’s functions with the point excitation. The point-excited resonant mode has been verified to be exactly the radial-order LGp,0 mode that can be asymptotic to the zero-order Bessel beam in the limit p→∞. In the experiment, an end-pumped solid-state laser with a nearly hemispherical resonator was employed to generate the tightly excited resonant modes from low to very high orders in an efficient way. It is believed that the present finding not only creates an important innovation to generate the structured beams for laser applications but also provides a remarkable method to visualize the quantum–classical correspondence.

    [1] K. Staliunas, V. J. Sanchez-Morcillo. Transverse Patterns in Nonlinear Optical Resonators(2003).

    [2] M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, C. O. Weiss. Transverse laser patterns. I. Phase singularity crystals. Phys. Rev. A, 43, 5090-5113(1991).

    [3] D. Dangoisse, D. Hennequin, C. Lepers, E. Louvergneaux, P. Glorieux. Two-dimensional optical lattices in a CO2 laser. Phys. Rev. A, 46, 5955-5958(1992).

    [4] E. Louvergneaux, D. Hennequin, D. Dangoisse, P. Glorieux. Transverse mode competition in a CO2 laser. Phys. Rev. A, 53, 4435-4438(1996).

    [5] K. Staliunas, G. Slekys, C. O. Weiss. Nonlinear pattern formation in active optical systems: shocks, domains of tilted waves, and cross-roll patterns. Phys. Rev. Lett., 79, 2658-2661(1997).

    [6] V. B. Taranenko, K. Staliunas, C. O. Weiss. Pattern formation and localized structures in degenerate optical parametric mixing. Phys. Rev. Lett., 81, 2236-2239(1998).

    [7] D. Dragoman, M. Dragoman. Quantum-Classical Analogies(2004).

    [8] V. Bužek, T. Quang. Generalized coherent state for bosonic realization of SU(2) Lie algebra. J. Opt. Soc. Am. B, 6, 2447-2449(1989).

    [9] G. S. Agarwal, J. Banerji. Entanglement by linear SU(2) transformations: generation and evolution of quantum vortex states. J. Phys. A, 39, 11503-11519(2006).

    [10] Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, S. C. Wang. Generation of Hermite–Gaussian modes in fiber-coupled laser-diode end-pumped lasers. IEEE J. Quantum Electron., 33, 1025-1031(1997).

    [11] H. Laabs, B. Ozygus. Excitation of Hermite Gaussian modes in end-pumped solid-state lasers via off-axis pumping. Opt. Laser Technol., 28, 213-214(1996).

    [12] Y. F. Chen, Y. P. Lan. Dynamics of the Laguerre Gaussian TEM0,l* mode in a solid-state laser. Phys. Rev. A, 63, 063807(2001).

    [13] C. J. Flood, G. Giuliani, H. M. van Driel. Preferential operation of an end-pumped Nd:YAG laser in high-order Laguerre–Gauss modes. Opt. Lett., 15, 215-217(1990).

    [14] S. Ngcobo, K. Aït-Ameur, N. Passilly, A. Hasnaoui, A. Forbes. Exciting higher-order radial Laguerre–Gaussian modes in a diode-pumped solid-state laser resonator. Appl. Opt., 52, 2093-2101(2013).

    [15] A. Hu, J. Lei, P. Chen, Y. Wang, S. Li. Numerical investigation on the generation of high-order Laguerre–Gaussian beams in end-pumped solid-state lasers by introducing loss control. Appl. Opt., 53, 7845-7853(2014).

    [16] M. A. Bandres, J. C. Gutiérrez-Vega. Ince–Gaussian modes of the paraxial wave equation and stable resonators. J. Opt. Soc. Am. A, 21, 873-880(2004).

    [17] U. T. Schwarz, M. A. Bandres, J. C. Gutiérrez-Vega. Observation of Ince–Gaussian modes in stable resonators. Opt. Lett., 29, 1870-1872(2004).

    [18] T. Ohtomo, K. Kamikariya, K. Otsuka, S. Chu. Single-frequency Ince–Gaussian mode operations of laser-diode-pumped microchip solid-state lasers. Opt. Express, 15, 10705-10717(2007).

    [19] N. Barré, M. Romanelli, M. Brunel. Role of cavity degeneracy for high-order mode excitation in end-pumped solid-state lasers. Opt. Lett., 39, 1022-1025(2014).

    [20] J. Durnin, J. J. Miceli, J. H. Eberly. Diffraction-free beams. Phys. Rev. Lett., 58, 1499-1501(1987).

    [21] L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, J. P. Woerdman. Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes. Phys. Rev. A, 45, 8185-8189(1992).

    [22] G. A. Siviloglou, J. Broky, A. Dogariu, D. N. Christodoulides. Observation of accelerating Airy beams. Phys. Rev. Lett., 99, 213901(2007).

    [23] A. Yu Okulov, A. N. Oraevsky. Space-temporal behavior of a light pulse propagating in a nonlinear nondispersive medium. J. Opt. Soc. Am. B, 3, 741-746(1986).

    [24] Y. F. Chen, Y. P. Lan. Transverse pattern formation of optical vortices in a microchip laser with a large Fresnel number. Phys. Rev. A, 65, 013802(2001).

    [25] A. Yu Okulov. Vortex–antivortex wavefunction of a degenerate quantum gas. Laser Phys., 19, 1796-1803(2009).

    [26] V. L. Berezinskii. Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II. Quantum systems. Sov. Phys. J. Exp. Theor. Phys., 34, 610-616(1972).

