Measuring orbital angular momentum of vortex beams in optomechanics

Abstract

Measuring the orbital angular momentum (OAM) of vortex beams, including the magnitude and the sign, has great application prospects due to its theoretically unbounded and orthogonal modes. Here, the sign-distinguishable OAM measurement in optomechanics is proposed, which is achieved by monitoring the shift of the transmission spectrum of the probe field in a double Laguerre–Gaussian (LG) rotational-cavity system. Compared with the traditional single LG rotational cavity, an asymmetric optomechanically induced transparency window can occur in our system. Meanwhile, the position of the resonance valley has a strong correlation with the magnitude and sign of OAM. This originally comes from the fact that the effective detuning of the cavity mode from the driving field can vary with the magnitude and sign of OAM, which causes the spectral shift to be directional for different signs of OAM. Our scheme solves the shortcoming of the inability to distinguish the sign of OAM in optomechanics, and works well for high-order vortex beams with topological charge value±45, which is a significant improvement for measuring OAM based on the cavity optomechanical system.

Keywords

orbital angular momentum / optomechanically induced transparency / Laguerre–Gaussian rotational-cavity system / optomechanics

References

[1] J. F. Nye and M. V. Berry, Dislocations in wave trains, Proc. R. Soc. Lond. A 336(1605), 165 (1974)

[2] L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes, Phys. Rev. A 45(11), 8185 (1992)

[3] M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Helical-wavefront laser beams produced with a spiral phaseplate, Opt. Commun. 112(5–6), 321 (1994)

[4] S. S. R. Oemrawsingh, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, and G. W. T. Hooft, Half-integral spiral phase plates for optical wave-lengths, J. Opt. A 6(5), S288 (2004)

[5] V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Screw dislocations in light wavefronts, J. Mod. Opt. 39(5), 985 (1992)

[6] I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Optics of light beams with screw dislocations, Opt. Commun. 103(5–6), 422 (1993)

[7] Z. Zhang, X. Qiao, B. Midya, K. Liu, J. Sun, T. Wu, W. Liu, R. Agarwal, J. M. Jornet, S. Longhi, N. M. Litchinitser, and L. Feng, Tunable topological charge vortex microlaser, Science 368(6492), 760 (2020)

[8] Z. Ji, W. Liu, S. Krylyuk, X. Fan, Z. Zhang, A. Pan, L. Feng, A. Davydov, and R. Agarwal, Photocurrent detection of the orbital angular momentum of light, Science 368(6492), 763 (2020)

[9] D. S. Ding, W. Zhang, Z. Y. Zhou, S. Shi, G. Y. Xiang, X. S. Wang, Y. K. Jiang, B. S. Shi, and G. C. Guo, Quantum storage of orbital angular momentum entanglement in an atomic ensemble, Phys. Rev. Lett. 114(5), 050502 (2015)

[10] J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Terabit free-space data transmission employing orbital angular momentum multiplexing, Nat. Photonics 6(7), 488 (2012)

[11] N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, Terabit-scale orbital angular momentum mode division multiplexing in fibers, Science 340(6140), 1545 (2013)

[12] M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, Dynamics of microparticles trapped in a perfect vortex beam, Opt. Lett. 38(22), 4919 (2013)

[13] M. J. Padgett and R. Bowman, Tweezers with a twist, Nat. Photonics 5(6), 343 (2011)

[14] M. Gecevičius, R. Drevinskas, M. Beresna, and P. G. Kazansky, Single beam optical vortex tweezers with tunable orbital angular momentum, Appl. Phys. Lett. 104(23), 231110 (2014)

[15] M. Harris, C. A. Hill, and J. M. Vaughan, Optical helices and spiral interference fringes, Opt. Commun. 106(4–6), 161 (1994)

[16] M. Harris, C. A. Hill, P. R. Tapster, and J. M. Vaughan, Laser modes with helical wave fronts, Phys. Rev. A 49(4), 3119 (1994)

[17] J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chavez-Cerda, Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum, Phys. Rev. Lett. 105(5), 053904 (2010)

[18] C. S. Guo, L. L. Lu, and H. T. Wang, Characterizing topological charge of optical vortices by using an annular aperture, Opt. Lett. 34(23), 3686 (2009)

