Journal Home Online First Current Issue Archive For Authors Journal Information 中文版

Engineering >> 2022, Volume 17, Issue 10 doi: 10.1016/j.eng.2022.04.022

Modulational Instability of Optical Vortices in Engineered Saturable Media

Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA

Received: 2021-11-28 Revised: 2022-03-29 Accepted: 2022-04-20 Available online: 2022-08-24

Next Previous

Abstract

Propagation of light beams in turbid media such as underwater environments, fog, clouds, or biological tissues finds increasingly important applications in science and technology, including bio-imaging, underwater and free-space communication technologies. While many of these applications traditionally relied on conventional, linearly polarized Gaussian beams, light possesses many degrees of freedom that are still largely unexplored, such as spin angular momentum (SAM) and orbital angular momentum (OAM). Here, we present nonlinear light–matter interactions of such complex light beams with "rotational" degrees of freedom in engineered nonlinear colloidal media. By making use of both variational and perturbative approach, we consider non-cylindrical optical vortices, elliptical optical vortices, and higher-order Bessel beams integrated in time (HOBBIT) to predict the dynamics and stability of the evolution of these beams. These results may find applications in many scenarios involving light transmission in strongly scattering environments.

Figures

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Fig. 11

Fig. 12

Fig. 13

Fig. 14

Fig. 15

Fig. 16

Fig. 17

References

[ 1 ] Allen L, Beijersbergen MW, Spreeuw RJC, Woerdman JP. Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes. Phys Rev A 1992;45(11):8185–9. link1

[ 2 ] Yao AM, Padgett MJ. Orbital angular momentum: origins, behavior and applications. Adv Opt Photonics 2011;3(2):161–204. link1

[ 3 ] Willner AE, Huang H, Yan Y, Ren Y, Ahmed N, Xie G, et al. Optical communications using orbital angular momentum beams. Adv Opt Photonics 2015;7(1):66–106. link1

[ 4 ] Padgett M, Bowman R. Tweezers with a twist. Nat Photonics 2011;5(6):343–8. link1

[ 5 ] Woerdemann M, Alpmann C, Esseling M, Denz C. Advanced optical trapping by complex beam shaping. Laser Photonics Rev 2013;7(6):839–54. link1

[ 6 ] Aolita L, Walborn SP. Quantum communication without alignment using multiple-qubit single-photon states. Phys Rev Lett 2007;98(10):100501. link1

[ 7 ] Mair A, Vaziri A, Weihs G, Zeilinger A. Entanglement of the orbital angular momentum states of photons. Nature 2001;412(6844):313–6. link1

[ 8 ] Leach J, Courtial J, Skeldon K, Barnett SM, Franke-Arnold S, Padgett MJ. Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon. Phys Rev Lett 2004;92(1):013601. link1

[ 9 ] Hickmann JM, Fonseca EJS, Soares WC, Chávez-Cerda S. Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum. Phys Rev Lett 2010;105(5):053904. link1

[10] Melo LA, Jesus-Silva AJ, Chávez-Cerda S, Ribeiro PHS, Soares WC. Direct measurement of the topological charge in elliptical beams using diffraction by a triangular aperture. Sci Rep 2018;8(1):6370. link1

[11] Alves CR, Jesus-Silva AJ, Fonseca EJS. Characterizing coherence vortices through geometry. Opt Lett 2015;40(12):2747–50. link1

[12] Vaity P, Banerji J, Singh RP. Measuring the topological charge of an optical vortex by using a tilted convex lens. Phys Lett A 2013;377(15):1154–6. link1

[13] Efron U, editor. Spatial light modulator technology: materials, devices, and applications. New York: Marcel Dekker Inc.; 1994. link1

[14] Chan WL, Chen HT, Taylor AJ, Brener I, Cich MJ, Mittleman DM. A spatial light modulator for terahertz beams. Appl Phys Lett 2009;94(21):213511. link1

[15] Kotlyar VV, Almazov AA, Khonina SN, Soifer VA, Elfstrom H, Turunen J. Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate. J Opt Soc Am A 2005;22(5):849–61. link1

[16] Khonina SN, Kotlyar VV, Shinkaryev MV, Soifer VA, Uspleniev GV. The phase rotor filter. J Mod Opt 1992;39(5):1147–54. link1

[17] Marrucci L. The q-plate and its future. J Nanophoton 2013;7(1):078598. link1

[18] Rubano A, Cardano F, Piccirillo B, Marrucci L. q-plate technology: a progress review. J Opt Soc Am B 2019;36(5):D70–87. link1

[19] Shalaev MI, Sun J, Tsukernik A, Pandey A, Nikolskiy K, Litchinitser NM. Highefficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode. Nano Lett 2015;15(9):6261–6. link1

[20] Zhao Y, Liu XX, Alù A. Recent advances on optical metasurfaces. J Opt 2014;16 (12):123001. link1