    [27] J. M. Kosterlitz, D. J. Thouless. Ordering, metastability and phase transitions in two-dimensional systems. J. Phys. C, 6, 1181-1203(1973).

    [28] Z. Hadzibabic, P. Krüger, M. Cheneau, B. Battelier, J. Dalibard. Berezinskii–Kosterlitz–Thouless crossover in a trapped atomic gas. Nature, 441, 1118-1121(2006).

    [29] A. Yu Okulov. Twisted speckle entities inside wavefront reversal mirrors. Phys. Rev. A, 80, 013837(2009).

    [30] M. Woerdemann, C. Alpmann, M. Esseling, C. Denz. Advanced optical trapping by complex beam shaping. Laser Photon. Rev., 7, 839-854(2013).

    [31] V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, Y. S. Kivshar. Giant optical manipulation. Phys. Rev. Lett., 105, 118103(2010).

    [32] W. N. Plick, M. Krenn, R. Fickler, S. Ramelow, A. Zeilinger. Quantum orbital angular momentum of elliptically symmetric light. Phys. Rev. A, 87, 033806(2013).

    [33] Y. F. Chen, J. C. Tung, P. H. Tuan, Y. T. Yu, H. C. Liang, K. F. Huang. Characterizing classical periodic orbits from quantum Green’s functions in two-dimensional integrable systems: harmonic oscillators and quantum billiards. Phys. Rev. E, 95, 012217(2017).

    [34] E. Schrödinger. Collected Papers on Wave Mechanics(1982).

    [35] P. Holland. The Quantum Theory of Motion(1993).

    [36] Y. F. Chen, Y. P. Lan, K. F. Huang. Observation of quantum-classical correspondence from high-order transverse patterns. Phys. Rev. A, 68, 043803(2003).

    [37] Y. F. Chen, T. H. Lu, K. W. Su, K. F. Huang. Devil’s staircase in three-dimensional coherent waves localized on Lissajous parametric surfaces. Phys. Rev. Lett., 96, 213902(2006).

    [38] J. Courtois, A. Mohamed, D. Romanini. Degenerate astigmatic cavities. Phys. Rev. A, 88, 043844(2013).

    [39] J. C. Tung, P. H. Tuan, H. C. Liang, K. F. Huang, Y. F. Chen. Fractal frequency spectrum in laser resonators and three-dimensional geometric topology of optical coherent waves. Phys. Rev. A, 94, 023811(2016).

    [40] K. F. Huang, Y. F. Chen, H. C. Lai, Y. P. Lan. Observation of the wave function of a quantum billiard from the transverse patterns of vertical cavity surface emitting lasers. Phys. Rev. Lett., 89, 224102(2002).

    [41] Y. T. Yu, P. H. Tuan, P. Y. Chiang, H. C. Liang, K. F. Huang, Y. F. Chen. Wave pattern and weak localization of chaotic versus scarred modes in stadium-shaped surface-emitting lasers. Phys. Rev. E, 84, 056201(2011).

    [42] A. Messiah. Quantum Mechanics(1966).

    [43] N. N. Lebedev. Special Functions & Their Applications(1972).

    [44] A. Hasnaoui, A. Bencheikh, K. Aït-Ameur. Tailored TEMp0 beams for large size 3-D laser prototyping. Opt. Lasers Eng., 49, 248-251(2011).

    [45] N. Hodgson, H. Weber. Laser Resonators and Beam Propagation(2005).

    [46] J. Dong, S. C. Bai, S. H. Liu, K. I. Ueda, A. A. Kaminskii. A high repetition rate passively Q-switched microchip laser for controllable transverse laser modes. J. Opt., 18, 055205(2016).

    [47] J. Dong, Y. He, S. C. Bai, K. I. Ueda, A. A. Kaminskii. A Cr4+:YAG passively Q-switched Nd:YVO4 microchip laser for controllable high-order Hermite–Gaussian modes. Laser Phys., 26, 095004(2016).

    [48] J. Dong, Y. He, X. Zhou, S. Bai. Highly efficient, versatile, self-Q-switched, high-repetition-rate microchip laser generating Ince–Gaussian modes for optical trapping. Quantum Electron., 46, 218-222(2016).

    [49] H. S. He, M. M. Zhang, J. Dong, K. I. Ueda. Linearly polarized pumped passively Q-switched Nd:YVO4 microchip laser for Ince–Gaussian laser modes with controllable orientations. J. Opt., 18, 055205(2016).

    [50] M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, J. P. Woerdman. Astigmatic laser mode converters and transfer of orbital angular momentum. Opt. Commun., 96, 123-132(1993).

    Tools

    Get Citation

    Copy Citation Text

    J. C. Tung, Y. H. Hsieh, T. Omatsu, K. F. Huang, Y. F. Chen. Generating laser transverse modes analogous to quantum Green’s functions of two-dimensional harmonic oscillators[J]. Photonics Research, 2017, 5(6): 733

    Download Citation

    EndNote(RIS)BibTexPlain Text
    Set citation alerts for article
    Save article for my favorites
    Paper Information

    Category: Lasers and Laser Optics

    Received: Oct. 5, 2017

    Accepted: Oct. 29, 2017

    Published Online: Jan. 10, 2019

    The Author Email: Y. F. Chen (yfchen@cc.nctu.edu.tw)

    DOI:10.1364/PRJ.5.000733

    Topics

    laser devices and laser physics
    Lasers and Laser Optics
    Laser physics
    laser manufacturing
    Instrumentation, Measurement and Metrology