[19] P. Vaity, J. Banerji, and R. P. Singh, Measuring the topological charge of an optical vortex by using a tilted convex lens, Phys. Lett. A 377(15), 1154 (2013)

[20] S. Zheng and J. Wang, Measuring orbital angular momentum (OAM) states of vortex beams with annular gratings, Sci. Rep. 7(1), 40781 (2017)

[21] S. E. Harris, Electromagnetically induced transparency, Phys. Today 50(7), 36 (1997)

[22] G. S. Agarwal and S. Huang, Electromagnetically induced transparency in mechanical effects of light, Phys. Rev. A81, 041803(R) (2010)

[23] S. Weis, R. Riviere, S. Deleglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, Optomechanically induced transparency, Science 330(6010), 1520 (2010)

[24] J. X. Peng, Z. Chen, Q. Z. Yuan, and X. L. Feng, Optomechanically induced transparency in a Laguerre–Gaussian rotational-cavity system and its application to the detection of orbital angular momentum of light fields, Phys. Rev. A 99(4), 043817 (2019)

[25] M. Bhattacharya and P. Meystre, Using a laguerregaussian beam to trap and cool the rotational motion of a mirror, Phys. Rev. Lett. 99(15), 153603 (2007)

[26] M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity optomechanics, Rev. Mod. Phys. 86(4), 1391 (2014)

[27] C. K. Law, Interaction between a moving mirror and radiation pressure: A Hamiltonian formulation, Phys. Rev. A 51(3), 2537 (1995)

[28] M. Bhattacharya, H. Uys, and P. Meystre, Optomechanical trapping and cooling of partially reflective mirrors, Phys. Rev. A 77(3), 033819 (2008)

[29] Y. Xiao, Y. F. Yu, and Z. M. Zhang, Controllable optomechanically induced transparency and ponderomotive squeezing in an optomechanical system assisted by an atomic ensemble, Opt. Express 22(15), 17979 (2014)

[30] Z. Zhang and X. Wang, Photon-assisted entanglement and squeezing generation and decoherence suppression via a quadratic optomechanical coupling, Opt. Express 28(3), 2732 (2020)

[31] M. Bhattacharya, P. L. Giscard, and P. Meystre, Entanglement of a Laguerre–Gaussian cavity mode with a rotating mirror, Phys. Rev. A 77(1), 013827 (2008)

[32] M. Bhattacharya, P. L. Giscard, and P. Meystre, Entangling the rovibrational modes of a macroscopic mirror using radiation pressure, Phys. Rev. A77, 030303(R) (2008)

[33] Z. Chen, J. X. Peng, J. J. Fu, and X. L. Feng, Entanglement of two rotating mirrors coupled to a single Laguerre– Gaussian cavity mode, Opt. Express 27(21), 29479 (2019)

[34] Y. M. Liu, C. H. Bai, D. Y. Wang, T. Wang, M. H. Zheng, H. F. Wang, A. D. Zhu, and S. Zhang, Ground-state cooling of rotating mirror in double-Laguerre–Gaussian-cavity with atomic ensemble, Opt. Express 26(5), 6143 (2018)

[35] J. X. Peng, Z. Chen, Q. Z. Yuan, and X. L. Feng, Double optomechanically induced transparency in a Laguerre– Gaussian rovibrational cavity, Phys. Lett. A 384(7), 126153 (2020)

[36] C. Sanavio, J. Z. Bernad, and A. Xuereb, Fisher information based estimation of optomechanical coupling strengths, Phys. Rev. A 102(1), 013508 (2020)

[37] S. Huang and G. S. Agarwal, Normal-mode splitting and antibunching in Stokes and anti-Stokes processes in cavity optomechanics: Radiation-pressure-induced four-wavemixing cavity optomechanics, Phys. Rev. A 81(3), 033830 (2010)

[38] C. W. Gardiner and P. Zoller, Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics, Springer-Verlag, 2004

[39] J. D. McCullen, P. Meystre, and E. M. Wright, Mirror confinement and control through radiation pressure, Opt. Lett. 9(6), 193 (1984)

[40] A. Baas, J. P. Karr, H. Eleuch, and E. Giacobino, Optical bistability in semiconductor microcavities, Phys. Rev. A 69(2), 023809 (2004)

RIGHTS & PERMISSIONS

2021 Higher Education Press