[21] Yu N, Capasso F. Flat optics with designer metasurfaces. Nat Mater 2014;13 (2):139–50. link1

[22] McGloin D, Dholakia K. Bessel beams: diffraction in a new light. Contemp Phys 2005;46(1):15–28. link1

[23] Volke-Sepulveda K, Garcés-Chávez V, Chávez-Cerda S, Arlt J, Dholakia K. Orbital angular momentum of a high-order Bessel light beam. J Opt B Quantum Semiclass Opt 2002;4(2):S82–9. link1

[24] Zhang K, Yuan Y, Zhang D, Ding X, Ratni B, Burokur SN, et al. Phase-engineered metalenses to generate converging and non-diffractive vortex beam carrying orbital angular momentum in microwave region. Opt Express 2018;26 (2):1351–60. link1

[25] Chu X. Analytical study on the self-healing property of Bessel beam. Eur Phys J D 2012;66(10):259. link1

[26] Vetter C, Steinkopf R, Bergner K, Ornigotti M, Nolte S, Gross H, et al. Realization of free-space long-distance self-healing Bessel beams. Laser Photonics Rev 2019;13(10):1900103. link1

[27] Arlt J, Garcés-Chávez V, Sibbett W, Dholakia K. Optical micromanipulation using a Bessel light beam. Opt Commun 2001;197(4–6):239–45. link1

[28] Choe Y, Kim JW, Shung KK, Kim ES. Microparticle trapping in an ultrasonic Bessel beam. Appl Phys Lett 2011;99(23):233704. link1

[29] Planchon TA, Gao L, Milkie DE, Davidson MW, Galbraith JA, Galbraith CG, et al. Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination. Nat Methods 2011;8(5):417–23. link1

[30] Gao L, Shao L, Chen BC, Betzig E. 3D live fluorescence imaging of cellular dynamics using Bessel beam plane illumination microscopy. Nat Protoc 2014;9(5):1083–101. link1

[31] Bandres MA, Gutiérrez-Vega JC. Ince–Gaussian modes of the paraxial wave equation and stable resonators. J Opt Soc Am A 2004;21(5):873–80. link1

[32] Bandres MA, Gutiérrez-Vega JC. Ince–Gaussian beams. Opt Lett 2004;29 (2):144–6. link1

[33] Schwarz UT, Bandres MA, Gutiérrez-Vega JC. Observation of Ince–Gaussian modes in stable resonators. Opt Lett 2004;29(16):1870–2. link1

[34] Kotlyar VV, Khonina SN, Almazov AA, Soifer VA, Jefimovs K, Turunen J. Elliptic Laguerre–Gaussian beams. J Opt Soc Am A 2006;23(1):43–56. link1

[35] Gutiérrez-Vega JC, Iturbe-Castillo MD, Chávez-Cerda S. Alternative formulation for invariant optical fields: Mathieu beams. Opt Lett 2000;25(20):1493–5. link1

[36] Chávez-Cerda S, Padgett MJ, Allison I, New GHC, Gutiérrez-Vega JC, O’Neil AT, et al. Holographic generation and orbital angular momentum of high-order Mathieu beams. J Opt B Quantum Semiclass Opt 2002;4(2):S52–7. link1

[37] Brzobohaty´ O, Cˇizˇmár T, Zemánek P. High quality quasi-Bessel beam generated by round-tip axicon. Opt Express 2008;16(17):12688–700. link1

[38] Li W, Morgan KS, Li Y, Miller JK, White G, Watkins RJ, et al. Rapidly tunable orbital angular momentum (OAM) system for higher order Bessel beams integrated in time (HOBBIT). Opt Express 2019;27(4):3920–34. link1

[39] Dai K, Li W, Morgan KS, Li Y, Miller JK, Watkins RJ, et al. Second–harmonic generation of asymmetric Bessel–Gaussian beams carrying orbital angular momentum. Opt Express 2020;28(2):2536–46. link1

[40] Watkins RJ, Dai K, White G, Li W, Miller JK, Morgan KS, et al. Experimental probing of turbulence using a continuous spectrum of asymmetric OAM beams. Opt Express 2020;28(2):924–35. link1

[41] Dholakia K, Simpson NB, Padgett MJ, Allen L. Second-harmonic generation and the orbital angular momentum of light. Phys Rev A 1996;54(5):R3742–5. link1

[42] Imoto N, Haus HA, Yamamoto Y. Quantum nondemolition measurement of the photon number via the optical Kerr effect. Phys Rev A 1985;32(4):2287–92. link1

[43] Tse WK, MacDonald AH. Giant magneto-optical Kerr effect and universal Faraday effect in thin-film topological insulators. Phys Rev Lett 2010;105 (5):057401. link1

[44] Kelley PL. Self-focusing of optical beams. Phys Rev Lett 1965;15(26):1005–8. link1

