Self-focusing of lemon and radial vector beam inside an atomic vapour

Partha Das, and Tarak Nath Dey
Department of Physics, Indian Institute of Technology Guwahati, Guwahati- 781 039, Assam, India

We present gain-assisted focusing of vector beams (VBs) inside an atomic system. The atoms are prepared in a four-level configuration in an active Raman-gain scheme. The transitions are coupled by a σ polarized control field and two orthogonally polarized components of a probe VB. The probe beam can be self-focused inside the medium at two-photon resonance by choosing the suitable input beam intensities. We use the probability-amplitude method to calculate the linear and third-order nonlinear susceptibilities of both the components of the probe VB. We find the gain that is induced by the spatial intensity distribution of the strong control beam is mainly responsible for intending the probe beam to self-focus. Additionally, we investigate the polarization state of the VB at the minimum beam radius. The observed self-focusing of the VB results in a reduced spot size, which holds potential for applications in resolution enhancement. © Anita Publications. All rights reserved.
Doi: 10.54955/AJP.33.11.2024.709-719
Keywords: Self-focusing, Vector beams, Kerr-nonlinearity.

Peer Review Information
Method: Single- anonymous; Screened for Plagiarism? Yes
Buy this Article in Print © Anita Publications. All rights reserve

References

1. Boyd R W, Lukishova S G, Shen Y R (eds), Self-focusing: Past and present: Fundamentals and prospects,(Springer Science), 2009.
2. Shen Y R, Self-focusing: Experimental, Prog Quantum Electron, 4(1975)1–34.
3. Marburger J H, Self-focusing: Theory, Quantum Electron, 4(1975)35–110.
4. Askaryan G A, Cerenkov radiation and transition radiation from electromagnetic waves, J Exptl Theoret Phys,42(1962)1360–1364.
5. Chiao R Y, Garmire E, Townes C H, Self-trapping of optical beams, Phys Rev Lett, 13(1964)479–482.
6. Kelley P L, Self-focusing of optical beams, Phys Rev Lett, 15(1965)1005–1008.
7. Lallemand P, Bloembergen N, Self-focusing of laser beams and stimulated raman gain in liquids, Phys Rev Lett, 15(1965)1010–1012.
8. Garmire E, Chiao R Y, Townes C H, Dynamics and characteristics of the self-trapping of intense light beams, Phys Rev Lett, 16(1966)347–349.
9. Vlasov S N, Petrishchev V A, Talanov V I, Averaged description of wave beams in linear and nonlinear media (the method of moments), Radiophys Quantum Electron, 14(1971)1062–1070.
10. Wong A Y, Cheung P Y, Three-dimensional self-collapse of langmuir waves, Phys Rev Lett, 52(1984)1222–1225.
11. Sackett C A, Gerton J M, Welling M, Hulet R G, Measurements of collective collapse in a bose-einstein condensate with attractive interactions, Phys Rev Lett, 82(1999)876–879.
12. Banerjee P P, Korpel A, Lonngren K E, Self-refraction of nonlinear capillary-gravity waves, Phys Fluids, 26(1983)2393–2398.
13. Houbiers M, Stoof H T C, Stability of bose condensed atomic ⁷Li, Phys Rev A, 54(1996)5055–5066.
14. Grischkowsky D, Self-focusing of light by potassium vapor, Phys Rev Lett, 24(1970)866–869.
15. Wang Y, Nonlinear self-focusing in cold Cesium atoms, (The University of Wisconsin-Madison),
16. Helle M H, Jones T G, Pen˜ano J R, Kaganovich D, Ting A, Formation and propagation of meter-scale laser filaments in water, Appl Phys Lett, 103(2013)121101; doi.org/10.1063/1.4821447.