[45] Shabat AB, Zakharov VE. Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media. Sov Phys JETP 1972;34(1):62–9. link1

[46] Berẑanskis A, Matijošius A, Piskarskas A, Smilgevicˇius V, Stabinis A. Conversion of topological charge of optical vortices in a parametric frequency converter. Opt Commun 1997;140(4–6):273–6. link1

[47] El-Ganainy R, Christodoulides DN, Rotschild C, Segev M. Soliton dynamics and self-induced transparency in nonlinear nanosuspensions. Opt Express 2007;15 (16):10207–18. link1

[48] Vinçotte A, Bergé L. Atmospheric propagation of gradient-shaped and spinning femtosecond light pulses. Physica D 2006;223(2):163–73. link1

[49] Silahli SZ, Walasik W, Litchinitser NM. Necklace beam generation in nonlinear colloidal engineered media. Opt Lett 2015;40(24):5714–7. link1

[50] Walasik W, Silahli SZ, Litchinitser NM. Dynamics of necklace beams in nonlinear colloidal suspensions. Sci Rep 2017;7(1):11709. link1

[51] Sun J, Silahli SZ, Walasik W, Li Q, Johnson E, Litchinitser NM. Nanoscale orbital angular momentum beam instabilities in engineered nonlinear colloidal media. Opt Express 2018;26(5):5118–25. link1

[52] Arlt J, Dholakia K. Generation of high-order Bessel beams by use of an axicon. Opt Commun 2000;177(1–6):297–301. link1

[53] Liu C, Liu J, Niu L, Wei X, Wang K, Yang Z. Terahertz circular airy vortex beams. Sci Rep 2017;7(1):3891. link1

[54] Thaning A, Jaroszewicz Z, Friberg AT. Diffractive axicons in oblique illumination: analysis and experiments and comparison with elliptical axicons. Appl Opt 2003;42(1):9–17. link1

[55] Bin Z, Zhu L. Diffraction property of an axicon in oblique illumination. Appl Opt 1998;37(13):2563–8. link1

[56] Rasmussen JJ, Rypdal K. Blow-up in nonlinear Schroedinger equations—I a general review. Phys Scr 1986;33(6):481–97. link1

[57] Firth WJ, Skryabin DV. Optical solitons carrying orbital angular momentum. Phys Rev Lett 1997;79(13):2450–3. link1

[58] Skryabin DV, Firth WJ. Dynamics of self-trapped beams with phase dislocation in saturable Kerr and quadratic nonlinear media. Phys Rev E 1998;58 (3):3916–30. link1

[59] Desyatnikov AS, Kivshar YS. Necklace-ring vector solitons. Phys Rev Lett 2001;87(3):033901. link1

[60] Berne BJ, Pecora R. Dynamic light scattering: with applications to chemistry, biology, and physics. Mineola: Dover Publications, Inc.; 2000. link1

[61] Jackson JD. Classical electrodynamics. 3rd ed. New York: John Wiley & Sons, Inc.; 1999. link1

[62] Garnett JCM, Larmor J. Colours in metal glasses and in metallic films. Philos Trans A 1904;203:443–5. link1

[63] Fardad S, Salandrino A, Heinrich M, Zhang P, Chen Z, Christodoulides DN. Plasmonic resonant solitons in metallic nanosuspensions. Nano Lett 2014;14 (5):2498–504. link1

[64] El-Ganainy R, Christodoulides DN, Musslimani ZH, Rotschild C, Segev M. Optical beam instabilities in nonlinear nanosuspensions. Opt Lett 2007;32 (21):3185–7. link1

[65] Van Roey J, van der Donk J, Lagasse PE. Beam-propagation method: analysis and assessment. J Opt Soc Am 1981;71(7):803–10. link1

[66] Chung Y, Dagli N. An assessment of finite difference beam propagation method. IEEE J Quantum Electron 1990;26(8):1335–9. link1

[67] Kovalev AA, Kotlyar VV, Porfirev AP. Asymmetric Laguerre–Gaussian beams. Phys Rev A 2016;93(6):063858. link1

[68] Zhu X, Kahn JM. Free-space optical communication through atmospheric turbulence channels. IEEE Trans Commun 2002;50(8):1293–300. link1

[69] Conan JM, Rousset G, Madec PY. Wave-front temporal spectra in highresolution imaging through turbulence. J Opt Soc Am A 1995;12(7):1559–70. link1

[70] Fan Y, Arwatz G, Van Buren TW, Hoffman DE, Hultmark M. Nanoscale sensing devices for turbulence measurements. Exp Fluids 2015;56(7):138. link1

[71] Bonesi M, Churmakov DY, Ritchie LJ, Meglinski IV. Turbulence monitoring with Doppler optical coherence tomography. Laser Phys Lett 2007;4(4):304–7. link1

Related Research