17. Hafizi B, Palastro J P, Pen˜ano J R, Gordon D F, Jones T G, Helle M H, Kaganovich D, Stimulated raman scattering and nonlinear focusing of high-power laser beams propagating in water, Opt Lett, 40(2015)1556–1558.
18. Soman S K O, A tutorial on fiber kerr nonlinearity effect and its com-pensation in optical communication systems, J Opt, 23(2021)123502; doi. 10.1088/2040-8986/ac362a.
19. Fleischhauer M, Imamoglu A, Marangos J P, Electromagnetically induced transparency: Optics in coherent media, Rev Mod Phys, 77(2005)633–673.
20. Wu Y, Deng L, Ultraslow optical solitons in a cold four-state medium, Phys Rev Lett, 93(2004)143904; doi.org/10.1103/PhysRevLett.93.143904.
21. Huang G, Jiang K, Payne M G, Deng L, Formation and propagation of coupled ultraslow optical soliton pairs in a cold three-state double-Λ system, Phys Rev E, 73(2006)056606; doi.org/10.1103/PhysRevE.73.056606.
22. Hang C, Huang G, Deng L, Generalized nonlinear schr¨odinger equation and ultraslow optical solitons in a cold four-state atomic system, Phys Rev E, 73(2006)036607; doi.org/10.1103/PhysRevE.73.036607.
23. Stenner M D, Gauthier D J, Pump-beam-instability limits to raman-gain-doublet “fast-light” pulse propagation, Phys Rev A, 67(2003)063801; doi.org/10.1103/PhysRevA.67.063801.
24. Jiang K J, Deng L, Payne M G, Superluminal propagation of an optical pulse in a doppler- broadened three-state single-channel active raman gain medium, Phys Rev A, 76(2007)033819; doi.org/10.1103/PhysRevA.76.033819.
25. Deng L, Payne M G, Gain-assisted large and rapidly responding kerr effect using a room- temperature active raman gain medium, Phys Rev Lett, 98(2007)253902; doi.org/10.1103/PhysRevLett.98.253902.
26. Hang C, Huang G, Giant kerr nonlinearity and weak-light superluminal optical solitons in a four-state atomic system with gain doublet, Opt Express, 18(2010)2952–2966.
27. Firth W J, Skryabin D V, Optical solitons carrying orbital angular momentum, Phys Rev Lett, 79(1997)2450–2453.
28. Desyatnikov A S, Kivshar Y S, Necklace-ring vector solitons, Phys Rev Lett, 87(2001)033901; doi.org/10.1103/PhysRevLett.87.033901.
29. Zhu Z H, Chen P, Li H W, Zhao B, Zhou Z Y, Hu W, Gao W, Lu Y Q, Shi B S, Fragmentation of twisted light in photon–phonon nonlinear propagation, Appl Phys Lett, 112(2018)161103; doi.org/10.1063/1.5020082.
30. Bigelow M S, Zerom P, Boyd R W, Breakup of ring beams carrying orbital angular momen- tum in sodium vapor, Phys Rev Lett, 92(2004)083902.
31. Izdebskaya Y V, Rebling J, Desyatnikov A S, Kivshar Y S, Observation of vector solitons with hidden vorticity, Opt Lett, 37(2012)767–769.
32. Yao A M, Padgett M J, Orbital angular momentum: origins, behavior and applications, Adv Opt Photon, 3(2011)161–204.
33. Zhan Q, Cylindrical vector beams: from mathematical concepts to applications, Adv Opt Photon, 1(2009)1–57.
34. Galvez E J, Khadka S, Schubert W H, and Nomoto S, Poincar´e-beam patterns produced by nonseparable superpositions of laguerre–gauss and polarization modes of light, Appl Opt, 51(2012)2925–2934.
35. Beckley A M, Brown T G, Alonso M A, Full poincar´e beams, Opt Express, 18(2010)10777–10785.
36. Qiufang Z, Rongfu Z, Sitong D, Guanxue W, and Xiumin G, Focusing pattern of axisym- metric bessel–gaussian beam with helical polarization under triangular modulation, Appl Opt, 59(2020)648–652.
37. Lu C, Li J, Zhang H, Li S, Gao X, Focusing pattern of the laguerre–gaussian beam with polarization mixing helical-conical phase modulation, J Opt Soc Am A, 40(2023)1303–1309